Matemática

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Learning and imitation: transitional dynamics in variants of the BAM
(2004) Heymann, D.; Perazzo, Roberto P. J.; Schuschny, A. R.
"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."
Uniform stability properties of switched systems with switchings governed by digraphs
(2005-05) Mancilla-Aguilar, J. L.; García Galiñanes, Rafael; Sontag, E.; Wang, Y.
"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."
An extension of LaSalle’s invariance principle for switched systems
(2006) Mancilla-Aguilar, J. L.; García Galiñanes, Rafael
"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."
Two classes of bipartite networks: nested biological and social systems
(2008) Burgos, Enrique; Ceva, Horacio; Hernández, Laura; Perazzo, Roberto P. J.; Devoto, Mariano; Medan, Diego
"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."
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.
"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."
An extension of chaotic probability models to real-valued variables
(2008-07) Fierens, Pablo Ignacio
"Previous works have presented a frequentist interpretation of sets of measures as probabilistic models which have denominated chaotic models. Those models, however, dealt only with sets of probability measures on ﬁnite algebras, that is, probability measures which can be related to variables with a ﬁnite number of possible values. In this paper, an extension of chaotic models is proposed in order to deal with the more general case of real-valued variables."
Diseño de observadores en modos cuasi-deslizantes vía LMIs
(2008-07) Fraguío, Alberto Javier; Mancilla-Aguilar, J. L.; Zanini, Aníbal
"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."
Invariance results for constrained switched systems
(2010) Mancilla-Aguilar, J. L.; García Galiñanes, Rafael
"In this paper we address invariance principles for nonlinear switched systems with otherwise arbitrary compact index set and with constrained switchings. We present an extension of LaSalle's invariance principle for these systems and derive by using detectability notions some convergence and asymptotic stability criteria. These results enable to take into account in the analysis of stability not only state-dependent constraints but also to treat the case in which the switching logic has memory, i.e., the active subsystem only can switch to a prescribed subset of subsystems."
Some invariance principles for constrained switched systems
(2010) Mancilla-Aguilar, J. L.; García Galiñanes, Rafael
"In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these systems and derive by using observability-like notions some convergence and asymptotic stability criteria. These results may enable us to analyze the stability of solutions of switched systems with both state-dependent constrained switching and switching whose logic has memory, i.e., the active subsystem only can switch to a prescribed subset of subsystems."
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, Antonio
"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."
Using linear difference equations to model nonlinear cryptographic sequences
(2010-03) Caballero-Gil, Pino; Fúster-Sabater, Amparo; Pazo-Robles, María Eugenia
"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."
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.
"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."
An alternative approach to the state observation problem for Lipschitz continuous systems with controls
(2010-07) Hernández, Santiago M.; García Galiñanes, Rafael
"In the present work we propose an alternative approach to the state observation problem for Lipschitz continuous systems with open-loop controls. We construct an observer based on a concept of observability weaker than that of the instantaneous observability. The resulting observation algorithm is then applicable under mild assumptions about the considered dynamical system".
Some results for switched homogeneous systems
(2016) Mancilla Aguilar, Jose Luis; García Galiñanes, Rafael
"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."
Crude oil market and geopolitical events: an analysis based on information-theory-based quantifiers
(2016) Fernández Bariviera, Aurelio; Zunino, Luciano; Rosso, Osvaldo A.
"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."
Robustness properties of an algorithm for the stabilisation of switched systems with unbounded perturbations
(2017-05) Mancilla-Aguilar, J. L.; García Galiñanes, Rafael
"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. "
On zero-input stability inheritance for time-varying systems with decaying-to-zero input power
(2017-06) Mancilla-Aguilar, J. L.; Haimovich, Hernán
"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."
Global stability results for switched systems based on weak Lyapunov functions
(2017-06) Mancilla-Aguilar, J. L.; Haimovich, Hernán; García Galiñanes, Rafael
"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."
On bounding a nonlinear system with a monotone positive system
(2017-12) Haimovich, Hernán; Mancilla-Aguilar, J. L.
"How to bound the state vector trajectory of a nonlinear system in a way so that the obtained bound be of practical value is an open problem. If some norm is employed for bounding the state vector trajectory, then this norm should be carefully selected and the state vector components suitably scaled. In addition, practical applications usually require separate bounds on every state variable. Bearing this context in mind, we develop a novel componentwise bounding procedure applicable to both real and complex nonlinear systems with additive disturbances. A bound on the magnitude of the evolution of each state variable is obtained by computing a single trajectory of a well-specified 'bounding' system constructed from the original system equations and the available disturbance bounds. The bounding system is shown to have highly desirable properties, such as being monotone and positive. We provide preliminary results establishing that key stability features are preserved by the bounding system for systems in triangular form."
Uniform asymptotic stability of switched nonlinear time-varying systems and detectability of reduced limiting control systems
(2018) Mancilla-Aguilar, J. L.; García Galiñanes, Rafael
"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."

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