Applied Mathematics and
Mathematical Neuroscience Seminar
Fall 2009-Spring 2010
Questions or comments? Please e-mail Tuwaner Lamar or Igor Belykh
DATE: Monday, November 23
TIME: 1:30 PM - 2:30 PM
LOCATION: COE 796
Speaker: Dr. GuanTao Chen, Department of Mathematics and Statistics, GSU
Title: TBA
DATE: Monday, November 16
TIME: 1:30 PM - 2:30 PM
LOCATION: COE 796
Speaker: Steven Damelin, Georgia Southern University and Wits. (Joint work with Charles Fefferman, Princeton).
Title: "Extensions of diffeomorphisms of small distortion in euclidean space and their applications to rigid data allignment and medical imaging."
Abstract: PDF
http://math.georgiasouthern.edu/~damelin
DATE: Monday, November 9
TIME: 1:30 PM - 2:30 PM
LOCATION: COE 796
Speaker: Dr. Alexandra Smirnova, Department of Mathematics and Statistics, GSU
Title: "Continuous Methods for Solving Nonlinear Ill-Posed Problems"
Abstract: In the theory of ill-posed problems many different discrete methods based on a regularization are known. Different convergence theorems for such schemes describe the efficiency of the numerical algorithms for solving various nonlinear problems, and give existence results. However it is quite difficult to navigate in the sea of discrete schemes and corresponding convergence theorems. Proofs of these theorems are usually based on the contraction mapping principle and are sometimes rather complicated. On the other hand an analysis of continuous processes is based on the investigation of the asymptotical behavior of nonlinear dynamical systems in Banach and Hilbert spaces. If a convergence theorem is proved for a continuous method, one can construct various discrete schemes generated by this continuous process. Thus construction of a discrete numerical scheme is split into two parts: construction of the continuous process and numerical integration of the corresponding nonlinear operator differential equation. The goal of this talk is to present a general approach to continuous analogs of discrete methods for nonlinear ill-posed problems and to establish fairly general convergence theorems.
DATE: Monday, October 28
TIME: 1:30 PM - 2:30 PM
LOCATION: COE 796
Speaker: Dr. Predrag Punosevac, Department of Mathematics and Statistics, GSU
Title: "Regularization of Simultaneous Binary Collisions in Some Gravitational Systems"
DATE: Monday, October 14
TIME: 1:30 PM - 2:30 PM
LOCATION: COE 796
Speaker: Sajiya Jalil, Department of Mathematics and Statistics, GSU
Title: "Synchronized bursting in a half-center: the dual role of inhibition"
Abstract: We find the co-existence of stable in-phase and anti-phase synchronization in a half-center oscillator, formed by two bursting neurons with fast non-delayed inhibitory connections. This contrasts with the conventional belief that fast non-delayed reciprocal inhibition cannot stably produce in-phase synchronization. Through the stability analysis, we reveal the dual property of fast non-delayed reciprocal inhibition to establish synchronization of both types and describe its synchronization mechanism. We also discuss the implications of the analysis for different types of bursting and larger inhibitory networks.
Speaker: Jeremy Wojcik, Department of Mathematics and Statistics, GSU
Title: "Poincare mapping technique for eliiptic bursting"
DATE: Monday, September 28
TIME: 1:30 PM - 2:30 PM
LOCATION: COE 796
Speaker: Dr. Tuwaner Lamar, Department of Mathematics and Statistics, GSU
Title: "On Analyzing a 2n-th Order Differential Equation with Lidstone Boundary Conditions – Part I: Lateral Vibration of Beams"
DATE: Monday, September 14
TIME: 1:30 PM - 2:30 PM
LOCATION: COE 796
Speaker: Tatiana Malaschenko, Department of Physics and Astronomy, GSU
Title: "The propensity to bi-stability of bursting and silence of the leech heart interneuron"
Spring 2009
DATE: Thursday, May 7
TIME: 3:30 PM - 4:30 PM
LOCATION: South CB 500
Speaker:
Maxim Bazhenov, Department of Cell Biology & Neuroscience
University of California, Riverside
http://cbns.ucr.edu/index.php?content=people/faculty/bazhenov/bazhenov.html
Title: "Extracellular Potassium Dynamics and Epileptogenesis"
Abstract:
Extracellular ion concentrations change as a function of neuronal activity and also represent important factors influencing the dynamic state of a population of neurons. In particular, relatively small changes in extracellular potassium concentration mediate substantial changes in neuronal excitability and intrinsic firing patterns. While experimental approaches are limited in their ability to shed light on the dynamic feedback interaction between ion concentration and neural activity, computational models and dynamic system theory provide powerful tools to study activity-dependent modulation of intrinsic excitability mediated by extracellular ion concentration dynamics. Drawing on results obtained with biophysical network models of the thalamocortical system, I will discuss the potential role of extracellular potassium concentration dynamics in the generation of epileptoform activity in neocortical networks. Detailed bifurcation analysis of a model pyramidal cell revealed a bistability with hysteresis between two distinct firing modes (tonic firing and slow bursting) for mildly elevated extracellular potassium. In neocortical network models, this bistability gives rise to previously unexplained slow alternating epochs of fast runs and slow bursting as recorded in vivo during neocortical electrographic seizures in cats and in human patients with the Lennox-Gastaut syndrome. We conclude that extracellular potassium concentration dynamics may play an important role in the generation of seizures.
