Non linear dynamical systems can present a diversity of unconventional features when perturbed by an external noise, such as an enhancing of transport properties, stabilization of spatial patterns and noise induced phase transitions. In particular, the external noise can improve the system s response to weak external periodic pulses, a phenomenon termed as stochastic resonance due to its similarity with the resonance phenomena displayed by deterministic dynamical systems. Stochastic resonance ideas have been widely applied to better understand the behavior of many physical, chemical and biological systems, such as optical, electronic and magnetic systems, chemical reactions, as well as several features regarding neuro-physiological aspects of sensory systems. In this work, we study the stochastic resonance phenomenon in the integrate-fire model for the neuronal response by a sub-threshold periodic signal. In the traditional approach the threshold level is reached by superposing a gaussian noise to the periodic drive. As non gaussian noises have been shown to be quite overspread in natural systems, we investigate the sensitivity of the stochastic resonance condition upon the noise s probability distribution function. To generate a power-law distributed noise, we considered a stochastic process with both additive and multiplicative noises which allows for a fine tuning of the asymptotic power-law decay exponent. We employed both analogical and computational solutions of the stochastic differential equations which produced similar results. The dependence of the optimal noise intensity for the stochastic resonance condition on the power-law exponent of the non gaussian noise is reported. Our main finding is that the stochastic resonance condition is achieved with a minimum intensity of the input noise when it has a probability distribution with a finite decay exponent. Therefore, neural systems can explore the non gaussian character of the input noise to improve the ability to identify sub-threshold signals. Instituto de F´ısica - UFAL / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Sistemas dinâmicos não lineares podem apresentar uma diversidade de características não convencionais quando perturbados por ruídos externos, tais como uma otimização das propriedades de transporte, estabilização de padrões espaciais e transições de fase. Em particular, o ruído pode melhorar a resposta do sistema a pulsos periódicos externos fracos, um fenômeno conhecido como ressonância estocástica devido a sua similaridade com o fenômeno de ressonância mostrado por sistemas dinâmicos determinísticos. A idéia de ressonância estocástica foi largamente aplicada para se entender o comportamento de muitos sistemas físicos, químicos e biológicos, tais como sistemas magnéticos, ópticos, eletrônicos, reações químicas, assim como vários aspectos neurofisiológicos de sistemas sensoriais. Nesta dissertação, nós estudamos o fenômeno de ressonância estocástica em um modelo integra-dispara para resposta neuronal estimulada por um sinal periódico sub-limiar. No enfoque tradicional, o nível de limiar de disparo é alcançado por uma superposição de um ruído gaussiano com um estímulo periódico. Como ruídos não gaussianos surgem em sistemas naturais com elevada freqüência, nós investigamos a sensibilidade da condição de ressonância estocástica em relação à função distribuição de probabilidade do ruído. Para gerarmos um ruído distribuído tipo lei de potência, nós consideramos um processo estocástico com ruído multiplicativo e aditivo que permite o ajuste fino do expoente de decaimento assintótico da lei de potência. Utilizamos tanto solução analógica quanto digital de equações diferenciais estocásticas que produzem resultados similares. A dependência da intensidade ótima de ruído para a condição de ressonância estocástica com o expoente da lei de potência de um ruído não gaussiano é relatada. Em particular, obtivemos que a condição de ressonância é atingida com o mínimo ruído possível para ruídos que apresentam um expoente da lei de decaimento finito. Portanto, a natureza não gaussiana do ruído pode ser explorada para otimizar a identificação de sinais sub-limiares por sistemas neuronais.

