Symbolic dynamics and renormalization of non-autonomous k periodic dynamical systems

The purpose of this paper was to introduce the symbolic formalism based on kneading theory, which allows us to study the renormalization of non-autonomous periodic dynamical systems.

Reversible current power supply for fast-field cycling nuclear magnetic resonance equipment

The Fast Field-Cycling Nuclear Magnetic Resonance (FFC-NMR) is a technique used to study the molecular dynamics of different types of materials. The main elements of this equipment are a magnet and its power supply. The magnet used as reference in this work is basically a ferromagnetic core with two sets of coils and an air-gap where the materials' sample is placed. The power supply should supply the magnet being the magnet current controlled in order to perform cycles. One of the technical issues of this type of solution is the compensation of the non-linearities associated to the magnetic characteristic of the magnet and to parasitic magnetic fields. To overcome this problem, this paper describes and discusses a solution for the FFC-NMR power supply based on a four quadrant DC/DC converter.

Stochastic model of transcription initiation of closely spaced promoters in escherichia coli

Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica

Identity dynamics in non-profit organizations: Ideological and methodological identity orientations

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and Economics

Evolutionary dynamics of coding and non-coding transcriptomes.

Gene expression changes may underlie much of phenotypic evolution. The development of high-throughput RNA sequencing protocols has opened the door to unprecedented large-scale and cross-species transcriptome comparisons by allowing accurate and sensitive assessments of transcript sequences and expression levels. Here, we review the initial wave of the new generation of comparative transcriptomic studies in mammals and vertebrate outgroup species in the context of earlier work. Together with various large-scale genomic and epigenomic data, these studies have unveiled commonalities and differences in the dynamics of gene expression evolution for various types of coding and non-coding genes across mammalian lineages, organs, developmental stages, chromosomes and sexes. They have also provided intriguing new clues to the regulatory basis and phenotypic implications of evolutionary gene expression changes.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Dynamical properties of nonmarkovian stochastic differential equations

We study nonstationary non-Markovian processes defined by Langevin-type stochastic differential equations with an OrnsteinUhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non-Markovian process, and we discuss its consequences. Non-Markovicity can introduce a dependence on noise parameters in the dynamics of the correlation function in cases in which it becomes independent of these parameters in the Markovian limit. Several examples are discussed in which the relaxation time increases with respect to the Markovian limit. For a Brownian harmonic oscillator with fluctuating frequency, the non-Markovicity of the process decreases the domain of stability of the system, and it can change an infradamped evolution into an overdamped one.

Stochastic semiclassical fluctuations in Minkowski spacetime

The semiclassical Einstein-Langevin equations which describe the dynamics of stochastic perturbations of the metric induced by quantum stress-energy fluctuations of matter fields in a given state are considered on the background of the ground state of semiclassical gravity, namely, Minkowski spacetime and a scalar field in its vacuum state. The relevant equations are explicitly derived for massless and massive fields arbitrarily coupled to the curvature. In doing so, some semiclassical results, such as the expectation value of the stress-energy tensor to linear order in the metric perturbations and particle creation effects, are obtained. We then solve the equations and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. In the conformal field case, explicit results are obtained. These results hint that gravitational fluctuations in stochastic semiclassical gravity have a non-perturbative behavior in some characteristic correlation lengths.

Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter H > 1/2. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann¿Stieltjes integral.

