Relevant bibliographies by topics / Multiplicative convolution

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Multiplicative convolution'

Author: Grafiati
Published: 4 June 2021
Last updated: 27 April 2022

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Journal articles on the topic "Multiplicative convolution"

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Bercovici, Hari. "Multiplicative monotonic convolution." Illinois Journal of Mathematics 49, no. 3 (July 2005): 929–51. http://dx.doi.org/10.1215/ijm/1258138229.

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Gao, Mingchu. "On bi-free multiplicative convolution." Studia Mathematica 248, no. 2 (2019): 129–46. http://dx.doi.org/10.4064/sm171024-4-5.

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Popa, Mihai, and Jiun-Chau Wang. "On multiplicative conditionally free convolution." Transactions of the American Mathematical Society 363, no. 12 (December 1, 2011): 6309–35. http://dx.doi.org/10.1090/s0002-9947-2011-05242-6.

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Kieburg, Mario. "Additive matrix convolutions of Pólya ensembles and polynomial ensembles." Random Matrices: Theory and Applications 09, no. 04 (November 8, 2019): 2150002. http://dx.doi.org/10.1142/s2010326321500027.

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Recently, subclasses of polynomial ensembles for additive and multiplicative matrix convolutions were identified which were called Pólya ensembles (or polynomial ensembles of derivative type). Those ensembles are closed under the respective convolutions and, thus, build a semi-group when adding by hand a unit element. They even have a semi-group action on the polynomial ensembles. Moreover, in several works transformations of the bi-orthogonal functions and kernels of a given polynomial ensemble were derived when performing an additive or multiplicative matrix convolution with particular Pólya ensembles. For the multiplicative matrix convolution on the complex square matrices the transformations were even done for general Pólya ensembles. In the present work, we generalize these results to the additive convolution on Hermitian matrices, on Hermitian anti-symmetric matrices, on Hermitian anti-self-dual matrices and on rectangular complex matrices. For this purpose, we derive the bi-orthogonal functions and the corresponding kernel for a general Pólya ensemble which was not done before. With the help of these results, we find transformation formulas for the convolution with a fixed matrix or a random matrix drawn from a general polynomial ensemble. As an example, we consider Pólya ensembles with an associated weight which is a Pólya frequency function of infinite order. But we also explicitly evaluate the Gaussian unitary ensemble as well as the complex Laguerre (aka Wishart, Ginibre or chiral Gaussian unitary) ensemble. All results hold for finite matrix dimension. Furthermore, we derive a recursive relation between Toeplitz determinants which appears as a by-product of our results.
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Belinschi, S. T., and H. Bercovici. "Hinčin's Theorem for Multiplicative Free Convolution." Canadian Mathematical Bulletin 51, no. 1 (March 1, 2008): 26–31. http://dx.doi.org/10.4153/cmb-2008-004-3.

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AbstractHinčin proved that any limit law, associated with a triangular array of infinitesimal random variables, is infinitely divisible. The analogous result for additive free convolution was proved earlier by Bercovici and Pata. In this paper we will prove corresponding results for the multiplicative free convolution of measures defined on the unit circle and on the positive half-line.
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Bormetti, Giacomo, and Sofia Cazzaniga. "Multiplicative noise, fast convolution and pricing." Quantitative Finance 14, no. 3 (November 16, 2012): 481–94. http://dx.doi.org/10.1080/14697688.2012.729857.

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Haraoka, Yoshishige. "Multiplicative middle convolution for KZ equations." Mathematische Zeitschrift 294, no. 3-4 (May 14, 2019): 1787–839. http://dx.doi.org/10.1007/s00209-019-02322-9.

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Astola, Jaakko. "Multiplicative complexity, convolution, and the DFT." Signal Processing 20, no. 1 (May 1990): 95. http://dx.doi.org/10.1016/0165-1684(90)90081-9.

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Leake, Jonathan, and Nick Ryder. "Connecting the q-multiplicative convolution and the finite difference convolution." Advances in Mathematics 374 (November 2020): 107334. http://dx.doi.org/10.1016/j.aim.2020.107334.

