A. Gnedin · 2016
Models for random permutations with nonuniform probability distribution are ubiq-uitous in many branches of pure and applied mathematics. Many models step away from the uniformity by ‘biasing ’ the distribution of some permutation statistic, which may be either a numerical statistic (the number of cycles, descents, etc) or a more complex char-acteristic associated with the factoring into cycles or decomposition into increasing runs. A classical instance is the family Ewens ’ distributions [4] under which the probability of permutation is proportional to θc, where c is the number of cycles and θ a positive pa-rameter. The idea of permutation structure complements this approach to nonuniformity by also requiring consistency for various sizes n. From a viewpoint, a random permuta-tion structure is a process in which permutation grows bit-by-bit as elements added, for instance like in the famous ‘Chinese Restaurant Process’, where elements are successively inserted in cycles using a simple rule [5]. A combinatorial part of the project aims to understand the compatibility of permu-tation statistics with systems of projections that connect various sizes, to see how the structures behave under transformations and what is the nature of the projective limit of the finite sets of permutations. Once the framework is established, a fundamental char-acterisation problem is representing a generic permutation structure in the spirit of de Finetti’s theorem, that is in the form of a convex mixture of some basic processes (see e.g. [3], [2]). The latter includes understanding the topology of the boundary (which itself may be a finite or infinite-dimensional simplex, or some kind of ‘discrete ’ set) as well as the decomposability of the family of uniform distributions. Apart from the classifica-tion issues, the circle of questions of interest for applications is constructing Markovian permutation-valued processes with tractable transition probabilities, and analysing the asymptotic features of big permutations (see e.g. [1]).
Cited by 0
Yong Deng · International Journal of Computers Communications & Control · 2022
For exploring the meaning of the power set in evidence theory, a possible explanation of power set is proposed from the view of Pascal’s triangle and combinatorial number. Here comes the question: what would happen if the combinatorial number is replaced by permutation number? To address this issue, a new kind of set, named as random permutation set (RPS), is proposed in this paper, which consists of permutation event space (PES) and permutation mass function (PMF). The PES of a certain set considers all the permutation of that set. The elements of PES are called the permutation events. PMF describes the chance of a certain permutation event that would happen. Based on PES and PMF, RPS can be viewed as a permutation-based generalization of random finite set. Besides, the right intersection (RI) and left intersection (LI) of permutation events are presented. Based on RI and LI, the right orthogonal sum (ROS) and left orthogonal sum (LOS) of PMFs are proposed. In addition, numerical examples are shown to illustrate the proposed conceptions. The comparisons of probability theory, evidence theory, and RPS are discussed and summarized. Moreover, an RPS-based data fusion algorithm is proposed and applied in threat assessment. The experimental results show that the proposed RPS-based algorithm can reasonably and efficiently deal with uncertainty in threat assessment with respect to threat ranking and reliability ranking.
Cited by 185Open access
Stephen W. Schaeffer, Zachary L. Fuller, Gwylim D. Haynes et al. · ScholarSphere (Penn State Libraries)
Citation: These programs perform random permutation tests on outliers and non-outliers based on different mutation types in different gene regions (proximal, inverted, distal) or estimates of Rho, the population scaled recombination rate.
Cited by 0Open access
Luyuan Chen, Yong Deng, Kang Hao Cheong · Engineering Applications of Artificial Intelligence · 2022
Cited by 39
Jiefeng Zhou, Zhen Li, Yong Deng · Chaos An Interdisciplinary Journal of Nonlinear Science · 2024
Random walk is an explainable approach for modeling natural processes at the molecular level. The random permutation set theory (RPST) serves as a framework for uncertainty reasoning, extending the applicability of Dempster-Shafer theory. Recent explorations indicate a promising link between RPST and random walk. In this study, we conduct an analysis and construct a random walk model based on the properties of RPST, with Monte Carlo simulations of such random walk. Our findings reveal that the random walk generated through RPST exhibits characteristics similar to those of a Gaussian random walk and can be transformed into a Wiener process through a specific limiting scaling procedure. This investigation establishes a novel connection between RPST and random walk theory, thereby not only expanding the applicability of RPST but also demonstrating the potential for combining the strengths of both approaches to improve problem-solving abilities.
