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Zeitschriftenartikel zum Thema „Bernoulli-Gaussian“

Autor: Grafiati

Veröffentlicht am 25. Mai 2024

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1

Hrabovets, Anastasiia. "Feynman diagrams and their limits for Bernoulli noise." Theory of Stochastic Processes 27(43), no. 1 (2023): 11–30. http://dx.doi.org/10.3842/tsp-4311781209-33.

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In this article, we will construct an approximation of Gaussian white noise based on the sequence of Bernoulli random variables and define Wick products and the stochastic exponent for the Bernoulli case. Here we will propose a method to calculate the expectations of Wick products for Bernoulli noise using diagrams, that converge to Feynman diagrams in the Gaussian case. We will prove that orthogonal polynomials for Bernoulli noise converge to Hermite polynomials, which form an orthogonal system in the Gaussian case.

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2

Törő, Olivér, Tamás Bécsi, Szilárd Aradi, and Péter Gáspár. "IMM Bernoulli Gaussian Particle Filter." IFAC-PapersOnLine 51, no. 22 (2018): 274–79. http://dx.doi.org/10.1016/j.ifacol.2018.11.554.

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3

Xie, Shaohao, Shaohua Zhuang, and Yusong Du. "Improved Bernoulli Sampling for Discrete Gaussian Distributions over the Integers." Mathematics 9, no. 4 (2021): 378. http://dx.doi.org/10.3390/math9040378.

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Discrete Gaussian sampling is one of the fundamental mathematical tools for lattice-based cryptography. In this paper, we revisit the Bernoulli(-type) sampling for centered discrete Gaussian distributions over the integers, which was proposed by Ducas et al. in 2013. Combining the idea of Karney’s algorithm for sampling from the Bernoulli distribution Be−1/2, we present an improved Bernoulli sampling algorithm. It does not require the use of floating-point arithmetic to generate a precomputed table, as the original Bernoulli sampling algorithm did. It only needs a fixed look-up table of very small size (e.g., 128 bits) that stores the binary expansion of ln2. We also propose a noncentered version of Bernoulli sampling algorithm for discrete Gaussian distributions with varying centers over the integers. It requires no floating-point arithmetic and can support centers of precision up to 52 bits. The experimental results show that our proposed algorithms have a significant improvement in the sampling efficiency as compared to other rejection algorithms.

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4

Finamore, Weiler, Marcelo Pinho, Manish Sharma, and Moises Ribeiro. "Modeling Noise as a Bernoulli-Gaussian Process." Journal of Communication and Information Systems 38 (2023): 175–86. http://dx.doi.org/10.14209/jcis.2023.20.

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Transmission medium is always perturbed by noise with a random nature which can be characterized by taking a sequence of noise samples and, after analyzing the sequence, attributing a probabilistic model to represent the randomness of the noise. If thermal noise (receiver generated) is the only noise impairing the transmission (our only focus is digital transmission) the memoryless stationary discrete-time Gaussian process is the best model to probabilistically represent the noise. The mathematical representation of the transmission medium in such a situation yields the well known Gaussian Channel. As Information Theory points out, for a fixed noise power, the Gaussian channel is the worst channel to send information through. If thermal noise is not the only noise impairing the transmission (as in sonar communication and power line communication) finding the probabilistic model other than the single-parameter Gaussian process, which best match the noise can much improve the communication system design. The Bernoulli-Gaussian process, a three parameters model, is a common considered option. Finding the three parameters of the Bernoulli-Gaussian model (from known noise samples) is a formidable task that can be made simpler by considering the (original) results presented in the current paper. The Bernoulli-Gaussian model can be characterized, analytically, by using the noise power and two additional quantities: the expectation of the absolute value of the noise process plus the expected value of the third power of the absolute value. In practice the parameters would be calculated using estimates of the mentioned expected values. The communication system design can be much improved if a well fit Bernoulli-Gaussian stochastic process is selected to model the noise. This is an alternative to model the communication using power lines which is often modeled as Middleton Class-A. The rate harvested when modeling the medium as a Bernoulli-Gaussian channel, it is shown, is increased when compared to modeling the medium with the easily obtained Gaussian channel.

