An extension of the invariance principle for dwell-time switched nonlinear systems

In this paper, we propose an extension of the invariance principle for nonlinear switched systems under dwell-time switched solutions. This extension allows the derivative of an auxiliary function V, also called a Lyapunov-like function, along the solutions of the switched system to be positive on some sets. The results of this paper are useful to estimate attractors of nonlinear switched systems and corresponding basins of attraction. Uniform estimates of attractors and basin of attractions with respect to time-invariant uncertain parameters are also obtained. Results for a common Lyapunov-like function and multiple Lyapunov-like functions are given. Illustrative examples show the potential of the theoretical results in providing information on the asymptotic behavior of nonlinear dynamical switched systems. (C) 2012 Elsevier B.V. All rights reserved.

Nonlinear estimation of neural processing time from BOLD signal with application to decision-making

The extraction of information about neural activity timing from BOLD signal is a challenging task as the shape of the BOLD curve does not directly reflect the temporal characteristics of electrical activity of neurons. In this work, we introduce the concept of neural processing time (NPT) as a parameter of the biophysical model of the hemodynamic response function (HRF). Through this new concept we aim to infer more accurately the duration of neuronal response from the highly nonlinear BOLD effect. The face validity and applicability of the concept of NPT are evaluated through simulations and analysis of experimental time series. The results of both simulation and application were compared with summary measures of HRF shape. The experiment that was analyzed consisted of a decision-making paradigm with simultaneous emotional distracters. We hypothesize that the NPT in primary sensory areas, like the fusiform gyrus, is approximately the stimulus presentation duration. On the other hand, in areas related to processing of an emotional distracter, the NPT should depend on the experimental condition. As predicted, the NPT in fusiform gyrus is close to the stimulus duration and the NPT in dorsal anterior cingulate gyrus depends on the presence of an emotional distracter. Interestingly, the NPT in right but not left dorsal lateral prefrontal cortex depends on the stimulus emotional content. The summary measures of HRF obtained by a standard approach did not detect the variations observed in the NPT. Hum Brain Mapp, 2012. (C) 2010 Wiley Periodicals, Inc.

The effects of hypocalcemia on spatial alternans and ventricular fibrillation studied with the optical mapping technique

The heart is a wonderful but complex organ: it uses electrochemical mechanisms in order to produce mechanical energy to pump the blood throughout the body and allow the life of humans and animals. This organ can be subject to several diseases and sudden cardiac death (SCD) is the most catastrophic manifestation of these diseases, responsible for the death of a large number of people throughout the world. It is estimated that 325000 Americans annually die for SCD. SCD most commonly occurs as a result of reentrant tachyarrhythmias (ventricular tachycardia (VT) and ventricular fibrillation (VF)) and the identification of those patients at higher risk for the development of SCD has been a difficult clinical challenge. Nowadays, a particular electrocardiogram (ECG) abnormality, “T-wave alternans” (TWA), is considered a precursor of lethal cardiac arrhythmias and sudden death, a sensitive indicator of risk for SCD. TWA is defined as a beat-to-beat alternation in the shape, amplitude, or timing of the T-wave on the ECG, indicative of the underlying repolarization of cardiac cells [5]. In other words TWA is the macroscopic effect of subcellular and celluar mechanisms involving ionic kinetics and the consequent depolarization and repolarization of the myocytes. Experimental activities have shown that TWA on the ECG is a manifestation of an underlying alternation of long and short action potential durations (APDs), the so called APD-alternans, of cardiac myocytes in the myocardium. Understanding the mechanism of APDs-alternans is the first step for preventing them to occur. In order to investigate these mechanisms it’s very important to understand that the biological systems are complex systems and their macroscopic properties arise from the nonlinear interactions among the parts. The whole is greater than the sum of the parts, and it cannot be understood only by studying the single parts. In this sense the heart is a complex nonlinear system and its way of working follows nonlinear dynamics; alternans also, they are a manifestation of a phenomenon typical in nonlinear dynamical systems, called “period-dubling bifurcation”. Over the past decade, it has been demonstrated that electrical alternans in cardiac tissue is an important marker for the development of ventricular fibrillation and a significant predictor for mortality. It has been observed that acute exposure to low concentration of calcium does not decrease the magnitude of alternans and sustained ventricular Fibrillation (VF) is still easily induced under these condition. However with prolonged exposure to low concentration of calcium, alternans disappears, but VF is still inducible. This work is based on this observation and tries to make it clearer. The aim of this thesis is investigate the effect of hypocalcemia spatial alternans and VF doing experiments with canine hearts and perfusing them with a solution with physiological ionic concentration and with a solution with low calcium concentration (hypocalcemia); in order to investigate the so called memory effect, the experimental activity was modified during the way. The experiments were performed with the optical mapping technique, using voltage-sensitive dye, and a custom made Java code was used in post-processing. Finding the Nolasco and Dahlen’s criterion [8] inadequate for the prediction of alternans, and takin into account the experimental results, another criterion, which consider the memory effect, has been implemented. The implementation of this criterion could be the first step in the creation of a method, AP-based, discriminating who is at risk if developing VF. This work is divided into four chapters: the first is a brief presentation of the physiology of the heart; the second is a review of the major theories and discovers in the study of cardiac dynamics; the third chapter presents an overview on the experimental activity and the optical mapping technique; the forth chapter contains the presentation of the results and the conclusions.

