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Готові списки джерел за темами / Multiplicatif gaussien

Добірка наукової літератури з теми "Multiplicatif gaussien"

Автор: Grafiati

Опубліковано: 23 вересня 2022

Оновлено: 28 вересня 2022

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Статті в журналах з теми "Multiplicatif gaussien":

1

Lemańczyk, M. "Multiplicative Gaussian cocycles." Aequationes Mathematicae 61, no. 1-2 (February 1, 2001): 162–78. http://dx.doi.org/10.1007/s000100050168.

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2

Robert, Raoul, and Vincent Vargas. "Gaussian multiplicative chaos revisited." Annals of Probability 38, no. 2 (March 2010): 605–31. http://dx.doi.org/10.1214/09-aop490.

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3

Shamov, Alexander. "On Gaussian multiplicative chaos." Journal of Functional Analysis 270, no. 9 (May 2016): 3224–61. http://dx.doi.org/10.1016/j.jfa.2016.03.001.

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4

Lacoin, Hubert, Rémi Rhodes, and Vincent Vargas. "Complex Gaussian Multiplicative Chaos." Communications in Mathematical Physics 337, no. 2 (April 22, 2015): 569–632. http://dx.doi.org/10.1007/s00220-015-2362-4.

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5

KODOGIANNIS, VASSILIS S., MAHDI AMINA, and ILIAS PETROUNIAS. "A CLUSTERING-BASED FUZZY WAVELET NEURAL NETWORK MODEL FOR SHORT-TERM LOAD FORECASTING." International Journal of Neural Systems 23, no. 05 (August 7, 2013): 1350024. http://dx.doi.org/10.1142/s012906571350024x.

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Load forecasting is a critical element of power system operation, involving prediction of the future level of demand to serve as the basis for supply and demand planning. This paper presents the development of a novel clustering-based fuzzy wavelet neural network (CB-FWNN) model and validates its prediction on the short-term electric load forecasting of the Power System of the Greek Island of Crete. The proposed model is obtained from the traditional Takagi–Sugeno–Kang fuzzy system by replacing the THEN part of fuzzy rules with a "multiplication" wavelet neural network (MWNN). Multidimensional Gaussian type of activation functions have been used in the IF part of the fuzzyrules. A Fuzzy Subtractive Clustering scheme is employed as a pre-processing technique to find out the initial set and adequate number of clusters and ultimately the number of multiplication nodes in MWNN, while Gaussian Mixture Models with the Expectation Maximization algorithm are utilized for the definition of the multidimensional Gaussians. The results corresponding to the minimum and maximum power load indicate that the proposed load forecasting model provides significantly accurate forecasts, compared to conventional neural networks models.

6

Dahab, R., D. Hankerson, F. Hu, M. Long, J. Lopez, and A. Menezes. "Software multiplication using Gaussian normal bases." IEEE Transactions on Computers 55, no. 8 (August 2006): 974–84. http://dx.doi.org/10.1109/tc.2006.132.

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7

Barral, Julien, Xiong Jin, Rémi Rhodes, and Vincent Vargas. "Gaussian Multiplicative Chaos and KPZ Duality." Communications in Mathematical Physics 323, no. 2 (August 3, 2013): 451–85. http://dx.doi.org/10.1007/s00220-013-1769-z.

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8

Safieh, Malek, and Jürgen Freudenberger. "Montgomery Reduction for Gaussian Integers." Cryptography 5, no. 1 (February 1, 2021): 6. http://dx.doi.org/10.3390/cryptography5010006.

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Modular arithmetic over integers is required for many cryptography systems. Montgomery reduction is an efficient algorithm for the modulo reduction after a multiplication. Typically, Montgomery reduction is used for rings of ordinary integers. In contrast, we investigate the modular reduction over rings of Gaussian integers. Gaussian integers are complex numbers where the real and imaginary parts are integers. Rings over Gaussian integers are isomorphic to ordinary integer rings. In this work, we show that Montgomery reduction can be applied to Gaussian integer rings. Two algorithms for the precision reduction are presented. We demonstrate that the proposed Montgomery reduction enables an efficient Gaussian integer arithmetic that is suitable for elliptic curve cryptography. In particular, we consider the elliptic curve point multiplication according to the randomized initial point method which is protected against side-channel attacks. The implementation of this protected point multiplication is significantly faster than comparable algorithms over ordinary prime fields.