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5

Bobkov, Sergey G., Friedrich Gotze, and Christian Houdre. "On Gaussian and Bernoulli Covariance Representations." Bernoulli 7, no. 3 (2001): 439. http://dx.doi.org/10.2307/3318495.

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6

Lavielle, Marc. "Bayesian deconvolution of Bernoulli-Gaussian processes." Signal Processing 33, no. 1 (1993): 67–79. http://dx.doi.org/10.1016/0165-1684(93)90079-p.

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7

De La Rue, Thierry. "Systèmes dynamiques gaussiens d'entropie nulle, lâchement et non lâchement Bernoulli." Ergodic Theory and Dynamical Systems 16, no. 2 (1996): 379–404. http://dx.doi.org/10.1017/s0143385700008865.

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AbstractWe construct two real Gaussian dynamical systems of zero entropy; the first one is not loosely Bernoulli, and the second is a loosely Bernoulli Gaussian-Kronecker system. To get loose-Bernoullicity for the second system, we prove and use a property of planar Brownian motion on [0, 1]: we can recover the whole trajectory knowing only some angles formed by the motion.

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8

Al-Zuhairi, Dheyaa T., and Abbas Salman Hameed. "DOA estimation under Bernoulli-Gaussian impulsive noise." IOP Conference Series: Materials Science and Engineering 1090, no. 1 (2021): 012096. http://dx.doi.org/10.1088/1757-899x/1090/1/012096.

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9

Chong-Yung Chi and J. Mendel. "Viterbi algorithm detector for Bernoulli-Gaussian processes." IEEE Transactions on Acoustics, Speech, and Signal Processing 33, no. 3 (1985): 511–19. http://dx.doi.org/10.1109/tassp.1985.1164580.

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10

Talagrand, Michel. "Gaussian averages, Bernoulli averages, and Gibbs' measures." Random Structures and Algorithms 21, no. 3-4 (2002): 197–204. http://dx.doi.org/10.1002/rsa.10059.

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11

Thoriq Nurchaidir, Widodo, and Bambang Prasetya Adhi. "KLASIFIKASI GENRE MUSIK MENGGUNAKAN ALGORITMA NAÏVE BAYES CLASSIFIER UNTUK LAYANAN STREAMING YOUTUBE." PINTER : Jurnal Pendidikan Teknik Informatika dan Komputer 7, no. 1 (2023): 1–6. http://dx.doi.org/10.21009/pinter.7.1.1.

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Genre musik adalah cara yang paling umum digunakan untuk mengorganisasi database musik digital. Klasifikasi merupakan pengelompokan data menjadi beberapa bagian yang telah ditentukan sehingga dapat mempermudah pengelolaan dan pencarian file musik bedasarkan genre musiknya. Penelitian ini melakukan klasifikasi genre musik untuk layanan streaming youtube. Metode penelitian yang digunakan pada penelitian ini adalah penelitian eksperimen laboratorium. Model pada penelitian mengklasifikasikan file musik menggunakan 3 jenis Algoritma Naïve Bayes Classifier yaitu: Gaussian Naïve Bayes, Bernoulli Naïve Bayes, dan Multinomial Naïve Bayes. Data yang digunakan adalah dataset GTZAN dan klip video yang diunduh dari layanan streaming youtube. Nilai akurasi yang dihasilkan oleh Gaussian Naïve Bayes adalah 63%, nilai akurasi yang dihasilkan oleh Bernoulli Naïve Bayes adalah 33% dan nilai akurasi yang dihasilkan oleh Multinomial Naïve Bayes adalah 10%. Jenis algoritma Naïve Bayes dengan nilai akurasi tertinggi dianggap sebagai jenis algoritma paling baik dalam melakukan klasifikasi. Hasil pengujian menyatakan bahwa Gaussian Naïve Bayes merupakan algoritma yang paling baik dalam melakukanm klasifikasi genre musik dibandingkan Bernoulli Naïve Bayes dan Multinomial Naïve Bayes.

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12

Miniailyk, Y. "Gaussian noise related to generalised Ehrenfest model." Theory of Stochastic Processes 26(42), no. 1 (2022): 21–26. http://dx.doi.org/10.37863/tsp-0919442573-40.

