The work presented in this dissertation focuses on the use of computational and mathematical models to investigate how mammalian brains construct and maintain stable representations of space and location. Recordings of the activities of cells in the hippocampus and entorhinal cortex have provided strong, direct evidence that these cells and brain areas are involved in generating internal representations of the location of an animal in space. The emphasis of the first two portions of the dissertation are on understanding the factors that influence the scale and stability of these representations, both of which are important for accurate spatial navigation. In addition, it is argued in both cases that many of the computations observed in these systems emerge at least in part as a consequence of a particular type of network structure, where excitatory neurons are driven by external sources, and then mutually inhibit each other via interactions mediated by inhibitory cells. The first contribution of this thesis, which is described in chapter 2, is an investigation into the origin of the change in the scale of spatial representations across the dorsoventral axis of the hippocampus. Here it will be argued that this change in scale is due to increased processing of nonspatial information, rather than a dorsoventral change in the scale of the spatially-modulated inputs to this structure. Chapter 3 explores the factors influencing the dynamical stability of class of pattern-forming networks known as continuous attractor networks, which have been used to model various components of the spatial navigation systems, including head direction cells, place cells, and grid cells. Here it will be shown that network architecture, the amount of input drive, and the timescales at which cells interact all influence the stability of the patterns formed by these networks. Finally, in chapter 4, a new technique for analyzing neural data is introduced. This technique is a spike train similarity measure designed to compare spike trains on the basis of shared inhibition and bursts.

The central purpose of this study is the integration of modem philosophical thinking with different chaos theory principles and definitions to form relational perspectives. Relations are used in different contexts to base the causes of deterministic chaos (chaost) in the laws of nature which constitutes order. The chaost-attractor is used as subjective conception to investigate the possibilities of hidden order in a seemingly chaotic state of the objective reality. Relevant definitions of the chaos theory were analysed methodically and transcendentally with the aid of concepts of order and relations. Attention is given to the broad associations and analogies from philosophy and other disciplines which relate to the connectivity of objects to form systems. Subjective model development was done which is used to consequentially analyse some statements from published research which applied principles of chaost. It is argued that: the intrinsic properties of objects determine the causality of forces which bind objects to compose systems; a web of interactive bonds functions subjective to laws of nature which determine whether a system is in a state of order, chaost or real chaos; a dynamical transfer of many intrinsic and asymmetric properties via internal bonds constitutes non-linear connectivity which causes a sensitivity for initial conditions. It is found that the chaost of the chaos theory is not the same as real, objective chaos. The random-like evolution of a dynamic system is determined by the occurrence of irregularities and uncertainties in its internal order. A web of interactive bonds distribute small changes self-similar and scale-relevant. The difficulty in describing and explaining the complex behaviour of composed entities is simplified by the proposed web-chaost model. / Thesis (M.A. (Philosophy))--North-West University, Potchefstroom Campus, 2006.

