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Colloquia

David Swigon 11/6/2014

Dynamics of price and wealth in a
multi-group asset flow model

Date: 11/6/2014
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Professor David Swigon

Abstract: A recently developed model of asset flow dynamics allows one to use
the tools of nonlinear dynamics to study various market conditions and
trading scenarios. I will present the results of two such studies. In the
first we focused on the stability of market equilibria in cases in which
investor groups follow commonly used trading strategies, such as
fundamentalist or trend-based. We show that a market comprised of
fundamental traders is always stable while the presence of trend-based (also
called momentum) traders destabilizes market equilibria and potentially
leads to market bubbles or flash crashes. In the second study we analyzed
the constant rebalanced portfolio (CRP) strategy, in which investor divides
his wealth equally between different types of assets and maintains those
proportions constant as the price changes. We show that CRP strategy is
optimal in that it minimizes the potential losses incurred during price
fluctuations in the market. We also show that any other trading strategy can
be taken advantage by other investors in the market and lead to a loss of
wealth.

Date, Location: 
2014-11-06

Richard Coultas 11/5/2014

K-Crossing
Free Antichains

Date: 11/5/2014
Time: 3:45PM-4:45PM
Place: 315 Armstrong Hall

Professor Richard Coultas

Abstract:
A set S of vectors in Z^w is an antichain if no vector in S has all coordinates less than or equal to the coordinates of some other vector in S, and is k-crossing free if a certain condition on the maximum difference between corresponding coordinates of different vectors is satisfied. This paper considers how large a k-crossing free antichain of vectors in Z^w can be. The problem is solved for w=3, and some partial results are given for w>3.

Date, Location: 
2014-11-05

C.S. Aravinda 9/30/2014

Dynamics of geodesic
conjugacies

Date: 9/30/2014
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Professor C. S. Aravinda

abstract:
The question of whether a time-preserving geodesic conjugacy
determines a closed, negatively curved Riemannian manifold up to an
isometry is one of the central problems in Riemannian geometry. While an
answer to the question in this generality has yet remained elusive, we
discuss some available affirmative results.

Date, Location: 
2014-09-30

Dr. Dejan Slepcev 9/26/2014

Introduction to optimal transportation and Wasserstein gradient flows

Two Different Times.

1. Date: 9/26/2014
1. Time: 10:00AM-10:50AM
1. Place: Mountaineer Room, Mountainlair

2. Date: 9/26/2014
2. Time: 2:35PM-3:25PM
2. Place: Mountaineer Room, Mountainlair

Professor Dejan Slepcev

abstract:
I will cover some of the basics of the theory of optimal transportation and gradient flows in spaces of measures endowed with Wasserstein metric. The goal it to provide the background material for the geometric approaches to the PDE the workshop focuses on. In the first part I will introduce the notion of optimal transport, the Monge and Kantorovich formulations and discuss some properties of the optimal transportation maps. I will then discuss the geometry of the space of probability measures, in particular the McCann interpolation, its connection to pressureless Euler equation and the Benamou-Brenier characterization of the Wasserstein distance.
In the second part I will discuss the notion of a gradient flow in the spaces of probability measures, and in particular the characterization of some PDE like the heat equation, porous medium equation and nonlocal-interaction (a.k.a aggregation) equation as such gradient flows. Finally I will discuss the applications of this viewpoint to existence, uniqueness and stability of the solutions.

Date, Location: 
2014-09-26

Professor Alexandre Xavier Falcão 9/10/2014

Image Segmentation using
The Image Foresting Transform

Date: 9/10/2014
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Professor Alexandre Xavier Falcão

Abstract:
Image segmentation is a challenging task that consists of an image
partition into either superpixels (regions) that include the
delineation of the desired object borders, or define the precise
spatial extent of such objects in the image. The image foresting
transform (IFT) provides a unified framework to the design of
operators based on optimum connectivity between image elements
(pixels, superpixels, or their components). Its applications include
filtering, segmentation, distance transforms, skeletonization, shape
description, clustering, and classification.

This lecture presents a short overview on the IFT in order to discuss
several aspects related to boundary-based, region-based, interactive,
and automated image segmentation. The IFT algorithms rely on the
suitable choice of an adjacency relation and a connectivity
function. The adjacency relation defines an image graph, whose nodes
are the image elements and arcs connect the adjacent ones. The
connectivity function assigns a value to any path in the graph,
including trivial ones formed by a single node. The maxima (minima) of
the trivial connectivity map are called "seeds" --- they compete among
themselves to conquer their most strongly connected nodes such that
the image is partitioned into an optimum-path forest rooted at the
winner seeds. The image operators result from the attributes of the
forest (optimum paths, their connectivity values, root labels).

The lecture shows how to extend the IFT to the design of pattern
classifiers and discusses connectivity functions for boundary-based
and region-based segmentation, seed selection and imposition, oriented
boundaries and regions, and the incorporation of object information
(texture and shape models) into the interactive and automated
segmentation processes. Most IFT-based methods execute in time
proportional to the number of nodes (linear or sublinear time). The
lecture discusses how to correct segmentation errors in sublinear time
(without starting the process from the beginning, even when the image
was processed by other segmentation approach) and how to obtain smooth
object boundaries without loosing consistency in segmentation (i.e.,
the nodes remain connected to their respective roots). Finally, it
concludes with the current research on IFT-based image segmentation.

