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Conjugate Gradient Derived kernel Affine Projection Method for Post-distortion in Visible Light Communication Systems

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WIRELESS PERSONAL COMMUNICATIONS 2024年第1期135卷 183-200页

作者： Shen, Yujie Wang, Jieling Kang, Zihan Shen, Ba-Zhong Xidian Univ Sch Telecommun Engn Xian 710071 Shannxi Peoples R China

With the explosive growth in the demand of spectrum, conventional radio frequency systems are increasingly facing the challenge of catering to high-speed transmissions. Visible light communication (VLC) has been considered as a promising supplement technique, since it can provide efficient energy efficiency and unlimited bandwidth. However, the nonlinearity effect is one of the fundamental problems in the VLC systems, which usually brings distortion to the transmitted signal and deteriorates the system performance. Aiming at this problem, numerous post-distortion schemes are proposed, where the kernel methods over reproducing kernel hilbert spaces are identified to have successful applications. In this paper, we present a new post-distortion method with low computational cost, by utilizing the conjugate gradient (CG) based kernel affine projection algorithm (KAPA), where the objective parameters are updated adaptively along the conjugate direction. Simulation results show that the proposed CG-KAPA based post-distorter can efficiently mitigate nonlinear impairment in VLC systems, which can provide better bit error rate performance with fast convergence over the commonly-used gradient descent algorithms.

关键词： Visible light communications Nonlinear distortion kernel affine projection algorithm Conjugate gradient algorithm reproducing kernel hilbert spaces

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Quasi-radial operators on the Fock space and C*-algebras of entire functions

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LINEAR & MULTILINEAR ALGEBRA 2025年第7期73卷 1486-1507页

作者： Bais, Shubham R. Naidu, D. Venku A CI Homi Bhabha Natl Inst Inst Math Sci CIT Campus Chennai 600113 India IIT Hyderabad Dept Math Sangareddy India

In this article, we consider quasi-radial operators on the Fock space of holomorphic functions on C-n that are square integrable with respect to the Gaussian measure on C-n. We provide an integral representation for quasi-radial operators. As a consequence, we study several operator theoretic properties of these operators and the Toeplitz operators with quasi-radial defining symbols. In addition to this, we construct various examples of commutative C*-algebras of analytic functions on C-n each associated with a particular class of quasi-radial operators.

关键词： Fock space reproducing kernel hilbert spaces Toeplitz operator quasi-radial operator C*-algebra of entire functions von Neumann algebra

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Nearly invariant Brangesian subspaces

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CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES 2025年第1期68卷 318-337页

作者： Khan, Arshad Lata, Sneh Singh, Dinesh Shiv Nadar Inst Eminence Dept Math Greater Noida 201314 Uttar Pradesh India OP Jindal Global Univ Ctr Digital Sci Sonipat 131001 Haryana India

This article describes hilbert spaces contractively contained in certain reproducing kernel hilbert spaces of analytic functions on the open unit disc which are nearly invariant under division by an inner function. We extend Hitt's theorem on nearly invariant subspaces of the backward shift operator on H-2 ( D ) as well as its many generalizations to the setting of de Branges spaces.

关键词： de Branges spaces nearly invariant subspaces Hardy spaces multiplication operator reproducing kernel hilbert spaces

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J-contractive operator valued functions, vector valued de Branges spaces and functional models

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2025年第2期549卷

作者： Garg, Bharti Sarkar, Santanu Indian Inst Technol Ropar Dept Math Ropar 140001 India

The aim of this paper is to study the vector valued de Branges spaces, which are based onJcontractive operator valued analytic functions, and to explore their role in the functional models for simple, closed, densely defined, symmetric operators with infinite deficiency indices. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： J- contractive operator valued functions reproducing kernel hilbert spaces Vector valued de Branges spaces deficiency indices Symmetric operators with infinite

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Sobolev regularity of Gaussian random fields

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JOURNAL OF FUNCTIONAL ANALYSIS 2024年第3期286卷

