相关论文: Intriguing symmetry in statistical structures of S…
This work explores structured matrix sequences arising in mean-field quantum spin systems. We express these sequences within the framework of generalized locally Toeplitz (GLT) $*$-algebras, leveraging the fact that each GLT matrix sequence…
In this review we discuss the relationship between random matrix theories and symmetric spaces. We show that the integration manifolds of random matrix theories, the eigenvalue distribution, and the Dyson and boundary indices characterizing…
In several recent papers new gene-detection algorithms were proposed for detecting protein-coding regions without requiring learning dataset of already known genes. The fact that unsupervised gene-detection is possible closely connected to…
We analyse a group of radio sources, a subset of the 200 mJy sample, all of which have core-jet radio structures measured with VLBI and have flat spectra stretching from the radio to the millimetre/sub-millimetre band. Thus the objects have…
The spectral symbols are useful tools to analyse the eigenvalue distribution when dealing with high dimensional linear systems. Given a matrix sequence with an asymptotic symbol, the last one depends only on the spectra of the individual…
The singular value and spectral distribution of Toeplitz matrix sequences with Lebesgue integrable generating functions is well studied. Early results were provided in the classical Szeg{\H{o}} theorem and the Avram-Parter theorem, in which…
Previous work done in collaboration with David Brink is reviewed in the light of the recent observation of new charmonium-like resonances which can be interpreted as tetraquarks. In the framework of a schematic quark model the spectrum of…
In graph signal processing, the graph adjacency matrix or the graph Laplacian commonly define the shift operator. The spectral decomposition of the shift operator plays an important role in that the eigenvalues represent frequencies and the…
Understanding the effects of the choice of the tree on the joint distribution of a tree-structured Markov random field (MRF) is crucial for fully exploiting the intelligibility of such probabilistic graphical models. Tools must be developed…
In the letter we give new symmetries for the isospectral and non-isospectral Ablowitz-Ladik hierarchies by means of the zero curvature representations of evolution equations related to the Ablowitz-Ladik spectral problem. Lie algebras…
Symplectic (respectively orthogonal) triple systems provide constructions of Lie algebras (resp. superalgebras). However, in characteristic 3, it is shown that this role can be interchanged and that Lie superalgebras (resp. algebras) can be…
Tools that effectively analyze and compare sequences are of great importance in various areas of applied computational research, especially in the framework of molecular biology. In the present paper, we introduce simple geometric criteria…
Two-dimensional linear spaces of symmetric matrices are classified by Segre symbols. After reviewing known facts from linear algebra and projective geometry, we address new questions motivated by algebraic statistics and optimization. We…
Neural network architectures have been augmented with differentiable stacks in order to introduce a bias toward learning hierarchy-sensitive regularities. It has, however, proven difficult to assess the degree to which such a bias is…
We present a robust analysis of the spectral fluctuations exhibited by the light meson spectrum. This analysis provides information about the degree of chaos in light mesons and may be useful to get some insight on the underlying…
The multi-frequency `Sedentary Survey' is a deep, statistically complete, radio flux limited sample comprising 150 BL Lacertae objects distinguished by their extremely high X-ray to radio flux ratio, ranging from five hundred to over five…
A detailed discussion of semiclassical trace formulae is presented and it is demonstrated how a regularized trace formula can be derived while dealing only with finite and convergent expressions. Furthermore, several applications of trace…
We propose a novel unsupervised approach for linking records across arbitrarily many files, while simultaneously detecting duplicate records within files. Our key innovation is to represent the pattern of links between records as a {\em…
This paper offers a new technique of incoherent scattering signal processing. The technique is based on the experimentally observed comb structure of the spectral power of separate realizations. The technique implies determining the…
The asymptotic behaviour of Linear Spectral Statistics (LSS) of the smoothed periodogram estimator of the spectral coherency matrix of a complex Gaussian high-dimensional time series $(\y_n)_{n \in \mathbb{Z}}$ with independent components…