Estudo de ciclos limites em uma classe de equações diferenciais descontínuas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Sobre a estabilidade estrutural e regularizações de campos de vetores descontínuos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Confluências entre mito, literatura e direito em Édipo Rei, de Sófocles

Pós-graduação em Letras - IBILCE

Equações de diferenças: aplicações no ensino médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

Equações diferenciais ordinárias não suaves autônomas e não autônomas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Intencionalidade e linguagem (II): algumas considerações sobre Tomaselo, Searle e Dennett

Propomos, neste trabalho, que o conceito de intencionalidade é uma ferramenta relevante para a interpretação de repertórios simbólicos humanos. Analisamos como os conceitos de intencionalidade e de linguagem verbal são articulados na Teoria da Aquisição da Linguagem Baseada no Uso de Tomasello, na Teoria dos Atos Ilocucionários de Searle e na Teoria dos Sistemas Intencionais de Dennett, buscando identificar seu papel na determinação da cognição humana. Essas teorias propõem uma interdependência entre esses conceitos, os quais difeririam entre si quanto ao modo como se dá essa articulação. Elas também destacam a importância dos repertórios simbólicos, especialmente a linguagem verbal, para a cognição humana. Como a intencionalidade é um aspecto da cognição humana, uma conexão entre linguagem verbal e intencionalidade para o funcionamento cognitivo humano é uma questão a ser investigada na psicologia científica.

Equações diferenciais ordinárias não suaves autônomas e não autônomas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Continuity of Lyapunov functions and of energy level for generalized gradient semigroup

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (differentiable along solutions)-defined on the whole phase space- which proves relevant information on the structure of the attractor. In this paper we prove the continuity of these Lyapunov functions under perturbation. On the other hand, the attractor of a gradient-like semigroup also has an energy level decomposition which is again a Morse decomposition but with a total order between any two components. We claim that, from a dynamical point of view, this is the optimal decomposition of a global attractor; that is, if we start from the finest Morse decomposition, the energy level decomposition is the coarsest Morse decomposition that still produces a Lyapunov function which gives the same information about the structure of the attractor. We also establish sufficient conditions which ensure the stability of this kind of decomposition under perturbation. In particular, if connections between different isolated invariant sets inside the attractor remain under perturbation, we show the continuity of the energy level Morse decomposition. The class of Morse-Smale systems illustrates our results.

Evaluation of physiologic complexity in time series using generalized sample entropy and surrogate data analysis

Complexity in time series is an intriguing feature of living dynamical systems, with potential use for identification of system state. Although various methods have been proposed for measuring physiologic complexity, uncorrelated time series are often assigned high values of complexity, errouneously classifying them as a complex physiological signals. Here, we propose and discuss a method for complex system analysis based on generalized statistical formalism and surrogate time series. Sample entropy (SampEn) was rewritten inspired in Tsallis generalized entropy, as function of q parameter (qSampEn). qSDiff curves were calculated, which consist of differences between original and surrogate series qSampEn. We evaluated qSDiff for 125 real heart rate variability (HRV) dynamics, divided into groups of 70 healthy, 44 congestive heart failure (CHF), and 11 atrial fibrillation (AF) subjects, and for simulated series of stochastic and chaotic process. The evaluations showed that, for nonperiodic signals, qSDiff curves have a maximum point (qSDiff(max)) for q not equal 1. Values of q where the maximum point occurs and where qSDiff is zero were also evaluated. Only qSDiff(max) values were capable of distinguish HRV groups (p-values 5.10 x 10(-3); 1.11 x 10(-7), and 5.50 x 10(-7) for healthy vs. CHF, healthy vs. AF, and CHF vs. AF, respectively), consistently with the concept of physiologic complexity, and suggests a potential use for chaotic system analysis. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4758815]

