Adam Pantel, Rutgers University, New Brunswick, NJ

The Curry-Howard Isomorphism is an important theorem in computer
science that provides a close correspondence between types (in
programming) and propositions (in mathematical logic), whereby
expressions of a given type correspond to proofs of the associated
proposition. Under this correspondence, inductive proofs correspond to
recursive programs, and proofs by contradiction correspond to programs
that include backtracking.

Jordan Ledvina, Rutgers University, New Brunswick, NJ

In order to solve the 19th problem, a crucial result is needed
concerning the regularity of a solution to a particular differential equation.
Given very weak assumptions on the coefficients of this equation, Ennio De
Giorgi was able to show using geometric arguments that the derivative of this
solution is Holder continuous. And from this result, everything falls into
place.

Jeremy Engel, Rutgers University, New Brunswick, NJ

The limiting free boundary problem is an important problem in applied
mathematics. We consider the one-dimensional profile for systems with
fully nonlinear elliptic operators and describe a process of
homogenization for fully nonlinear elliptic equations.

Matthew Samuel and Charles Siegel, Rutgers University, New Brunswick, NJ

For every topological space with a group action, there is a rule
called Equivariant Cohomology which assigns a ring. This ring captures the
intersection theory of the space and takes into account the group's action.
For the special case of the Lagrangian Grassmanian, this ring is determined by
the structure constants with respect to a basis of Schubert classes. In this
case, certain positivity conditions are known for the structure constants,
which are actually polynomials in several variables, but no formula for
computing them is known which explicitly exhibits these conditions. We present
a formula for a special class of structure constants which manifestly satisfies
the known positivity conditions.

Chris Sadowski, Rutgers University, New Brunswick, NJ

There are certain modules for affine Lie algebras which happen to be
modules for a vertex operator algebra also. We examined how the module
structure changes when our vertex operator is changed by a certain
function called delta, and when our modules are what are called
"standard" or "highest weight integrable" irreducible modules for an
affine Lie algebra. It is well know that elements of the coroot lattice,
when applied with this delta, cause delta to give us a module isomorphic
to the module with which we started. We examined the more general case,
in which we used elements of the coweight lattice (an important set
containing the coroot lattice as a subset) with delta and determined what
module structure delta had given us.

James Long, Columbia University, New York, NY

Researchers frequently use goodness of fit statistics from factor
analysis applied to categorical data despite model assumptions
requiring multivariate normal manifest variables and continuous
latent variables. When these model assumptions are violated,
hypothesis testing regarding the number of latent factors may
produce erroneous type I and type II error rates. In this paper,
we compare type I and type II error rates generated by factor
analysis applied to categorical manifest variables with error rates
produced by latent class analysis applied to the same data. In
general factor analysis applied to categorical data produces
correct type I error rates and has roughly the same power as latent
class analysis.

Justin Thaler, Yale University, New Haven, CT

A massive data stream is a sequence of information that is so long it
cannot be
stored completely in memory, and as a result algorithms on data streams should
not just be time efficient, but space efficient as well. According to
"Estimating entropy and entropy norm on data streams" by Chakrabarti, Ba,
and Muthukrishnan, "Sublinear space is mandatory and polylogarithmic space is
often the goal."
Chakrabarti et al. present a space-efficient algorithm for estimating the
entropy of a data stream in the paper "A Near-optimal algorithm for computing
the entropy of a stream". We implemented three versions of this algorithm. In
this talk, we will present the results of controlled experiments with these
implementations.

Nicole Scholtz, Denison University, Granville, OH

The completion of any type of special mission requires selecting the
best team for the job. Here, we examine the best way to
simultaneously compose such teams from a limited population. In doing
so, each team must meet certain competency and resiliency
requirements, as dictated by the mission. Our aim is to create an
efficient algorithm to assign people to teams such that these
requirements are met, while minimizing the number of people assigned
to teams.

Anne Eaton, Grinnell College, Grinnell, IA and Johanna Tam, California State Polytechnic University, Pomona, CA

We are building two different models of the spread of a respiratory disease at
CRAF, which is the New Jersey State intake prison. Johanna Tam is using SIR
modeling techniques and dividing the population into 16 subgroups while Anne
Eaton is using network theory and analyzing at the individual level. These
models follow the same daily schedule and the same population. We hope to
compare our models and analyze our data.

Barton J. Willage, Beloit College, Beloit, WI

Sick children have a multi-faceted impact on society, adversely affecting schools, business and the income of parents. The entities with the most responsibility and power in keeping the spread of illness among children are schools and parents. However, parents and schools interest are neither completely aligned nor completely divergent: This gives rise to a non-zero-sum game. However, a sequence of games in matrix form where parties have imperfect information leads to poor outcomes for both parties. On the other hand, games in tree form are sometimes unreasonably large and tend to give rise to outcomes that are impractical from a policy perspective.

