Готові списки джерел за темами / Convolution inequality

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Добірка наукової літератури з теми "Convolution inequality"

Автор: Grafiati

Опубліковано: 8 березня 2025

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Статті в журналах з теми "Convolution inequality"

Pycia, M. "A convolution inequality." Aequationes Mathematicae 57, no. 2-3 (May 1, 1999): 185–200. http://dx.doi.org/10.1007/s000100050076.

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Latała, R., and J. O. Wojtaszczyk. "On the infimum convolution inequality." Studia Mathematica 189, no. 2 (2008): 147–87. http://dx.doi.org/10.4064/sm189-2-5.

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Beckner, William. "Pitt's inequality with sharp convolution estimates." Proceedings of the American Mathematical Society 136, no. 05 (November 30, 2007): 1871–86. http://dx.doi.org/10.1090/s0002-9939-07-09216-7.

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Walter, W., and V. Weckesser. "An integral inequality of convolution type." Aequationes Mathematicae 46, no. 1-2 (August 1993): 200. http://dx.doi.org/10.1007/bf01834008.

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Cwikel, Michael, and Ronald Kerman. "On a convolution inequality of Saitoh." Proceedings of the American Mathematical Society 124, no. 3 (1996): 773–77. http://dx.doi.org/10.1090/s0002-9939-96-03068-7.

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Zhao, Junjian, Wei-Shih Du, and Yasong Chen. "New Generalizations and Results in Shift-Invariant Subspaces of Mixed-Norm Lebesgue Spaces ${L_{\vec{p}}(\mathbb{R}^d)}$." Mathematics 9, no. 3 (January 25, 2021): 227. http://dx.doi.org/10.3390/math9030227.

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In this paper, we establish new generalizations and results in shift-invariant subspaces of mixed-norm Lebesgue spaces Lp→(Rd). We obtain a mixed-norm Hölder inequality, a mixed-norm Minkowski inequality, a mixed-norm convolution inequality, a convolution-Hölder type inequality and a stability theorem to mixed-norm case in the setting of shift-invariant subspace of Lp→(Rd). Our new results unify and refine the existing results in the literature.

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Oberlin, Daniel M. "A Multilinear Young's Inequality." Canadian Mathematical Bulletin 31, no. 3 (September 1, 1988): 380–84. http://dx.doi.org/10.4153/cmb-1988-054-0.

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Borwein, David, та Werner Kratz. "Weighted Convolution Operators on ℓp". Canadian Mathematical Bulletin 48, № 2 (1 червня 2005): 175–79. http://dx.doi.org/10.4153/cmb-2005-015-x.

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Christ, Michael, and Qingying Xue. "Smoothness of extremizers of a convolution inequality." Journal de Mathématiques Pures et Appliquées 97, no. 2 (February 2012): 120–41. http://dx.doi.org/10.1016/j.matpur.2011.09.002.

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Román-Flores, H., A. Flores-Franulič, and Y. Chalco-Cano. "A convolution type inequality for fuzzy integrals." Applied Mathematics and Computation 195, no. 1 (January 2008): 94–99. http://dx.doi.org/10.1016/j.amc.2007.04.072.

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Більше джерел

Дисертації з теми "Convolution inequality"

Křepela, Martin. "Forever Young : Convolution Inequalities in Weighted Lorentz-type Spaces." Licentiate thesis, Karlstads universitet, Institutionen för matematik och datavetenskap, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-31754.

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This thesis is devoted to an investigation of boundedness of a general convolution operator between certain weighted Lorentz-type spaces with the aim of proving analogues of the Young convolution inequality for these spaces. Necessary and sufficient conditions on the kernel function are given, for which the convolution operator with the fixed kernel is bounded between a certain domain space and the weighted Lorentz space of type Gamma. The considered domain spaces are the weighted Lorentz-type spaces defined in terms of the nondecreasing rearrangement of a function, the maximal function or the difference of these two quantities. In each case of the domain space, the corresponding Young-type convolution inequality is proved and the optimality of involved rearrangement-invariant spaces in shown. Furthermore, covering of the previously existing results is also discussed and some properties of the new rearrangement-invariant function spaces obtained during the process are studied.

