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This paper gives a precise characterization of the fundamental limits of adaptive sensing for diverse estimation and testing problems concerning sparse signals. We consider in particular the setting i...
This paper deals with the task of finding certified lower bounds for the performance of Analog to Digital Converters (ADCs). A general ADC is modeled as a causal, discrete-time dynamical system with o...
This article considers the problem of \min_{\xi}\vec{Pr}(\vert \xi^Tx\vert\leq \alpha)\quad s.t.\quad \Vert\xi\Vert_2=1. We first concentrate on the case that x_i,i=1,\cdots,n are binary random variab...
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...
Abstract: The classical Cauchy-Davenport theorem implies the lower bound n+1 for the number of distinct subsums that can be formed from a sequence of n elements of the cyclic group Z_p (when p is prim...
Abstract: We use the Dong-Sogge-Zelditch formula to obtain a lower bound for the volume of the nodal sets of eigenfunctions. Our result improves the recent results of Sogge-Zelditch and in dimensions ...
The determinantal complexity of a polynomial f (x1, x2, . . . , xn) is the minimum m such that f = detm(L(x1, x2, . . . , xn)), where L(x1, x2, . . . , xn) is a matrix whose entries are affine forms i...
We prove some improved estimates for the Ginzburg-Landau energy (with or without magnetic field) in two dimensions, relating the asymptotic energy of an arbitrary configuration to its vortices and th...
Let N' be the nodal hypersurface of a -eigenfunction ' of eigenvalue 2on a smooth Riemannian manifold. We prove that Hn−1(N') ≥ C7 4− 3n 4 on the surface measure of its nodal set. Th...
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 .
This paper is a corrigendum on a paper published in an earlier volume of JIPAM, 'Lower Bounds for the Infimum of the Spectrum of the Schrodinger Operator in and the Sobolev Inequalities' published in...
Second order lower bounds for the entropy function expressed in terms of the index of coincidence are derived. Equivalently, these bounds involve entropy and Rényi entropy of order 2. The constants fo...
Lower Bounds for the Infimum of the Spectrum of the Schrödinger Operator in $\mathbb{R}^n$ and the Sobolev Inequalities.
Correlation coefficient, Bessis-Moussa-Villani conjecture, Robust portfolio.

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