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Journal articles on the topic 'Random finite set'

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Author: Grafiati

Published: 10 December 2022

Last updated: 10 March 2023

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1

Gao, Lin, Giorgio Battistelli, and Luigi Chisci. "Random-Finite-Set-Based Distributed Multirobot SLAM." IEEE Transactions on Robotics 36, no. 6 (December 2020): 1758–77. http://dx.doi.org/10.1109/tro.2020.3001664.

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2

Vo, Ba-Tuong, Ba-Ngu Vo, and Antonio Cantoni. "Bayesian Filtering With Random Finite Set Observations." IEEE Transactions on Signal Processing 56, no. 4 (April 2008): 1313–26. http://dx.doi.org/10.1109/tsp.2007.908968.

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3

Mullane, John, Ba-Ngu Vo, Martin D. Adams, and Ba-Tuong Vo. "A Random-Finite-Set Approach to Bayesian SLAM." IEEE Transactions on Robotics 27, no. 2 (April 2011): 268–82. http://dx.doi.org/10.1109/tro.2010.2101370.

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4

Nasekhian, Ali, and Helmut F. Schweiger. "Random set finite element method application to tunnelling." International Journal of Reliability and Safety 5, no. 3/4 (2011): 299. http://dx.doi.org/10.1504/ijrs.2011.041182.

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5

MACLEAN, C. F., and NEIL O'CONNELL. "Random Finite Topologies and their Thresholds." Combinatorics, Probability and Computing 10, no. 3 (May 2001): 239–49. http://dx.doi.org/10.1017/s0963548301004680.

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For each integer n, there is a natural family of probability distributions on the set of topologies on a set of n elements, parametrized by an integer variable, m. We will describe how these are constructed and analysed, and find threshold functions (for m in terms of n) for various topological properties; we focus attention on connectivity and the size of the largest component.

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6

Okazaki, Hiroyuki, and Yasunari Shidama. "Probability on Finite Set and Real-Valued Random Variables." Formalized Mathematics 17, no. 2 (January 1, 2009): 129–36. http://dx.doi.org/10.2478/v10037-009-0014-x.

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Probability on Finite Set and Real-Valued Random Variables In the various branches of science, probability and randomness provide us with useful theoretical frameworks. The Formalized Mathematics has already published some articles concerning the probability: [23], [24], [25], and [30]. In order to apply those articles, we shall give some theorems concerning the probability and the real-valued random variables to prepare for further studies.

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7

Uchiyama, Kôhei. "One dimensional random walks killed on a finite set." Stochastic Processes and their Applications 127, no. 9 (September 2017): 2864–99. http://dx.doi.org/10.1016/j.spa.2017.01.003.

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8

Yang, Wei, Yaowen Fu, and Xiang Li. "Multiple-model Bayesian filtering with random finite set observation." Journal of Systems Engineering and Electronics 23, no. 3 (June 2012): 364–71. http://dx.doi.org/10.1109/jsee.2012.00045.

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9

Osthus, Deryk. "Maximum Antichains in Random Subsets of a Finite Set." Journal of Combinatorial Theory, Series A 90, no. 2 (May 2000): 336–46. http://dx.doi.org/10.1006/jcta.1999.3048.

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10

GREENHALGH, ANDREW S. "A Model for Random Random-Walks on Finite Groups." Combinatorics, Probability and Computing 6, no. 1 (March 1997): 49–56. http://dx.doi.org/10.1017/s096354839600257x.

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A model for a random random-walk on a finite group is developed where the group elements that generate the random-walk are chosen uniformly and with replacement from the group. When the group is the d-cube Zd2, it is shown that if the generating set is size k then as d → ∞ with k − d → ∞ almost all of the random-walks converge to uniform in k ln (k/(k − d))/4+ρk steps, where ρ is any constant satisfying ρ > −ln (ln 2)/4.

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11

Leung, Keith Y. K., Felipe Inostroza, and Martin Adams. "Relating Random Vector and Random Finite Set Estimation in Navigation, Mapping, and Tracking." IEEE Transactions on Signal Processing 65, no. 17 (September 1, 2017): 4609–23. http://dx.doi.org/10.1109/tsp.2017.2701330.

