# Matemática

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Artículo de Publicación Periódica Learning and imitation: transitional dynamics in variants of the BAM(2004) Heymann, D.; Perazzo, Roberto P. J.; Schuschny, A. R.Más... "We study the dynamics of self-organized systems when disturbed by shocks. For this purpose, we consider extensions of the “Bar Attendance Model” [1] (BAM), which provides a stylized setting for the analysis of the emergence of coordination in the behavior of a large collection of agents. We represent the learning process of the agents through genetic algorithms, which respond to global (publicly available) information. In addition, we allow the actions of agents to be influenced by local information, as expressed in the behavior and performance of neighboring individuals. In the context of the BAM, we show that, in the event of a shock, the imitation behavior may become widespread and generate a contagion cascade which mimics a collective panic. We use this framework to represent features of the dynamics of an actual bank run."Más... Artículo de Publicación Periódica Uniform stability properties of switched systems with switchings governed by digraphs(2005-05) Mancilla-Aguilar, J. L.; García Galiñanes, Rafael; Sontag, E.; Wang, Y.Más... "Characterizations of various uniform stability properties of switched systems described by differential inclusions, and whose switchings are governed by a digraph, are developed. These characterizations are given in terms of stability properties of the system with restricted switchings and also in terms of Lyapunov functions."Más... Artículo de Publicación Periódica An extension of LaSalle’s invariance principle for switched systems(2006) Mancilla-Aguilar, J. L.; García Galiñanes, RafaelMás... "This paper addresses invariance principles for a certain class of switched nonlinear systems. We provide an extension of LaSalle’s Invariance Principle for these systems and state asymptotic stability criteria. We also present some related results that deal with the compactness of the trajectories of these switched systems and that are interesting by their own."Más... Artículo de Publicación Periódica Two classes of bipartite networks: nested biological and social systems(2008) Burgos, Enrique; Ceva, Horacio; Hernández, Laura; Perazzo, Roberto P. J.; Devoto, Mariano; Medan, DiegoMás... "Bipartite graphs have received some attention in the study of social networks and of biological mutualistic systems. A generalization of a previous model is presented, that evolves the topology of the graph in order to optimally account for a given Contact Preference Rule between the two guilds of the network. As a result, social and biological graphs are classified as belonging to two clearly different classes. Projected graphs, linking the agents of only one guild, are obtained from the original bipartite graph. The corresponding evolution of its statistical properties is also studied. An example of a biological mutualistic network is analyzed in detail, and it is found that the model provides a very good fitting of all the main statistical features. The model also provides a proper qualitative description of the same features observed in social webs, suggesting the possible reasons underlying the difference in the organization of these two kinds of bipartite networks."Más... Artículo de Publicación Periódica Causality study and numerical response of the magnetic permeability as a function of the frequency of ferrites using Kramers–Kronig relations(2008) Fano, Walter Gustavo; Boggi, Silvina; Razzitte, Adrián C.Más... "In this paper, the numerical treatment of magnetic loss of NiZn, MnZn, Ni2Y, and NiZnCu ferrite and their composites, by using Krameres–Kronig relations, is investigated. The complex magnetic permeability spectra for ferromagnetic materials have been studied. Due to the principle of causality and time independence in the relation between magnetic induction B and magnetic field H, the real and the imaginary part of the complex magnetic permeability are mutually dependent, and the correlation is given by the Krameres–Kronig equations. Through them, it is possible to measure the real component of the complex magnetic permeability, assuming the real component is given, and by the Hilbert transform, the imaginary part of the magnetic permeability can be calculated. Magnetic circuit model has been studied theoretically, focusing on the model’s poles in the complex plane to verify the principle of causality and the temporary independence."Más... Artículo de Publicación Periódica Diseño de observadores en modos cuasi-deslizantes vía LMIs(2008-07) Fraguío, Alberto Javier; Mancilla-Aguilar, J. L.; Zanini, AníbalMás... "En este trabajo se presenta un observador robusto por modos cuasi-deslizantes para plantas con modelo nominal lineal e