A&S Home » Mathematics » Events » Department Colloquiums » 2002 - 2003 Colloquium Archive
Time and place: January 21 (Tuesday), 2:00 p.m. Jones 131.
Speaker: Cameron Parker (Department of Mathematics, University of California, San Diego)
Title: Unit Root Testing via the Stationary Bootstrap
Abstract: A nonparametric, residual-based stationary bootstrap procedure is proposed
for testing for the presence of a unit root in a given time series. The procedure gives a way
of generating a pseudo series which mimics the original in terms of dependence structure but
that has the property of having a unit root. To develop this test a brief introduction to the
bootstrap and time series analysis is given as well as defining both the
stationary bootstrap and unit root processes.
Time and place: February 10 (Monday), 3:00 p.m. Jones 131.
Speaker: Jeff Moehlis (Program in Applied and Computational Mathematics, Princeton University)
Title: Response of Neurons in the Brain Region Locus Coeruleus to Stimuli
Abstract: Experimental data shows that neurons in a region of the brain known as the locus coeruleus (LC) can exhibit two distinct firing patterns which are strongly correlated with performance on cognitive tasks. In the phasic mode, associated with good performance, the baseline firing rate is lower and the neurons show enhanced reponse. In the tonic mode, associated with poor performance, the average baseline firing rate is higher and the neurons are less reponsive. From membrane voltage and
ion channel equations, we derive a phase oscillator model for LC neurons. Average firing probabilities of a pool of neurons in response to stimuli over many trials are then computed via a probability density formulation. Using this, we show that: (1) Response is elevated in populations with lower baseline firing rates; and (2) Response decays due to noise and distributions of neuron frequencies. These results may account for much of the experimental response variability.
Time and place: February 14 (Friday), 3:00 p.m. Jones 131.
Speaker: Loius Tao (Courant Institute of Mathematical Sciences, New York University)
Title: A Neuronal Network Model of the Primary Visual Cortex
Abstract: Visually responsive neurons in the primary visual cortex (V1) are generally separated into two broad classes: those that show approximately linear responses (Simple cells) and those that do not (Complex cells). It is an open problem as to how these differing responses actually arise within V1. Guided by simulations of a large-scale, biologically realistic neuronal network model, I offer an explanation. My results suggest that a broad spectrum of balances between visual stimulation and network excitation underlies the Simple-Complex response diversity as is seen in recent experiments. I will also discuss future directions for large-scale cortical modeling.
Time and place: February 17 (Monday), 3:00 p.m. Jones 131.
Speaker: William Casey (Courant Institute of Mathematical Sciences, New York University)
Title: Graph Embeddings with Application to Genomic Experiments
Abstract: Inference of global structure from data which are accurate only on a local scale is common to many problems in mathematical biology. In an application called `probe-mapping', motivated by goals to characterize gene copy events in cancer cells, we address an NP-hard problem concerning Graph Embeddings with efficient heuristics. We provide model-based analysis of the heuristic argument and prove the correctness of its result with probability very close to 1 on a relevant set of inputs. The result is a design for realistic experiments capable of characterizing genome structure.
Time and place: February 20 (Thursday), 4:00 p.m. Morton 20.
Speaker: Michael Gertz (Northwestern University)
Title: Interior-Point Optimization through Trust Regions
Abstract: We describe a trust-region approach to non-convex, nonlinear optimization. The method, based on a merit function of Forsgren & Gill, handles non-convexity correctly and has excellent convergence properties. The algorithm uses off-the-shelf linear equation solvers, allowing us to leverage years of research in numerical linear algebra.
Time and place: March 14 (Friday), 4:00 p.m. Jones 131.
Speaker: Alexander Pankov (Department of Mathematics, Texas A&M University)
Title: Traveling waves in lattice dynamical systems
Abstract: We consider the following class of 1-dimensional lattice dynamical
systems: chains of particles with nearest neighbor interaction. We prove
the existence of spatially periodic traveling waves with prescribed speed
and an arbitrary period. We also study the asymptotic behavior of such waves
for large values of periods and show that they converge in an appropriate
topology to a solitary traveling wave. As a consequence, the existence of
solitary waves is obtained.
