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A Periodic Tracking MPC that is Locally Equivalent to Periodic Economic MPC
No full textStability for economic Model Predictive Control (MPC) is in general difficult to establish. In contrast, tracking MPC has well-established stability guarantees, but can yield poor closed-loop performance in terms of the selected economic criterion. In Zanon et al. (2016), a formal procedure to design a tracking MPC scheme so as to locally approximate the behaviour of economic MPC was proposed for the case of optimal steady-state operation. In this paper, we extend that result to the periodic case and provide a procedure to compute the tracking stage cost numerically. We illustrate our developments in a simulated example
Reconstruction of multiplex networks with correlated layers
Full text linkThe characterization of various properties of real-world systems requires the knowledge of the underlying network of connections among the system's components. Unfortunately, in many situations the complete topology of this network is empirically inaccessible, and one has to resort to probabilistic techniques to infer it from limited information. While network reconstruction methods have reached some degree of maturity in the case of single-layer networks (where nodes can be connected only by one type of links), the problem is practically unexplored in the case of multiplex networks, where several interdependent layers, each with a different type of links, coexist. Even the most advanced network reconstruction techniques, if applied to each layer separately, fail in replicating the observed inter-layer dependencies making up the whole coupled multiplex. Here we develop a methodology to reconstruct a class of correlated multiplexes which includes the World Trade Multiplex as a specific example we study in detail. Our method starts from any reconstruction model that successfully reproduces some desired marginal properties, including node strengths and/or node degrees, of each layer separately. It then introduces the minimal dependency structure required to replicate an additional set of higher-order properties that quantify the portion of each node's degree and each node's strength that is shared and/or reciprocated across pairs of layers. These properties are found to provide empirically robust measures of inter-layer coupling. Our method allows joint multi-layer connection probabilities to be reliably reconstructed from marginal ones, effectively bridging the gap between single-layer properties and truly multiplex information
Maximum-Entropy Networks: pattern detection, network reconstruction, and graph combinatorics
No full textThis book is an introduction to maximum-entropy models of random graphs with given topological properties and their applications. Its original contribution is the reformulation of many seemingly different problems in the study of both real networks and graph theory within the unified framework of maximum entropy. Particular emphasis is put on the detection of structural patterns in real networks, on the reconstruction of the properties of networks from partial information, and on the enumeration and sampling of graphs with given properties. After a first introductory chapter explaining the motivation, focus, aim and message of the book, chapter 2 introduces the formal construction of maximum-entropy ensembles of graphs with local topological constraints. Chapter 3 focuses on the problem of pattern detection in real networks and provides a powerful way to disentangle nontrivial higher-order structural features from those that can be traced back to simpler local constraints. Chapter 4 focuses on the problem of network reconstruction and introduces various advanced techniques to reliably infer the topology of a network from partial local information. Chapter 5 is devoted to the reformulation of certain “hard” combinatorial operations, such as the enumeration and unbiased sampling of graphs with given constraints, within a “softened” maximum-entropy framework. A final chapter offers various overarching remarks and take-home messages.By requiring no prior knowledge of network theory, the book targets a broad audience ranging from PhD students approaching these topics for the first time to senior researchers interested in the application of advanced network techniques to their field
Covariance structure behind breaking of ensemble equivalence in random graphs
Full text linkFor a random graph subject to a topological constraint, the microcanonical ensemble requires the constraint to be met by every realisation of the graph (`hard constraint'), while the canonical ensemble requires the constraint to be met only on average (`soft constraint'). It is known that breaking of ensemble equivalence may occur when the size of the random graph tends to infinity, signalled by a non-zero specific relative entropy of the two ensembles. In this paper we analyse a formula for the relative entropy of generic random discrete structures recently put forward by Squartini and Garlaschelli. We consider the case of random graphs with given degree sequence (configuration model) and show that this formula correctly predicts that the specific relative entropy in the dense regime is determined by the matrix of canonical covariances of the constraints. The formula also correctly predicts that an extra correction term is required in the sparse regime and the ultra-dense regime. We further show that the different expressions correspond to the degrees in the canonical ensemble being asymptotically Gaussian in the dense regime and asymptotically Poisson in the sparse and the ultra-dense regime, as we found in earlier work. In general, we show that the degrees follow a multivariate version of the Poisson- Binomial distribution in the canonical ensemble
