Schedule 
Saturday,
October 2 TESEQ201
(Hewlett 201)

10:0010:30
. 
Welcome and opening
remarks
. 
Session I: Probability Theory,
Chair
and moderator: Persi
Diaconis (10:3012:00) 
10:3011:15 
Thomas M. Liggett 
The Role of Inequalities in Interacting Particle Systems 
11:2011:45 
Larry Shepp  Karlin
and Convexity 
11:4512:00 
Discussion 
12:001:30
. 
Workshop light lunch
. 
Session
II: Mathematical Economics, Chair and moderator: Theodore W Anderson
(1:302:10) 
1:301:55 
Anna R. Karlin  Algorithmic
Mechanism Design 
1:552:10
. 
Discussion
. 
Session III: Bioinformatics,
Chair and moderator: Douglas L. Brutlag (2:155:10) 
2:153:00 
David O. Siegmund 
Sam Karlin and Biomolecular Sequence Analysis 
3:003:30 
Coffee Break 
3:303:55 
Chris Burge  Prediction
of Mammalian MicroRNA Targets 

Molecular biology:
impact and challenges for mathematics.
Panel: Allan M. Campbell, Kenneth Karlin, George L. Miklos (moderator),
Edward S. Mocarski

Banquet:
Oak Room, Tresidder Union (2nd Floor), Chair:
Amir Dembo 
6:00

Toasts: Manny Karlin,
Yosef Rinott, Larry Shepp

Sunday,
October 3 TESEQ201
(Hewlett 201) 
9:009:30
. 
Continental breakfast
. 
Session IV: Total Positivity
and approximation Theory, Chair
and moderator: Ingram
Olkin (9:3011:00) 
9:3010:15 
Yosef Rinott
 A glimpse into Sam Karlin's work in Total Positivity 
10:2010:45

Charles A. Micchelli
 Moment Spaces on Hinfinity 
10:4511:00

Discussion

11:0011:30
. 
Coffee break
. 
Session V: Evolutionary Theory,
Chair and moderator: Alfred M Spromann (11:301:00) 
11:3012:15 
Warren D. Ewens  Sam
Karlin and the stochastic theory of evolutionary population genetics 
12:2012:45 
Marcus W. Feldman 
Models for the evolution of interactions between genes

12:451:00 
Discussion and Workshop
conclusion 
Abstracts 
Chris
Burge  MIT
Title: Prediction of Mammalian MicroRNA Targets
Abstract: Sam Karlin has pioneered the statistical analysis
of the distribution of short oligonucleotides in genomic DNA
sequences. Recently, a class of genes encoding small,
noncoding regulatory RNAs only ~22 nucleotides in length has
been discovered. This class of genes, known as microRNAs,
play important gene regulatory roles in nematodes, insects,
and plants by basepairing to mRNAs to specify posttranscriptional
repression of these messages. Thus, RNA oligonucleotides  including
the microRNAs themselves as well as their complementary sites
in mRNAs  play fundamental but still poorly understood roles
in eukaryotic biology, providing a unique opportunity for the
application of bioinformatics approaches making use of oligonucleotide
statistics. The mRNAs regulated by vertebrate microRNAs
are essentially all unknown. To address this question,
we recently developed an algorithm called TargetScan, in collaboration
with the David Bartel lab (Whitehead Institute/MIT). In
this talk, I will describe this and other algorithms developed
for microRNA target prediction, and discuss the statistical
and experimental evidence that supports the reliability of TargetScan's
predictions, and resulting insights into the roles of microRNAs
in mammalian biology.

Warren
Ewens  University of Pennsylvania
Title: Sam Karlin and the stochastic theory of evolutionary
population genetics
Abstract: Sam Karlin entered the field of genetics through his
research concerning stochastic models of evolutionary population
genetics. In particular, he applied the theory that he developed
together with McGregor on birthanddearth processes to give
a full analysis of the socalled Moran evolutionary genetics
model. From there he went on to analyze many stochastic evolutionary
genetics models and later to the analysis of deterministic models
and models used in bioinformatics.
This talk will describe his work in the stochastic theory, placing
this in its historical context and outlining developments of
the theory in more recent times.