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In this article we consider the generalization of Ehrenfest model, where at each moment of time not 1 but some k of n particles go from one box to another. We describe this process by a sequence of Bernoulli random vectors. We define related Bernoulli noise on a set of continuous functions for different times, and prove that it converges to Ornstein-Uhlenbeck sequence of Gaussian white noises when number of particles tends to infinity.

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13

Sukumar, C. V., and Andrew Hodges. "Quantum algebras and parity-dependent spectra." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2086 (2007): 2415–27. http://dx.doi.org/10.1098/rspa.2007.0003.

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We study the structure of a quantum algebra in which a parity-violating term modifies the standard commutation relation between the creation and annihilation operators of the simple harmonic oscillator. We discuss several useful applications of the modified algebra. We show that the Bernoulli and Euler numbers arise naturally in a special case. We also show a connection with Gaussian and non-Gaussian squeezed states of the simple harmonic oscillator. Such states have been considered in quantum optics. The combinatorial theory of Bernoulli and Euler numbers is developed and used to calculate matrix elements for squeezed states.

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14

Lavenia, Nur Lickha, and Reisa Permatasari. "Sentiment Analysis on Twitter Social Media Regarding Depression Disorder Using the Naive Bayes Method." CoreID Journal 1, no. 2 (2023): 66–74. http://dx.doi.org/10.60005/coreid.v1i2.14.

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Depression disorder is a serious issue in mental health that affects many individuals worldwide. This research analyzes the sentiments related to depression disorder on Twitter using the Naïve Bayes method. Depression-related tweet data was collected through snscrape and processed to eliminate irrelevant information. Three Naïve Bayes methods, namely Multinomial, Gaussian, and Bernoulli, were compared to classify positive, negative, or neutral sentiments in each tweet. The results of the study indicate that Multinomial Naïve Bayes exhibited the best performance with an accuracy rate of 90.13%, followed by Gaussian Naïve Bayes (88.38%), and Bernoulli Naïve Bayes (85.37%).

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15

Soussen, Charles, Jérôme Idier, David Brie, and Junbo Duan. "From Bernoulli–Gaussian Deconvolution to Sparse Signal Restoration." IEEE Transactions on Signal Processing 59, no. 10 (2011): 4572–84. http://dx.doi.org/10.1109/tsp.2011.2160633.

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16

Sheri, Ahmad Muqeem, Muhammad Aasim Rafique, Moongu Jeon, and Witold Pedrycz. "Background subtraction using Gaussian–Bernoulli restricted Boltzmann machine." IET Image Processing 12, no. 9 (2018): 1646–54. http://dx.doi.org/10.1049/iet-ipr.2017.1055.

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17

Chi, C. Y., and W. T. Chen. "Recursive smlr deconvolution algorithm for bernoulli-gaussian signals." IEE Proceedings F Radar and Signal Processing 138, no. 3 (1991): 263. http://dx.doi.org/10.1049/ip-f-2.1991.0034.

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18

Yasuda, Muneki. "Effective sampling on Gaussian-Bernoulli restricted Boltzmann machines." Nonlinear Theory and Its Applications, IEICE 15, no. 2 (2024): 217–25. http://dx.doi.org/10.1587/nolta.15.217.

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19

Ren, Yayun, and Benlian Xu. "A Quantitative Analysis on Two RFS-Based Filtering Methods for Multicell Tracking." Mathematical Problems in Engineering 2014 (2014): 1–17. http://dx.doi.org/10.1155/2014/495765.

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Multiobject filters developed from the theory of random finite sets (RFS) have recently become well-known methods for solving multiobject tracking problem. In this paper, we present two RFS-based filtering methods, Gaussian mixture probability hypothesis density (GM-PHD) filter and multi-Bernoulli filter, to quantitatively analyze their performance on tracking multiple cells in a series of low-contrast image sequences. The GM-PHD filter, under linear Gaussian assumptions on the cell dynamics and birth process, applies the PHD recursion to propagate the posterior intensity in an analytic form, while the multi-Bernoulli filter estimates the multitarget posterior density through propagating the parameters of a multi-Bernoulli RFS that approximates the posterior density of multitarget RFS. Numerous performance comparisons between the two RFS-based methods are carried out on two real cell images sequences and demonstrate that both yield satisfactory results that are in good agreement with manual tracking method.

