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 […]
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 […]
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 […]
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 […]
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 […]
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 […]
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 […]
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 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 […]
Joint work with Larry Shepp & Philip Ernst In this paper we develop a mathematical model to address an ongoing politico-economic debate between Democrats and Republicans. Democrats in the US say that government spending can be used to “grease the wheels’ of the economy, create wealth, and increase employment; the Republicans say that government spending […]