作者： Henderson, Iain Inst Math Toulouse F-31077 Toulouse France Univ Toulouse UMR 5219 F-31077 Toulouse France CNRS INSA Toulouse France

In this article, we fully characterize the measurable Gaussian processes (U(x))(x is an element of D) whose sample paths lie in the Sobolev space of integer order W-m,W-p(D), m is an element of N-0,1 < p < +infinity, where D is an arbitrary open set of R-d. The result is phrased in terms of a form of Sobolev regularity of the covariance function on the diagonal. This is then linked to the existence of suitable Mercer or otherwise nuclear decompositions of the integral operators associated to the covariance function and its cross-derivatives. In the hilbert case p = 2, additional links are made w.r.t. the Mercer decompositions of the said integral operators, their trace and the imbedding of the RKHS in W-m,W-2(D). We provide simple examples and partially recover recent results pertaining to the Sobolev regularity of Gaussian processes. (c) 2023 Elsevier Inc. All rights reserved.

关键词： Gaussian processes Sobolev spaces Integral operators reproducing kernel hilbert spaces

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Dynamic Mode Decomposition of Control-Affine Nonlinear Systems Using Discrete Control Liouville Operators

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IEEE CONTROL SYSTEMS LETTERS 2024年 8卷 79-84页

作者： Morrison, Zachary Abudia, Moad Rosenfeld, Joel A. Kamalapurkar, Rushikesh Oklahoma State Univ Sch Mech & Aerosp Engn Stillwater OK 74074 USA Univ S Florida Dept Math & Stat Tampa FL 33620 USA

The representation of a nonlinear dynamical system as infinite-dimensional linear operator over a hilbert space of functions enables the study of the nonlinear system via pseudo-spectral analysis of the corresponding operator. In this letter, we develop a novel operator representation of discrete-time, control-affine nonlinear dynamical systems. We also demonstrate that this representation can be used to predict the behavior of the closed-loop system in response to a given feedback law. The representation is learned using recorded snapshots of the system state resulting from arbitrary, potentially open-loop control inputs. We thereby extend the predictive capabilities of dynamic mode decomposition to discrete-time nonlinear systems that are affine in control. We validate the method using two numerical experiments by predicting the response of a controlled Duffing oscillator to a known feedback law. The advantages of the developed method relative to existing techniques in the literature are also demonstrated.

关键词： kernel hilbert space Nonlinear dynamical systems Control systems Aerospace electronics Heuristic algorithms Symbols Dynamic mode decomposition with control composition operators reproducing kernel hilbert spaces nonlinear system ID

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The Matérn Model: A Journey Through Statistics, Numerical Analysis and Machine Learning

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STATISTICAL SCIENCE 2024年第3期39卷 469-492页

作者： Porcu, Emilio Bevilacqua, Moreno Schaback, Robert Oates, Chris J. Khalifa Univ Dept Math Abu Dhabi U Arab Emirates ADIA Lab Abu Dhabi U Arab Emirates Univ Adolfo Ibanez Dept Stat Santiago Chile Univ Gottingen Dept Math Gottingen Germany Newcastle Univ Sch Math Stat & Phys Newcastle Upon Tyne England

The Mat & eacute;rn model has been a cornerstone of spatial statistics for more than half a century. More recently, the Mat & eacute;rn model has been exploited in disciplines as diverse as numerical analysis, approximation theory, computational statistics, machine learning, and probability theory. In this article, we take a Mat & eacute;rn-based journey across these disciplines. First, we reflect on the importance of the Mat & eacute;rn model for estimation and prediction in spatial statistics, establishing also connections to other disciplines in which the Mat & eacute;rn model has been influential. Then, we position the Mat & eacute;rn model within the literature on big data and scalable computation: the SPDE approach, the Vecchia likelihood approximation, and recent applications in Bayesian computation are all discussed. Finally, we review recent devlopments, including flexible alternatives to the Mat & eacute;rn model, whose performance we compare in terms of estimation, prediction, screening effect, computation, and Sobolev regularity properties.

