Related papers: Software realization of the complex spectra analys…
The object of this work is to design an adequate regularization for the problem of recovering missing Fourier coefficients, particularly in some non standard situations were low frequency coefficients are lost. In the framework of non-local…
Spectroscopy is an indispensable tool in understanding the structures and dynamics of molecular systems. However computational modelling of spectroscopy is challenging due to the exponential scaling of computational complexity with system…
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral…
Spectral fitting of X-ray data usually involves minimizing statistics like the chi-square and the Cash statistic. Here we discuss their limitations and introduce two measures based on the cumulative sum (CuSum) of model residuals to…
Two iterative techniques are described for decomposing a long-slit spectrum into the individual spectra of the point sources along the slit and the spectrum of the underlying background. One technique imposes the strong constraint that the…
This paper presents a regularized recursive identification algorithm with simultaneous on-line estimation of both the model parameters and the algorithms hyperparameters. A new kernel is proposed to facilitate the algorithm development. The…
We implement an algorithm which is aimed to reduce the dimensions of the Hilbert space of quantum many-body systems by means of a renormalization procedure. We test the role and importance of different representations on the reduction…
This work compares the performance of software implementations of different Gabidulin decoders. The parameter sets used within the comparison stem from their applications in recently proposed cryptographic schemes. The complexity analysis…
We consider the uniqueness of solution (i.e., nonsingularity) of systems of $r$ generalized Sylvester and $\star$-Sylvester equations with $n\times n$ coefficients. After several reductions, we show that it is sufficient to analyze periodic…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are…
We explore the sensitivity of several core-level spectroscopic methods to the underlying atomistic structure by using the water molecule as our test system. We first define a metric that measures the magnitude of spectral change as a…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
Cumulant mapping employs a statistical reconstruction of the whole by sampling its parts. The theory developed in this work formalises and extends ad hoc methods of `multi-fold' or `multi-dimensional' covariance mapping. Explicit formulae…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical ``black box'' function drawn from some set of such black box functions, we investigate a more general quantum query model…
This paper studies two spectrum estimation methods for the case that the samples are obtained at a rate lower than the Nyquist rate. The first method is the correlogram method for undersampled data. The algorithm partitions the spectrum…
This paper describes a very efficient algorithm for image signal extrapolation. It can be used for various applications in image and video communication, e.g. the concealment of data corrupted by transmission errors or prediction in video…
Two new concepts, generic regular decomposition and regular-decomposition-unstable (RDU) variety for generic zero-dimensional systems, are introduced in this paper and an algorithm is proposed for computing a generic regular decomposition…