incertidumbres/pertubaciones de cierta clase particular. Las señales utilizadas para la estimación del vector de estados se suponen contaminadas con ruido del que sólo se conocen cotas. El diseño del observador se plantea como un problema de factibilidad LMI (Linear Matrix Inequalities) y se encuentran cotas para el error de estimación que pueden ser calculadas a priori. Posteriormente el diseño del observador se reformula como un problema de optimización GEVP (Generalized Eigen Value Problem) con el objeto de minimizar las cotas del error de estimación. El trabajo incluye un ejemplo numérico y simulaciones de un brazo robótico con un eje manejado por un motor de corriente continua."Más... Artículo de Publicación Periódica A truncated version of the birnbaum-saunders distribution with an application in financial risk(2010-01) Ahmed, Syed Ejaz; Castro-Kuriss, Claudia; Flores, Esteban; Leiva, Víctor; Sanhueza, AntonioMás... "In many Solvency and Basel loss data, there are thresholds or deductibles that affect the analysis capability. On the other hand, the Birnbaum-Saunders model has received great attention during the last two decades and it can be used as a loss distribution. In this paper, we propose a solution to the problem of deductibles using a truncated version of the Birnbaum-Saunders distribution. The probability density function, cumulative distribution function, and moments of this distribution are obtained. In addition, properties regularly used in insurance industry, such as multiplication by a constant (inflation effect) and reciprocal transformation, are discussed. Furthermore, a study of the behavior of the risk rate and of risk measures is carried out. Moreover, estimation aspects are also considered in this work. Finally, an application based on real loss data from a commercial bank is conducted."Más... Artículo de Publicación Periódica Using linear difference equations to model nonlinear cryptographic sequences(2010-03) Caballero-Gil, Pino; Fúster-Sabater, Amparo; Pazo-Robles, María EugeniaMás... "A new class of linear sequence generators based on cellular automata is here introduced in order to model several nonlinear keystream generators with practical applications in symmetric cryptography. The output sequences are written as solutions of linear difference equations, and three basic properties (period, linear complexity and number of different output sequences) are analyzed."Más... Artículo de Publicación Periódica On a goodness-of-fit test for normality with unknown parameters and type-II censored data(2010-07) Castro-Kuriss, Claudia; Kelmansky, Diana M.; Leiva, Víctor; Martínez, Elena J.Más... "We propose a new goodness-of-fit test for normal and lognormal distributions with unknown parameters and type-II censored data. This test is a generalization of Michael's test for censored samples, which is based on the empirical distribution and a variance stabilizing transformation. We estimate the parameters of the model by using maximum likelihood and Gupta's methods. The quantiles of the distribution of the test statistic under the null hypothesis are obtained through Monte Carlo simulations. The power of the proposed test is estimated and compared to that of the Kolmogorov-Smirnov test also using simulations. The new test is more powerful than the Kolmogorov-Smirnov test in most of the studied cases. Acceptance regions for the PP, QQ and Michael's stabilized probability plots are derived, making it possible to visualize which data contribute to the decision of rejecting the null hypothesis. Finally, an illustrative example is presented."Más... Artículo de Publicación Periódica Some results for switched homogeneous systems(2016) Mancilla Aguilar, Jose Luis; García Galiñanes, RafaelMás... "In this paper, we prove the equivalence of weak attractivity, attractivity, global uniform asymptotic stability and exponential stability of switched homogeneous systems whose switching signals verify a certain property P. In addition we show that these stability properties imply that the system stability is robust with respect to disturbances in a power-like sense, which comprises both, the exponential ISS and iISS."Más... Artículo de Publicación Periódica Crude oil market and geopolitical events: an analysis based on information-theory-based quantifiers(2016) Fernández Bariviera, Aurelio; Zunino, Luciano; Rosso, Osvaldo A.Más... "This paper analyzes the informational efficiency of oil market during the last three decades, and examines changes in informational efficiency with major geopolitical events, such as terrorist attacks, financial crisis and other important events. The series under study is the daily prices of West Texas Intermediate (WTI) in USD/BBL, commonly used as a benchmark in oil pricing. The analysis is performed using information-theory-derived quantifiers, namely permutation entropy