Paper II was a manuscript at the time of the defense.

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Shu, Yan. "Opérateurs d’inf-convolution et inégalités de transport sur les graphes." Thesis, Paris 10, 2016. http://www.theses.fr/2016PA100096/document.

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Dans cette thèse, nous nous intéressons à différents opérateurs d'inf-convolutions et à leurs applications à une classe d'inégalités de transport générales, plus spécifiquement sur les graphes. Notre objet de recherche s'inscrit donc dans les théories du transport de mesure et de l'analyse fonctionnelle. En introduisant une notion de gradient adapté au cadre discret (et plus généralement à tout espace métrique dont les boules sont compactes), nous prouvons que certains opérateurs d'inf-convolution sont solutions d'une inéquation d'Hamilton Jacobi sur les graphes. Ce résultat nous permet d'étendre au cadre discret un théorème classique de Bobkov, Gentil et Ledoux. Plus précisément nous montrons que des inégalités de transport faible (adaptées au cadre discret) sont équivalentes, sur un graphe, à l'hypercontractivité des opérateurs d'inf-convolutions. On en déduit plusieurs résultats concernant différentes inégalités fonctionnelles, dont celle de Sobolev logarithmique et de transport faible. Nous étudions par ailleurs les propriétés générales de différents opérateurs d'inf-convolutions, incluant le précédent, mais aussi un opérateur relié à un modèle issu de la physique (et au phénomène de grande déviation), toujours sur les graphes (dérivabilités, convexité, points extremum etc.). Dans un deuxième temps, nous nous intéressons aux liens entre différentes notions de courbure de Ricci sur les graphes -- proposées récemment par plusieurs auteurs -- et les inégalités fonctionnelles de type transport-entropie, ou transport-information associées à une chaîne de Markov. Nous obtenons également une borne supérieure sur le diamètre d'un graphe dont la courbure, en un certain sens, est minorée, un résultat à la Bonnet-Myers. Enfin, en nous restreignant au cas de la dimension 1, sur la droite réelle, nous obtenons une caractérisation d'une inégalité de transport faible et de l'inégalité de Sobolev logarithmique restreinte aux fonctions convexes. Ces résultats utilisent des propriétés géométriques liés à l'ordre convexe
In this thesis, we interest in different inf-convolution operators and their applications to a class of general transportation inequalities, more specifically in the graphs. Therefore, our research topic fits in the theories of transportation and functional analysis. By introducing a gradient notion adapting to a discrete space (more generally to all space in which all closed balls are compact), we prove that some inf-convolution operators are solutions of a Hamilton-Jacobi's inequation. This result allows us to extend a classical theorem from Bobkov, Gentil and Ledoux. More precisely, we prove that, in a graph, some weak transport inequalities are equivalent to the hypercontractivity of inf-convolution operators. Thanks to this result, we deduce some properties concerning different functional inequalities, including Log-Sobolev inequalities and weak-transport inequalities. Besides, we study some general properties (differentiability, convexity, extreme points etc.) of different inf-convolution operators, including the one before, but also an operator related to a physical model (and to a large deviation phenomenon). We stay always in a graph. Secondly, we interest in connections between different notions of discrete Ricci curvature on the graphs which are proposed by several authors in the recent years, and functional inequalities of type transport-entropy, or transport-information related to a Markov chain. We also obtain an extension of Bonnet-Myers' result: an upper bound on the diameter of a graph of which the curvature is floored in some ways. Finally, restricting in the real line, we obtains a characterisation of a weak transport inequality and a log-Sobolev inequality restricted to convex functions. These results are from the geometrical properties related to the convex ordering

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Gozé, Vincent. "Une version effective du théorème des nombres premiers de Wen Chao Lu." Electronic Thesis or Diss., Littoral, 2024. http://www.theses.fr/2024DUNK0725.

