# Colloquia

## Professor Lianying Miao 2/22/2016

On the extremal values of the
eccentric distance sum of trees

Date: 2/22/2016
Time: 3:30PM-5:00PM
Place: 315 Armstrong Hall

Lianying Miao

Abstract:Let G = (V,E) be a simple connected graph. The eccentricity ε(v) of a vertex v is the maximum distance from v to any other vertex. The eccentric distance sum of G is deﬁned as ξd(G) = Pv∈V ε(v)D(v), where D(v) = Pu∈V d(u,v) is the sum of all distance from the vertex v.

In this paper, we continue to study the eccentric distance sum of trees. The trees of order n with domination number at most dn

3e are characterized.

Date, Location:
2016-02-22

Entropy and the additive combinatorics of probability densities
on locally compact abelian groups

Date: 1/27/2016
Time: 3:30PM-4:50PM
Place: 315 Armstrong Hall

Abstract: Additive number theory contains a number of so-called
"sumset inequalities" that relate the cardinalities of various finite
subsets of an abelian group G, for instance, the sumset A+A and the
difference set A-A of a finite subset A of G. It also contains
“inverse" results such as Freiman’s theorem, which asserts that sets A
such that A+A is relatively small must have some "additive structure".
Motivated by considerations coming from multiple directions including
probability theory, combinatorics, information theory, and convex
geometry, we explore probabilistic analogues of such results in the
general setting of locally compact abelian groups.

For instance, we show that for independent, identically distributed random variables X
and X’ whose distribution has a density with respect to Haar measure
on a locally compact abelian group G, the entropies of X+X' and X-X'
strongly constrain each other. We will also discuss stronger
statements that can be made for specific groups of interest, such as
R^n, the integers, and finite cyclic groups.

Based on (multiple) joint works with Ioannis Kontoyiannis (Athens Univ. of Economics),
Jiange Li (Univ. of Delaware), Liyao Wang (Yale Univ.), and Jaeoh Woo
(Univ. of Texas, Austin).

Date, Location:
2016-01-27

## Professor Hao Shen 10/29/2015

Resolvable group divisible designs and (k,r)-colorings of complete graphs

Date: 10/29/2015
Time: 4:30PM-5:30PM
Place: 315 Armstrong Hall

Hao Shen

Abstract: Let k and r be given positive integers, a
(k,r)-coloring of a complete graph K is a coloring of the edges of K with r colors such that all monochromatic connected subgraphs have at most k vertices. The Ramsey number f(k,r) is defined to be the smallest u such that the complete graph with u vertices does not admit a (k,r)-coloring.

A group divisible design is called resolvable if all the blocks can be partitioned into parallel classes. In this talk, we will introduce the known results on the existence of resolvable group divisible designs and their applications in the study of (k,r)-colorings of complete graphs.

Date, Location:
2015-10-15

Steady states of polynomial ODEs arising in biology with application
to multisite phosphorylation

Date: 10/1/2015
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Abstract:Polynomial Ordinary Differential Equations are an important tool in many areas of quantitative biology. Due to high measurement uncertainty, few experimental repetitions and a limited number of measurable components, parameters are subject to high uncertainty and can vary in large intervals. One therefore effectively has to study families of parametrized polynomial ODEs. In this talk a class of ODEs is discussed, where the steady states can be parametrized by solutions of parameter independent linear inequality systems. To this class belong, for example, multisite phosphorylation systems. For a special instance of this subclass, one can formulate parameter conditions that guarantee the existence of three steady states.

Date, Location:
2015-10-01

## Professor Alan Rendall 9/29/2015

Date: 9/29/2015
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Alan Rendall

Abstract:Signalling networks are sets of chemical reactions used to transmit information
in living cells. One pattern frequently encountered in this context is that of a
successive stages. In this talk I report on work with Juliette Hell on the existence
of periodic solutions in systems of ODE modelling a key example of
a cascade of this type, the MAP kinase cascade. The mathematical tools used
for this are bifurcation theory and geometric singular perturbation theory.
I will also describe the relation of these results to the idea that oscillations
are often related to negative feedback loops, where the feedback may arise
in an implicit way due to sequestration effects.