9

Wang, Kang-Kang, Hui Ye, Ya-Jun Wang, and Ping-Xin Wang. "Impact of Time Delay and Non-Gaussian Noise on Stochastic Resonance and Stability for a Stochastic Metapopulation System Driven by a Multiplicative Periodic Signal." Fluctuation and Noise Letters 18, no. 03 (July 16, 2019): 1950017. http://dx.doi.org/10.1142/s0219477519500172.

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In the present paper, the stability of the population system and the phenomena of the stochastic resonance (SR) for a metapopulation system induced by the terms of time delay, the multiplicative non-Gaussian noise, the additive colored Gaussian noise and a multiplicative periodic signal are investigated in detail. By applying the fast descent method, the unified colored noise approximation and the SR theory, the expressions of the steady-state probability function and the SNR are derived. It is shown that multiplicative non-Gaussian noise, the additive Gaussian noise and time delay can all weaken the stability of the population system, and even result in population extinction. Conversely, the two noise correlation times can both strengthen the stability of the biological system and contribute to group survival. In regard to the SNR for the metapopulation system impacted by the noise terms and time delay, it is revealed that the correlation time of the multiplicative noise can improve effectively the SR effect, while time delay would all along restrain the SR phenomena. On the other hand, although the additive noise and its correlation time can stimulate easily the SR effect, they cannot change the maximum of the SNR. In addition, the departure parameter from the Gaussian noise and the multiplicative noise play the opposite roles in motivating the SR effect in different cases.

10

Guo, Yong-Feng, Ya-Jun Shen, Bei Xi, and Jian-Guo Tan. "Colored correlated multiplicative and additive Gaussian colored noises-induced transition of a piecewise nonlinear bistable model." Modern Physics Letters B 31, no. 28 (October 10, 2017): 1750256. http://dx.doi.org/10.1142/s0217984917502566.

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In this paper, we investigate the steady-state properties of a piecewise nonlinear bistable model driven by multiplicative and additive Gaussian colored noises with colored cross-correlation. Using the unified colored noise approximation, we derive the analytical expression of the steady-state probability density (SPD) function. Then the effects of colored correlated Gaussian colored noises on SPD are presented. According to the research results, it is found that there appear some new nonlinear phenomena in this system. The multiplicative colored noise intensity, the additive colored noise intensity and the cross-correlation strength between noises can induce the transition. However, the transition cannot be induced by the auto-correlation time of multiplicative and additive Gaussian colored noises as well as the cross-correlation time between noises.

Більше джерел

Дисертації з теми "Multiplicatif gaussien":

1

Allez, Romain. "Chaos multiplicatif Gaussien, matrices aléatoires et applications." Phd thesis, Université Paris Dauphine - Paris IX, 2012. http://tel.archives-ouvertes.fr/tel-00780270.

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Dans ce travail, nous nous sommes intéressés d'une part à la théorie du chaos multiplicatif Gaussien introduite par Kahane en 1985 et d'autre part à la théorie des matrices aléatoires dont les pionniers sont Wigner, Wishart et Dyson. La première partie de ce manuscrit contient une brève introduction à ces deux théories ainsi que les contributions personnelles de ce manuscrit expliquées rapidement. Les parties suivantes contiennent les textes des articles publiés [1], [2], [3], [4], [5] et pré-publiés [6], [7], [8] sur ces résultats dans lesquels le lecteur pourra trouver des développements plus détaillés

2

Remy, Guillaume. "Intégrabilité du chaos multiplicatif gaussien et théorie conforme des champs de Liouville." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLEE051/document.

