Denna avhandling i datalogi föreslår modeller för hur vissa beräkningsmässiga uppgifter kan utföras av hjärnbarken. Utgångspunkten är dels kända fakta om hur en area i hjärnbarken är uppbyggd och fungerar, dels etablerade modellklasser inom beräkningsneurobiologi, såsom attraktorminnen och system för gles kodning. Ett neuralt nätverk som producerar en effektiv gles kod i binär mening för sensoriska, särskilt visuella, intryck presenteras. Jag visar att detta nätverk, när det har tränats med naturliga bilder, reproducerar vissa egenskaper (receptiva fält) hos nervceller i lager IV i den primära synbarken och att de koder som det producerar är lämpliga för lagring i associativa minnesmodeller. Vidare visar jag hur ett enkelt autoassociativt minne kan modifieras till att fungera som ett generellt sekvenslärande system genom att utrustas med synapsdynamik. Jag undersöker hur ett abstrakt attraktorminnessystem kan implementeras i en detaljerad modell baserad på data om hjärnbarken. Denna modell kan sedan analyseras med verktyg som simulerar experiment som kan utföras på en riktig hjärnbark. Hypotesen att hjärnbarken till avsevärd del fungerar som ett attraktorminne undersöks och visar sig leda till prediktioner för dess kopplingsstruktur. Jag diskuterar också metodologiska aspekter på beräkningsneurobiologin idag. / In this thesis I take a modular approach to cortical function. I investigate how the cerebral cortex may realise a number of basic computational tasks, within the framework of its generic architecture. I present novel mechanisms for certain assumed computational capabilities of the cerebral cortex, building on the established notions of attractor memory and sparse coding. A sparse binary coding network for generating efficient representations of sensory input is presented. It is demonstrated that this network model well reproduces the simple cell receptive field shapes seen in the primary visual cortex and that its representations are efficient with respect to storage in associative memory. I show how an autoassociative memory, augmented with dynamical synapses, can function as a general sequence learning network. I demonstrate how an abstract attractor memory system may be realised on the microcircuit level -- and how it may be analysed using tools similar to those used experimentally. I outline some predictions from the hypothesis that the macroscopic connectivity of the cortex is optimised for attractor memory function. I also discuss methodological aspects of modelling in computational neuroscience. / QC 20100916

The concept of LR-nets was introduced and investigated firstly by H.P. Lotz in [27] and by F. Raebiger in [30]. Therefore we call such nets Lotz-Raebiger nets, shortly LR-nets. In this thesis we treat two problems on asymptotic behavior of these operator nets. First problem is to generalize well known theorems for Ces`aro averages of a single operator to LR-nets, namely to generalize the Eberlein and Sine theorems. The second problem is related to the strong convergence of Markov LR-nets on L1-spaces. We prove that the existence of a lower-bound functions is necessary and sufficient for asymptotic stability of LR-nets of Markov operators.

The purpose of this thesis is to generalize the growing theory of iterated function systems (IFSs). Earlier, hyperbolic IFSs with finitely many functions have been studied extensively. Also, hyperbolic IFSs with infinitely many functions have been studied. In this thesis, more general IFSs are studied. The Hausdorff pseudometric is studied. This is a generalization of the Hausdorff metric. Wide and narrow limit sets are studied. These are two types of limits of sequences of sets in a complete pseudometric space. Stable Iterated Function Systems, a kind of generalization of hyperbolic IFSs, are defined. Some different, but closely related, types of stability for the IFSs are considered. It is proved that the IFSs with the most general type of stability have unique attractors. Also, invariant sets, addressing, and periodic points for stable IFSs are studied. Hutchinson’s metric (also called Vaserhstein’s metric) is generalized from being defined on a space of probability measures, into a class of norms, the £-norms, on a space of real measures (on certain metric spaces). Under rather general conditions, it is proved that these norms, when they are restricted to positive measures, give rise to complete metric spaces with the metric topology coinciding with the weak*-topology. Then, IFSs with probabilities (IFSPs) are studied, in particular, stable IFSPs. The £-norm-results are used to prove that, as in the case of hyperbolic IFSPs, IFSPs with the most general kind of stability have unique invariant measures. These measures are ”attractive”. Also, an invariant measure is constructed by first ”lifting” the IFSP to the code space. Finally, it is proved that the Random Iteration Algorithm in a sense will ”work” for some stable IFSPs. / <p>Diss. Umeå : Umeå universitet, 1992</p> / digitalisering@umu

