Related papers: Complex Equiangular Cyclic Frames and Erasures
This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding…
An analysis of the characteristic function of Gaussian quadratic forms is presented in [1] to study the performance of multichannel communication systems. This technical report reviews this analysis, obtaining alternative expressions to…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
In this paper we describe some new algebraic features of the Gram matrices of complex Equiangular Tight Frames (ETF). This lead on the one hand to the nonexistence of several low dimensional complex ETFs; and on the other hand to the full…
We propose a new approach to the problem of recovering signal from frame coefficients with erasures. Such problems arise naturally from applications where some of the coefficients could be corrupted or erased during the data transmission.…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
A number of new terminating series involving $\sin(n^2/k)$ and $\cos(n^2/k)$ are presented and connected to Gauss quadratic sums. Several new closed forms of generic Gauss quadratic sums are obtained and previously known results are…
Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra of some composed ensembles and demonstrate…
We study spanning properties of a family of functions translated along simple model sets. We characterize tight frame and dual frame generators for such irregular translates and we apply the results to Gabor systems. We use the connection…
In this paper we study the problem of recovering a signal from frame coefficients with erasures. Suppose that erased coefficients are indexed by a finite set $E$. Starting from a frame $(x_n)_{n=1}^\infty$ and its arbitrary dual frame, we…
In the paper Optimal Dual Frames for Probabilistic Erasures, the authors have given conditions under which the canonical dual is claimed to be the unique probability optimal dual for 1-erasure reconstruction. In this paper, we demonstrate…
We prove an instance of the cyclic sieving phenomenon, occurring in the context of noncrossing parititions for well-generated complex reflection groups.
Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…
Complex fission phenomena are studied in a unified way. Very general reflection asymmetrical equilibrium (saddle point) nuclear shapes are obtained by solving an integro-differential equation without being necessary to specify a certain…
We study several interesting examples of Biangular Tight Frames (BTFs) - basis-like sets of unit vectors admitting exactly two distinct frame angles (ie, pairwise absolute inner products) - and examine their relationships with Equiangular…
The most efficient MC weights for the calculation of physical, canonical expectation values are not necessarily those of the canonical ensemble. The use of suitably generalized ensembles can lead to a much faster convergence of the…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
We prove that the generalised non-crossing partitions associated to well-generated complex reflection groups of exceptional type obey two different cyclic sieving phenomena, as conjectured by Armstrong, respectively by Bessis and Reiner.…
Equiangular Algorithm generates a set of equiangular normalized vectors with given angle {\theta} using a set of linearly independence vectors in a real inner product space, which span the same subspaces. The outcome of EA on column vectors…
Two-uniform frames and their use for the coding of vectors are the main subject of this paper. These frames are known to be optimal for handling up to two erasures, in the sense that they minimize the largest possible error when up to two…