Title: "What do a system’s dynamics tell us about its health?"
Abstract. A physician uses dynamic data and models to diagnose an illness and render a prognosis. Similarly, engineers use dynamic data and models along with computational methods to assess the condition of a wide range of components (automotive, aerospace, etc.). In this talk, examples of medical diagnostic and prognostic techniques from a layman’s perspective are used to motivate applications of health monitoring in composite missile casings, tactical vehicle wheel assemblies, spacecraft thermal barriers, marine engine valves, and automotive suspensions. Computational challenges that are addressed in these applications include: the solution of underdetermined inverse problems, detection of mechanical degradation in highly variable components, quantification of mechanical damage in the absence of complete physics-based models, effects of nonlinear dynamics on rate of degradation, and effects of damage accumulation on component life prediction.
Title: "Building Bridges between Neural Models and Complex Decision-Making Behavior"
Abstract. Diffusion processes, and their discrete time counterparts, random walk models, have demonstrated an ability to account for a wide range of findings from behavioral decision making for which the purely algebraic and deterministic models often used in economics and psychology cannot account. Recent studies that record neural activations in non-human primates during perceptual decision making tasks have revealed that neural firing rates closely mimic the accumulation of preference theorized by behaviorally-derived diffusion models of decision making. This presentation bridges the expanse between the neurophysiological and behavioral decision making literatures; specifically, decision field theory, a dynamic and stochastic theory of decision making, is presented as a model positioned between lower-level neural activation patterns and more complex notions of decision making found in psychology and economics. Potential neural correlates of this model are proposed, and relevant competing models are also addressed.
Title: "Images of Dynamics and Symmetry"
Abstract. A classical problem in mathematics is to solve a polynomial equation. One approach to this question takes account of the fact that polynomials have symmetries that can be realized in geometric spaces. The motivating idea is to use elegant geometry to solve an equation. During the past decade I've pursued this goal by developing algorithms that are both dynamical and symmetrical. At its core such an algorithm involves an iterative procedure that possesses the very symmetries of the polynomial to be solved. The process is two-fold:
- Geometric: a space where the polynomial's symmetry is realized
- Dynamic: an iterated transformation--a "map"--that moves the points in this space in a way that respects the symmetry of the equation.
I'll discuss the emergence and interplay of these two features in the case of the sixth-degree equation. Whatever their aesthetic appeal, graphical results play a significant role in understanding a map's geometric and dynamical properties. By revealing attracting, repelling, and chaotic behavior as well as fractal structures, they provide crucial experimental evidence.
Title: "Dynamical Modeling of Human Behavior"
Abstract. Human behavior exhibits many of the signatures of complex dynamical systems, including stable fixed-point and periodic attractors, nonlinear transitions, mode-locking, quadiperiodicity, and self-organization. This raises the prospect that the organization of behavior may emerge from the dynamics of the interaction between an agent and its environment, rather than being simply attributed to prior structure in the nervous system. In this talk, I will discuss how simple dynamical systems can be applied to modeling human perception and action, using several case studies: infants in a “jolly jumper,” bouncing a ball on a racket, and steering locomotion through a cluttered environment. In each case, modeling demonstrates how organization can arise a posteriori from the behavioral dynamics rather than being imposed a priori by the brain.
Title: "Oscillations in Biology: the Mathematics of Rhythms"
Abstract. I will discuss the mathematics of coupled nonlinear oscillations with particular attention to applications to neuroscience. Concepts such as the phase resetting curve play a major role in the interactions between oscillators, so this will be the starting point. I will then describe the method of averaging and how it allows one to reduce large high dimensional systems to much simpler models. I will look at waves, patterns and synchrony in these simplified models
Speaker: Mike Simpson, Oak Ridge National Laboratory
Title: "The Role of Stochastic Fluctuations in Biological Decision Circuits"
Abstract. The emerging field of noise biology focuses on the sources, processing, and biological consequences of the inherent stochastic fluctuations in the populations, concentrations, positions, or states of molecules that control cellular behavior. While one could argue that noise biology has a long history – dating to work in the 1940s by Max Delbruck – noise biology as a distinct field has emerged over the last decade in the broader context of computational, physical sciences, and engineering approaches to biology that have also spawned bioinformatics, systems biology, and synthetic biology. In these approaches biology, perhaps in a very fundamental sense, is thought to be an informational science and biochemical processes are conceptualized as circuits and networks. This conceptualization places the focus firmly on the transport and processing of information within these systems, and begs the question of how such seemingly robust function emerges from information that resides within the inherent noise of low molecular populations. Within a specific gene circuit there are three possible consequences of noise: (1) noise is negligible with little or no influence over function; (2) noise is detrimental to function and gene circuit architecture has evolved to minimize noise; or (3) noise is important for circuit function. Over the last few years there have been several proposed or reported example of consequence (3), and much of the effort in noise biology has focused on understanding the structure and function of gene circuits that use noise to generate function. Decision circuits are especially suited to derive functional advantage from noise, and these fluctuations are likely to play an important role in the establishment of active/latent states in viral infection. In this talk I will focus on the measurement of noise in the HIV Tat switch and demonstrate how these noise measurements may be used to characterize the structure and function of this important gene circuit. Additionally, I will discuss possible roles for this noise in the selection of latent or active infection.