Seminars and Colloquia by Series

Some Applications of Nonlinear Dynamics and Statistical Physics in Critical Care

Series
Mathematical Biology Seminar
Time
Wednesday, October 27, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 169
Speaker
Anton BurykinEmory University Center for Critical Care
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.

Network Models for Infectious Disease Dynamics

Series
Mathematical Biology Seminar
Time
Wednesday, September 29, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 169
Speaker
Shweta BansalCenter for Infectious Disease Dynamics, Penn State
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 circuits

Series
Mathematical Biology Seminar
Time
Wednesday, September 15, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 169
Speaker
Abhinav SinghUniversity College London
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.

Synchronization of Cows

Series
Mathematical Biology Seminar
Time
Tuesday, September 7, 2010 - 17:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Mason PorterOxford University
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.]

Phylogenetic Supertree Methods: tools for reconstructing the Tree of Life

Series
Mathematical Biology Seminar
Time
Monday, August 16, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 271
Speaker
Shel SwensonUT Austin
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.

Stochastic molecular modeling and reduction in reacting systems

Series
Mathematical Biology Seminar
Time
Wednesday, April 7, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Martha GroverSchool of Chemical & Biomolecular Engineering, Georgia Tech
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.

Diffusion Models of Sequential Decision Making

Series
Mathematical Biology Seminar
Time
Wednesday, March 10, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Yuri BakhtinGeorgia Tech
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.

Irregular activity and propagation of synchrony in complex, spiking neural networks

Series
Mathematical Biology Seminar
Time
Wednesday, February 17, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Raoul-Martin MemmesheimerCenter for Brain Science, Faculty of Arts and Sciences Harvard University
Mean field theory for infinite sparse networks of spiking neurons shows that a balanced state of highly irregular activity arises under a variety of conditions. The state is considered to be a model for the ground state of cortical activity. In the first part, we analytically investigate its irregular dynamics in finite networks keeping track of all individual spike times and the identities of individual neurons. For delayed, purely inhibitory interactions, we show that the dynamics is not chaotic but in fact stable. Moreover, we demonstrate that after long transients the dynamics converges towards periodic orbits and that every generic periodic orbit of these dynamical systems is stable. These results indicate that chaotic and stable dynamics are equally capable of generating the irregular neuronal activity. More generally, chaos apparently is not essential for generating high irregularity of balanced activity, and we suggest that a mechanism different from chaos and stochasticity significantly contributes to irregular activity in cortical circuits. In the second part, we study the propagation of synchrony in front of a background of irregular spiking activity. We show numerically and analytically that supra-additive dendritic interactions, as recently discovered in single neuron experiments, enable the propagation of synchronous activity even in random networks. This can lead to intermittent events, characterized by strong increases of activity with high-frequency oscillations; our model predicts the shape of these events and the oscillation frequency. As an example, for the hippocampal region CA1, events with 200Hz oscillations are predicted. We argue that these dynamics provide a plausible explanation for experimentally observed sharp-wave/ripple events.

Modeling coral disease: within-host dynamics, individual demography, and population consequences

Series
Mathematical Biology Seminar
Time
Wednesday, February 10, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
255 Skiles
Speaker
Steven EllnerCornell
Emerging diseases have played an important role in the major recent declinesof coral reef cover worldwide. I will present some theoretical efforts aimedat understanding processes of coral disease development and itsconsequences: (1) how the development of coral disease is regulated bymicrobial population interactions within the mucus layer surrounding thecoral, and (2) the effects of a recent fungal epizootic on populations of aCaribbean sea fan coral, focusing on how this species was able to recover tohigh abundance and low disease prevalence. Collaborators on this workinclude John Bruno (UNC-CH); C. Drew Harvell, Laura Jones, and JustinMao-Jones (Cornell), and Kim Ritchie (MOTE Marine Lab).

Universality of first passage time in stochastic biochemical processes

Series
Mathematical Biology Seminar
Time
Wednesday, February 3, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Ilya NemenmanEmory University
Even the simplest biochemical networks often have more degrees of freedoms than one can (or should!) analyze. Can we ever hope to do the physicists' favorite trick of coarse-graining, simplifying the networks to a much smaller set of effective dynamical variables that still capture the relevant aspects of the kinetics? I will argue then that methods of statistical physics provide hints at the existence of rigorous coarse-grained methodologies in modeling biological information processing systems, allowing to identify features of the systems that are relevant to their functions. While a general solution is still far away, I will focus on a specific example illustrating the approach. Namely, for a a general stochastic network exhibiting the kinetic proofreading behavior, I will show that the microscopic parameters of the system are largely important only to the extent that they contribute to a single aggregate parameter, the mean first passage time through the network, and the higher cumulants of the escape time distribution are related to this parameter uniquely. Thus a phenomenological model with a single parameter does a good job explaining all of the observable data generated by this complex system.

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