IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2021-10-21T02:47:46ZEPrintshttp://eprints.imtlucca.it/images/logowhite.pnghttp://eprints.imtlucca.it/2018-03-05T09:56:48Z2018-03-05T09:56:48Zhttp://eprints.imtlucca.it/id/eprint/3942This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/39422018-03-05T09:56:48ZSynchronization and functional central limit theorems for interacting reinforced random walksWe obtain Central Limit Theorems in Functional form for a class of time-inhomogeneous interacting random walks. Due to a reinforcement mechanism and interaction, the walks are strongly correlated and converge almost surely to the same, possibly random, limit. We study random walks interacting through a mean-field rule and compare the rate they converge to their limit with the rate of synchronization, i.e. the rate at which their mutual distances converge to zero. We show that, under certain conditions, synchronization is faster than convergence. Even if our focus is on theoretical results, we propose as main motivations two contexts in which such results could directly apply: urn models and opinion dynamics in a random network evolving via preferential attachment.Irene Crimaldiirene.crimaldi@imtlucca.itPaolo Dai Pradaipra@math.unipd.itPierre-Yves Louispierre-yves.louis@math.cnrs.frIda G. Minelliida.minelli@dm.univaq.it2018-01-16T09:53:09Z2018-01-16T09:53:09Zhttp://eprints.imtlucca.it/id/eprint/3859This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/38592018-01-16T09:53:09ZA Complex Network Approach for the Estimation of the Energy Demand of Electric MobilityWe study how renewable energy impacts regional infrastructures considering the full deployment of electric mobility at that scale. We use the Sardinia Island in Italy as a paradigmatic case study of a semi-closed system both by energy and mobility point of view. Human mobility patterns are estimated by means of census data listing the mobility dynamics of about 700,000 vehicles, the energy demand is estimated by modeling the charging behavior of electric vehicle owners. Here we show that current renewable energy production of Sardinia is able to sustain the commuter mobility even in the theoretical case of a full switch from internal combustion vehicles to electric ones. Centrality measures from network theory on the reconstructed network of commuter trips allows to identify the most important areas (hubs) involved in regional mobility. The analysis of the expected energy flows reveals long-range effects on infrastructures outside metropolitan areas and points out that the most relevant unbalances are caused by spatial segregation between production and consumption areas. Finally, results suggest the adoption of planning actions supporting the installation of renewable energy plants in areas mostly involved by the commuting mobility, avoiding spatial segregation between consumption and generation areas.Mario MuredduAngelo Facchiniangelo.facchini@imtlucca.itAntonio ScalaGuido Caldarelliguido.caldarelli@imtlucca.itAlfonso Damiano2017-09-04T14:28:17Z2017-09-04T14:28:17Zhttp://eprints.imtlucca.it/id/eprint/3777This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/37772017-09-04T14:28:17ZOptimal Varicella immunization programs for both Varicella and Herpes Zoster ControlA main obstacle to the widespread adoption of varicella immunization in Europe has been the fear of a subsequent boom in natural herpes zoster caused by the decline in the protective effect of natural immunity boosting due to reduced virus circulation. We apply optimal control to simple models for VZV transmission and reactivation to investigate existence and feasibility of temporal paths of varicella childhood immunization that are optimal in controlling both varicella and zoster. We analyze the optimality system numerically focusing on the role played by the structure of the cost functional, the relative cost zoster-varicella, and the length of the planning horizon. We show that optimal programs exist but will mostly be unfeasible in real public health contexts due to their complex temporal profiles. This complexity is the consequence of the intrinsically antagonistic nature of varicella immunization programs when aimed to control both varicella and herpes zoster. However we could show that gradually increasing, smooth – thereby feasible - vaccination schedules, can perform largely better than routine programs with constant vaccine uptake. Moreover we show the optimal temporal profiles of feasible immunization
programs targeting with priority the mitigation of the post-immunization natural zoster boom.Monica Bettamonica.betta@imtlucca.itMarco LaurinoAndrea PuglieseGiorgio GuzzettaAlberto LandiPiero Manfredi2017-09-04T14:16:28Z2017-09-04T14:17:39Zhttp://eprints.imtlucca.it/id/eprint/3776This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/37762017-09-04T14:16:28ZPerspectives on optimal control of Varicella and Herpes Zoster by mass routine varicella vaccination: the effects of Immunity BoostingMonica Bettamonica.betta@imtlucca.itMarco LaurinoA. PuglieseGiorgio GuzzettaAlberto LandiPiero Manfredi2017-08-04T11:42:06Z2017-08-04T11:42:06Zhttp://eprints.imtlucca.it/id/eprint/3758This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/37582017-08-04T11:42:06ZGraph-restricted Game Approach for Investigating Human Movement QualitiesA novel computational method for the analysis of expressive full-body movement qualities is introduced, which exploits concepts and tools from graph theory and game theory. The human skeletal structure is modeled as an undirected graph, where the joints are the vertices and the edge set contains both physical and non-physical links. Physical links correspond to connections between adjacent physical body joints (e.g., the forearm, which connects the elbow to the wrist). Nonphysical links act as "bridges" between parts of the body not directly connected by the skeletal structure, but sharing very similar feature values. The edge weights depend on features obtained by using Motion Capture data. Then, a mathematical game is constructed over the graph structure, where the vertices represent the players and the edges represent communication channels between them. Hence, the body movement is modeled in terms of a game built on the graph structure. Since the vertices and the edges contribute to the overall quality of the movement, the adopted game-theoretical model is of cooperative nature. A game-theoretical concept, called Shapley value, is exploited as a centrality index to estimate the contribution of each vertex to a shared goal (e.g., to the way a particular movement quality is transferred among the vertices). The proposed method is applied to a data set of Motion Capture data of subjects performing expressive movements, recorded in the framework of the H2020-ICT-2015 EU Project WhoLoDance, Project no. 688865. Preliminary results are presented.Ksenia KolykhalovaGiorgio Gneccogiorgio.gnecco@imtlucca.itMarcello SanguinetiAntonio CamurriGualtiero Volpe2017-08-04T10:38:09Z2018-03-08T16:56:04Zhttp://eprints.imtlucca.it/id/eprint/3749This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/37492017-08-04T10:38:09ZNetwork reconstruction via density samplingReconstructing weighted networks from partial information is necessary in many important circumstances, e.g. for a correct estimation of systemic risk. It has been shown that, in order to achieve an accurate reconstruction, it is crucial to reliably replicate the empirical degree sequence, which is however unknown in many realistic situations. More recently, it has been found that the knowledge of the degree sequence can be replaced by the knowledge of the strength sequence, which is typically accessible, complemented by that of the total number of links, thus considerably relaxing the observational requirements. Here we further relax these requirements and devise a procedure valid when even the the total number of links is unavailable. We assume that, apart from the heterogeneity induced by the degree sequence itself, the network is homogeneous, so that its (global) link density can be estimated by sampling subsets of nodes with representative density. We show that the best way of sampling nodes is the random selection scheme, any other procedure being biased towards unrealistically large, or small, link densities. We then introduce our core technique for reconstructing both the topology and the link weights of the unknown network in detail. When tested on real economic and financial data sets, our method achieves a remarkable accuracy and is very robust with respect to the sampled subsets, thus representing a reliable practical tool whenever the available topological information is restricted to small portions of nodes.Tiziano Squartinitiziano.squartini@imtlucca.itGiulio Ciminigiulio.cimini@imtlucca.itAndrea GabrielliDiego Garlaschellidiego.garlaschelli@imtlucca.it2017-08-04T08:43:58Z2017-08-04T08:43:58Zhttp://eprints.imtlucca.it/id/eprint/3738This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/37382017-08-04T08:43:58ZRiver Networks and Optimal Channel NetworksRiver networks represent a perfect example of a physical
phenomenon that can be described by means of graph theory.
Water collected by rainfall flows from one point to another
one (downstream) in the river basin creates a spanning (water
flows uniformly on the terrain and therefore from every point
of the basin we have water flow) tree (water cannot flow uphill).
Rivers on Earth and even those that might have been
present on Mars all display similar statistical properties
thereby calling for a model based on basic properties.
A class of models named Optimal Channel Networks (OCN) derive
the final configuration by minimising a given cost function.
The physical inspiration for the minimization problem traces
back to the ideas of Nobel laureate Prigogine on a general
theory of irreversible processes in open dissipative systems.
Actually, theoretical results from OCN allowed to provide an
explanation to universal allometric behaviour in a variety
of different physical situations from species distribution to food webs optimisation alternative to the traditional
approach. In the specific case of river networks, the OCN
model postulates that the total gravitational energy loss in the
system is minimised. Empirical and theoretical works focus
generally on two dimensional case, while recently (inspired by
vascular systems) also the three dimensional case has been
analysed.
Here we devise some new analytical results that illustrate
the role and the properties of the structure that minimises
the cost function proposed in the ABM and we also provide
some insight about the structure of the absolute minimum by varying some of the parameters of the model. In what follows we will give a theoretical characterization of river networks and provide a simple rule to distinguish spanning trees from natural river trees. Furthermore, we extend the study of OCNs embedded on a lattice finding a lower and upper bound for the energy of an OCN in any dimension D.Paul BalisterJószef BaloghBéla BollobásGuido Caldarelliguido.caldarelli@imtlucca.itRossana Mastrandrearossana.mastrandrea@imtlucca.itRob Morris2017-05-08T12:57:15Z2017-05-08T12:57:15Zhttp://eprints.imtlucca.it/id/eprint/3701This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/37012017-05-08T12:57:15ZNetworks of reinforced stochastic processes: Asymptotics for the empirical meansThis work deals with systems of interacting reinforced stochastic processes, where each process X^j = (X_{n,j})_n is located at a vertex j of a finite weighted direct graph, and it can be interpreted as the sequence of “actions” adopted by an agent j of the network. The interaction
among the evolving dynamics of these processes depends on the weighted adjacency matrix W associated to the underlying graph: indeed, the probability that an agent j chooses a certain action depends on its personal “inclination” Z_{n,j} and on the inclinations Z_{n,h} , with h not equal to j, of the other agents according to the elements of W.
Asymptotic results for the stochastic processes of the personal inclinations Z^j = (Z_{n,j})_n have
been subject of studies in recent papers (e.g. [2, 21]); while the asymptotic behavior of the stochastic
processes of the actions (X_{n,j})_n has never been studied yet. In this paper, we fill this gap by characterizing the asymptotic behavior of the empirical means N_{n,j} = \sum_{k=1}^n X_{k,j} /n, proving their almost sure synchronization and some central limit theorems in the sense of stable convergence. Moreover, we discuss some statistical applications of these convergence results concerning confidence intervals for the random limit toward which all the processes of the system converge and tools to
make inference on the matrix W.Giacomo Alettigiacomo.aletti@unimi.itIrene Crimaldiirene.crimaldi@imtlucca.itAndrea Ghigliettiandrea.ghiglietti@unimi.it2017-05-08T12:28:10Z2017-12-18T15:22:58Zhttp://eprints.imtlucca.it/id/eprint/3699This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/36992017-05-08T12:28:10ZSynchronization of Reinforced Stochastic Processes with a Network-based InteractionRandomly evolving systems composed by elements which interact among each other have always been of great interest in several scientific fields. This work deals with the synchronization phenomenon, that could be roughly defined as the tendency of different components to adopt a common behavior. We continue the study of a model of interacting stochastic processes with reinforcement, that
recently has been introduced in [21]. Generally speaking, by reinforcement we mean any mechanism for which the probability that a given event occurs has an increasing dependence on the number of times that events of the same type occurred in the past. The particularity of systems of such interacting stochastic processes is that synchronization is induced along time by the reinforcement mechanism itself and does not require a large-scale limit. We focus on the relationship between the topology of the network of the interactions and the long-time synchronization phenomenon. After proving the almost sure synchronization, we provide some CLTs in the sense
of stable convergence that establish the convergence rates and the asymptotic distributions for both convergence to the common limit and synchronization. The obtained results lead to the construction of asymptotic confidence intervals for the limit random variable and of statistical tests to make inference on the topology of the network.Giacomo AlettiIrene Crimaldiirene.crimaldi@imtlucca.itAndrea Ghiglietti2016-11-14T11:56:25Z2016-11-14T11:56:25Zhttp://eprints.imtlucca.it/id/eprint/3597This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/35972016-11-14T11:56:25ZCentral limit theorems for a hypergeometric randomly reinforced urnWe consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number of extracted balls of a certain color given the past is assumed to be hypergeometric. We prove some central limit theorems in the sense of stable convergence and of almost sure conditional convergence, which are stronger than convergence in distribution. The proven results provide asymptotic confidence intervals for the limit proportion, whose distribution is generally unknown. Moreover, we also consider the case of more urns subjected to some random common factors.Irene Crimaldiirene.crimaldi@imtlucca.it2016-05-31T12:09:02Z2016-05-31T12:09:02Zhttp://eprints.imtlucca.it/id/eprint/3494This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/34942016-05-31T12:09:02ZIntroduzione alla nozione di convergenza stabile e sue variantiIrene Crimaldiirene.crimaldi@imtlucca.it2016-04-28T07:52:35Z2016-04-28T07:52:35Zhttp://eprints.imtlucca.it/id/eprint/3475This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/34752016-04-28T07:52:35ZA Network Model characterized by a Latent Attribute Structure with CompetitionThe quest for a model that is able to explain, describe, analyze and simulate real-world complex networks is of uttermost practical, as well as theoretical, interest. In fact, networks can be a natural way to represent many phenomena; often, they arise from a complex interweaving of some features of the nodes. For example, in a co-authorship network, a link stems more easily between authors with similar interests; similarly, in a genetic regulatory network, links are affected by the different biological functions of the regulators.
In this paper we introduce and study a novel network model that is based on a latent attribute structure: this model, inspired by a generalization of the Indian Buffet process, is simple and contains a small number of parameters, with a clear and intuitive role. Each node is characterized by a number of features and the probability of the existence of an edge between two nodes depends on the features they share; the number of possible features is not fixed a priori and can grow indefinitely. Moreover, a random fitness parameter is introduced for each node in order to determine its ability to transmit its own features to other nodes; this behavior is added on top of a process of Indian-Buffet type. Because of the fitness property, a node’s connectivity does not depend on its age alone, so that also
“young but fit” nodes are able to compete and succeed in propagating their features and acquiring links. We also show how, considering the resulting bipartite node-attribute network, it is possible to gain some insight about which nodes were originally the most “fit”.
Our model for this bipartite network depends on few parameters, that are characterized by their straightforward interpretation and by the availability of proper estimators. Even if the parameters are easy to interpret and tune, the model is general enough to represent
complex phenomena—e.g., homophily, heterophily, or any interplay between features. We provide some theoretical as well as experimental results regarding the power-law behavior of the model and the proposed tools for the estimation of the parameters. We also show, through a number of experiments, how the proposed model naturally captures most local and global properties (e.g., degree distributions, connectivity and distance distributions)
real networks exhibit.Paolo Boldiboldi@di.unimi.itIrene Crimaldiirene.crimaldi@imtlucca.itCorrado Monticorrado.monti@unimi.it2016-02-24T12:03:56Z2016-12-19T10:00:37Zhttp://eprints.imtlucca.it/id/eprint/3113This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/31132016-02-24T12:03:56ZAsymptotics for randomly reinforced urns with random barriersAn urn contains black and red balls. Let Zn be the proportion of black balls at time n and 0≤L<U≤1 random barriers. At each time n, a ball bn is drawn. If bn is black and Zn-1<U, then bn is replaced together with a random number Bn of black balls. If bn is red and Zn-1>L, then bn is replaced together with a random number Rn of red balls. Otherwise, no additional balls are added, and bn alone is replaced. In this paper we assume that Rn=Bn. Then, under mild conditions, it is shown that Zn→a.s.Z for some random variable Z, and Dn≔√n(Zn-Z)→Patrizia BertiIrene Crimaldiirene.crimaldi@imtlucca.itLuca PratelliPietro Rigo2016-01-25T09:41:37Z2016-03-22T16:00:42Zhttp://eprints.imtlucca.it/id/eprint/3031This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/30312016-01-25T09:41:37ZFluctuation Theorems for Synchronization of Interacting Polya's urnsWe consider a model of N two-colors urns in which the reinforcement of each urn depends also on the content of all the other urns. This interaction is of mean-field type and it is tuned by a parameter \alpha in [0,1]; in particular, for \alpha=0 the N urns behave as N independent Polya's urns. For \alpha>0 urns synchronize, in the sense that the fraction of balls of a given color converges a.s. to the same (random) limit in all urns. In this paper we study fluctuations around this synchronized regime. The scaling of these fluctuations depends on the parameter \alpha. In particular, the standard scaling t^{-1/2} appears only for \alpha>1/2. For \alpha\geq 1/2 we also determine the limit distribution of the rescaled fluctuations. We use the notion of stable convergence, which is stronger than convergence in distribution.Irene Crimaldiirene.crimaldi@imtlucca.itPaolo Dai Pradaipra@math.unipd.itIda G. Minelliida.minelli@dm.univaq.it2016-01-11T09:11:26Z2016-02-26T15:56:01Zhttp://eprints.imtlucca.it/id/eprint/2978This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/29782016-01-11T09:11:26ZBasis Risk in Static versus Dynamic Longevity Risk HedgingThis paper provides a simple model for basis risk in a longevity framework, by separating common and idiosyncratic risk factors. Basis risk is captured by a single parameter, that measures the co-movement between the portfolio and the reference population. In this framework, the paper sets out the static, swap-based hedge for an annuity, and compares it with the dynamic, delta-based hedge, achieved using longevity bonds. We assume that the longevity intensity is distributed according to a CIR-type process and provide closed-form derivatives prices and hedges, also in the presence of an analogous CIR process for interest rate risk.Clemente De RosaElisa LucianoLuca Regisluca.regis@imtlucca.it2015-12-11T11:32:13Z2015-12-11T11:32:13Zhttp://eprints.imtlucca.it/id/eprint/2971This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/29712015-12-11T11:32:13ZDouglas-rachford splitting: Complexity estimates and accelerated variantsWe propose a new approach for analyzing convergence of the Douglas-Rachford splitting method for solving convex composite optimization problems. The approach is based on a continuously differentiable function, the Douglas-Rachford Envelope (DRE), whose stationary points correspond to the solutions of the original (possibly nonsmooth) problem. By proving the equivalence between the Douglas-Rachford splitting method and a scaled gradient method applied to the DRE, results from smooth unconstrained optimization are employed to analyze convergence properties of DRS, to tune the method and to derive an accelerated version of it.Panagiotis Patrinospanagiotis.patrinos@imtlucca.itLorenzo Stellalorenzo.stella@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2015-12-03T15:37:21Z2018-03-08T17:02:20Zhttp://eprints.imtlucca.it/id/eprint/2966This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/29662015-12-03T15:37:21ZOptimal Scales in Weighted NetworksThe analysis of networks characterized by links with heterogeneous intensity or weight suffers from two long-standing problems of arbitrariness. On one hand, the definitions of topological properties introduced for binary graphs can be generalized in non-unique ways to weighted networks. On the other hand, even when a definition is given, there is no natural choice of the (optimal) scale of link intensities (e.g. the money unit in economic networks). Here we show that these two seemingly independent problems can be regarded as intimately related, and propose a common solution to both. Using a formalism that we recently proposed in order to map a weighted network to an ensemble of binary graphs, we introduce an information-theoretic approach leading to the least biased generalization of binary properties to weighted networks, and at the same time fixing the optimal scale of link intensities. We illustrate our method on various social and economic networks.Diego Garlaschellidiego.garlaschelli@imtlucca.itSebastian E. AhnertThomas M.A. FinkGuido Caldarelliguido.caldarelli@imtlucca.it2015-11-16T15:32:44Z2015-11-16T15:32:44Zhttp://eprints.imtlucca.it/id/eprint/2902This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/29022015-11-16T15:32:44ZFrom Innovation to Diversification: A Simple Competitive Model<p>Few attempts have been proposed in order to describe the statistical features and historical evolution of the export bipartite matrix countries/products. An important standpoint is the introduction of a products network, namely a hierarchical forest of products that models the formation and the evolution of commodities. In the present article, we propose a simple dynamical model where countries compete with each other to acquire the ability to produce and export new products. Countries will have two possibilities to expand their export: innovating, i.e. introducing new goods, namely new nodes in the product networks, or copying the productive process of others, i.e. occupying a node already present in the same network. In this way, the topology of the products network and the country-product matrix evolve simultaneously, driven by the countries push toward innovation.</p>Fabio Saraccofabio.saracco@imtlucca.itRiccardo Di ClementeAndrea GabrielliLuciano Pietronero2015-11-16T09:10:37Z2015-11-16T09:10:37Zhttp://eprints.imtlucca.it/id/eprint/2900This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/29002015-11-16T09:10:37ZMemory Kernel in the Expertise of Chess PlayersIn this work we investigate a mechanism for the emergence of long-range time correlations observed in a chronologically ordered database of chess games. We analyze a modified Yule-Simon preferential growth process proposed by Cattuto et al., which includes memory effects by means of a probabilistic kernel. According to the Hurst exponent of different constructed time series from the record of games, artificially generated databases from the model exhibit similar long-range correlations. In addition, the inter-event time frequency distribution is well reproduced by the model for realistic parameter values. In particular, we find the inter-event time distribution properties to be correlated with the expertise of the chess players through the memory kernel extension. Our work provides new information about the strategies implemented by players with different levels of expertise, showing an interesting example of how popularities and long-range correlations build together during a collective learning process.Ana L. Schaigorodskyalschaigorodsky@gmail.comJuan I. Perottijuanignacio.perotti@imtlucca.itOrlando V. Billonialschaigorodsky@gmail.com2015-11-16T09:04:49Z2015-11-16T09:04:49Zhttp://eprints.imtlucca.it/id/eprint/2899This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28992015-11-16T09:04:49ZCorrelated bursts and the role of memory rangeInhomogeneous temporal processes in natural and social phenomena have been described by bursts that are rapidly occurring events within short time periods alternating with long periods of low activity. In addition to the analysis of heavy-tailed inter-event time distributions, higher-order correlations between inter-event times, called correlated bursts, have been studied only recently. As the possible mechanisms underlying such correlated bursts are far from being fully understood, we devise a simple model for correlated bursts by using a self-exciting point process with variable memory range. Here the probability that a new event occurs is determined by a memory function that is the sum of decaying memories of the past events. In order to incorporate the noise and/or limited memory capacity of systems, we apply two memory loss mechanisms, namely either fixed number or variable number of memories. By using theoretical analysis and numerical simulations we find that excessive amount of memory effect may lead to a Poissonian process, which implies that for memory effect there exists an intermediate range that will generate correlated bursts of magnitude comparable to empirical findings. Hence our results provide deeper understanding of how long-range memory affects correlated bursts.Hang-Hyun JoJuan I. Perottijuanignacio.perotti@imtlucca.itKimmo KaskiJános Kertész2015-11-06T13:27:40Z2015-11-06T13:27:40Zhttp://eprints.imtlucca.it/id/eprint/2853This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28532015-11-06T13:27:40ZEvolutionary network games: equilibria from imitation and best-response dynamicsWe consider games of strategic substitutes and strategic complements on networks. We introduce two different evolutionary dynamics in order to refine their multiplicity of equilibria, and we analyse the system through a mean field approach. We find that for the best-shot game, taken as a model for substitutes, a replicator-like dynamics does not lead to Nash equilibria, whereas it leads to unique equilibria (full cooperation or full defection, depending on the initial condition and the game parameter) for complements, represented by a coordination game. On the other hand, when the dynamics becomes more cognitively demanding in the form of a best response evolution, predictions are always Nash equilibria (at least when individuals are fully rational): For the best-shot game we find equilibria with a definite value of the fraction of contributors, whereas for the coordination game symmetric equilibria arise only for low or high initial fractions of cooperators. We also extend our study by considering complex heterogeneous topologies, and show that the nature of the selected equilibria does not change for the best-shot game. However for coordination games we reveal an important difference, namely that on infinitely large scale-free networks cooperation arises for any value of the incentive to cooperate.Giulio Ciminigiulio.cimini@imtlucca.itClaudio CastellanoAngel Sánchez2015-11-06T13:16:21Z2015-11-06T13:16:21Zhttp://eprints.imtlucca.it/id/eprint/2852This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28522015-11-06T13:16:21ZDynamics to Equilibrium in Network Games: Individual Behavior and Global ResponseVarious social contexts can be depicted as games of strategic interactions on networks, where an individual’s welfare depends on both her and her partners’ actions. Whereas much attention has been devoted to Bayes-Nash equilibria in such games, here we look at strategic interactions from an evolutionary perspective. To this end, we present the results of a numerical simulations program for these games, which allows us to find out whether Nash equilibria are accessible by adaptation of player strategies, and in general to identify the attractors of the evolution. Simulations allow us to go beyond a global characterization of the cooperativeness at equilibrium and probe into individual behavior. We find that when players imitate each other, evolution does not reach Nash equilibria and, worse, leads to very unfavorable states in terms of welfare. On the contrary, when players update their behavior rationally, they self-organize into a rich variety of Nash equilibria, where individual behavior and payoffs are shaped by the nature of the game, the social network’s structure and the players’ position within the network. Our results allow to assess the validity of mean-field approaches we use to describe the dynamics of these games. Interestingly, our dynamically-found equilibria generally do not coincide with (but show qualitatively the same features of) those resulting from theoretical predictions in the context of one-shot games under incomplete information.Giulio Ciminigiulio.cimini@imtlucca.itClaudio CastellanoAngel Sánchez2015-11-06T12:36:51Z2015-11-06T12:36:51Zhttp://eprints.imtlucca.it/id/eprint/2848This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28482015-11-06T12:36:51ZLearning dynamics explains human behaviour in Prisoner’s Dilemma on networksCooperative behaviour lies at the very basis of human societies, yet its evolutionary origin remains a key unsolved puzzle. Whereas reciprocity or conditional cooperation is one of the most prominent mechanisms proposed to explain the emergence of cooperation in social dilemmas, recent experimental findings on networked Prisoner’s Dilemma games suggest that conditional cooperation also depends on the previous action of the player—namely on the ‘mood’ in which the player is currently in. Roughly, a majority of people behave as conditional cooperators if they cooperated in the past, whereas they ignore the context and free ride with high probability if they did not. However, the ultimate origin of this behaviour represents a conundrum itself. Here, we aim specifically to provide an evolutionary explanation of moody conditional cooperation (MCC). To this end, we perform an extensive analysis of different evolutionary dynamics for players’ behavioural traits—ranging from standard processes used in game theory based on pay-off comparison to others that include non-economic or social factors. Our results show that only a dynamic built upon reinforcement learning is able to give rise to evolutionarily stable MCC, and at the end to reproduce the human behaviours observed in the experiments.Giulio Ciminigiulio.cimini@imtlucca.itAngel Sánchez2015-11-06T11:09:48Z2015-11-06T11:09:48Zhttp://eprints.imtlucca.it/id/eprint/2843This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28432015-11-06T11:09:48ZEnhancing topology adaptation in information-sharing social networksThe advent of the Internet and World Wide Web has led to unprecedent growth of the information available. People usually face the information overload by following a limited number of sources which best fit their interests. It has thus become important to address issues like who gets followed and how to allow people to discover new and better information sources. In this paper we conduct an empirical analysis of different online social networking sites and draw inspiration from its results to present different source selection strategies in an adaptive model for social recommendation. We show that local search rules which enhance the typical topological features of real social communities give rise to network configurations that are globally optimal. These rules create networks which are effective in information diffusion and resemble structures resulting from real social systems.Giulio Ciminigiulio.cimini@imtlucca.itDuanbing ChenMatúš MedoLinyuan LüYi-Cheng ZhangTao Zhou2015-11-06T11:07:28Z2015-11-06T11:07:28Zhttp://eprints.imtlucca.it/id/eprint/2842This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28422015-11-06T11:07:28ZTemporal Effects in the Growth of NetworksWe show that to explain the growth of the citation network by preferential attachment (PA), one has to accept that individual nodes exhibit heterogeneous fitness values that decay with time. While previous PA-based models assumed either heterogeneity or decay in isolation, we propose a simple analytically treatable model that combines these two factors. Depending on the input assumptions, the resulting degree distribution shows an exponential, log-normal or power-law decay, which makes the model an apt candidate for modeling a wide range of real systems.Matúš MedoGiulio Ciminigiulio.cimini@imtlucca.itStanislao Gualdi2015-11-06T11:04:00Z2015-11-06T11:04:00Zhttp://eprints.imtlucca.it/id/eprint/2841This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28412015-11-06T11:04:00ZEmergence of Scale-Free Leadership Structure in Social Recommender Systems<p>The study of the organization of social networks is important for the understanding of opinion formation, rumor spreading, and the emergence of trends and fashion. This paper reports empirical analysis of networks extracted from four leading sites with social functionality (Delicious, Flickr, Twitter and YouTube) and shows that they all display a scale-free leadership structure. To reproduce this feature, we propose an adaptive network model driven by social recommending. Artificial agent-based simulations of this model highlight a “good get richer” mechanism where users with broad interests and good judgments are likely to become popular leaders for the others. Simulations also indicate that the studied social recommendation mechanism can gradually improve the user experience by adapting to tastes of its users. Finally we outline implications for real online resource-sharing systems.