Computational Schemes for Optimizing Domains of Attraction in Dynamical Systems

In this paper, several computational schemes are presented for the optimal tuning of the global behavior of nonlinear dynamical sys- tems. Specifically, the maximization of the size of domains of attraction associated with invariants in parametrized dynamical sys- tems is addressed. Cell Mapping (CM) tech- niques are used to estimate the size of the domains, and such size is then maximized via different optimization tools. First, a ge- netic algorithm is tested whose performance shows to be good for determining global maxima at the expense of high computa- tional cost. Secondly, an iterative scheme based on a Stochastic Approximation proce- dure (the Kiefer-Wolfowitz algorithm) is eval- uated showing acceptable performance at low cost. Finally, several schemes combining neu- ral network based estimations and optimiza- tion procedures are addressed with promising results. The performance of the methods is illus- trated with two applications: first on the well-known van der Pol equation with stan- dard parametrization, and second the tuning of a controller for saturated systems.

Pitch perception: A dynamical-systems perspective

Two and a half millennia ago Pythagoras initiated the scientific study of the pitch of sounds; yet our understanding of the mechanisms of pitch perception remains incomplete. Physical models of pitch perception try to explain from elementary principles why certain physical characteristics of the stimulus lead to particular pitch sensations. There are two broad categories of pitch-perception models: place or spectral models consider that pitch is mainly related to the Fourier spectrum of the stimulus, whereas for periodicity or temporal models its characteristics in the time domain are more important. Current models from either class are usually computationally intensive, implementing a series of steps more or less supported by auditory physiology. However, the brain has to analyze and react in real time to an enormous amount of information from the ear and other senses. How is all this information efficiently represented and processed in the nervous system? A proposal of nonlinear and complex systems research is that dynamical attractors may form the basis of neural information processing. Because the auditory system is a complex and highly nonlinear dynamical system, it is natural to suppose that dynamical attractors may carry perceptual and functional meaning. Here we show that this idea, scarcely developed in current pitch models, can be successfully applied to pitch perception.

Amplifier similariton fiber laser with nonlinear spectral compression

We propose a new concept of a fiber laser architecture supporting self-similar pulse evolution in the amplifier and nonlinear spectral pulse compression in the passive fiber. The latter process allows for transform-limited picosecond pulse generation, and improves the laser’s power efficiency by preventing strong spectral filtering from being highly dissipative. Aside from laser technology, the proposed scheme opens new possibilities for studying nonlinear dynamical processes. As an example, we demonstrate a clear period-doubling route to chaos in such a nonlinear laser system.

New insights in the moderating effect of switching costs on the satisfaction-repurchase behavior link

Existing studies on the role of switching costs (SC) as moderator of the relationship between satisfaction and repurchase behavior are inconclusive. We attempt to explain these inconclusive findings by synthesizing an amplifying and a lock-in effect, and hypothesize a nonlinear moderating effect. In Study 1 (a main study and three replications), we find strong evidence for an inverted u-shaped moderating effect of overall SC. Our results suggest that satisfaction is a particularly important predictor of repurchase behavior in situations characterized by medium-levels of SC. Based on Prospect Theory, Study 2 (a main study and one replication) reveals that this inverted u-shaped moderating effect of SC is stronger for positive (relational and financial) SC than for negative (procedural) SC. We conclude with recommendations for satisfaction management of different customer segments, and describe possibilities to influence customer switching costs in various industries. © 2014 New York University.