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LE, T. A., and J. W. SANDER. "CONVOLUTIONS OF RAMANUJAN SUMS AND INTEGRAL CIRCULANT GRAPHS." International Journal of Number Theory 08, no. 07 (August 28, 2012): 1777–88. http://dx.doi.org/10.1142/s1793042112501023.

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There exist several generalizations of the classical Dirichlet convolution, for instance the so-called A-convolutions analyzed by Narkiewicz. We shall connect the concept of A-convolutions satisfying a weak form of regularity and Ramanujan sums with the spectrum of integral circulant graphs. These generalized Cayley graphs, having circulant adjacency matrix and integral eigenvalues, comprise a great amount of arithmetical features. By use of our concept we obtain a multiplicative decomposition of the so-called energy of integral circulant graphs with multiplicative divisor sets. This will be fundamental for the study of open problems, in particular concerning the detection of integral circulant graphs with maximal or minimal energy.
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Dissertations / Theses on the topic "Multiplicative convolution"

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Hofmann, B., and G. Fleischer. "Stability Rates for Linear Ill-Posed Problems with Convolution and Multiplication Operators." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800987.

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In this paper we deal with the `strength' of ill-posedness for ill-posed linear operator equations Ax = y in Hilbert spaces, where we distinguish according_to_M. Z. Nashed [15] the ill-posedness of type I if A is not compact, but we have R(A) 6= R(A) for the range R(A) of A; and the ill-posedness of type II for compact operators A: From our considerations it seems to follow that the problems with noncompact operators A are not in general `less' ill-posed than the problems with compact operators. We motivate this statement by comparing the approximation and stability behaviour of discrete least-squares solutions and the growth rate of Galerkin matrices in both cases. Ill-posedness measures for compact operators A as discussed in [10] are derived from the decay rate of the nonincreasing sequence of singular values of A. Since singular values do not exist for noncompact operators A; we introduce stability rates in order to have a common measure for the compact and noncompact cases. Properties of these rates are illustrated by means of convolution equations in the compact case and by means of equations with multiplication operators in the noncompact case. Moreover using increasing rearrangements of the multiplier functions specific measures of ill-posedness called ill-posedness rates are considered for the multiplication operators. In this context, the character of sufficient conditions providing convergence rates of Tikhonov regularization are compared for compact operators and multiplication operators.
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Escande, Paul. "Compression et inférence des opérateurs intégraux : applications à la restauration d’images dégradées par des flous variables." Thesis, Toulouse, ISAE, 2016. http://www.theses.fr/2016ESAE0020/document.

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Le problème de restauration d'images dégradées par des flous variables connaît un attrait croissant et touche plusieurs domaines tels que l'astronomie, la vision par ordinateur et la microscopie à feuille de lumière où les images sont de taille un milliard de pixels. Les flous variables peuvent être modélisés par des opérateurs intégraux qui associent à une image nette u, une image floue Hu. Une fois discrétisé pour être appliqué sur des images de N pixels, l'opérateur H peut être vu comme une matrice de taille N x N. Pour les applications visées, la matrice est stockée en mémoire avec un exaoctet. On voit apparaître ici les difficultés liées à ce problème de restauration des images qui sont i) le stockage de ce grand volume de données, ii) les coûts de calculs prohibitifs des produits matrice-vecteur. Ce problème souffre du fléau de la dimension. D'autre part, dans beaucoup d'applications, l'opérateur de flou n'est pas ou que partialement connu. Il y a donc deux problèmes complémentaires mais étroitement liés qui sont l'approximation et l'estimation des opérateurs de flou. Cette thèse a consisté à développer des nouveaux modèles et méthodes numériques permettant de traiter ces problèmes
The restoration of images degraded by spatially varying blurs is a problem of increasing importance. It is encountered in many applications such as astronomy, computer vision and fluorescence microscopy where images can be of size one billion pixels. Variable blurs can be modelled by linear integral operators H that map a sharp image u to its blurred version Hu. After discretization of the image on a grid of N pixels, H can be viewed as a matrix of size N x N. For targeted applications, matrices is stored with using exabytes on the memory. This simple observation illustrates the difficulties associated to this problem: i) the storage of a huge amount of data, ii) the prohibitive computation costs of matrix-vector products. This problems suffers from the challenging curse of dimensionality. In addition, in many applications, the operator is usually unknown or only partially known. There are therefore two different problems, the approximation and the estimation of blurring operators. They are intricate and have to be addressed with a global overview. Most of the work of this thesis is dedicated to the development of new models and computational methods to address those issues
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Venkataraman, Mahalingam. "Improving accuracy in logarithmic multiplication using operand decomposition." [Tampa, Fla.] : University of South Florida, 2005. http://purl.fcla.edu/fcla/etd/SFE0001140.