Chaos theory is well known as one of three revolutions in physical sciences in 20th-century, as one physicist called it: Relativity eliminated the Newtonian illusion of absolute space and time; quantum theory eliminated the Newtonian dream of a controllable measurable process; and chaos eliminates the Laplacian fantasy of deterministic predictability". Specially, when chaos synchronization was found in 1991, chaos theory becomes more and more attractive. Chaos has been widely applied to many scientific disciplines: mathematics, programming, microbiology, biology, computer science, economics, engineering, finance, philosophy, physics, politics, population dynamics, psychology, and robotics. One of most important engineering applications is secure communication because of the properties of random behaviours and sensitivity to initial conditions of chaos systems. Noise-like dynamical behaviours can be used to mask the original information in symmetric cryptography. Sensitivity to initial conditions and unpredictability make chaotic systems very suitable to construct one-way function in public-key cryptography. In chaos-based secure communication schemes, information signals are masked or modulated (encrypted) by chaotic signals at the transmitter and the resulting encrypted signals are sent to the corresponding receiver across a public channel (unsafe channel). Perfect chaos synchronization is usually expected to recover the original information signals. In other words, the recovery of the information signals requires the receiver's own copy of the chaotic signals which are synchronized with the transmitter ones. Thus, chaos synchronization is the key technique throughout this whole process. Due to the difficulties of generating and synchronizing chaotic systems and the limit of digital computer precision, there exist many challenges in chaos-based secure communication. In this thesis, we try to solve chaos generation and chaos synchronization problems. Starting from designing chaotic and hyperchaotic system by first-order delay differential equation, we present a family of novel cell attractors with multiple positive Lyapunov exponents. Compared with previously reported hyperchaos systems with complex mathematic structure (more than 3 dimensions), our system is relatively simple while its dynamical behaviours are very complicated. We present a systemic parameter control method to adjust the number of positive Lyapunov exponents, which is an index of chaos degree. Furthermore, we develop a delay feedback controller and apply it to Chen system to generate multi-scroll attractors. It can be generalized to Chua system, Lorenz system, Jerk equation, etc. Since chaos synchronization is the critical technique in chaos-based secure communication, we present corresponding impulsive synchronization criteria to guarantee that the receiver can generate the same chaotic signals at the receiver when time delay and uncertainty emerge in the transmission process. Aiming at the weakness of general impulsive synchronization scheme, i.e., there always exists an upper boundary to limit impulsive intervals during the synchronization process, we design a novel synchronization scheme, intermittent impulsive synchronization scheme (IISS). IISS can not only be flexibly applied to the scenario where the control window is restricted but also improve the security of chaos-based secure communication via reducing the control window width and decreasing the redundancy of synchronization signals. Finally, we propose chaos-based public-key cryptography algorithms which can be used to encrypt synchronization signals and guarantee their security across the public channel.

The central purpose of this study is the integration of modem philosophical thinking with different chaos theory principles and definitions to form relational perspectives. Relations are used in different contexts to base the causes of deterministic chaos (chaost) in the laws of nature which constitutes order. The chaost-attractor is used as subjective conception to investigate the possibilities of hidden order in a seemingly chaotic state of the objective reality. Relevant definitions of the chaos theory were analysed methodically and transcendentally with the aid of concepts of order and relations. Attention is given to the broad associations and analogies from philosophy and other disciplines which relate to the connectivity of objects to form systems. Subjective model development was done which is used to consequentially analyse some statements from published research which applied principles of chaost. It is argued that: the intrinsic properties of objects determine the causality of forces which bind objects to compose systems; a web of interactive bonds functions subjective to laws of nature which determine whether a system is in a state of order, chaost or real chaos; a dynamical transfer of many intrinsic and asymmetric properties via internal bonds constitutes non-linear connectivity which causes a sensitivity for initial conditions. It is found that the chaost of the chaos theory is not the same as real, objective chaos. The random-like evolution of a dynamic system is determined by the occurrence of irregularities and uncertainties in its internal order. A web of interactive bonds distribute small changes self-similar and scale-relevant. The difficulty in describing and explaining the complex behaviour of composed entities is simplified by the proposed web-chaost model. / Thesis (M.A. (Philosophy))--North-West University, Potchefstroom Campus, 2006.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-10T17:51:03Z No. of bitstreams: 1 BRUNO ARTHUR SANTOS DE ALMEIDA - DISSERTAÇÃO PPGMAT 2015..pdf: 938463 bytes, checksum: ad040a3bd6379e6ea801856f1925dcca (MD5) / Made available in DSpace on 2018-08-10T17:51:03Z (GMT). No. of bitstreams: 1 BRUNO ARTHUR SANTOS DE ALMEIDA - DISSERTAÇÃO PPGMAT 2015..pdf: 938463 bytes, checksum: ad040a3bd6379e6ea801856f1925dcca (MD5) Previous issue date: 2015-08 / Capes / Para ler o resumo deste trabalho recomendamos o download do arquivo, uma vez que o mesmo possui fórmulas e caracteres matemáticos que não foram possíveis trascreve-los aqui. / To read the summary of this work we recommend downloading the file, since it has formulas and mathematical characters that were not possible to transcribe them here.