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Le théorème des nombres premiers, démontré pour la première fois en 1896 à l'aide de l'analyse complexe, donne le terme principal pour la répartition asymptotique des nombres premiers. Ce n'est qu'en 1949 que la première démonstration dite "élémentaire" fut publiée : elle repose uniquement sur l'analyse réelle. En 1999, Wen Chao Lu a obtenu de manière élémentaire un terme d'erreur dans le théorème des nombres premiers très proche de celui fourni par la région sans zéro de la fonction zêta de Riemann donnée par La Vallée Poussin à la fin du XIXe siècle. Dans cette thèse, nous rendons explicite le résultat de Lu afin d'une part, de donner le meilleur terme d'erreur obtenu par méthodes élémentaires à ce jour, et d'autre part, de déterminer les limites de sa méthode
The prime number theorem, first proved in 1896 using complex analysis, gives the main term for the asymptotic distribution of prime numbers. It was not until 1949 that the first so-called "elementary" proof was published: it rests strictly on real analysis.In 1999, Wen Chao Lu obtained by an elementary method an error term in the prime number theorem very close to the one provided by the zero-free region of the Riemann zeta function given by La Vallée Poussin at the end of the 19th century. In this thesis, we make Lu's result explicit in order, firstly, to give the best error term obtained by elementary methods so far, and secondly, to explore the limits of his method

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Křepela, Martin. "The Weighted Space Odyssey." Doctoral thesis, Karlstads universitet, Institutionen för matematik och datavetenskap, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-41944.

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The common topic of this thesis is boundedness of integral and supremal operators between weighted function spaces. The first type of results are characterizations of boundedness of a convolution-type operator between general weighted Lorentz spaces. Weighted Young-type convolution inequalities are obtained and an optimality property of involved domain spaces is proved. Additional provided information includes an overview of basic properties of some new function spaces appearing in the proven inequalities. In the next part, product-based bilinear and multilinear Hardy-type operators are investigated. It is characterized when a bilinear Hardy operator inequality holds either for all nonnegative or all nonnegative and nonincreasing functions on the real semiaxis. The proof technique is based on a reduction of the bilinear problems to linear ones to which known weighted inequalities are applicable. Further objects of study are iterated supremal and integral Hardy operators, a basic Hardy operator with a kernel and applications of these to more complicated weighted problems and embeddings of generalized Lorentz spaces. Several open problems related to missing cases of parameters are solved, thus completing the theory of the involved fundamental Hardy-type operators.
Operators acting on function spaces are classical subjects of study in functional analysis. This thesis contributes to the research on this topic, focusing particularly on integral and supremal operators and weighted function spaces. Proving boundedness conditions of a convolution-type operator between weighted Lorentz spaces is the first type of a problem investigated here. The results have a form of weighted Young-type convolution inequalities, addressing also optimality properties of involved domain spaces. In addition to that, the outcome includes an overview of basic properties of some new function spaces appearing in the proven inequalities. Product-based bilinear and multilinear Hardy-type operators are another matter of focus. It is characterized when a bilinear Hardy operator inequality holds either for all nonnegative or all nonnegative and nonincreasing functions on the real semiaxis. The proof technique is based on a reduction of the bilinear problems to linear ones to which known weighted inequalities are applicable. The last part of the presented work concerns iterated supremal and integral Hardy operators, a basic Hardy operator with a kernel and applications of these to more complicated weighted problems and embeddings of generalized Lorentz spaces. Several open problems related to missing cases of parameters are solved, completing the theory of the involved fundamental Hardy-type operators.

Artikel 9 publicerad i avhandlingen som manuskript med samma titel.

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Strzelecki, Michał. "Functional and transport inequalities and their applications to concentration of measure." Doctoral thesis, 2019. https://depotuw.ceon.pl/handle/item/3539.