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Santos, Pedro. "Approximation Methods for Convolution Operators on the Real Line." Doctoral thesis, Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200500362.

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This work is concerned with the applicability of several approximation methods (finite section method, Galerkin and collocation methods with maximum defect splines for uniform and non uniform meshes) to operators belonging to the closed subalgebra generated by operators of multiplication bz piecewise continuous functions and convolution operators also with piecewise continuous generating function.
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Kato, Fernando Hideki. "Análise de carteiras em tempo discreto." Universidade de São Paulo, 2004. http://www.teses.usp.br/teses/disponiveis/12/12139/tde-24022005-005812/.

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Nesta dissertação, o modelo de seleção de carteiras de Markowitz será estendido com uma análise em tempo discreto e hipóteses mais realísticas. Um produto tensorial finito de densidades Erlang será usado para aproximar a densidade de probabilidade multivariada dos retornos discretos uniperiódicos de ativos dependentes. A Erlang é um caso particular da distribuição Gama. Uma mistura finita pode gerar densidades multimodais não-simétricas e o produto tensorial generaliza este conceito para dimensões maiores. Assumindo que a densidade multivariada foi independente e identicamente distribuída (i.i.d.) no passado, a aproximação pode ser calibrada com dados históricos usando o critério da máxima verossimilhança. Este é um problema de otimização em larga escala, mas com uma estrutura especial. Assumindo que esta densidade multivariada será i.i.d. no futuro, então a densidade dos retornos discretos de uma carteira de ativos com pesos não-negativos será uma mistura finita de densidades Erlang. O risco será calculado com a medida Downside Risk, que é convexa para determinados parâmetros, não é baseada em quantis, não causa a subestimação do risco e torna os problemas de otimização uni e multiperiódico convexos. O retorno discreto é uma variável aleatória multiplicativa ao longo do tempo. A distribuição multiperiódica dos retornos discretos de uma seqüência de T carteiras será uma mistura finita de distribuições Meijer G. Após uma mudança na medida de probabilidade para a composta média, é possível calcular o risco e o retorno, que levará à fronteira eficiente multiperiódica, na qual cada ponto representa uma ou mais seqüências ordenadas de T carteiras. As carteiras de cada seqüência devem ser calculadas do futuro para o presente, mantendo o retorno esperado no nível desejado, o qual pode ser função do tempo. Uma estratégia de alocação dinâmica de ativos é refazer os cálculos a cada período, usando as novas informações disponíveis. Se o horizonte de tempo tender a infinito, então a fronteira eficiente, na medida de probabilidade composta média, tenderá a um único ponto, dado pela carteira de Kelly, qualquer que seja a medida de risco. Para selecionar um dentre vários modelos de otimização de carteira, é necessário comparar seus desempenhos relativos. A fronteira eficiente de cada modelo deve ser traçada em seu respectivo gráfico. Como os pesos dos ativos das carteiras sobre estas curvas são conhecidos, é possível traçar todas as curvas em um mesmo gráfico. Para um dado retorno esperado, as carteiras eficientes dos modelos podem ser calculadas, e os retornos realizados e suas diferenças ao longo de um backtest podem ser comparados.
In this thesis, Markowitz’s portfolio selection model will be extended by means of a discrete time analysis and more realistic hypotheses. A finite tensor product of Erlang densities will be used to approximate the multivariate probability density function of the single-period discrete returns of dependent assets. The Erlang is a particular case of the Gamma distribution. A finite mixture can generate multimodal asymmetric densities and the tensor product generalizes this concept to higher dimensions. Assuming that the multivariate density was independent and identically distributed (i.i.d.) in the past, the approximation can be calibrated with historical data using the maximum likelihood criterion. This is a large-scale optimization problem, but with a special structure. Assuming that this multivariate density will be i.i.d. in the future, then the density of the discrete returns of a portfolio of assets with nonnegative weights will be a finite mixture of Erlang densities. The risk will be calculated with the Downside Risk measure, which is convex for certain parameters, is not based on quantiles, does not cause risk underestimation and makes the single and multiperiod optimization problems convex. The discrete return is a multiplicative random variable along the time. The multiperiod distribution of the discrete returns of a sequence of T portfolios will be a finite mixture of Meijer G distributions. After a change of the distribution to the average compound, it is possible to calculate the risk and the return, which will lead to the multiperiod efficient frontier, where each point represents one or more ordered sequences of T portfolios. The portfolios of each sequence must be calculated from the future to the present, keeping the expected return at the desired level, which can be a function of time. A dynamic asset allocation strategy is to redo the calculations at each period, using new available information. If the time horizon tends to infinite, then the efficient frontier, in the average compound probability measure, will tend to only one point, given by the Kelly’s portfolio, whatever the risk measure is. To select one among several portfolio optimization models, it is necessary to compare their relative performances. The efficient frontier of each model must be plotted in its respective graph. As the weights of the assets of the portfolios on these curves are known, it is possible to plot all curves in the same graph. For a given expected return, the efficient portfolios of the models can be calculated, and the realized returns and their differences along a backtest can be compared.
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Juhaňák, Pavel. "Zjednodušené násobení v konvolučních neuronových sítích." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2019. http://www.nusl.cz/ntk/nusl-403135.