</p>Tao ZhouMatúš MedoGiulio Ciminigiulio.cimini@imtlucca.itZi-Ke ZhangYi-Cheng Zhang2015-11-06T10:51:58Z2015-11-06T10:51:58Zhttp://eprints.imtlucca.it/id/eprint/2838This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28382015-11-06T10:51:58ZDynamics of movie competition and popularity spreading in recommender systemsWe introduce a simple model to study movie competition in recommender systems. Movies of heterogeneous quality compete against each other through viewers’ reviews and generate interesting dynamics at the box office. By assuming mean-field interactions between the competing movies, we show that the runaway effect of popularity spreading is triggered by defeating the average review score, leading to box-office hits: Popularity rises and peaks before fade-out. The average review score thus characterizes the critical movie quality necessary for transition from box-office bombs to blockbusters. The major factors affecting the critical review score are examined. By iterating the mean-field dynamical equations, we obtain qualitative agreements with simulations and real systems in the dynamical box-office forms, revealing the significant role of competition in understanding box-office dynamics.C. H. YeungGiulio Ciminigiulio.cimini@imtlucca.itC.-H. Jin2015-11-05T15:07:16Z2018-03-08T16:58:21Zhttp://eprints.imtlucca.it/id/eprint/2836This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28362015-11-05T15:07:16ZMultiplexity and multireciprocity in directed multiplexesIn recent years, the study of multi-layer networks has received much attention. Here, we provide new measures of dependency between directed links across different layers of multiplex networks. We show that this operation requires more than a straightforward extension of the corresponding multiplexity measures that have been developed for undirected multiplexes. In particular, one should take into account the effects of reciprocity, i.e. the tendency of pairs of vertices to establish mutual connections. We extend this quantity to multiplexes and introduce the notion of multireciprocity, defined as the tendency of links in one layer to be reciprocated by links in a different layer. While ordinary reciprocity reduces to a scalar quantity, multireciprocity requires a square matrix generated by all the possible pairs of layers. We introduce multireciprocity metrics valid for both binary and weighted networks and then measure these quantities on the World Trade Multiplex (WTM), representing the import-export relationships between world countries in different products. We show that several pairs of layers exhibit strong multiplexity, an effect which can however be largely encoded into the degree or strength sequences of individual layers. We also find that most pairs of commodities are characterised by positive multireciprocity, and that such values are significantly lower than the usual reciprocity measured on the aggregated network. We finally identify robust empirical patterns that allow us to use the multireciprocity matrix to retrieve the two-layer reciprocated degree (strength) of a node from the ordinary in-degree (in-strength) in a single layer and to reconstruct joint multi-layer connection probabilities from marginal ones, hence bridging the gap between single-layer properties and truly multiplex information.Valerio GemmettoTiziano Squartinitiziano.squartini@imtlucca.itFrancesco PiccioloFranco RuzzenentiDiego Garlaschellidiego.garlaschelli@imtlucca.it2015-11-05T15:04:15Z2018-03-08T16:57:32Zhttp://eprints.imtlucca.it/id/eprint/2835This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28352015-11-05T15:04:15ZBreaking of ensemble equivalence in networksIt is generally believed that, in the thermodynamic limit, the microcanonical description as a function of energy coincides with the canonical description as a function of temperature. However, various examples of systems for which the microcanonical and canonical ensembles are not equivalent have been identified. A complete theory of this intriguing phenomenon is still missing. Here we show that ensemble nonequivalence can manifest itself also in random graphs with topological constraints. We find that, while graphs with a given number of links are ensemble-equivalent, graphs with a given degree sequence are not. This result holds irrespective of whether the energy is nonadditive (as in unipartite graphs) or additive (as in bipartite graphs). In contrast with previous expectations, our results show that: (1) physically, nonequivalence can be induced by an extensive number of local constraints, and not necessarily by long-range interactions or nonadditivity; (2) mathematically, nonquivalence is determined by a different large-deviation behaviour of microcanonical and canonical probabilities for a single microstate, and not necessarily for almost all microstates. The latter criterion, which is entirely local, is not restricted to networks and holds in generalTiziano Squartinitiziano.squartini@imtlucca.itJoey de MolFrank den HollanderDiego Garlaschellidiego.garlaschelli@imtlucca.it2015-11-05T14:49:22Z2015-11-05T14:49:22Zhttp://eprints.imtlucca.it/id/eprint/2833This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28332015-11-05T14:49:22ZConformism-driven phases of opinion formation on heterogeneous networks: the q -voter model caseThe q -voter model, a variant of the classic voter model, has been analyzed by several authors. While allowing us to study opinion dynamics, this model is also believed to be one of the most representative among the many defined in the wide field of sociophysics. Here, we investigate the consequences of conformity on the consensus reaching process, by numerically simulating a q -voter model with agents behaving either as conformists or nonconformists, embedded on heterogeneous network topologies (as small-world and scale-free). In fact, although it is already known that conformity enhances the reaching of consensus, the related process is often studied only on fully-connected networks, thus strongly limiting our full understanding of it. This paper represents a first step in the direction of analyzing more realistic social models, showing that different opinion formation phases, driven by the conformist agents density, are observable. As a result, we identify threshold values of the density of conformist agents, varying across different topologies and separating different regimes of our system, ranging from a disordered phase, where different opinions coexist, to a gradually more ordered phase, where consensus is eventually reached.Marco Alberto JavaroneTiziano Squartinitiziano.squartini@imtlucca.it2015-11-05T14:34:43Z2018-03-08T16:56:43Zhttp://eprints.imtlucca.it/id/eprint/2832This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28322015-11-05T14:34:43ZEstimating topological properties of weighted networks from limited informationA problem typically encountered when studying complex systems is the limitedness of the information available on their topology, which hinders our understanding of their structure and of the dynamical processes taking place on them. A paramount example is provided by financial networks, whose data are privacy protected: Banks publicly disclose only their aggregate exposure towards other banks, keeping individual exposures towards each single bank secret. Yet, the estimation of systemic risk strongly depends on the detailed structure of the interbank network. The resulting challenge is that of using aggregate information to statistically reconstruct a network and correctly predict its higher-order properties. Standard approaches either generate unrealistically dense networks, or fail to reproduce the observed topology by assigning homogeneous link weights. Here, we develop a reconstruction method, based on statistical mechanics concepts, that makes use of the empirical link density in a highly nontrivial way. Technically, our approach consists in the preliminary estimation of node degrees from empirical node strengths and link density, followed by a maximum-entropy inference based on a combination of empirical strengths and estimated degrees. Our method is successfully tested on the international trade network and the interbank money market, and represents a valuable tool for gaining insights on privacy-protected or partially accessible systems.Giulio Ciminigiulio.cimini@imtlucca.itTiziano Squartinitiziano.squartini@imtlucca.itAndrea GabrielliDiego Garlaschellidiego.garlaschelli@imtlucca.it2015-11-05T14:29:28Z2015-11-16T15:27:33Zhttp://eprints.imtlucca.it/id/eprint/2831This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28312015-11-05T14:29:28ZRandomizing bipartite networks: the case of the World Trade WebWithin the last fifteen years, network theory has been successfully applied both to natural sciences and to socioeconomic disciplines. In particular, bipartite networks have been recognized to provide a particularly insightful representation of many systems, ranging from mutualistic networks in ecology to trade networks in economy, whence the need of a pattern detection-oriented analysis in order to identify statistically-significant structural properties. Such an analysis rests upon the definition of suitable null models, i.e. upon the choice of the portion of network structure to be preserved while randomizing everything else. However, quite surprisingly, little work has been done so far to define null models for real bipartite networks. The aim of the present work is to fill this gap, extending a recently-proposed method to randomize monopartite networks to bipartite networks. While the proposed formalism is perfectly general, we apply our method to the binary, undirected, bipartite representation of the World Trade Web, comparing the observed values of a number of structural quantities of interest with the expected ones, calculated via our randomization procedure. Interestingly, the behavior of the World Trade Web in this new representation is strongly different from the monopartite analogue, showing highly non-trivial patterns of self-organization.Fabio Saraccofabio.saracco@imtlucca.itRiccardo Di Clementericcardo.diclemente@alumni.imtlucca.itAndrea GabrielliTiziano Squartinitiziano.squartini@imtlucca.it2015-11-05T14:21:49Z2018-03-08T16:58:02Zhttp://eprints.imtlucca.it/id/eprint/2830This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28302015-11-05T14:21:49ZInformation Recovery in Behavioral NetworksIn the context of agent based modeling and network theory, we focus on the problem of recovering behavior-related choice information from origin-destination type data, a topic also known under the name of network tomography. As a basis for predicting agents' choices we emphasize the connection between adaptive intelligent behavior, causal entropy maximization, and self-organized behavior in an open dynamic system. We cast this problem in the form of binary and weighted networks and suggest information theoretic entropy-driven methods to recover estimates of the unknown behavioral flow parameters. Our objective is to recover the unknown behavioral values across the ensemble analytically, without explicitly sampling the configuration space. In order to do so, we consider the Cressie-Read family of entropic functionals, enlarging the set of estimators commonly employed to make optimal use of the available information. More specifically, we explicitly work out two cases of particular interest: Shannon functional and the likelihood functional. We then employ them for the analysis of both univariate and bivariate data sets, comparing their accuracy in reproducing the observed trends.Tiziano Squartinitiziano.squartini@imtlucca.itEnrico Ser-GiacomiDiego Garlaschellidiego.garlaschelli@imtlucca.itGeorge Judge2015-11-05T14:07:32Z2015-11-05T14:07:32Zhttp://eprints.imtlucca.it/id/eprint/2828This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28282015-11-05T14:07:32ZSEDNAM - Socio-Economic Dynamics: Networks and Agent-Based Models - IntroductionRecent years have witnessed the increasing interest of physicists, mathematicians and computer scientists for socio-economic systems. In our view, the many reasons behind this can be summarized by observing that traditional approaches to disciplines as sociology and economics have dramatically shown their limitations.Serge GalamMarco Alberto JavaroneTiziano Squartinitiziano.squartini@imtlucca.it2015-11-05T14:03:25Z2018-03-08T16:58:46Zhttp://eprints.imtlucca.it/id/eprint/2827This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28272015-11-05T14:03:25ZUnbiased sampling of network ensemblesSampling random graphs with given properties is a key step in the analysis of networks, as random ensembles represent basic null models required to identify patterns such as communities and motifs. An important requirement is that the sampling process is unbiased and efficient. The main approaches are microcanonical, i.e. they sample graphs that match the enforced constraints exactly. Unfortunately, when applied to strongly heterogeneous networks (like most real-world examples), the majority of these approaches become biased and/or time-consuming. Moreover, the algorithms defined in the simplest cases, such as binary graphs with given degrees, are not easily generalizable to more complicated ensembles. Here we propose a solution to the problem via the introduction of a ‘Maximize and Sample’ (‘Max & Sam’ for short) method to correctly sample ensembles of networks where the constraints are ‘soft’, i.e. realized as ensemble averages. Our method is based on exact maximum-entropy distributions and is therefore unbiased by construction, even for strongly heterogeneous networks. It is also more computationally efficient than most microcanonical alternatives. Finally, it works for both binary and weighted networks with a variety of constraints, including combined degree-strength sequences and full reciprocity structure, for which no alternative method exists. Our canonical approach can in principle be turned into an unbiased microcanonical one, via a restriction to the relevant subset. Importantly, the analysis of the fluctuations of the constraints suggests that the microcanonical and canonical versions of all the ensembles considered here are not equivalent. We show various real-world applications and provide a code implementing all our algorithms.Tiziano Squartinitiziano.squartini@imtlucca.itRossana Mastrandrearossana.mastrandrea@imtlucca.itDiego Garlaschellidiego.garlaschelli@imtlucca.it2015-11-05T13:51:23Z2018-03-08T16:57:47Zhttp://eprints.imtlucca.it/id/eprint/2826This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28262015-11-05T13:51:23ZA GDP-driven model for the binary and weighted structure of the International Trade NetworkRecent events such as the global financial crisis have renewed the interest in the topic of economic networks. One of the main channels of shock propagation among countries is the International Trade Network (ITN). Two important models for the ITN structure, the classical gravity model of trade (more popular among economists) and the fitness model (more popular among networks scientists), are both limited to the characterization of only one representation of the ITN. The gravity model satisfactorily predicts the volume of trade between connected countries, but cannot reproduce the missing links (i.e. the topology). On the other hand, the fitness model can successfully replicate the topology of the ITN, but cannot predict the volumes. This paper tries to make an important step forward in the unification of those two frameworks, by proposing a new gross domestic product (GDP) driven model which can simultaneously reproduce the binary and the weighted properties of the ITN. Specifically, we adopt a maximum-entropy approach where both the degree and the strength of each node are preserved. We then identify strong nonlinear relationships between the GDP and the parameters of the model. This ultimately results in a weighted generalization of the fitness model of trade, where the GDP plays the role of a ‘macroeconomic fitness’ shaping the binary and the weighted structure of the ITN simultaneously. Our model mathematically explains an important asymmetry in the role of binary and weighted network properties, namely the fact that binary properties can be inferred without the knowledge of weighted ones, while the opposite is not true.Assaf AlmogTiziano Squartinitiziano.squartini@imtlucca.itDiego Garlaschellidiego.garlaschelli@imtlucca.it2015-11-05T13:44:04Z2018-03-08T17:00:39Zhttp://eprints.imtlucca.it/id/eprint/2824This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28242015-11-05T13:44:04ZStationarity, non-stationarity and early warning signals in economic networksEconomic integration, globalization and financial crises represent examples of processes whose understanding requires the analysis of the underlying network structure. Of particular interest is establishing whether a real economic network is in a state of (quasi)stationary equilibrium, i.e. characterized by smooth structural changes rather than abrupt transitions. While in the former case the behaviour of the system can be reasonably controlled and predicted, in the latter case this is generally impossible. Here, we propose a method to assess whether a real economic network is in a quasi-stationary state by checking the consistency of its structural evolution with appropriate quasi-equilibrium maximum-entropy ensembles of graphs. As illustrative examples, we consider the International Trade Network (ITN) and the Dutch Interbank Network (DIN). We find that the ITN is an almost perfect example of quasi-equilibrium network, while the DIN is clearly out-of-equilibrium. In the latter, the entity of the deviation from quasi-stationarity contains precious information that allows us to identify remarkable early warning signals of the interbank crisis of 2008. These early warning signals involve certain dyadic and triadic topological properties, including dangerous ‘debt loops’ with different levels of interbank reciprocity.Tiziano Squartinitiziano.squartini@imtlucca.itDiego Garlaschellidiego.garlaschelli@imtlucca.it2015-11-05T13:08:20Z2018-03-08T17:00:11Zhttp://eprints.imtlucca.it/id/eprint/2823This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28232015-11-05T13:08:20ZEnhanced reconstruction of weighted networks from strengths and degreesNetwork topology plays a key role in many phenomena, from the spreading of diseases to that of financial crises. Whenever the whole structure of a network is unknown, one must resort to reconstruction methods that identify the least biased ensemble of networks consistent with the partial information available. A challenging case, frequently encountered due to privacy issues in the analysis of interbank flows and Big Data, is when there is only local (node-specific) aggregate information available. For binary networks, the relevant ensemble is one where the degree (number of links) of each node is constrained to its observed value. However, for weighted networks the problem is much more complicated. While the naïve approach prescribes to constrain the strengths (total link weights) of all nodes, recent counter-intuitive results suggest that in weighted networks the degrees are often more informative than the strengths. This implies that the reconstruction of weighted networks would be significantly enhanced by the specification of both strengths and degrees, a computationally hard and bias-prone procedure. Here we solve this problem by introducing an analytical and unbiased maximum-entropy method that works in the shortest possible time and does not require the explicit generation of reconstructed samples. We consider several real-world examples and show that, while the strengths alone give poor results, the additional knowledge of the degrees yields accurately reconstructed networks. Information-theoretic criteria rigorously confirm that the degree sequence, as soon as it is non-trivial, is irreducible to the strength sequence. Our results have strong implications for the analysis of motifs and communities and whenever the reconstructed ensemble is required as a null model to detect higher-order patterns.Rossana Mastrandrearossana.mastrandrea@imtlucca.itTiziano Squartinitiziano.squartini@imtlucca.itGiorgio FagioloDiego Garlaschellidiego.garlaschelli@imtlucca.it2015-11-05T13:05:35Z2018-03-08T17:01:13Zhttp://eprints.imtlucca.it/id/eprint/2822This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28222015-11-05T13:05:35ZEconomic Networks In and Out of EquilibriumEconomic and financial networks play a crucial role in various important processes, including economic integration, globalization, and financial crises. Of particular interest is understanding whether the temporal evolution of a real economic network is in a (quasi-)stationary equilibrium, i.e. characterized by smooth structural changes rather than abrupt transitions. Smooth changes in quasi-equilibrium networks can be generally controlled for, and largely predicted, while this is generally not possible for abrupt transitions in non-stationary networks. Here we study whether real economic networks are in or out of equilibrium by checking their consistency with quasi-equilibrium maximum-entropy ensembles of graphs. As illustrative examples, we consider the International Trade Network (ITN) and the Dutch Interbank Network (DIN). We show that, despite the globalization process, the ITN is an almost perfect example of quasi-equilibrium network, while the DIN is clearly an out-of-equilibrium network undergoing major structural changes and displaying non-stationary dynamics. Among the out-of-equilibrium properties of the DIN, we find striking early-warning signals of the interbank crisis of 2008.Tiziano Squartinitiziano.squartini@imtlucca.itDiego Garlaschellidiego.garlaschelli@imtlucca.it2015-11-05T12:59:14Z2018-03-08T16:59:55Zhttp://eprints.imtlucca.it/id/eprint/2821This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28212015-11-05T12:59:14ZDisentangling spatial and non-spatial effects in real networksTiziano Squartinitiziano.squartini@imtlucca.itFrancesco PiccioloFranco RuzzenentiDiego Garlaschellidiego.garlaschelli@imtlucca.itRiccardo Basosi2015-11-05T12:03:38Z2018-03-08T17:01:28Zhttp://eprints.imtlucca.it/id/eprint/2819This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28192015-11-05T12:03:38ZEarly-warning signals of topological collapse in interbank networksThe financial crisis clearly illustrated the importance of characterizing the level of ‘systemic’ risk associated with an entire credit network, rather than with single institutions. However, the interplay between financial distress and topological changes is still poorly understood. Here we analyze the quarterly interbank exposures among Dutch banks over the period 1998–2008, ending with the crisis. After controlling for the link density, many topological properties display an abrupt change in 2008, providing a clear – but unpredictable – signature of the crisis. By contrast, if the heterogeneity of banks' connectivity is controlled for, the same properties show a gradual transition to the crisis, starting in 2005 and preceded by an even earlier period during which anomalous debt loops could have led to the underestimation of counter-party risk. These early-warning signals are undetectable if the network is reconstructed from partial bank-specific data, as routinely done. We discuss important implications for bank regulatory policies.Tiziano Squartinitiziano.squartini@imtlucca.itIman van LelyveldDiego Garlaschellidiego.garlaschelli@imtlucca.it2015-11-05T11:58:38Z2018-03-08T17:02:35Zhttp://eprints.imtlucca.it/id/eprint/2818This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28182015-11-05T11:58:38ZReciprocity of weighted networksIn directed networks, reciprocal links have dramatic effects on dynamical processes, network growth, and higher-order structures such as motifs and communities. While the reciprocity of binary networks has been extensively studied, that of weighted networks is still poorly understood, implying an ever-increasing gap between the availability of weighted network data and our understanding of their dyadic properties. Here we introduce a general approach to the reciprocity of weighted networks, and define quantities and null models that consistently capture empirical reciprocity patterns at different structural levels. We show that, counter-intuitively, previous reciprocity measures based on the similarity of mutual weights are uninformative. By contrast, our measures allow to consistently classify different weighted networks according to their reciprocity, track the evolution of a network's reciprocity over time, identify patterns at the level of dyads and vertices, and distinguish the effects of flux (im)balances or other (a)symmetries from a true tendency towards (anti-)reciprocation.Tiziano Squartinitiziano.squartini@imtlucca.itFrancesco PiccioloFranco RuzzenentiDiego Garlaschellidiego.garlaschelli@imtlucca.it2015-11-05T11:48:40Z2018-03-08T17:03:03Zhttp://eprints.imtlucca.it/id/eprint/2817This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28172015-11-05T11:48:40ZThe Role of Distances in the World Trade WebIn the economic literature, geographic distances are considered fundamental factors to be included in any theoretical model whose aim is the quantification of the trade between countries. Quantitatively, distances enter into the so-called gravity models that successfully predict the weight of non-zero trade flows. However, it has been recently shown that gravity models fail to reproduce the binary topology of the World Trade Web. In this paper a different approach is presented: the formalism of exponential random graphs is used and the distances are treated as constraints, to be imposed on a previously chosen ensemble of graphs. Then, the information encoded in the geographical distances is used to explain the binary structure of the World Trade Web, by testing it on the degree-degree correlations and the reciprocity structure. This leads to the definition of a novel null model that combines spatial and non-spatial effects. The effectiveness of spatial constraints is compared to that of nonspatial ones by means of the Akaike Information Criterion and the Bayesian Information Criterion. Even if it is commonly believed that the World Trade Web is strongly dependent on the distances, what emerges from our analysis is that distances do not play a crucial role in shaping the World Trade Web binary structure and that the information encoded into the reciprocity is far more useful in explaining the observed patterns.Francesco PiccioloFranco RuzzenentiRiccardo BasosiTiziano Squartinitiziano.squartini@imtlucca.itDiego Garlaschellidiego.garlaschelli@imtlucca.it2015-11-05T11:43:19Z2018-03-08T17:01:55Zhttp://eprints.imtlucca.it/id/eprint/2816This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28162015-11-05T11:43:19ZNull models of economic networks: the case of the world trade webIn all empirical-network studies, the observed properties of economic networks are informative only if compared with a well-defined null model that can quantitatively predict the behavior of such properties in constrained graphs. However, predictions of the available null-model methods can be derived analytically only under assumptions (e.g., sparseness of the network) that are unrealistic for most economic networks like the world trade web (WTW). In this paper we study the evolution of the WTW using a recently-proposed family of null network models. The method allows to analytically obtain the expected value of any network statistic across the ensemble of networks that preserve on average some local properties, and are otherwise fully random. We compare expected and observed properties of the WTW in the period 1950–2000, when either the expected number of trade partners or total country trade is kept fixed and equal to observed quantities. We show that, in the binary WTW, node-degree sequences are sufficient to explain higher-order network properties such as disassortativity and clustering-degree correlation, especially in the last part of the sample. Conversely, in the weighted WTW, the observed sequence of total country imports and exports are not sufficient to predict higher-order patterns of the WTW. We discuss some important implications of these findings for international-trade models.Giorgio FagioloTiziano Squartinitiziano.squartini@imtlucca.itDiego Garlaschellidiego.garlaschelli@imtlucca.it2015-11-05T11:24:01Z2018-03-08T17:03:45Zhttp://eprints.imtlucca.it/id/eprint/2814This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28142015-11-05T11:24:01ZTriadic Motifs and Dyadic Self-Organization in the World Trade NetworkIn self-organizing networks, topology and dynamics coevolve in a continuous feedback, without exogenous driving. The World Trade Network (WTN) is one of the few empirically well documented examples of self-organizing networks: its topology depends on the GDP of world countries, which in turn depends on the structure of trade. Therefore, understanding the WTN topological properties deviating from randomness provides direct empirical information about the structural effects of self-organization. Here, using an analytical pattern-detection method we have recently proposed, we study the occurrence of triadic ‘motifs’ (three-vertices subgraphs) in the WTN between 1950 and 2000. We find that motifs are not explained by only the in- and out-degree sequences, but they are completely explained if also the numbers of reciprocal edges are taken into account. This implies that the self-organization process underlying the evolution of the WTN is almost completely encoded into the dyadic structure, which strongly depends on reciprocity.Tiziano Squartinitiziano.squartini@imtlucca.itDiego Garlaschellidiego.garlaschelli@imtlucca.it2015-11-05T11:16:04Z2018-03-08T17:04:19Zhttp://eprints.imtlucca.it/id/eprint/2813This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28132015-11-05T11:16:04ZRandomizing world trade. II. A weighted network analysisBased on the misleading expectation that weighted network properties always offer a more complete description than purely topological ones, current economic models of the International Trade Network (ITN) generally aim at explaining local weighted properties, not local binary ones. Here we complement our analysis of the binary projections of the ITN by considering its weighted representations. We show that, unlike the binary case, all possible weighted representations of the ITN (directed and undirected, aggregated and disaggregated) cannot be traced back to local country-specific properties, which are therefore of limited informativeness. Our two papers show that traditional macroeconomic approaches systematically fail to capture the key properties of the ITN. In the binary case, they do not focus on the degree sequence and hence cannot characterize or replicate higher-order properties. In the weighted case, they generally focus on the strength sequence, but the knowledge of the latter is not enough in order to understand or reproduce indirect effects.Tiziano Squartinitiziano.squartini@imtlucca.itGiorgio FagioloDiego Garlaschellidiego.garlaschelli@imtlucca.it2015-11-05T11:14:29Z2018-03-08T17:04:07Zhttp://eprints.imtlucca.it/id/eprint/2812This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28122015-11-05T11:14:29ZRandomizing world trade. I. A binary network analysisThe international trade network (ITN) has received renewed multidisciplinary interest due to recent advances in network theory. However, it is still unclear whether a network approach conveys additional, nontrivial information with respect to traditional international-economics analyses that describe world trade only in terms of local (first-order) properties. In this and in a companion paper, we employ a recently proposed randomization method to assess in detail the role that local properties have in shaping higher-order patterns of the ITN in all its possible representations (binary or weighted, directed or undirected, aggregated or disaggregated by commodity) and across several years. Here we show that, remarkably, the properties of all binary projections of the network can be completely traced back to the degree sequence, which is therefore maximally informative. Our results imply that explaining the observed degree sequence of the ITN, which has not received particular attention in economic theory, should instead become one the main focuses of models of trade.Tiziano Squartinitiziano.squartini@imtlucca.itGiorgio FagioloDiego Garlaschellidiego.garlaschelli@imtlucca.it2015-11-05T10:48:48Z2018-03-08T17:05:17Zhttp://eprints.imtlucca.it/id/eprint/2807This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28072015-11-05T10:48:48ZWeighted Random GraphTiziano Squartinitiziano.squartini@imtlucca.itDiego Garlaschellidiego.garlaschelli@imtlucca.it2015-11-05T10:42:16Z2015-11-05T15:23:16Zhttp://eprints.imtlucca.it/id/eprint/2806This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28062015-11-05T10:42:16ZNeural networks: A reviewTiziano Squartinitiziano.squartini@imtlucca.it2015-11-02T14:20:02Z2015-11-02T14:20:02Zhttp://eprints.imtlucca.it/id/eprint/2801This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/28012015-11-02T14:20:02ZQuantifying randomness in real networksRepresented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the dk-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks—the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain—and find that many important local and global structural properties of these networks are closely reproduced by dk-random graphs whose degree distributions, degree correlations and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness, and release software to generate dk-random graphs.Chiara OrsiniMarija M. DankulovPol Colomer-de-SimónAlmerima JamakovicPriya MahadevanAmin VahdatKevin E. BasslerZoltán ToroczkaiMarián BoguñáGuido Caldarelliguido.caldarelli@imtlucca.itSanto FortunatoDmitri Krioukov2015-10-28T14:52:49Z2016-05-04T09:46:22Zhttp://eprints.imtlucca.it/id/eprint/2787This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/27872015-10-28T14:52:49ZA Quadratic Programming Algorithm Based on Nonnegative Least Squares with Applications to Embedded Model Predictive ControlThis paper proposes an active set method based on nonnegative least squares (NNLS) to solve strictly convex quadratic programming (QP) problems, such as those that arise in Model Predictive Control (MPC). The main idea is to rephrase the QP problem as a Least Distance Problem (LDP) that is solved via a NNLS reformulation. While the method is rather general for solving strictly convex QP’s subject to linear inequality constraints, it is particularly useful for embedded MPC because (i) is very fast, compared to other existing state-of-theart QP algorithms, (ii) is very simple to code, requiring only basic arithmetic operations for computing LDLT decompositions recursively to solve linear systems of equations, (iii) contrary to iterative methods, provides the solution or recognizes infeasibility in a finite number of steps.Alberto Bemporadalberto.bemporad@imtlucca.it2015-10-22T13:41:13Z2015-10-22T13:41:13Zhttp://eprints.imtlucca.it/id/eprint/2779This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/27792015-10-22T13:41:13ZDistributed solution of stochastic optimal control problems on GPUsStochastic optimal control problems arise in many applications and are, in principle, large-scale involving up to millions of decision variables. Their applicability in control applications is often limited by the availability of algorithms that can solve them efficiently and within the sampling time of the controlled system.