Objective Deterioration of cutaneous perception may be one reason for the increased rate of falling in the elderly. The stochastic resonance phenomenon may compensate this loss of information by improving the capability to detect and transfer weak signals. In the present study, we hypothesize that subliminal electrical and mechanical noise applied to the sole of the foot of healthy elderly subjects improves vibration perception thresholds (VPT). Methods VPTs of 99 healthy elderly subjects were measured at 30 Hz at the heel and first metatarsal head (MET I). Participants were randomly assigned to one of five groups: vibration (Vi-G), current (Cu-G), control (Co-G), placebo-vibration (Pl-Vi), and placebo-current (Pl-Cu). Vi-G and Cu-G were stimulated using 90% (subliminal) of their individual perception thresholds for five minutes in a standing position. Co-G received no stimulation. The placebo groups were treated with mock stimulation. VPTs were measured twice before the intervention (baseline (BASE) and pre-measurement (PRE)), and once after the intervention (post-measurement (POST)). Results Significant differences were found between measurement conditions comparing BASE and POST, and PRE and POST. VPTs between groups within each measurement condition showed no significant differences. Vi-G was the only group that showed significantly higher VPTs in POST compared to BASE and PRE, which contradicts previous studies. Conclusion We analyzed increased VPTs after subliminal mechanical stimulation. The pressure load of standing for five minutes combined with subliminal stimulation may have shifted the initial level of mechanoreceptor sensitivity, which may lead to a deterioration of the VPT. The subliminal electrical stimulation had no effect on VPT. Significance Based on our results, we cannot confirm positive effects of subliminal electrical or mechanical stimulation on the sole of the foot.

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Diese Arbeit behandelt die Asymptotik von Austritts- und Übergangszeiten für gewisse schwach zeitinhomogene Diffusionsprozesse. Darauf basierend wird ein probabilistischer Begriff der stochastischen Resonanz (SR) studiert. Techniken der großen Abweichungen spielen eine zentrale Rolle. Im ersten Teil der Arbeit (Kapitel 1-3) werden Resultate aus der Theorie der großen Abweichungen für zeithomogene Diffusionen rekapituliert. Es werden die klassischen Resultate von Freidlin und Wentzell und Erweiterungen dieser Theorie präsentiert, und es wird an das Kramers''sche Austrittszeitengesetz erinnert. Teil II befasst sich mit dem Phänomen der SR, d.h. mit Periodizitätseigenschaften von Diffusionen. In Kapitel 4 werden physikalische Maße zur Messung der Periodizität diskutiert. Deren Nachteile legen es nahe, einem alternativen, probabilistischen Ansatz zu folgen, der hier behandelt wird. Das 5. Kapitel dient der Herleitung eines gleichmäßigen Prinzips der großen Abweichungen für Diffusionen mit schwach zeitabhängigem, periodischem Drift. Die Gleichmäßigkeit des Prinzips ermöglicht die exakte Bestimmung exponentieller Übergangsraten in Kapitel 6, das die zentralen Ergebnisse des 2. Teils beinhaltet. Hierdurch wird die Maximierung gewisser Übergangswahrscheinlichkeiten ermöglicht, was zum in Kapitel 7 studierten Resonanzbegriff führt. Teil III der Arbeit setzt sich mit der Asymptotik von Austrittszeiten sogenannter selbststabilisierender Diffusionen auseinander. In Kapitel 8 wird der Zusammenhang zwischen interagierenden Teilchensystemen und selbststabilisierenden Diffusionen erläutert und die Existenz- und Eindeutigkeitsfrage behandelt. Das 9. Kapitel dient dem Studium der großen Abweichungen dieser Klasse von Diffusionen. In Kapitel 10 wird das Kramers''sche Austrittszeitengesetz auf selbststabilisierende Diffusionen übertragen, und in Kapitel 11 wird der Einfluß der selbststabilisierenden Komponente auf das Austrittszeitengesetz illustriert. / In this thesis, we study the asymptotic behavior of exit and transition times of certain weakly time inhomogeneous diffusion processes. Based on these asymptotics, a probabilistic notion of stochastic resonance (SR) is investigated. Large deviations techniques play the key role throughout this work. In the first part (Chapters 1-3) we recall the large deviations theory for time homogeneous diffusions. We present the classical results due to Freidlin and Wentzell and extensions thereof, and we remind of Kramers'' exit time law. Part II deals with the phenomenon of stochastic resonance. That is, we study periodicity properties of diffusion processes. In Chapter 4 we explain the paradigm of stochastic resonance and discuss physical notions of measuring periodicity of diffusions. Their drawbacks suggest to follow an alternative probabilistic approach, which is treated in this work. In Chapter 5 we derive a large deviations principle for diffusions subject to a weakly time dependent periodic drift term. The uniformity of the obtained large deviations bounds w.r.t. the system''s parameters plays a key role for the treatment of transition time asymptotics in Chapter 6, which contains the main result of the second part. The exact exponential transition rates obtained here allow for maximizing transition probabilities, which finally leads to the announced probabilistic notion of resonance studied in Chapter 7. In the third part we investigate the exit time asymptotics of a certain class of so-called self-stabilizing diffusions. In Chapter 8 we explain the connection between interacting particle systems and self-stabilizing diffusions, and we address the question of existence. The following Chapter 9 is devoted to the study of the large deviations behavior of these diffusions. In Chapter 10 Kramers'' exit law is carried over to our class of self-stabilizing diffusions. Finally, the influence of self-stabilization is illustrated in Chapter 11.