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Cette thèse de doctorat porte sur l’étude de deux objets probabilistes, les mesures de chaos multiplicatif gaussien (GMC) et la théorie conforme des champs de Liouville (LCFT). Le GMC fut introduit par Kahane en 1985 et il s’agit aujourd’hui d’un objet extrêmement important en théorie des probabilités et en physique mathématique. Très récemment le GMC a été utilisé pour définir les fonctions de corrélation de la LCFT, une théorie qui est apparue pour la première fois en 1981 dans le célèbre article de Polyakov, “Quantum geometry of bosonic strings”. Grâce à ce lien établi entre GMC et LCFT, nous pouvons traduire les techniques de la théorie conforme des champs dans un langage probabiliste pour effectuer des calculs exacts sur les mesures de GMC. Ceci est précisément ce que nous développerons pour le GMC sur le cercle unité. Nous écrirons les équations BPZ qui fournissent des relations non triviales sur le GMC. Le résultat final est la densité de probabilité pour la masse totale de la mesure de GMC sur cercle unité ce qui résout une conjecture établie par Fyodorov et Bouchaud en 2008. Par ailleurs, il s'avère que des techniques similaires permettent également de traiter un autre cas, celui du GMC sur le segment unité, et nous obtiendrons de même des formules qui avaient été conjecturées indépendamment par Ostrovsky et par Fyodorov, Le Doussal, et Rosso en 2009. La dernière partie de cette thèse consiste en la construction de la LCFT sur un domaine possédant la topologie d’une couronne. Nous suivrons les méthodes introduites par David- Kupiainen-Rhodes-Vargas même si de nouvelles techniques seront requises car la couronne possède deux bords et un espace des modules non trivial. Nous donnerons également des preuves plus concises de certains résultats connus
Throughout this PhD thesis we will study two probabilistic objects, Gaussian multiplicative chaos (GMC) measures and Liouville conformal field theory (LCFT). GMC measures were first introduced by Kahane in 1985 and have grown into an extremely important field of probability theory and mathematical physics. Very recently GMC has been used to give a probabilistic definition of the correlation functions of LCFT, a theory that first appeared in Polyakov’s 1981 seminal work, “Quantum geometry of bosonic strings”. Once the connection between GMC and LCFT is established, one can hope to translate the techniques of conformal field theory in a probabilistic framework to perform exact computations on the GMC measures. This is precisely what we develop for GMC on the unit circle. We write down the BPZ equations which lead to non-trivial relations on the GMC. Our final result is an exact probability density for the total mass of the GMC measure on the unit circle. This proves a conjecture of Fyodorov and Bouchaud stated in 2008. Furthermore, it turns out that the same techniques also work on a more difficult model, the GMC on the unit interval, and thus we also prove conjectures put forward independently by Ostrovsky and by Fyodorov, Le Doussal, and Rosso in 2009. The last part of this thesis deals with the construction of LCFT on a domain with the topology of an annulus. We follow the techniques introduced by David-Kupiainen- Rhodes-Vargas although novel ingredients are required as the annulus possesses two boundaries and a non-trivial moduli space. We also provide more direct proofs of known results

3

Huang, Yichao. "Chaos multiplicatif gaussien et applications à la gravité quantique de Liouville." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066623/document.

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Dans cette thèse, nous nous intéressons par des approches probabilistes à la gravité quantique de Liouville, introduite par Polyakov en 1981 sous la forme d'une intégrale de chemin sur les surfaces 2d. Pour définir cette intégrale de chemin avec interaction exponentielle, nous partons du chaos multiplicatif Gaussien, l'outil fondamental pour définir l'exponentielle des champs Gaussiens de corrélation logarithmique. Dans un premier temps, nous généralisons la construction de la gravité quantique de Liouville sur la sphère de Riemann à une autre géométrie avec bord, celle du disque unité. La nouveauté de ce travail réalisé en collaboration avec R.Rhodes et V.Vargas, est d'analyser avec soin le terme du bord dans l'intégrale de chemin ainsi que l'interaction entre la mesure du bord et la mesure du disque. Nous établissons rigoureusement les formules de la théorie conforme des champs en physique, telles que la covariance conforme, la formule KPZ, l'anomalie de Weyl ainsi que la borne de Seiberg. Une borne de Seiberg relaxée dans le cas de la gravité de Liouville à volume total fixé sur le disque est aussi formulée et étudiée. Dans la seconde moitié de cette thèse, nous comparons cette construction à la Polyakov avec une autre approche de la gravité quantique de Liouville. En collaboration avec deux autres jeunes chercheurs J.Aru et X.Sun, nous fournissons une correspondance entre ces deux approches dans un cas simple et important, celui de la sphère de Riemann avec trois points marqués. En mélangeant les techniques de ces deux approches, nous fournissons une nouvelle procédure d'approximation qui permet de relier ces deux différentes approches
In this thesis, we study the theory of Liouville Quantum Gravity via probabilist approach, introduced in the seminal paper of Polyakov in 1981, using path integral formalism on 2d surfaces. To define this path integral with exponential interaction, we started from the theory of Gaussian Multiplicative Chaos in order to define exponential of log-correlated Gaussian fields. In the first part, we generalise the construction of Liouville Quantum Gravity on the Riemann sphere to another geometry, the one of the unit disk. The novelty of this work, in collaboration with R.Rhodes and V.Vargas, is to analyse carefully the boundary term in the path integral formalism and its interaction with the bulk measure. We establish rigorously formulae from Conformal Field Theory in Physics, such as conformal covariance, KPZ relation, conformal anomaly and Seiberg bounds. A relaxed Seiberg bound in the unit volume case of Liouville Quantum Gravity on the disk is also announced and studied. In the second part of this thesis, we compare this construction in the spirit of Polyakov to another approach to the Liouville Quantum Gravity. In collaboration with two other young researchers, J.Aru and X.Sun, we give a correspondance between these two approaches in a simple but conceptually important case, namely the one on the Riemann sphere with three marked points. Using technics coming from these two approches, we give a new way of regularisation procedure that eventually allow us to link these two pictures