and permutation statistical complexity. These metrics allow capturing the hidden structure in the market dynamics, and allow discriminating different degrees of informational efficiency. We find that some geopolitical events impact on the underlying dynamical structure of the market."Más... Artículo de Publicación Periódica Robustness properties of an algorithm for the stabilisation of switched systems with unbounded perturbations(2017-05) Mancilla-Aguilar, J. L.; García Galiñanes, RafaelMás... "In this paper, it is shown that an algorithm for the stabilisation of switched systems introduced by the authors is robust with respect to perturbations which are unbounded in the supremum norm, but bounded in a power-like sense. The obtained stability results comprise, among others, both the exponential input-to-state stability and the exponential integral input-to-state stability properties of the closed-loop system and give a better description of the behaviour of the closed-loop system. "Más... Artículo de Publicación Periódica Global stability results for switched systems based on weak Lyapunov functions(2017-06) Mancilla-Aguilar, J. L.; Haimovich, Hernán; García Galiñanes, RafaelMás... "In this paper we study the stability of nonlinear and time-varying switched systems under restricted switching. We approach the problem by decomposing the system dynamics into a nominal-like part and a perturbationlike one. Most stability results for perturbed systems are based on the use of strong Lyapunov functions, i.e. functions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, switched systems under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contribution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov function. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is switched linear-timevarying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm."Más... Artículo de Publicación Periódica On zero-input stability inheritance for time-varying systems with decaying-to-zero input power(2017-06) Mancilla-Aguilar, J. L.; Haimovich, HernánMás... "Stability results for time-varying systems with inputs are relatively scarce, as opposed to the abundant literature available for time-invariant systems. This paper extends to time-varying systems existing results that ensure that if the input converges to zero in some specific sense, then the state trajectory will inherit stability properties from the corresponding zero-input system. This extension is non-trivial, in the sense that the proof technique is completely novel, and allows to recover the existing results under weaker assumptions in a unifying way."Más... Artículo de Publicación Periódica Uniform asymptotic stability of switched nonlinear time-varying systems and detectability of reduced limiting control systems(2018) Mancilla-Aguilar, J. L.; García Galiñanes, RafaelMás... "This paper is concerned with the study of both, local and global, uniform asymptotic stability for switched nonlinear time-varying (NLTV) systems through the detectability of outputmaps. With this aim the notion of reduced limiting control systems for switched NLTV systems whose switchings verify time/state dependent constraints, and the concept of weakly zerostate detectability for those reduced limiting systems are introduced. Necessary and sufficient conditions for the (global)uniform asymptotic stability of families of trajectories of the switched system are obtained in terms of this detectability property. These sufficient conditions in conjunction with the existence of multiple weak Lyapunov functions, yield a criterion for the (global) uniform asymptotic stability of families of trajectories of the switched system. This criterion can be seen as an extension of the classical Krasovskii-LaSalle theorem. An interesting feature of the results is that no dwell-time assumptions are made. Moreover, they can be used for establishing the global uniform asymptotic stability of switched NLTV system under arbitrary switchings. The effectiveness of the proposed results is illustrated by means of various interesting examples, including the stability analysis of a semi-quasi-Z-source inverter."Más... Artículo de Publicación Periódica A characterization of Integral ISS for switched and time-varying systems(2018-02) Haimovich, Hernán; Mancilla-Aguilar, J. L.Más... "Most of the existing characterizations of the integral input-to-state stability (iISS) property are not valid for time-varying or switched systems in cases where converse Lyapunov theorems for stability are not available. This paper provides a characterization that is valid for switched and time-varying systems, and shows that natural extensions of some of the existing characterizations result in only sufficient but not necessary conditions. The results provided also pinpoint suitable iISS gains and relate these to supply