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20

Chi, Luo-jia, Xin-xi Feng, and Lu Miao. "Generalized Labeled Multi-Bernoulli Extended Target Tracking Based on Gaussian Process Regression." MATEC Web of Conferences 176 (2018): 01017. http://dx.doi.org/10.1051/matecconf/201817601017.

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For the problems that Gamma Gaussian Inverse Wishart Cardinalized Probability Hypothesis Density (GGIW-CPHD) filter cannot accurately estimate the extended target shape and has a bad tracking performance under the condition of low SNR, a new generalized labeled multi-Bernoulli algorithm based on Gaussian process regression is proposed. The algorithm adopts the star convex to model the extended target, and realizes the online learning of the Gaussian process by constructing the state space model to complete the estimation of the extended target shape. At the same time, in the low SNR environment, the target motion state is tracked by the good tracking performance of the generalized label Bernoulli filter. Simulation results show that for any target with unknown shape, the proposed algorithm can well offer its extended shape and in the low SNR environment it can greatly improve the accuracy and stability of target tracking.

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21

Dai, G. Z., and J. M. Mendel. "Maximum a posteriori estimation of multichannel Bernoulli-Gaussian sequences." IEEE Transactions on Information Theory 35, no. 1 (1989): 181–83. http://dx.doi.org/10.1109/18.42189.

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22

Wang, Li-Xing, and Guan-Zhong Dai. "New Recursive Smoothing Algorithms for Bernoulli-gaussian Input Sequence." IFAC Proceedings Volumes 21, no. 9 (1988): 781–86. http://dx.doi.org/10.1016/s1474-6670(17)54823-5.

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23

Chi, Chang-Yung, and Wu-Tan Chen. "Maximum-likelihood blind deconvolution: non-white Bernoulli-Gaussian case." IEEE Transactions on Geoscience and Remote Sensing 29, no. 5 (1991): 790–95. http://dx.doi.org/10.1109/36.83996.

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24

CARD, HOWARD C. "STOCHASTIC RADIAL BASIS FUNCTIONS." International Journal of Neural Systems 11, no. 02 (2001): 203–10. http://dx.doi.org/10.1142/s0129065701000552.

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Stochastic signal processing can implement gaussian activation functions for radial basis function networks, using stochastic counters. The statistics of neural inputs which control the increment and decrement operations of the counter are governed by Bernoulli distributions. The transfer functions relating the input and output pulse probabilities can closely approximate gaussian activation functions which improve with the number of states in the counter. The means and variances of these gaussian approximations can be controlled by varying the output combinational logic function of the binary counter variables.

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25

Xu, Shuo. "Bayesian Naïve Bayes classifiers to text classification." Journal of Information Science 44, no. 1 (2016): 48–59. http://dx.doi.org/10.1177/0165551516677946.

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Text classification is the task of assigning predefined categories to natural language documents, and it can provide conceptual views of document collections. The Naïve Bayes (NB) classifier is a family of simple probabilistic classifiers based on a common assumption that all features are independent of each other, given the category variable, and it is often used as the baseline in text classification. However, classical NB classifiers with multinomial, Bernoulli and Gaussian event models are not fully Bayesian. This study proposes three Bayesian counterparts, where it turns out that classical NB classifier with Bernoulli event model is equivalent to Bayesian counterpart. Finally, experimental results on 20 newsgroups and WebKB data sets show that the performance of Bayesian NB classifier with multinomial event model is similar to that of classical counterpart, but Bayesian NB classifier with Gaussian event model is obviously better than classical counterpart.

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26

Ünal, Gazanfer. "Stochastic symmetries of Wick type stochastic ordinary differential equations." International Journal of Modern Physics: Conference Series 38 (January 2015): 1560079. http://dx.doi.org/10.1142/s2010194515600794.