4

Sauzedde, Isao. "Windings of the planar Brownian motion and Green’s formula." Thesis, Sorbonne université, 2021. http://www.theses.fr/2021SORUS437.

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On s'intéresse dans cette thèse à l'enlacement du mouvement Brownien plan autour des points, dans la succession des travaux de Wendelin Werner en particulier. Dans le premier chapitre, on motive cette étude par celle du cas des courbes plus lisses que le mouvement Brownien. On y démontre notamment une formule de Green pour l'intégrale de Young, sans hypothèse de simplicité de la courbe. Dans le chapitre 2, on étudie l'aire de l'ensemble des points autour desquels l'enlacement du mouvement brownien est plus grand que N. On donne, au sens presque sûr et dans les espaces Lp, une estimation asymptotique au second ordre de cette aire lorsque N tend vers l'infini. Le chapitre 3 est dévoué à la preuve d'un résultat qui montre que les points de grands enlacements se répartissent de manière très équilibrée le long de la trajectoire. Dans le chapitre 4, on utilise les résultats des deux précédents chapitres pour énoncer une formule de Green pour le mouvement brownien. On étudie aussi l'enlacement moyen de points répartis aléatoirement dans le plan. On montre que cet enlacement moyen converge en distribution (presque surement pour la trajectoire), non pas vers une constante (qui serait alors l’aire de Lévy) mais vers une variable de Cauchy centrée en l’aire de Lévy. Dans les deux derniers chapitres, on applique les idées des précédents chapitres pour définir et étudier l’aire de Lévy du mouvement Brownien lorsque la mesure d’aire sous-jacente n’est plus la mesure de Lebesgue mais une mesure aléatoire particulièrement irrégulière. On traite le cas du chaos multiplicatif gaussien en particulier, mais la méthode s’applique dans un cadre plus général
We study the windings of the planar Brownian motion around points, following the previous works of Wendelin Werner in particular. In the first chapter, we motivate this study by the one of smoother curves. We prove in particular a Green formula for Young integration, without simplicity assumption for the curve. In the second chapter, we study the area of the set of points around which the Brownian motion winds at least N times. We give an asymptotic estimation for this area, up to the second order, both in the almost sure sense and in the Lp spaces, when N goes to infinity.The third chapter is devoted to the proof of a result which shows that the points with large winding are distributed in a very balanced way along the trajectory. In the fourth chapter, we use the results from the two previous chapters to give a new Green formula for the Brownian motion. We also study the averaged winding around randomly distributed points in the plan. We show that, almost surely for the trajectory, this averaged winding converges in distribution, not toward a constant (which would be the Lévy area), but toward a Cauchy distribution centered at the Lévy area. In the last two chapters, we apply the ideas from the previous chapters to define and study the Lévy area of the Brownian motion, when the underlying area measure is not the Lebesgue measure anymore, but instead a random and highly irregular measure. We deal with the case of the Gaussian multiplicative chaos in particular, but the tools can be used in a much more general framework

5

Astoquillca, Aguilar Jhon Kevin. "Gaussian Multiplicative Chaos." Master's thesis, Pontificia Universidad Católica del Perú, 2020. http://hdl.handle.net/20.500.12404/17752.