Probabilistic DHP adaptive critic for nonlinear stochastic control systems

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Kárnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained.

New nonlinear regimes of pulse generation in mode- locked fiber lasers

Mode-locked fiber lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes. The complex interplay among the effects of gain/loss, dispersion and nonlinearity in a fiber cavity can be used to shape the pulses and manipulate and control the light dynamics and, hence, lead to different mode-locking regimes. Major steps forward in pulse energy and peak power performance of passively mode-locked fiber lasers have been made with the recent discovery of new nonlinear regimes of pulse generation, namely, dissipative solitons in all-normal-dispersion cavities and parabolic self-similar pulses (similaritons) in passive and active fibers. Despite substantial research in this field, qualitatively new phenomena are still being discovered. In this talk, we review recent progress in the research on nonlinear mechanisms of pulse generation in passively mode-locked fiber lasers. These include similariton mode-locking, a mode-locking regime featuring pulses with a triangular distribution of the intensity, and spectral compression arising from nonlinear pulse propagation. We also report on the possibility of achieving various regimes of advanced temporal waveform generation in a mode-locked fiber laser by inclusion of a spectral filter into the laser cavity.

Capacity of nonlinear fibre channels and eigenvalue division multiplexing for optical transmissions

The nonlinear Fourier transform, also known as eigenvalue communications, is a coding, transmission and signal processing technique that makes positive use of the nonlinear Kerr effect in fibre channels. I will discuss recent progress in this field. © 2015 OSA.

Dimensionality hyper-reduction and machine learning for dynamical systems with varying parameters

Thesis (Ph.D.)--University of Washington, 2016-08

On the zeros of the Abelian integrals for a class of Liénard systems

A planar polynomial differential system has a finite number of limit cycles. However, finding the upper bound of the number of limit cycles is an open problem for the general nonlinear dynamical systems. In this paper, we investigated a class of Liénard systems of the form x'=y, y'=f(x)+y g(x) with deg f=5 and deg g=4. We proved that the related elliptic integrals of the Liénard systems have at most three zeros including multiple zeros, which implies that the number of limit cycles bifurcated from the periodic orbits of the unperturbed system is less than or equal to 3.

Information for regulating action in sport : metastability and emergence of tactical solutions under ecological constraints

The aims of this chapter are twofold. First, we show how experiments related to nonlinear dynamical systems theory can bring about insights on the interconnectedness of different information sources for action. These include the amount of information as emphasised in conventional models of cognition and action in sport and the nature of perceptual information typically emphasised in the ecological approach. The second aim was to show how, through examining the interconnectedness of these information sources, one can study the emergence of novel tactical solutions in sport; and design experiments where tactical/decisional creativity can be observed. Within this approach it is proposed that perceptual and affective information can be manipulated during practice so that the athlete's cognitive and action systems can be transposed to a meta-stable dynamical performance region where the creation of novel action information may reside.

Dynamic Image-based visual servo control using centroid and optic flow features

This paper considers the question of designing a fully image-based visual servo control for a class of dynamic systems. The work is motivated by the ongoing development of image-based visual servo control of small aerial robotic vehicles. The kinematics and dynamics of a rigid-body dynamical system (such as a vehicle airframe) maneuvering over a flat target plane with observable features are expressed in terms of an unnormalized spherical centroid and an optic flow measurement. The image-plane dynamics with respect to force input are dependent on the height of the camera above the target plane. This dependence is compensated by introducing virtual height dynamics and adaptive estimation in the proposed control. A fully nonlinear adaptive control design is provided that ensures asymptotic stability of the closed-loop system for all feasible initial conditions. The choice of control gains is based on an analysis of the asymptotic dynamics of the system. Results from a realistic simulation are presented that demonstrate the performance of the closed-loop system. To the author's knowledge, this paper documents the first time that an image-based visual servo control has been proposed for a dynamic system using vision measurement for both position and velocity.