Este estudo aborda a enunciação juvenil no viés da função estética enredada ao fetichismo contemporâneo e à Cultura Digital. O contexto de pesquisa envolve a função estética disposta nos vídeos caseiros digitais de trabalhos escolares publicados na internet, em especial na interface digital de compartilhamento YouTube. Esta interface onde se encontram as publicações dos vídeos que se apresentam em um tempo de tentativas de convergência tecnológica, mercadológica, cultural e social, tem em especial um falante — neste caso o jovem, — como seu principal espect-autor que vive e transita entre essa a escola e a Cultura Digital. A linha teórica analítica de pesquisa dessa composição (produçãovídeo- imagem) é construída com os conceitos de Estética e Atrator no diálogo com BAKHTIN e CANEVACCI. No limiar desse suporte de comunicação, Massimo CANEVACCI discute o conceito de atrator visual enquanto código de alto valor fetish que, acoplado à mercadoria comunicacional contemporânea, seduz espetc-atores e encena enigmas silenciados. A partir da indagação filosófica e sob sua orientação, foi utilizada como ferramenta metodológica de apreciação a noção de estético considerando o princípio ético-estético bakhtiniano que entende o pensamento teórico articulado à vida, focado na perspectiva sócio-histórica tanto da criação quanto da expressão. A relevância do processo emerge desse cronotopo singular enunciativo juvenil que se manifesta na forma de vídeos caseiros com um típico traço estilístico e sistemático firmando-se cada vez mais em seu inacabamento e dialogicidade digital. Uma experiência oportunizada não só pela intertextualidade já oferecida pelas redes sociais digitais, mas também pela atividade estética avizinhada aos espaços escolares em que este jovem está hoje imerso. / This study approaches the juvenile enunciation bias in the aesthetic function entangled to contemporary fetishism and digital culture. The research context involves the aesthetic function arranged in school work digital home videos published on the internet, especially on YouTube digital sharing interface.This interface where the publications of the videos that are presented in a trial time of technological, market, cultural and social convergence are localizated, in particular has a speaker - in this case the young’s - as its main “spect-author” who lives and moves between this school and Digital Culture.The analytical theoretical line research in this composition is built on the concepts of Aesthetics and Attractor in dialogue with Bakhtin and Canevacci.On the threshold of this communication support, Massimo Canevacci discusses the concept of visual attractor while the high value fetish code that, coupled with good contemporary communication, seduces espetc-actors and performs silenced puzzles.From the philosophical inquiry and under his guidance, was used as a methodological tool for assessing the notion of aesthetic from the ethical-aesthetic principle that understands the Bakhtinian theoretical thinking articulated to life, focused on the socio-historical perspective same as the creation and the expression. The relevance of this process emerges from the single young enunciative chronotope that is manifested in the form of home made videos with a typical stylistic trait and systematically establishing “itself” in their incompleteness and digital dialogicity.An experience not only nurtured by intertextuality already offered by social digital networks, but also by the aesthetic activity around school spaces which this young people are now immersed.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-07-27T16:36:24Z No. of bitstreams: 1 RODRIGO TOLEDO TEIXEIRA CÂMARA - DISSERTAÇÃO PPGMAT 2011..pdf: 613119 bytes, checksum: 87759133ae4ab596c12042ee64e93dff (MD5) / Made available in DSpace on 2018-07-27T16:36:24Z (GMT). No. of bitstreams: 1 RODRIGO TOLEDO TEIXEIRA CÂMARA - DISSERTAÇÃO PPGMAT 2011..pdf: 613119 bytes, checksum: 87759133ae4ab596c12042ee64e93dff (MD5) Previous issue date: 2011-11 / CNPq / Neste trabalho consideramos uma equação de evolução não local com convolução e provamos a existência de um atrator global para o fluxo gerado por esta equação. Além disso, mostramos que o funcional energia associado a esta equação satisfaz a propriedade de Lyapunov de decrescer ao longo de soluções. Mostramos também a existência de equilíbrios não triviais e estudamos a instabilidade destes equilíbrios. / In this work, we consider a non local evolution equation with convolution and we prove the existence of a global attractor for the flow generated by that equation. Futhermore, we show that the energy functional associated with this equation satisfies the Lyapunov’s property of decreasing under the solutions. We also show the existence of non trivial equilibria and study its instability