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La teoría de Kolmogorov-Obukhov-Mandelbrot de disipación de energía en desarrollo de turbulencia se estableció para estudiar el comportamiento caótico de los fluidos. En ausencia de una base matemática rigurosa, Kahane introduce el caos gaussiano multiplicativo como un objeto aleatorio inspirado en la teoría del caos aditivo desarrollada por Wiener. En esta tesis desarrollamos teoría aleatoria en el espacio de medidas de Radon con el objetivo de definir rigurosamente el caos multiplicativo gaussiano. Seguimos el artículo de Kahane y debilitamos algunas condiciones para proporcionar una introducción accesible y autocontenida.
The Kolmogorov-Obukhov-Mandelbrot theory of energy dissipation in turbulence developed was established to study the chaotic behavior of fluids. In the absence of a rigorous mathematical basis, Kahane introduced the Gaussian multiplicative chaos as a random object inspired by the additive chaos theory developed by Wiener. In this thesis we developed random theory in the spaces of Radon measures in order to rigorously define Gaussian multiplicative chaos. We follow Kahane’s paper and weaken some conditions to provide an accessible and selfcontained introduction.

6

Watson, Stephen M. "Frequency demodulation in the presence of multiplicative speckle noise." Thesis, University of Nottingham, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.246382.

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7

Tian, Kuanhou. "Some properties of a class of stochastic heat and wave equations with multiplicative Gaussian noises." Thesis, Loughborough University, 2015. https://dspace.lboro.ac.uk/2134/19611.

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8

Shao, Qiliang. "FPGA Realization of Low Register Systolic Multipliers over GF(2^m)." Wright State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=wright1481808131971019.

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9

Vestin, Albin, and Gustav Strandberg. "Evaluation of Target Tracking Using Multiple Sensors and Non-Causal Algorithms." Thesis, Linköpings universitet, Reglerteknik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-160020.

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Today, the main research field for the automotive industry is to find solutions for active safety. In order to perceive the surrounding environment, tracking nearby traffic objects plays an important role. Validation of the tracking performance is often done in staged traffic scenarios, where additional sensors, mounted on the vehicles, are used to obtain their true positions and velocities. The difficulty of evaluating the tracking performance complicates its development. An alternative approach studied in this thesis, is to record sequences and use non-causal algorithms, such as smoothing, instead of filtering to estimate the true target states. With this method, validation data for online, causal, target tracking algorithms can be obtained for all traffic scenarios without the need of extra sensors. We investigate how non-causal algorithms affects the target tracking performance using multiple sensors and dynamic models of different complexity. This is done to evaluate real-time methods against estimates obtained from non-causal filtering. Two different measurement units, a monocular camera and a LIDAR sensor, and two dynamic models are evaluated and compared using both causal and non-causal methods. The system is tested in two single object scenarios where ground truth is available and in three multi object scenarios without ground truth. Results from the two single object scenarios shows that tracking using only a monocular camera performs poorly since it is unable to measure the distance to objects. Here, a complementary LIDAR sensor improves the tracking performance significantly. The dynamic models are shown to have a small impact on the tracking performance, while the non-causal application gives a distinct improvement when tracking objects at large distances. Since the sequence can be reversed, the non-causal estimates are propagated from more certain states when the target is closer to the ego vehicle. For multiple object tracking, we find that correct associations between measurements and tracks are crucial for improving the tracking performance with non-causal algorithms.

10

Jarrett, Nicholas Walton Daniel. "Nonlinear Prediction in Credit Forecasting and Cloud Computing Deployment Optimization." Diss., 2015. http://hdl.handle.net/10161/9974.

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This thesis presents data analysis and methodology for two prediction problems. The first problem is forecasting midlife credit ratings from personality information collected during early adulthood. The second problem is analysis of matrix multiplication in cloud computing.

The goal of the credit forecasting problem is to determine if there is a link between personality assessments of young adults with their propensity to develop credit in middle age. The data we use is from a long term longitudinal study of over 40 years. We do find an association between credit risk and personality in this cohort Such a link has obvious implications for lenders but also can be used to improve social utility via more efficient resource allocation

We analyze matrix multiplication in the cloud and model I/O and local computation for individual tasks. We established conditions for which the distribution of job completion times can be explicitly obtained. We further generalize these results to cases where analytic derivations are intractable.

We develop models that emulate the multiplication procedure, allowing job times for different deployment parameter settings to be emulated after only witnessing a subset of tasks, or subsets of tasks for nearby deployment parameter settings.

The modeling framework developed sheds new light on the problem of determining expected job completion time for sparse matrix multiplication.