References:
http://www.snl.salk.edu/~bazhenov/Journals/DrugDiscovery.pdf
http://www.snl.salk.edu/~bazhenov/Journals/Frohlich_JN2006.pdf
http://www.snl.salk.edu/~bazhenov/Journals/Bazhenov-PRE2006.pdf .
DATE: Wednesday, May 6
TIME: 1:00 PM - 2:30 PM
LOCATION: COE 796
Speaker: Vladimir Bondarenko (Department of Mathematics and Statistics)
Title: "Ion channels, their gating and Markov models" (second part)
Abstract: This is a two-lecture presentation that covers the following topics: 1) diversity of ion channels; 2) amino acid sequences of ion channels; 3) high-resolution structure of K+ ion channels; 4) channel gating: activation, deactivation, inactivation, and recovery from inactivation; 5) N- and C-type inactivation of K+ channels; 6) two-state Markov model; 7) Markov model for activation of K+ channel; 8) development of Markov model for K+ channel from experimental data. Second lecture will cover topics 6) -8).
DATE: Thursday, April 9
TIME: 1:00 PM - 2:30 PM
LOCATION: COE 796
Speaker: Vladimir Bondarenko (Department of Mathematics and Statistics)
Title: "Ion channels, their gating and Markov models" (first part)
Abstract: This is a two-lecture presentation that covers the following topics: 1) diversity of ion channels; 2) amino acid sequences of ion channels; 3) high-resolution structure of K+ ion channels; 4) channel gating: activation, deactivation, inactivation, and recovery from inactivation; 5) N- and C-type inactivation of K+ channels; 6) two-state Markov model; 7) Markov model for activation of K+ channel; 8) development of Markov model for K+ channel from experimental data. First lecture will cover topics 1) - 5).
Fall 2007- Spring 2008
Atlanta Computational Neuroscience Conference
as a part of our regular seminar.
DATE: Friday, April 8
LOCATION: Loudermilk Center, GSU
Round table seminar (special guest: Nancy Kopell, Boston University)
DATE: Friday, April 7
TIME: 2:30 PM- 6:30 PM
LOCATION: COE 796
DATE: Friday, April 7
TIME: 4:30 PM
LOCATION: COE 796
Speaker: Gennady Cymbalyuk (Department of Physics and Astronomy)
Title: "Co-existence of bursting with other regimes ”
DATE: Friday, April 7
TIME: 5:00 PM
LOCATION: COE 796
Speaker: Igor Belykh (Math and Stat)
Title: "Fast threshold modulation and synchronization of excitatory bursting neurons"
DATE: Friday, March 7
TIME: 5:30 PM
LOCATION: COE 796
Speaker: Mukesh Dhamala (Physics and Astronomy)
Title: "Estimating information flow in dynamic networks with nonparametric granger causality"
DATE: Friday, April 4
TIME: 1:00 PM
LOCATION: COE 796
Speaker: Tatiana Malaschenko (Physics and Astronomy)
Title: "Co-existence of silent and oscillatory regimes of a single neuron's activity"
DATE: Friday, March 28
TIME: 1:00 PM
LOCATION: COE 796
Speaker: Andrey Shilnikov (Math and Stat)
Title: "Polyrhythmic synchronization in network motifs"
DATE: Friday, March 21
TIME: 1:00 PM
LOCATION: COE 796
Speaker: Paul Channell (Math and Stat)
Title: "Variability of bursting patterns in a neuronal model"
DATE: Friday, March 14
TIME: 1:00 PM
LOCATION: COE 796
Speaker: Mukesh Dhamala (Physics and Astronomy)
DATE: Friday, February 1
TIME: 1:15 PM
LOCATION: COE 796
Speaker: Andrey Shilnikov (Math and Stat)
Title: "Methods of the qualitative theory for the Hindmarsh-Rose model."