Made available in DSpace on 2017-07-21T19:25:55Z (GMT). No. of bitstreams: 1 Ricardo Oyarzabal.pdf: 9526420 bytes, checksum: efaea71ba33c01d1cc5ff4456b4f0665 (MD5) Previous issue date: 2017-02-21 / Fundação de Amparo a Pesquisa do Estado de São Paulo / We investigated chaotic transport of particles in a magnetized plasma with two waves of electrostatic drift. Considering the dissipation, we verify the appearance of periodic attractors and show that the properties of the basin depend on the dissipation. The average escape time of the initial conditions of an established frontier obeys a power law decay type with increasing of the dissipation. We find positive finite time Lyapunov exponents in dissipative drift motion, consequently the trajectories exhibit transient chaotic transport. The increase in noise dissipative drift motion enhances escape peaks in the average time for a given critical value of the noise intensity. The optimization of a system feature is the situation that occurs stochastic resonance (SR). It is observed that the noise changes the distribution in the escape time. This work is important to improve the understanding of the drift wave model in the presence of dissipation and noise, a natural ingredient in the environment of this kind of physical problem. / Neste estudo investigamos o transporte caótico de partículas em um plasma magnetizado com duas ondas de deriva eletrostáticas. Considerando a dissipação, verificamos o surgimento de atratores periódicos e mostramos que as propriedades das bacias dependem da dissipação. O tempo de escape médio das condições iniciais, em uma fronteira estabelecida, obedece um decaimento do tipo lei de potência com o aumento da dissipação. Encontramos também expoentes de Lyapunov a tempo finito positivos, consequentemente, as trajetórias apresentam transiente caótico. Com o acréscimo de ruído no movimento de deriva dissipativo, notamos um aumento nos picos relativos ao tempo de escape médio. Estes valores máximos ocorrem para determinado valor crítico da intensidade do ruído A otimização de uma característica do sistema é a situação em que ocorre a ressonância estocàstica (RE). Observa-se que o ruído altera a distribuição no tempo de escape. Este trabalho é relevante no sentido de melhorar a compreensão do modelo de ondas de deriva na presença de dissipação e ruído.

<p>This thesis is concerned with detection of transient signal families and detectors in nonlinear static sensor systems. The detection problems are treated within the framework of likelihood ratio based binary hypothesis testing.</p><p>An analytical solution to the noncoherent detection problem is derived, which in contrast to the classical noncoherent detector, is optimal for wideband signals. An optimal detector for multiple transient signals with unknown arrival times is also derived and shown to yield higher detection performance compared to the classical approach based on the generalized likelihood ratio test.</p><p>An application that is treated in some detail is that of ultrasonic nondestructive testing, particularly pulse-echo detection of defects in elastic solids. The defect detection problem is cast as a composite hypothesis test and a methodology, based on physical models, for designing statistically optimal detectors for cracks in elastic solids is presented. Detectors for defects with low computational complexity are also formulated based on a simple phenomenological model of the defect echoes. The performance of these detectors are compared with the physical model-based optimal detector and is shown to yield moderate performance degradation.</p><p>Various aspects of optimal detection in static nonlinear sensor systems are also treated, in particular the stochastic resonance (SR) phenomenon which, in this context, implies noise enhanced detectability. Traditionally, SR has been quantified by means of the signal-to-noise ratio (SNR) and interpreted as an increase of a system's information processing capability. Instead of the SNR, rigorous information theoretic distance measures, which truly can support the claim of noise enhanced information processing capability, are proposed as quantifiers for SR. Optimal detectors are formulated for two static nonlinear sensor systems and shown to exhibit noise enhanced detectability.</p>