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12

Uda, Kenneth. "Existence of random invariant periodic curves via random semiuniform ergodic theorem." Stochastics and Dynamics 17, no. 01 (December 15, 2016): 1750007. http://dx.doi.org/10.1142/s0219493717500071.

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We employ an extension of ergodic theory to the random setting to investigate the existence of random periodic solutions of random dynamical systems. Given that a random dynamical system on a cylinder [Formula: see text] has a dissipative structure, we proved that a random invariant compact set can be expressed as a union of finite of number of random periodic curves. The idea in this paper is closely related to the work recently considered by Zhao and Zheng [46].

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13

Da, Kai, Tiancheng Li, Yongfeng Zhu, Hongqi Fan, and Qiang Fu. "Recent advances in multisensor multitarget tracking using random finite set." Frontiers of Information Technology & Electronic Engineering 22, no. 1 (January 2021): 5–24. http://dx.doi.org/10.1631/fitee.2000266.

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14

Lukyanova, Natalia A., and Daria V. Semenova. "Set Functions and Probability Distributions of a Finite Random Sets." Journal of Siberian Federal University. Mathematics & Physics 10, no. 3 (September 2017): 362–71. http://dx.doi.org/10.17516/1997-1397-2017-10-3-362-371.

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15

Yang, Bin, Jun Wang, and Wenguang Wang. "An efficient approximate implementation for labeled random finite set filtering." Signal Processing 150 (September 2018): 215–27. http://dx.doi.org/10.1016/j.sigpro.2018.04.015.

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16

Sibuya, Masaaki. "Random partition of a finite set by cycles of permutation." Japan Journal of Industrial and Applied Mathematics 10, no. 1 (February 1993): 69–84. http://dx.doi.org/10.1007/bf03167203.

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17

Ristic, Branko, Michael Beard, and Claudio Fantacci. "An overview of particle methods for random finite set models." Information Fusion 31 (September 2016): 110–26. http://dx.doi.org/10.1016/j.inffus.2016.02.004.

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18

Siegrist, Kyle. "RANDOM FINITE SUBSETS WITH EXPONENTIAL DISTRIBUTIONS." Probability in the Engineering and Informational Sciences 21, no. 1 (December 15, 2006): 117–32. http://dx.doi.org/10.1017/s0269964807070088.

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Let S denote the collection of all finite subsets of . We define an operation on S that makes S into a positive semigroup with set inclusion as the associated partial order. Positive semigroups are the natural home for probability distributions with exponential properties, such as the memoryless and constant rate properties. We show that there are no exponential distributions on S, but that S can be partitioned into subsemigroups, each of which supports a one-parameter family of exponential distributions. We then find the distribution on S that is closest to exponential, in a certain sense. This work might have applications to the problem of selecting a finite sample from a countably infinite population in the most random way.

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19

Okazaki, Hiroyuki. "Probability on Finite and Discrete Set and Uniform Distribution." Formalized Mathematics 17, no. 2 (January 1, 2009): 173–78. http://dx.doi.org/10.2478/v10037-009-0020-z.

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Probability on Finite and Discrete Set and Uniform DistributionA pseudorandom number generator plays an important role in practice in computer science. For example: computer simulations, cryptology, and so on. A pseudorandom number generator is an algorithm to generate a sequence of numbers that is indistinguishable from the true random number sequence. In this article, we shall formalize the "Uniform Distribution" that is the idealized set of true random number sequences. The basic idea of our formalization is due to [15].

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20

CALKIN, NEIL J., and P. J. CAMERON. "Almost Odd Random Sum-Free Sets." Combinatorics, Probability and Computing 7, no. 1 (March 1998): 27–32. http://dx.doi.org/10.1017/s096354839700312x.

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We show that if S1 is a strongly complete sum-free set of positive integers, and if S0 is a finite sum-free set, then, with positive probability, a random sum-free set U contains S0 and is contained in S0∪S1. As a corollary we show that, with positive probability, 2 is the only even element of a random sum-free set.

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21

Wang, Gang, and Yanbin Tang. "Fractal Dimension of a Random Invariant Set and Applications." Journal of Applied Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/415764.