Este trabalho foca no estudo de duas redes complexas. A primeira é um modelo de Ising com campo aleatório. Este modelo segue uma distribuição de campo gaussiana e bimodal. Uma técnica de conectividade finita foi utilizada para resolvê-lo. Assim como um método de Monte Carlo foi aplicado para verificar os resultados. Há uma indicação em nossos resultados que para a distribuição gaussiana a transição de fase é sempre de segunda ordem. Para as distribuições bimodais há um ponto tricrítico, dependente do valor da conectividade . Abaixo de um certo mínimo de , só existe transição de segunda ordem. A segunda é uma rede neural atratora métrica. Mais precisamente, estudamos a capacidade deste modelo para armazenar os padrões estruturados. Em particular, os padrões escolhidos foram retirados de impressões digitais, que apresentam algumas características locais. Os resultados mostram que quanto menor a atividade de padrões de impressões digitais, maior a relação de carga e a qualidade de recuperação. Uma teoria, também foi desenvolvido como uma função de cinco parâmetros: a relação de carga, a conectividade, o grau de densidade da rede, a relação de aleatoriedade e a correlação do padrão espacial. / This work focus on the study of two complex networks. The first one is a random field Ising model. This model follows a gaussian and bimodal distribution, for the random field. A finite connectivity technique was utilized to solve it. As well as a Monte Carlo method was applied to verify our results. There is an indication in our results that for a gaussian distribution the phase transition is always second-order. For the bimodal distribution there is a tricritical point, tha depends on the value of the connectivity . Below a certain minimum , there is only a second-order transition. The second one is a metric attractor neural network. More precisely we study the ability of this model to learn structured patterns. In particular, the chosen patterns were taken from fingerprints, which present some local features. Our results show that the higher the load ratio and retrieval quality are the lower is the fingerprint patterns activity. A theoretical framework was also developed as a function of five parameters: the load ratio, the connectivity, the density degree of the network, the randomness ratio and the spatial pattern correlation.

We study asymptotic properties of evolution partial differential equations posed in unbounded spatial domain in the context of locally uniform spaces. This context allows the use of non-integrable data and carries an inherent non-compactness and non-separability. We establish the existence of a lo- cally compact attractor for non-local parabolic equation and weakly damped semilinear wave equation and provide an upper bound on the Kolmogorov's ε-entropy of these attractors and the attractor of strongly damped wave equation in the subcritical case using the method of trajectories. Finally we also investigate infinite dimensional exponential attractors of nonlinear reaction-diffusion equation in its natural energy setting. 1

Les ondes internes de gravité jouent un rôle essentiel dans la dynamique océanique. La relation de dispersion anisotrope de ces ondes conduit à des lois de réflexion qui sont différentes de celles dont nous avons l'habitude avec les ondes acoustiques ou les rayons lumineux. Dans cette thèse de doctorat, nous nous intéressons aux structures créées par ces ondes en deux dimensions puis en trois dimensions. Dans la plupart des géométries 2D, le parcours des ondes va converger vers un attracteur. Nous étudions d'abord expérimentalement, dans une géométrie trapézoïdale, l'aspect énergétique d'un de ces attracteurs d'ondes. Nous examinons ensuite expérimentalement la transformation de ces attracteurs dans des géométries tridimensionnelles. Dans certaines géométries, la réflexion des ondes conduit à un phénomène de piégeage dans un plan 2D. Ce phénomène, d'abord étudié à l'aide de tracés de rayons, a été reproduit dans une géométrie trapézoïdale ainsi que dans une géométrie de canal. Cette mise en évidence expérimentale du piégeage pourrait expliquer certaines mesures in-situ réalisées dans l'estuaire du Saint Laurent où la propagation des ondes internes est encore mal comprise. Cette thèse est enrichie par deux études expérimentales portant sur la propagation et la réflexion d'un faisceau d'ondes interne : d'une part, l'instabilité créant un courant moyen dans le cas d'un faisceau se propageant dans une géométrie tridimensionnelle et d'autre part la génération d'ondes rétro-réfléchies lors de la réflexion sur des surfaces courbes. / Internal waves play a critical rôle in the ocean dynamics. The anisotropic dispersion relation of these waves leads to reflexion law which are different from what we are used to with acoustic waves or light rays. In the PhD thesis, we are interested in structures generated by these waves, in two dimensions then in three dimensions. In most of the 2D geometries, wave path will converge onto an attractor. We firstly study experimentally, in a trapezoidal geometry, the energy aspect of one of these attractors. Then, we survey experimentally the future of these attractors in tridimensional geometries. In some of them, reflexion leads to a trapping event in a 2D plan. This phenomenon was firstly studied by means of ray tracing, and was reproduced in both a trapezoidal and a canal geometry. The experimental obtainment of trapping could explain some in-situ measurements done in the Saint Laurent estuary, where internal wave propagation is still under scrutiny. This thesis is enhanced by two experimental studies on propagation and reflexion of an internal wave beam. Firstly, the instability generating a mean flow from a beam propagating in a three-dimensional geometry. Secondly, the generation of back-reflected waves from beam reflexion on a curved surface.