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We consider Wick type stochastic ordinary differential equations with Gaussian white noise. We define the stochastic symmetry transformations and Lie equations in Kondratiev space [Formula: see text]. We derive the determining system of Wick type stochastic partial differential equations with Gaussian white noise. Stochastic symmetries for stochastic Bernoulli, Riccati and general stochastic linear equation in [Formula: see text] are obtained. A stochastic version of canonical variables is also introduced.

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27

Shan, Chenghao, Weidong Zhou, Yefeng Yang, and Hanyu Shan. "A New Variational Bayesian-Based Kalman Filter with Unknown Time-Varying Measurement Loss Probability and Non-Stationary Heavy-Tailed Measurement Noise." Entropy 23, no. 10 (2021): 1351. http://dx.doi.org/10.3390/e23101351.

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In this paper, a new variational Bayesian-based Kalman filter (KF) is presented to solve the filtering problem for a linear system with unknown time-varying measurement loss probability (UTVMLP) and non-stationary heavy-tailed measurement noise (NSHTMN). Firstly, the NSHTMN was modelled as a Gaussian-Student’s t-mixture distribution via employing a Bernoulli random variable (BM). Secondly, by utilizing another Bernoulli random variable (BL), the form of the likelihood function consisting of two mixture distributions was converted from a weight sum to an exponential product and a new hierarchical Gaussian state-space model was therefore established. Finally, the system state vector, BM, BL, the intermediate random variables, the mixing probability, and the UTVMLP were jointly inferred by employing the variational Bayesian technique. Simulation results revealed that in the scenario of NSHTMN, the proposed filter had a better performance than current algorithms and further improved the estimation accuracy of UTVMLP.

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28

Ristic, Branko, Daniel Angley, Sofia Suvorova, et al. "Gaussian mixture multitarget–multisensor Bernoulli tracker for multistatic sonobuoy fields." IET Radar, Sonar & Navigation 11, no. 12 (2017): 1790–97. http://dx.doi.org/10.1049/iet-rsn.2017.0077.

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29

Zhang, Ji, Hongjun Wang, Jielei Chu, Shudong Huang, Tianrui Li, and Qigang Zhao. "Improved Gaussian–Bernoulli restricted Boltzmann machine for learning discriminative representations." Knowledge-Based Systems 185 (December 2019): 104911. http://dx.doi.org/10.1016/j.knosys.2019.104911.

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30

Kim, T. "q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients." Russian Journal of Mathematical Physics 15, no. 1 (2008): 51–57. http://dx.doi.org/10.1134/s1061920808010068.

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31

Ge, D., J. Idier, and E. Le Carpentier. "Enhanced sampling schemes for MCMC based blind Bernoulli–Gaussian deconvolution." Signal Processing 91, no. 4 (2011): 759–72. http://dx.doi.org/10.1016/j.sigpro.2010.08.009.

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32

Batenkov, K. A. "Estimation of the Parameters of a Bernoulli–Gaussian Communications Channel." Measurement Techniques 61, no. 6 (2018): 572–78. http://dx.doi.org/10.1007/s11018-018-1467-5.

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33

Foudopoulos, P., S. Kollias, and C. Halkias. "An efficient approach to the detection of Bernoulli-Gaussian processes." Automatica 30, no. 6 (1994): 1009–13. http://dx.doi.org/10.1016/0005-1098(94)90194-5.

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34

Yu, Nam Yul. "Indistinguishability and Energy Sensitivity of Gaussian and Bernoulli Compressed Encryption." IEEE Transactions on Information Forensics and Security 13, no. 7 (2018): 1722–35. http://dx.doi.org/10.1109/tifs.2018.2800726.

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35

Goussard, Y., and G. Demoment. "Recursive deconvolution of Bernoulli-Gaussian processes using a MA representation." IEEE Transactions on Geoscience and Remote Sensing 27, no. 4 (1989): 384–94. http://dx.doi.org/10.1109/36.29558.

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36

Acala, Nestor Gonzales. "A Unification of the Generalized Multiparameter Apostol-type Bernoulli, Euler, Fubini, and Genocchi Polynomials of Higher Order." European Journal of Pure and Applied Mathematics 13, no. 3 (2020): 587–607. http://dx.doi.org/10.29020/nybg.ejpam.v13i3.3757.

