Related papers: Character analysis using Fourier series
This paper contains an exposition of the theory of character sheaves for reductive groups and some attempts to extend it to other cases: unipotent groups, reductive groups modulo the unipotent radical of a parabolic.
The convergence of DP Fourier series which are neither strongly convergent nor strongly divergent is discussed in terms of the Taylor series of the corresponding inner analytic functions. These are the cases in which the maximum disk of…
In this investigation of character tables of finite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy classes. For the symmetric groups we find unexpected properties of characters on…
A characterization of the general linear equation in standard form admitting a maximal symmetry algebra is obtained in terms of a simple set of conditions relating the coefficients of the equation. As a consequence, it is shown that in its…
A fast new algorithm is used compute the zeros of the quadratic character L-functions for all negative fundamental discriminants with absolute value 10^12<d<10^12+10^7. These are compared to the 1-level density, including various lower…
Handwritten character recognition (HCR) is a challenging problem for machine learning researchers. Unlike printed text data, handwritten character datasets have more variation due to human-introduced bias. With numerous unique character…
In this survey one discusses the notion of the Poincar\'e series of multi-index filtrations, an alternative approach to the definition, a method of computation of the Poincar\'e series based on the notion of integration with respect to the…
The paper explores the possibility for summing Fourier series nonlinearly via the Pythagorean harmonic mean. It reports on new results for this summability with introduction of new concepts like the smoothing operator and semi-harmonic…
Statistics has moved beyond the frequentist-Bayesian controversies of the past. Where does this leave our ability to interpret results? I suggest that a philosophy compatible with statistical practice, labeled here statistical pragmatism,…
The study of register in computational language research has historically been divided into register analysis, seeking to determine the registerial character of a text or corpus, and register synthesis, seeking to generate a text in a…
A physical data (such as astrophysical, geophysical, meteorological etc.) may appear as an output of an experiment or it may come out as a signal from a dynamical system or it may contain some sociological, economic or biological…
The behavior of objects associated with general extended affine Lie algebras is typically distinct from their counterparts in affine Lie algebras. Our research focuses on studying characters and Cartan automorphisms, which appear in the…
The research of attribute characters in information system which contains core, necessary, unnecessary is a basic and important issue in attribute reduct. Many methods for the judgement of attribute characters are based on the relationship…
The field of natural language processing has seen impressive progress in recent years, with neural network models replacing many of the traditional systems. A plethora of new models have been proposed, many of which are thought to be opaque…
Recognition of Off-line Chinese characters is still a challenging problem, especially in historical documents, not only in the number of classes extremely large in comparison to contemporary image retrieval methods, but also new unseen…
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…
While research on explainable AI (XAI) is booming and explanation techniques have proven promising in many application domains, standardised human-centred evaluation procedures are still missing. In addition, current evaluation procedures…
Character language models have access to surface morphological patterns, but it is not clear whether or how they learn abstract morphological regularities. We instrument a character language model with several probes, finding that it can…
We prove an exponential integral estimate for the quadratic partial sums of multiple Fourier series on large sets that implies some new properties of Fourier series.
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…