Time and place: March 21 (Friday), 4:00 p.m. Jones 131.
Speaker: Simon Gindikin (Department of Mathematics, Rutgers University)
Title: Complex geometry of real symmetric spaces
Abstract: The discovery of symmetric spaces by E. Cartan is one of the most brilliant achievements of geometry of XX century. These spaces possess a very expressive non Euclidean geometry and as a result they are a field for very deep multidimensional analysis. In XIX century Poncelet and Pluecker found that complex geometry is responsible for many facts of real geometry. I will discuss several new examples of such nature in geometry of symmetric spaces. It was shown that each (real) Riemannian symmetric space has a canonical complex neighborhood - a complex crown , which universally appears in geometric and analytic problems. In special cases this construction reduces to some problems about matrices, partly classical, partly new ones.
See also Cissy Patterson Lecture by Professor Gindikin
Time and place: April 25 (Friday), 3:00 p.m. Jones 131
Speaker: Ratnasingham Shivaji (Deptment of Mathematics and Statistics, Mississippi State University)
Title: An Existence result on positive solutions for a class of semilinear elliptic systems.
Abstract: Consider the system
-\Delta u=\lambda f(v)\text{ \ in }\Omega \\
-\Delta v=\lambda g(u)\text{ \ in }\Omega \\
u=v=0\;\text{\ on }\partial \Omega ,
where $\lambda $ is a positive parameter and $\Omega $ is a bounded domain in $R^{N}.\;$We prove the existence of a large positive solution for $\lambda $ large when lim$_{x\rightarrow \infty }\frac{f(Mg(x))}{x}=0$ for every $M>0.$ In particular, we do not need any monotonicity assumptions on $ f,g$ nor any sign conditions on $f(0),g(0).$
Time and place: May 14th (Wednesday), 3:00 p.m. Jones 301
Speaker: Tiancheng Ouyang (Deptment of Mathematics, Brigham Young University)
Title: Periodic Orbits of N-body Problems in Celestial Mechanics and Computer Simulation
Abstract: The classical N-body problem of celestial mechanics concerns the motion of N point masses governed by the universal gravitation law in the Euclidean space. In this talk I will introduce a new approach for the existence and the construction of preassigned orbits. This approach uses variational method to minimize an energy functional and optimize the corresponding boundary value problem. Many interesting periodic and quasi-periodic solutions in two and three dimensional spaces with different topological structures have been constructed. Our numerical simulation shows many interesting properties of those orbits.
Time and place: November 1 (Friday), 3:00 p.m., Jones 131.
Speaker: Robert Reams (Instructor, Department of Mathematics, College of William and Mary)
Title: Constructions of trace zero symmetric stochastic matrices for the inverse eigenvalue problem
Time and place: November 8 (Friday), 3:00 p.m., Jones 131.
Speaker: John H. Lowenstein (Professor, Department of Physics, New York University)
Title: Computer-assisted analysis of two-dimensional piecewise isometries with rational rotation number.
Time and place: November 11 (Monday), 1:00 p.m., Jones 302.
Speaker: James R. Wilson (Professor and Head, Department of Industrial Engineering, North Carolina State University)
Title: Using nonhomogeneous Poisson processes to drive the UNOS Liver Allocation Model (UNOS is the Organ Sharing organization headquartered in Richmond and a large-scale simulation model was developed to determine optimal distribution policies)
Time and place: November 22 (Friday), 3:00 p.m., Jones 131.
Speaker: Sivaram Narayan (Professor, Department of Mathematics, Central Michigan University and College of William and Mary)
Title: Nonnegative matrices with prescribed spectra
Time and place: December 9th (Monday), 3:00 p.m., Jones 131.
Speaker: Percy Deift, (Professor, Courant Institute of Mathematical Sciences, New York University)
Title: Perturbation theory for infinite dimenional integrable systems. A case study
2002 - 2003 Colloquium Archive
Talks in Spring 2003
Time and place: January 21 (Tuesday), 2:00 p.m. Jones 131.