Este estudo aborda a enunciação juvenil no viés da função estética enredada ao fetichismo contemporâneo e à Cultura Digital. O contexto de pesquisa envolve a função estética disposta nos vídeos caseiros digitais de trabalhos escolares publicados na internet, em especial na interface digital de compartilhamento YouTube. Esta interface onde se encontram as publicações dos vídeos que se apresentam em um tempo de tentativas de convergência tecnológica, mercadológica, cultural e social, tem em especial um falante — neste caso o jovem, — como seu principal espect-autor que vive e transita entre essa a escola e a Cultura Digital. A linha teórica analítica de pesquisa dessa composição (produçãovídeo- imagem) é construída com os conceitos de Estética e Atrator no diálogo com BAKHTIN e CANEVACCI. No limiar desse suporte de comunicação, Massimo CANEVACCI discute o conceito de atrator visual enquanto código de alto valor fetish que, acoplado à mercadoria comunicacional contemporânea, seduz espetc-atores e encena enigmas silenciados. A partir da indagação filosófica e sob sua orientação, foi utilizada como ferramenta metodológica de apreciação a noção de estético considerando o princípio ético-estético bakhtiniano que entende o pensamento teórico articulado à vida, focado na perspectiva sócio-histórica tanto da criação quanto da expressão. A relevância do processo emerge desse cronotopo singular enunciativo juvenil que se manifesta na forma de vídeos caseiros com um típico traço estilístico e sistemático firmando-se cada vez mais em seu inacabamento e dialogicidade digital. Uma experiência oportunizada não só pela intertextualidade já oferecida pelas redes sociais digitais, mas também pela atividade estética avizinhada aos espaços escolares em que este jovem está hoje imerso. / This study approaches the juvenile enunciation bias in the aesthetic function entangled to contemporary fetishism and digital culture. The research context involves the aesthetic function arranged in school work digital home videos published on the internet, especially on YouTube digital sharing interface.This interface where the publications of the videos that are presented in a trial time of technological, market, cultural and social convergence are localizated, in particular has a speaker - in this case the young’s - as its main “spect-author” who lives and moves between this school and Digital Culture.The analytical theoretical line research in this composition is built on the concepts of Aesthetics and Attractor in dialogue with Bakhtin and Canevacci.On the threshold of this communication support, Massimo Canevacci discusses the concept of visual attractor while the high value fetish code that, coupled with good contemporary communication, seduces espetc-actors and performs silenced puzzles.From the philosophical inquiry and under his guidance, was used as a methodological tool for assessing the notion of aesthetic from the ethical-aesthetic principle that understands the Bakhtinian theoretical thinking articulated to life, focused on the socio-historical perspective same as the creation and the expression. The relevance of this process emerges from the single young enunciative chronotope that is manifested in the form of home made videos with a typical stylistic trait and systematically establishing “itself” in their incompleteness and digital dialogicity.An experience not only nurtured by intertextuality already offered by social digital networks, but also by the aesthetic activity around school spaces which this young people are now immersed.