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This thesis provides an introduction to classical and convolutional neural networks. It describes how hardware multiplication is conventionally performed and optimized. A simplified multiplication method is proposed, namely multiplierless multiplication. This method is implemented and integrated into the TypeCNN library. The cost of the hardware solution of both conventional and simplified multipliers is estimated. The thesis also introduces software tools developed to work with convolutional neural networks and datasets used to test them in the image classification task. Test architectures and experimentation methodology are proposed. The results are evaluated, and both the classification accuracy and cost of the hardware solution are discussed.
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Slouka, Lukáš. "Implementace neuronové sítě bez operace násobení." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2018. http://www.nusl.cz/ntk/nusl-386017.

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The subject of this thesis is neural network acceleration with the goal of reducing the number of floating point multiplications. The theoretical part of the thesis surveys current trends and methods used in the field of neural network acceleration. However, the focus is on the binarization techniques which allow replacing multiplications with logical operators. The theoretical base is put into practice in two ways. First is the GPU implementation of crucial binary operators in the Tensorflow framework with a performance benchmark. Second is an application of these operators in simple image classifier. Results are certainly encouraging. Implemented operators achieve speed-up by a factor of 2.5 when compared to highly optimized cuBLAS operators. The last chapter compares accuracies achieved by binarized models and their full-precision counterparts on various architectures.
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HEIDEMAN, MICHAEL THOMAS. "APPLICATIONS OF MULTIPLICATIVE COMPLEXITY THEORY TO CONVOLUTION AND THE DISCRETE FOURIER TRANSFORM (FAST, COMPUTATIONAL, DIGITAL FILTERING, SIGNAL PROCESSING, ALGORITHMS)." Thesis, 1986. http://hdl.handle.net/1911/15979.