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We prove an abstract result on random invariant sets of finite fractal dimension. Then this result is applied to a stochastic semilinear degenerate parabolic equation and an upper bound is obtained for the random attractors of fractal dimension.

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22

MIRANDA, ENRIQUE, INÉS COUSO, and PEDRO GIL. "RELATIONSHIPS BETWEEN POSSIBILITY MEASURES AND NESTED RANDOM SETS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10, no. 01 (February 2002): 1–15. http://dx.doi.org/10.1142/s0218488502001302.

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Different authors have observed some relationships between consonant random sets and possibility measures, specially for finite universes. In this paper, we go deeply into this matter and propose several possible definitions for the concept of consonant random set. Three of these conditions are equivalent for finite universes. In that case, the random set considered is associated to a possibility measure if and only if any of them is satisfied. However, in a general context, none of the six definitions here proposed is sufficient for a random set to induce a possibility measure. Moreover, only one of them seems to be necessary.

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23

Doerr, Bryce, and Richard Linares. "Decentralized Control of Large Collaborative Swarms Using Random Finite Set Theory." IEEE Transactions on Control of Network Systems 8, no. 2 (June 2021): 587–97. http://dx.doi.org/10.1109/tcns.2021.3059793.

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24

Yi, Wei, and Lei Chai. "Heterogeneous Multi-Sensor Fusion With Random Finite Set Multi-Object Densities." IEEE Transactions on Signal Processing 69 (2021): 3399–414. http://dx.doi.org/10.1109/tsp.2021.3087033.

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25

Yang, Feng, Litao Zheng, Tiancheng Li, and Lihong Shi. "A computationally efficient distributed Bayesian filter with random finite set observations." Signal Processing 194 (May 2022): 108454. http://dx.doi.org/10.1016/j.sigpro.2022.108454.

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26

Wei, Baishen, and Brett Nener. "Distributed Space Debris Tracking with Consensus Labeled Random Finite Set Filtering." Sensors 18, no. 9 (September 7, 2018): 3005. http://dx.doi.org/10.3390/s18093005.

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Space debris tracking is a challenge for spacecraft operation because of the increasing number of both satellites and the amount of space debris. This paper investigates space debris tracking using marginalized δ -generalized labeled multi-Bernoulli filtering on a network of nodes consisting of a collection of sensors with different observation volumes. A consensus algorithm is used to achieve the global average by iterative regional averages. The sensor network can have unknown or time-varying topology. The proposed space debris tracking algorithm provides an efficient solution to the key challenges (e.g., detection uncertainty, data association uncertainty, clutter, etc.) for space situational awareness. The performance of the proposed algorithm is verified by simulation results.

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27

Liu, Weifeng, Yimei Chen, Hailong Cui, and Chenglin Wen. "A Nonuniform Clutter Intensity Estimation Algorithm for Random Finite Set Filters." IEEE Transactions on Aerospace and Electronic Systems 54, no. 6 (December 2018): 2911–25. http://dx.doi.org/10.1109/taes.2018.2832958.

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28

Li, Guchong, Wei Yi, Suqi Li, Bailu Wang, and Lingjiang Kong. "Asynchronous multi-rate multi-sensor fusion based on random finite set." Signal Processing 160 (July 2019): 113–26. http://dx.doi.org/10.1016/j.sigpro.2019.01.028.

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29

Schweiger, H. F., and G. M. Peschl. "Reliability analysis in geotechnics with the random set finite element method." Computers and Geotechnics 32, no. 6 (September 2005): 422–35. http://dx.doi.org/10.1016/j.compgeo.2005.07.002.

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30

Wang, Peng, Ge Li, Yong Peng, and Rusheng Ju. "Random Finite Set Based Parameter Estimation Algorithm for Identifying Stochastic Systems." Entropy 20, no. 8 (July 31, 2018): 569. http://dx.doi.org/10.3390/e20080569.

