# Colloquium:  Spring 2013

(Tentative Schedule)

Time & location: All talks are on Thursday in Gibson 414 at 3:30pm unless otherwise noted. Refreshments in Gibson 426 after the talk.

Comments indicating vacations, special lectures, or change in location or time are made in green.

Organizer: Gustavo Didier

January 15

## Modeling Dynamic Networks in Changing Populations Based on Static Egocentrically-Sampled Data

Pavel KrivitskyPenn state university

Abstract:

Dynamic network models — models for evolution of networks over time — have manifold applications. In epidemiology, in particular, of interest is not just the presence of relationships of interest but their timing, as well as the impact of changing size and composition of the network. Yet, the data available are often limited to egocentric views of the network processes at a single time point. We develop and apply a discrete-time generative model for social network evolution that seeks to inherit the richness and flexibility of exponential-family random graph models, while adjusting for changing network size and composition and facilitating modeling of tie duration distributions; and we develop a generalized method of moments estimation technique to fit the model to available cross-sectional, egocentric network and/or tie duration data.  We illustrate our development with an application to sexual partnership data in the context of modeling the structure of HIV spread.

January 17

Christian BergUniversity of copenhagen

Abstract:

January 18

## Evaluation of the Cooling Trend in the Ionosphere Using Functional Regression with Incomplete Curves

Oleksandr GromenkoUtah State University

Abstract:

The increased concentration of greenhouse gases is associated with the global warming in the lower troposphere. For over twenty years, the space physics community has studied a hypothesis of global cooling in the thermosphere, attributable to greenhouse gases. While the global temperature increase in the lower troposphere has been relatively well established, the existence of global changes in the thermosphere is still under investigation.

A central difficulty in reaching definite conclusions is the absence of data with sufficiently long temporal and sufficiently broad spatial coverage. Time series of data that cover several decades exist only in a few separated (industrialized) regions. The space physics community has struggled to combine the information contained in these data, and often contradictory conclusions have been reported based on the analyses relying on one or a few locations.

To detect global changes in the ionosphere we present a novel statistical methodology that uses all data, even those with incomplete temporal coverage. It is based on a new functional regression approach that can handle unevenly spaced, partially observed curves. While this research makes a solid contribution to the space physics community, our statistical methodology is very flexible and can be useful in other applied problems including spatio-temporal data.

LOCATION:  Gibson 414

TIME:  3:30 PM

January 22

## Sufficient Dimension Reduction through Inverse Regression and Machine Learning

Andreas Artimioumichigan Technological university

Abstract:

Sufficient dimension reduction (SDR) ideas are used for supervised dimension reduction in regression problems.  Support Vector Machine (SVM) algorithms belong to the class of machine learning techniques which are used for classification.  In this talk, we discuss Principal Support Vector Machine (PSVM) a method which utilizes SVM to achieve sufficient dimension reduction.  PSVM has several advantages over existing methodology for sufficient dimension reduction, with the most one being the fact that we can do linear and nonlinear dimension reduction under a unified framework.  We will give an overview of basic theoretical and simulation results.  We also discuss extensions where different machine learning algorithms can be used for improving the performance and the properties of PSVM.

LOCATION:  Gibson 310

TIME:
3:30 PM

January 24

## An Introduction to Hyperbolic Nets

Suncica CanicUniversity of Houston

Abstract:

From local to global, and from simple to complex, hyperbolic nets capture the structural properties of various multi-component, net-like objects whose global properties emerge from complex combinations of local components modeled by 1D conservation laws. Examples include emerging new constructs  such as tissue scaffolds, carbon nano-tubes,  and endovascular stents, or classical  structures such as bridges and buildings made of metallic frames, which have been modeled using simplified net-based truss theory.

This talk will present our first steps in the development of a general theory, modeling, numerical simulation, and applications of nonlinear hyperbolic nets. As a prototypical example, we will focus on studying the structural properties of endovascular stents modeled as hyperbolic nets in 3D. The speaker will talk about a novel modeling approach to studying mechanical properties of these cardiovascular devices, and about the consequences of the numerical results in cardiovascular applications.  The new modeling approach based on dimension reduction and hyperbolic net ideas, provides substantial computational savings, it provides new information about the emergent mechanic behavior of stents, and it provides a novel framework for the development of general mathematical hyperbolic net theory.

January 25

## Identify Interactions for High Dimensional Data

Ning HaoUniversity of Arizona

Abstract:

Contemporary statistical research is being motivated and reshaped by the big data produced from emerging technologies and innovations in science and engineering. The high dimensionality, which characterizes many modern data sets, is one of the main challenges for statisticians in the new century. In spite of the rapid development in high dimensional statistical learning, it has not been touched until recently that the problem of interaction selection for high dimensional data. In this talk, I will introduce a new class of methodologies to solve regression models with interactions. The new methods are featured with feasible implementation, fast speed in computation, and desired theoretical properties. Various examples are presented to illustrate the new proposals.