<p>In every living cell, millions of different types of molecules constantly interact and react chemically in a complex system that can adapt to fluctuating environments and extreme conditions, living to survive and reproduce itself. The information required to produce these components is stored in the genome, which is copied in each cell division and transferred and mixed with another genome from parent to child. The regulatory mechanisms that control biological systems, for instance the regulation of expression levels for each gene, has evolved so that global robustness and ability to survive under harsh conditions is a strength, at the same time as biological tasks on a detailed molecular level must be carried out with good precision and without failures. This has resulted in systems that can be described as a hierarchy of levels of complexity: from the lowest level, where molecular mechanisms control other components at the same level, to pathways of coordinated interactions between components, formed to carry out particular biological tasks, and up to large-scale systems consisting of all components, connected in a network with a topology that makes the system robust and flexible. This thesis reports on work that model and analyze complex biological systems, and the signals and noise that regulate them, at all different levels of complexity. Also, it shows how signals are transduced vertically from one level to another, as when a single mutation can cause errors in low level mechanisms, disrupting pathways and create systemwide imbalances, such as in type 2 diabetes. The advancement of our knowledge of biological systems requires both that we go deeper and towards more detail, of single molecules in single cells, as well as taking a step back to understand the organisation and dynamics in the large networks of all components, and unite the different levels of complexity.</p>

Meine Dissertation behandelt verschiedene neue rauschinduzierte Phänomene in anregbaren Neuronenmodellen, insbesondere solche mit FitzHugh-Nagumo Dynamik. Ich beschreibe das Auftreten von vibronischer Resonanz in anregbaren Systemen. Sowohl in einer anregbaren elektronischen Schaltung als auch im FitzHugh-Nagumo Modell zeige ich, daß eine optimale Amplitude einer hochfrequenten externen Kraft die Signalantwort bezüglich eines niederfrequenten Signals verbessert. Weiterhin wird der Einfluß von additivem Rauschen auf das Zusammenwirken von stochastischer und vibronischer Resonanz untersucht. Weiterhin untersuche ich Systeme, die sowohl oszillierende als auch anregbare Eigenschaften beinhalten und dadurch zwei interne Frequenzen aufweisen. Ich zeige, daß in solchen Systemen der Effekt der stochastischen Resonanz deutlich erhöht werden kann, wenn eine zusätzliche hochfrequente Kraft in Resonanz mit den kleinen Oszillationen unterhalb der Anregungsschwelle hinzugenommen wird. Es ist beachtenswert, daß diese Verstärkung der stochastischen Resonanz eine geringere Rauschintensität zum Erreichen des Optimums benötigt als die standartmäßige stochastische Resonanz in anregbaren Systemen. Ich untersuche Frequenzselektivität bei der rauschinduzierten Signalverarbeitung von Signalen unterhalb der Anregungsschwelle in Systemen mit vielen rauschunterstützten stochastischen Attraktoren. Diese neuen Attraktoren mit abweichenden gemittelten Perioden weisen auch unterschiedliche Phasenbeziehungen zwischen den einzelnen Elementen auf. Ich zeige, daß die Signalantwort des gekoppelten Systems unter verschiedenen Rauscheinwirkungen deutlich verbessert oder auch reduziert werden kann durch das Treiben einzelner Elemente in Resonanz mit diesen neuen Resonanzfrequenzen, die mit passenden Phasenbeziehungen korrespondieren. Weiterhin konnte ich einen rauschinduzierten Phasenübergang von einem selbstoszillierenden System zu einem anregbaren System nachweisen. Dieser Übergang erfolgt durch eine rauschinduzierte Stabilisierung eines deterministisch instabilen Fixpunktes der lokalen Dynamik, während die gesamte Phasenraumstruktur des Systems erhalten bleibt. Die gemeinsame Wirkung von Kopplung und Rauschen führt zu einem neuen Typ von Phasenübergängen und bewirkt eine Stabilisierung des Systems. Das sich daraus ergebende rauschinduziert anregbare Regime zeigt charakteristische Eigenschaften von klassisch anregbaren Systemen, wie stochastische Resonanz und Wellenausbreitung. Dieser rauschinduzierte Phasenübergang ermöglicht dadurch die Übertragung von Signalen durch ansonsten global oszillierende Systeme und die Kontrolle der Signalübertragung durch Veränderung der Rauschintensität. Insbesondere eröffnen diese theoretischen Ergebnisse einen möglichen Mechanismus zur Unterdrückung unerwünschter globaler Oszillationen in neuronalen Netzwerken, welche charakteristisch für abnorme medizinische Zustände, wie z.B. bei der Parkinson&prime;schen Krankheit oder