Tsvetan Asamov, Kenyon College, Gambier, OH

Sick children have a multi-faceted impact on society, adversely affecting schools, business and the income of parents. The entities with the most responsibility and power in keeping the spread of illness among children are schools and parents. However, parents and schools interest are neither completely aligned nor completely divergent: This gives rise to a non-zero-sum game. However, a sequence of games in matrix form where parties have imperfect information leads to poor outcomes for both parties. On the other hand, games in tree form are sometimes unreasonably large and tend to give rise to outcomes that are impractical from a policy perspective.

Daniel Kral, Jan Kynčl and Bernard Lidický, Charles University, Prague

A 6-critical graph is an inclusion-minimal graph which is not 5-colorable. We
describe a complete list of nine 6-critical graphs for the graphs embeddable in
the Klein bottle, together with their nineteen nonisomorphic embeddings. This
gives us a polynomial algorithm for deciding 5-colorability of graphs embedded
in the Klein bottle.

Jan Kynčl, Marek Sterzik and Tomáš Vyskočil, Charles University, Prague

An input of the st-reachability problem is a directed graph G together with a pair of vertices s and t. The goal is to determine if s and t are connected by a directed path in G.

L (logspace) is the class of decision problems solvable by a Turing machine restricted to use an amount of memory logarithmic in the size of the input, n. (The input itself is not counted as part of the memory.) The class NL is a non-deterministic version of L.

It is known that st-reachability is a complete problem for NL, whereas the undirected version lies in L. The complexity of the planar st-reachability problem, where the input is a planar graph, is an open question.

We present a logspace reduction from st-reachability on a fixed genus surface
to the st-reachability in the plane. Previously, this reduction was known only
for the torus.

Mario De Franco, Princeton University, Princeton, NJ

This project explores the sequence dependence of the structural properties of
DNA at lengths of a few hundred base pairs. A dimeric base-pair step can be
modeled by two planar slabs; its configuration in three dimensional space
can then be determined by rotational and translational parameters known as
twist, tilt, roll, shift, slide, and rise. With step parameter data obtained
from the Nucleic Acid Database, empirically-derived potential functions
have been created to gauge the likelihood of a particular step type conforming
to a set of the six parameters. My work mainly is concerned with applying
clustering analysis to the step parameter data, devising new functions that
more accurately assess the data distribution, and testing the functions with
nucleosome threading, i.e., determining the affinity of a sequence for binding
to a nucleosome.

Aleksandar Nikolov, Saint Peter's College, Jersey City, NJ

Two important directions for data mining research are distributed data
mining and privacy-preserving data mining. Potentially useful data is
often distributed among multiple parties and it is not always feasible to
aggregate all the data in one site before it is mined. Privacy issues are
one major barrier to aggregation and unrestricted sharing of data. For
these reasons, it is useful to have efficient techniques for mining data
in a distributed environment while preserving private information.
Current research has focused on data which is horizontally or vertically
fragmented. However, in many real-world situations, data comes from
heterogeneous sources and is neither horizontally, nor vertically
distributed. In this talk, we will present an overview of some
privacy-preserving data mining techniques and we will discuss the
challenges of privacy-preserving mining of hybrid fragmented data.

Paul Bonamy, Lake Superior State University, Sault Ste. Marie, MI

Traditionally, author identification focuses on assigning a document to
a single author with a high level of confidence. Using existing
techniques and software as a starting point, we attempt to determine
whether two documents share a common author without considering the
identity of that author. Initial results show high accuracy using both
raw feature vectors and existing author identification models. Analyses
using these existing models appear to be particularly effective at
identifying pairs of documents with a common author.

Latoya Clay, Clark Atlanta University, Atlanta, GA

Epilepsy is the second most common brain disorder after stroke and
currently afflicts at least 2 million Americans. The most common symptom
of epilepsy is spontaneous recurrent seizures. There has been recent
research indicating promising signs of seizure predictability. The
objective of this study is to determine whether the
correlations/synchronizations among different brain areas during normal
and pre-seizure periods is significantly different. This difference
should be demonstrated through a higher correlation among brain areas
during the period closer to a seizure.

Liyang Diao, Wake Forest University, Winston-Salem, NC

Short-interfering RNA, or siRNA, has much potential in the area of gene
silencing. The current problem lies in determining which strings of siRNA are
effective in suppressing gene expression and which strings are not: Given a
string of siRNA of twenty nucleotides, there are 4^20 number of potential
strings of siRNA, only a few of which may actually be useful. We created an
algorithm based on a weighted levenshtein distance such that the distance from
functional siRNAs to other functional siRNAs is less than the distance from
functional to nonfunctional siRNAs.

AJ Stewart, Humboldt State University, Arcata, CA

For a given reaction network there exists a graph called the species
reaction graph, which corresponds to the network. This graph contains two
sets of nodes, reaction nodes and species nodes. In this talk we will
present some conjectures involving the requirements for bistability in
reaction networks as related to the algebraic properties of its species
reaction graph and the labeling of its reaction nodes.