Short Biography

Alexandre Xavier Falcão is professor at the Institute of Computing,
University of Campinas (UNICAMP), Brazil. He received a B.Sc. in
Electrical Engineering from the Federal University of Pernambuco,
Brazil, in 1988. He has worked in biomedical image processing,
visualization, and analysis since 1991. In 1993, he received a
M.Sc. in Electrical Engineering from UNICAMP. During 1994-1996, he
worked with the Medical Image Processing Group at the Department of
Radiology, University of Pennsylvania, USA, on interactive image
segmentation for his doctorate. He got his doctorate in Electrical
Engineering from UNICAMP in 1996. In 1997, he worked in a research
center (CPqD-TELEBRAS) developing methods for video quality
assessment. His experience as professor of Computer Science started in
1998 at UNICAMP. His main research interests include graph algorithms
for image processing, image segmentation, volume visualization,
content-based image retrieval, mathematical morphology, digital video
processing, remote sensing image analysis, machine learning, pattern
recognition, and biomedical image analysis.

Date, Location: 
2014-09-10

Dr. Pete Donnell 9/9/14

Monotonicity, nonexpansivity
and chemical reaction networks

Date: 9/9/2014
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Dr. Pete Donnell

Abstract:
There is currently significant research interest into chemical reaction networks (CRNs), largely due to their importance in biochemistry. CRNs are commonly modelled as ODEs. Given an ODE representing a CRN, characterising its possible asymptotic behaviour is in general a difficult task. A significant proportion of real world CRNs exhibit very simple behaviour, for example global convergence to a unique steady state. However, more exotic CRNs such as the Belousov-Zhabotinsky reactions, which can have a stable nontrivial periodic orbit, are not uncommon.

In this talk I will give a brief overview of two areas of theory, monotonicity and nonexpansivity, that can be used to constrain the possible dynamics of an ODE. It is known that a monotone ODE cannot have stable periodic orbits. If a monotone ODE also has a linear first integral, it is possible in some cases to show that it is nonexpansive and that every bounded trajectory converges to a steady state. Examples drawn from chemical reaction network theory will be presented as applications of this result.

Date, Location: 
2014-09-09

Professor Andreas Brandstädt 9/3/2014

The complexity of the efficient
domination problem

Date: 9/3/2014
Time: 4:00PM-5:00PM
Place: 315 Armstrong Hall

Professor Andreas Brandstädt

Abstract:
Packing and covering problems in graphs and hypergraphs and their relationship
belong to the most fundamental topics in combinatorics and graph algorithms and
have a wide spectrum of applications in computer science, operations research and
many other fields.
Recently, there has been an increasing interest in graph and hypergraph problems
combining packing and covering properties, and the NP-complete Exact Cover problem
on hypergraphs (asking for a collection of hyperedges covering each vertex exactly
once) is a good example for this. Closely related graph problems are the Efficient
Domination (ED) and Efficient Edge Domination (EED) problems; the ED problem
corresponds to the exact cover problem for the closed neighborhoods of a graph,
and the EED problem on a graph G is the ED problem on its line graph L(G).
We give a survey on previous results, describe some connections to other problems
such as Maximum Weight Independent Set and Minimum Weight Dominating
Set, consider some new cases where the problems are efficiently solvable by
using structural properties of graph classes and using closure properties under the
square operation, and we also extend the graph problems to hypergraphs.

Date, Location: 
2014-09-03

Dr. Xin He 7/10/14

Some Graph-Based Models
and Algorithms in Genomics

Date: 7/10/2014
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Dr. Xin He

Abstract:
Graph theory has a number of applications in bioinformatics and genomics
research. In this talk, I will discuss two recent problems that can
formulated in graphical theoretical terms. Next generation sequencing (NGS)
technology greatly reduces the cost of DNA sequencing. Such NGS data
typically consists of a large number of short "reads" of length a few
hundred base pairs or less, and how to assemble these reads to the full
genomic sequences is a challenging combinatorial problem. I will review
some of the algorithms that have been proposed for this problem, which are
essentially finding Hamiltonian or Eulerian path in a graph. In practice,
the problem is made harder by the errors in sequencing, repeats in genomic
sequences, and so on. In the second part of my talk, I will discuss a
problem of mapping genes that contribute to human diseases. Existing
studies tend to analyze one gene at a time through association studies,
which test if the variation of DNA sequences in a gene correlates with the
status of a disease (whether a person is affected or not). Genomic data, on
the other hand, creates a map of how genes are related to each other. I
will discuss some of our attempts at integrating association data (at the
level of individual genes) and gene network data. Such an approach
effectively identifies highly related gene groups (dense subgraphs) that
are most likely to contribute to diseases.

Date, Location: 
2014-07-10

Professor Jerrold Griggs 5/14/2014

Symmetric Venn Diagrams and
Symmetric Chain Decompositions

Date: 5/14/2014
Time: 3:00PM-4:00PM
Place: 315 Armstrong Hall

Jerrold Griggs

Abstract: Here

Date, Location: 
2014-05-14

Professor Gheorghe Craciun 5/2/2014

Date: 5/2/2014
Time: 2:30PM-3:30PM
Place: 315 Armstrong Hall

Gheorghe Craciun

Abstract: Complex interaction networks are present in all areas of biology, and
manifest themselves at very different spatial and temporal scales. Persistence,
permanence and global stability are emergent properties of complex networks, and
play key roles in the dynamics of living systems.
Mathematically, a dynamical system is called persistent if, for all positive
solutions, no variable approaches zero. In addition, for a permanent system, all
variables are uniformly bounded. We describe criteria for persistence and permanence
of solutions, and for global convergence of solutions to an unique equilibrium, in a
manner that is robust with respect to initial conditions and parameter values.
We will also point out some connections to classical problems about general
dynamical systems, such as the construction of invariant sets and Hilbert's 16th
problem.

Date, Location: 
2014-05-02

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