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Consider an elliptic curve E without complex multiplication defined over the rationals.The absolute Galois group of Q acts on the group of torsion points of E, and this action can be expressed in term...
For a non-CM elliptic curve E/Q, Lang and Trotter made very deep conjectures concerning the number of primes p ≤ x for which ap(E) is a fixed integer (and for which the Frobeniusfield at p is a fixed ...
Let f be a Hecke–Maass cusp form of eigenvalue λ and square-free level N. Normalize the hyperbolic measure such that vol(Y0(N)) = 1 and the form f such that kfk2 = 1. It is shown that kfk1 ≪1...
A new method for analyzing low density parity check (LDPC) codes and low density generator matrix (LDGM) codes under bit maximum a posteriori probability (MAP) decoding is introduced. The method is ba...
For1 dimension reduction in the l1 norm, the method of Cauchy random projections multiplies the original data matrix A ∈ Rn×D with a random matrix R ∈ RD×k (k  D) whose entries are i.i.d. samples of ...
In this paper we study multi-input multi-output (MIMO) linear time-invariant (LTI) control systems. We show that some well known constraints on the performance of single-input single-output (SISO) lin...
Robust stability of a linear multivariable system, in the sense of robustness under multiplicative transfer function perturbation, is necessarily preserved under sufficiently small perturbations in th...
We describe an interior point algorithm for computing the upper bound for the structured singular value described in the paper by Fan, Tits and Doyle, IEEE Trans AC, Jan. 1991. We demonstrate the perf...
The second smallest eigenvalue of the Laplacian matrix L of a graph is called its algebraic connectivity. We describe a method for obtaining an upper bound on the algebraic connectivity of a family of...
A sharp lower bound on the probability of a set defined by quadratic inequalities, given the first two moments of the distribution, can be efficiently computed using convex optimization. This result g...
We develop computational bounds on performance for causal state feedback stochastic control with linear dynamics, arbitrary noise distribution, and arbitrary input constraint set. This can be very use...
In a recent paper, the authors showed how to compute performance bounds for infinite horizon stochastic control problems with linear system dynamics and arbitrary constraints, objective, and noise dis...
We consider a reaction-diffusion-advection equation with a nonlinearity of the KPP type in a cellular flow. We show that the minimal pulsating traveling front speed c∗(A) in a flow ofamplitude A...
We develop bounds for the second largest eigenvalue and spectral gap of a reversible Markov chain. The bounds depend on geometric quantities such as the maximum degree, diameter and covering numbe...
We consider the Fisher-KPP equation with a non-local interaction term. We establish a condition on the interaction that allows for existence of non-constant periodic solutions,and prove uniform upper ...

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