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Most unifications of the classical or generalized Bernoulli, Euler, and Genocchi polynomials involve unifying any two or all of the three special types of polynomials (see, [1, 4, 9, 18, 19,21, 24–26, 30, 31]). In this paper, we introduce a new class of multiparameter Fubini-type gener-alized polynomials that unifies four families of higher order generalized Apostol-type polynomials such as the Apostol-Bernoulli, Apostol-Euler, Apostol-Genocchi, and Apostol-Fubini polynomials. Moreover, we obtain an explicit formula of these unified generalized polynomials in terms of the Gaussian hypergeometric function, and establish several symmetry identities.

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37

DE LA RUE, THIERRY. "L'induction ne donne pas toutes les mesures spectrales." Ergodic Theory and Dynamical Systems 18, no. 6 (1998): 1447–66. http://dx.doi.org/10.1017/s0143385798118059.

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We show here that some finite measure on $[-\pi,\pi]$ can never be obtained as a spectral measure of a transformation induced by a rotation. For this, we propose a new way to build a Kronecker set, which leads to a non loosely Bernoulli Gaussian–Kronecker automorphism.On montre ici qu'une certaine mesure finie sur $[-\pi,\pi]$ ne peut jamais être obtenue comme mesure spectrale d'une transformation induite par une rotation. On propose pour cela une nouvelle façon de construire un ensemble de Kronecker, qui permet de voir que certains systèmes dynamiques gaussiens–Kronecker ne sont pas lâchement Bernoulli.

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38

Wang, Ping, Liang Ma, and Kai Xue. "Efficient Approximation of the Labeled Multi-Bernoulli Filter for Online Multitarget Tracking." Mathematical Problems in Engineering 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/8742897.

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Online tracking time-varying number of targets is a challenging issue due to measurement noise, target birth or death, and association uncertainty, especially when target number is large. In this paper, we propose an efficient approximation of the Labeled Multi-Bernoulli (LMB) filter to perform online multitarget state estimation and track maintenance efficiently. On the basis of the original LMB filer, we propose a target posterior approximation technique to use a weighted single Gaussian component representing each individual target. Moreover, we present the Gaussian mixture implementation of the proposed efficient approximation of the LMB filter under linear, Gaussian assumptions on the target dynamic model and measurement model. Numerical results verify that our proposed efficient approximation of the LMB filer achieves accurate tracking performance and runs several times faster than the original LMB filer.

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39

Zhang, Zijing, Fei Zhang, and Chuantang Ji. "Multi-robot cardinality-balanced multi-Bernoulli filter simultaneous localization and mapping method." Measurement Science and Technology 33, no. 3 (2021): 035101. http://dx.doi.org/10.1088/1361-6501/ac3784.

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Abstract In order to improve the simultaneous localization and mapping (SLAM) accuracy of mobile robots in complex indoor environments, the multi-robot cardinality-balanced multi-Bernoulli filter SLAM (MR-CBMber-SLAM) method is proposed. First of all, this method introduces a multi-Bernoulli filter based on the random finite set (RFS) theory to solve the complex data association problem. This method aims to overcome the problem that the multi-Bernoulli filter will overestimate the aspect of SLAM map feature estimation, and combines the strategy of balancing cardinality with a multi-Bernoulli filter. What is more, in order to further improve the accuracy and operating efficiency of SLAM, a multi-robot strategy and a multi-robot Gaussian information-fusion method are proposed. In the experiment, the MR-CBMber-SLAM method is compared with the multi-vehicle probability hypothesis density SLAM (MV-PHD-SLAM) method. The experimental results show that the MR-CBMber-SLAM method is better than MV-PHD-SLAM method. Therefore, it effectively verifies that the MR-CBMber-SLAM method is more adaptable to a complex indoor environment.

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40

Qian, Wei. "Gaussian estimation of first order time series models with Bernoulli observations." Stochastic Processes and their Applications 27 (1987): 85–96. http://dx.doi.org/10.1016/0304-4149(87)90007-x.

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41

Idier, J., and Y. Goussard. "Stack algorithm for recursive deconvolution of Bernoulli-Gaussian processes (seismic exploration)." IEEE Transactions on Geoscience and Remote Sensing 28, no. 5 (1990): 975–78. http://dx.doi.org/10.1109/36.58988.