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Niniejsza rozprawa poświęcona jest nierównościom funkcyjnym i transportowym związanym ze zjawiskiem koncentracji miary. W pierwszej części zajmujemy się koncentracją dla funkcji gładkich. Dowodzimy, że miara probabilistyczna, która spełnia pochodzącą od Latały i Oleszkiewicza nierówność typu Becknera, spełnia także odpowiednią zmodyfikowaną nierówność logarytmiczną Sobolewa. Jako wniosek dostajemy wzmocnioną dwupoziomową koncentrację dla produktów takich miar. Druga część jest obszerniejsza i dotyczy koncentracji dla funkcji wypukłych. Naszym głównym narzędziem technicznym jest teoria słabych nierówności transportowych wprowadzonych niedawno przez Gozlana, Roberta, Samsona i Tetaliego. Najpierw przedstawiamy charakteryzację miar probabilistycznych, które spełniają wypukłą nierówność logarytmiczną Sobolewa na prostej. Pozwala nam to wyprowadzić oszacowania koncentracyjne dla górnego i dolnego ogona lipszycowskich funkcji wypukłych (wcześniej znane były jedynie oszacowania dla górnego ogona). Następnie dowodzimy, że miara probabilistyczna na $\mathbb{R}^n$, spełniająca wypukłą nierówność Poincar\'ego, spełnia także pochodzącą od Bobkova i Ledoux zmodyfikowaną nierówność logarytmiczną Sobolewa. Wzmacnia to wyniki otrzymane przez innych autorów w przypadku miar na prostej. Opisujemy także, jakie ogólne nierówności koncentracyjne wynikają ze słabych nierówności transportowych (równoważnie: z ich dualnych sformułowań, czyli wypukłych nierówności splotu infimum). Obejmuje to także wyniki dla nielipszycowskich funkcji wypukłych. Ostatni wynik dotyczy wypukłych nierówności splotu infimum z optymalnymi funkcjami kosztu dla miar o log-wklęsłych ogonach. Jako wniosek otrzymujemy porównywanie słabych i silnych momentów wektorów losowych o niezależnych współrzędnych z log-wklęsłymi ogonami.
This thesis is devoted to the study of functional and transportation inequalities connected to the concentration of measure phenomenon. In the first part, we work in the classical setting of smooth functions and are interested in the concentration between the exponential and Gaussian levels. We prove that a probability measure which satisfies a Beckner-type inequality of Latała and Oleszkiewicz, also satisfies a modified log-Sobolev inequality. As a corollary, we obtain improved (dimension-free) two-level concentration for products of such measures. The second, more extensive, part is concerned with concentration of measure for convex functions. Our main tool, used throughout, is the theory of weak transportation inequalities introduced recently by Gozlan, Roberto, Samson, and Tetali. We start by presenting a characterization of probability measures on the real line which satisfy the convex log-Sobolev inequality. This allows us to give concentration estimates of the lower and upper tails of convex Lipschitz functions (the latter were not known before). We then prove that a probability measure on $\mathbb{R}^n$ which satisfies the convex Poincar\'e inequality also satisfies a Bobkov--Ledoux modified log-Sobolev inequality, extending results obtained by other authors for measures on $\mathbb{R}$. We also present refined concentration of measure inequalities, which are consequences of weak transportation inequalities (or, equivalently, their dual formulations: convex infimum convolution inequalities). This includes applications to concentration for non-Lipschitz convex functions. Our last result concerns convex infimum convolution inequalities with optimal cost functions for measures with log-concave tails. As a corollary, we obtain comparison of weak and strong moments of random vectors with independent coordinates with log-concave tails.

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Lemańczyk, Michał. "Recurrence of stochastic processes in some concentration of measure and entropy problems." Doctoral thesis, 2022. https://depotuw.ceon.pl/handle/item/4158.

