3,304 research outputs found
Introduction to the Koopman operator in dynamical systems and control theory
No full textThis introductory chapter provides an overview of the Koopman operator framework. We present basic notions and definitions, including those related to the spectral properties of the operator. We also review numerical methods that are used to represent the operator on a finite-dimensional basis and to compute its spectral properties from data (DMD algorithm and Arnoldi-based methods). Finally, several extensions of the Koopman operator to input–output systems are reviewed.</p
Koopman Framework for Global stability analysis
No full textIn this chapter, we present a new framework to study global stability of nonlinear systems. The proposed approach is based on the stability properties of the Koopman operator and can be seen as an extension of classic stability analysis of linear systems. In the case of (hyperbolic) equilibria, we show that the existence of specific eigenfunctions of the operator is a necessary and sufficient condition for global stability of the attractor. Moreover, using the realization of the operator in a finite-dimensional basis, we provide a systematic method to compute candidate Lyapunov functions of stable systems.</p
Clustering behaviors in networks of integrate-and-fire oscillators
Full text linkpeer reviewedClustering behavior is studied in a model of integrate-and-fire oscillators with excitatory pulse
coupling. When considering a population of identical oscillators, the main result is a proof of global
convergence to a phase-locked clustered behavior. The robustness of this clustering behavior is then investigated in a population of nonidentical oscillators by studying the transition from total clustering to the absence of clustering as the group coherence decreases. A robust intermediate situation of partial clustering, characterized by few oscillators traveling among nearly phase-locked clusters, is of particular interest. The analysis complements earlier studies of synchronization in a closely related model
Global Analysis of Firing Maps
Full text linkpeer reviewedIn this paper, we study the behavior of pulse-coupled integrate-and-fire oscillators. Each oscillator is characterized by a state evolving between two threshold values. As the state reaches the upper threshold, it is reset to the lower threshold and emits a pulse which increments by a constant value the state of every other oscillator. The behavior of the system is described by the so-called firing map: depending on the stability of the firing map, an important dichotomy characterizes the behavior of the oscillators (synchronization or clustering). The firing map is
the composition of a linear map with a scalar nonlinearity. After briefly discussing the case of the scalar firing map (corresponding to two oscillators), the stability analysis is extended to the general n-dimensional firing map (for n +1 oscillators). Different models are considered (leaky oscillators, quadratic oscillators,...), with a particular emphasis on the persistence of the dichotomy in higher dimensions
Alexandre Moatti, Un regard sur les élites françaises L’Institut Auguste-Comte
Full text linkL’objet de ce livre est l’éphémère Institut Auguste-Comte (IAC) pour l’étude des sciences de l’action, créé le 26 juillet 1977 par un décret du président Valéry Giscard d’Estaing et supprimé le 12 novembre 1981 par celui du Premier ministre Pierre Mauroy. Alexandre Moatti qualifie ces quatre ans d’existence de l’Institut comme un des rares moments, selon lui, où l’élite dirigeante française – celle représentée par des polytechniciens – aurait voulu ou tenté de se remettre en cause.Né en 1959..
La filosofía del derecho de Alexandre Kojève
No full textThis article is a presentation of Alexandre Kojève’s philosophy of law, exposed in his Esquisse d’une phénoménologie du droit (1981). Little attention has been paid to this work. So there is a gap that has to be filled with a critical reflection of its strengths. Among them, undoubtedly, we count the fact that Kojève is introducing a conception of international justice that casts a singular light on current debates about cosmopolitanism and globalization. According to this author, citizenship is the key element of the process of global expansion of the juridical sphere. In sum, Kojève’s philosophy is useful to reflect upon the contrast between the juridical and the political, which is the basis for all philosophy of law, in order to achieve world peace and international justice.Este artículo es una presentación de la filosofía del derecho de Alexandre Kojève contenida en su Esquisse d’une phénoménologie du droit (1981). La poca atención que dicha obra ha recibido es un vacío que debiera llenarse con una reflexión crítica de sus puntos fuertes. Entre ellos destaca una concepción de la justicia internacional que proyecta una luz muy singular sobre los actuales debates en torno a la globalización y el cosmopolitismo. A ojos de este autor, la ciudadanía es el elemento clave para aquilatar la expansión global de lo jurídico. En suma, Kojève aparece como un valioso referente en la labor de pensar la contraposición entre lo jurídico y lo político que está en la base de toda filosofía del derecho, con la aspiración al logro de la justicia internacional y la paz mundial en el horizonte
Reconfiguração do consensualismo contratual: as ações tituladas nominativas e os limites à transmissão
No full textPartimos da evolução histórica do consensualismo contratual salientando os
principais carateres que, nos diversos momentos históricos, se foram evidenciando.