In this paper we propose a dual accelerated proximal gradient algorithm which is amenable to parallelization and demonstrate that its GPU implementation affords high speed-up values (with respect to a CPU implementation) and greatly outperforms well-established commercial optimizers such as Gurobi.Ajay Kumar SampathiraoPantelis Sopasakispantelis.sopasakis@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.itPanagiotis Patrinospanagiotis.patrinos@imtlucca.it2015-10-22T13:39:05Z2016-05-04T10:15:53Zhttp://eprints.imtlucca.it/id/eprint/2780This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/27802015-10-22T13:39:05ZScenario-Based Model Predictive Operation Control of Islanded MicrogridsWe propose a model predictive control (MPC) approach for the operation of islanded microgrids that takes into account the stochasticity of wind and load forecasts. In comparison to worst case approaches, the probability distribution of the prediction is used to optimize the operation of the microgrid, leading to less conservative solutions. Suitable models for time series forecast are derived and employed to create scenarios. These scenarios and the system measurements are used as inputs for a stochastic MPC, wherein a mixed-integer problem is solved to derive the optimal controls. In the provided case study, the stochastic MPC yields an increase of wind power generation and decrease of conventional generation.Christian Hanshans@control.tu-berlin.dePantelis Sopasakispantelis.sopasakis@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.itRaisch Jörgraisch@control.tu-berlin.deCarsten Reincke-Collon2015-10-19T09:22:53Z2015-10-19T09:22:53Zhttp://eprints.imtlucca.it/id/eprint/2774This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/27742015-10-19T09:22:53ZSparse Solutions to the Average Consensus Problem via Various Regularizations of the Fastest Mixing Markov-Chain ProblemIn the consensus problem on multi-agent systems, in which the states of the agents represent opinions, the agents aim at reaching a common opinion (or consensus state) through local exchange of information. An important design problem is to choose the degree of interconnection of the subsystems to achieve a good trade-off between a small number of interconnections and a fast convergence to the consensus state, which is the average of the initial opinions under mild conditions. This paper addresses this problem through l₁ -norm and l₀ -“pseudo-norm” regularized versions of the well-known Fastest Mixing Markov-Chain (FMMC) problem. We show that such versions can be interpreted as robust forms of the FMMC problem and provide results to guide the choice of the regularization parameter.Giorgio Gneccogiorgio.gnecco@imtlucca.itRita Morisirita.morisi@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2015-10-08T07:52:15Z2016-04-06T08:05:07Zhttp://eprints.imtlucca.it/id/eprint/2759This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/27592015-10-08T07:52:15ZThe self-organization of meaning and the reflexive communication of informationFollowing a suggestion of Warren Weaver, we extend the Shannon model of communication piecemeal into a complex systems model in which communication is differentiated both vertically and horizontally. This model enables us to bridge the divide between Niklas Luhmann’s theory of the self-organization of meaning in communications and empirical research using information theory. First, we distinguish between communication relations and correlations between patterns of relations. The correlations span a vector space in which relations are positioned and thus provided with meaning. Second, positions provide reflexive perspectives. Whereas the different meanings are integrated locally, each instantiation opens horizons of meaning that can be codified along eigenvectors of the communication matrix. The next-order specification of codified meaning can generate redundancies (as feedback on the forward arrow of entropy production). The horizontal differentiation among the codes of communication enables us to quantify the creation of new options as mutual redundancy. Increases in redundancy can then be measured as local reduction of prevailing uncertainty (in bits). The generation of options can also be considered as a hallmark of the knowledge-based economy: new knowledge provides new options. Both the communication-theoretical and the operational (information-theoretical) perspectives.Loet LeydesdorffInga IvanovaAlexander M. Petersenalexander.petersen@imtlucca.it2015-07-08T09:45:55Z2015-07-08T09:45:55Zhttp://eprints.imtlucca.it/id/eprint/2726This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/27262015-07-08T09:45:55ZSingle and cross-generation natural hedging of longevity and financial riskThe paper provides natural hedging strategies among death benefits and annuities written on a single and on different generations. It obtains closed-form Delta and Gamma hedges, in the presence of both longevity and interest rate risk. We present an application to UK data on survivorship and bond dynamics. We first compare longevity and financial risk exposures: Deltas and Gammas for longevity risk are greater in absolute value than the corresponding sensitivities for interest rate risk. We then calculate the optimal hedges, both within and across generations. Our results apply to both asset and asset-liability management.Elisa LucianoLuca Regisluca.regis@imtlucca.itElena Vigna2015-06-15T09:27:55Z2015-06-15T09:27:55Zhttp://eprints.imtlucca.it/id/eprint/2707This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/27072015-06-15T09:27:55ZA uniform definition of stochastic process calculiWe introduce a unifying framework to provide the semantics of process algebras, including their quantitative variants useful for modeling quantitative aspects of behaviors. The unifying framework is then used to describe some of the most representative stochastic process algebras. This provides a general and clear support for an understanding of their similarities and differences. The framework is based on State to Function Labeled Transition Systems, FuTSs for short, that are state transition structures where each transition is a triple of the form (s,α,Rocco De Nicolar.denicola@imtlucca.itDiego LatellaMichele LoretiMieke Massink2015-05-19T09:35:54Z2015-10-28T14:47:41Zhttp://eprints.imtlucca.it/id/eprint/2681This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/26812015-05-19T09:35:54ZModel Predictive Control for Linear Impulsive Systems Linear impulsive control systems have been extensively studied with respect to their equilibrium points which, in most cases, are no other than the origin. However, the trajectory of an impulsive system cannot be stabilized to arbitrary desired points hindering their utilization in a great many applications. In this paper, we study the equilibrium of linear impulsive systems with respect to target-sets. We properly extend the notion of invariance and design stabilizing model predictive controllers (MPC). Finally, we apply the proposed methodology to control the intravenous bolus administration of Lithium.Pantelis Sopasakispantelis.sopasakis@imtlucca.itPanagiotis Patrinospanagiotis.patrinos@imtlucca.itHaralambos SarimveisAlberto Bemporadalberto.bemporad@imtlucca.it2015-05-18T14:51:11Z2015-05-18T14:51:11Zhttp://eprints.imtlucca.it/id/eprint/2679This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/26792015-05-18T14:51:11ZDecentralised hierarchical multi-rate control of large-scale drinking water networksAjay Kumar SampathiraoPantelis Sopasakispantelis.sopasakis@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2015-05-12T10:26:46Z2017-01-26T14:22:08Zhttp://eprints.imtlucca.it/id/eprint/2674This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/26742015-05-12T10:26:46ZA Hybrid Model Predictive Control Approach to Attitude Control with Minimum-Impulse-Bit ThrustersThis paper studies an important aspect of attitude control for a launcher's upper stage: the minimum impulse bit (MIB), that is, the minimum torque that can be exerted by the thrusters. We model this effect using principles of hybrid systems theory and we design a hybrid model predictive control scheme for the attitude control of a launcher during its long coasting period, aiming at minimizing the number of thrusters' actuations. We apply the proposed methodology to a nonlinear model of a typical upper stage with multi-payload capability. Pantelis Sopasakispantelis.sopasakis@imtlucca.itDaniele Bernardinidaniele.bernardini@imtlucca.itHans StrauchSamir BennaniAlberto Bemporadalberto.bemporad@imtlucca.it2015-05-12T10:23:59Z2015-05-12T10:23:59Zhttp://eprints.imtlucca.it/id/eprint/2673This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/26732015-05-12T10:23:59ZSloshing-aware attitude control of impulsively actuated spacecraftUpper stages of launchers sometimes drift, with the main engine switched-off, for a longer period of time until re-ignition and subsequent payload release. During this period a large amount of propellant is still in the tank and the motion of the fluid (sloshing) has an impact on the attitude of the stage. For the flight phase the classical spring/damper or pendulum models cannot be applied. A more elaborate sloshing-aware model is described in the paper involving a time-varying inertia tensor.
Using principles of hybrid systems theory we model the minimum impulse bit (MIB) effect, that is, the minimum torque that can be exerted by the thrusters. We design a hybrid model predictive control scheme for the attitude control of a launcher during its long coasting period, aiming at minimising the actuation count of the thrusters.Pantelis Sopasakispantelis.sopasakis@imtlucca.itDaniele Bernardinidaniele.bernardini@imtlucca.itHans StrauchSamir BennaniAlberto Bemporadalberto.bemporad@imtlucca.it2015-03-23T14:18:55Z2015-03-23T14:20:30Zhttp://eprints.imtlucca.it/id/eprint/2635This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/26352015-03-23T14:18:55ZStatic versus dynamic longevity risk hedgingThis paper provides the static, swap-based hedge for an annuity, and
compares it with the dynamic, delta-based hedge, achieved using longevity
bonds. We assume that the longevity intensity is distributed according to
a CIR-type process and provide closed-form derivatives prices and hedges,
also in presence of an analogous CIR process for interest rate risk. Our
calibration to 65-year old UK males shows that – once interest rate risk
is perfectly hedged – the average hedging error of the dynamic hedge
is moderate, and both its variance and the thickness of the tails of its
distribution are decreasing with the rebalancing frequency. The spread
over the basic "swap rate" which makes 99.5% quantile of the distribution
of the dynamic hedging error equal to the cost of the static hedge lies
between 0.01 and 0.04%.Clemente De RosaElisa LucianoLuca Regisluca.regis@imtlucca.it2015-02-23T08:34:38Z2015-02-23T08:34:38Zhttp://eprints.imtlucca.it/id/eprint/2612This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/26122015-02-23T08:34:38ZCentral Limit Theorems for an Indian Buffet Model with Random WeightsThe three-parameter Indian buffet process is generalized. The possibly different role played by customers is taken into account by suitable (random) weights. Various limit theorems are also proved for such generalized Indian buffet process. Let L_n be the number of dishes experimented by the first n customers, and let
{\bar K}_n=(1/n)\sum_{i=1}^n K_i
where K_i is the number of dishes tried by customer i. The asymptotic distributions of L_n and {\bar K}_n, suitably
centered and scaled, are obtained. The convergence turns out to be stable (and not only in distribution). As a particular case, the results apply to the standard (i.e., non generalized) Indian buffet process.Patrizia BertiIrene Crimaldiirene.crimaldi@imtlucca.itLuca PratelliPietro Rigo2014-12-16T10:32:30Z2016-04-06T08:06:17Zhttp://eprints.imtlucca.it/id/eprint/2395This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/23952014-12-16T10:32:30ZAssessing the solvency of insurance portfolios via a continuous-time cohort modelThis paper evaluates the solvency of a portfolio of assets and liabilities of an insurer subject to both longevity and financial risks. Liabilities are evaluated at fair-value and, as a consequence, interest-rate risk can affect both the assets and the liabilities. Longevity risk is described via a continuous-time cohort model. We evaluate the effects of natural hedging strategies on the risk profile of an insurance portfolio in run-off. Numerical simulations, calibrated to UK historical data, show that systematic longevity risk is of particular importance and needs to be hedged. Natural hedging can improve the solvency of the insurer, if interest-rate risk is appropriately managed. We stress that asset allocation choices should not be independent of the composition of the liability portfolio of the insurer.Petar JevtićLuca Regisluca.regis@imtlucca.it2014-12-03T11:12:58Z2014-12-18T13:55:51Zhttp://eprints.imtlucca.it/id/eprint/2387This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/23872014-12-03T11:12:58ZConsistent community identification in complex networksWe have found that known community identification algorithmsproduce inconsistent communities when the node ordering changes atinput. We propose two metrics to quantify the level of consistencyacross multiple runs of an algorithm: pairwise membershipprobability and consistency. Based on these two metrics, weaddress the consistency problem without compromising themodularity. Our solution uses pairwise membership probabilitiesas link weights and generates consistent communities within six orfewer cycles. It offers a new tool in the study of communitystructures and their evolutions.Haewoon KwakSue MoonYoung-Ho Eomyoungho.eom@imtlucca.itYoonchan ChoiHawoong Jeong2014-10-14T09:21:06Z2014-10-27T10:33:58Zhttp://eprints.imtlucca.it/id/eprint/2324This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/23242014-10-14T09:21:06ZCluster analysis of weighted bipartite networks: a new copula-based approachIn this work we are interested in identifying clusters of “positional equivalent” actors, i.e. actors who play a similar role in a system. In particular, we analyze weighted bipartite networks that describes the relationships between actors on one side and features or traits on the other, together with the intensity level to which actors show their features. We develop a methodological approach that takes into account the underlying multivariate dependence among groups of actors. The idea is that positions in a network could be defined on the basis of the similar intensity levels that the actors exhibit in expressing some features, instead of just considering relationships that actors hold with each others. Moreover, we propose a new clustering procedure that exploits the potentiality of copula functions, a mathematical instrument for the modelization of the stochastic dependence structure. Our clustering algorithm can be applied both to binary and real-valued matrices. We validate it with simulations and applications to real-world data.Alessandro Chessaalessandro.chessa@imtlucca.itIrene Crimaldiirene.crimaldi@imtlucca.itMassimo Riccabonimassimo.riccaboni@imtlucca.itLuca Trapinluca.trapin@imtlucca.it2014-07-02T10:54:06Z2014-07-02T10:54:06Zhttp://eprints.imtlucca.it/id/eprint/2231This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/22312014-07-02T10:54:06ZOn the Predictability of Future Impact in ScienceCorrectly assessing a scientist’s past research impact and potential for future impact is key in recruitment decisions and other evaluation processes. While a candidate’s future impact is the main concern for these decisions, most measures only quantify the impact of previous work. Recently, it has been argued that linear regression models are capable of predicting a scientist’s future impact. By applying that future impact model to 762 careers drawn from three disciplines: physics, biology, and mathematics, we identify a number of subtle, but critical, flaws in current models. Specifically, cumulative non-decreasing measures like the h-index contain intrinsic autocorrelation, resulting in significant overestimation of their ‘‘predictive power’’. Moreover, the predictive power of these models depend heavily upon scientists’ career age, producing least accurate estimates for young researchers. Our results place in doubt the suitability of such models, and indicate further investigation is required before they can be used in recruiting decisions.Orion Pennerorion.penner@imtlucca.itRaj K. PanAlexander M. Petersenalexander.petersen@imtlucca.itKimmo KaskiSanto Fortunato2014-04-10T12:19:02Z2014-10-27T10:46:30Zhttp://eprints.imtlucca.it/id/eprint/2189This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/21892014-04-10T12:19:02ZCluster analysis of weighted bipartite networks: a new copula-based approachIn this work we are interested in identifying clusters of "positional equivalent" actors, i.e. actors who play a similar role in a system. In particular, we analyze weighted bipartite networks that describes the relationships between actors on one side and features or traits on the other, together with the intensity level to which actors show their features. The main contribution of our work is twofold. First, we develop a methodological approach that takes into account the underlying multivariate dependence among groups of actors. The idea is that positions in a network could be defined on the basis of the similar intensity levels that the actors exhibit in expressing some features, instead of just considering relationships that actors hold with each others. Second, we propose a new clustering procedure that exploits the potentiality of copula functions, a mathematical instrument for the modelization of the stochastic dependence structure. Our clustering algorithm can be applied both to binary and real-valued matrices. We validate it with simulations and applications to real-world data. Alessandro Chessaalessandro.chessa@imtlucca.itIrene Crimaldiirene.crimaldi@imtlucca.itMassimo Riccabonimassimo.riccaboni@imtlucca.itLuca Trapinluca.trapin@imtlucca.it2014-01-20T10:23:48Z2014-01-20T10:23:48Zhttp://eprints.imtlucca.it/id/eprint/2097This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20972014-01-20T10:23:48ZDealing with Interaction for Complex Systems Modelling and PredictionThe increasing complexity of problems in the context of system modeling is leading to a new epistemological approach able to provide a representation which allows from one hand, to model complex phenomena with the support of mathematical and computational instruments, and on the other hand able to capture the global system description. In this article is presented a methodology for complex dynamical systems modeling which is an extension of the supervised learning paradigm. The theoretical aspects of our methodology are introduced and then two different and heterogeneous case studies are presented.Walter Quattrociocchiwalter.quattrociocchi@imtlucca.itDaniela LatorreElena LodiMirco Nanni2013-12-23T08:31:58Z2013-12-23T08:31:58Zhttp://eprints.imtlucca.it/id/eprint/2084This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20842013-12-23T08:31:58ZA generalized telegraph process with velocity driven by random trialsWe consider a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions. At each epoch of the underlying counting process the new velocity is determined by the outcome of a random trial. Two schemes are taken into account: Bernoulli trials and classical Pòlya urn trials. We investigate the probability law of the process and the mean of the velocity of the moving particle. We finally discuss two cases of interest: (i) the case of Bernoulli trials and intertimes having exponential distributions with linear rates (in which, interestingly, the process exhibits a logistic stationary density with non-zero mean), and (ii) the case of Pòlya trials and intertimes having first Gamma and then exponential distributions with constant rates. Irene Crimaldiirene.crimaldi@imtlucca.itAntonio Di CrescenzoAntonella IulianoBarbara Martinucci2013-12-17T15:29:35Z2014-01-28T15:24:51Zhttp://eprints.imtlucca.it/id/eprint/2075This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20752013-12-17T15:29:35ZEfficient versus inefficient hedging strategies in the presence of financial and longevity (value at) riskThis paper provides a closed-form Value-at-Risk (VaR) for the net exposure of an annuity provider, taking into account both mortality and interest-rate risk, on both assets and liabilities. It builds a classical risk-return frontier and shows that hedging strategies–such as the transfer of longevity risk–may increase the overall risk while decreasing expected returns, thus resulting in inefficient outcomes. Once calibrated to the 2010 UK longevity and bond market, the model gives conditions under which hedging policies become inefficient.
Elisa LucianoLuca Regisluca.regis@imtlucca.it2013-11-08T10:45:37Z2014-07-07T10:29:45Zhttp://eprints.imtlucca.it/id/eprint/1896This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/18962013-11-08T10:45:37ZSapRete: saperi in rete per il recupero delle competenze logico matematiche e scientifiche
Susanna SetzuAlessandro Chessaalessandro.chessa@imtlucca.itMichelangelo Puligamichelangelo.puliga@imtlucca.itMaria PoloMaria Cristina Mereu2013-10-25T08:56:20Z2014-06-12T10:09:34Zhttp://eprints.imtlucca.it/id/eprint/1844This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/18442013-10-25T08:56:20ZConstrained Model Predictive Control Based on Reduced-Order ModelsThe need for reduced-order approximations of dynamical systems emerges naturally in model-based control of very large-scale systems, such as those arising from the discretisation of partial differential equation models. The controller based on the reduced-order model, when in closed-loop with the large-scale system, ought to endow certain properties, in primis stability, but also satisfaction of state constraints and recursive computability of the control law in the case of constrained control. In this paper we introduce a new approach to the design of model predictive controllers to meet the aforementioned requirements while the on-line complexity is essentially tantamount to the one that corresponds to the low-dimensional approximate model.Pantelis Sopasakispantelis.sopasakis@imtlucca.itDaniele Bernardinidaniele.bernardini@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2013-10-25T08:30:43Z2014-06-16T10:17:42Zhttp://eprints.imtlucca.it/id/eprint/1841This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/18412013-10-25T08:30:43ZMPC for Sampled-Data Linear Systems: guaranteeing continuous-time positive invarianceModel Predictive Controllers (MPC) designed for sampled-data systems can be shown to violate the constraints in continuous time. A reformulation of the initial problem will guarantee constraint satisfaction throughout the intersample period. Polytopic inclusions of the continuous trajectory are used in this paper to establish additional constraints leading to a linearly constrained quadratic optimization problem. Continuous time asymptotic stability and continuous-time positive invariance are proven for the reformulated problem.Pantelis Sopasakispantelis.sopasakis@imtlucca.itPanagiotis Patrinospanagiotis.patrinos@imtlucca.itHaralambos Sarimveis2013-10-04T10:20:55Z2013-10-04T10:20:55Zhttp://eprints.imtlucca.it/id/eprint/1824This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/18242013-10-04T10:20:55ZAsymmetric network connectivity using weighted harmonic averagesWe propose a non-metric measure of the "closeness" felt between two nodes in an undirected, weighted graph using a simple weighted harmonic average of connectivity, that is a real-valued Generalized Erdös Number (GEN). While our measure is developed with a collaborative network in mind, the approach can be of use in a variety of artificial and real-world networks. We are able to distinguish between network topologies that standard distance metrics view as identical, and use our measure to study some simple analytically tractable networks. We show how this might be used to look at asymmetry in authorship networks such as those that inspired the integer Erdös numbers in mathematical coauthorships. We also show the utility of our approach to devise a ratings scheme that we apply to the data from the NetFlix prize, and find a significant improvement using our method over a baseline.Greg Morrisongreg.morrison@imtlucca.itL. Mahadevan2013-09-02T09:32:09Z2013-09-02T09:32:09Zhttp://eprints.imtlucca.it/id/eprint/1656This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/16562013-09-02T09:32:09ZLean thinking in radiologia: allineare i servizi fuori linea al percorso di cura del paziente in Pronto Soccorso per ridurre i tempi di attraversamentoDario RicciSimone MagazziniAlberto CoppiAlessandro BoganiFrancesco BellomoAlessandro SergiGabriella Dellinogabriella.dellino@imtlucca.it2013-06-27T10:52:34Z2016-03-18T10:39:55Zhttp://eprints.imtlucca.it/id/eprint/1624This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/16242013-06-27T10:52:34ZA decomposition approach for the combined master surgical schedule and surgical case assignment problemsThis research aims at supporting hospital management in making prompt Operating Room (OR) planning decisions, when either unpredicted events occur or alternative scenarios or configurations need to be rapidly evaluated. We design and test a planning tool enabling managers to efficiently analyse several alternatives to the current OR planning and scheduling. To this aim, we propose a decomposition approach. More specifically, we first focus on determining the Master Surgical Schedule (MSS) on a weekly basis, by assigning the different surgical disciplines to the available sessions. Next, we allocate surgeries to each session, focusing on elective patients only. Patients are selected from the waiting lists according to several parameters, including surgery duration, waiting time and priority class of the operations. We performed computational experiments to compare the performance of our decomposition approach with an (exact) integrated approach. The case study selected for our simulations is based on the characteristics of the operating theatre (OT) of a medium-size public Italian hospital. Scalability of the method is tested for different OT sizes. A pilot example is also proposed to highlight the usefulness of our approach for decision support. The proposed decomposition approach finds satisfactory solutions with significant savings in computation time.Alessandro AgnetisAlberto CoppiMatteo CorsiniGabriella Dellinogabriella.dellino@imtlucca.itCarlo MeloniMarco Pranzo2013-06-21T11:23:24Z2014-01-29T14:34:19Zhttp://eprints.imtlucca.it/id/eprint/1622This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/16222013-06-21T11:23:24ZAn Anscombe-type theoremLet (X_n) be a sequence of random variables (with values in a
separable metric space) and (N_n) a sequence of random indices. Conditions for X_{N_n} to converge stably (in particular, in distribution) are provided. Some examples, where such conditions work but those already existing fail, are given as well.Patrizia BertiIrene Crimaldiirene.crimaldi@imtlucca.itLuca PratelliPietro Rigo2013-05-14T08:41:54Z2016-10-04T15:31:34Zhttp://eprints.imtlucca.it/id/eprint/1580This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/15802013-05-14T08:41:54ZAnalysis of a Hurst parameter estimator based on the modified Allan variance In order to estimate the Hurst parameter of Internet
traffic data, it has been recently proposed a log-regression estimator based on the so-called modified Allan variance (MAVAR). Simulations have shown that this estimator achieves higher accuracy and better confidence when compared with an other method of common use based on wavelet analysis. Here we link it to the wavelets setting and stress why a different analysis for the two approaches is required. We then focus on the asymptotic analysis of the MAVAR log-regression estimator and provide new formulas for the related confidence intervals. By numerical evaluation, we analyze these formulas and make a comparison
between three suitable choices on the regression weights, also optimizing over different choices on the data progression.Alessandra BianchiStefano BregniIrene Crimaldiirene.crimaldi@imtlucca.itMarco Ferrari2013-04-29T10:06:00Z2016-04-07T09:55:54Zhttp://eprints.imtlucca.it/id/eprint/1554This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/15542013-04-29T10:06:00ZEconomic complexity: Conceptual grounding of a new metrics for global competitivenessThe availability of data corresponding to the products exported by all countries provides an excellent dataset to test economic ideas and extract new information about the process of economic development. The matrix of countries and exported products shows a marked triangular structure instead of the block-diagonal structure expected from Ricardian arguments of specialization. This observation points to the fact that diversification is instead the dominant effect in the globalized market. We discuss how to define a suitable non-monetary metrics for the value of diversification and the effective complexity of products. We discuss in detail the previous proposed approaches to assess this challenge and their limitations. We introduce a new approach to the definition of these metrics which seems to overcome the previous problems and we test it in a series of model systems.Andrea TacchellaMatthieu CristelliGuido Caldarelliguido.caldarelli@imtlucca.itAndrea GabrielliLuciano Pietronero2013-04-15T13:48:49Z2016-04-07T09:38:58Zhttp://eprints.imtlucca.it/id/eprint/1543This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/15432013-04-15T13:48:49ZEvolution of controllability in interbank networksThe Statistical Physics of Complex Networks has recently provided new theoretical tools for policy makers. Here we extend the notion of network controllability to detect the financial institutions, i.e. the drivers, that are most crucial to the functioning of an interbank market. The system we investigate is a paradigmatic case study for complex networks since it undergoes dramatic structural changes over time and links among nodes can be observed at several time scales. We find a scale-free decay of the fraction of drivers with increasing time resolution, implying that policies have to be adjusted to the time scales in order to be effective. Moreover, drivers are often not the most highly connected “hub” institutions, nor the largest lenders, contrary to the results of other studies. Our findings contribute quantitative indicators which can support regulators in developing more effective supervision and intervention policies.Danilo DelpiniStefano BattistonMassimo Riccabonimassimo.riccaboni@imtlucca.itGiampaolo GabbiFabio Pammollif.pammolli@imtlucca.itGuido Caldarelliguido.caldarelli@imtlucca.it2013-03-04T08:37:55Z2016-04-07T09:57:58Zhttp://eprints.imtlucca.it/id/eprint/1495This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14952013-03-04T08:37:55ZWeighted Networks as Randomly Reinforced Urn ProcessesWe analyze weighted networks as randomly reinforced urn processes, in which the edge-total weights are determined by a reinforcement mechanism. We develop a new statistical test and a new procedure, based on it, to study the evolution of networks over time, detecting the “dominance”
of some edges with respect to the others and then assessing if a given instance of the network is taken at its steady state or not. Distance from the steady state can be considered as a measure of the relevance of the observed properties of the network. Our results are quite general, in the sense that they are not based on a particular probability distribution or functional form of the
random weights. Moreover, the proposed tool can be applied also to dense networks, which have received little attention by network community so far since they are often problematic. We apply our procedure in the context of the International Trade Network, determining a core of “dominant
edges”.Guido Caldarelliguido.caldarelli@imtlucca.itAlessandro Chessaalessandro.chessa@imtlucca.itIrene Crimaldiirene.crimaldi@imtlucca.itFabio Pammollif.pammolli@imtlucca.it2012-12-14T08:37:47Z2014-01-24T14:13:11Zhttp://eprints.imtlucca.it/id/eprint/1446This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14462012-12-14T08:37:47ZMetamodel variability in robust simulation-optimization: a bootstrap analysisMetamodels are often used in simulation-optimization for the design and management of complex systems enabling the integration of discipline-dependent analysis into the
overall decision process. These metamodels yield insight into the relationship between responses and decision variables, providing fast analysis tools in place of the more expensive computer simulations. The combined use of stochastic simulation experiments and metamodels introduces a source of uncertainty in the decision process that we refer to as metamodel variability. To quantify this variability, we combine validation and bootstrapping techniques. The rationale behind the method relies on the fact that, after the validation process, the relative validation errors are small indicating that the metamodels give an adequate approximation, and bootstrapping these errors allows to quantify the metamodels' variability in an acceptable way. The method has the advantage to be general and can be used with different kind of metamodels and validation techniques. The resulting methodology is illustrated through some examples using regression and Kriging metamodels.Gabriella Dellinogabriella.dellino@imtlucca.itCarlo Meloni2012-12-14T08:37:25Z2012-12-14T08:37:25Zhttp://eprints.imtlucca.it/id/eprint/1447This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14472012-12-14T08:37:25ZOperations management e sanità: un sistema di supporto alle decisioni per la programmazione della chirurgia elettivaThe operating theater is the most critical resource of the surgical process. From a lean perspective, the planning of surgical activities must maintain an alignment between demand and offer. Therefore, it is necessary to find the right trade-off between the need of keeping organizational complexity low, and the need to give appropriate precedence to surgeries in view of their priority class and waiting times. In this paper we introduce decisional models to determine the Master Surgical Schedule (MSS) and the detailed surgical case assignment. Experimental results carried out on the operating theater of San Giuseppe hospital in Empoli (Italy) show that the introduction of even small amounts of flexibility in the MSS allows to improve operating room usage and quality of service.Alessandro AgnetisAlberto CoppiMatteo CorsiniGabriella Dellinogabriella.dellino@imtlucca.itCarlo MeloniMarco Pranzo2012-12-14T08:26:02Z2014-01-29T13:54:33Zhttp://eprints.imtlucca.it/id/eprint/1444This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14442012-12-14T08:26:02ZMetamodel variability analysis combining bootstrapping and validation techniquesResearch on metamodel-based optimization has received considerably increasing interest in recent years, and has found successful applications in solving computationally expensive problems. The joint use of computer simulation experiments and metamodels introduces a source of uncertainty that we refer to as metamodel variability. To analyze and quantify this variability, we apply bootstrapping to residuals derived as prediction errors computed from cross-validation. The proposed method can be used with different types of metamodels, especially when limited knowledge on parameters’ distribution is available or when a limited computational budget is allowed. Our preliminary experiments based on the robust version of
the EOQ model show encouraging results.Gabriella Dellinogabriella.dellino@imtlucca.itCarlo Meloni2012-11-30T08:34:15Z2012-11-30T08:34:15Zhttp://eprints.imtlucca.it/id/eprint/1441This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14412012-11-30T08:34:15ZSimulation-optimization under uncertainty through metamodeling and bootstrappingMost methods in simulation-optimization assume known environments, whereas this research accounts for uncertain environments combining Taguchi's world view with either regression or Kriging (Gaussian Process) metamodels (response surfaces). These metamodels are combined with Non-Linear Mathematical Programming (NLMP) to find a robust optimal solution. Varying the constraint values in the NLMP model gives an estimated Pareto frontier. To account for the variability of the estimated Pareto frontier, this research uses bootstrapping which gives confidence regions for the robust optimal solution. This methodology is illustrated through the Economic Order Quantity (EOQ) inventory-management model, accounting for the uncertainties in the demand rate and the cost coefficients.Gabriella Dellinogabriella.dellino@imtlucca.itJack P.C. KleijnenCarlo Meloni2012-11-30T08:27:56Z2012-11-30T08:27:56Zhttp://eprints.imtlucca.it/id/eprint/1439This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14392012-11-30T08:27:56ZSimulation-Optimization in Modeling Ionic Polymer-Metal Composites ActuatorsThe increasing pressure on the development time of new materials and devices has changed the modelling and design process over the years. In the past, they mainly consisted of experimentation and physical prototyping. Clearly, it is hard to incorporate changes in finished prototypes, while producing a variety of different prototypes at once may be very expensive. To this aim, computer simulation models such as circuit design models and continuous system simulation models are widely used in engineering modelling, design and analysis. The studies towards a better understanding of complex systems require quantitative model development, making optimisation and experimental data fitting tools indispensable. In this framework, the modelling of ionic polymer-metal composites (IPMCs) is studied. In particular, this paper deals with simulation-optimisation issues arising in the model calibration of a particular IPMC-based actuator in air. We consider a non-linear dynamical model of the device, with lumped parameters, able to estimate the IPMC actuator absorbed current, together with the mechanical quantities of interest, which, in the case under study, are the free deflection and/or the blocked force. Two optimisation problems have been formulated, focusing on different stages of the model parameters identification. The strategies adopted to solve the problems allow to achieve some promising - although preliminary - results.Gabriella Dellinogabriella.dellino@imtlucca.itPaolo LinoCarlo MeloniAlessandro RizzoClaudia BonomoLuigi FortunaPietro GiannoneSalvatore Graziani2012-11-30T08:25:08Z2012-11-30T08:25:08Zhttp://eprints.imtlucca.it/id/eprint/1438This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14382012-11-30T08:25:08ZDynamic Objectives Aggregation Methods for Evolutionary Portfolio Optimization. A computational studyThis paper proposes a study of different dynamic objectives aggregation methods (DOAMs) in the context of a multi-objective evolutionary approach to portfolio optimisation. Since the incorporation of chaotic rules or behaviour in population-based optimisation algorithms has been shown to possibly enhance their searching ability, this study considers and evaluates also some chaotic rules in the dynamic weights generation process. The ability of the DOAMs to solve the portfolio rebalancing problem is investigated conducting a computational study on a set of instances based on real data. The portfolio model considers a set of realistic constraints and entails the simultaneous optimisation of the risk on portfolio, the expected return and the transaction cost.Gabriella Dellinogabriella.dellino@imtlucca.itMariagrazia FedeleCarlo Meloni2012-11-30T08:16:21Z2012-11-30T08:16:21Zhttp://eprints.imtlucca.it/id/eprint/1442This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14422012-11-30T08:16:21ZAn efficient decomposition approach for surgical planningThis talk presents an efficient decomposition approach to surgical planning. Given a set of surgical waiting lists (one for each discipline) and an operating theater, the problem is to decide the room-to-discipline assignment for the next planning period (Master Surgical Schedule), and the surgical cases to be performed (Surgical Case Assignment), with the objective of optimizing a score related to priority and current waiting time of the cases. While in general MSS and SCA may be concurrently found by solving a complex integer programming problem, we propose an effective decomposition algorithm which does not require expensive or sophisticated computational resources, and is therefore suitable for implementation in any real-life setting.