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Let X = (Xi)i∈Z, where Xi ∈ X and X is a (measurable) state space, be a stochastic process. The thesis is focused on the role played by the return time process R = (Ri)i∈Z of consecutive return times of X to some prescribed subset of X Z, both in probability and in ergodic theory. In the most simple case, given A ⊂ X , the corresponding return time process is de ned as Ri =    inf{j ≥ 0 : Xj ∈ A}, i = 0, inf{j > Ri−1 : Xj ∈ A}, i ≥ 1, sup{j < Ri+1 : Xj ∈ A}, i ≤ −1. (1.1) The main result on the probability side is proving a Bernstein inequality for additive functionals of general not necessarily strongly aperiodic Markov chains (see [A3]), thus answering an open question from [1]. We also prove a new version of the Bernstein inequality for 1-dependent processes (this class is strongly related to Markov chains due to the regeneration technique). On the ergodic theory side, the main results contain explicit formulas and estimates for the entropy rate of coordinatewise products of processes (see [A1]). This, in turn, serves as a tool in solving several problems. We give a new explicit formula for the topological pressure of BBB-free systems (for short BFSs). We prove the uniqueness of equilibrium measures for BFSs for potentials depending on one coordinate (thus extending the result on the intrinsic ergodicity from [3, 2]). At last, we answer open questions on the entropy of BFSs from [2] (see [A1]) and we show that the measure of maximal entropy does not satisfy the Gibbs property (see [A2]) which answers the question posed by Peckner in [3]. Part of the material included in this thesis is new, part of it is based on the following three articles: [A1] J. Kuªaga-Przymus and M.D. Lema«czyk. Entropy rate of product of independent processes. Preprint: arXiv:2004.07648, 2020. [A2] J. Kuªaga-Przymus and M.D. Lema«czyk. Hereditary subshifts whose measure of maximal en- tropy has no Gibbs property. To appear in Colloquium Mathematicum, arXiv:2004.07643, 2020. [A3] M.D. Lema«czyk. General Bernstein-like inequality for additive functionals of Markov chains. Journal of Theoretical Probability, 2020.
Niech X = (Xi)i∈Z, gdzie Xi ∈ X a X jest (mierzaln¡) przestrzeni¡ stanów, b¦dzie procesem stochasty- cznym. Niniejsza rozprawa doktorska koncentruje si¦ na procesach czasów powrotu R = (Ri)i∈Z kolejnych powrotów Xi do A oraz ich roli zarówno w teorii prawdopodobie«stwa, jak i w teorii ergody- cznej. Przypomnijmy, »e dla danego podzbioru A ⊂ X odpowiadaj¡cy mu proces czasów powrotu jest zde niowany jako Ri =    inf{j ≥ 0 : Xj ∈ A}, i = 0, inf{j > Ri−1 : Xj ∈ A}, i ≥ 1, sup{j < Ri+1 : Xj ∈ A}, i ≤ −1. (1.1) Gªównym rezultatem rozprawy w teorii prawdopodobie«stwa jest dowód nierówno±ci Bernsteina dla funkcjonaªów addytywnych ogólnych, niekoniecznie silnie aperiodycznych, ªa«cuchów Markowa, co daje odpowied¹ na pytanie sformuªowane w pracy [1] (patrz [A3]). Dowodzimy równie» pewnej nowej wersji nierówno±ci Bernsteina dla 1-zale»nych procesów (klasa ta jest silnie zwi¡zana z ªa«cuchami Markowa dzi¦ki tzw. technice regeneracji). Gªówne rezultaty w teorii ergodycznej dotycz¡ dokªadnych wzorów, b¡d¹ nierówno±ci, zwi¡zanych z entropi¡ (ang. entropy rate) punktowego iloczynu procesów (patrz [A1]). Staj¡ si¦ one narz¦dziem do rozwi¡zania kilku otwartych problemów. Podajemy nowy, jawny wzór na ci±nienie topologiczne ukªadów BBB-wolnych oraz, w pewnych przypadkach, dowodzimy jedyno±ci stanów równowagi dla ukªadu wyznaczonego przez BBB (co rozszerza rezultaty o wewn¦trznej ergodyczno±ci udowodnione w [3, 2]). Odpowiadamy na pytanie postawione w [3] o braku wªasno±ci Gibbsa dla miary o maksymalnej entropii (patrz [A2]). W ko«cu, odpowiadamy na kilka pyta« doty- cz¡cych entropii ukªadów BBB-wolnych z pracy [2] (patrz [A1]). Cz¦±¢ rezultatów rozprawy jest nowa, pozostaªe rezultaty pochodz¡ z nast¦puj¡cych trzech artykuªów: [A1] J. Kuªaga-Przymus and M.D. Lema«czyk. Entropy rate of product of independent processes. Preprint: arXiv:2004.07648, 2020. [A2] J. Kuªaga-Przymus and M.D. Lema«czyk. Hereditary subshifts whose measure of maximal en- tropy has no Gibbs property. To appear in Colloquium Mathematicum, arXiv:2004.07643, 2020. [A3] M.D. Lema«czyk. General Bernstein-like inequality for additive functionals of Markov chains. Journal of Theoretical Probability, 2020.