Marcus
W. Feldman  Stanford University
Title: Models for the evolution of interactions between
genes
Abstract: Various lines of evolutionary genetic theory suggest
that the action of genes should evolve to become modular. In
classical terms, this would amount to a tendency for gene action
to become more additive across genes. The talk will suggest
a mathematical framework for posing the question of whether
genes evolve to act more independently or whether tighter interactions
should form. The analysis will bear similarities to earlier
general theorems on evolution of modifiers of gene action.

Anna Karlin
 U. of Washington
Title: Algorithmic Mechanism Design
Abstract: We survey a relatively new field of interest within
theoretical computer science motivated by the emergence of the
Internet as one of the most important arenas for resource sharing
between parties with diverse and selfish interests. To study
these issues, we draw on ideas from a number of fields many
of which Sam Karlin (my dad) has contributed to, including game
theory, economics, probability and algorithm design and analysis.

Thomas Liggett
 UCLA
Title: The Role of Inequalities in Interacting Particle
Systems
Abstract: Sam Karlin has made important contributions to many
areas of probability theory. Among these are branching processes
and random walks. Two of the most important models in interacting
particle systems  the contact process and the exclusion process
 can be viewed as interacting versions of branching processes
and random walks, respectively.
The interactions make explicit calculations difficult or impossible.
A tool that often replaces these calculations is monotonicity
and the use of inequalities. The application of inequalities
to many areas of mathematics is another of Sam's major contributions.
In this talk, I will explain some important applications of
inequalities in the analysis of the contact process and exclusion
process.

Charles A.
Micchelli  SUNY Albany
Title: Moment Spaces on Hinfinity
Abstract: We will apply the geometry of moment spaces for functions
holomorphic on the unit disc to envelope all such functions
known at a finite number of points.

Yosef Rinott
 Hebrew University
Title: A glimpse into Sam Karlin's work in Total Positivity
Abstract: A kernel K(x,y) is totally positive if the associated
determinants of the matrices (K(x(i),y(j)) are all positive.
These determinants were given a probabilistic interpretation
by Karlin and McGregor which led to a characterization of Total
Positivity, and to numerous applications. Another characterization
is related to the Variation Diminishing Property: given a a
totally positive kernel K and function f, the the number of
sign changes of g(x) = \int f(y) K(x,y) q(dy) can not exceed
that of f. The Variation Diminishing Property and its applications
to diverse areas such as inequalities, approximation theory
and generalized convexity, probability and statistics were studied
extensively by Karlin.
In this talk I will discuss some of the history of these ideas
and some of Karlin's contributions to characterizations and
applications of Total Positivity in combinatorics, probability
and statistics.
Time permitting I will discuss notions of Multivariate Total
Positivity and their relation to statistical dependence, an
area
in which I had the honor of collaborating with Sam Karlin.

Larry Shepp
 Rutgers
Title: Karlin and Convexity
Abstract: In an earlier incarnation, Sam proved a more general
version of the nice result that for any measurable function
f on [0,1],
bounded between 0 and 1, there is another function g, taking
values only 0 and 1, and having the same first n moments as
f.
Kemperman proved the analogous result for the Radon transform
of any measurable function f = f(x,y) on the unit square: if
f is bounded between 0 and 1, there is a g = g(x,y) taking values
only 0 and 1, with the same line integral as f along every line
L in the plane as long as the slope of L lies in a finite set
of numbers. The proofs consider the convex set of all g's with
the same "moments" with g bounded between 0 and 1.
The extreme points of this convex set are shown to have only
values 0 and 1. I will discuss these issues and consider them
in the light of Muntz's and Lyapounov's theorem. Interesting
questions remain open.

David O.
Siegmund  Stanford
University
Title: Sam Karlin and Biomolecular Sequence Analysis
Abstract: I will review Sam Karlin's research in DNA/Amino Acid
sequence analysis, starting from his analysis of single sequences
and leading up to his contributions to the problem of local
pairwise alignments. Although there will be a brief discussion
of algorithms, emphasis will be on statistical analysis. Some
recent developments will also be discussed.