Essays in equilibrium asset pricing

Introduction This dissertation consists of three essays in equilibrium asset pricing. The first chapter studies the asset pricing implications of a general equilibrium model in which real investment is reversible at a cost. Firms face higher costs in contracting than in expanding their capital stock and decide to invest when their productive capital is scarce relative to the overall capital of the economy. Positive shocks to the capital of the firm increase the size of the firm and reduce the value of growth options. As a result, the firm is burdened with more unproductive capital and its value lowers with respect to the accumulated capital. The optimal consumption policy alters the optimal allocation of resources and affects firm's value, generating mean-reverting dynamics for the M/B ratios. The model (1) captures convergence of price-to-book ratios -negative for growth stocks and positive for value stocks - (firm migration), (2) generates deviations from the classic CAPM in line with the cross-sectional variation in expected stock returns and (3) generates a non-monotone relationship between Tobin's q and conditional volatility consistent with the empirical evidence. The second chapter proposes a standard portfolio-choice problem with transaction costs and mean reversion in expected returns. In the presence of transactions costs, no matter how small, arbitrage activity does not necessarily render equal all riskless rates of return. When two such rates follow stochastic processes, it is not optimal immediately to arbitrage out any discrepancy that arises between them. The reason is that immediate arbitrage would induce a definite expenditure of transactions costs whereas, without arbitrage intervention, there exists some, perhaps sufficient, probability that these two interest rates will come back together without any costs having been incurred. Hence, one can surmise that at equilibrium the financial market will permit the coexistence of two riskless rates that are not equal to each other. For analogous reasons, randomly fluctuating expected rates of return on risky assets will be allowed to differ even after correction for risk, leading to important violations of the Capital Asset Pricing Model. The combination of randomness in expected rates of return and proportional transactions costs is a serious blow to existing frictionless pricing models. Finally, in the last chapter I propose a two-countries two-goods general equilibrium economy with uncertainty about the fundamentals' growth rates to study the joint behavior of equity volatilities and correlation at the business cycle frequency. I assume that dividend growth rates jump from one state to other, while countries' switches are possibly correlated. The model is solved in closed-form and the analytical expressions for stock prices are reported. When calibrated to the empirical data of United States and United Kingdom, the results show that, given the existing degree of synchronization across these business cycles, the model captures quite well the historical patterns of stock return volatilities. Moreover, I can explain the time behavior of the correlation, but exclusively under the assumption of a global business cycle.

On learning dynamics underlying the evolution of learning rules.

In order to understand the development of non-genetically encoded actions during an animal's lifespan, it is necessary to analyze the dynamics and evolution of learning rules producing behavior. Owing to the intrinsic stochastic and frequency-dependent nature of learning dynamics, these rules are often studied in evolutionary biology via agent-based computer simulations. In this paper, we show that stochastic approximation theory can help to qualitatively understand learning dynamics and formulate analytical models for the evolution of learning rules. We consider a population of individuals repeatedly interacting during their lifespan, and where the stage game faced by the individuals fluctuates according to an environmental stochastic process. Individuals adjust their behavioral actions according to learning rules belonging to the class of experience-weighted attraction learning mechanisms, which includes standard reinforcement and Bayesian learning as special cases. We use stochastic approximation theory in order to derive differential equations governing action play probabilities, which turn out to have qualitative features of mutator-selection equations. We then perform agent-based simulations to find the conditions where the deterministic approximation is closest to the original stochastic learning process for standard 2-action 2-player fluctuating games, where interaction between learning rules and preference reversal may occur. Finally, we analyze a simplified model for the evolution of learning in a producer-scrounger game, which shows that the exploration rate can interact in a non-intuitive way with other features of co-evolving learning rules. Overall, our analyses illustrate the usefulness of applying stochastic approximation theory in the study of animal learning.

Ruin problems under IBNR Dynamics

In this paper, we consider a discrete-time risk process allowing for delay in claim settlement, which introduces a certain type of dependence in the process. From martingale theory, an expression for the ultimate ruin probability is obtained, and Lundberg-type inequalities are derived. The impact of delay in claim settlement is then investigated. To this end, a convex order comparison of the aggregate claim amounts is performed with the corresponding non-delayed risk model, and numerical simulations are carried out with Belgian market data.

Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Alonso et al. [J. Phys. A: Math. Theor. 44, 396004 (2011)10.1088/1751-8113/44/39/395004]. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along with the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory, and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space D, and on the number of classical trajectories N of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.