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Частини книг з теми "Convolution inequality"

Brown, Gavin, and Larry Shepp. "A Convolution Inequality." In Contributions to Probability and Statistics, 51–57. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-3678-8_4.

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Christ, Michael. "On Young’s Convolution Inequality for Heisenberg Groups." In Geometric Aspects of Harmonic Analysis, 223–60. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-72058-2_6.

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Götze, Friedrich, and Andrei Yu Zaitsev. "A Multiplicative Inequality for Concentration Functions of n-Fold Convolutions." In High Dimensional Probability II, 39–47. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1358-1_3.

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Grimmett, Geoffrey R., and David R. Stirzaker. "Discrete random variables." In Probability and Random Processes, 46–88. Oxford University PressOxford, 2001. http://dx.doi.org/10.1093/oso/9780198572237.003.0003.

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Abstract The distribution of a discrete random variable may be specified via its probability mass function. The key notion of independence for discrete random variables is introduced. The concept of expectation, or mean value, is defined for discrete variables, leading to a definition of the variance and the moments of a discrete random variable. Joint distributions, conditional distributions, and conditional expectation are introduced, together with the ideas of covariance and correlation. The Cauchy–Schwarz inequality is presented. The analysis of sums of random variables leads to the convolution formula for mass functions. Random walks are studied in some depth, including the reflection principle, the ballot theorem, the hitting time theorem, and the arc sine laws for visits to the origin and for sojourn times.

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Chambers, Robert G. "Differentials and Convex Analysis." In Competitive Agents in Certain and Uncertain Markets, 7–64. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780190063016.003.0002.

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Mathematical tools necessary to the argument are presented and discussed. The focus is on concepts borrowed from the convex analysis and variational analysis literatures. The chapter starts by introducing the notions of a correspondence, upper hemi-continuity, and lower hemi-continuity. Superdifferential and subdifferential correspondences for real-valued functions are then introduced, and their essential properties and their role in characterizing global optima are surveyed. Convex sets are introduced and related to functional concavity (convexity). The relationship between functional concavity (convexity), superdifferentiability (subdifferentiability), and the existence of (one-sided) directional derivatives is examined. The theory of convex conjugates and essential conjugate duality results are discussed. Topics treated include Berge's Maximum Theorem, cyclical monotonicity of superdifferential (subdifferential) correspondences, concave (convex) conjugates and biconjugates, Fenchel's Inequality, the Fenchel-Rockafellar Conjugate Duality Theorem, support functions, superlinear functions, sublinear functions, the theory of infimal convolutions and supremal convolutions, and Fenchel's Duality Theorem.

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T. Nanthikattu, Joel, Navaneeth N, Gokul D, Sonette T, Binesh T, Binish M C, and Vinu Thomas. "GPU based Segmentation and Classification of Brain Tumour from MRI Images." In New Frontiers in Communication and Intelligent Systems, 17–23. Soft Computing Research Society, 2021. http://dx.doi.org/10.52458/978-81-95502-00-4-3.

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Detection of Brain Tumour in its initial stage leads to an advancement in treatment methods. This paves the way for a consequent higher rate of life expectancy for the patient. These tumours can be successfully assessed by Magnetic resonance imaging (MRI). Alternatively, the immense amount of data generated by MRI causes manual segmentation to be highly time-consuming, thereby restricting the use of precise quantitative measurements in clinical practice. Brain tumours possess sizeable spatial and structural inequality among them which makes automatic segmentation a demanding task. Here in this work, Convolutional Neural Networks (CNN) are utilized to devise an accurate and efficient real time tumor tracking algorithm for detecting the different types of brain tumours. Python programming language is used for the development and the implementation is carried out on a typical Graphics Processing Unit (GPU).

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Тези доповідей конференцій з теми "Convolution inequality"

Jog, Varun. "A convolution inequality for entropy over Z2." In 2017 IEEE International Symposium on Information Theory (ISIT). IEEE, 2017. http://dx.doi.org/10.1109/isit.2017.8007114.