Speaker: Cameron Parker (Department of Mathematics, University of California, San Diego)
Title: Unit Root Testing via the Stationary Bootstrap
Abstract: A nonparametric, residual-based stationary bootstrap procedure is proposed
for testing for the presence of a unit root in a given time series. The procedure gives a way
of generating a pseudo series which mimics the original in terms of dependence structure but
that has the property of having a unit root. To develop this test a brief introduction to the
bootstrap and time series analysis is given as well as defining both the
stationary bootstrap and unit root processes.
Time and place: February 10 (Monday), 3:00 p.m. Jones 131.
Speaker: Jeff Moehlis (Program in Applied and Computational Mathematics, Princeton University)
Title: Response of Neurons in the Brain Region Locus Coeruleus to Stimuli
Abstract: Experimental data shows that neurons in a region of the brain known as the locus coeruleus (LC) can exhibit two distinct firing patterns which are strongly correlated with performance on cognitive tasks. In the phasic mode, associated with good performance, the baseline firing rate is lower and the neurons show enhanced reponse. In the tonic mode, associated with poor performance, the average baseline firing rate is higher and the neurons are less reponsive. From membrane voltage and
ion channel equations, we derive a phase oscillator model for LC neurons. Average firing probabilities of a pool of neurons in response to stimuli over many trials are then computed via a probability density formulation. Using this, we show that: (1) Response is elevated in populations with lower baseline firing rates; and (2) Response decays due to noise and distributions of neuron frequencies. These results may account for much of the experimental response variability.
Time and place: February 14 (Friday), 3:00 p.m. Jones 131.
Speaker: Loius Tao (Courant Institute of Mathematical Sciences, New York University)
Title: A Neuronal Network Model of the Primary Visual Cortex
Abstract: Visually responsive neurons in the primary visual cortex (V1) are generally separated into two broad classes: those that show approximately linear responses (Simple cells) and those that do not (Complex cells). It is an open problem as to how these differing responses actually arise within V1. Guided by simulations of a large-scale, biologically realistic neuronal network model, I offer an explanation. My results suggest that a broad spectrum of balances between visual stimulation and network excitation underlies the Simple-Complex response diversity as is seen in recent experiments. I will also discuss future directions for large-scale cortical modeling.
Time and place: February 17 (Monday), 3:00 p.m. Jones 131.
Speaker: William Casey (Courant Institute of Mathematical Sciences, New York University)
Title: Graph Embeddings with Application to Genomic Experiments
Abstract: Inference of global structure from data which are accurate only on a local scale is common to many problems in mathematical biology. In an application called `probe-mapping', motivated by goals to characterize gene copy events in cancer cells, we address an NP-hard problem concerning Graph Embeddings with efficient heuristics. We provide model-based analysis of the heuristic argument and prove the correctness of its result with probability very close to 1 on a relevant set of inputs. The result is a design for realistic experiments capable of characterizing genome structure.
Time and place: February 20 (Thursday), 4:00 p.m. Morton 20.
Speaker: Michael Gertz (Northwestern University)
Title: Interior-Point Optimization through Trust Regions
Abstract: We describe a trust-region approach to non-convex, nonlinear optimization. The method, based on a merit function of Forsgren & Gill, handles non-convexity correctly and has excellent convergence properties. The algorithm uses off-the-shelf linear equation solvers, allowing us to leverage years of research in numerical linear algebra.
Time and place: March 14 (Friday), 4:00 p.m. Jones 131.
Speaker: Alexander Pankov (Department of Mathematics, Texas A&M University)
Title: Traveling waves in lattice dynamical systems
Abstract: We consider the following class of 1-dimensional lattice dynamical
systems: chains of particles with nearest neighbor interaction. We prove
the existence of spatially periodic traveling waves with prescribed speed
and an arbitrary period. We also study the asymptotic behavior of such waves
for large values of periods and show that they converge in an appropriate
topology to a solitary traveling wave. As a consequence, the existence of
solitary waves is obtained.
Time and place: March 21 (Friday), 4:00 p.m. Jones 131.