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Parameter estimation is one of the key technologies for system identification. The Bayesian parameter estimation algorithms are very important for identifying stochastic systems. In this paper, a random finite set based algorithm is proposed to overcome the disadvantages of the existing Bayesian parameter estimation algorithms. It can estimate the unknown parameters of the stochastic system which consists of a varying number of constituent elements by using the measurements disturbed by false detections, missed detections and noises. The models used for parameter estimation are constructed by using random finite set. Based on the proposed system model and measurement model, the key principles and formula derivation of the proposed algorithm are detailed. Then, the implementation of the algorithm is presented by using sequential Monte Carlo based Probability Hypothesis Density (PHD) filter and simulated tempering based importance sampling. Finally, the experiments of systematic errors estimation of multiple sensors are provided to prove the main advantages of the proposed algorithm. The sensitivity analysis is carried out to further study the mechanism of the algorithm. The experimental results verify the superiority of the proposed algorithm.

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31

Qiu, Hao, Gaoming Huang, and Jun Gao. "Centralized multi-sensor multi-target tracking with labeled random finite set." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 231, no. 4 (August 6, 2016): 669–76. http://dx.doi.org/10.1177/0954410016641447.

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Tracking multiple objects with multiple sensors is widely recognized to be much more complex than the single-sensor scenario. This contribution proposes a computationally tractable multi-sensor multi-target tracker. Based on Bayes equation and multi-senor observation model, a new corrector for multi-senor is derived. To lower the complexity of update operation, a parallel track-to-measurement association strategy is applied to the corrector. Hypotheses truncation scheme along with first-moment approximation of multi-target density are also employed to improve the tracking efficiency. The tracker is applied to a couple-sensor scenario. Experiment results validate the advantages of proposed method compared to the standard single-sensor δ-generalized labeled multi-Bernoulli filter and the iterated-corrector probability hypothesis density filter.

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32

Luo, Xiao-bo, Hong-qi Fan, Zhi-yong Song, and Qiang Fu. "Passive target tracking with intermittent measurement based on random finite set." Journal of Central South University 21, no. 6 (June 2014): 2282–91. http://dx.doi.org/10.1007/s11771-014-2179-x.

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33

Uchiyama, Kôhei. "Asymptotic Behaviour of a Random Walk Killed on a Finite Set." Potential Analysis 46, no. 4 (October 4, 2016): 689–703. http://dx.doi.org/10.1007/s11118-016-9598-2.

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34

Brown, B., and P. M. Higgins. "Finite full transformation semigroups as collections of random functions." Glasgow Mathematical Journal 30, no. 2 (May 1988): 203–11. http://dx.doi.org/10.1017/s0017089500007230.

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The collection of all self-maps on a non-empty set X under composition is known in algebraic semigroup theory as the full transformation semigroup on X and is written x. Its importance lies in the fact that any semigroup S can be embedded in the full transformation semigroup (where S1 is the semigroup S with identity 1 adjoined, if S does not already possess one). The proof is similar to Cayley's Theorem that a group G can be embedded in SG, the group of all bijections of G to itself. In this paper X will be a finite set of order n, which we take to be and so we shall write Tn for X.

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35

John, R. D., and J. Robinson. "Rates of convergence to normality for samples from a finite set of random variables." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 60, no. 3 (June 1996): 355–62. http://dx.doi.org/10.1017/s1446788700037861.

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AbstractRates of convergence to normality of O(N-½) are obtained for a standardized sum of m random variables selected at random from a finite set of N random variables in two cases. In the first case, the sum is randomly normed and the variables are not restricted to being independent. The second case is an alternative proof of a result due to von Bahr, which deals with independent variables. Both results derive from a rate obtained by Höglund in the case of sampling from a finite population.

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36

Yang, Jianbin. "Random sampling and reconstruction in multiply generated shift-invariant spaces." Analysis and Applications 17, no. 02 (March 2019): 323–47. http://dx.doi.org/10.1142/s0219530518500185.

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Shift-invariant spaces play an important role in approximation theory, wavelet analysis, finite elements, etc. In this paper, we consider the stability and reconstruction algorithm of random sampling in multiply generated shift-invariant spaces [Formula: see text]. Under some decay conditions of the generator [Formula: see text], we approximate [Formula: see text] with finite-dimensional subspaces and prove that with overwhelming probability, the stability of sampling set conditions holds uniformly for all functions in certain compact subsets of [Formula: see text] when the sampling size is sufficiently large. Moreover, we show that this stability problem is connected with properties of the random matrix generated by [Formula: see text]. In the end, we give a reconstruction algorithm for the random sampling of functions in [Formula: see text].

