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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 ...
Performance bounds for linear stochastic control
Stochastic control Model predictive control Linear matrix inequality Convex optimization
2015/8/10
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...
Simple Bounds for Recovering Low-complexity Models
`1-norm minimization nuclear-norm minimization block-sparsity duality random matrices
2015/6/17
This note presents a unified analysis of the recovery of simple objects from random linear measurements. When the linear functionals are Gaussian, we show that an s-sparse vector in Rn can be efficien...
Lower bounds for finiteness of generalized local cohomology modules and their associated primes
Generalized local cohomology modules associatted prime Serre subcategories
2011/7/25
Abstract: Let $R$ be a commutative Noetherian ring with non-zero identity, $\fa$ an ideal of $R$, $M$ a finite $R$--module and $X$ an arbitrary $R$--module. In this paper, we study relations between f...
Bounds for coefficients of cusp forms and extremal lattices
coefficients of cusp forms extremal lattices
2010/12/31
A cusp form f(z) of weight k for SL2(Z) is determined uniquely by its first ℓ := dim Sk Fourier coefficients. We derive an explicit bound on the nth coefficient of f in terms of its first ℓ...
Improved linear programming decoding of LDPC codes and bounds on the minimum and fractional distance
Improved linear programming LDPC codes bounds minimum fractional distance
2010/12/31
We examine LDPC codes decoded using linear programming (LP). Four contributions to the LP framework are presented. First, a new method of tightening the LP relaxation,and thus improving the LP decoder...
Orlov spectra: bounds and gaps
Orlov spectra bounds gaps
2010/12/31
The Orlov spectrum is a new invariant of a triangulated category. It was intro-duced by D. Orlov building on work of A. Bondal-M. van den Bergh and R. Rouquier. The supremum of the Orlov spectrum of a...
Sub-Gaussian tail bounds for the width and height of conditioned Galton--Watson trees
Sub-Gaussian tail conditioned Galton--Watson trees
2010/11/17
We study the height and width of a Galton--Watson tree with offspring distribution B satisfying E(B)=1, 0 < Var(B) < infinity, conditioned on having exactly n nodes. Under this conditioning, we deriv...
Optimal error bounds for two-grid schemes applied to the Navier-Stokes equations
two-grid schemes the Navier-Stokes equations
2010/11/1
We consider two-grid mixed-finite element schemes for the spatial discretization of the incompressible Navier-Stokes equations. A standard mixed-finite element method is applied over the coarse grid ...
A pebbling move on a graph removes two pebbles at a vertex and adds one pebble at an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed.In this new move, one pebble...
Let M be a smooth closed Riemannian manifold and the Laplace operator. A function u is said to be an eigenfunction with eigenvalue if u = − u .
The interior transmission problem and bounds on transmission eigenvalues
interior transmission problem bounds transmission eigenvalues
2010/9/1
We study the interior transmission eigenvalue problem for signdefinite multiplicative perturbations of the Laplacian in a bounded domain. We show that all but finitely many complex transmission eigenv...
Explicit incidence bounds over general finite fields
Explicit incidence bounds general finite fields
2010/9/1
Let Fq be a finite field of order q = pk where p is prime. Let P and L be sets of points and lines respectively in Fq×Fq with |P| = |L| = n. We establish the incidence bound I(P,L)
n 3 2 − 1...
Rank Bounds for Design Matrices with Applications to Combinatorial Geometry and Locally Correctable Codes
Design Matrices Applications Combinatorial Geometry Locally Correctable Codes
2010/9/1
A (q, k, t)-design matrix is an m×n matrix whose pattern of zeros/non-zeros satisfies the
following design-like condition: each row has at most q non-zeros, each column has at least
k non-zeros and ...