Este trabalho foca no estudo de duas redes complexas. A primeira é um modelo de Ising com campo aleatório. Este modelo segue uma distribuição de campo gaussiana e bimodal. Uma técnica de conectividade finita foi utilizada para resolvê-lo. Assim como um método de Monte Carlo foi aplicado para verificar os resultados. Há uma indicação em nossos resultados que para a distribuição gaussiana a transição de fase é sempre de segunda ordem. Para as distribuições bimodais há um ponto tricrítico, dependente do valor da conectividade . Abaixo de um certo mínimo de , só existe transição de segunda ordem. A segunda é uma rede neural atratora métrica. Mais precisamente, estudamos a capacidade deste modelo para armazenar os padrões estruturados. Em particular, os padrões escolhidos foram retirados de impressões digitais, que apresentam algumas características locais. Os resultados mostram que quanto menor a atividade de padrões de impressões digitais, maior a relação de carga e a qualidade de recuperação. Uma teoria, também foi desenvolvido como uma função de cinco parâmetros: a relação de carga, a conectividade, o grau de densidade da rede, a relação de aleatoriedade e a correlação do padrão espacial. / This work focus on the study of two complex networks. The first one is a random field Ising model. This model follows a gaussian and bimodal distribution, for the random field. A finite connectivity technique was utilized to solve it. As well as a Monte Carlo method was applied to verify our results. There is an indication in our results that for a gaussian distribution the phase transition is always second-order. For the bimodal distribution there is a tricritical point, tha depends on the value of the connectivity . Below a certain minimum , there is only a second-order transition. The second one is a metric attractor neural network. More precisely we study the ability of this model to learn structured patterns. In particular, the chosen patterns were taken from fingerprints, which present some local features. Our results show that the higher the load ratio and retrieval quality are the lower is the fingerprint patterns activity. A theoretical framework was also developed as a function of five parameters: the load ratio, the connectivity, the density degree of the network, the randomness ratio and the spatial pattern correlation.

Submitted by HERACLIO LEDGAR LÓPEZ LÁZARO null (herack_11@hotmail.com) on 2016-03-21T12:48:28Z No. of bitstreams: 1 Heracliodissertação.pdf: 1074830 bytes, checksum: eacc291c2e8f474bef30477ea2c47a2f (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-03-22T14:20:35Z (GMT) No. of bitstreams: 1 lazaro_hll_me_sjrp.pdf: 1074830 bytes, checksum: eacc291c2e8f474bef30477ea2c47a2f (MD5) / Made available in DSpace on 2016-03-22T14:20:35Z (GMT). No. of bitstreams: 1 lazaro_hll_me_sjrp.pdf: 1074830 bytes, checksum: eacc291c2e8f474bef30477ea2c47a2f (MD5) Previous issue date: 2016-03-07 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / The problem that we are going to study in this work, is motivated by the dynamics of differential equations nonautonomous. We will establish the existence and uniqueness of solution for a class of parabolic semilineares equations with Dirichlet boundary condition, in a family of domains that varies with time. In addition, certain hypotheses about the non-linearity, we will show the existence of a family of attractors pullback. / O problema que vamos estudar neste trabalho é motivado pela dinâmica de equações diferenciais não autônomas. Vamos estabelecer a existência e unicidade de solução para uma classe de equaçõoes parabólicas semilineares com condição de fronteira de Dirichlet, em uma família de domínios que varia com o tempo. Além disso, sob certas hipóteses sobre a não linearidade, mostraremos a existência de uma família de atratores pullback.