LOCATION:  Gibson 414

TIME:  3:30 PM

January 28

## Bivariate Spatial Regression Models for Binary Data

Petruta Carageaiowa state university

Abstract:

Central to environmental monitoring is the detection and modeling of changes in the structure of the underlying scientific processes that govern the observable phenomena of interest.  Ideally, a statistical model used in this type of situation contains parameter values, for which we can assess, for example, the patterns of interaction between species, their relationship to spatial covariates, or changes over time, that correspond to components of the underlying scientific process in an interpretable manner.  A traditional approach for observations available on a discrete index random field, is to consider the overall level of a process, possibly adjusted by the influence of covariates, to be appropriately modeled as what is called the large-scale model component. When there is only one binary response variable, a typical approach is to use the logistic automodel. In this work, we introduce a bivariate autologistic model, which accounts for the statistical dependence in two response variables simultaneously, the association between them and the effect of spatial covariates. The framework introduced here is very flexible, and can be generalized to modeling simultaneously more than two variables, or to spatio-temporal models. An illustration of this model is provided, using the Pre-Euro-American Data from a Public Land Survey in the Driftless Area in the Midwest. The conceptual advantages of using the proposed model are illustrated by using a parametric bootstrap approach.

LOCATION:  Gibson 414

TIME:  3:30 PM

January 31

## Topic

Speakerinstitution

Abstract: TBA

February 7

## Modeling Data Network Sessions: Why is Traffic at a Busy Hub Gaussian?

Sid ResnickCornell university

Abstract:

A session is a higher order entity in data network modeling resulting from amalgamating packets, connections, or groups of connections according to specified but not unique rules. For example, packets flowing past a sensor can be amalgamated into sessions using a threshold rule based on gaps between packet arrivals. We review and illustrate heavy tailed probability and statistical modeling based on sessions. Statistical analysis of these sessions based on packets is complex: session duration (D) and size (S) are jointly heavy tailed but average transmission rate (R = S/D) is sometimes not heavy tailed and arrival times of sessions is typically not Poisson. By segmenting sessions in various ways, for instance using a peak rate covariate, we find conditional on a peak rate decile, within this decile segment session initiations can be modeled as Poisson. We discuss why traffic at a heavily loaded hub subject to a high degree of user aggregation is Gaussian.

February 14

## A Multilayer Grow-or-Go Model for GBM: Understanding the Effects of Anti-Angiogenic Drugs

Hassan Fathallah-ShaykhUniversity of alabama

Abstract:

The recent use of anti-angiogenesis (AA) drugs for the treatment of glioblastoma multiforme (GBM) has uncovered unusual tumor responses. I will discuss a new mathematical model that takes into account the ability of proliferative cells to become invasive under hypoxic conditions. We show that the model simulations generate the multilayer structure of GBM, namely proliferation, brain invasion, and necrosis. The model is validated and interrogated to derive fundamental insights in cancer biology and on the clinical and biological effects of AA drugs.

February 21

## Functional Convergence of Stochastic Integrals with Application to Inference in Time Series Models

Richard A. DavisColumbia university

Abstract:

Assuming that {(U_n,V_n) is a sequence of càdlàg processes converging in distribution to (U,V) in the Skorohod topology, conditions are given under which {\int\int f_n(beta,u,v) dU_ndV_n} converges weakly to \int\int f(beta,x,y)dUdV in the space C(R), where f_n(beta,u,v) is a sequence of smooth'' functions converging to f(beta,u,v).  Integrals of this form arise as the objective function for inference about a parameter beta in a stochastic model. Convergence of these integrals play a key role in describing the asymptotics of the estimator of beta which optimizes the objective function. We illustrate this with a non-invertible moving average process.  (This is joint work with Li Song.)

February 28

## Optima and Equilibria for Traffic Flow on a Network of Roads

Alberto BressanPenn state university

Abstract:

Daily traffic patterns are the result of a large number of individual decisions, where each driver chooses an optimal departure time and an optimal route to reach destination.

From a mathematical perspective, traffic flow can be modeled by a family of conservation laws, describing the density of cars along each road.  In addition, one can introduce a cost functional, accounting for the time that each driver spends on the road and a penalty for late arrival.

In the case of a single road, under natural assumptions one can prove the existence of a unique globally optimal solution, minimizing the sum of the costs to all drivers.

In a realistic situation, however, the actual traffic is better described as a Nash equilibrium, where no driver can lower his individual cost by changing his own departure time.  For a single road, a characterization of the Nash equilibrium solution can be provided, establishing its existence and uniqueness.

It is interesting to compare the costs of the optimal and of the equilibrium solution.  This yields indications on how to optimally design time-dependent fees to impose on toll roads.

Using topological techniques, existence results have recently been extended to the general case of several groups of drivers, with different origins and destinations and different cost functions, traveling on a network of roads.

An intriguing mathematical problem is to understand the dynamic stability of Nash equilibria.  In this direction, some numerical experiments and conjectures will be discussed.