Dissertation

Книги з теми "Multiplicatif gaussien":

1

Rhodes1, Rémi, and Vincent Vargas2. Gaussian multiplicative chaos and Liouville quantum gravity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0012.

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The purpose of this chapter is to explain the probabilistic construction of Polyakov’s Liouville quantum gravity using the theory of Gaussian multiplicative chaos. In particular, this chapter contains a detailed description of the so-called Liouville measures of the theory and their conjectured relation to the scaling limit of large planar maps properly embedded in the sphere. This chapter is rather short and requires no prior knowledge on the topic.

Частини книг з теми "Multiplicatif gaussien":

1

Saksman, Eero, and Christian Webb. "On the Riemann Zeta Function and Gaussian Multiplicative Chaos." In Advancements in Complex Analysis, 473–96. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-40120-7_12.

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2

Chiou, C. W., Y. S. Sun, C. M. Lee, Y. L. Chiu, J. M. Lin, and C. Y. Lee. "Problems on Gaussian Normal Basis Multiplication for Elliptic Curve Cryptosystem." In Advances in Intelligent Systems and Computing, 201–7. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-23207-2_20.

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3

Wang, Zhen, Xiaozhe Wang, and Shuqin Fan. "Concurrent Error Detection Architectures for Field Multiplication Using Gaussian Normal Basis." In Information Security, Practice and Experience, 96–109. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-12827-1_8.

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4

Fedorov, Eugene, Tetyana Utkina, and Tetyana Neskorodeva. "A Voice Signal Filtering Methods for Speaker Biometric Identification." In Recent Advances in Biometrics [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.101975.

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The preliminary stage of the personality biometric identification on a voice is voice signal filtering. For biometric identification are considered and in number investigated the following methods of noise suppression in a voice signal. The smoothing adaptive linear time filtering (algorithm of the minimum root mean square error, an algorithm of recursive least squares, an algorithm of Kalman filtering, a Lee algorithm), the smoothing adaptive linear frequency filtering (the generalized method, the MLEE (maximum likelihood envelope estimation) method, a wavelet analysis with threshold processing (universal threshold, SURE (Stein’s Unbiased Risk Estimator)-threshold, minimax threshold, FDR (False Discovery Rate)-threshold, Bayesian threshold were used), the smoothing non-adaptive linear time filtering (the arithmetic mean filter, the normalized Gauss’s filter, the normalized binomial filter), the smoothing nonlinear filtering (geometric mean filter, the harmonic mean filter, the contraharmonic filter, the α-trimmed mean filter, the median filter, the rank filter, the midpoint filter, the conservative filter, the morphological filter). Results of a numerical research of denoising methods for voice signals people from the TIMIT (Texas Instruments and Massachusetts Institute of Technology) database which were noise an additive Gaussian noise and multiplicative Gaussian noise were received.

5

Pawlowsky-Glahn, Vera, and Richardo A. Olea. "Cokriging." In Geostatistical Analysis of Compositional Data. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780195171662.003.0011.

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The problem of estimation of a coregionalization of size q using cokriging will be discussed in this chapter. Cokriging—a multivariate extension of kriging—is the usual procedure applied to multivariate regionalized problems within the framework of geostatistics. Its fundament is a distribution-free, linear, unbiased estimator with minimum estimation variance, although the absence of constraints on the estimator is an implicit assumption that the multidimensional real space is the sample space of the variables under consideration. If a multivariate normal distribution can be assumed for the vector random function, then the simple kriging estimator is identical with the conditional expectation, given a sample of size N. See Journel (1977, pp. 576-577), Journel (1980, pp. 288-290), Cressie (1991, p. 110), and Diggle, Tawn, and Moyeed (1998, p. 300) for further details. This estimator is in general the best possible linear estimator, as it is unbiased and has minimum estimation variance, but it is not very robust in the face of strong departures from normality. Therefore, for the estimation of regionalized compositions other distributions must also be taken into consideration. Recall that compositions cannot follow a multivariate normal distribution by definition, their sample space being the simplex. Consequently, regionalized compositions in general cannot be modeled under explicit or implicit assumptions of multivariate Gaussian processes. Here only the multivariate lognormal and additive logistic normal distributions will be addressed. Besides the logarithmic and additive logratio transformations, others can be applied, such as the multivariate Box-Cox transformation, as stated by Andrews et al. (1971), Rayens and Srinivasan (1991), and Barcelo-Vidal (1996). Furthermore, distributions such as the multiplicative logistic normal distribution introduced by Aitchison (1986, p. 131) or the additive logistic skew-normal distribution defined by Azzalini and Dalla Valle (1996) can be investigated in a similar fashion. References to the literature for the fundamental principles of the theory discussed in this chapter were given in Chapter 2. Among those, special attention is drawn to the work of Myers (1982), where matrix formulation of cokriging was first presented and the properties included in the first section of this chapter were stated.