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Jin, Ce, and Yinzhan Xu. "Shaving Logs via Large Sieve Inequality: Faster Algorithms for Sparse Convolution and More." In STOC '24: 56th Annual ACM Symposium on Theory of Computing. New York, NY, USA: ACM, 2024. http://dx.doi.org/10.1145/3618260.3649605.

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Kumar, Sivaprasad, and Virendra Kumar. "On the Fekete-Szego Inequality for a Class of Analytic Functions Defined by Convolution." In Annual International Conference on Computational Mathematics, Computational Geometry & Statistics. Global Science and Technology Forum (GSTF), 2012. http://dx.doi.org/10.5176/2251-1911_cmcgs59.

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Yao, Yunxiang, and Wai Ho Mow. "Optimal Index Assignment for Scalar Quantizers and M-PSK via a Discrete Convolution-Rearrangement Inequality." In 2021 IEEE International Symposium on Information Theory (ISIT). IEEE, 2021. http://dx.doi.org/10.1109/isit45174.2021.9517984.

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Papoulia, Katerina D., Vassilis P. Panoskaltsis, and Igor Korovajchuk. "Some Equivalences in the Theory of Linear Viscoelasticity and Their Implications in Modeling and Simulation." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-1191.

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Abstract A class of linear viscoelastic models is examined which accurately represent the response of many materials in a wide frequency range. These include power law and logarithmic type models, such as those of fractional order, the Kuhn model of linear viscoelasticity and generalizations thereof. An equivalence between the fractional element and the generalized Kuhn model is established. A continuous representation of these models is naturally available. It is shown that a discrete rheological representation, in the form of series of springs and dashpots, is also possible. This allows an internal variable formulation, which establishes the thermodynamic admissibility of this class of models, in the sense that they satisfy the dissipation inequality. Introduction of appropriate state variables leads to convolution type equations, which, in the finite deformation case, retain much of the structure of linear viscoelasticity. Numerical implementation of the models is enhanced by the equivalence principles. It is shown that the accuracy expected of a long chain of classical structural units is achieved with a greatly reduced number of model parameters.

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Jing Su, Qing Liu, Meilin Wang, Jiangzhong Cao, and Wing-Kuen Ling. "Design of convolution neural network with frequency selectivity for wearable camera embed glasses based image recognition systems via nonconvex functional inequality constrained sparse optimization approach." In 2016 IEEE 25th International Symposium on Industrial Electronics (ISIE). IEEE, 2016. http://dx.doi.org/10.1109/isie.2016.7745045.

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Walk, Philipp, and Peter Jung. "On a reverse ℓ2-inequality for sparse circular convolutions." In ICASSP 2013 - 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2013. http://dx.doi.org/10.1109/icassp.2013.6638539.

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Wang, Wenxiao, Cong Fu, Jishun Guo, Deng Cai, and Xiaofei He. "COP: Customized Deep Model Compression via Regularized Correlation-Based Filter-Level Pruning." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. California: International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/525.

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Neural network compression empowers the effective yet unwieldy deep convolutional neural networks (CNN) to be deployed in resource-constrained scenarios. Most state-of-the-art approaches prune the model in filter-level according to the "importance" of filters. Despite their success, we notice they suffer from at least two of the following problems: 1) The redundancy among filters is not considered because the importance is evaluated independently. 2) Cross-layer filter comparison is unachievable since the importance is defined locally within each layer. Consequently, we must manually specify layer-wise pruning ratios. 3) They are prone to generate sub-optimal solutions because they neglect the inequality between reducing parameters and reducing computational cost. Reducing the same number of parameters in different positions in the network may reduce different computational cost. To address the above problems, we develop a novel algorithm named as COP (correlation-based pruning), which can detect the redundant filters efficiently. We enable the cross-layer filter comparison through global normalization. We add parameter-quantity and computational-cost regularization terms to the importance, which enables the users to customize the compression according to their preference (smaller or faster). Extensive experiments have shown COP outperforms the others significantly. The code is released at https://github.com/ZJULearning/COP.

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