Este trabalho se propõe a estudar o comportamento assintótico dos sistemas dinâmicos autônomos respaldado na Teoria das Dimensões. Mais precisamente, vamos compreender de que maneira nos é útil limitar a dimensão fractal do atrator global de um semigrupo a fim de estudar a dinâmica em dimensão finita, sem que se perca informações sobre a dinâmica ao fazê-lo. Para tanto, o Teorema de Mañé tem um papel decisivo junto às propriedades da dimensão de Hausdorff e a da dimensão fractal; nos permitindo encontrar uma projeção cuja restrição ao atrator é injetora sobre um espaço de dimensão finita. Constatamos ainda que esta abordagem por projeções se aplica largamente a semigrupos originados de equações diferenciais em espaços de Banach de dimensão infinita. / In this work, we study the asymptotic behavior of autonomous dynamical systems supported on the Dimension Theory. More precisely, we understand how fractal dimension finiteness of the global attractor of a semigroup can be used to study the dynamics in finite dimension, without losing information on the dynamics in doing so. For this purpose, the Mañés Theorem plays a decisive role considering the Hausdorff dimension properties and the fractal dimension; thanks to which we managed to find a projection whose restriction to the attractor is an injective application over a finite dimensional space. Besides, we also acknowledge that this projections approach is largely applied to semigroups arrising from differential equations in infinite dimensional Banach spaces.

Este estudo aborda a enunciação juvenil no viés da função estética enredada ao fetichismo contemporâneo e à Cultura Digital. O contexto de pesquisa envolve a função estética disposta nos vídeos caseiros digitais de trabalhos escolares publicados na internet, em especial na interface digital de compartilhamento YouTube. Esta interface onde se encontram as publicações dos vídeos que se apresentam em um tempo de tentativas de convergência tecnológica, mercadológica, cultural e social, tem em especial um falante — neste caso o jovem, — como seu principal espect-autor que vive e transita entre essa a escola e a Cultura Digital. A linha teórica analítica de pesquisa dessa composição (produçãovídeo- imagem) é construída com os conceitos de Estética e Atrator no diálogo com BAKHTIN e CANEVACCI. No limiar desse suporte de comunicação, Massimo CANEVACCI discute o conceito de atrator visual enquanto código de alto valor fetish que, acoplado à mercadoria comunicacional contemporânea, seduz espetc-atores e encena enigmas silenciados. A partir da indagação filosófica e sob sua orientação, foi utilizada como ferramenta metodológica de apreciação a noção de estético considerando o princípio ético-estético bakhtiniano que entende o pensamento teórico articulado à vida, focado na perspectiva sócio-histórica tanto da criação quanto da expressão. A relevância do processo emerge desse cronotopo singular enunciativo juvenil que se manifesta na forma de vídeos caseiros com um típico traço estilístico e sistemático firmando-se cada vez mais em seu inacabamento e dialogicidade digital. Uma experiência oportunizada não só pela intertextualidade já oferecida pelas redes sociais digitais, mas também pela atividade estética avizinhada aos espaços escolares em que este jovem está hoje imerso. / This study approaches the juvenile enunciation bias in the aesthetic function entangled to contemporary fetishism and digital culture. The research context involves the aesthetic function arranged in school work digital home videos published on the internet, especially on YouTube digital sharing interface.This interface where the publications of the videos that are presented in a trial time of technological, market, cultural and social convergence are localizated, in particular has a speaker - in this case the young’s - as its main “spect-author” who lives and moves between this school and Digital Culture.The analytical theoretical line research in this composition is built on the concepts of Aesthetics and Attractor in dialogue with Bakhtin and Canevacci.On the threshold of this communication support, Massimo Canevacci discusses the concept of visual attractor while the high value fetish code that, coupled with good contemporary communication, seduces espetc-actors and performs silenced puzzles.From the philosophical inquiry and under his guidance, was used as a methodological tool for assessing the notion of aesthetic from the ethical-aesthetic principle that understands the Bakhtinian theoretical thinking articulated to life, focused on the socio-historical perspective same as the creation and the expression. The relevance of this process emerges from the single young enunciative chronotope that is manifested in the form of home made videos with a typical stylistic trait and systematically establishing “itself” in their incompleteness and digital dialogicity.An experience not only nurtured by intertextuality already offered by social digital networks, but also by the aesthetic activity around school spaces which this young people are now immersed.