Our decomposition approach consists in first producing a number of subsets of surgical cases for each discipline (potential OR sessions), and select a subset of them. The surgical cases in the selected potential sessions are then discarded, and only the structure of the MSS is retained. A detailed surgical case assignment is then devised filling the MSS obtained with cases from the waiting lists, via an exact optimization model.
The quality of the plan obtained is assessed by comparing it with the plan obtained by solving the exact integrated formulation for MSS and SCA. Nine different scenarios are considered, for various operating theater sizes and management policies. The results on instances concerning a medium-size hospital show that the decomposition method produces comparable solutions with the exact method in much smaller computation time.Alessandro AgnetisAlberto CoppiMatteo CorsiniGabriella Dellinogabriella.dellino@imtlucca.itCarlo MeloniMarco Pranzo2012-11-29T16:39:01Z2012-11-29T16:39:01Zhttp://eprints.imtlucca.it/id/eprint/1436This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14362012-11-29T16:39:01ZRobust optimization in simulation: Taguchi and Krige combinedOptimization of simulated systems is the goal of many methods, but most methods assume known environments. We, however, develop a "robust" methodology that accounts for uncertain environments. Our methodology uses Taguchi's view of the uncertain world but replaces his statistical techniques by design and analysis of simulation experiments based on Kriging (Gaussian process model); moreover, we use bootstrapping to quantify the variability in the estimated Kriging metamodels. In addition, we combine Kriging with nonlinear programming, and we estimate the Pareto frontier. We illustrate the resulting methodology through economic order quantity (EOQ) inventory models. Our results suggest that robust optimization requires order quantities that differ from the classic EOQ. We also compare our results with results we previously obtained using response surface methodology instead of Kriging. Gabriella Dellinogabriella.dellino@imtlucca.itJack P.C. KleijnenCarlo Meloni2012-11-28T13:24:24Z2012-11-29T13:17:37Zhttp://eprints.imtlucca.it/id/eprint/1434This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14342012-11-28T13:24:24ZAsymptotic Normality of a Hurst Parameter Estimator Based on the Modified Allan VarianceIn order to estimate the memory parameter of Internet traffic data, it has been recently proposed a log-regression estimator based on the so-called modified Allan variance (MAVAR). Simulations have shown that this estimator achieves higher accuracy and better confidence when compared with other methods. In this paper we present a rigorous study of the MAVAR log-regression estimator. In particular, under the assumption that the signal process is a fractional Brownian motion, we prove that it is consistent and asymptotically normally distributed. Finally, we discuss its connection with the wavelets estimators.Alessandra BianchiMassimo CampaninoIrene Crimaldiirene.crimaldi@imtlucca.it2012-11-27T13:59:45Z2014-01-29T14:40:13Zhttp://eprints.imtlucca.it/id/eprint/1433This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14332012-11-27T13:59:45ZReversing conditional orderingsWe analyze some specific aspects concerning conditional orderings and relations among them. To this purpose we define a suitable concept of reversed conditional ordering and prove some related results. In particular we aim to compare the univariate stochastic orderings ≤ st, ≤ hr, and ≤ lr in terms of differences among different notions of conditional orderings. Some applications of our result to the analysis of positive dependence will be detailed. We concentrate attention to the case of a pair of scalar random variables X, Y . Suitable extensions to multivariate cases are possible.Rachele Foschirachele.foschi@imtlucca.itFabio Spizzichino2012-11-27T13:55:26Z2012-11-27T13:59:25Zhttp://eprints.imtlucca.it/id/eprint/1432This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14322012-11-27T13:55:26ZInterval bounds for the optimal burn-in times for concave or convex reward functionsAn interesting problem in reliability is to determine the optimal burn-in time.
In a previous work, the authors studied the solution of such a problem under a particular cost structure.
It has been shown there that a key role in the problem is played by a function $\rho$, representing the reward coming from the use of a component in the field. A relevant case in this investigation is the one when $\rho$ is linear.
In this paper, we explore further the linear case and use its solutions as a benchmark for determining the locally optimal times when the function $\rho$ is not linear or
under a different cost structure.
Rachele Foschirachele.foschi@imtlucca.it2012-11-27T13:44:26Z2014-01-29T14:36:24Zhttp://eprints.imtlucca.it/id/eprint/1431This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14312012-11-27T13:44:26ZHyper-dependence, hyper-ageing properties and analogies between them: a semigroup-based approachIn previous papers, evolution of dependence and ageing, for vectors of non-negative random variables, have been separately considered. Some analogies between the two evolutions emerge however in those studies. In the present paper, we propose a unified approach, based on semigroup arguments, explaining the origin of such analogies and relations among properties of stochastic dependence and ageing.
Rachele Foschirachele.foschi@imtlucca.it2012-10-24T09:30:20Z2012-11-13T14:35:48Zhttp://eprints.imtlucca.it/id/eprint/1425This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14252012-10-24T09:30:20ZLong term evaluation of operating theater planning policiesThis paper addresses Operating Room (OR) planning policies in elective surgery. In particular, we investigate long-term policies for determining the Master Surgical Schedule (MSS) throughout the year, analyzing the tradeoff between organizational simplicity, favored by an MSS that does not change completely every week, and quality of the service offered to the patients, favored by an MSS that dynamically adapts to the current state of waiting lists, the latter objective being related to a lean approach to hospital management. Surgical cases are selected from the waiting lists according to several parameters, including surgery duration, waiting time and priority class of the operations. We apply the proposed models to the operating theater of a public, medium-size hospital in Empoli, Italy, using Integer Linear Programming formulations, and analyze the scalability of the approach on larger hospitals. The simulations point out that introducing a very limited degree of variability in MSS in terms of OR sessions assignment can largely pay off in terms of resource efficiency and due date performance.Alessandro AgnetisAlberto CoppiMatteo CorsiniGabriella Dellinogabriella.dellino@imtlucca.itCarlo MeloniMarco Pranzo2012-10-22T07:27:04Z2016-04-07T09:28:16Zhttp://eprints.imtlucca.it/id/eprint/1422This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14222012-10-22T07:27:04ZA Network Analysis of Countries’ Export Flows: Firm Grounds for the Building Blocks of the EconomyIn this paper we analyze the bipartite network of countries and products from UN data on country production. We define the country-country and product-product projected networks and introduce a novel method of filtering information based on elements’ similarity. As a result we find that country clustering reveals unexpected socio-geographic links among the most competing countries. On the same footings the products clustering can be efficiently used for a bottom-up classification of produced goods. Furthermore we mathematically reformulate the “reflections method” introduced by Hidalgo and Hausmann as a fixpoint problem; such formulation highlights some conceptual weaknesses of the approach. To overcome such an issue, we introduce an alternative methodology (based on biased Markov chains) that allows to rank countries in a conceptually consistent way. Our analysis uncovers a strong non-linear interaction between the diversification of a country and the ubiquity of its products, thus suggesting the possible need of moving towards more efficient and direct non-linear fixpoint algorithms to rank countries and products in the global market.</p>Guido Caldarelliguido.caldarelli@imtlucca.itMatthieu CristelliAndrea GabrielliLuciano PietroneroAntonio ScalaAndrea Tacchella2012-09-24T08:26:07Z2012-09-24T08:26:07Zhttp://eprints.imtlucca.it/id/eprint/1369This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/13692012-09-24T08:26:07ZUsing Networks To Understand Medical Data: The Case of Class III Malocclusions<p>A system of elements that interact or regulate each other can be represented by a mathematical object called a network. While network analysis has been successfully applied to high-throughput biological systems, less has been done regarding their application in more applied fields of medicine; here we show an application based on standard medical diagnostic data. We apply network analysis to Class III malocclusion, one of the most difficult to understand and treat orofacial anomaly. We hypothesize that different interactions of the skeletal components can contribute to pathological disequilibrium; in order to test this hypothesis, we apply network analysis to 532 Class III young female patients. The topology of the Class III malocclusion obtained by network analysis shows a strong co-occurrence of abnormal skeletal features. The pattern of these occurrences influences the vertical and horizontal balance of disharmony in skeletal form and position. Patients with more unbalanced orthodontic phenotypes show preponderance of the pathological skeletal nodes and minor relevance of adaptive dentoalveolar equilibrating nodes. Furthermore, by applying Power Graphs analysis we identify some functional modules among orthodontic nodes. These modules correspond to groups of tightly inter-related features and presumably constitute the key regulators of plasticity and the sites of unbalance of the growing dentofacial Class III system. The data of the present study show that, in their most basic abstraction level, the orofacial characteristics can be represented as graphs using nodes to represent orthodontic characteristics, and edges to represent their various types of interactions. The applications of this mathematical model could improve the interpretation of the quantitative, patient-specific information, and help to better targeting therapy. Last but not least, the methodology we have applied in analyzing orthodontic features can be applied easily to other fields of the medical science.</p>Antonio ScalaPietro AuconiMarco ScazzocchioGuido Caldarelliguido.caldarelli@imtlucca.itJames A. McNamaraLorenzo Franchi2012-09-19T10:28:08Z2014-01-29T10:29:12Zhttp://eprints.imtlucca.it/id/eprint/1368This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/13682012-09-19T10:28:08ZEvolution of the Dependence of Residual LifetimesWe investigate the dependence properties of a vector of residual lifetimes by means of the copula associated with the conditional distribution function. In particular, the evolution of positive dependence properties (like quadrant dependence and total positivity) are analyzed and expressions for the evolution of measures of association are given.Fabrizio DuranteRachele Foschirachele.foschi@imtlucca.it2012-08-10T08:02:12Z2012-08-10T08:02:12Zhttp://eprints.imtlucca.it/id/eprint/1332This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/13322012-08-10T08:02:12ZTomas Bjork, A geometric view of the term structure of interest rates, Cattedra Galileiana 2000 (Lecture notes written by Irene Crimaldi)This set of lecture notes is the outcome of a lecture series, given in April 2000 by Prof. Tomas Bjork while holding the "Cattedra Galileiana" at Scuola Normale Superiore in Pisa. The purpose of the lectures was to give an overview of some recent work concerning structural properties of the evolution of the forward rate curve in an arbitrage free bond market.Irene Crimaldiirene.crimaldi@imtlucca.it2012-07-03T12:13:49Z2013-11-21T11:59:27Zhttp://eprints.imtlucca.it/id/eprint/1310This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/13102012-07-03T12:13:49ZNode similarity within subgraphs of protein interaction networksWe propose a biologically motivated quantity, twinness, to evaluate local similarity between nodes in a network. The twinness of a pair of nodes is the number of connected, labeled subgraphs of size n in which the two nodes possess identical neighbours. The graph animal algorithm is used to estimate twinness for each pair of nodes (for subgraph sizes n=4 to n=12) in four different protein interaction networks (PINs). These include an Escherichia coli PIN and three Saccharomyces cerevisiae PINs -- each obtained using state-of-the-art high throughput methods. In almost all cases, the average twinness of node pairs is vastly higher than expected from a null model obtained by switching links. For all n, we observe a difference in the ratio of type A twins (which are unlinked pairs) to type B twins (which are linked pairs) distinguishing the prokaryote E. coli from the eukaryote S. cerevisiae. Interaction similarity is expected due to gene duplication, and whole genome duplication paralogues in S. cerevisiae have been reported to co-cluster into the same complexes. Indeed, we find that these paralogous proteins are over-represented as twins compared to pairs chosen at random. These results indicate that twinness can detect ancestral relationships from currently available PIN data. Orion Pennerorion.penner@imtlucca.itVishal SoodGabriel MussoKim BaskervillePeter GrassbergerMaya Paczuski2012-07-03T12:03:34Z2012-07-03T12:03:34Zhttp://eprints.imtlucca.it/id/eprint/1309This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/13092012-07-03T12:03:34ZSequence alignment, mutual information, and dissimilarity measures for constructing phylogeniesBackground:
Existing sequence alignment algorithms use heuristic scoring schemes based on biological expertise, which cannot be used as objective distance metrics. As a result one relies on crude measures, like the p- or log-det distances, or makes explicit, and often too simplistic, a priori assumptions about sequence evolution. Information theory provides an alternative, in the form of mutual information (MI). MI is, in principle, an objective and model independent similarity measure, but it is not widely used in this context and no algorithm for extracting MI from a given alignment (without assuming an evolutionary model) is known. MI can be estimated without alignments, by concatenating and zipping sequences, but so far this has only produced estimates with uncontrolled errors, despite the fact that the normalized compression distance based on it has shown promising results.
Results:
We describe a simple approach to get robust estimates of MI from global pairwise alignments. Our main result uses algorithmic (Kolmogorov) information theory, but we show that similar results can also be obtained from Shannon theory. For animal mitochondrial DNA our approach uses the alignments made by popular global alignment algorithms to produce MI estimates that are strikingly close to estimates obtained from the alignment free methods mentioned above. We point out that, due to the fact that it is not additive, normalized compression distance is not an optimal metric for phylogenetics but we propose a simple modification that overcomes the issue of additivity. We test several versions of our MI based distance measures on a large number of randomly chosen quartets and demonstrate that they all perform better than traditional measures like the Kimura or log-det (resp. paralinear) distances.
Conclusions:
Several versions of MI based distances outperform conventional distances in distance-based phylogeny. Even a simplified version based on single letter Shannon entropies, which can be easily incorporated in existing software packages, gave superior results throughout the entire animal kingdom. But we see the main virtue of our approach in a more general way. For example, it can also help to judge the relative merits of different alignment algorithms, by estimating the significance of specific alignments. It strongly suggests that information theory concepts can be exploited further in sequence analysis.Orion Pennerorion.penner@imtlucca.itPeter GrassbergerMaya Paczuski2012-05-15T10:59:51Z2012-05-15T10:59:51Zhttp://eprints.imtlucca.it/id/eprint/1268This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12682012-05-15T10:59:51ZAgeing and risk aspects in predictive inference based on proportional Hazard ModelsProportional Hazard Models arise from a straightforward generalization of the simple case of conditionally i.i.d., exponentially distributed random variables and, in a sense, can be considered as the idealized models in the statistical analysis of failure and survival data for
lifetimes. For these reasons, they have been extensively studied in the literature. Despite of the richness of related contributions, there are still special aspects of these models that are worthwhile focusing. In this discussion paper we aim to present some contributions, in the frame of a Bayesian approach and by using some very basic notions of stochastic ordering.Rachele Foschirachele.foschi@imtlucca.itFabio Spizzichino2012-04-04T09:18:53Z2012-04-04T09:18:53Zhttp://eprints.imtlucca.it/id/eprint/1256This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12562012-04-04T09:18:53ZAn upper Riemann-Stieltjes approach to stochastic design problemsIn this paper we study a class of stochastic design problems formulated in terms of general inequality conditions on expectations. These inequalities can be used to express various mean square or almost sure stabilization conditions for stochastic systems. In contrast with existing probabilistic methods that only solve such problems with a certain probability (degree of confidence), we propose a novel method that provides a full guarantee that the constructed solution truly solves the original problem. The main idea of our method is based on overapproximating the expectations by suitably constructed upper Riemann-Stieltjes sums and imposing the inequalities on these sums instead. Next to the full guarantee on the constructed solution, the method offers three other advantages. First, it applies to arbitrary probability distributions. Second, under rather mild conditions we can derive a #x201C;converse theorem #x201D; that states that if the original problem is solvable, our method will find a solution by sufficiently refining the upper Riemann-Stieltjes sums. Finally, we will show that convexity of the function used in the expectation can be exploited to obtain convex design conditions in our approach.W.P.M.H. HeemelsAlberto Bemporadalberto.bemporad@imtlucca.it2012-02-27T11:35:45Z2014-06-26T11:17:43Zhttp://eprints.imtlucca.it/id/eprint/1193This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/11932012-02-27T11:35:45ZA numerical study on the evolution of portfolio rulesIn this paper we test computationally the performance of CAPM in an evolutionary setting. In particular we study the stability of distribution of wealth in a financial market where some traders invest as prescribed by CAPM and others behave according to different portfolio rules. Our study is motivated by recent analytical results that show that, whenever a logarithmic utility maximiser enters the market, CAPM traders vanish in the long run. Our analysis provides further insights and extends these results. We simulate a sequence of trades in a financial market and: first, we address the issue of how long is the long run in different parametric settings; second, we study the effect of heterogeneous savings behaviour on asymptotic wealth shares. We find that CAPM is particularly “unfit” for highly risky environments.Guido Caldarelliguido.caldarelli@imtlucca.itMarina PiccioniEmanuela Sciubba2012-02-27T10:57:19Z2012-02-27T10:57:19Zhttp://eprints.imtlucca.it/id/eprint/1191This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/11912012-02-27T10:57:19ZThe mathematics of networks: the structure of social and biological systemsNetwork organization is just about universal in the real worldGuido Caldarelliguido.caldarelli@imtlucca.it2012-02-23T10:07:06Z2012-02-23T10:07:06Zhttp://eprints.imtlucca.it/id/eprint/1153This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/11532012-02-23T10:07:06ZSex-oriented stable matchings of the marriage problem with correlated and incomplete informationIn the stable marriage problem two sets of agents must be paired according to mutual preferences, which may happen to conflict. We present two generalizations of its sex-oriented version, aiming to take into account correlations between the preferences of agents and costly information. Their effects are investigated both numerically and analytically.Guido Caldarelliguido.caldarelli@imtlucca.itAndrea CapocciPaolo Laureti2012-02-14T14:31:41Z2013-11-20T14:32:59Zhttp://eprints.imtlucca.it/id/eprint/1120This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/11202012-02-14T14:31:41ZAssortative model for social networksIn this Brief Report we present a version of a network growth model, generalized in order to describe the behavior of social networks. The case of study considered is the preprint archive at cul.arxiv.org. Each node corresponds to a scientist, and a link is present whenever two authors wrote a paper together. This graph is a nice example of degree-assortative network, that is, to say a network where sites with similar degree are connected to each other. The model presented is one of the few able to reproduce such behavior, giving some insight on the microscopic dynamics at the basis of the graph structure.Michele CatanzaroGuido Caldarelliguido.caldarelli@imtlucca.itLuciano Pietronero2012-02-14T14:21:09Z2013-11-20T14:58:49Zhttp://eprints.imtlucca.it/id/eprint/1119This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/11192012-02-14T14:21:09ZVertex intrinsic fitness: How to produce arbitrary scale-free networksWe study a recent model of random networks based on the presence of an intrinsic character of the vertices called fitness. The vertex fitnesses are drawn from a given probability distribution density. The edges between pairs of vertices are drawn according to a linking probability function depending on the fitnesses of the two vertices involved. We study here different choices for the probability distribution densities and the linking functions. We find that, irrespective of the particular choices, the generation of scale-free networks is straightforward. We then derive the general conditions under which scale-free behavior appears. This model could then represent a possible explanation for the ubiquity and robustness of such structures.Vito D. P. ServedioGuido Caldarelliguido.caldarelli@imtlucca.itPaolo Buttà2012-02-13T14:30:32Z2013-11-21T09:04:26Zhttp://eprints.imtlucca.it/id/eprint/1114This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/11142012-02-13T14:30:32ZDetecting communities in large networksWe develop an algorithm to detect community structure in complex networks. The algorithm is based on spectral methods and takes into account weights and link orientation. Since the method detects efficiently clustered nodes in large networks even when these are not sharply partitioned, it turns to be specially suitable for the analysis of social and information networks. We test the algorithm on a large-scale data-set from a psychological experiment of word association. In this case, it proves to be successful both in clustering words, and in uncovering mental association patterns.Andrea CapocciVito D. P. ServedioGuido Caldarelliguido.caldarelli@imtlucca.itFrancesca Colaiori2012-02-13T14:15:03Z2012-02-13T14:15:03Zhttp://eprints.imtlucca.it/id/eprint/1113This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/11132012-02-13T14:15:03ZCommunities Detection in Large NetworksWe develop an algorithm to detect community structure in complex networks. The algorithm is based on spectral methods and takes into account weights and links orientations. Since the method detects efficiently clustered nodes in large networks even when these are not sharply partitioned, it turns to be specially suitable to the analysis of social and information networks. We test the algorithm on a large-scale data-set from a psychological experiment of word association. In this case, it proves to be successful both in clustering words, and in uncovering mental association patterns. Andrea CapocciVito D. P. ServedioGuido Caldarelliguido.caldarelli@imtlucca.itFrancesca Colaiori2012-02-03T14:52:07Z2018-03-08T17:07:59Zhttp://eprints.imtlucca.it/id/eprint/1110This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/11102012-02-03T14:52:07ZThe topology of shareholding networksWe study the statistical properties of the network of shareholding relationships in the Italian stock market (MIB) and in two US stock markets (NYSE and NASDAQ). The networks are found to be scale free a feature which doesn't seem to be in accord with classical theories of portfolio optimization. Several statistical properties differ across markets and allow for a classification. We introduce two quantities, HI and SI, analogous to in-degree and out-degree for weighted graphs. The distribution of HI and SI allow us to characterize from a statistical perspective the individual ownership concentration of stocks and the individual power of holders. They also suggest two different global pictures of the structure of the networks: the MIB seems characterized by medium size holders controlling separate subsets of stocks, while the US markets seem characterized by very large holders sharing control over subsets of stocks.Stefano BattistonDiego Garlaschellidiego.garlaschelli@imtlucca.itGuido Caldarelliguido.caldarelli@imtlucca.it2012-02-01T11:39:20Z2018-03-08T17:06:00Zhttp://eprints.imtlucca.it/id/eprint/1095This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10952012-02-01T11:39:20ZQuantifying the taxonomic diversity in real species communitiesWe analyze several florae (collections of plant species populating specific areas) in different geographic and climatic regions. For every list of species we produce a taxonomic classification tree and we consider its statistical properties. We find that regardless of the geographical location, the climate and the environment all species collections have universal statistical properties that we show to be also robust in time. We then compare observed data sets with simulated communities obtained by randomly sampling a large pool of species from all over the world. We find differences in the behavior of the statistical properties of the corresponding taxonomic trees. Our results suggest that it is possible to distinguish quantitatively real species assemblages from random collections and thus demonstrate the existence of correlations between species.Cécile Caretta CartozoDiego Garlaschellidiego.garlaschelli@imtlucca.itCarlo RicottaMarc BarthélemyGuido Caldarelliguido.caldarelli@imtlucca.it2012-02-01T11:33:12Z2018-03-08T17:05:45Zhttp://eprints.imtlucca.it/id/eprint/1094This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10942012-02-01T11:33:12ZApplying weighted network measures to microarray distance matricesIn recent work we presented a new approach to the analysis of weighted networks, by providing a straightforward generalization of any network measure defined on unweighted networks. This approach is based on the translation of a weighted network into an ensemble of edges, and is particularly suited to the analysis of fully connected weighted networks. Here we apply our method to several such networks including distance matrices, and show that the clustering coefficient, constructed by using the ensemble approach, provides meaningful insights into the systems studied. In the particular case of two datasets from microarray experiments the clustering coefficient identifies a number of biologically significant genes, outperforming existing identification approaches.Sebastian E. AhnertDiego Garlaschellidiego.garlaschelli@imtlucca.itThomas M.A. FinkGuido Caldarelliguido.caldarelli@imtlucca.it2012-01-26T09:16:41Z2016-04-07T08:03:08Zhttp://eprints.imtlucca.it/id/eprint/1080This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10802012-01-26T09:16:41ZTopologically biased random walk and community finding in networksWe present an approach of topology biased random walks for undirected networks. We focus on a one-parameter family of biases, and by using a formal analogy with perturbation theory in quantum mechanics we investigate the features of biased random walks. This analogy is extended through the use of parametric equations of motion to study the features of random walks vs parameter values. Furthermore, we show an analysis of the spectral gap maximum associated with the value of the second eigenvalue of the transition matrix related to the relaxation rate to the stationary state. Applications of these studies allow ad hoc algorithms for the exploration of complex networks and their communities.Vinko ZlaticAndrea GabrielliGuido Caldarelliguido.caldarelli@imtlucca.it2012-01-25T13:12:31Z2012-01-25T13:12:31Zhttp://eprints.imtlucca.it/id/eprint/1077This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10772012-01-25T13:12:31ZScale-free networks : complex webs in nature and technologyA variety of different social, natural and technological systems can be described by the same mathematical framework. This holds from the Internet to food webs and to boards of company directors. In all these situations, a graph of the elements of the system and their interconnections displays a universal feature. There are only a few elements with many connections and many elements with few connections. This book reports the experimental evidence of these ‘Scale-free networks’ and provides students and researchers with a corpus of theoretical results and algorithms to analyse and understand these features. The content of this book and the exposition makes it a clear textbook for beginners and a reference book for experts.Guido Caldarelliguido.caldarelli@imtlucca.it2012-01-20T08:52:55Z2012-01-20T09:28:17Zhttp://eprints.imtlucca.it/id/eprint/1072This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10722012-01-20T08:52:55ZProcess AlgebrasProcess Algebras are mathematically rigorous languages with well defined semantics that permit describing and verifying properties of concurrent communicating systems.