March 7

## Fokker-Planck Equations for a Free Energy Functional or Markov Process on a Graph

Shui-Nee ChowGeorgia Tech

Abstract:

March 14

## Modeling the Evolution of Dispersal with Reaction-Advection-Diffusion Equations and their Discrete and Nonlocal Analogues

Chris CosnerUniversity of miami

Abstract:

This talk will describe the formulation and analysis of some models related to the evolution of dispersal in the context of reaction-diffusion-advection systems and the analogous discrete or nonlocal models, where the differential operator describing dispersal is replaced with a matrix or an integral operator.  It will present some basic ideas and results in an approach to the evolution of dispersal motivated by adaptive dynamics.  Those ideas include the notions of evolutionarily stable, convergent stable, and neighborhood invader strategies.   These types of strategies are characterized by their ability to give a population the ability to invade populations using other strategies or to resist invasion by them.  For example, an evolutionarily stable strategy has the property that a population using it cannot be invaded by another small population that uses a different strategy but which is otherwise ecologically similar to the first population.  Modeling the invasion of one population by another using a different dispersal strategy leads to competition models with different diffusion, advection, or nonlocal dispersal terms for the two competitors.   The analysis of those models is similar in general terms to that of reaction-diffusion models but the technical details and predictions of the analysis can be significantly different.   The analysis typically involves various ideas in the theory of differential and integral equations, including monotone methods, eigenvalue estimates, and Lyapunov functions.  In situations where the environment varies in space but not in time, it turns out in many cases that the evolutionarily stable strategies are those that lead to an ideal free distribution of the population.  An ideal free distribution of a population is one where all individuals at all locations have equal fitness and there is no net movement between locations.  The talk will describe how the ideal free distribution can be characterized and seen to be evolutionarily stable in different modeling frameworks.

March 21

## Active Scalar Equations and a Geodynamo Model

Susan FriedlanderUniversity of Southern California

Abstract:

We discuss an advection-diffusion equation that has been proposed by Keith Moffatt as a model for the Geodynamo.  Even though the drift velocity can be strongly singular, we prove that the critically diffusive PDE is globally well-posed.  We examine the nonlinear instability of a particular steady state and use continued fractions to construct a lower bound on the growth rate of a solution. This lower bound grows as the inverse of the diffusivity coefficient. In the Earth's fluid core this coefficient is expected to be very small.  Thus the model does indeed produce very strong Geodynamo action.

This work is joint with Vlad Vicol.

March 28

April 4

## Sparsity, Convexity, and Algorithms in Blind Source Separation

Jack XinUniversity of california-irvine

Abstract:

Blind source separation refers to the inverse problem of recovering source signals from their linear mixtures with no knowledge of the mixing conditions. An example is the cocktail party problem where humans are able to pay attention to one speaker in a multiple speaker environment. It is not known how our brain performs this task computationally. A corresponding mathematical problem is to factorize a data matrix into a product of a mixing matrix and a signal matrix, similar to composite number factorization.  However, such a formulation is severely under-determined in general unless certain property of source signals is known. In this talk, we explore signal sparsity, short time stationarity of mixing process, and multiple segments of data to identify reduced convex optimization problems for efficient solutions. We show related algorithms and results in spectroscopic imaging and speech enhancement.

April 11

## Connections Between Monomial Ideals and Combinatorics

Chris FranciscoOklahoma State University

Abstract:

Combinatorial commutative algebra is a relatively young field that has flourished
recently in part due to great improvements in computer algebra systems. The
goal of the area is to use combinatorial methods and structures to solve problems
in algebra and vice versa. We will survey typical questions in this field and
highlight some successful interactions between combinatorics and commutative
algebra.

LOCATION:  Dinwiddie 102

TIME:  2:00 PM

No refreshments following.

April 18

## The Challenge of Sustainability and the Promise of Mathematics

Simon A. LevinPrinceton Univeristy

Abstract:

The continual increase in the human population, magnified by increasing percapita demands on Earth's limited resources, raises the urgent mandate of understanding the degree to which these patterns are sustainable. The scientific challenges posed by this simply stated goal are enormous; mathematics provides a common language and a way to cross disciplines and cross scales.  What measures of human welfare should be at the core of definitions of sustainability, and how do we discount the future and deal with problems of intragenerational and inter-generational equity? How do environmental and socioeconomic systems become organized as complex adaptive systems, and what are the implications for dealing with public goods at scales from the local to the global? How does the increasing interconnectedness of natural and human systems affect us, and what are the implications for management? What is the role of social norms, and how do we achieve cooperation at the global level?  Mathematical tools help in understanding the collective dynamics of systems from bacterial biofilms to bird flocks and fish schools to ecosystems and the biosphere, and the emergent features that support life on the planet. They also provide ways to resolve the game-theoretic challenges of achieving cooperation among individuals and among nations in providing for our common future.

Location:  Dinwiddie 103G

Time:  3:30 PM

April 25

## Topic

Speakerinstitution

Abstract: TBA

Mathematics Department, 424 Gibson Hall, New Orleans, LA 70118 504-865-5727 math@math.tulane.edu