Magnetic flux transport by turbulent reconnection in astrophysical flows

The role of magnetohydrodynamics (MHD) turbulence in astrophysical environments is still highly debated. An important question that permeates this debate is the transport of magnetic flux. This is particularly important, for instance, in the context of star formation. When clouds collapse gravitationally to form stars, there must be some magnetic flux transport. Otherwise, the newborn stars would have magnetic fields several orders of magnitude larger than the observed ones. Also, the magnetic flux that is dragged in the late stages of the formation of a star can remove all the rotational support from the accretion disc that grows around the protostar. The efficiency of the mechanism that is often invoked to allow transport of magnetic fields at different stages of star formation, namely ambipolar diffusion, has recently been put in check. We discuss here an alternative mechanism for magnetic flux transport which is based on turbulent fast magnetic reconnection. We review recent results from three-dimensional MHD numerical simulations that indicate that this mechanism is very efficient in decoupling and transporting magnetic flux from the inner denser regions to the outskirts of collapsing clouds at different stages of star formation. We discuss this mechanism also in the context of dynamo processes and speculate that it can play a role both in solar dynamo and in accretion disc dynamo processes.

Mutual Information Rate and Bounds for It

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

Entanglement of excited states in critical spin chains

Renyi and von Neumann entropies quantifying the amount of entanglement in ground states of critical spin chains are known to satisfy a universal law which is given by the conformal field theory (CFT) describing their scaling regime. This law can be generalized to excitations described by primary fields in CFT, as was done by Alcaraz et al in 2011 (see reference [1], of which this work is a completion). An alternative derivation is presented, together with numerical verifications of our results in different models belonging to the c = 1, 1/2 universality classes. Oscillations of the Renyi entropy in excited states are also discussed.

Both the dorsal hippocampus and the dorsolateral striatum are needed for rat navigation in the Morris water maze

The multiple memory systems theory proposes that the hippocampus and the dorsolateral striatum are the core structures of the spatial/relational and stimulus-response (S-R) memory systems, respectively. This theory is supported by double dissociation studies showing that the spatial and cue (S-R) versions of the Morris water maze are impaired by lesions in the dorsal hippocarnpus and dorsal striatum, respectively. In the present study we further investigated whether adult male Wistar rats bearing double and bilateral electrolytic lesions in the dorsal hippocampus and dorsolateral striatum were as impaired as rats bearing single lesions in just one of these structures in learning both versions of the water maze. Such a prediction, based on the multiple memory systems theory, was not confirmed. Compared to the controls, the animals with double lesions exhibited no improvement at all in the spatial version and learned the cued version very slowly. These results suggest that, instead of independent systems competing for holding control over navigational behaviour, the hippocampus and dorsal striatum both play critical roles in navigation based on spatial or cue-based strategies. (C) 2011 Elsevier B.V. All rights reserved.

STRUCTURE AND BIFURCATION OF PULLBACK ATTRACTORS IN A NON-AUTONOMOUS CHAFEE-INFANTE EQUATION

The Chafee-Infante equation is one of the canonical infinite-dimensional dynamical systems for which a complete description of the global attractor is available. In this paper we study the structure of the pullback attractor for a non-autonomous version of this equation, u(t) = u(xx) + lambda(xx) - lambda u beta(t)u(3), and investigate the bifurcations that this attractor undergoes as A is varied. We are able to describe these in some detail, despite the fact that our model is truly non-autonomous; i.e., we do not restrict to 'small perturbations' of the autonomous case.

Um balanço de parte da teoria dos sistemas intencionais de Dennett

Dennett (1981/1987b) caracteriza sua abordagem do funcionamento dos termos intencionais (aqueles para as assim chamadas atitudes proposicionais) como um "behaviorismo lógico holista", ou versão holista de delineamentos conceituais traçados por Ryle (1949). Este artigo avalia algumas de suas possíveis contribuições e desvantagens para tais delineamentos, e algumas consequências para sua proposta de utilização destes termos em psicologia. Argumenta-se que a abordagem não se mostra mais plausível do que a de seu predecessor, caso a dimensão mentalista que lhe acrescenta seja equivocada, e que de fato este é o caso. Disso resulta que suas contribuições e proposta correlata devem ser entendidas com independência daquilo que tal dimensão implica. Uma alternativa não-mentalista, baseada no modelo selecionista de Skinner, para uma eventual adoção dos termos intencionais em psicologia, é brevemente discutida.