Date, Location:
2015-09-29

## Professor Martha Alibali 9/28/2015

Defining and Measuring Conceptual Knowledge of Mathematics

Date: 9/28/2015
Time: 3:30PM-4:30PM
Place: 121 Armstrong Hall

Martha Alibali

Abstract:Both researchers and educators recognize the importance of conceptual knowledge in mathematics. However, it has proven difficult to identify and measure conceptual knowledge in many mathematical domains. This talk provides an overview of research on conceptual knowledge in the literature on mathematical thinking. I discuss (1) how conceptual knowledge is defined in the mathematical thinking literature, broadly speaking, and (2) how conceptual knowledge is defined, operationalized, and measured in three specific mathematical domains: equivalence, cardinality, and inversion. This review uncovers several shortcomings in this body of literature, most notably a lack of consistency in definitions of conceptual knowledge and a lack of alignment between definitions and measures. To address these issues, I propose a general framework that divides conceptual knowledge into two facets: knowledge of general principles and knowledge of the principles underlying procedures.

Date, Location:
2015-09-28

## Professor Bing Wei 9/25/2015

Hamiltonian properties, branch number and k-tree related graphs

Date: 9/25/2015
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Bing Wei

Date, Location:
2015-09-25

## Professor Suohai Fan 8/13/2015

On $r$-hued colorings
of graphs

Date: 8/13/2015
Time: 2:30PM-3:20PM
Place: 315 Armstrong Hall

Suohai Fan

Abstract:For integers $k, r > 0$, a $(k, r )$-coloring of a graph $G$
is a proper $k$-coloring $c$ such that for any vertex $v$ with degree
$d(v)$, $v$ is adjacent to at least
min$\{d(v),r\}$ different colors. Such coloring is also called as an $r$-hued
coloring. The {\it $r$-hued chromatic number} of $G$, $\chi_{r}(G)$, is the least integer
$k$ such that a $(k, r )$-coloring of $G$ exists. In this talk, we will present some
of the progresses in this area.

Date, Location:
2015-08-13

## Michael Wester 4/29/2015

Determining the Parameters in Spatially Resolved Models of the
Motion of Proteins in the Membranes of Stimulated Cells

Date: 4/29/2015
Time: 3:30PM-4:30PM
Place: 315 Armstrong Hall

Michael Wester

Abstract: We show how to compute a dimerization rate from stimulated cell diffusion
data which can be used in a spatially resolved stochastic simulator to
accurately reproduce the data. For our data and for strong stimuli,
the time dependent diffusion coefficient rapidly transitions from the
diffusion constant for unstimulated cells to a significantly smaller
value. The diffusion data is generated using sparse labeling with
quantum dots which allows us to analyze using a non-spatial system
of two linear differential equations. We then use a closely related
system of two non-spatial nonlinear differential equations to compute a
spatially resolved reaction rate to use in our simulation code. Using
these reaction rates we successfully reproduce the biological data.
The framework developed here can be extended to analyze other time
dependent diffusion data.

Date, Location:
2015-04-29

## John Thompson 4/15/2015

Investigating student understanding and application of mathematics needed in physics: Definite integrals and the Fundamental Theorem of Calculus

Date: 4/15/2015
Time: 4:30PM-5:30PM
Place: 422 Armstrong Hall

John Thompson

Abstract: Learning physics concepts often requires the ability to interpret and manipulate the underlying mathematical representations and formalism (e.g., equations, graphs, and diagrams). Physics students are expected to be able to apply mathematics concepts to find connections between various physical quantities that are related via derivatives and/or integrals. Our own research into student conceptual understanding of physics has led us to investigate how students think about and use prerequisite, relevant mathematics, especially calculus, to solve physics problems. This is a rapidly growing research area in physics education.
Based on responses to questions administered in thermodynamics, we developed or adapted questions related to definite integrals and the Fundamental Theorem of Calculus (FTC), specifically with graphical representations, that are relevant in physics contexts, including some integrals that result in a negative quantity. Questions were administered in written form and in individual interviews; some questions had parallel versions in both mathematics and physics. Eye-tracking experiments provided additional information on visual attention during problem solving. Our findings are consistent with much of the literature in undergraduate mathematics education; we also have identified new difficulties and reasoning in students’ responses to the given problems.

Date, Location:
2015-04-15