functions and bounds on the function defining the system dynamics."Más... Artículo de Publicación Periódica Linear parameter-varying model to design control laws for an artificial pancreas(2018-02) Colmegna, Patricio; Sánchez-Peña, Ricardo; Gondhalekar, RaviMás... "The contribution of this work is the generation of a control-oriented model for insulin-glucose dynamic regulation in type1 diabetes mellitus (T1DM). The novelty of this model is that it includes the time-varying nature, and the inter-patient variability of the glucose-control problem. In addition, the model is well suited for well-known and standard controller synthesis procedures. The outcome is an average linear parameter-varying (LPV) model that captures the dynamics from the insulin delivery input to the glucose concentration output constructed based on the UVA/Padova metabolic simulator. Finally, a system-oriented reinterpretation of the classical ad-hoc 1800 rule is applied to adapt the model’s gain."Más... Artículo de Publicación Periódica ISS implies iISS even for switched and time-varying systems (if you are careful enough)(2019-06) Haimovich, Hernán; Mancilla-Aguilar, J. L.Más... "For time-invariant systems, the property of input-to-state stability (ISS) is known to be strictly stronger than integral-ISS (iISS). Known proofs of the fact that ISS implies iISS employ Lyapunov characterizations of both properties. For time-varying and switched systems, such Lyapunov characterizations may not exist, and hence establishing the exact relationship between ISS and iISS remained an open problem, until now. In this paper, we solve this problem by providing a direct proof, i.e. without requiring Lyapunov characterizations, of the fact that ISS implies iISS, in a very general time-varying and switched-system context. In addition, we show how to construct suitable iISS gains based on the comparison functions that characterize the ISS property, and on bounds on the function f defining the system dynamics. When particularized to time-invariant systems, our assumptions are even weaker than existing ones. Another contribution is to show that for time-varying systems, local Lipschitz continuity of f in all variables is not sufficient to guarantee that ISS implies iISS. We illustrate application of our results on an example that does not admit an iISS-Lyapunov function."Más... Artículo de Publicación Periódica Uniform asymptotic stability of switched nonlinear time-varying systems and detectability of reduced limiting control systems(2019-07) Mancilla-Aguilar, J. L.; García Galiñanes, RafaelMás... "This paper is concerned with the study of both, local and global, uniform asymptotic stability for switched nonlinear time-varying (NLTV) systems through the detectability of output-maps. With this aim, the notion of reduced limiting control systems for switched NLTV systems whose switchings verify time/state-dependent constraints, and the concept of weak zero-state detectability for those reduced limiting systems are introduced. Necessary and sufficient conditions for the (global)uniform asymptotic stability of families of trajectories of the switched system are obtained in terms of this detectability property. These sufficient conditions in conjunction with the existence of multiple weak Lyapunov functions yield a criterion for the (global) uniform asymptotic stability of families of trajectories of the switched system. This criterion can be seen as an extension of the classical Krasovskii-LaSalle theorem. An interesting feature of the results is that no dwell-Time assumptions are made. Moreover, they can be used for establishing the global uniform asymptotic stability of the switched NLTV system under arbitrary switchings. The effectiveness of the proposed results is illustrated by means of various interesting examples, including the stability analysis of a semiquasi-Z-source inverter."Más... Artículo de Publicación Periódica Converging-input convergent-state and related properties of time-varying impulsive systems(2020-07-03) Mancilla-Aguilar, J. L.; Haimovich, HernánMás... "Very recently, it has been shown that the standard notion of stability for impulsive systems, whereby the state is ensured to approach the equilibrium only as continuous time elapses, is too weak to allow for any meaningful type of robustness in a time-varying impulsive system setting. By strengthening the notion of stability so that convergence to the equilibrium occurs not only as time elapses but also as the number of jumps increases, some facts that are well-established for time-invariant nonimpulsive systems can be recovered for impulsive systems. In this context, our contribution is to provide novel results consisting in rather mild conditions under which stability under zero input implies stability under inputs that converge to zero in some appropriate sense."Más...