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42

Yuan, Xianghui, Feng Lian, and Chongzhao Han. "Multiple-Model Cardinality Balanced Multitarget Multi-Bernoulli Filter for Tracking Maneuvering Targets." Journal of Applied Mathematics 2013 (2013): 1–16. http://dx.doi.org/10.1155/2013/727430.

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By integrating the cardinality balanced multitarget multi-Bernoulli (CBMeMBer) filter with the interacting multiple models (IMM) algorithm, an MM-CBMeMBer filter is proposed in this paper for tracking multiple maneuvering targets in clutter. The sequential Monte Carlo (SMC) method is used to implement the filter for generic multi-target models and the Gaussian mixture (GM) method is used to implement the filter for linear-Gaussian multi-target models. Then, the extended Kalman (EK) and unscented Kalman filtering approximations for the GM-MM-CBMeMBer filter to accommodate mildly nonlinear models are described briefly. Simulation results are presented to show the effectiveness of the proposed filter.

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D. Le, Anh, Hung V. Vu, Nghi H. Tran, and Vo Nguyen Quoc Bao. "Capacity of Bernoulli-Gaussian Interference Channels in Rayleigh Fading with Full CSI." Journal of Science and Technology: Issue on Information and Communications Technology 1 (August 31, 2015): 53. http://dx.doi.org/10.31130/jst.2015.12.

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In this paper, we investigate the channel capacity of a Bernoulli-Gaussian (BG) interference channel in Rayleigh fading when the channel state information (CSI) is known at both the transmitter and receiver via tight lower and upper bounds. Specifically, we first derive an upper bound on the channel capacity assuming a Gaussian-distributed output. Under this assumption, an optimal power adaptation scheme is established and the upper-bound is obtained in closed-form. By assuming a Gaussian-distributed input, we then adopt the derived power adaptation scheme to establish a lower bound on channel capacity. A simple approximation of the instantaneous output entropy using a piecewise-linear curve fitting(PWLCF)-based scheme is then developed, which provides a closed-form estimation of the lower bound with a predetermined error level. Finally, a comparison between the derived upper and lower bounds are made. Both analytical and numerical results show that these two bounds are tight in a wide range of input power levels and they can be used effectively to estimate the channel capacity.

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Gloter, A., I. Honoré, and D. Loukianova. "Approximation of the invariant distribution for a class of ergodic jump diffusions." ESAIM: Probability and Statistics 24 (2020): 883–913. http://dx.doi.org/10.1051/ps/2020023.

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In this article, we approximate the invariant distribution ν of an ergodic Jump Diffusion driven by the sum of a Brownian motion and a Compound Poisson process with sub-Gaussian jumps. We first construct an Euler discretization scheme with decreasing time steps. This scheme is similar to those introduced in Lamberton and Pagès Bernoulli 8 (2002) 367-405. for a Brownian diffusion and extended in F. Panloup, Ann. Appl. Probab. 18 (2008) 379-426. to a diffusion with Lévy jumps. We obtain a non-asymptotic quasi Gaussian (asymptotically Gaussian) concentration bound for the difference between the invariant distribution and the empirical distribution computed with the scheme of decreasing time step along appropriate test functions f such that f − ν(f) is a coboundary of the infinitesimal generator.

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Chandra, Tapas K., and Subhashis Ghosal. "On Extensions of an Inequality of Kolmogorov." Calcutta Statistical Association Bulletin 47, no. 1-2 (1997): 1–10. http://dx.doi.org/10.1177/0008068319970101.

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The inequality of Kolmogorov (Sankhya, 1963) has been extended to a sequence of independent sub-Gaussian and other random variables. All the earlier results in the literature on this problem concerned only on the very special case of Bernoulli variables. We use martingale inequalities to establish a key result. A similar inequality is also proved for U-statistics based on exchangeable random variables.

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Taslim, Taslim, Susi Handayani, and Fajrizal Fajrizal. "Kinerja Komparatif Optimasi Algoritma Naive Bayes dalam Klasifikasi Teks untuk Uji Klinis Kanker." Jurnal Eksplora Informatika 13, no. 1 (2023): 113–23. http://dx.doi.org/10.30864/eksplora.v13i1.994.