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37

Goldfarb, Warren. "Random models and the Maslov class." Journal of Symbolic Logic 54, no. 2 (June 1989): 460–66. http://dx.doi.org/10.2307/2274860.

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In [GS] Gurevich and Shelah introduce a novel method for proving that every satisfiable formula in the Gödel class has a finite model (the Gödel class is the class of prenex formulas of pure quantification theory with prefixes ∀∀∃ … ∃). They dub their method “random models”: it proceeds by delineating, given any F in the Gödel class and any integer p, a set of structures for F with universe {1, …, p} that can be treated as a finite probability space S. They then show how to calculate an upper bound on the probability that a structure chosen at random from S makes F false; from this bound they are able to infer that if p is sufficiently large, that probability will be less than one, so that there will exist a structure in S that is a model for F. The Gurevich-Shelah proof is somewhat simpler than those known heretofore. In particular, there is no need for the combinatorial partitionings of finite universes that play a central role in the earlier proofs (see [G] and [DG, p. 86]). To be sure, Gurevich and Shelah obtain a larger bound on the size of the finite models, but this is relatively unimportant, since searching for finite models is not the most efficient method to decide satisfiability.Gurevich and Shelah note that the random model method can be used to treat the Gödel class extended by initial existential quantifiers, that is, the prefix-class ∀…∀∃…∃; but they do not investigate further its range of applicability to syntactically specified classes.

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38

Barber, D., D. Saad, and P. Sollich. "Test Error Fluctuations in Finite Linear Perceptrons." Neural Computation 7, no. 4 (July 1995): 809–21. http://dx.doi.org/10.1162/neco.1995.7.4.809.

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We examine the fluctuations in the test error induced by random, finite, training and test sets for the linear perceptron of input dimension n with a spherically constrained weight vector. This variance enables us to address such issues as the partitioning of a data set into a test and training set. We find that the optimal assignment of the test set size scales with n2/3.

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39

Hu, Biao, Uzair Sharif, Rajat Koner, Guang Chen, Kai Huang, Feihu Zhang, Walter Stechele, and Alois Knoll. "Random Finite Set Based Bayesian Filtering with OpenCL in a Heterogeneous Platform." Sensors 17, no. 4 (April 12, 2017): 843. http://dx.doi.org/10.3390/s17040843.

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40

Jiang, Defu, Ming Liu, Yiyue Gao, Yang Gao, Wei Fu, and Yan Han. "Time-Matching Random Finite Set-Based Filter for Radar Multi-Target Tracking." Sensors 18, no. 12 (December 13, 2018): 4416. http://dx.doi.org/10.3390/s18124416.

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The random finite set (RFS) approach provides an elegant Bayesian formulation of the multi-target tracking (MTT) problem without the requirement of explicit data association. In order to improve the performance of the RFS-based filter in radar MTT applications, this paper proposes a time-matching Bayesian filtering framework to deal with the problem caused by the diversity of target sampling times. Based on this framework, we develop a time-matching joint generalized labeled multi-Bernoulli filter and a time-matching probability hypothesis density filter. Simulations are performed by their Gaussian mixture implementations. The results show that the proposed approach can improve the accuracy of target state estimation, as well as the robustness.

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41

Trezza, Anthony, Donald J. Bucci, and Pramod K. Varshney. "Multi-Sensor Joint Adaptive Birth Sampler for Labeled Random Finite Set Tracking." IEEE Transactions on Signal Processing 70 (2022): 1010–25. http://dx.doi.org/10.1109/tsp.2022.3151553.

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42

Schweiger, H. F., G. M. Peschl, and R. Pöttler. "Application of the random set finite element method for analysing tunnel excavation." Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards 1, no. 1 (February 28, 2007): 43–56. http://dx.doi.org/10.1080/17499510701204141.

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43

Kim, Du Yong, Ba-Ngu Vo, Ba-Tuong Vo, and Moongu Jeon. "A labeled random finite set online multi-object tracker for video data." Pattern Recognition 90 (June 2019): 377–89. http://dx.doi.org/10.1016/j.patcog.2019.02.004.