Тези доповідей конференцій з теми "Multiplicatif gaussien":

1

Muravev, Nikita, and Aleksandr Petiushko. "Certified Robustness via Randomized Smoothing over Multiplicative Parameters of Input Transformations." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/467.

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Currently the most popular method of providing robustness certificates is randomized smoothing where an input is smoothed via some probability distribution. We propose a novel approach to randomized smoothing over multiplicative parameters. Using this method we construct certifiably robust classifiers with respect to a gamma correction perturbation and compare the result with classifiers obtained via other smoothing distributions (Gaussian, Laplace, uniform). The experiments show that asymmetrical Rayleigh distribution allows to obtain better certificates for some values of perturbation parameters. To the best of our knowledge it is the first work concerning certified robustness against the multiplicative gamma correction transformation and the first to study effects of asymmetrical distributions in randomized smoothing.

2

Ye, Yalan, Zhi-lin Zhang, Shaozhi Wu, and Xiaobin Zhou. "Improved Multiplicative Orthogonal-Group Based ICA for Separating Mixed Sub-Gaussian and Super-Gaussian Sources." In 2006 International Conference on Communications, Circuits and Systems. IEEE, 2006. http://dx.doi.org/10.1109/icccas.2006.284649.

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3

Tian, Xuemei, Xingiun Wu, and Guoqiang Bai. "Towards Low Space Complexity Design of Gaussian Normal Basis Multiplication." In 2019 IEEE International Conference on Electron Devices and Solid-State Circuits (EDSSC). IEEE, 2019. http://dx.doi.org/10.1109/edssc.2019.8754096.

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4

Kiyono, Ken, Zbigniew R. Struzik, and Yoshiharu Yamamoto. "Characterisation of non-Gaussian fluctuations in multiplicative log-normal models." In NOISE AND FLUCTUATIONS: 19th International Conference on Noise and Fluctuations; ICNF 2007. AIP, 2007. http://dx.doi.org/10.1063/1.2759758.

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5

Phalakarn, Kittiphon, and Athasit Surarerks. "A Matrix Decomposition Method for Odd-Type Gaussian Normal Basis Multiplication." In 2018 3rd International Conference on Computer and Communication Systems (ICCCS). IEEE, 2018. http://dx.doi.org/10.1109/ccoms.2018.8463251.

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6

Palahina, Elena, and Volodymyr Palahin. "Signal detection in additive-multiplicative non-Gaussian noise using higher order statistics." In 2016 26th International Conference Radioelektronika (RADIOELEKTRONIKA). IEEE, 2016. http://dx.doi.org/10.1109/radioelek.2016.7477367.

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7

Trujillo-Olaya, Vladimir, Jaime Velasco-Medina, and Julio C. Lopez-Hernandez. "Efficient Hardware Implementations for the Gaussian Normal Basis Multiplication Over GF(2163)." In 2007 3rd Southern Conference on Programmable Logic. IEEE, 2007. http://dx.doi.org/10.1109/spl.2007.371722.

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8

Sokouti, Massoud, and Ali Zakerolhosseini. "Increasing the speed of QTRU using the Gaussian and Brent equations multiplication." In 2014 22nd Iranian Conference on Electrical Engineering (ICEE). IEEE, 2014. http://dx.doi.org/10.1109/iraniancee.2014.6999653.

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9

Ciblat, P., and M. Ghogho. "ZIV-ZAKAI bound for harmonic retrieval in multiplicative and additive gaussian noise." In 2005 Microwave Electronics: Measurements, Identification, Applications. IEEE, 2005. http://dx.doi.org/10.1109/ssp.2005.1628658.

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10

Artyushenko, V. M., V. I. Volovach, and M. V. Shakursky. "The demodulation signal under the influence of additive and multiplicative non-Gaussian noise." In 2016 IEEE East-West Design & Test Symposium (EWDTS). IEEE, 2016. http://dx.doi.org/10.1109/ewdts.2016.7807704.

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