Tuesday, March 8, 2011 - 11:00 , Location: Skiles 006 , Vadim L. Stefanuk , Russian Academy of Sciences , Organizer:
Some properties of biological memory are briefly described. The examples of short term memory and extra long term memory are drawn from psychological literature and from the personal experience. The short term memory is modeled here with the two types of mathematical models, both models being special cases of the Locally Organized Systems (LOS). The first model belongs to Prof. Mikhail Tsetlin of Moscow State University. His original ?pile of books? model was independently rediscovered a new by a number of scientists throughout the World. Tsetlin?s model demonstrates some very important properties of a natural memory organization. However mathematical study of his model turned out to be rather complicated. The second model belongs to the present author and has somewhat similar properties. However, it is organized in a completely different manner. In particular it contains some parameters, which makes the model rather interesting mathematically and pragmatically. The Stefanuk?s model has many interpretations and will be illustrated here with some biologically inspired examples. Both models founded a number of practical applications. These models demonstrate that the short term memory, which is heavily used by humans and by many biological subsystems is arranged reasonably. For humans it helps to keep the knowledge in the way facilitating its fast extraction. For biological systems the models explain the arrangement of storage of various micro organisms in a cell in an optimal manner to provide for the living.
Wednesday, January 26, 2011 - 11:00 , Location: Skiles 005 , Emmanuel Tannenbaum , Ben-Gurion University , Organizer: Christine Heitsch
We develop mathematical models describing the evolutionary dynamics of asexual and sexual reproduction pathways based on the yeast life cycle. By explicitly considering the semiconservative nature of DNA replication and a diploid genome, we are able to obtain a selective advantage for sex under much more general conditions than required by previous models. We are also able to suggest an evolutionary basis for the use of sex as a stress response in unicellular organisms such as Baker's yeast. Some additional features associated with both asexual and sexual aspects of the cell life cycle also fall out of our work. Finally, our work suggests that sex and diploidy may be useful as generalized strategies for preventing information degredation in replicating systems, and may therefore have applications beyond biology.
Wednesday, November 17, 2010 - 11:00 , Location: Skiles 168 , Michael Cortez , School of Biology, Georgia Tech , Organizer:
Interactions between trophic levels are influenced not only by species abundances, but also by the behavioral, life history, morphological traits of the interacting species as well. Adaptive changes in these traits can be heritable or plastic in nature and both yield phenotypic change that occurs as fast as changes in population abundances. I present how fast-slow systems theory can be used to understand the effects rapid adaptation has on community dynamics in predator-prey systems. This analysis emphasizes that heritable and plastic traits have different effects on community dynamics.
Wednesday, October 27, 2010 - 11:00 , Location: Skiles 169 , Anton Burykin , Emory University Center for Critical Care , Organizer:
Critical care is a branch of medicine concerned with the provision of life support or organ support systems in patients who are critically ill and require intensive monitoring. Such monitoring allows us to collect massive amounts of data (usually at the level of organ dynamics, such as electrocardiogram, but recently also at the level of genes). In my talk I’ll show several examples of how ideas from nonlinear dynamics and statistical physics can be applied for the analysis of these data in order to understand and eventually predict physiologic status of critically ill patients: (1) Heart beats, respiration and blood pressure variations can be viewed as a dynamics of a system of coupled nonlinear oscillators (heart, lungs, vessels). From this perspective, a live support devise (e.g. mechanical ventilator used to support breathing) acts as an external driving force on one of the oscillators (lungs). I’ll show that mechanical ventilator entrances the dynamics of whole cardiovascular system and leads to phase synchronization between respiration and heart beats. (2) Then I’ll discuss how fluctuation-dissipation theorem can be used in order to predict heart rate relaxation after a stress (e.g. treadmill exercise test) from the heart rate fluctuations during the stress. (3) Finally, I’ll demonstrate that phase space dynamics of leukocyte gene expression during critical illness and recovery has an attractor state, associated with immunological health.
Wednesday, September 29, 2010 - 11:00 , Location: Skiles 169 , Shweta Bansal , Center for Infectious Disease Dynamics, Penn State , Organizer: Christine Heitsch
Many infectious agents spread via close contact between infected and susceptible individuals. The nature and structure of interactions among individuals is thus of fundamental importance to the spread of infectious disease. Heterogeneities among host interactions can be modeled with contact networks, and analyzed using tools of percolation theory. Thus far, the field of contact network epidemiology has largely been focused on the impact of network structure on the progression of disease epidemics. In this talk, we introduce network models which incorporate feedback of the disease spread on network structure, and explore how this feedback limits the potential for future outbreaks. This has implications for seasonal diseases such as influenza, and supports the need for more adaptive public health policies in response to disease dynamics.