Este trabalho é dedicado ao estudo do comportamento a longo prazo de uma classe de equações viscoelásticas não lineares com memória, da forma |\'upsilon IND. t\'| POT. ho\' \'upsilon IND. tt\' - DELTA \'upsilon\' - \'DELTA upsilon IND. tt\' + \'INT. SUP. t INF. \\tau\' upsilon (t- s) \'DELTA epsilon\' (s) ds = h, \'\\tau\' > 0, definida num domínio limitado de \'R POT. N\'. Tal classe de problemas foi estudada por diversos autores desde 2001, com \'\\tau = 0. Os resultados existentes são principalmente devotados à existência de soluções globais, decaimento da energia, com ou sem dissipações adicionais, existência com dados pequenos, entre outros. Entretanto, a questão da unicidade de soluções e existência de atratores globais não foram discutidas em trabalhos anteriores. No presente trabalho, apresentamos resultados de unicidade e existência de atratores globais para essa classe de problemas num contexto mais geral, incluindo o caso em que \'\\tau\' = -\'INFINITO\'. Além disso, incluímos um problema complementar, de quarta ordem onde estudamos a existência de atratores exponenciais / This work is concerned with the long-time behaviour of a class nonlinear viscoelastic equations of the form |\'upsilon IND. t\'| POT. ho\' \'upsilon IND. tt\' - DELTA \'upsilon\' - \'DELTA upsilon IND. tt\' + \'INT. SUP. t INF. \\tau\' upsilon (t- s) \'DELTA epsilon\' (s) ds = h, \'ho\' > 0, defined in a bounded domain of \'R POT. N\'. Such class of problems was studied by several authors since 2001, with \'\\tau\' = 0. Existing results are mainly devoted to global existence, energy decay, with or without additional dampings, existence with small data, among others. However, uniqueness and existence of global attractors were not considered previously. In the present work, we establish some results on the uniqueness of solutions and existence of global attractors in a more general setting, including \'\\tau\' = - \'INFINITY\'. In addition, we have added a second problem concerned with a fourth order equation where we study the existence of exponential attractors

Made available in DSpace on 2015-05-15T11:46:19Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 903709 bytes, checksum: 4a8dba984b00ee5480eecf90097b2745 (MD5) Previous issue date: 2014-06-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we study the Navier-Stokes flow in R2 8> >>>>>><> >>>>>>: @u @t − ⌫!u + (u ·r)u + rp = f em ⌦ ⇥ [0,+1) , divu = r· u = 0 em ⌦⇥ [0,+1) , u = 0 sobre @⌦ ⇥ [0,+1) , u(·, 0) = u0 em ⌦, in an unbounded domain such that the Poincar´e s inequality is holds, i.e., there is a constant #1 > 0 such that we have the following inequality Z⌦ $2dx  1 #1 Z⌦ |r$|2dx, for all $ 2 H1 0 (⌦). We show the existence of global attractor in the natural phases spaces for this system exploring the energy equation of the problem / Neste trabalho, estudamos o sistema de equa¸c oes de Navier-Stokes em R2 8> >>>>>><> >>>>>>: @u @t − ⌫!u + (u ·r)u + rp = f em ⌦ ⇥ [0,+1) , divu = r· u = 0 em ⌦⇥ [0,+1) , u = 0 sobre @⌦ ⇥ [0,+1) , u(·, 0) = u0 em ⌦, em dom´ınios ilimitados sob os quais vale a desigualdade de Poincar´e, isto ´e, existe uma constante #1 > 0 tal que Z⌦ $2dx  1 #1 Z⌦ |r$|2dx, para todo $ 2 H1 0 (⌦). Provamos a exist encia de atrator global no espa¸co de fases natural para este sistema explorando a equa¸c ao de energia do problema.