Related papers: Asymptotic optimality of scalar Gersho quantizers
This paper studies the asymptotic distribution of a constrained lasso-type estimator for denoising signals defined on the nodes of a graph, where the underlying structure encodes relationships between variables. We show that, under suitable…
This paper is concerned with scalar quantization of transform coefficients in an audio codec. The generalized Gaussian distribution (GGD) is used as an approximation of one-dimensional probability density function for transform coefficients…
Asymptotic expansions are derived for Gegenbauer (ultraspherical) polynomials for large order $n$ that are uniformly valid for unbounded complex values of the argument $z$, including the real interval $0 \leq z \leq 1$ in which the zeros in…
In this paper we extend the works \cite{gegeng2,XLZD} further in two directions and compute the weight distribution of these cyclic codes under more relaxed conditions. It is interesting to note that many cyclic codes in the family are…
In this paper we argue that the well-known maximal extensions of the Kerr and Kerr-Newman spacetimes characterized by a specific gluing (on disks) of two asymptotically flat regions with ADM masses of opposite signs are physically…
The statistical analysis of Randomized Numerical Linear Algebra (RandNLA) algorithms within the past few years has mostly focused on their performance as point estimators. However, this is insufficient for conducting statistical inference,…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
The asymptotic conformal Yano--Killing tensor proposed in J. Jezierski, On the relation between metric and spin-2 formulation of linearized Einstein theory [GRG, in print (1994)] is analyzed for Schwarzschild metric and tensor equations…
Bosonic encoding of quantum information into harmonic oscillators is a hardware efficient approach to battle noise. In this regard, oscillator-to-oscillator codes not only provide an additional opportunity in bosonic encoding, but also…
Gradient Symbolic Computation is proposed as a means of solving discrete global optimization problems using a neurally plausible continuous stochastic dynamical system. Gradient symbolic dynamics involves two free parameters that must be…
We study the asymptotic behavior of piecewise constant least squares regression estimates, when the number of partitions of the estimate is penalized. We show that the estimator is consistent in the relevant metric if the signal is in…
When is optimal estimation linear? It is well known that, when a Gaussian source is contaminated with Gaussian noise, a linear estimator minimizes the mean square estimation error. This paper analyzes, more generally, the conditions for…
Questions concerning quantitative and asymptotic properties of the elliptic measure corresponding to a uniformly elliptic divergence form operator have been the focus of recent studies. In this setting we show that the elliptic measure of…
We construct a semiparametric estimator in case-control studies where the gene and the environment are assumed to be independent. A discrete or continuous parametric distribution of the genes is assumed in the model. A discrete distribution…
We give a survey of the two remarkable analytical problems of quantum information theory. The main part is a detailed report of the recent (partial) solution of the quantum Gaussian optimizers problem which establishes an optimal property…
We review and elaborate on recent work of Chang and Rabinowitz on scaling asymptotics of Poisson and Szeg\"{o} kernels on Grauert tubes, providing additional results that may be useful in applications. In particular, focusing on the…
We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of…
We obtain non asymptotic bounds for the Monte Carlo algorithm associated to the Euler discretization of some diffusion processes. The key tool is the Gaussian concentration satisfied by the density of the discretization scheme. This…
Bell inequalities are central tools for studying nonlocal correlations and their applications in quantum information processing. Identifying inequalities for many particles or measurements is, however, difficult due to the computational…
We prove that the q-Schur algebras of finite type introduced in [LW22] are cellular in the sense of Graham and Lehrer, which is a generalization of Geck's theorem on the cellularity of Hecke algebras of finite type. Moreover, we study…