Incremental mutual information: a new method for characterizing the strength and dynamics of connections in neuronal circuitsWednesday, September 15, 2010 - 11:00 , Location: Skiles 169 , Abhinav Singh , University College London , email@example.com , Organizer:
Understanding the computations performed by neuronal circuits requires characterizing the strength and dynamics of the connections between individual neurons. This characterization is typically achieved by measuring the correlation in the activity of two neurons through the computation of a cross-correlogram or one its variants. We have developed a new measure for studying connectivity in neuronal circuits based on information theory, the incremental mutual information (IMI). IMI improves on correlation in several important ways: 1) IMI removes any requirement or assumption that the interactions between neurons is linear, 2) IMI enables interactions that reflect the connection between neurons to be differentiated from statistical dependencies caused by other sources (e.g. shared inputs or intrinsic cellular or network mechanisms), and 3) for the study of early sen- sory systems, IMI does not require that the external stimulus have any specific properties, nor does it require responses to repeated trials of identical stimulation. We describe the theory of IMI and demonstrate its utility on simulated data and experimental recordings from the visual system.
Tuesday, September 7, 2010 - 17:00 , Location: Skiles 269 , Mason Porter , Oxford University , Organizer:
The study of collective behavior---of animals, mechanical systems, or even abstract oscillators---has fascinated a large number of researchers from observational geologists to pure mathematicians. We consider the collective behavior of herds of cattle. We first consider some results from an agent-based model and then formulate a mathematical model for the daily activities of a cow (eating, lying down, and standing) in terms of a piecewise affine dynamical system. We analyze the properties of this bovine dynamical system representing the single animal and develop an exact integrative form as a discrete-time mapping. We then couple multiple cow "oscillators" together to study synchrony and cooperation in cattle herds, finding that it is possible for cows to synchronize less when the coupling is increased. [This research is in collaboration with Jie Sun, Erik Bollt, and Marian Dawkins.]
Monday, August 16, 2010 - 11:00 , Location: Skiles 271 , Shel Swenson , UT Austin , Organizer: Christine Heitsch
Estimating the Tree of Life, an evolutionary tree describing how all life evolved from a common ancestor, is one of the major scientific objectives facing modern biologists. This estimation problem is extremely computationally intensive, given that the most accurate methods (e.g., maximum likelihood heuristics) are based upon attempts to solve NP-hard optimization problems. Most computational biologists assume that the only feasible strategy will involve a divide-and-conquer approach where the large taxon set is divided into subsets, trees are estimated on these subsets, and a supertree method is applied to assemble a tree on the entire set of taxa from the smaller "source" trees. I will present supertree methods in a mathematical context, focusing on some theoretical properties of MRP (Matrix Representation with Parsimony), the most popular supertree method, and SuperFine, a new supertree method that outperforms MRP.
Wednesday, April 7, 2010 - 11:00 , Location: Skiles 255 , Martha Grover , School of Chemical & Biomolecular Engineering, Georgia Tech , Organizer:
Individual chemical reactions between molecules are inherently stochastic, although for a large collection of molecules, the overall system behavior may appear to be deterministic. When deterministic chemical reaction models are sufficient to describe the behavior of interest, they are a compact way to describe chemical reactions. However, in other cases, these mass-action kinetics models are not applicable, such as when the number of molecules of a particular type is small, or when no closed-form expressions exist to describe the dynamic evolution of overall system properties. The former case is common in biological systems, such as intracellular reactions. The latter case may occur in either small or large systems, due to a lack of smoothness in the reaction rates. In both cases, kinetic Monte Carlo simulations are a useful tool to predict the evolution of overall system properties of interest. In this talk, an approach will be presented for generating approximate low-order dynamic models from kinetic Monte Carlo simulations. The low-order model describes the dynamic evolution of several expected properties of the system, and thus is not a stochastic model. The method is demonstrated using a kinetic Monte Carlo simulation of atomic cluster formation on a crystalline surface. The extremely high dimension of the molecular state is reduced using linear and nonlinear principal component analysis, and the state space is discretized using clustering, via a self-organizing map. The transitions between the discrete states are then computed using short simulations of the kinetic Monte Carlo simulations. These transitions may depend on external control inputs―in this application, we use dynamic programming to compute the optimal trajectory of gallium flux to achieve a desired surface structure.
Wednesday, March 10, 2010 - 11:00 , Location: Skiles 255 , Yuri Bakhtin , Georgia Tech , Organizer: Christine Heitsch
I will consider a class of mathematical models of decision making. These models are based on dynamics in the neighborhood of unstable equilibria and involve random perturbations due to small noise. I will report results on the vanishing noise limit for these systems, providing precise predictions about the statistics of decision making times and sequences of unstable equilibria visited by the process. Mathematically, the results are based on the analysis of random Poincare maps in the neighborhood of each equilibrium point. I will also discuss some experimental data.