Discussion

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

6:00

Toasts: Manny Karlin, Yosef Rinott, Larry Shepp

9:30-10:15

10:20-10:45

10:45-11:00

Discussion

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, non-coding 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 birth-and-dearth processes to give a full analysis of the so-called 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 H-infinity
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.