They can be seen as models of processes, regarded as agents that act and interact continuously with other similar agents and with their common environment. The agents may be real-world objects (even people), or they may be artifacts, embodied perhaps in computer hardware or software systems.
Many different approaches (operational, denotational, algebraic) are taken for describing the meaning of processes. However, the operational approach is the reference one. By relying on the so called Structural Operational Semantics (SOS), labelled transition systems are built and composed by using the different operators of the many different process algebras. Behavioral equivalences are used to abstract from unwanted details and identify those systems that react similarly to external
experiments.Rocco De Nicolar.denicola@imtlucca.it2011-12-14T15:06:51Z2014-12-04T11:46:29Zhttp://eprints.imtlucca.it/id/eprint/1041This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10412011-12-14T15:06:51ZPareto versus lognormal: a maximum entropy testIt is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of many physical, natural, and social events (earthquake size, species abundance, income and wealth, as well as file, city, and firm sizes) display this structure. We present a test for the occurrence of power-law tails in statistical distributions based on maximum entropy. This methodology allows one to identify the true data-generating processes even in the case when it is neither lognormal nor Pareto. The maximum entropy approach is then compared with other widely used methods and applied to different levels of aggregation of complex systems. Our results provide support for the theory that distributions with lognormal body and Pareto tail can be generated as mixtures of lognormally distributed units.Marco BeeMassimo Riccabonimassimo.riccaboni@imtlucca.itStefano Schiavo2011-12-13T14:45:12Z2011-12-13T14:45:12Zhttp://eprints.imtlucca.it/id/eprint/1040This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10402011-12-13T14:45:12ZA few special cases: scientific creativity and network dynamics in the field of rare diseasesWe develop a model of scientific creativity and test it in the field of rare diseases. Our model is based on the results of an in-depth case study of the Rett Syndrome. Archival analysis, bibliometric techniques and expert surveys are combined with network analysis to identify the most creative scientists. First, we compare alternative measures of generative and combinatorial creativity. Then, we generalize our results in a stochastic model of socio-semantic network evolution. The model predictions are tested with an extended set of rare diseases. We find that new scientific collaborations among experts in a field enhance combinatorial creativity. Instead, high entry rates of novices are negatively related to generative creativity. By expanding the set of useful concepts, creative scientists gain in centrality. At the same time, by increasing their centrality in the scientific community, scientists can replicate and generalize their results, thus contributing to a scientific paradigm. M. Laura FrigottoMassimo Riccabonimassimo.riccaboni@imtlucca.it2011-12-06T13:27:59Z2011-12-06T13:27:59Zhttp://eprints.imtlucca.it/id/eprint/1039This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10392011-12-06T13:27:59ZDevelopment of nonlinear quantitative structure-activity relationships using RBF networks and evolutionary computingQuantitative Structure Activity Relationships (QSARs) are mathematical models that correlate structural or property descriptions of compounds (hydrophobicity, topology, electronic properties etc.) with activities, such as chemical measurements and biological assays. In this paper we propose a modeling methodology suitable for QSAR studies which selects the proper descriptors based on evolutionary computing and finally produces Radial Basis Function (RBF) neural network models. The method is successfully applied to the benchmark Selwood data set.Panagiotis Patrinospanagiotis.patrinos@imtlucca.itAlex AlexandridisAntreas AfantitisHaralambos SarimveisOlga Igglesi-Markopoulou2011-12-06T11:36:57Z2011-12-06T11:36:57Zhttp://eprints.imtlucca.it/id/eprint/1037This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10372011-12-06T11:36:57ZNeural network model-based paper machine marginal cost curvesIn this paper we present a methodology for developing paper machine marginal cost curves, which include variable material and energy costs, fixed costs and overhead costs. The methodology is based on the radial basis function (RBF) neural network architecture and takes into account the complex interactions between the different mill departments. The outcome of the proposed method is the calculation of marginal costs for different paper machine production rates and different grades. The resulting cost curves can be used to take optimal decisions regarding paper machine loadings and optimize production allocation.Panagiotis Patrinospanagiotis.patrinos@imtlucca.itHaralambos SarimveisTh RetsinaS.R RutherfordAlex Alexandridis2011-12-06T11:03:54Z2011-12-06T11:03:54Zhttp://eprints.imtlucca.it/id/eprint/1036This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10362011-12-06T11:03:54ZOptimal production scheduling for dairy industriesIn this work, a complete two-level framework for use in food and in particular dairy industries is proposed. The specific characteristics of the dairy industry have been taken into consideration, in terms of the behavior of food sales over time and the special requirements in the production phase. At the scheduling level, an MILP (Mixed Integer Linear Programming) model of the system was developed, using a continuous representation of time.Philip DoganisHaralambos SarimveisAlex AlexandridisPanagiotis Patrinospanagiotis.patrinos@imtlucca.it2011-12-06T10:51:35Z2011-12-06T10:51:35Zhttp://eprints.imtlucca.it/id/eprint/1035This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10352011-12-06T10:51:35ZAn RBF based neuro-dynamic approach for the control of stochastic dynamic systemsThis paper presents a neuro-dynamic programming methodology for the control of markov decision processes. The proposed method can be considered as a variant of the optimistic policy iteration, where radial basis function (RBF) networks are employed as a compact representation of the cost-to-go function and the ॕ-LSPE is used for policy evaluation. We also emphasize the reformulation of the Bellman equation around the post-decision state in order to circumvent the calculation of the expectation. The proposed algorithm is applied to a retailer-inventory management problem.Panagiotis Patrinospanagiotis.patrinos@imtlucca.itHaralambos Sarimveis2011-12-05T11:40:26Z2011-12-05T11:40:26Zhttp://eprints.imtlucca.it/id/eprint/1027This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10272011-12-05T11:40:26ZA two-stage evolutionary algorithm for variable selection in the development of RBF neural network modelsIn many modeling problems that are based on input–output data, information about a plethora of variables is available. In these cases, the proper selection of explanatory variables is very critical for the success of the produced model, since it eliminates noisy variables and possible correlations, reduces the size of the model and accomplishes more accurate predictions. Many variable selection procedures have been proposed in the literature, but most of them consider only linear models. In this work, we present a novel methodology for variable selection in nonlinear modeling, which combines the advantages of several artificial intelligence technologies. More specifically, the Radial Basis Function (RBF) neural network architecture serves as the nonlinear modeling tool, by exploiting the simplicity of its topology and the fast fuzzy means training algorithm. The proper variables are selected in two stages using a multi-objective optimization approach: in the first stage, a specially designed genetic algorithm minimizes the prediction error over a monitoring data set, while in the second stage a simulated annealing technique aims at the reduction of the number of explanatory variables. The efficiency of the proposed method is illustrated through its application to a number of benchmark problems.Alex AlexandridisPanagiotis Patrinospanagiotis.patrinos@imtlucca.itHaralambos SarimveisGeorge Tsekouras2011-12-05T11:15:09Z2011-12-05T11:15:09Zhttp://eprints.imtlucca.it/id/eprint/1026This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10262011-12-05T11:15:09ZTime series sales forecasting for short shelf-life food products based on artificial neural networks and evolutionary computingDue to the strong competition that exists today, most manufacturing organizations are in a continuous effort for increasing their profits and reducing their costs. Accurate sales forecasting is certainly an inexpensive way to meet the aforementioned goals, since this leads to improved customer service, reduced lost sales and product returns and more efficient production planning. Especially for the food industry, successful sales forecasting systems can be very beneficial, due to the short shelf-life of many food products and the importance of the product quality which is closely related to human health. In this paper we present a complete framework that can be used for developing nonlinear time series sales forecasting models. The method is a combination of two artificial intelligence technologies, namely the radial basis function (RBF) neural network architecture and a specially designed genetic algorithm (GA). The methodology is applied successfully to sales data of fresh milk provided by a major manufacturing company of dairy products.Philip DoganisAlex AlexandridisPanagiotis Patrinospanagiotis.patrinos@imtlucca.itHaralambos Sarimveis2011-12-05T10:30:11Z2011-12-05T10:30:11Zhttp://eprints.imtlucca.it/id/eprint/1024This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10242011-12-05T10:30:11ZVariable selection in nonlinear modeling based on RBF networks and evolutionary computationIn this paper a novel variable selection method based on Radial Basis Function (RBF) neural networks and genetic algorithms is presented. The fuzzy means algorithm is utilized as the training method for the RBF networks, due to its inherent speed, the deterministic approach of selecting the hidden node centers and the fact that it involves only a single tuning parameter. The trade-off between the accuracy and parsimony of the produced model is handled by using Final Prediction Error criterion, based on the RBF training and validation errors, as a fitness function of the proposed genetic algorithm. The tuning parameter required by the fuzzy means algorithm is treated as a free variable by the genetic algorithm. The proposed method was tested in benchmark data sets stemming from the scientific communities of time-series prediction and medicinal chemistry and produced promising results.Panagiotis Patrinospanagiotis.patrinos@imtlucca.itAlex AlexandridisKonstantinos NinosHaralambos Sarimveis2011-12-05T10:20:42Z2011-12-05T10:20:42Zhttp://eprints.imtlucca.it/id/eprint/1023This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10232011-12-05T10:20:42ZA new algorithm for solving convex parametric quadratic programs based on graphical derivatives of solution mappingsIn this paper we derive formulas for computing graphical derivatives of the (possibly multivalued) solution mapping for convex parametric quadratic programs. Parametric programming has recently received much attention in the control community, however most algorithms are based on the restrictive assumption that the so called critical regions of the solution form a polyhedral subdivision, i.e. the intersection of two critical regions is either empty or a face of both regions. Based on the theoretical results of this paper, we relax this assumption and show how we can efficiently compute all adjacent full dimensional critical regions along a facet of an already discovered critical region. Coupling the proposed approach with the graph traversal paradigm, we obtain very efficient algorithms for the solution of parametric convex quadratic programsPanagiotis Patrinospanagiotis.patrinos@imtlucca.itHaralambos Sarimveis2011-11-02T11:27:05Z2011-11-14T11:35:18Zhttp://eprints.imtlucca.it/id/eprint/1000This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10002011-11-02T11:27:05ZLo spazio di SkorohodLo spazio di Skorohod, la cui introduzione risale agli anni '60 è ormai divenuto uno strumento classico nello studio di quei processi stocastici le cui traiettorie siano funzioni cadlag, ossia funzioni continue a destra e dotate di limite a sinistra in ciascun punto. Esso è ottenuto considerando, sull'insieme di tutte le funzioni di questo tipo, un'opportuna topologia (detta topologia di Skorohod). La sua utilità si rivela soprattutto nello studio di problemi di convergenza o di compattezza per leggi di processi dotati di traiettorie cadlag. Il presente lavoro vuol essere un'introduzione all'argomento. Esso si propone di rendere più chiare e più semplici alcune delle dimostrazioni presenti in [Billingsley,1968] e di puntualizzare certi particolari tecnici un po' delicati che, in alcune esposizioni, sono trattati con eccessiva disinvoltura. Particolare attenzione è rivolta alla tribù boreliana dello spazio di Skorohod.Irene Crimaldiirene.crimaldi@imtlucca.it2011-11-02T11:17:55Z2011-11-14T11:35:21Zhttp://eprints.imtlucca.it/id/eprint/999This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9992011-11-02T11:17:55ZIntroduzione alla teoria delle misure aleatorie puntualiIl presente lavoro è un'introduzione alla teoria delle misure aleatorie puntuali. Gli argomenti trattati sono i seguenti:
concetto di classe fondamentale,
concetto di misura aleatoria,
indipendenza di misure aleatorie,
misure aleatorie puntuali e misure aleatorie di Poisson, esistenza di una misura aleatoria di Poisson di assegnata intensità, misure aleatorie puntuali semplici, nucleo di Poisson e misure aleatorie di Cox, estensione aleatoria di una misura puntuale, estensione aleatoria di una misura aleatoria puntuale, misure aleatorie marcate.Irene Crimaldiirene.crimaldi@imtlucca.it2011-10-31T15:45:47Z2012-01-18T08:02:03Zhttp://eprints.imtlucca.it/id/eprint/995This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9952011-10-31T15:45:47ZA dose-finding sequential method for targeting a given mean response: Up&Down experimentsTradizionalmente, gli studi dose-risposta sono esperimenti di tipo binario volti a stimare un determinato “quantile” di interesse di una curva di risposta. In questo lavoro si considera il caso in cui la risposta osservata sia una generica variabile aleatoria reale, non necessariamente dicotomica, e lo scopo dell’esperimento consiste nello stimare la dose target associata ad una preassegnata risposta media. Ripercorrendo i risultati di Giovagnoli e Pintacuda (1998) e Baldi Antognini et al (2006), viene proposta ed analizzata un’estensione randomizzata dell’algoritmo up-and-down, fornendo inoltre una
procedura di stima della risposta media basata sul metodo di massima verosimiglianza.Alessandro Baldi AntogniniIrene Crimaldiirene.crimaldi@imtlucca.it2011-10-31T15:19:03Z2011-11-14T11:37:51Zhttp://eprints.imtlucca.it/id/eprint/991This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9912011-10-31T15:19:03ZPaul Lévy type inequalities for symmetric random variablesWe prove some inequalites for a jointly symmetric system of n random variables with values in a measurable group. These inequalites include, as a particular case, the classical Paul Lévy's inequalities.
Irene Crimaldiirene.crimaldi@imtlucca.itLuca Pratelli2011-10-31T15:12:09Z2011-11-14T11:37:17Zhttp://eprints.imtlucca.it/id/eprint/990This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9902011-10-31T15:12:09ZSur la tribu borélienne de l'espace de SkorohodDans le chapitre VII de [Parthasarathy, 1967], consacré à l'espace de Skorohod, l'auteur introduit tout d'abord un espace un peu plus grand: à savoir l'espace costitué par les fonctions réglée, définies das [0,1], pour lesquelles chaque point de ]0,1[ est, soit un point de continuité à droite, soit un point de continuité à gauche (le type de continuité pouvant dépendre du point considéré). Dans le présent article, aprés avoir montré que la définition et un certain nombre de propriétés de la topologie de Skorohod s'étendent de manière quasi automatique à cet espace plus grand, on prouve qu'il n'en est pas de meme pour les propriétées concernant la tribu borélienne: dans le nouveau cadre, non seulement la tribu borélienne n'est plus engendrée par les projections canoniques, mais celles-ci ne sont meme pas boréliennes.Irene Crimaldiirene.crimaldi@imtlucca.itGiorgio Letta2011-10-31T15:04:57Z2011-11-03T13:19:36Zhttp://eprints.imtlucca.it/id/eprint/989This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9892011-10-31T15:04:57ZConvergence results for a normalized triangular array of symmetric random variablesFor a triangular array of symmetric random variables (without any integrability condition) we replace the classical assumption of row-wise independence by that of row-wise joint symmetry. Under this weaker assumption we prove some results concerning the convergence in distribution of a suitable sequence of randomly normalized sums to the standard normal distribution. Then we exhibit a class of row-wise independent triangular arrays for which the ordinary sums fail to converge in distribution, while our results enable us to affirm the convergence in distribution of the normalized sums.Irene Crimaldiirene.crimaldi@imtlucca.it2011-10-31T15:01:12Z2011-11-03T13:19:36Zhttp://eprints.imtlucca.it/id/eprint/988This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9882011-10-31T15:01:12ZOn the behavior of the conditional expectations in Skorohod representation theoremIn this paper we deal with the Skorohod representation of a given system of probability measures. More precisely, we give conditions for the existence of a Skorohod representation (X,(Xn)) with the following additional property: for each real number p⩾1 and each real random variable Z in Lp, the conditional expectation E[Z|Xn] converges in Lp to the conditional expectation E[Z|X]
Irene Crimaldiirene.crimaldi@imtlucca.it2011-10-31T14:55:36Z2011-11-03T13:19:36Zhttp://eprints.imtlucca.it/id/eprint/987This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9872011-10-31T14:55:36ZTwo inequalities for conditional expectations and convergence results for filtersIn this paper we prove, first of all, two inequalities for conditional expectations, from which we easily deduce a result by Landers and Rogge. Then we prove convergence results for conditional expectations of the form Pn [f(Xn)|Yn] to a conditional expectation of the form P [f(X)|Y]. We study, in particular, the case in which the random variables Yn Y are of the type hn (Xn), h(X)Irene Crimaldiirene.crimaldi@imtlucca.itLuca Pratelli2011-10-31T14:48:17Z2011-11-03T13:19:36Zhttp://eprints.imtlucca.it/id/eprint/986This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9862011-10-31T14:48:17ZConvergence results for multivariate martingalesWe present a new version of the Central Limit Theorem for multivariate martingales.Irene Crimaldiirene.crimaldi@imtlucca.itLuca Pratelli2011-10-31T14:40:32Z2012-08-09T08:24:43Zhttp://eprints.imtlucca.it/id/eprint/985This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9852011-10-31T14:40:32ZConvergence results for conditional expectationsLet E,F be two Polish spaces and [Xn,Yn],[X,Y] random variables with values in E×F (not necessarily defined on the same probability space). We show some conditions which are sufficient in order to assure that, for each bounded continuous function f on E×F, the conditional expectation of f(Xn,Yn) given Yn converges in distribution to the conditional expectation of f(X,Y) given Y.Irene Crimaldiirene.crimaldi@imtlucca.itLuca Pratelli2011-10-31T14:19:25Z2012-01-18T08:01:43Zhttp://eprints.imtlucca.it/id/eprint/984This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9842011-10-31T14:19:25ZSur l'interversion de l'ordre entre deux opérations sur les tribusWe characterize the measurable spaces (Ω,A) such that, for each sub-σ-field G of A and each decreasing filtered family (F_t) of sub-σ-fields of A, with F_t ↓ F_∞, we have F_t ∨ G ↓ F_∞ ∨ G. It follows a characterization of the probability spaces (Ω, A, P) such that, for each sub-σ-field G of A and each decreasing sequence (F_n) of sub-σ-fields of A, with F_n ↓ F_∞, we have ⋂_n (F_n ∨ G) ∼ F_∞ ∨ G (mod P). Irene Crimaldiirene.crimaldi@imtlucca.itGiorgio LettaLuca Pratelli2011-10-31T13:49:03Z2011-11-17T09:37:52Zhttp://eprints.imtlucca.it/id/eprint/983This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9832011-10-31T13:49:03ZA strong form of stable convergenceWe introduce and study a strengthening of the notion of stable convergence. Irene Crimaldiirene.crimaldi@imtlucca.itGiorgio LettaLuca Pratelli2011-10-31T13:38:27Z2012-01-18T08:01:11Zhttp://eprints.imtlucca.it/id/eprint/981This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9812011-10-31T13:38:27ZAsymptotic results for a generalized Pólya urn with “multi-updating” and applications to clinical trialsIn this article, a new Pólya urn model is introduced and studied; in particular, a strong law of large numbers and two central limit theorems are proved. This urn generalizes a model studied in Berti et al. (2004), May et al. (2005), and in Crimaldi (2007), and it has natural applications in clinical trials. Indeed, the model includes both delayed and missing (or null) responses. Moreover, a connection with the conditional identity in distribution of Berti et al. (2004) is given.Irene Crimaldiirene.crimaldi@imtlucca.itFabrizio Leisen2011-10-31T13:28:39Z2011-11-03T13:19:36Zhttp://eprints.imtlucca.it/id/eprint/980This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9802011-10-31T13:28:39ZRate of convergence of predictive distributions for dependent dataThis paper deals with empirical processes of the type
[C_{n}(B)=\sqrt{n}\{\mu_{n}(B)-P(X_{n+1}\in B\mid X_{1},\ldots,X_{n})\},\]
where (Xn) is a sequence of random variables and μn=(1/n)∑i=1nδXi the empirical measure. Conditions for supB|Cn(B)| to converge stably (in particular, in distribution) are given, where B ranges over a suitable class of measurable sets. These conditions apply when (Xn) is exchangeable or, more generally, conditionally identically distributed (in the sense of Berti et al. [Ann. Probab. 32 (2004) 2029–2052]). By such conditions, in some relevant situations, one obtains that $\sup_{B}|C_{n}(B)|\stackrel{P}{\rightarrow}0$ or even that $\sqrt{n}\sup_{B}|C_{n}(B)|$ converges a.s. Results of this type are useful in Bayesian statistics.
