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We propose a test for testing the Kronecker product structure of a factor loading matrix implied by a tensor factor model with Tucker decomposition in the common component. Through defining a Kronecker product structure set, we define if a…
This paper deals with the problem of classifying signals. The new method for building so called local classifiers and local features is presented. The method is a combination of the lifting scheme and the support vector machines. Its main…
Independent component analysis (ICA) has become a standard data analysis technique applied to an array of problems in signal processing and machine learning. This tutorial provides an introduction to ICA based on linear algebra formulating…
Graded rings provide a natural algebraic framework for encoding symmetry via decompositions into homogeneous components indexed by a group, together with multiplication rules reflecting the group operation. Among graded rings, strongly…
Controllability and observability Gramians, along with their inverses, are widely used to solve various problems in control theory. This paper proposes spectral decompositions of the controllability Gramian and its inverse based on system…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…
Periodic multilayers of various periods were prepared according to an algorithm proposed by the authors. The reflectivity properties of these systems were investigated using neutron reflectometry.The obtained experimental results were…
Multi-dimensional magnetic resonance spectroscopy is an important tool for studying molecular structures, interactions and dynamics in bio-engineering. The data acquisition time, however, is relatively long and non-uniform sampling can be…
Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve…
A phenomenological approach is presented that allows one to model, and thereby interpret, photoemission spectra of strongly correlated electron systems. A simple analytical formula for the self-energy is proposed. This self-energy describes…
We propose a universal decomposition of unitary maps over a tensorial power of C^2, introducing the key concept of "phase maps", and investigate how this decomposition can be used to implement unitary maps directly in the measurement-based…
Doppler reflectometry is considered in slab plasma model in the frameworks of analytical theory. The diagnostics locality is analyzed for both regimes: linear and nonlinear in turbulence amplitude. The toroidal antenna focusing of probing…
The use of machine learning algorithms is an attractive way to produce very fast detector simulations for scattering reactions that can otherwise be computationally expensive. Here we develop a factorised approach where we deal with each…
We describe a novel tool for the quantum characterization of optical devices. The experimental setup involves a stable reference state that undergoes an unknown quantum transformation and is then revealed by balanced homodyne detection.…
Multivariate polynomials arise in many different disciplines. Representing such a polynomial as a vector of univariate polynomials can offer useful insight, as well as more intuitive understanding. For this, techniques based on tensor…
This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered…
In frameworks of the phenomenological approach we analyze of the phase diagram of mixed compounds. We obtain space groups of symmetry of the real structures as result of phase transition from close-packed degenerate structure. The theory of…
We investigate the structure of join tensors, which may be regarded as the multivariable extension of lattice-theoretic join matrices. Explicit formulae for a polyadic decomposition (i.e., a linear combination of rank-1 tensors) and a…
Inspired by factorized scattering from delta-type impurities in (1+1)-dimensional space-time, we propose and analyse a generalization of the Zamolodchikov-Faddeev algebra. Distinguished elements of the new algebra, called reflection and…
We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings; that is, we study the number of ways a permutation can be decomposed into a product of a given number of 2-cycles, 3-cycles, etc.…