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A review of the theory of multiplicative complexity and its application to common signal processing operations is presented. This review collects results on the multiplicative complexity of polynomial multiplication, products in extension fields, multivariate polynomial multiplication, and multiple products in the same extension field with one or more fixed polynomials. In addition, new results are obtained for the multiplicative complexity of multidimensional cyclic convolution, the one-dimensional discrete Fourier transform (DFT), and convolutions and DFTs with input constraints or output restrictions. The multiplicative complexity of multidimensional cyclic convolution is determined for any possible combination of lengths in any number of dimensions, extending a result of Winograd for one- and two-dimensional cyclic convolution. This result is shown to be applicable in determining the multiplicative complexity of the one-dimensional discrete Fourier transform (DFT). The multiplicative complexity of the DFT for all possible lengths is determined starting with Winograd's result for odd prime lengths and then extending it to power-of-prime lengths, power-of-two lengths, and finally to arbitrary lengths. The multiplicative complexity of systems of polynomial multiplication with constrained inputs is considered. An input constraint must imply a nontrivial factorization of one input polynomial for which one factor has coefficients only in the ground field if the multiplicative complexity is to be reduced over unconstrained polynomial multiplication. This result is applied to symmetric polynomial multiplication. The multiplicative complexity of polynomial products for which only selected outputs are needed is analyzed. Complexities are derived for polynomial products with decimated and truncated outputs, but no general rule is apparent for arbitrary output restrictions. The effect of input constraints and output restrictions on the multiplicative complexity of the discrete Fourier transform are considered. Specifically, restrictions to one input or output are analyzed as are even- or odd-symmetric inputs.
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Santos, Pedro. "Approximation Methods for Convolution Operators on the Real Line." Doctoral thesis, 1998. https://monarch.qucosa.de/id/qucosa%3A18294.

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This work is concerned with the applicability of several approximation methods (finite section method, Galerkin and collocation methods with maximum defect splines for uniform and non uniform meshes) to operators belonging to the closed subalgebra generated by operators of multiplication bz piecewise continuous functions and convolution operators also with piecewise continuous generating function.
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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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Books on the topic "Multiplicative convolution"

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Heideman, Michael T. Multiplicative Complexity, Convolution, and the DFT. New York, NY: Springer New York, 1988.

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S, Burrus C., ed. Multiplicative complexity, convolution, and the DFT. New York: Springer-Verlag, 1988.

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Heideman, Michael T. Multiplicative Complexity, Convolution, and the DFT. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-3912-3.

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Multiplicative Complexity, Convolution, and the DFT. Springer, 2013.

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Book chapters on the topic "Multiplicative convolution"

1

Ramaré, Olivier. "Arithmetic Convolution." In Excursions in Multiplicative Number Theory, 3–16. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-73169-4_1.

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Ramaré, Olivier. "The Convolution Method." In Excursions in Multiplicative Number Theory, 79–86. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-73169-4_8.

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Heideman, Michael T. "Convolution and Polynomial Multiplication." In Multiplicative Complexity, Convolution, and the DFT, 27–60. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-3912-3_3.

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Heideman, Michael T. "Multiplicative Complexity of Discrete Fourier Transform." In Multiplicative Complexity, Convolution, and the DFT, 76–107. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-3912-3_5.

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Ramaré, Olivier. "Convolution Method and Non-Positive Functions." In Excursions in Multiplicative Number Theory, 275–78. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-73169-4_27.

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Heideman, Michael T. "Multiplicative Complexity of Linear and Bilinear Systems." In Multiplicative Complexity, Convolution, and the DFT, 5–26. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-3912-3_2.

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Heideman, Michael T. "Introduction." In Multiplicative Complexity, Convolution, and the DFT, 1–4. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-3912-3_1.

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Heideman, Michael T. "Constrained Polynomial Multiplication." In Multiplicative Complexity, Convolution, and the DFT, 61–75. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-3912-3_4.

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Heideman, Michael T. "Restricted and Constrained DFTs." In Multiplicative Complexity, Convolution, and the DFT, 108–18. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4612-3912-3_6.

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Dettweiler, Michael, and Mirjam Jöllenbeck. "Monodromy of the Multiplicative and the Additive Convolution." In Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 177–97. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-70566-8_7.

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Conference papers on the topic "Multiplicative convolution"

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Tong, Gan, and Libo Huang. "Fast Convolution based on Winograd Minimum Filtering: Introduction and Development." In 5th International Conference on Computer Science and Information Technology (COMIT 2021). Academy and Industry Research Collaboration Center (AIRCC), 2021. http://dx.doi.org/10.5121/csit.2021.111716.