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Teknik klasifikasi teks dalam pemrosesan bahasa alami memegang peranan penting dalam mengelompokkan data digital ke dalam kategori yang telah ditentukan sebelumnya. Khususnya dalam bidang medis, klasifikasi teks klinis sangat penting untuk memahami dokumen medis, terutama teks klinis tentang kanker. Penelitian ini bertujuan untuk membandingkan kinerja tiga varian algoritma Naive Bayes yaitu Multinomial, Bernoulli, dan Gaussian, pada data uji klinis kanker. Untuk mengoptimalkan kinerja algoritma, kami menggunakan pendekatan GridSearch dan cross-validation dengan k-fold (k=10). Pilihan algoritma memiliki pengaruh signifikan terhadap akurasi, presisi, recall, dan metrik kinerja lainnya. Melalui perbandingan varian Naive Bayes, kami dapat mengidentifikasi algoritma terbaik untuk dataset dan tugas klasifikasi teks klinis kanker. Hasil analisis menunjukkan bahwa Bernoulli Naive Bayes mencapai akurasi 0,79, presisi 0,88, dan recall 0,68. Sementara itu, Gaussian Naive Bayes mencapai akurasi 0,76, presisi 0,83, dan recall 0,65. Algoritma Multinomial Naive Bayes berhasil mencapai akurasi 0,80, presisi 0,84, dan recall 0,75. Penelitian ini memberikan panduan dalam memilih algoritma yang sesuai dengan tujuan dan prioritas klasifikasi. Hal ini dapat dikembangkan lebih lanjut dalam bahasa alami medis dan proses pengambilan keputusan medis. Melalui pengetahuan yang diperoleh dari penelitian ini, analisis teks medis dalam konteks klinis dapat dioptimalkan dengan lebih efektif.

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Dawood, Afrah Salman. "Performance Evaluation of Machine Learning Nave Bayes Algorithms for Network Traffic Classification." Technium: Romanian Journal of Applied Sciences and Technology 13 (August 30, 2023): 12–26. http://dx.doi.org/10.47577/technium.v13i.9473.

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Network Traffic Classification (NTC) is an important field for different network statistics like management, malware detection and other paramount constraints. Artificial Intelligence (AI) including Machine Learning (ML) and Deep Learning (DL), on the other hand, plays a very important field nowadays due to its significant capabilities with an extremely different fields and for complex problems. ML, specifically, provides tools in the most important network fields like traffic management, security, etc. Performance evaluation is a very important aspect of any system. This research paper provides a method for NTC using ML Nave Bayes (NB) algorithm in terms of Bernoulli, Multinominal and Gaussian for classifying captured network traffic in two different datasets and perform a performance evaluation and a comparison among these algorithms. The first dataset is a VPN-nonVPN (ISCXVPN2016) dataset while the second is a packet-captured regular Wi-Fi traffic flow dataset for video browsing on the web. Results were comparable in terms of f1-score, accuracy and processing time. Bernoulli NB provides average 93.05% accuracy with 742 ms, Multinominal NB provides average 98.78% accuracy with 78.3 ms processing time and finally, Gaussian NB provides average 69.14% with 46.85 ms processing time.

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Benammar, A., R. Drai, A. Kechida, and A. Guessoum. "Deconvolution of ultrasonic echoes using Bernoulli-Gaussian processes for composite materials inspection." International Journal for Simulation and Multidisciplinary Design Optimization 2, no. 2 (2008): 107–11. http://dx.doi.org/10.1051/smdo:2008014.

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Chong-Yung Chi. "A fast maximum likelihood estimation and detection algorithm for Bernoulli-Gaussian processes." IEEE Transactions on Acoustics, Speech, and Signal Processing 35, no. 11 (1987): 1636–39. http://dx.doi.org/10.1109/tassp.1987.1165073.

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Choo, Sanghyun, and Hyunsoo Lee. "Learning framework of multimodal Gaussian–Bernoulli RBM handling real-value input data." Neurocomputing 275 (January 2018): 1813–22. http://dx.doi.org/10.1016/j.neucom.2017.10.018.

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