Abstract. Homoclinic bifurcations of both equilibria and periodic orbits are argued to be critical for understanding the dynamics of the Hindmarsh-Rose model in particular, as well as in some square-wave bursting models of neurons of the Hodgkin-Huxley type. They explain very well various transitions between the tonic spiking and bursting oscillations in the model. We present the approach that allows for constructing Poincar´e return mapping via the averaging technique. We show that a modified model can exhibit the blue sky bifurcation, as well as, a bistability of the coexisting tonic spiking and bursting activities. A new technique for localizing the slow motion manifold and periodic orbits on it is also presented.
References:
Shilnikov A. L. and Kolomiets M.L., Methods of the qualitative theory for the Hindmarsh-Rose model: a case study. SIADS 2008, submitted.
DATE: Friday, November 30
TIME: 2:00 PM
LOCATION: COE 796
Speaker:
Dr. Sergey Dashkovskiy (Department of Mathematics and Informatics, University of Bremen, Germany).
Title: "Small-gain theorems for networks of ISS systems".
Abstract.
We will consider a number of systems which are interconnected in a network. Each system is assumed to be input-to-state stable (ISS). In general such an interconnection is not ISS. We are looking for stability conditions for such networks. In case of feedback interconnection of two ISS systems such condition of a small-gain type were derived by Jiang et al. in 1994. A construction of an ISS-Lyapunov function for this case was performed in Jiang et al. 1996. In my presentation I will show a stability condition for a general interconnection of many systems and a construction of an ISS-Lyapunov function for a network. As we will see our condition is a natural generalization of the results mentioned above. We will consider some interpretations of this generalized small-gain condition and discuss on approaches how to check this condition numerically.
DATE: Friday, November 9
TIME: 2:00 PM
LOCATION: COE 796
Speaker: Sajiya Jalil, University of Toronto
Title: "Role of synaptic plasticity in the generation of complex patterns and ability to learn by the brain".
Abstract.
Short-term synaptic plasticity contributes significantly to the function of synapses. Similarly, long-term synaptic plasticity is thought to be at the heart of complex patterns such as learning and memory. Consequently, studies of synaptic weight evolution over different time scales are thriving areas of research in neuroscience. Specifically following two studies will be discussed:
• Novel bursting pattern emerging from model inhibitory networks with synaptic depression (research collaboration with Professor Frances Skinner)
• Computational consequences of experimentally derived STDP based learning rule (research collaboration with Professor Thomas Trappenberg) .
DATE: Friday, August 24
TIME: 2:00 PM
LOCATION: COE 796
Speaker: Dr. Oleksandr Burilko
Institute of Mathematics, Kiev, Ukraine/Institute of Medicine, Julich Research Center, Julich, Germany
Title: "Bifurcation to heteroclinic cycles and sensitivity in three
and four coupled phase oscillators".
Abstract.
We study the bifurcation and dynamical behaviour of the system of N globally coupled identical phase oscillators introduced by Hansel, Mato and Meunier, in the cases N=3 and N=4. This model has been found to exhibit robust `slow switching' oscillations that are caused by the presence of robust heteroclinic attractors. We consider bifurcations that occur in a system of identical oscillators on varying parameters in the coupling function. These bifurcations preserve the permutation symmetry of the system. We then investigate implications of these bifurcations for the sensitivity to detuning (i.e. the size of the smallest perturbations that give rise to loss of frequency locking). For N=3 we find three types of heteroclinic bifurcation that are codimension-one with symmetry. On varying two parameters in the coupling function we find three curves giving (a) an S3-transcritical homoclinic bifurcation, (b) a saddle-node/heteroclinic bifurcation and (c) a Z3-heteroclinic bifurcation. We also identify several global bifurcations with symmetry that organize the bifurcation diagram; these are codimension-two with symmetry. For N=4 oscillators we determine many (but not all) codimension-one bifurcations with symmetry, including those that lead to a robust heteroclinic cycle. A robust heteroclinic cycle is stable in an open region of parameter space and unstable in another open region. Furthermore, we verify that there is a subregion where the heteroclinic cycle is the only attractor of the system, while for other parts of the phase plane it can coexist with stable limit cycles. We finish with a discussion of bifurcations that appear for this coupling function and general N, as well as for more general coupling functions.