Patrizia BertiIrene Crimaldiirene.crimaldi@imtlucca.itLuca PratelliPietro Rigo2011-10-31T13:16:20Z2011-11-03T13:19:36Zhttp://eprints.imtlucca.it/id/eprint/979This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9792011-10-31T13:16:20ZAn almost sure conditional convergence result and an application to a generalized Polya urn We prove an almost sure conditional convergence result toward a Gaussian kernel and we apply it to a two-colors randomly reinforced urn.Irene Crimaldiirene.crimaldi@imtlucca.it2011-10-31T12:04:05Z2011-11-03T13:19:36Zhttp://eprints.imtlucca.it/id/eprint/978This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9782011-10-31T12:04:05ZCentral limit theorems for multicolor urns with dominated colorsAn urn contains balls of d≥2 colors. At each time n≥1, a ball is drawn and then replaced together with a random number of balls of the same color. Let A n = diag (An,1,…,An,d) be the n-th reinforce matrix. Assuming that EAn,j=EAn,1 for all n and j, a few central limit theorems (CLTs) are available for such urns. In real problems, however, it is more reasonable to assume that EA n,j = EA n,1 whenever n ≥ 1 and 1 ≤ j ≤ d0 , liminfn EAn,1 > limsupn EAn,j whenever j > d0 for some integer 1≤d0≤d. Under this condition, the usual weak limit theorems may fail, but it is still possible to prove the CLTs for some slightly different random quantities. These random quantities are obtained by neglecting dominated colors, i.e., colors from d0+1 to d, and they allow the same inference on the urn structure. The sequence (An : n ≥ 1) is independent but need not be identically distributed. Some statistical applications are given as well.Patrizia BertiIrene Crimaldiirene.crimaldi@imtlucca.itLuca PratelliPietro Rigo2011-10-31T11:30:01Z2011-11-03T13:19:36Zhttp://eprints.imtlucca.it/id/eprint/976This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9762011-10-31T11:30:01ZConditionally identically distributed species sampling sequencesIn this paper the theory of species sampling sequences is linked to the theory of conditionally identically distributed sequences in order to enlarge the set of species sampling sequences which are mathematically tractable. The conditional identity in distribution (see Berti, Pratelli and Rigo (2004)) is a new type of dependence for random variables, which generalizes the well-known notion of exchangeability. In this paper a class of random sequences, called generalized species sampling sequences, is defined and a condition to have conditional identity in distribution is given. Moreover, two types of generalized species sampling sequence that are conditionally identically distributed are introduced and studied: the generalized Poisson-Dirichlet sequence and the generalized Ottawa sequence. Some examples are discussed. Federico BassettiIrene Crimaldiirene.crimaldi@imtlucca.itFabrizio Leisen2011-10-31T11:23:14Z2011-11-17T14:44:57Zhttp://eprints.imtlucca.it/id/eprint/975This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/9752011-10-31T11:23:14ZA central limit theorem and its applications to multicolor randomly reinforced urnsLet Xn be a sequence of integrable real random variables, adapted to a filtration (Gn). Define Cn = √{(1 / n)∑k=1nXk - E(Xn+1 | Gn)} and Dn = √n{E(Xn+1 | Gn) - Z}, where Z is the almost-sure limit of E(Xn+1 | Gn) (assumed to exist). Conditions for (Cn, Dn) → N(0, U) x N(0, V) stably are given, where U and V are certain random variables. In particular, under such conditions, we obtain √n{(1 / n)∑k=1nX_k - Z} = Cn + Dn → N(0, U + V) stably. This central limit theorem has natural applications to Bayesian statistics and urn problems. The latter are investigated, by paying special attention to multicolor randomly reinforced urns. Patrizia BertiIrene Crimaldiirene.crimaldi@imtlucca.itLuca PratelliPietro Rigo2011-09-07T12:58:03Z2014-01-24T14:19:09Zhttp://eprints.imtlucca.it/id/eprint/825This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/8252011-09-07T12:58:03ZInnovation and corporate dynamics: a theoretical frameworkWe provide a detailed analysis of a generalized proportional growth model (GPGM) of innovation and corporate dynamics that encompasses the Gibrat’s Law of Proportionate Effect and the Simon growth process as particular instances. The predictions of the model are derived in terms of (i) firm size distribution, (ii) the distribution of firm growth rates, and (iii-iv) the relationships between firm size and the mean and variance of firm growth rates. We test the model against data from the worldwide pharmaceutical industry and find its predictions to be in good agreement with empirical evidence on all four dimensions.Jakub GrowiecFabio Pammollif.pammolli@imtlucca.itMassimo Riccabonimassimo.riccaboni@imtlucca.it2011-08-11T08:37:32Z2011-09-27T13:11:38Zhttp://eprints.imtlucca.it/id/eprint/794This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7942011-08-11T08:37:32ZUniform labeled transition systems for nondeterministic, probabilistic, and stochastic process calculiLabeled transition systems are typically used to represent the behavior of nondeterministic processes, with labeled transitions defining a one-step state to-state reachability relation. This model has been recently made more general by modifying the transition relation in such a way that it associates with any source state and transition label a reachability distribution, i.e., a function mapping each possible target state to a value of some domain that expresses the degree of one-step reachability of that target state. In this extended abstract, we show how the resulting model, called ULTraS from Uniform Labeled Transition System, can be naturally used to give semantics to a fully nondeterministic, a fully probabilistic, and a fully stochastic variant of a CSP-like process language. Marco BernardoRocco De Nicolar.denicola@imtlucca.itMichele Loreti2011-08-03T10:52:17Z2011-08-04T07:30:21Zhttp://eprints.imtlucca.it/id/eprint/765This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7652011-08-03T10:52:17ZKriging metamodels in design optimization: an automotive engineering applicationGabriella Dellinogabriella.dellino@imtlucca.itPaolo LinoCarlo MeloniAlessandro Rizzo2011-08-03T10:42:23Z2011-08-04T07:30:21Zhttp://eprints.imtlucca.it/id/eprint/764This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7642011-08-03T10:42:23ZModeling and simulation study for the design of controlled IPMC actuatorsGabriella Dellinogabriella.dellino@imtlucca.itPaolo LinoCarlo MeloniAlessandro RizzoPaolo Di GiambernardinoAndrea Usai2011-08-02T09:13:43Z2011-08-04T07:30:21Zhttp://eprints.imtlucca.it/id/eprint/759This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7592011-08-02T09:13:43ZPerformance evaluation of the evolution control in design optimization assisted by Kriging surrogatesGabriella Dellinogabriella.dellino@imtlucca.itCarlo MeloniPaolo LinoAlessandro Rizzo2011-08-01T13:49:28Z2011-08-08T08:40:22Zhttp://eprints.imtlucca.it/id/eprint/757This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7572011-08-01T13:49:28ZRobust simulation-optimization methodologyThis contribution summarizes a methodology for simulation
optimization assuming some simulation inputs are
uncertain. This methodology integrates Taguchi’s worldview
(distinguishing between decision and environmental
inputs), metamodeling (either Response Surface Methodology
or Kriging), and mathematical programming. Instead
of Taguchi’s statistical designs, this contribution uses Latin Hypercube Sampling for the environmental inputs. Mathematical programming is used to estimate the decision inputs that minimize the mean output, subject to a threshold for the standard deviation of the simulation output. Changing that threshold gives the estimated Pareto frontier. Confidence regions for the Pareto-optimal solution based on that frontier can be estimated through bootstrapping. This methodology is illustrated through Economic Order Quantity (EOQ)
simulations.Jack P.C. KleijnenGabriella Dellinogabriella.dellino@imtlucca.itCarlo Meloni2011-08-01T13:42:54Z2011-10-07T08:21:48Zhttp://eprints.imtlucca.it/id/eprint/756This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7562011-08-01T13:42:54ZRobust simulation-optimization using metamodelsOptimization of simulated systems is the goal of many methods, but most methods assume known environments. In this paper we present a methodology that does account for uncertain environments. Our methodology uses Taguchi's view of the uncertain world, but replaces his statistical techniques by either Response Surface Methodology or Kriging metamodeling. We illustrate the resulting methodology through the well-known Economic Order Quantity (EOQ) modelGabriella Dellinogabriella.dellino@imtlucca.itJack P.C. KleijnenCarlo Meloni2011-08-01T13:34:28Z2011-08-08T08:38:45Zhttp://eprints.imtlucca.it/id/eprint/755This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7552011-08-01T13:34:28ZA rollout algorithmic approach for complex parallel machine scheduling in healthcare operationsMichele CiavottaGabriella Dellinogabriella.dellino@imtlucca.itCarlo MeloniMarco Pranzo2011-08-01T12:52:38Z2011-08-04T07:30:21Zhttp://eprints.imtlucca.it/id/eprint/753This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7532011-08-01T12:52:38ZParametric and distribution-free bootstrapping in robust simulation-optimizationMost methods in simulation-optimization assume known environments, whereas this research accounts for uncertain environments combining Taguchi's world view with either regression or Kriging (also called Gaussian Process) metamodels (emulators, response surfaces, surrogates). These metamodels are combined with Non-Linear Mathematical Programming (NLMP) to find robust solutions. Varying the constraint values in this NLMP gives an estimated Pareto frontier. To account for the variability of this estimated Pareto frontier, this contribution considers different bootstrap methods to obtain confidence regions for a given solution. This methodology is illustrated through some case studies selected from the literature.Gabriella Dellinogabriella.dellino@imtlucca.itJack P.C. KleijnenCarlo Meloni2011-08-01T12:19:29Z2011-08-04T07:30:21Zhttp://eprints.imtlucca.it/id/eprint/751This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7512011-08-01T12:19:29ZRobust simulation optimization methods using Kriging metamodelsGabriella Dellinogabriella.dellino@imtlucca.it2011-08-01T10:52:00Z2011-08-04T07:30:21Zhttp://eprints.imtlucca.it/id/eprint/749This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7492011-08-01T10:52:00ZEnhanced evolutionary algorithms for multidisciplinary design optimization: a control engineering perspectiveThis chapter deals with the application of hybrid evolutionary methods to design optimization issues in which approximation techniques and model management strategies can be used to guide the decision making process in a multidisciplinary context. An enhanced evolutionary algorithmic scheme devoted to design optimization is proposed, and its use in real applications is illustrated in the framework of the multidisciplinary design optimization (MDO). At this aim, a case study is discussed. It relies to the field of automotive engineering in which the design optimization of a system is carried out considering simultaneously both mechanical and control requirements. The studied system is the regulator of the injection pressure of an innovative common rail system for compressed natural gas (CNG) engines, whose engineering design optimization includes several practical and numerical difficulties. To tackle such a situation, a multiobjective optimization formulation of the problem is proposed. The adopted optimization strategy pursues the Pareto optimality on the basis of fitness functions that capture domain specific design aspects as well as static and dynamic objectives. The computational experiments show the ability of the proposed method for finding a satisfactory set of efficient solutions. Gabriella Dellinogabriella.dellino@imtlucca.itPaolo LinoCarlo MeloniAlessandro Rizzo2011-08-01T10:24:59Z2011-08-04T07:30:21Zhttp://eprints.imtlucca.it/id/eprint/747This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7472011-08-01T10:24:59ZKriging metamodel management in the design optimization of a CNG injection systemThis paper deals with the use of Kriging metamodels in multi-objective engineering design optimization. The metamodel management issue to find the tradeoff between accuracy and efficiency is addressed. A comparative analysis of different strategies is conducted for a case study devoted to the design of a component of the injection system for Compressed Natural Gas (CNG) engines. The computational results are reported and analyzed for a performance assessment conducted with a data envelopment analysis approach.Gabriella Dellinogabriella.dellino@imtlucca.itPaolo LinoCarlo MeloniAlessandro Rizzo2011-08-01T10:24:49Z2011-08-04T07:30:21Zhttp://eprints.imtlucca.it/id/eprint/748This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7482011-08-01T10:24:49ZDynamic objectives aggregation methods in multi-objective evolutionary optimization Several approaches for solving multi-objective optimization problems entail a form of scalarization of the objectives. This chapter proposes a study of different dynamic objectives aggregation methods in the context of evolutionary algorithms. These methods are mainly based on both weighted sum aggregations and curvature variations. Since the incorporation of chaotic rules or behaviour in population-based optimization algorithms has been shown to possibly enhance their searching ability, this study proposes to introduce and evaluate also some chaotic rules in the dynamic weights generation process. A comparison analysis is presented on the basis of a campaign of computational experiments on a set of benchmark problems from the literature. Gabriella Dellinogabriella.dellino@imtlucca.itMariagrazia FedeleCarlo Meloni2011-08-01T10:23:29Z2011-08-04T07:30:21Zhttp://eprints.imtlucca.it/id/eprint/746This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7462011-08-01T10:23:29ZRobust optimization in simulation: Taguchi and response surface methodologyOptimization of simulated systems is tackled by many methods, but most methods assume known environments. This article, however, develops a `robust' methodology for uncertain environments. This methodology uses Taguchi's view of the uncertain world, but replaces his statistical techniques by Response Surface Methodology (RSM). George Box originated RSM, and Douglas Montgomery recently extended RSM to robust optimization of real (non-simulated) systems. We combine Taguchi's view with RSM for simulated systems. We illustrate the resulting methodology through classic Economic Order Quantity (EOQ) inventory models, which demonstrate that robust optimization may require order quantities that differ from the classic EOQ.Gabriella Dellinogabriella.dellino@imtlucca.itJack P.C. KleijnenCarlo Meloni2011-07-29T11:00:09Z2012-07-09T09:42:48Zhttp://eprints.imtlucca.it/id/eprint/745This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7452011-07-29T11:00:09ZA stochastic model predictive control approach to dynamic option hedging with transaction costsThis paper proposes a stochastic model predictive control (SMPC) approach to hedging derivative contracts (such as plain vanilla and exotic options) in the presence of transaction costs. The methodology is based on the minimization of a stochastic measures of the hedging error predicted for the next trading date. Three different measures are proposed to determine the optimal composition of the replicating portfolio. The first measure is a combination of variance and expected value of the hedging error, leading to a quadratic program (QP) to solve at each trading date; the second measure is the conditional value at risk (CVaR), a common index used in finance quantifying the average loss over a subset of worst-case realizations, leading to a linear programming (LP) formulation; the third approach is of min-max type and attempts at minimizing the largest possible hedging error, also leading to a (smaller scale) linear program. The hedging performance obtained by the three different measures is tested and compared in simulation on a European call and a barrier option.Alberto Bemporadalberto.bemporad@imtlucca.itLaura PugliaTommaso Gabbriellini2011-07-29T10:52:58Z2013-09-30T12:29:47Zhttp://eprints.imtlucca.it/id/eprint/740This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7402011-07-29T10:52:58ZStability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functionsFor piecewise affine (PWA) systems whose dynamics are only defined in a bounded and possibly non-invariant set X, this paper proposes a numerical approach to analyze the stability of the origin and to find a region of attraction. The approach relies on introducing fake dynamics outside X and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function on a larger bounded set containing X by solving a linear program. The existence of a solution proves that the origin is an asymptotically stable equilibrium of the original PWA system and determines a region of attraction contained in X. The procedure is particularly useful in practical applications for analyzing a posteriori the stability properties of approximate explicit model predictive control laws defined over a bounded set X of states, and to determine whether, for a given set of initial states, the closed-loop system evolves within the domain X where the control law is defined.Matteo RubagottiSergio TrimboliDaniele Bernardinidaniele.bernardini@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-29T10:52:50Z2011-08-04T07:29:05Zhttp://eprints.imtlucca.it/id/eprint/739This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7392011-07-29T10:52:50ZScenario-based stochastic model predictive control for dynamic option hedgingFor a rather broad class of financial options, this paper proposes a stochastic model predictive control (SMPC) approach for dynamically hedging a portfolio of underlying assets. By employing an option pricing engine to estimate future realizations of option prices on a finite set of one-step-ahead scenarios, the resulting stochastic optimization problem is easily solved as a least-squares problem at each trading date with as many variables as the number of traded assets and as many constraints as the number of predicted scenarios. After formulating the dynamic hedging problem as a stochastic control problem, we test its ability to replicate the payoff at expiration date for plain vanilla and exotic options. We show not only that relatively small hedging errors are obtained in spite of price realizations, but also that the approach is robust with respect to market modeling errors.Alberto Bemporadalberto.bemporad@imtlucca.itTommaso GabbrielliniLaura PugliaLeonardo Bellucci2011-07-29T10:52:40Z2011-11-17T11:01:57Zhttp://eprints.imtlucca.it/id/eprint/738This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7382011-07-29T10:52:40ZStochastic model predictive control with driver behavior learning for improved powertrain controlIn this paper we advocate the use of stochastic model predictive control (SMPC) for improving the performance of powertrain control algorithms, by optimally controlling the complex system composed of driver and vehicle. While the powertrain is modeled as the deterministic component of the dynamics, the driver behavior is represented as a
stochastic system which affects the vehicle dynamics. Since stochastic MPC is based on online numerical optimization, the driver model can be learned online, hence allowing the control algorithm to adapt to different drivers and drivers' behaviors. The proposed technique is evaluated in two applications: adaptive cruise control, where the driver behavioral model is used to predict the leading vehicle dynamics, and series hybrid electric vehicle (SHEV) energy management, where the driver model is used to predict the future power requests.M. BichiGiulio RipaccioliStefano Di CairanoDaniele Bernardinidaniele.bernardini@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.itIlya Kolmanovsky2011-07-29T10:49:00Z2011-08-04T07:29:05Zhttp://eprints.imtlucca.it/id/eprint/737This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7372011-07-29T10:49:00ZSynthesis of stabilizing model predictive controllers via canonical piecewise affine approximationsThis paper proposes the use of canonical piecewise affine (PWA) functions for the approximation of linear MPC controllers over a regular simplicial partition of a given set of states of interest. Analysis tools based on the construction of PWA Lyapunov functions are provided for certifying the asymptotic stability of the resulting closed-loop system. The main advantage of the proposed controller synthesis approach is that the resulting stabilizing approximate MPC controller can be implemented on chip with sampling times in the order of tens of nanoseconds.Alberto Bemporadalberto.bemporad@imtlucca.itAlberto OliveriTomaso PoggiMarco Storace2011-07-29T10:18:42Z2011-11-17T11:05:36Zhttp://eprints.imtlucca.it/id/eprint/735This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7352011-07-29T10:18:42ZSynthesis of networked switching linear decentralized controllersThis paper proposes an approach based on linear matrix inequalities for synthesizing a set of decentralized regulators for discrete-time linear systems subject to input and state constraints. Measurements and command signals are exchanged over a sensor/actuator network, in which some links are subject to packet dropout. The resulting closed-loop system is guaranteed to asymptotically reach the origin, even if every local actuator can exploit only a (possibly time-varying) subset of state measurements. A model of packet dropout based on a finite-state Markov chain is also considered to exploit available knowledge about the stochastic nature of the network. For such model, a set of decentralized switching linear controllers is synthesized that guarantees mean-square stability of the overall controlled process under packet dropout and soft input and state constraints.Davide BarcelliDaniele Bernardinidaniele.bernardini@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-28T09:52:57Z2012-04-03T07:18:16Zhttp://eprints.imtlucca.it/id/eprint/729This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7292011-07-28T09:52:57ZModel predictive idle speed control: design, analysis, and experimental evaluationIdle speed control is a landmark application of feedback control in automotive vehicles that continues to be of significant interest to automotive industry practitioners, since improved idle performance and robustness translate into better fuel economy, emissions and drivability. In this paper, we develop a model predictive control (MPC) strategy for regulating the engine speed to the idle speed set-point by actuating the electronic throttle and the spark timing. The MPC controller coordinates the two actuators according to a specified cost function, while explicitly taking into account constraints on the control and requirements on the acceptable engine speed range, e.g., to avoid engine stalls. Following a process proposed here for the implementation of MPC in automotive applications, an MPC controller is obtained with excellent performance and robustness as demonstrated in actual vehicle tests. In particular, the MPC controller performs better than an existing baseline controller in the vehicle, is robust to changes in operating conditions, and to different types of disturbances. It is also shown that the MPC computational complexity is well within the capability of production electronic control unit and that the improved performance achieved by the MPC controller can translate into fuel economy improvements.Stefano Di CairanoDiana YanakievAlberto Bemporadalberto.bemporad@imtlucca.itIlya KolmanovskyDavor Hrovat2011-07-28T09:52:00Z2012-07-06T12:30:20Zhttp://eprints.imtlucca.it/id/eprint/730This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7302011-07-28T09:52:00ZUltra-fast stabilizing model predictive control via canonical piecewise affine approximationsThis paper investigates the use of canonical piecewise affine (PWA) functions for approximation and fast implementation of linear MPC controllers. The control law is approximated in an optimal way over a regular simplicial partition of a given set of states of interest. The stability properties of the resulting closed-loop system are analyzed by constructing a suitable PWA Lyapunov function. The main advantage of the proposed approach to the implementation of MPC controllers is that the resulting stabilizing approximate MPC controller can be implemented on chip with sampling times in the order of tens of nanoseconds.Alberto Bemporadalberto.bemporad@imtlucca.itAlberto OliveriTomaso PoggiMarco Storace2011-07-27T12:51:25Z2011-08-05T11:12:37Zhttp://eprints.imtlucca.it/id/eprint/725This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7252011-07-27T12:51:25ZDecentralized model predictive control of dynamically coupled linear systemsThis paper proposes a decentralized model predictive control (DMPC) scheme for large-scale dynamical processes subject to input constraints. The global model of the process is approximated as the decomposition of several (possibly overlapping) smaller models used for local predictions. The degree of decoupling among submodels represents a tuning knob of the approach: the less coupled are the submodels, the lighter the computational burden and the load for transmission of shared information; but the smaller is the degree of cooperativeness of the decentralized controllers and the overall performance of the control system. Sufficient criteria for analyzing asymptotic closed-loop stability are provided for input constrained open-loop asymptotically stable systems and for unconstrained open-loop unstable systems, under possible intermittent lack of communication of measurement data between controllers. The DMPC approach is also extended to asymptotic tracking of output set-points and rejection of constant measured disturbances. The effectiveness of the approach is shown on a relatively large-scale simulation example on decentralized temperature control based on wireless sensor feedback.Alessandro AlessioDavide BarcelliAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T10:14:44Z2014-07-03T13:45:30Zhttp://eprints.imtlucca.it/id/eprint/437This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4372011-07-27T10:14:44ZModeling and control of hybrid dynamical systems: the hybrid toolbox for MATLABAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:32:44Z2014-07-17T12:39:20Zhttp://eprints.imtlucca.it/id/eprint/468This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4682011-07-27T09:32:44ZConvexity recognition of the union of polyhedraIn this paper we consider the following basic problem in polyhedral computation: Given two polyhedra in Rd, P and Q, decide whether their union is convex, and, if so, compute it. We consider the three natural specializations of the problem: 1) when the polyhedra are given by halfspaces (H-polyhedra), 2) when they are given by vertices and extreme rays (V-polyhedra), and 3) when both H- and V-polyhedral representations are available. Both the bounded (polytopes) and the unbounded case are considered. We show that the first two problems are polynomially solvable, and that the third problem is strongly-polynomially solvable.Alberto Bemporadalberto.bemporad@imtlucca.itKomei FukudaFabio Danilo Torrisi2011-07-27T09:20:41Z2014-01-28T09:15:39Zhttp://eprints.imtlucca.it/id/eprint/480This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4802011-07-27T09:20:41ZFiltraggio predittivo del riferimento per il controllo di sistemi vincolatiAlberto Bemporadalberto.bemporad@imtlucca.itEdoardo Mosca2011-07-27T09:20:39Z2014-07-16T13:07:37Zhttp://eprints.imtlucca.it/id/eprint/597This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5972011-07-27T09:20:39ZRobust nonlinear reference filtering for constrained linear systems with uncertain impulse/step responsesA method based on conceptual tools of predictive control is described for solving tracking problems wherein pointwise-in-time input and/or state inequality constraints and model uncertainties are present. It consists of adding to a primal compensated system a nonlinear device called predictive reference filter (PRF) which manipulates the desired trajectory in order to fulfill the prescribed constraints. Provided that an admissibility condition on the initial state is satisfied, the control scheme is proved to fulfill the constraints and be asymptotically stable for all the systems whose impulse-response and step-response descriptions lie within given uncertainty rangesAlberto Bemporadalberto.bemporad@imtlucca.itEdoardo Mosca2011-07-27T09:20:35Z2014-07-16T13:04:04Zhttp://eprints.imtlucca.it/id/eprint/594This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5942011-07-27T09:20:35ZA predictive reference governor for constrained control systemsAlberto Bemporadalberto.bemporad@imtlucca.itAlessandro CasavolaEdoardo Mosca2011-07-27T09:20:25Z2014-07-16T14:08:56Zhttp://eprints.imtlucca.it/id/eprint/603This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6032011-07-27T09:20:25ZConstrained predictive control with terminal ellipsoid constraint and artificial Lyapunov functionsWe deal with the problem of satisfying input and/or state hard constraints in set-point tracking problems. Stability is guaranteed by synthesizing a Lyapunov quadratic function for the system, and by imposing that the terminal state lies within a level set of the function. Algorithmic procedures to maximize the volume of such an ellipsoidal set are providedAlberto Bemporadalberto.bemporad@imtlucca.itEdoardo Mosca2011-07-27T09:19:40Z2014-07-16T13:56:49Zhttp://eprints.imtlucca.it/id/eprint/598This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5982011-07-27T09:19:40ZOttimizzazione in linea del set-point per processi industriali soggetti a saturazioni o vincoli sullo statoIn questa memoria si affronta il problema del controllo di processi industriali soggetti a vincoli sulle variabili di stato e/o di ingresso. La soluzione che si propone consiste nel modificare in linea, quando necessario, il set-point di riferimento in modo da garantire evoluzioni del processo che soddisfino i vincoli imposti. L’idea di modificare soltanto il set-point di riferimento ha il vantaggio di potere essere implementata senza modificare la struttura dei loop interni di controllo già esistenti. La soluzione proposta consente di ottenere il rispetto dei vincoli e buone prestazioni in termini di inseguimento del set-point, richiedendo potenze di calcolo contenute, ampiamente disponibili su hardware commerciale a basso costo.Alberto Bemporadalberto.bemporad@imtlucca.itAlessandro CasavolaEdoardo Mosca2011-07-27T09:19:32Z2014-07-16T14:14:51Zhttp://eprints.imtlucca.it/id/eprint/605This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6052011-07-27T09:19:32ZReducing conservativeness in predictive control of constrained systems with disturbancesPredictive controllers which are able to guarantee constraint fulfilment in the presence of input disturbances, typically based on min-max formulations, often suffer excessive conservativeness. One of the main reasons for this is that the control action is based on the open-loop prediction of the evolution of the system, because the uncertainty due to the disturbance grows as time proceeds on the prediction horizon. On the other hand, such an effect can be moderated by adopting a closed-loop prediction. In this paper, closed-loop prediction is achieved by including a free feedback matrix gain in the set of optimization variables. This allows one to balance computational burden and reduction of conservativenessAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:19:28Z2014-07-16T14:12:54Zhttp://eprints.imtlucca.it/id/eprint/466This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4662011-07-27T09:19:28ZReference governor for constrained nonlinear systemsThis paper addresses the problem of satisfying pointwise-in-time input and/or state hard constraints in nonlinear control systems. The approach is based on conceptual tools of predictive control and consists of adding to a primal compensated nonlinear system a reference governor. This is a discrete-time device which online handles the reference to be tracked, taking into account the current value of the state in order to satisfy the prescribed constraints. The resulting hybrid system is proved to fulfil the constraints as well as stability and tracking requirementsAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:18:23Z2014-07-16T14:11:17Zhttp://eprints.imtlucca.it/id/eprint/481This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4812011-07-27T09:18:23ZA predictive reference governor for constrained control systemsA method based on conceptual tools of predictive control is described for solving tracking problems wherein pointwise-in-time input and/or state inequality constraints are present. It consists of adding to a primal compensated system a nonlinear device called reference governor (RG) whose action is based on the current state, set-point, and prescribed constraints. The aim of the RG device is that of modifying, when necessary, the reference in such a way that the constraints are enforced and the primal compensated system maintains its linear behavior. The RG action is computed on-line by solving, at each sampling time, a constrained quadratic programming problem that usually requires low computational times also for systems of relatively high order. The overall system is proved to fulfill the constraints, be asymptotically stable, and exhibit an offset-free tracking behaviour, provided that an admissibility condition on the initial state is satisfied.Alberto Bemporadalberto.bemporad@imtlucca.itAlessandro CasavolaEdoardo Mosca2011-07-27T09:18:20Z2014-07-16T14:10:13Zhttp://eprints.imtlucca.it/id/eprint/467This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4672011-07-27T09:18:20ZA predictive controller with artificial Lyapunov function for linear systems with input/state constraintsThis paper copes with the problem of satisfying input and/or state hard constraints in set-point tracking problems. Stability is guaranteed by synthesizing a Lyapunov quadratic function for the system, and by imposing that the terminal state lies within a level set of the function. Procedures to maximize the volume of such an ellipsoidal set are provided, and interiorpoint methods to solve on-line optimization are considered.Alberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:18:17Z2014-07-16T14:27:00Zhttp://eprints.imtlucca.it/id/eprint/500This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5002011-07-27T09:18:17ZVerification of hybrid systems via mathematical programmingThis paper proposes a novel approach to the verification of hybrid systems based on linear and mixed-integer linear programming. Models are described using the Mixed Logical Dynamical (MLD) formalism introduced in [5]. The proposed technique is demonstrated on a verification case study for an automotive suspension system.Alberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T09:18:12Z2011-08-08T08:26:41Zhttp://eprints.imtlucca.it/id/eprint/608This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6082011-07-27T09:18:12ZA framework for control, fault detection, state estimation and verification of hybrid systemsThis paper presents a modeling formalism for hybrid systems which allows one to formulate and solve several practical problems, such as control, formal verification, state estimation, and fault detection. As an extension to previous works we report a technique that allows one to reduce the number of auxiliary binary variables in the modeling phase Domenico MignoneAlberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T09:18:05Z2014-07-16T14:22:27Zhttp://eprints.imtlucca.it/id/eprint/611This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6112011-07-27T09:18:05ZObservability and controllability of piecewise affine and hybrid systemsWe prove, in a constructive way, the equivalence between hybrid and piecewise affine systems. By focusing our investigation on the latter class, we show through counter-examples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems. Instead, we propose practical numerical tests based on mixed-integer linear programmingAlberto Bemporadalberto.bemporad@imtlucca.itGiancarlo Ferrari-TrecateManfred Morari2011-07-27T09:18:03Z2014-07-16T14:21:03Zhttp://eprints.imtlucca.it/id/eprint/610This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6102011-07-27T09:18:03ZModel predictive control - ideas for the next generationMixed Logical Dynamical (MLD) systems are introduced
as a new system type. The MLD form is capable to model
a broad class of systems arising in many applications: linear hybrid systems; sequential logical systems (finite state machines, automata); nonlinear dynamic systems, where
the nonlinearity can be expressed through combinational
logic; some classes of discrete event systems; constrained
linear systems. Controllability/verification and observability of MLD systems and other system theoretic properties are defined. Tests for these properties are formulated in the form of Mixed-Integer Linear Programs. Moving horizon control and estimation strategies with stability guarantees are proposed. These strategies require the iterative solution of Mixed-Integer Quadratic Programs.
