Related papers: Software realization of the complex spectra analys…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
In the series of our earlier papers on the subject, we proposed a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We developed…
In this paper, we first describe a matricial Newton-type algorithm designed to solve the multivariable spectrum approximation problem. We then prove its global convergence. Finally, we apply this approximation procedure to multivariate…
A new method is proposed for fitting non-relativistic binary-scattering data and for extracting the parameters of possible quantum resonances in the compound system that is formed during the collision. The method combines the well-known…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
Reconstruction of undersampled periodic signals of unknown period is an important signal processing operation. It is especially difficult operation when the sequences of samples are short and no information on the inter-sequence time…
We compute the spectral statistics of the sum H of two independent complex Wishart matrices, each of which is correlated with a different covariance matrix. Random matrix theory enjoys many applications including sums and products of random…
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…
We provide a multilevel approach for analysing performances of parallel algorithms. The main outcome of such approach is that the algorithm is described by using a set of operators which are related to each other according to the problem…
Recursive decoding techniques are considered for Reed-Muller (RM) codes of growing length $n$ and fixed order $r.$ An algorithm is designed that has complexity of order $n\log n$ and corrects most error patterns of weight up to…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
We consider the problem of super-resolving the line spectrum of a multisinusoidal signal from a finite number of samples, some of which may be completely corrupted. Measurements of this form can be modeled as an additive mixture of a…
The Schur decomposition of a square matrix $A$ is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following…
Approaches to automated grouping in singular spectrum analysis are considered. A new method for the identification of periodic components is proposed. The possibilities of extensions to multivariate time series and images are discussed.
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
We propose a linear algorithm for determining two function parameters by their linear combination. These functions must satisfy the first order differential equations with polynomial coefficients and our parameters are the coefficients of…
In this report, we present work towards a framework for modeling and checking behavior of spatially distributed component systems. Design goals of our framework are the ability to model spatial behavior in a component oriented, simple and…
In this paper, we define a Mathematical model of program structure. Mathematical model of program structure defined here provides unified mathematical treatment of program structure, which reveals that a program is a large and finite set of…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
Network alignment consists of finding a structure-preserving correspondence between the nodes of two correlated, but not necessarily identical, networks. This problem finds applications in a wide variety of fields, from the alignment of…