In this paper we show how the theory of dynamical systems can be employed to solve problems in motion vision. In particular we develop algorithms for the recovery of dense depth maps and motion parameters using state space observers or filters. Four different dynamical models of the imaging situation are investigated and corresponding filters/ observers derived. The most powerful of these algorithms recovers depth and motion of general nature using a brightness change constraint assumption. No feature-matching preprocessor is required.

This paper considers the problem of language change. Linguists must explain not only how languages are learned but also how and why they have evolved along certain trajectories and not others. While the language learning problem has focused on the behavior of individuals and how they acquire a particular grammar from a class of grammars ${cal G}$, here we consider a population of such learners and investigate the emergent, global population characteristics of linguistic communities over several generations. We argue that language change follows logically from specific assumptions about grammatical theories and learning paradigms. In particular, we are able to transform parameterized theories and memoryless acquisition algorithms into grammatical dynamical systems, whose evolution depicts a population's evolving linguistic composition. We investigate the linguistic and computational consequences of this model, showing that the formalization allows one to ask questions about diachronic that one otherwise could not ask, such as the effect of varying initial conditions on the resulting diachronic trajectories. From a more programmatic perspective, we give an example of how the dynamical system model for language change can serve as a way to distinguish among alternative grammatical theories, introducing a formal diachronic adequacy criterion for linguistic theories.

Formalizing linguists' intuitions of language change as a dynamical system, we quantify the time course of language change including sudden vs. gradual changes in languages. We apply the computer model to the historical loss of Verb Second from Old French to modern French, showing that otherwise adequate grammatical theories can fail our new evolutionary criterion.

Omar Hijab, Shankar Sastry. / Bibliography: leaf [4]. / Caption title. "September, 1981." / Supported in part by NASA Grant no. 2384 Office of Naval Research under the JSEP Contract N00014-75-C-0648 DOE Grant no. ET-A01-2295T050

Dynamics with choice is a generalization of discrete-time dynamics where instead of the same evolution operator at every time step there is a choice of operators to transform the current state of the system. Many real life processes studied in chemical physics, engineering, biology and medicine, from autocatalytic reaction systems to switched systems to cellular biochemical processes to malaria transmission in urban environments, exhibit the properties described by dynamics with choice. We study the long-term behavior in dynamics with choice. We prove very general results on the existence and properties of global compact attractors in dynamics with choice. In addition, we study the dynamics with restricted choice when the allowed sequences of operators correspond to subshifts of the full shift. One of practical consequences of our results is that when the parameters of a discrete-time system are not known exactly and/or are subject to change due to internal instability, or a strategy, or Nature's intervention, the long term behavior of the system may not be correctly described by a system with "averaged" values for the parameters. There may be a Gestalt effect.

Dengue (pronounced den'guee) Fever (DF) and Dengue Hemorrhagic Fever (DHF), collectively known as "dengue," are mosquito-borne, potentially mortal, flu-like viral diseases that affect humans worldwide. Transmitted to humans by the bite of an infected mosquito, dengue is caused by any one of four serotypes, or antigen-specific viruses. In this thesis, both the spatial and temporal dynamics of dengue transmission are investigated. Different chapters present new models while building on themes of previous chapters. In Chapter 2, we explore the temporal dynamics of dengue viral transmission by presenting and analyzing an ODE model that combines an SIR human host- with a multi-stage SI mosquito vector transmission system. In the case where the juvenile populations are at carrying capacity, juvenile mosquito mortality rates are sufficiently small to be absorbed by juvenile maturation rates, and no humans die from dengue, both the analysis and numerical simulations demonstrate that an epidemic will persist if the oviposition rate is greater than the adult mosquito death rate. In Chapter 3, we present and analyze a non-autonomous, non-linear ODE system that incorporates seasonality into the modeling of the transmission of the dengue virus. We derive conditions for the existence of a threshold parameter, the basic reproductive ratio, denoting the expected number of secondary cases produced by a typically infective individual. In Chapter 4, we present and analyze a non-linear system of coupled reaction-diffusion equations modeling the virus' spatial spread. In formulating our model, we seek to establish the existence of traveling wave solutions and to calculate spread rates for the spatial dissemination of the disease. We determine that the epidemic wave speed increases as average annual, and in our case, winter, temperatures increase. In Chapter 5, we present and analyze an ODE model that incorporates two serotypes of the dengue virus and allows for the possibility of both primary and secondary infections with each serotype. We obtain an analytical expression for the basic reproductive number, R_0, that defines it as the maximum of the reproduction numbers for each strain/serotype of the virus. In each chapter, numerical simulations are conducted to support the analytical conclusions.

No description available.

Perception is a fundamental function because it allows organisms to be in contact with the environment and adjust to environmental conditions. Humans also possess higher intellectual functions, which allow for elaborate handling of perceptually obtained information. The thesis concerns a distinction between an inferential ("cognitive") mode and a (direct-)perceptual mode of apprehension, and a notion of perceptual skill acquisition as a transition from the inferential to the perceptual mode. The mode distinction and the mode-transition model was formulated by Runeson, Juslin, and Olsson (2000) within the ecological direct-perception framework (Gibson, 1966, 1979). The modes of apprehension were investigated in an experimental paradigm that concerned visual perception of the relative mass of two colliding objects. The relative mass is specified by an optical variable in the collision movement pattern, which observers may pick up while functioning in the perceptual mode. However, novices often rely on other, nonspecifying, optical variables that may constitute cues that are used in the inferential mode (Runeson et al., 2000). Four tentative mode indicators were employed: participants' realism of confidence, introspective mode reports, amplitudes of brain event-related potentials, and response times. Generally, the results did not support the mode-transition model of skill acquisition. Furthermore, results suggested that reliance both on the specifying and nonspecifying variables might have occurred either in the inferential or in the perceptual mode. However, the mode indicators may not have captured mode as intended. For instance, the discriminability of used optical variables, and not the mode of apprehension, may have affected both amplitudes of event-related potentials and mode reports. It is argued that the mode-transition model and the distinction between two modes of apprehension should be further investigated employing other methodologies, and, furthermore, that the mode distinction has a place within an ecological framework.

Dans cette thèse, nous nous intéressons aux critères d'existence et à la construction effective de fractions rationnelles à dynamique prescrite. Nous commençons par étudier le même problème pour certains revêtements ramifiés post-critiquement finis et nous donnons une méthode de construction à partir de dynamiques d'arbres. Puis nous présentons un théorème de Thurston qui fournit une caractérisation combinatoire pour passer du cadre topologique au cadre analytique. En particulier, nous généralisons aux applications non post-critiquement finies un résultat de Levy qui simplifie le critère de Thurston dans le cas polynomial. Nous illustrons cette généralisation par une condition suffisante d'existence de polynômes ayant un disque de Siegel fixe de type borné. Ensuite nous détaillons la construction par chirurgie quasiconforme d'un exemple de fraction rationnelle non post-critiquement finie dont la dynamique est décrite par un arbre. Plus généralement, nous montrons qu'un résultat de Cui Guizhen et Tan Lei permet de construire une famille de fractions rationnelles à ensemble de Julia disconnexe à partir de certains arbres de Hubbard pondérés.

No description available.