Numa segunda etapa exploramos os fundamentos dogmáticos do modelo de
transmissão contratual assumido pelo legislador e a sua viabilidade no sistema
jurídico global, em particular, no direito dos valores mobiliários. Constatamos a
crescente necessidade na prática mercantil e inevitabilidade no sistema jurídico
global da admissibilidade da existência de contratos de compra e venda de natureza
meramente obrigacional. Num terceiro momento desenvolvemos os principais
aspetos do regime jurídico aplicável às ações tituladas nominativas fora do mercado
regulado, em particular, os principais limites à transmissão, enquanto instrumentos/barreiras ao consensualismo contratual.We start from the historical evolution of contractual consensualism emphasizing the
main aspects that, in different historical moments, were showing up. In a second
stage we explore the dogmatic foundations of the transmission model contractual
assumed by the legislator and its viability in the global legal system, in particular, in
securities law. We note the growing need in commercial practice and inevitability in
the global legal system the admissibility of the existence of contracts of sale purely
obligatory. In the third stage we develop the main aspects of the legal regime
applicable to nominative titled actions outside the regulated market, in particular,
the main limits to the transmission, as instruments / barriers to contractual
consensualism
“Era por Alexandre tod’esto demostrado”: ¿pruebas verídicas y pruebas engañosas en el Libro de Alexandre?
No full textEl Libro de Alexandre es un texto de s. XIII, que se escribió en la España medieval. En este escrito, el autor pretende demostrar que, en el Alexandre, algunas de las situaciones que se ponen a prueba son aceptadas, pero eso no significa que el macedonio gane la prueba. El articulo esta dividido en tres apartados. En el primero, el autor da cuenta de la historia textual de la obra y también dedica ciertas líneas al Estado de la cuestión del texto; mientras que, en la segunda parte, nos guía a conceptos etimológicos de los términos prueba, evidencia y demás. En el tercer apartado se centra en algunas pruebas expuestas en el Libro de Alexandre.The Libro de Alexandre is a literary work, written during the medieval Spain. In this paper, the author tries to demonstrate that, carefully reading the L.A, some of the situations that are set as proves are accepted, but it does not mean that Alexander can be a victor. This paper is divided in three sections: firstly, the author tells the textual history of the L.A and, then, tries to update the State of art: on the other hand, in the second part, the author offers meanings about terms as: prueba and evidencia. Finally, the author focuses on certain passages contained in the Libro de Alexandre that can be taken as failed proves
Mixing the Immiscible: Improvisation within Fixed-Media Composition
No full textThis paper will explore ways in which mastered improvisation practice, with the studio as an instrument, is a proposed avenue to bridge the historical dichotomy between what Ted Gioia describe as ‘the aesthetics of perfection’ and ‘the aesthetics of imperfection’. It is proposed as a way to re-embody fixed music, as experimented by the author through the composition of his last fixed-media work. This will be put in the context of a wider trend observed amongst the current emerging generation of composers interested in the aesthesics of the work, by opposition to the previous generations that placed the value of the work in its poietics. The vital and primal importance of practice outcome as practice-based research’s main document will also be advocated for, as these trends are happening in the laboratory of live music
Converging to and escaping from the global equilibrium: Isostables and optimal control
Full text linkpeer reviewedThis paper studies the optimal control of trajectories converging to or escaping from a stable equilibrium. The control duration is assumed to be short. When the control is turned off, the trajectories have not reached the target and they subsequently evolve according to the free motion dynamics. In this context, we show that the problem can be formulated as a finite-horizon optimal control problem which relies on the notion of isostables. For linear and nonlinear systems, we solve this problem using Pontryagin’s maximum principle and we study the relationship between the optimal solutions and the geometry of the isostables. Finally, optimal strategies for choosing the magnitude and duration of the control are considered
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