Speaker: Simon Gindikin (Department of Mathematics, Rutgers University)
Title: Complex geometry of real symmetric spaces
Abstract: The discovery of symmetric spaces by E. Cartan is one of the most brilliant achievements of geometry of XX century. These spaces possess a very expressive non Euclidean geometry and as a result they are a field for very deep multidimensional analysis. In XIX century Poncelet and Pluecker found that complex geometry is responsible for many facts of real geometry. I will discuss several new examples of such nature in geometry of symmetric spaces. It was shown that each (real) Riemannian symmetric space has a canonical complex neighborhood - a complex crown , which universally appears in geometric and analytic problems. In special cases this construction reduces to some problems about matrices, partly classical, partly new ones.
See also Cissy Patterson Lecture by Professor Gindikin
Time and place: April 25 (Friday), 3:00 p.m. Jones 131
Speaker: Ratnasingham Shivaji (Deptment of Mathematics and Statistics, Mississippi State University)
Title: An Existence result on positive solutions for a class of semilinear elliptic systems.
Abstract: Consider the system
-\Delta u=\lambda f(v)\text{ \ in }\Omega \\
-\Delta v=\lambda g(u)\text{ \ in }\Omega \\
u=v=0\;\text{\ on }\partial \Omega ,
where $\lambda $ is a positive parameter and $\Omega $ is a bounded domain in $R^{N}.\;$We prove the existence of a large positive solution for $\lambda $ large when lim$_{x\rightarrow \infty }\frac{f(Mg(x))}{x}=0$ for every $M>0.$ In particular, we do not need any monotonicity assumptions on $ f,g$ nor any sign conditions on $f(0),g(0).$
Time and place: May 14th (Wednesday), 3:00 p.m. Jones 301
Speaker: Tiancheng Ouyang (Deptment of Mathematics, Brigham Young University)
Title: Periodic Orbits of N-body Problems in Celestial Mechanics and Computer Simulation
Abstract: The classical N-body problem of celestial mechanics concerns the motion of N point masses governed by the universal gravitation law in the Euclidean space. In this talk I will introduce a new approach for the existence and the construction of preassigned orbits. This approach uses variational method to minimize an energy functional and optimize the corresponding boundary value problem. Many interesting periodic and quasi-periodic solutions in two and three dimensional spaces with different topological structures have been constructed. Our numerical simulation shows many interesting properties of those orbits.
Talks in Fall 2002
Time and place: September 27 (Friday), 3:00 p.m. Jones 131.
Speaker: Peter W. Bates (Professor and Chairman, Department of Mathematics, Michigan State University)
Title: A new class of evolution equations suggested by phase transition in materials
Abstract: Starting with the basic idea of energy and the need to decrease energy (increase entropy) during the evolution of a state one may derive some mathematically interesting equations. I will show this derivation and attempt to justify the word "interesting". If there is time, I will discuss homotopy methods, spectral theory, and the use of weak convergence to be employed in the analysis of the equations.
Time and place: November 1 (Friday), 3:00 p.m., Jones 131.
Speaker: Robert Reams (Instructor, Department of Mathematics, College of William and Mary)
Title: Constructions of trace zero symmetric stochastic matrices for the inverse eigenvalue problem
Time and place: November 8 (Friday), 3:00 p.m., Jones 131.
Speaker: John H. Lowenstein (Professor, Department of Physics, New York University)
Title: Computer-assisted analysis of two-dimensional piecewise isometries with rational rotation number.
Time and place: November 11 (Monday), 1:00 p.m., Jones 302.
Speaker: James R. Wilson (Professor and Head, Department of Industrial Engineering, North Carolina State University)
Title: Using nonhomogeneous Poisson processes to drive the UNOS Liver Allocation Model (UNOS is the Organ Sharing organization headquartered in Richmond and a large-scale simulation model was developed to determine optimal distribution policies)
Time and place: November 22 (Friday), 3:00 p.m., Jones 131.
Speaker: Sivaram Narayan (Professor, Department of Mathematics, Central Michigan University and College of William and Mary)
Title: Nonnegative matrices with prescribed spectra
Time and place: December 9th (Monday), 3:00 p.m., Jones 131.
Speaker: Percy Deift, (Professor, Courant Institute of Mathematical Sciences, New York University)
Title: Perturbation theory for infinite dimenional integrable systems. A case study