Festivals, institutional maintenance and change: The case of the Lucca Comics & Games Festival
No full textSpatio-Temporal Patterns of the International Merger and Acquisition Network
No full textThis paper analyses the world web of mergers and acquisitions (M&As) using a complex network approach. We use data of
M&As to build a temporal sequence of binary and weighted-directed networks for the period 1995-2010 and 224 countries
(nodes) connected according to their M&As flows (links). We study different geographical and temporal aspects of the international
M&A network (IMAN), building sequences of filtered sub-networks whose links belong to specific intervals of distance
or time. Given that M&As and trade are complementary ways of reaching foreign markets, we perform our analysis using
statistics employed for the study of the international trade network (ITN), highlighting the similarities and differences between
the ITN and the IMAN. In contrast to the ITN, the IMAN is a low density network characterized by a persistent giant component
with many external nodes and low reciprocity. Clustering patterns are very heterogeneous and dynamic. High-income
economies are the main acquirers and are characterized by high connectivity, implying that most countries are targets of a few
acquirers. Like in the ITN, geographical distance strongly impacts the structure of the IMAN: link-weights and node degrees
have a non-linear relation with distance, and an assortative pattern is present at short distances
Who's who in global value chains? A weighted network approach
No full textThis paper represents global value chains (GVCs) as weighted networks of foreign value
added in exports, which allows for the identification of the specific roles of countries and
for the quantification of their relative importance over time. A major structural change
occurred in the beginning of the century as GVCs steadily turned into global networks,
amid an unprecedented growth of value-added flows and the rise of China as a major
player. First-order network metrics highlight the vital but also distinct roles of Germany,
the US, China and Japan in the international organisation of production. Germany is very relevant both as a user and as a supplier of foreign inputs, while the US acts mostly as a supplier of value added to other countries. Second-order properties of networks shed light on the complex architecture of GVCs, notably in terms of cyclical triangular relationships. Germany's GVCs mostly root in direct relationships, while Japanese ones typically involve more than two countries
Multi-parametric sensitivity analysis of the band structure for tetrachiral inertial metamaterials
No full textTetrachiral materials are characterized by a cellular microstructure made by a periodic pattern of stiff rings and flexible ligaments. Their mechanical behaviour can be described by a planar lattice of rigid massive bodies and elastic massless beams. The periodic cell dynamics is governed by a monoatomic structural model, conveniently reduced to the only active degrees-of-freedom. The paper presents an explicit parametric description of the band structure governing the free propagation of elastic waves. By virtue of multiparametric perturbation techniques, sensitivity analyses are performed to achieve analytical asymptotic approximation of the dispersion functions. The parametric conditions for the existence of full band gaps in the low-frequency range are established. Furthermore, the band gap amplitude is analytically assessed in the admissible parameter range. In inertial tetrachiral metamaterials, stop bands can be opened by the introduction of intra-ring resonators. Perturbation methods can efficiently deal with the consequent enlargement of the mechanical parameter space. Indeed high-accuracy parametric approximations are achieved for the band structure, enriched by the new optical branches related to the resonator frequencies. In particular, target stop bands in the metamaterial spectrum are analytically designed through the asymptotic solution of inverse spectral problems.
Subjects: Materials Science (cond-mat.mtrl-sci)
Cite as: arXiv:1706.08754 [cond-mat.mtrl-sci]
(or arXiv:1706.08754v1 [cond-mat.mtrl-sci] for this version
A computational approach to steady-state convergence of fluid limits for Coxian queuing networks with abandonment
No full textMany-server queuing networks with general service and abandonment times have proven to be a realistic model for scenarios such as call centers and health-care systems. The presence of abandonment makes analytical treatment difficult for general topologies. Hence, such networks are usually studied by means of fluid limits. The current state of the art, however, suffers from two drawbacks. First, convergence to a fluid limit has been established only for the transient, but not for the steady state regime. Second, in the case of general distributed service and abandonment times, convergence to a fluid limit has been either established only for a single queue, or has been given by means of a system of coupled integral equations which does not allow for a numerical solution. By making the mild assumption of Coxian-distributed service and abandonment times, in this paper we address both drawbacks by establishing convergence in probability to a system of coupled ordinary differential equations (ODEs) using the theory of Kurtz. The presence of abandonments leads in many cases to ODE systems with a global attractor, which is known to be a sufficient condition for the fluid and the stochastic steady state to coincide in the limiting regime. The fact that our ODE systems are piecewise affine enables a computational method for establishing the presence of a global attractor, based on a solution of a system of linear matrix inequalities