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44

Li, Gen, and Yuantao Gu. "Restricted Isometry Property of Gaussian Random Projection for Finite Set of Subspaces." IEEE Transactions on Signal Processing 66, no. 7 (April 1, 2018): 1705–20. http://dx.doi.org/10.1109/tsp.2017.2778685.

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45

Uchiyama, Kôhei. "Scaling Limits of Random Walk Bridges Conditioned to Avoid a Finite Set." Journal of Theoretical Probability 33, no. 3 (May 9, 2019): 1296–326. http://dx.doi.org/10.1007/s10959-019-00908-x.

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46

Kamoona, Ammar Mansoor, Amirali Khodadadian Gostar, Ruwan Tennakoon, Alireza Bab-Hadiashar, David Accadia, Joshua Thorpe, and Reza Hoseinnezhad. "Random Finite Set-Based Anomaly Detection for Safety Monitoring in Construction Sites." IEEE Access 7 (2019): 105710–20. http://dx.doi.org/10.1109/access.2019.2932137.

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47

Yang, Chaoqun, Zhiguo Shi, Heng Zhang, Junfeng Wu, and Xiufang Shi. "Multiple Attacks Detection in Cyber-Physical Systems Using Random Finite Set Theory." IEEE Transactions on Cybernetics 50, no. 9 (September 2020): 4066–75. http://dx.doi.org/10.1109/tcyb.2019.2912939.

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48

Yashunsky, Alexey D. "Finite algebras of Bernoulli distributions." Discrete Mathematics and Applications 29, no. 4 (August 27, 2019): 267–76. http://dx.doi.org/10.1515/dma-2019-0024.

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Abstract The paper is concerned with sets of Bernoulli distributions which are closed under substitutions of independent random variables into Boolean functions from a given set (an algebra of Bernoulli distributions). A description of all finite algebras of Bernoulli distributions is given.

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49

Cui, Yuxin, Shu Li, Yunxiao Shan, and Fengqiu Liu. "Finite-Time Set Reachability of Probabilistic Boolean Multiplex Control Networks." Applied Sciences 12, no. 2 (January 16, 2022): 883. http://dx.doi.org/10.3390/app12020883.

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This study focuses on the finite-time set reachability of probabilistic Boolean multiplex control networks (PBMCNs). Firstly, based on the state transfer graph (STG) reconstruction technique, the PBMCNs are extended to random logic dynamical systems. Then, a necessary and sufficient condition for the finite-time set reachability of PBMCNs is obtained. Finally, the obtained results are effectively illustrated by an example.

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50

Baldi, Marco, Alessandro Barenghi, Franco Chiaraluce, Gerardo Pelosi, and Paolo Santini. "A Finite Regime Analysis of Information Set Decoding Algorithms." Algorithms 12, no. 10 (October 1, 2019): 209. http://dx.doi.org/10.3390/a12100209.

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Decoding of random linear block codes has been long exploited as a computationally hard problem on which it is possible to build secure asymmetric cryptosystems. In particular, both correcting an error-affected codeword, and deriving the error vector corresponding to a given syndrome were proven to be equally difficult tasks. Since the pioneering work of Eugene Prange in the early 1960s, a significant research effort has been put into finding more efficient methods to solve the random code decoding problem through a family of algorithms known as information set decoding. The obtained improvements effectively reduce the overall complexity, which was shown to decrease asymptotically at each optimization, while remaining substantially exponential in the number of errors to be either found or corrected. In this work, we provide a comprehensive survey of the information set decoding techniques, providing finite regime temporal and spatial complexities for them. We exploit these formulas to assess the effectiveness of the asymptotic speedups obtained by the improved information set decoding techniques when working with code parameters relevant for cryptographic purposes. We also delineate computational complexities taking into account the achievable speedup via quantum computers and similarly assess such speedups in the finite regime. To provide practical grounding to the choice of cryptographically relevant parameters, we employ as our validation suite the ones chosen by cryptosystems admitted to the second round of the ongoing standardization initiative promoted by the US National Institute of Standards and Technology.

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