关键词： Approximation theory compact support covariance kernel kriging machine learning maximum likelihood reproducing kernel hilbert spaces spatial statistics Sobolev spaces

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A uniform kernel trick for high and infinite-dimensional two-sample problems

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JOURNAL OF MULTIVARIATE ANALYSIS 2024年 202卷

作者： Carcamo, Javier Cuevas, Antonio Rodriguez, Luis-Alberto Euskal Herriko Unibertsitatea Univ Pais Vasco Leioa Spain Univ Autonoma Madrid Madrid Spain UC3M UCM UAM Inst Ciencias Matemat ICMATCSIC Madrid Spain Georg August Univ Gottingen Gottingen Germany

We use a suitable version of the so-called "kernel trick" to devise two -sample tests, especially focussed on high -dimensional and functional data. Our proposal entails a simplification of the practical problem of selecting an appropriate kernel function. Specifically, we apply a uniform variant of the kernel trick which involves the supremum within a class of kernelbased distances. We obtain the asymptotic distribution of the test statistic under the null and alternative hypotheses. The proofs rely on empirical processes theory, combined with the delta method and Hadamard directional differentiability techniques, and functional Karhunen- Lo & egrave;ve-type expansions of the underlying processes. This methodology has some advantages over other standard approaches in the literature. We also give some experimental insight into the performance of our proposal compared to other kernel -based approaches (the original proposal by Borgwardt et al. (2006) and some variants based on splitting methods) as well as tests based on energy distances (Rizzo and Sz & eacute;kely, 2017).

关键词： Homogeneity test reproducing kernel hilbert spaces Supremum-like distances

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On the geometry of Stein variational gradient descent

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JOURNAL OF MACHINE LEARNING RESEARCH 2023年第1期24卷 1-39页

作者： Duncan, A. Nusken, N. Szpruch, L. Imperial Coll London Dept Math London SW7 2AZ England Alan Turing Inst London England Kingss Coll London Dept Math London WC2R 2LS England Univ Edinburgh Sch Math Edinburgh EH9 3JZ Scotland

Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely on iterated steepest descent steps with respect to a reproducing kernel hilbert space norm. This construction leads to interacting particle systems, the mean-field limit of which is a gradient flow on the space of probability distributions equipped with a certain geometrical structure. We leverage this viewpoint to shed some light on the convergence properties of the algorithm, in particular addressing the problem of choosing a suitable positive definite kernel function. Our analysis leads us to considering certain nondifferentiable kernels with adjusted tails. We demonstrate significant performance gains of these in various numerical experiments.

关键词： Bayesian inference gradient flows geometry of optimal transport Stein's method reproducing kernel hilbert spaces

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Randomness of Shapes and Statistical Inference on Shapes via the Smooth Euler Characteristic Transform

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2025年第549期120卷 498-510页

作者： Meng, Kun Wang, Jinyu Crawford, Lorin Eloyan, Ani Brown Univ Div Appl Math Providence RI 02912 USA Brown Univ Data Sci Inst Providence RI USA Brown Univ Sch Publ Hlth Dept Biostat Providence RI USA Microsoft Res New England Cambridge MA USA

In this article, we establish the mathematical foundations for modeling the randomness of shapes and conducting statistical inference on shapes using the smooth Euler characteristic transform. Based on these foundations, we propose two Chi-squared statistic-based algorithms for testing hypotheses on random shapes. Simulation studies are presented to validate our mathematical derivations and to compare our algorithms with state-of-the-art methods to demonstrate the utility of our proposed framework. As real applications, we analyze a dataset of mandibular molars from four genera of primates and show that our algorithms have the power to detect significant shape differences that recapitulate known morphological variation across suborders. Altogether, our discussions bridge the following fields: algebraic and computational topology, probability theory and stochastic processes, Sobolev spaces and functional analysis, analysis of variance for functional data, and geometric morphometrics. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

关键词： Functional data analysis Karhunen-Lo & egrave ve expansion o-minimal structures Persistence diagrams reproducing kernel hilbert spaces

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