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Convolutional Neural Network (CNN) has been widely used in various fields and played an important role. Convolution operators are the fundamental component of convolutional neural networks, and it is also the most time-consuming part of network training and inference. In recent years, researchers have proposed several fast convolution algorithms including FFT and Winograd. Among them, Winograd convolution significantly reduces the multiplication operations in convolution, and it also takes up less memory space than FFT convolution. Therefore, Winograd convolution has quickly become the first choice for fast convolution implementation within a few years. At present, there is no systematic summary of the convolution algorithm. This article aims to fill this gap and provide detailed references for follow-up researchers. This article summarizes the development of Winograd convolution from the three aspects of algorithm expansion, algorithm optimization, implementation, and application, and finally makes a simple outlook on the possible future directions.
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Makarov, Anatoly M., and Alexander S. Ermakov. "Method Development for Solving Fredholm Integral Equations of The Second Kind Based on The Mellin Multiplicative Convolution in The Class of Trigonometric-Logarithmic Functions." In 2021 Radiation and Scattering of Electromagnetic Waves (RSEMW). IEEE, 2021. http://dx.doi.org/10.1109/rsemw52378.2021.9494103.

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Franz, Uwe. "Multiplicative monotone convolutions." In Quantum Probability. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2006. http://dx.doi.org/10.4064/bc73-0-10.

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Limonova, Elena, Daniil Matveev, Dmitry Nikolaev, and Vladimir V. Arlazarov. "Bipolar morphological neural networks: convolution without multiplication." In Twelfth International Conference on Machine Vision, edited by Wolfgang Osten and Dmitry P. Nikolaev. SPIE, 2020. http://dx.doi.org/10.1117/12.2559299.

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Vasudevan, Aravind, Andrew Anderson, and David Gregg. "Parallel Multi Channel convolution using General Matrix Multiplication." In 2017 IEEE 28th International Conference on Application-specific Systems, Architectures and Processors (ASAP). IEEE, 2017. http://dx.doi.org/10.1109/asap.2017.7995254.

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Xu, Ziru, Yunbo Wang, Mingsheng Long, and Jianmin Wang. "PredCNN: Predictive Learning with Cascade Convolutions." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/408.

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Predicting future frames in videos remains an unsolved but challenging problem. Mainstream recurrent models suffer from huge memory usage and computation cost, while convolutional models are unable to effectively capture the temporal dependencies between consecutive video frames. To tackle this problem, we introduce an entirely CNN-based architecture, PredCNN, that models the dependencies between the next frame and the sequential video inputs. Inspired by the core idea of recurrent models that previous states have more transition operations than future states, we design a cascade multiplicative unit (CMU) that provides relatively more operations for previous video frames. This newly proposed unit enables PredCNN to predict future spatiotemporal data without any recurrent chain structures, which eases gradient propagation and enables a fully paralleled optimization. We show that PredCNN outperforms the state-of-the-art recurrent models for video prediction on the standard Moving MNIST dataset and two challenging crowd flow prediction datasets, and achieves a faster training speed and lower memory footprint.
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Korpi, Dani, Mikko Honkala, Janne M. J. Huttunen, and Vesa Starck. "DeepRx MIMO: Convolutional MIMO Detection with Learned Multiplicative Transformations." In ICC 2021 - IEEE International Conference on Communications. IEEE, 2021. http://dx.doi.org/10.1109/icc42927.2021.9500518.

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Bipin, B., and Jyothisha J. Nair. "Image convolution optimization using sparse matrix vector multiplication technique." In 2016 International Conference on Advances in Computing, Communications and Informatics (ICACCI). IEEE, 2016. http://dx.doi.org/10.1109/icacci.2016.7732252.

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Villasana T., Pedro J., and Stanislaw Gorlow. "Exact Multiplicative Factor Updates for Convolutional Beta-NMF in 2D." In 2019 27th European Signal Processing Conference (EUSIPCO). IEEE, 2019. http://dx.doi.org/10.23919/eusipco.2019.8902709.

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Das, Anindya B., and Aditya Ramamoorthy. "Distributed Matrix-Vector Multiplication: A Convolutional Coding Approach." In 2019 IEEE International Symposium on Information Theory (ISIT). IEEE, 2019. http://dx.doi.org/10.1109/isit.2019.8849395.

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