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Turning probability into polynomials (Mark Huber, CMC)

Millikan 2099, Pomona College 610 N. College Ave., Claremont, CA, United States

Moment generating functions (Laplace transforms) are a means for transforming probability problems into problems involving polynomials.  Here I will concentrate on the binomial distribution, and use the mgf to link this distributions probabilities directly to the binomial theorem.  The mgf is also a key ingredient in Chernoff bounds, which give upper bounds on the tail […]

The Legacy of Rudolph Kalman (Andrew Stuart, Caltech)

Argue Auditorium, Pomona College 610 N. College Ave., Claremont, CA, United States

Abstract: In 1960 Rudolph Kalman published what is arguably the first paper to develop a systematic, principled approach to the use of data to improve the predictive capability of mathematical models. As our ability to gather data grows at an enormous rate,  the importance of this work continues to grow too. The lecture will describe this paper, and developments that […]

Crossing the Threshold: The Role of Demographic Stochasticity in the Evolution of Cooperation (Tom LoFaro, Gustavus Adolphus College)

Shanahan 3465, Harvey Mudd College 301 Platt Blvd., Claremont, CA, United States

When Charles Darwin began writing “On the Origin of Species” he knew that explaining cooperative behavior in the context of “survival of the fittest” was problematic.  In fact, this apparent contradiction puzzled ecologists for many years after.  In this talk we will discuss a mathematical model of the evolution of cooperation developed by Doebeli, Blarer, […]

Digital sequences for frequency hopping CDMA systems (Lenny Fukshansky, CMC)

Emmy Noether Room, Millikan 1021, Pomona College 610 N. College Ave., Claremont, California

Frequency hopping is a method of transmitting signals by rapidly switching between many frequency channels, following some sequence of frequencies known to the transmitter and the receiver. This technique is used in the CDMA (code division multiple access) systems, and has many civilian and military applications. For successful transmission minimizing signal interference, we want to use sets […]

Cayley digraphs of matrix rings over finite fields (Yesim Demiroglu, HMC)

Millikan 2099, Pomona College 610 N. College Ave., Claremont, CA, United States

In this talk we use the unit-graphs and the special unit-digraphs on matrix rings to show that every n x n nonzero matrix over F_q can be written as a sum of two SL_n-matrices when n>1. We compute the eigenvalues of these graphs in terms of Kloosterman sums and study their spectral properties; and prove […]

Coupled Mechanochemical Multiscale Model to Study the Growth Regulation and Morphogenesis during Tissue Development (Weitao Chen, UCR)

Argue Auditorium, Pomona College 610 N. College Ave., Claremont, CA, United States

Growth regulation and pattern formation are two main problems in developmental biol- ogy. How cells know when to stop growing at certain tissue size with specic shape is an important question in both developmental biology and regenerative medicine, and it is still an unsolved mystery in many systems. During the growth, tissues and organs always […]

Turing mechanism for homeostatic control of synaptic density during C. elegans growth (Heather Zinn Brooks, UCLA)

Emmy Noether Room, Millikan 1021, Pomona College 610 N. College Ave., Claremont, California

It has been observed that motor neuron synapses in the worm C. elegans are remarkably evenly spaced, even during growth and development. In this work, we propose a novel mechanism for Turing pattern formation that provides a possible explanation for the regular spacing of synapses along the ventral cord of C. elegans during development. The […]

A renormalization approach to existence of the blow-up solutions of the Navier-Stokes equations (Denis Gaidashev, Uppsala University, Sweden)

Emmy Noether Room, Millikan 1021, Pomona College 610 N. College Ave., Claremont, California

The Navier-Stokes existence and smoothness problem is one of the most important open problems in modern mathematics.   Ya. Sinai and D. Li have proposed a renormalization approach to constructing a counter-example to existence. In this approach, existence of  a blow-up solution (a solution whose energy becomes infinite in finite time) is equivalent to existence of fixed […]

Weil sums of binomials: properties and applications (Daniel Katz, CSUN)

Millikan 2099, Pomona College 610 N. College Ave., Claremont, CA, United States

We consider sums in which an additive character of a finite field F is applied to a binomial whose individual terms (monomials) become permutations of F when regarded as functions.  These Weil sums characterize the nonlinearity of power permutations of interest in cryptography.  They also tell us about the correlation of linear recursive sequences over finite fields that are used […]

Convolutional Dictionary Learning for Tomographic Reconstruction (Cristina Garcia-Cardona, LANL)

Argue Auditorium, Pomona College 610 N. College Ave., Claremont, CA, United States

Convolutional sparse representation is an efficient tool for computing sparse representations for entire signals in terms of sums of a set of convolutions with dictionary filters. Unlike representations that are based on overlapping image patches, the convolutional representation optimizes over the entire image, yielding representations that are very sparse both spatially and across the filters. […]