Epilepsie, sind. Die Wirkung von Rauschen würde dann wieder die Anregbarkeit herstellen, die den normalen Zustand der erkrankten Neuronen darstellt. / My thesis is concerned with several new noise-induced phenomena in excitable neural models, especially those with FitzHugh-Nagumo dynamics. In these effects the fluctuations intrinsically present in any complex neural network play a constructive role and improve functionality. I report the occurrence of Vibrational Resonance in excitable systems. Both in an excitable electronic circuit and in the FitzHugh-Nagumo model, I show that an optimal amplitude of high-frequency driving enhances the response of an excitable system to a low-frequency signal. Additionally, the influence of additive noise and the interplay between Stochastic and Vibrational Resonance is analyzed. Further, I study systems which combine both oscillatory and excitable properties, and hence intrinsically possess two internal frequencies. I show that in such a system the effect of Stochastic Resonance can be amplified by an additional high-frequency signal which is in resonance with the oscillatory frequency. This amplification needs much lower noise intensities than for conventional Stochastic Resonance in excitable systems. I study frequency selectivity in noise-induced subthreshold signal processing in a system with many noise-supported stochastic attractors. I show that the response of the coupled elements at different noise levels can be significantly enhanced or reduced by forcing some elements into resonance with these new frequencies which correspond to appropriate phase-relations. A noise-induced phase transition to excitability is reported in oscillatory media with FitzHugh-Nagumo dynamics. This transition takes place via noise-induced stabilization of a deterministically unstable fixed point of the local dynamics, while the overall phase-space structure of the system is maintained. The joint action of coupling and noise leads to a different type of phase transition and results in a stabilization of the system. The resulting noise-induced regime is shown to display properties characteristic of excitable media, such as Stochastic Resonance and wave propagation. This effect thus allows the transmission of signals through an otherwise globally oscillating medium. In particular, these theoretical findings suggest a possible mechanism for suppressing undesirable global oscillations in neural networks (which are usually characteristic of abnormal medical conditions such as Parkinson&prime;s disease or epilepsy), using the action of noise to restore excitability, which is the normal state of neuronal ensembles.

This thesis is concerned with detection of transient signal families and detectors in nonlinear static sensor systems. The detection problems are treated within the framework of likelihood ratio based binary hypothesis testing. An analytical solution to the noncoherent detection problem is derived, which in contrast to the classical noncoherent detector, is optimal for wideband signals. An optimal detector for multiple transient signals with unknown arrival times is also derived and shown to yield higher detection performance compared to the classical approach based on the generalized likelihood ratio test. An application that is treated in some detail is that of ultrasonic nondestructive testing, particularly pulse-echo detection of defects in elastic solids. The defect detection problem is cast as a composite hypothesis test and a methodology, based on physical models, for designing statistically optimal detectors for cracks in elastic solids is presented. Detectors for defects with low computational complexity are also formulated based on a simple phenomenological model of the defect echoes. The performance of these detectors are compared with the physical model-based optimal detector and is shown to yield moderate performance degradation. Various aspects of optimal detection in static nonlinear sensor systems are also treated, in particular the stochastic resonance (SR) phenomenon which, in this context, implies noise enhanced detectability. Traditionally, SR has been quantified by means of the signal-to-noise ratio (SNR) and interpreted as an increase of a system's information processing capability. Instead of the SNR, rigorous information theoretic distance measures, which truly can support the claim of noise enhanced information processing capability, are proposed as quantifiers for SR. Optimal detectors are formulated for two static nonlinear sensor systems and shown to exhibit noise enhanced detectability.