Several examples communicate the power and versatility
of the proposed framework.Alberto Bemporadalberto.bemporad@imtlucca.itGiancarlo Ferrari-TrecateDomenico MignoneManfred MorariFabio Danilo Torrisi2011-07-27T09:18:01Z2014-07-16T14:20:22Zhttp://eprints.imtlucca.it/id/eprint/447This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4472011-07-27T09:18:01ZControl of systems integrating logic, dynamics, and constraintsThis paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as mixed logical dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real and integer variables. MLD systems include linear hybrid systems, finite state machines, some classes of discrete event systems, constrained linear systems, and nonlinear systems which can be approximated by piecewise linear functions. A predictive control scheme is proposed which is able to stabilize MLD systems on desired reference trajectories while fulfilling operating constraints, and possibly take into account previous qualitative knowledge in the form of heuristic rules. Due to the presence of integer variables, the resulting on-line optimization procedures are solved through mixed integer quadratic programming (MIQP), for which efficient solvers have been recently developed. Some examples and a simulation case study on a complex gas supply system are reported.Alberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T09:16:44Z2014-07-16T14:19:56Zhttp://eprints.imtlucca.it/id/eprint/496This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4962011-07-27T09:16:44ZPredictive path parameterization for constrained robot controlFor robotic systems tracking a given geometric path, the paper addresses the problem of satisfying input and state constraints. According to a prediction of the evolution of the robot from the current state, a discrete-time device called a path governor generates online a suitable time-parameterization of the path to be tracked, by solving at fixed intervals a constrained scalar look-ahead optimization problem. Higher level switching commands are also taken into account by simply associating a different optimization criterion to each mode of operation. Experimental results are reported for a three-degree-of-freedom PUMA 560 manipulator subject to absolute position error, Cartesian velocity, and motor voltage constraintsAlberto Bemporadalberto.bemporad@imtlucca.itTzyh-Jong TarnNing Xi2011-07-27T09:16:35Z2014-07-17T12:22:57Zhttp://eprints.imtlucca.it/id/eprint/482This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4822011-07-27T09:16:35ZOn-line optimization via off-line parametric optimization toolsIn this paper, on-line optimization problems with a quadratic performance criteria and linear constraints are formulated as multi-parametric quadratic programs, where the input and state variables, corresponding to a plant, are treated as optimization variables and parameters, respectively. The solution of such problems is given by (i) a complete set of profiles of all the optimal inputs to the plant as a function of state variables, and (ii) the regions in the space of state variables where these functions remain optimal. It is shown that these profiles are linear and the corresponding regions are described by linear inequalities. An algorithm for obtaining these profiles and corresponding regions of optimality is also presented. The key feature of the proposed approach is that the on-line optimization problem is solved off-line via parametric programming techniques, hence, at each time interval (i) no optimization solver is called on-line, (ii) simple function evaluations are required for obtaining the optimal inputs to the plant for the current state of the plant.Efstratios N. PistikopoulosVivek DuaNikolaos A. BozinisAlberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T09:16:26Z2014-07-17T12:19:29Zhttp://eprints.imtlucca.it/id/eprint/570This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5702011-07-27T09:16:26ZRobust simulation of nonlinear electronic circuitsThis paper proposes robust simulation of piecewise linear systems as a tool for the analysis of nonlinear electronic circuits. Rather than computing the evolution of a single trajectory, robust simulation computes the evolution from a set of initial conditions in the state space, for all forcing input signals within a given class. We describe here a tool to perform this analysis using mathematical programming. Among various applications, the tool allows to estimate the domain of attraction of equilibria, and to
determine if some design speci£cations — expressed
themselves in terms of reachability of subsets of the
state-space — are met. A test of the tool on Chua’s
circuit is presented.Alberto Bemporadalberto.bemporad@imtlucca.itL. GiovanardiFabio Danilo Torrisi2011-07-27T09:16:24Z2014-07-17T12:19:02Zhttp://eprints.imtlucca.it/id/eprint/575This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5752011-07-27T09:16:24ZPerformance driven reachability analysis for optimal scheduling and control of hybrid systemsWe deal with the optimal control problem for piecewise linear and hybrid systems by using a computational approach based on performance-driven reachability analysis. The idea consists of coupling a reach-set exploration algorithm, essentially based on a repetitive use of linear programming, to a quadratic programming solver which selectively drives the exploration. In particular, an upper bound on the optimal cost is continually updated during the procedure, and used as a criterion to discern non-optimal evolutions and to prevent their exploration. The result is an efficient strategy of branch-and-bound nature, which is especially attractive for solving long-horizon hybrid optimal control and scheduling problemsAlberto Bemporadalberto.bemporad@imtlucca.itL. GiovanardiFabio Danilo Torrisi2011-07-27T09:16:21Z2014-07-17T12:18:33Zhttp://eprints.imtlucca.it/id/eprint/456This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4562011-07-27T09:16:21ZOutput-feedback predictive control of constrained linear systems with disturbances via set-membership state estimationThis paper combines model predictive control (MPC) and set-membership (SM) state estimation techniques for controlling systems subject to hard input and state constraints. Linear systems with unknown but bounded disturbances and partial state information are considered. The adopted approach guarantees that the constraints are satisfied for all the states which are compatible with the available information and for all the disturbances within given bounds. Properties of the proposed MPC-SM algorithm and simulation studies are reported.Alberto Bemporadalberto.bemporad@imtlucca.itAndrea Garulli2011-07-27T09:11:28Z2014-07-17T12:18:14Zhttp://eprints.imtlucca.it/id/eprint/571This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5712011-07-27T09:11:28ZOn convexity recognition of the union of polyhedra
In this paper we consider the following basic problem in polyhedral computation: given two polyhedra in $R^d$, $P$ and $Q$, decide whether their union is convex, and eventually compute it. We consider the three natural specializations of the problem: 1) when the polyhedra are given by half-spaces (H-polyhedra) 2) when they are given by vertices and extreme rays (V-polyhedra) 3) when both H- and V-polyhedral representations are available. Both the bounded (polytopes) and the unbounded case are considered. We show that the first two problems are polynomially solvable, and that the third problem is solvable in linear time.Alberto Bemporadalberto.bemporad@imtlucca.itKomei FukudaFabio Danilo Torrisi2011-07-27T09:11:21Z2014-07-17T12:17:38Zhttp://eprints.imtlucca.it/id/eprint/568This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5682011-07-27T09:11:21ZPiecewise linear optimal controllers for hybrid systemsWe propose a procedure for synthesizing piecewise linear optimal controllers for discrete-time hybrid systems. A stabilizing controller is obtained by designing a model predictive controller, which is based on the minimization of a weighted l1/∞-norm of the tracking error and the input trajectories over a finite horizon. The control law is obtained by solving a multiparametric mixed-integer linear program, which avoids solving mixed-integer programs online. As the resulting control law is piecewise affine, online computation is drastically reduced to a simple linear function evaluationAlberto Bemporadalberto.bemporad@imtlucca.itFrancesco BorrelliManfred Morari2011-07-27T09:11:18Z2014-07-17T12:17:22Zhttp://eprints.imtlucca.it/id/eprint/572This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5722011-07-27T09:11:18ZOptimal controllers for hybrid systems: stability and piecewise linear explicit formWe propose a procedure for synthesizing piecewise linear optimal controllers for hybrid systems and investigate conditions for closed-loop stability. Hybrid systems are modeled in discrete-time within the mixed logical dynamical framework, or, equivalently, as piecewise affine systems. A stabilizing controller is obtained by designing a model predictive controller, which is based on the minimization of a weighted 1/∞-norm of the tracking error and the input trajectories over a finite horizon. The control law is obtained by solving a mixed-integer linear program (MILP) which depends on the current state. Although efficient branch and bound algorithms exist to solve MILPs, these are known to be NP-hard problems, which may prevent their online solution if the sampling-time is too small for the available computation power. Rather than solving the MILP online, we propose a different approach where all the computation is moved off line, by solving a multiparametric MILP. As the resulting control law is piecewise affine, online computation is drastically reduced to a simple linear function evaluation. An example of piecewise linear optimal control of a heat exchange system shows the potential of the methodAlberto Bemporadalberto.bemporad@imtlucca.itFrancesco BorrelliManfred Morari2011-07-27T09:11:08Z2014-07-17T12:49:10Zhttp://eprints.imtlucca.it/id/eprint/582This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5822011-07-27T09:11:08ZDiscrete-time hybrid modeling and verificationFor hybrid systems described by interconnections of linear dynamical systems and logic devices, we recently (A. Bemporad et al., 2000, 2001) proposed mixed logical-dynamical (MLD) systems and the language HYSDEL (HYbrid System DEscription Language) as a modeling tool. For MLD models, we developed a reachability analysis algorithm which combines forward reach-set computation and feasibility analysis of trajectories by linear and mixed-integer linear programming. In this paper, the versatility of the overall analysis tool is illustrated in the verification of an automotive cruise control system for a car with a robotized manual gear shiftFabio Danilo TorrisiAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:11:06Z2014-07-17T12:48:51Zhttp://eprints.imtlucca.it/id/eprint/581This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5812011-07-27T09:11:06ZAn algorithm for multi-parametric quadratic programming and explicit MPC solutionsExplicit solutions to constrained linear model-predictive control (MPC) problems can be obtained by solving multi-parametric quadratic programs (mp-QP) where the parameters are the components of the state vector. We study the properties of the polyhedral partition of the state space induced by the multi-parametric piecewise linear solution and propose a new mp-QP solver. Compared to existing algorithms, our approach adopts a different exploration strategy for subdividing the parameter space, avoiding unnecessary partitioning and QP problem solving, with a significant improvement in efficiencyPetter TondelTor Arne JohansenAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:09:10Z2014-07-17T12:47:36Zhttp://eprints.imtlucca.it/id/eprint/585This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5852011-07-27T09:09:10ZIdentification of hybrid systems via mixed-integer programmingAddresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes and Wiener piecewise affine autoregressive exogenous models. In particular, we provide algorithms based on mixed-integer linear or quadratic programming which are guaranteed to converge to a global optimumAlberto Bemporadalberto.bemporad@imtlucca.itJacob RollLennart Ljung2011-07-27T09:09:07Z2014-07-17T12:47:14Zhttp://eprints.imtlucca.it/id/eprint/577This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5772011-07-27T09:09:07ZOptimization-based hybrid control toolsThe paper discusses a framework for modeling, analyzing and controlling systems whose behavior is governed by interdependent physical laws, logic rules, and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. They are described by linear dynamic equations subject to linear inequalities involving real and integer variables. MLD models are equivalent to various other system descriptions like Piecewise Affine (PWA) systems and Linear Complementarity (LC) systems. They have the advantage, however, that many problems of system analysis (like reachability/controllability, observability, and verification) and many problems of synthesis (like controller design and filter design) can be readily expressed as mixed integer linear or quadratic programs, for which many commercial software packages exist. In this paper we first recall MLD models and the modeling language HYSDEL (HYbrid Systems DEscription Language). Subsequently, we illustrate the use of Model Predictive Control (MPC) based on mixed-integer programming for hybrid MLD models, and the use of multiparametric programming for obtaining explicitly the equivalent piecewise linear control form of MPC. The eventual practical success of these methods will depend on progress in the development of the various optimization algorithms and tools so that problems of realistic size can be tackledAlberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T09:09:02Z2014-07-17T12:46:56Zhttp://eprints.imtlucca.it/id/eprint/584This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5842011-07-27T09:09:02ZOn hybrid systems and closed-loop MPC systemsThe following five classes of hybrid systems were proved by W.P.M.H. Heemels et al. (2001) to be equivalent: linear complementarity (LC) systems, extended linear complementarity (ELC) systems, mixed logical-dynamical (MLD) systems, piecewise affine (PWA) systems and max-min-plus-scaling (MMPS) systems. Some of the equivalences were obtained under additional assumptions, such as boundedness of system variables. In this paper, for closed-loop linear or hybrid plants with model-predictive control (MPC) based on a linear model and fulfilling linear constraints on the input and state variables, we provide a simple and direct proof that the closed-loop system (cl-MPC) is a subclass of any of the former five classes of hybrid systems. This result opens up the use of tools developed for hybrid systems (such as stability, robust stability and safety analysis tools) to study the closed-loop properties of MPCAlberto Bemporadalberto.bemporad@imtlucca.itW.P.M.H. HeemelsBart De Schutter2011-07-27T09:08:58Z2014-07-17T12:46:26Zhttp://eprints.imtlucca.it/id/eprint/586This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5862011-07-27T09:08:58ZSuboptimal explicit MPC via approximate multiparametric quadratic programmingAlgorithms for solving multiparametric quadratic programming (mp-QP) were proposed in Bemporad et al. (2001) and Tondel et al. (2001) for computing explicit model predictive control (MPC) laws. The reason for this interest is that the solution to mp-QP is a piecewise affine function of the state vector and thus it is easily implementable on-line. The main drawback of solving mp-QP exactly is that whenever the number of linear constraints involved in the optimization problem increases, the number of polyhedral cells in the piecewise affine partition of the parameter space may increase exponentially. We address the problem of finding approximate solutions to mp-QP, where the degree of approximation is arbitrary and allows a trade off between optimality and a smaller number of cells in the piecewise affine solutionAlberto Bemporadalberto.bemporad@imtlucca.itCarlo Filippi2011-07-27T09:08:55Z2014-07-09T14:43:59Zhttp://eprints.imtlucca.it/id/eprint/580This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5802011-07-27T09:08:55ZEfficient on-line computation of constrained optimal control For discrete-time linear time-invariant systems with constraints on inputs and outputs, the constrained finite-time optimal controller can be obtained explicitly as a piecewise-affine function of the initial state via multi-parametric programming. By exploiting the properties of the value function, we present two algorithms that efficiently perform the online evaluation of the explicit optimal control law both in terms of storage demands and computational complexity. The algorithms are particularly effective when used for model-predictive control (MPC) where an open-loop constrained finite-time optimal control problem has to be solved at each sampling timeFrancesco BorrelliMato BaoticAlberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T09:08:53Z2014-07-17T12:46:08Zhttp://eprints.imtlucca.it/id/eprint/578This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5782011-07-27T09:08:53ZPiecewise linear robust model predictive controlFor discrete-time linear time-invariant systems with input disturbances and constraints on inputs and states, we develop an algorithm to determine explicitly, as a function of the initial state, the solution to robust optimal control problems based on min-max optimization. We show that the optimal control sequence is a piecewise linear function of the initial state. Thus, when the optimal control problem is solved at each time step according to a moving horizon scheme, the on-line computation of the resulting MPC controller is reduced to a simple linear function evaluation. In this paper the uncertainty is modeled as an additive norm-bounded input disturbance vector. The technique can be also extended to robust control of constrained systems affected by polyhedral parametric uncertainty.Alberto Bemporadalberto.bemporad@imtlucca.itFrancesco BorrelliManfred Morari2011-07-27T09:08:46Z2014-07-17T12:39:43Zhttp://eprints.imtlucca.it/id/eprint/458This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4582011-07-27T09:08:46ZDiscrete-time hybrid modeling and verification of the batch evaporator process benchmarkFor hybrid systems described by interconnections of linear discrete-time dynamical systems, automata, and propositional logic rules, we recently proposed the Mixed Logical Dynamical (MLD) systems formalism and the language HYSDEL (Hybrid System Descrip- tion Language) as a modeling tool. For MLD models, we developed a reachability analysis algorithm which combines forward reach set computation and feasibility analysis of trajectories by linear and mixed-integer linear programming. In this paper the versatility of the overall analysis tool is illustrated on the batch evaporator benchmark process. Alberto Bemporadalberto.bemporad@imtlucca.itFabio Danilo TorrisiManfred Morari2011-07-27T09:08:04Z2011-08-08T08:13:22Zhttp://eprints.imtlucca.it/id/eprint/547This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5472011-07-27T09:08:04ZComputation and approximation of piecewise affine control via binary search treeWe present an algorithm for generating a binary search tree that allows efficient computation of piecewise affine (PWA) functions defined on a polyhedral partition. This is useful for PWA control approaches, such as explicit model predictive control (MPC), as it allows the controller to be implemented on-line with small computational effort. The computation time is logarithmic in the number of regions in the PWA partition. A method for generating an approximate PWA function based on a binary search tree is also presented, giving further simplification of PWA control.Petter TondelTor Arne JohansenAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:08:02Z2011-08-08T08:11:46Zhttp://eprints.imtlucca.it/id/eprint/588This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5882011-07-27T09:08:02ZScheduling of hybrid systems: multi product batch plantThe paper proposes a solution to a class of scheduling problems where the goal is to minimize the schedule (production) time. The algorithm. which takes into account a model of a hybrid system described as MLD (mixed logical dynamical) system, is based on performance driven reachability analysis. The algorithm abstracts the behavior of the hybrid system by building a tree of evolution. Nodes of the tree represent reachable states of a process, and the branches connect two nodes if a transition exists between the corresponding states. To each node a cost function value is associated and based on this value. the tree exploration is driven. As soon as the tree is explored. the global solution to the scheduling problem is obtained.Bostjan PotocnikAlberto Bemporadalberto.bemporad@imtlucca.itFabio Danilo TorrisiGasper MusicBorut Zupancic2011-07-27T09:08:00Z2011-08-04T07:29:09Zhttp://eprints.imtlucca.it/id/eprint/590This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5902011-07-27T09:08:00ZAn iterative algorithm for the optimal control of continuous-time switched linear systemsFor continuous-time switched linear systems, this paper proposes an approach for solving infinite-horizon optimal control problems where the decision variables are the switching instants and the sequence of operating modes. The procedure iterates between a "master" procedure that finds an optimal switching sequence of modes, and a "slave" procedure that finds the optimal switching instants. The effectiveness of the approach is shown through simple simulation examples.Alberto Bemporadalberto.bemporad@imtlucca.itAlessandro GiuaCarla Seatzu2011-07-27T09:07:50Z2011-08-08T08:09:47Zhttp://eprints.imtlucca.it/id/eprint/587This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5872011-07-27T09:07:50ZMax-plus-algebraic problems and the extended linear complementarity problem - algorithmic aspectsMany fundamental problems in the max-plus-algebraic system theory for discrete event systems--among which the minimal state space realization problem--can be solved using an Extended Linear Complementarity Problem (ELCP). We present some new, more efficient methods to solve the ELCP. We show that an ELCP with a bounded feasible set can be recast as a standard Linear Complementarity Problem (LCP). Our proof results in three possible numerical solution methods for a given ELCP: regular ELCP algorithms, mixed integer linear programming algorithms, and regular LCP algorithms. We also apply these three methods to a basic max-plus-algebraic benchmark problem.Bart De SchutterW.P.M.H. HeemelsAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:05:54Z2011-08-04T07:29:09Zhttp://eprints.imtlucca.it/id/eprint/444This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4442011-07-27T09:05:54ZThe Explicit Linear Quadratic Regulator for Constrained SystemsFor discrete-time linear time invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly, the state feedback control law which minimizes a quadratic performance criterion. We show that the control law is piece-wise linear and continuous for both the finite horizon problem (model predictive control) and the usual infinite time measure (constrained linear quadratic regulation). Thus, the on-line control computation reduces to the simple evaluation of an explicitly defined piecewise linear function. By computing the inherent underlying controller structure, we also solve the equivalent of the Hamilton–Jacobi–Bellman equation for discrete-time linear constrained systems. Control based on on-line optimization has long been recognized as a superior alternative for constrained systems. The technique proposed in this paper is attractive for a wide range of practical problems where the computational complexity of on-line optimization is prohibitive. It also provides an insight into the structure underlying optimization-based controllers.Alberto BemporadManfred MorariVivek DuaEfstratios N. Pistikopoulos2011-07-27T09:05:50Z2011-08-08T08:07:22Zhttp://eprints.imtlucca.it/id/eprint/486This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4862011-07-27T09:05:50ZOn-line optimization via off-line parametric optimization toolsIn this paper, model predictive control (MPC) based previous termoptimizationnext term problems with a quadratic performance criterion and linear constraints are formulated as multi-previous termparametricnext term quadratic programs (mp-QP), where the input and state variables, corresponding to a plant model, are treated as previous termoptimizationnext term variables and parameters, respectively. The solution of such problems is given by (i) a complete set of profiles of all the optimal inputs to the plant as a function of state variables, and (ii) the regions in the space of state variables where these functions remain optimal. It is shown that these profiles are linear and the corresponding regions are described by linear inequalities. An algorithm for obtaining these profiles and corresponding regions of optimality is also presented. The key feature of the proposed approach is that the on-previous termline optimizationnext term problem is solved previous termoff-line via parametricnext term programming techniques. Hence (i) no previous termoptimizationnext term solver is called on-previous termline,next term and (ii) only simple function evaluations are required, to obtain the optimal inputs to the plant for the current state of the plant.Efstratios N. PistikopoulosVivek DuaNikolaos A. BozinisAlberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T09:05:45Z2014-07-17T12:51:46Zhttp://eprints.imtlucca.it/id/eprint/449This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4492011-07-27T09:05:45ZOn the equivalence of linear complementarity problemsWe show that the Extended Linear Complementarity Problem (ELCP) can be recast as a standard Linear Complementarity Problem (LCP) provided that the surplus variables or the feasible set of the ELCP are bounded. Since many extensions of the LCP are special cases of the ELCP, this implies that these extensions can be rewritten as an LCP as well. Our equivalence proof is constructive and leads to three possible numerical solution methods for a given ELCP: regular ELCP algorithms, mixed integer linear programming algorithms, and regular LCP algorithms.Bart De SchutterW.P.M.H. HeemelsAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:05:40Z2014-07-17T12:50:59Zhttp://eprints.imtlucca.it/id/eprint/550This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5502011-07-27T09:05:40ZA master-slave algorithm for the optimal control of continuous-time switched affine systemsFor continuous-time switched affine systems, this paper proposes an approach for solving infinite-horizon optimal control problems where the decision variables are the switching instants and the sequence of operating modes. The procedure iterates between a "master" procedure that finds an optimal switching sequence of modes, and a "slave" procedure that finds the optimal switching instants.Alberto Bemporadalberto.bemporad@imtlucca.itAlessandro GiuaCarla Seatzu2011-07-27T09:05:38Z2014-07-17T12:50:41Zhttp://eprints.imtlucca.it/id/eprint/549This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5492011-07-27T09:05:38ZSynthesis of state-feedback optimal controllers for switched linear systemsThe paper deals with the optimal control of switched piecewise linear autonomous systems, where the objective is to minimize a performance index over an infinite time horizon. We assume that the switching sequence has a finite length: the unknown switching times and the switching sequence are the optimization parameters. We also assume that a cost may be associated to each switch. The optimal control for this class of systems takes the form of a state feedback, i.e., it is possible to identify a set of regions of the state space such that an optimal switch should occur if and only if the present state belongs to one of them. We show how the tables containing these regions can be computed off-line through a numerical procedure.Alberto Bemporadalberto.bemporad@imtlucca.itAlessandro GiuaCarla Seatzu2011-07-27T09:02:33Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/560This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5602011-07-27T09:02:33ZMultiparametric nonlinear integer programming and explicit quantized optimal controlThis paper deals with multiparametric nonlinear integer programming problems where the optimization variables belong to a finite set and where the cost function and the constraints depend in an arbitrary nonlinear fashion on the optimization variables and in a linear fashion on the parameters. We examine the main theoretical properties of the optimizer and of the optimum as a function of the parameters, and propose a solution algorithm. The methodology is employed to investigate properties of quantized optimal control laws and optimal performance, and to obtain their explicit representation as a function of the state vector.Alberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:53:56Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/525This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5252011-07-27T08:53:56ZSAT-based branch & bound and optimal control of hybrid dynamical systemsA classical hybrid MIP-CSP approach for solving problems having a logical part and a mixed integer programming part is presented. A Branch and Bound procedure combines an MIP and a SAT solver to determine the optimal solution of a general class of optimization problems. The procedure explores the search tree, by solving at each node a linear relaxation and a satisfiability problem, until all integer variables of the linear relaxation are set to an integer value in the optimal solution. When all integer variables are fixed the procedure switches to the SAT solver which tries to extend the solution taking into account logical constraints. If this is impossible, a ldquono-goodrdquo cut is generated and added to the linear relaxation. We show that the class of problems we consider turns out to be very useful for solving complex optimal control problems for linear hybrid dynamical systems formulated in discrete-time. We describe how to model the ldquohybridrdquo dynamics so that the optimal control problem can be solved by the hybrid MIP+SAT solver, and show that the achieved performance is superior to the one achieved by commercial MIP solvers.Alberto Bemporadalberto.bemporad@imtlucca.itNicolò Giorgetti2011-07-27T08:53:53Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/504This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5042011-07-27T08:53:53ZA greedy approach to identification of piecewise affine modelsThis paper addresses the problem of identification of piecewise affine (PWA) models. This problem involves the estimation from data of both the parameters of the affine submodels and the partition of the PWA map. The procedure that we propose for PWA identification exploits a greedy strategy for partitioning an infeasible system of linear inequalities into a minimum number of feasible subsystems: this provides an initial clustering of the datapoints. Then a refinement procedure is applied repeatedly to the estimated clusters in order to improve both the data classification and the parameter estimation. The partition of the PWA map is finally estimated by considering pairwise the clusters of regression vectors, and by finding a separating hyperplane for each of such pairs. We show that our procedure does not require to fix a priori the number of affine submodels, which is instead automatically estimated from the data. Alberto Bemporadalberto.bemporad@imtlucca.itAndrea GarulliSimone PaolettiAntonio Vicino2011-07-27T08:53:49Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/566This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5662011-07-27T08:53:49ZData classification and parameter estimation for the identification of piecewise affine modelsThis paper proposes a three-stage procedure for parametric identification of piece wise affine auto regressive exogenous (PWARX) models. The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the MIN PFS problem (partition into a minimum number of feasible subsystems) for a set of linear complementary inequalities derived from input-output data. Then, a refinement procedure reduces misclassifications and improves parameter estimates. The last stage determines a polyhedral partition of the regressor set via two-class or multi-class linear separation techniques. As a main feature, the algorithm imposes that the identification error is bounded by a fixed quantity δ. Such a bound is a useful tuning parameter to trade off between quality of fit and model complexity. Ideas for efficiently addressing the MIN PFS problem, and for improving data classification are also discussed in the paper. The performance of the proposed identification procedure is demonstrated on experimental data from an electronic component placement process in a pick-and-place machine.Alberto Bemporadalberto.bemporad@imtlucca.itAndrea GarulliSimone PaolettiAntonio Vicino2011-07-27T08:53:46Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/463This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4632011-07-27T08:53:46ZEfficient conversion of mixed logical dynamical systems into an equivalent piecewise affine formFor hybrid systems described by switched linear difference equations, linear threshold conditions, automata, and propositional logic conditions, described in mixed logical dynamical form, this note describes two algorithms for transforming such systems into an equivalent piecewise affine form, where equivalent means that for the same initial conditions and input sequences the trajectories of the system are identical. The proposed techniques exploit ideas from mixed-integer programming and multiparametric programming.
Alberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:53:28Z2014-07-08T13:58:48Zhttp://eprints.imtlucca.it/id/eprint/470This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4702011-07-27T08:53:28ZInner and outer approximation of polytopes using boxesThis paper deals with the problem of approximating a convex polytope in any finite dimension by a collection of (hyper)boxes. More exactly, given a polytope by a system of linear inequalities, we look for two collections and of boxes with non-overlapping interiors such that the union of all boxes in is contained in and the union of all boxes in contains . We propose and test several techniques to construct and aimed at getting a good balance between two contrasting objectives: minimize the volume error and minimize the total number of generated boxes. We suggest how to modify the proposed techniques in order to approximate the projection of onto a given subspace without computing the projection explicitly.Alberto Bemporadalberto.bemporad@imtlucca.itCarlo FilippiFabio Danilo Torrisi2011-07-27T08:47:42Z2011-08-05T13:54:34Zhttp://eprints.imtlucca.it/id/eprint/564This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5642011-07-27T08:47:42ZA dynamic programming approach for determining the explicit solution of MPC controllersRecently multi-parametric methods have been applied with success to model predictive control (MPC) schemes. In this paper we propose a novel method for linear systems to obtain the explicit description of the control law that is based on dynamic programming and exploits the structure of the MPC formulation.David Muñoz de la PeñaTeodoro AlamoAlberto Bemporadalberto.bemporad@imtlucca.itEduardo F. Camacho2011-07-27T08:47:36Z2011-08-05T13:54:10Zhttp://eprints.imtlucca.it/id/eprint/521This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5212011-07-27T08:47:36ZStabilization conditions for model predictive control of constrained PWA systemsModel predictive control (MPC) has recently been applied to several relevant classes of hybrid systems with promising results. These developments generated an increasing interest towards issues such as stability and computational problems that arise in hybrid MPC. Stability aspects have been addressed only marginally. In this paper we present an extension of the terminal cost and constraint set method for guaranteeing stability in MPC to the class of constrained piecewise affine systems. Semidefinite programming is used to calculate the employed terminal weight matrix that ensures stability for quadratic cost based MPC. A procedure for computing a robust positively invariant set for piecewise linear systems is also developed. The implementation of the proposed method is illustrated by an example.Mircea LazarW.P.M.H. HeemelsSiep WeilandAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:47:30Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/522This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5222011-07-27T08:47:30ZExplicit hybrid optimal control of direct injection stratified charge enginesThis paper illustrates the application of hybrid
modeling and receding horizon optimal control techniques
to the problem of air-to-fuel ratio and torque management
in advanced technology gasoline direct injection stratified
charge (DISC) engines. A DISC engine represents an example
of a constrained hybrid system, because it can operate
in two discrete modes (stratified and homogeneous) and
because the mode-dependent constraints on the air-to-fuel
ratio and on the spark timing need to be enforced. The paper
extends the prior work by the authors [1] and reports the
development of an explicit controller which implements the
optimal solution using piecewise affine functions of the state, thereby avoiding the need for on-line optimization. Strategies to simplify the explicit controller by reducing the number of regions in its characterization are discussed.Nicolò GiorgettiAlberto Bemporadalberto.bemporad@imtlucca.itIlya KolmanovskyDavor Hrovat2011-07-27T08:47:28Z2011-08-05T13:53:02Zhttp://eprints.imtlucca.it/id/eprint/533This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5332011-07-27T08:47:28ZA decomposition algorithm for feedback min-max model predictive controlAn algorithm for solving feedback min-max model predictive control for discrete time uncertain linear systems with constraints is presented in the paper. The algorithm solves the corresponding multi-stage min-max linear optimization problem. It is based on applying recursively a decomposition technique to solve the min-max problem via a sequence of low complexity linear programs. It is proved that the algorithm converges to the optimal solution in finite time. Simulation results are provided to compare the proposed algorithm with other approaches. David Muñoz de la PeñaAlberto Bemporadalberto.bemporad@imtlucca.itTeodoro Alamo2011-07-27T08:47:26Z2011-08-05T13:52:41Zhttp://eprints.imtlucca.it/id/eprint/534This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5342011-07-27T08:47:26ZStochastic programming applied to model predictive controlMany robust model predictive control (MPC) schemes are based on min-max optimization, that is, the future control input trajectory is chosen as the one which minimizes the performance due to the worst disturbance realization. In this paper we take a different route to solve MPC problems under uncertainty. Disturbances are modelled as random variables and the expected value of the performance index is minimized. The MPC scheme that can be solved using Stochastic Programming (SP), for which several efficient solution techniques are available. We show that this formulation guarantees robust constraint fulfillment and that the expected value of the optimum cost function of the closed loop system decreases at each time step. David Muñoz de la PeñaAlberto Bemporadalberto.bemporad@imtlucca.itTeodoro Alamo2011-07-27T08:47:24Z2011-08-05T13:52:14Zhttp://eprints.imtlucca.it/id/eprint/526This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5262011-07-27T08:47:24ZInfinity norms as Lyapunov functions for model predictive control of constrained PWA systemsIn this paper we develop a priori stabilization conditions for infinity norm based hybrid MPC in the terminal cost and constraint set fashion. Closed-loop stability is achieved using infinity norm inequalities that guarantee that the value function corresponding to the MPC cost is a Lyapunov function of the controlled system. We show that Lyapunov asymptotic stability can be achieved even though the MPC value function may be discontinuous. One of the advantages of this hybrid MPC scheme is that the terminal constraint set can be directly obtained as a sublevel set of the calculated terminal cost, which is also a local piecewise linear Lyapunov function. This yields a new method to obtain positively invariant sets for PWA systems. Mircea LazarW.P.M.H. HeemelsSiep WeilandAlberto Bemporadalberto.bemporad@imtlucca.itOctavian Pastravanu2011-07-27T08:47:22Z2011-08-05T13:51:39Zhttp://eprints.imtlucca.it/id/eprint/530This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5302011-07-27T08:47:22ZOn the stability and robustness of non-smooth nonlinear MPCThis paper considers discrete-time nonlinear, possibly discontinuous, systems in closed-loop with Model Predictive
Controllers (MPC). The aim of the paper is to provide a priori sufficient conditions for asymptotic stability in
the Lyapunov sense and robust stability, while allowing for both the system dynamics and the value function of the MPC cost (the usual candidate Lyapunov function in MPC) to be discontinuous functions of the state. The motivation for this work lies in the recent development of MPC for hybrid systems, which are inherently discontinuous and nonlinear systems. As an application of the general theory, it is shown that Lyapunov stability is achieved in hybrid MPC. For a particular class of piecewise affine systems, a modified MPC set-up is proposed, which is proven to be robust to small additive disturbances via an input-to-state stability argument.Mircea LazarW.P.M.H. HeemelsAlberto Bemporadalberto.bemporad@imtlucca.itSiep Weiland2011-07-27T08:45:21Z2011-08-04T07:29:07Zhttp://eprints.imtlucca.it/id/eprint/529This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5292011-07-27T08:45:21ZPassivity analysis and passification of discrete-time hybrid systemsThis paper proposes several (sufficient) criteria based on the numerical solution of systems of linear matrix inequalities (LMIs) for proving the passivity of discrete-time hybrid systems in piecewise affine form, and for the synthesis of switched linear control laws that enforce passivity.Alberto Bemporadalberto.bemporad@imtlucca.itGianni BianchiniFilippo BrogiFederico Barbagli2011-07-27T08:45:16Z2011-08-05T13:48:46Zhttp://eprints.imtlucca.it/id/eprint/528This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5282011-07-27T08:45:16ZOn the stability of quadratic forms based model predictive control of constrained PWA systemsIn this paper we investigate the stability of discrete-time PWA systems in closed-loop with quadratic cost based Model Predictive Controllers (MPC) and we derive a priori sufficient conditions for Lyapunov asymptotic stability.
We prove that Lyapunov stability can be achieved for the
closed-loop system even though the considered Lyapunov
function and the system dynamics may be discontinuous.
The stabilization conditions are derived using a terminal
cost and constraint set method. An S-procedure technique
is employed to reduce conservativeness of the stabilization
conditions and a linear matrix inequalities set-up is developed in order to calculate the terminal cost. A new algorithm for computing piecewise polyhedral positively invariant sets for PWA systems is also presented. In this manner, the on-line optimization problem associated with MPC leads to a mixed integer quadratic programming problem, which can be solved by standard optimization tools.Mircea LazarW.P.M.H. HeemelsSiep WeilandAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:45:11Z2011-08-04T07:29:07Zhttp://eprints.imtlucca.it/id/eprint/453This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4532011-07-27T08:45:11ZA bounded-error approach to piecewise affine system identificationThis paper proposes a three-stage procedure for parametric identification of piecewise affine autoregressive exogenous (PWARX) models. The first stage simultaneously classifies the data points and estimates the number of submodels and the corresponding parameters by solving the partition into a minimum number of feasible subsystems (MIN PFS) problem for a suitable set of linear complementary inequalities derived from data. Second, a refinement procedure reduces misclassifications and improves parameter estimates. The third stage determines a polyhedral partition of the regressor set via two-class or multiclass linear separation techniques. As a main feature, the algorithm imposes that the identification error is bounded by a quantity δ. Such a bound is a useful tuning parameter to trade off between quality of fit and model complexity. The performance of the proposed PWA system identification procedure is demonstrated via numerical examples and on experimental data from an electronic component placement process in a pick-and-place machine.Alberto Bemporadalberto.bemporad@imtlucca.itAndrea GarulliSimone PaolettiAntonio Vicino2011-07-27T08:45:09Z2011-08-05T13:46:22Zhttp://eprints.imtlucca.it/id/eprint/452This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4522011-07-27T08:45:09ZDynamic programming for constrained optimal control of discrete-time linear hybrid systemsIn this paper we study the solution to optimal control problems for constrained discrete-time linear hybrid systems based on quadratic or linear performance criteria. The aim of the paper is twofold. First, we give basic theoretical results on the structure of the optimal state-feedback solution and of the value function. Second, we describe how the state-feedback optimal control law can be constructed by combining multiparametric programming and dynamic programming.Francesco BorrelliMato BaoticAlberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T08:45:04Z2014-03-05T13:44:04Zhttp://eprints.imtlucca.it/id/eprint/536This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5362011-07-27T08:45:04ZEvent-driven optimal control of integral continuous-time hybrid automataThis paper proposes an event-driven optimal control trategy for hybrid systems composed of continuous-time integral dynamics with inputs and of Anite state machines triggered by endgenous and exogenous events. Endogenous events are caused by continuous states or continuous inputs crossing certain linear thresholds or by the elapse of time intervals, while exogenous events are forced by changes of binary and continuous inputs. The advantages of the roposed strategy are the reduction of the amount of computation required to solve optimal control problems, and the reduction of approximation errors typical of discrete-time approaches. We examine several performance objectives and constraints that lead to mixed-integerlinear or quadratic optimization problems and we exemplify the approach on a simple example.Alberto Bemporadalberto.bemporad@imtlucca.itStefano Di CairanoJorge Júlvez2011-07-27T08:44:59Z2011-08-04T07:29:07Zhttp://eprints.imtlucca.it/id/eprint/503This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5032011-07-27T08:44:59ZOptimal control of discrete hybrid stochastic automataThis paper focuses on hybrid systems whose discrete state transitions depend on both deterministic and stochastic events. For such systems, after introducing a suitable hybrid model called Discrete Hybrid Stochastic Automaton (DHSA), different finite-time optimal control approaches are examined: (1) Stochastic Hybrid Optimal Control (SHOC), that “optimistically” determines the trajectory providing the best trade off between the tracking performance and the probability that stochastic events realize as expected, under specified chance constraints; (2) Robust Hybrid Optimal Control (RHOC) that, in addition, less optimistically, ensures that the system remains within a specified safety region for all possible realizations of stochastic events. Sufficient conditions for the asymptotic convergence of the state vector are given for receding-horizon implementations of the above schemes. The proposed approaches are exemplified on a simple benchmark problem in production system management. Alberto Bemporadalberto.bemporad@imtlucca.itStefano Di Cairano2011-07-27T08:44:57Z2011-08-04T07:29:07Zhttp://eprints.imtlucca.it/id/eprint/535This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5352011-07-27T08:44:57ZPassivity analysis of discrete-time hybrid systems using piecewise polynomial storage functionsThis paper proposes some sufficient criteria based on the computation of polynomial and piecewise polynomial storage functions for checking passivity of discrete-time hybrid systems in piecewise affine or piecewise polynomial form. The computation of such storage functions is performed by means of convex optimization techniques via the sum of squares decomposition of multivariate polynomials.Alberto Bemporadalberto.bemporad@imtlucca.itGianni BianchiniFilippo BrogiGraziano Chesi2011-07-27T08:44:00Z2011-08-05T13:44:03Zhttp://eprints.imtlucca.it/id/eprint/537This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5372011-07-27T08:44:00ZFeedback min-max model predictive control based on a quadratic cost functionFeedback min-max model predictive control based on a quadratic cost function is addressed in this paper. The main contribution is an algorithm for solving the min-max quadratic MPC problem with an arbitrary degree of approximation. The paper also introduces the "recourse horizon", which allows one to obtain a trade-off between computational complexity and performance of the control law. The results are illustrated by means of a simulation of a quadruple-tank processDavid Muñoz de la PeñaTeodoro AlamoAlberto Bemporadalberto.bemporad@imtlucca.itEduardo F. Camacho2011-07-27T08:43:54Z2013-09-13T09:50:06Zhttp://eprints.imtlucca.it/id/eprint/492This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4922011-07-27T08:43:54ZAn algorithm for approximate multiparametric convex programmingFor multiparametric convex nonlinear programming problems we propose a recursive algorithm for approximating, within a given suboptimality tolerance, the value function and an optimizer as functions of the parameters. The approximate solution is expressed as a piecewise affine function over a simplicial partition of a subset of the feasible parameters, and it is organized over a tree structure for efficiency of evaluation. Adaptations of the algorithm to deal with multiparametric semidefinite programming and multiparametric geometric programming are provided and exemplified. The approach is relevant for real-time implementation of several optimization-based feedback control strategies. Alberto Bemporadalberto.bemporad@imtlucca.itCarlo Filippi2011-07-27T08:43:43Z2011-08-05T13:38:38Zhttp://eprints.imtlucca.it/id/eprint/538This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5382011-07-27T08:43:43ZSquaring the circle: An algorithm for generating polyhedral invariant sets from ellipsoidal onesThis paper presents a new (geometrical) approach to the computation of polyhedral positively invariant sets for general (possibly discontinuous) nonlinear systems, possibly affected by disturbances. Given a beta-contractive ellipsoidal set E, the key idea is to construct a polyhedral set that lies between the ellipsoidal sets betaE and E. A proof that the resulting polyhedral set is positively invariant (and contractive under an additional assumption) is given, and a new algorithm is developed to construct the desired polyhedral set. An advantage of the proposed method is that the problem of computing polyhedral invariant sets is formulated as a number of quadratic programming (QP) problems. The number of QP problems is guaranteed to be finite and therefore, the algorithm has finite termination. An important application of the proposed algorithm is the computation of polyhedral terminal constraint sets for model predictive control based on quadratic costsMircea LazarAlessandro AlessioAlberto Bemporadalberto.bemporad@imtlucca.itW.P.M.H. Heemels2011-07-27T08:43:40Z2011-08-05T13:37:53Zhttp://eprints.imtlucca.it/id/eprint/543This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5432011-07-27T08:43:40ZConvex Polyhedral Invariant Sets for Closed-Loop Linear MPC Systems Given an asymptotically stabilizing linear MPC controller, this paper proposes an algorithm to construct invariant polyhedral sets for the closed-loop system. Rather than exploiting an explicit form of the MPC controller, the approach exploits a recently developed DC (Difference of Convex functions) programming technique developed by the authors to construct a polyhedral set in between two convex sets. Here, the inner convex set is any given level set V(x) les gamma of the MPC value function (implicitly defined by the quadratic programming problem associated with MPC or explicitly computed via multiparametric quadratic programming), while the outer convex set is the level set of a the value function of a modified multiparametric quadratic program (implicitly or explicitly defined). The level gamma acts as a tuning parameter for deciding the size of the polyhedral invariant containing the inner set, ranging from the origin (gamma = 0) to the maximum invariant set around the origin where the solution to the unconstrained MPC problem remains feasible, up to the whole domain of definition of the controller (possibly the whole state space Ropfn) (gamma = inf). Potential applications of the technique include reachability analysis of MPC systems and generation of constraints to supervisory decision algorithms on top of MPC loopsAlessandro AlessioAlberto Bemporadalberto.bemporad@imtlucca.itW.P.M.H. HeemelsMircea Lazar2011-07-27T08:40:40Z2011-08-05T13:20:31Zhttp://eprints.imtlucca.it/id/eprint/489This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4892011-07-27T08:40:40ZRobust explicit MPC based on approximate multi-parametric convex programmingMany robust model predictive control (MPC) schemes require the online solution of a computationally demanding convex program. For deterministic MPC schemes, multiparametric programming was successfully applied to move offline most of the computation. In this paper, we adopt a general approximate multiparametric algorithm recently suggested for convex problems and propose to apply it to a classical robust MPC scheme. This approach enables one to implement a robust MPC controller in real time for systems with polytopic uncertainty, ensuring robust constraint satisfaction and robust convergence to a given bounded setDavid Muñoz de la PeñaAlberto Bemporadalberto.bemporad@imtlucca.itCarlo Filippi2011-07-27T08:40:35Z2011-08-05T13:20:08Zhttp://eprints.imtlucca.it/id/eprint/490This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4902011-07-27T08:40:35ZA decomposition algorithm for feedback min-max model predictive controlAn algorithm for solving feedback min-max model predictive control for discrete-time uncertain linear systems with constraints is presented in this note. The algorithm is based on applying recursively a decomposition technique to solve the min-max problem via a sequence of low complexity linear programs. It is proved that the algorithm converges to the optimal solution in finite time. Simulation results are provided to compare the proposed algorithm with other approachesDavid Muñoz de la PeñaTeodoro AlamoAlberto Bemporadalberto.bemporad@imtlucca.itEduardo F. Camacho2011-07-27T08:39:18Z2011-08-05T13:17:43Zhttp://eprints.imtlucca.it/id/eprint/516This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5162011-07-27T08:39:18ZDiscrete-time non-smooth nonlinear MPC: Stability and robustnessThis paper considers discrete-time nonlinear, possibly discontinuous, systems in closed-loop with model predictive controllers (MPC). The aim of the paper is to provide a priori sufficient conditions for asymptotic stability in the Lyapunov sense and input-to-state stability (ISS), while allowing for both the system dynamics and the value function of the MPC cost to be discontinuous functions of the state. The motivation for this work lies in the recent development of MPC for hybrid systems, which are inherently discontinuous and nonlinear. For a particular class of discontinuous piecewise affine systems, a new MPC set-up based on infinity norms is proposed, which is proven to be ISS to bounded additive disturbances. This ISS result does not require continuity of the system dynamics nor of the MPC value function. Mircea LazarW.P.M.H. HeemelsAlberto Bemporadalberto.bemporad@imtlucca.itSiep Weiland2011-07-27T08:39:14Z2011-08-05T13:17:17Zhttp://eprints.imtlucca.it/id/eprint/510This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5102011-07-27T08:39:14ZHybrid model predictive control of induction of escherichia coliThe lactose regulation system of Escherichia coli is known to exhibit a bistable behavior. The stable states correspond to the phenotypical states of the system, induced and uninduced. Stochastic modeling of the system enables us to reproduce an experimentally observed phenomenon of spontaneous transitions between the induced and uninduced states. The average behavior of a colony of a large number of cells can be accurately described by an abstract model of the system, which is a two state Markov chain. In this paper, we consider a control problem that involves regulating the fraction of induction of a colony of Escherichia coli. We use the abstract model to design a feedback controller based on model predictive control strategy. Upon simulation, we show that the model predictive control is superior to other control strategies that we have designed before, in terms of less fluctuation in the control input and less tracking error.A. Agung JuliusM. Selman SakarAlberto Bemporadalberto.bemporad@imtlucca.itGeorge J. Pappas2011-07-27T08:36:50Z2011-08-05T13:03:30Zhttp://eprints.imtlucca.it/id/eprint/479This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4792011-07-27T08:36:50ZSquaring the circle: an algorithm for generating polyhedral invariant sets from ellipsoidal onesThis paper presents a new (geometrical) approach to the computation of polyhedral (robustly) positively invariant (PI) sets for general (possibly discontinuous) nonlinear discrete-time systems possibly affected by disturbances. Given a β-contractive ellipsoidal set View the MathML source, the key idea is to construct a polyhedral set that lies between the ellipsoidal sets View the MathML source and View the MathML source. A proof that the resulting polyhedral set is contractive and thus, PI, is given, and a new algorithm is developed to construct the desired polyhedral set. The problem of computing polyhedral invariant sets is formulated as a number of quadratic programming (QP) problems. The number of QP problems is guaranteed to be finite and therefore, the algorithm has finite termination. An important application of the proposed algorithm is the computation of polyhedral terminal constraint sets for model predictive control based on quadratic costs.
Alessandro AlessioMircea LazarAlberto Bemporadalberto.bemporad@imtlucca.itW.P.M.H. Heemels2011-07-27T08:36:36Z2011-08-05T12:59:53Zhttp://eprints.imtlucca.it/id/eprint/485This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4852011-07-27T08:36:36ZCombined design of disturbance model and observer for offset-free model predictive controlThis note presents a method for the combined design of an integrating disturbance model and of the observer (for the augmented system) to be used in offset-free model predictive controllers. A dynamic observer is designed for the original (nonaugmented) system by solving an Hprop control problem aimed at minimizing the effect of unmeasured disturbances and plant/model mismatch on the output prediction error. It is shown that, when offset-free control is sought, the dynamic observer is equivalent to choosing an integrating disturbance model and an observer for the augmented system. An example of a chemical reactor shows the main features and benefits of the proposed method.Gabriele PannocchiaAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:35:38Z2011-08-05T12:47:58Zhttp://eprints.imtlucca.it/id/eprint/617This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6172011-07-27T08:35:38ZConvergence properties of dynamic agents consensus networks with broken linksConvergence properties of distributed consensus protocols on networks of dynamical agents have been analyzed by combinations of algebraic graph theory and control theory tools under certain assumptions, such as strong connectivity. Strong connectivity can be regarded as the requirement that the information of each agent propagates to all the others, possibly with intermediate steps and manipulations. However, because of network failures or malicious attacks, it is possible that this assumption no longer holds, so that some agents are only receiving or only transmitting information from other subsets of agents. In this case, strong connectivity is replaced by weak connectivity. We analyze the convergence properties of distributed consensus on directed graphs with weakly connected components. We show conditions for which the agreement is reached, and, for the cases in which such conditions do not hold, we provide bounds on the residual disagreement.Stefano Di CairanoAlessandro PasiniAlberto Bemporadalberto.bemporad@imtlucca.itRichard M. Murray2011-07-27T08:35:37Z2012-03-02T15:26:02Zhttp://eprints.imtlucca.it/id/eprint/476This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4762011-07-27T08:35:37ZPassivity analysis and passification of discrete-time hybrid systemsFor discrete-time hybrid systems in piecewise affine or piece-wise polynomial (PWP) form, this note proposes sufficient passivity analysis and synthesis criteria based on the computation of piecewise quadratic or PWP storage functions. By exploiting linear matrix inequality techniques and sum of squares decomposition methods, passivity analysis and synthesis of passifying controllers can be carried out through standard semidefinite programming packages, providing a tool particularly important for stability of interconnected heterogeneous dynamical systems.Alberto Bemporadalberto.bemporad@imtlucca.itGianni BianchiniFilippo Brogi2011-07-27T08:34:04Z2011-08-04T07:29:06Zhttp://eprints.imtlucca.it/id/eprint/442This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4422011-07-27T08:34:04ZMultiobjective model predictive controlThis paper proposes a novel model predictive control (MPC) scheme based on multiobjective optimization. At each sampling time, the MPC control action is chosen among the set of Pareto optimal solutions based on a time-varying, state-dependent decision criterion. Compared to standard single-objective MPC formulations, such a criterion allows one to take into account several, often irreconcilable, control specifications, such as high bandwidth (closed-loop promptness) when the state vector is far away from the equilibrium and low bandwidth (good noise rejection properties) near the equilibrium. After recasting the optimization problem associated with the multiobjective MPC controller as a multiparametric multiobjective linear or quadratic program, we show that it is possible to compute each Pareto optimal solution as an explicit piecewise affine function of the state vector and of the vector of weights to be assigned to the different objectives in order to get that particular Pareto optimal solution. Furthermore, we provide conditions for selecting Pareto optimal solutions so that the MPC control loop is asymptotically stable, and show the effectiveness of the approach in simulation examples.Alberto Bemporadalberto.bemporad@imtlucca.itDavid Muñoz de la Peña2011-07-27T08:34:02Z2011-11-17T14:32:55Zhttp://eprints.imtlucca.it/id/eprint/435This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4352011-07-27T08:34:02ZMultiobjective model predictive control based on convex piecewise affine costsThis paper proposes a novel model predictive control (MPC) scheme based on multiobjective optimization. At each sampling time, the MPC control action is chosen among the set of Pareto optimal solutions based on a time-varying and state-dependent decision criterion. After recasting the optimization problem associated with the multiobjective MPC controller as a multiparametric multiobjective linear problem, we show that it is possible to compute each Pareto optimal solution as an explicit piecewise affine function of the state vector and of the vector of weights to be assigned to the different objectives in order to get that particular Pareto optimal solution. Furthermore, we provide conditions for selecting Pareto optimal solutions so that the MPC control loop is asymptotically stable, and show the effectiveness of the approach in simulation examples.Alberto Bemporadalberto.bemporad@imtlucca.itDavid Muñoz de la Peña2011-07-27T08:32:04Z2011-10-12T14:23:42Zhttp://eprints.imtlucca.it/id/eprint/512This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5122011-07-27T08:32:04ZSimultaneous optimal control and discrete stochastic sensor selectionIn this paper we present the problem of combining optimal control with efficient information gathering in an uncertain environment. We assume that the decision maker has the ability to choose among a discrete set of sources of information, where the outcome of each source is stochastic. Different sources and outcomes determine a reduction of uncertainty, expressed in terms of constraints on system variables and set-points, in different directions. This paper proposes an optimization-based decision making algorithm that simultaneously determines the best source to query and the optimal sequence of control moves, according to the minimization of the expected value of an index that weights both dynamic performance and the cost of querying. The problem is formulated using stochastic programming ideas with decision-dependent scenario trees, and a solution based on mixed-integer linear programming is presented. The results are demonstrated on a simple supply-chain management example with uncertain market demand. Daniele Bernardinidaniele.bernardini@imtlucca.itDavid Muñoz de la PeñaAlberto Bemporadalberto.bemporad@imtlucca.itEmilio Frazzoli2011-07-27T08:32:01Z2016-04-06T10:26:11Zhttp://eprints.imtlucca.it/id/eprint/430This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4302011-07-27T08:32:01ZDrive-by-wire vehicle stabilization and yaw regulation: A hybrid model predictive control designElectronic Stability Control (ESC) and Active Front Steering (AFS) have been introduced in production vehicles in recent years, due to improved vehicle maneuverability and the effects in reducing single vehicle accident. We propose a hybrid Model Predictive Control (MPC) design for coordinated control of AFS and ESC. By formulating the vehicle dynamics with respect to the front and rear tire slip angles and by approximating the tire-force characteristics by piecewise affine functions, the vehicle dynamics are formulated as a linear hybrid dynamical system. This model is used to design a hybrid model predictive controller. The proposed model formulation allows one to visually analyze the stability region of the closed-loop system and to assess the stabilizing capability of the hybrid MPC controller. Simulations of the controller in closed-loop with an accurate nonlinear model are presented.Daniele Bernardinidaniele.bernardini@imtlucca.itStefano Di CairanoAlberto Bemporadalberto.bemporad@imtlucca.itH. E. Tseng2011-07-27T08:31:59Z2011-11-17T11:28:12Zhttp://eprints.imtlucca.it/id/eprint/429This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4292011-07-27T08:31:59ZScenario-based model predictive control of stochastic constrained linear systemsIn this paper we propose a stochastic model predictive control (MPC) formulation based on scenario generation for linear systems affected by discrete multiplicative disturbances. By separating the problems of (1) stochastic performance, and (2) stochastic stabilization and robust constraints fulfillment of the closed-loop system, we aim at obtaining a less conservative control action with respect to classical robust MPC schemes, still enforcing convergence and feasibility properties for the controlled system. Stochastic performance is addressed for very general classes of stochastic disturbance processes, although discretized in the probability space, by adopting ideas from multi-stage stochastic optimization. Stochastic stability and recursive feasibility are enforced through linear matrix inequality (LMI) problems, which are solved off-line; stochastic performance is optimized by an on-line MPC problem which is formulated as a convex quadratically constrained quadratic program (QCQP) and solved in a receding horizon fashion. The performance achieved by the proposed approach is shown in simulation and compared to the one obtained by standard robust and deterministic MPC schemes.Daniele Bernardinidaniele.bernardini@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:31:54Z2011-08-05T12:39:58Zhttp://eprints.imtlucca.it/id/eprint/607This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6072011-07-27T08:31:54ZAutomotive controlLuca BenvenutiAndrea BalluchiAlberto Bemporadalberto.bemporad@imtlucca.itStefano Di CairanoBengt JohanssonRolf JohanssonAlberto Sangiovanni VincentelliPer Tunest2011-07-27T08:31:52Z2011-08-05T12:34:42Zhttp://eprints.imtlucca.it/id/eprint/431This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4312011-07-27T08:31:52ZDecentralized model predictive control of dynamically-coupled linear systems: tracking under packet lossFor large-scale processes whose dynamics can be represented as the interaction of several dynamically-coupled linear subsystems, this paper proposes a decentralized model predictive control (MPC) design approach for set-point tracking under input constraints and possible loss of information packets. Following earlier results in (Alessio and Bemporad, 2007 and 2008), the global model of the process is approximated as the decomposition of several (possibly overlapping) smaller models used for local predictions. We present sufficient criteria for asymptotic tracking of output set-points and rejection of constant measured disturbances when the overall process is in closed loop with the set of decentralized MPC controllers, under possible intermittent lack of communication of measurement data between controllers. The effectiveness of the approach is shown in a simulation example on distributed temperature control in the passenger area of a railcar.Davide BarcelliAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:31:50Z2011-08-05T12:33:40Zhttp://eprints.imtlucca.it/id/eprint/511This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5112011-07-27T08:31:50ZA survey on explicit model predictive controlExplicit model predictive control (MPC) addresses the problem of removing one of the main drawbacks of MPC, namely the need to solve a mathematical program on line to compute the control action. This computation prevents the application of MPC in several contexts, either because the computer technology needed to solve the optimization problem within the sampling time is too expensive or simply infeasible, or because the computer code implementing the numerical solver causes software certification concerns,especially in safety critical applications.
Explicit MPC allows one to solve the optimization problem off-line for a given range of operating conditions of interest. By exploiting multiparametric programming techniques, explicit MPC computes the optimal control action off line as an “explicit” function of the state and reference vectors, so that on-line operations reduce to a simple function evaluation. Such a function is piecewise affine in most cases, so that the MPC controller maps into a lookup table of linear gains.
In this paper we survey the main contributions on explicit MPC appeared in the scientific literature. After recalling the basic concepts and problem formulations of MPC, we review the main approaches to solve explicit MPC problems, including a novel and simple suboptimal practical approach to reduce the complexity of the explicit form. The paper concludes with some comments on future research directions.
Alessandro AlessioAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-06T10:42:15Z2011-07-11T14:37:42Zhttp://eprints.imtlucca.it/id/eprint/711This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7112011-07-06T10:42:15ZDynamics of Dependence Properties for Lifetimes Influenced by Unobservable Environmental FactorsWe consider non-negative conditionally independent and identically distributed random variables and analyze conditions for monotonicity of survival copulas of residual lifetimes. Concentrating attention on the bivariate copula, we compare its behavior at the instant of default with its evolution between two defaults. The assumptions for our results will be expressed in terms of conditional hazard rates.Rachele Foschirachele.foschi@imtlucca.itFabio Spizzichino2011-07-06T09:44:42Z2011-07-11T14:37:42Zhttp://eprints.imtlucca.it/id/eprint/707This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7072011-07-06T09:44:42ZA spatial mixed Poisson framework for combination of excess-of-loss and proportional reinsurance contractsIn this paper a purely theoretical reinsurance model is presented, where the reinsurance contract is assumed to be simultaneously of an excess-of-loss and of a proportional type. The stochastic structure of the set of pairs (claim’s arrival time, claim’s size) is described by a Spatial Mixed Poisson Process. By using an invariance property of the Spatial Mixed Poisson Processes, we estimate the amount that the ceding company obtains in a fixed time interval in force of the reinsurance contract.Roy CerquetiRachele Foschirachele.foschi@imtlucca.itFabio Spizzichino2011-07-06T09:22:43Z2011-07-11T14:37:42Zhttp://eprints.imtlucca.it/id/eprint/705This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7052011-07-06T09:22:43ZSemigroups of Semi-copulas and Evolution of Dependence at Increase of AgeWe consider a pair of exchangeable lifetimes X, Y and the families of the conditional survival functions F t (x, y) of
(X − t, Y − t) given (X > t, Y > t). We analyze some properties of dependence and of ageing for F t (x, y) and
some relations among themRachele Foschirachele.foschi@imtlucca.itFabio Spizzichino2011-06-06T08:45:50Z2011-07-11T14:36:26Zhttp://eprints.imtlucca.it/id/eprint/329This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/3292011-06-06T08:45:50ZProof Techniques for Cryptographic ProcessesContextual equivalences for cryptographic process calculi, like the spi-calculus, can be used to reason about correctness of protocols, but their definition suffers from quantification over all possible contexts. Here, we focus on two such equivalences, namely may-testing and barbed equivalence, and investigate tractable proof methods for them. To this aim, we design an enriched labelled transition system, where transitions are constrained by the knowledge the environment has of names and keys. The new transition system is then used to define a trace equivalence and a weak bisimulation equivalence that avoid quantification over contexts. Our main results are soundness and completeness of trace and weak bisimulation equivalence with respect to may-testing and barbed equivalence, respectively. They lead to more direct proof methods for equivalence checking. The use of these methods is illustrated with a few examples concerning implementation of secure channels and verification of protocol correctness.Michele BorealeRocco De Nicolar.denicola@imtlucca.itRosario Pugliese