Cited by 13
David Gries, Jinyun Xue · BIT Numerical Mathematics · 1988
Cited by 11
B. M. Hambly, Peter Keevash, Dudley Stark et al. · 2000
random matrix theory, characteristic polynomial permutations, central limit theorem We establish a central limit theorem for the logarithm of the characteristic polynomial of a random permutation matrix. With this result we can obtain a central limit theorem for the counting function for the eigenvalues lying in some interval on the unit circle. 1
Cited by 0
ZHANG Zhi-qiang, ZENG Ben-sheng, LI Shi-qu · SHILAP Revista de lepidopterología · 2006
Based on selecting permutations on 0,1,…n?1randomly,a probability model were built.In sense of selecting permutations randomly,the distribution of distance which was between one point and its neighbor in Zn（called distance for short）and the mathematic expectation,the variance of number of the points with distance a（1≤a≤n?1）were presented.When distance a and the permutation order n were prime to each other,the distribution of number of the points with distance a was also given.By these results,the cryptographic security of random permutation is analyzed,and a new explication is presented on the significance of choosing quick trickle permutation in cipher designs.
Cited by 0Open access
Sean P. Beeman (11539688), Andrea M. Morrison (11539691), Thomas R. Unnasch (7444841) et al. · Figshare · 2021
Cited by 0Open access
Valentin Bahier · theses.fr (ABES) · 2018
Dans cette thèse, nous nous intéressons à des matrices aléatoires en lien avec des permutations. Nous abordons l'étude de leurs spectres de plusieurs manières, et à différentes échelles d'observation. Dans un premier temps, nous prolongeons l'étude de Wieand à propos des nombres de valeurs propres appartenant à certains arcs fixés du cercle unité. Pour cela nous tirons parti des travaux réalisés par Ben Arous et Dang sur les statistiques linéaires du spectre de matrices de permutation pour une famille de lois à un paramètre englobant le cas de la loi uniforme sur le groupe symétrique, appelée famille des lois d'Ewens. Une partie innovante de notre travail réside dans la généralisation à des arcs non nécessairement fixés. Nous obtenons en effet des résultats similaires en autorisant les longueurs des arcs à décroître lentement vers zéro avec la taille des matrices. Dans un deuxième temps, nous regardons le spectre à échelle microscopique. En nous inspirant des travaux de Najnudel et Nikeghbali en rapport avec la convergence de mesures empiriques des angles propres normalisés, nous commençons par donner un sens à la convergence en terme de comptages de points sur des intervalles fixés. A partir du processus ponctuel limite, nous montrons que le nombre de points dans un intervalle a des fluctuations asymptotiquement gaussiennes lorsque la longueur de l'intervalle tend vers l'infini. Enfin, nous adaptons certains résultats de Chhaibi, Najnudel et Nikeghbali sur le polynôme caractéristique de matrices du CUE à échelle microscopique, et les développons dans notre cadre. De manière analogue mais avec d'autres techniques de preuves, nous obtenons des convergences des polynômes caractéristiques vers des fonctions entières, et cela pour une grande famille de lois pour le tirage des permutations, incluant les lois d'Ewens.
Cited by 0Open access
Angela Andreella · 2021
It provides functions to perform permutation conditional random one-sample and twosamples t-tests in a multivariate framework.
Cited by 0Open access
Shaolong Liu, Niu Wang, Ningkui Wang et al. · Communication in Statistics- Theory and Methods · 2025
Cited by 0
Stefan Lutz, Ashley B. Daugherty, Ying Yu et al. · Methods in molecular biology · 2014
Cited by 3
Clyde H. Schoolfield · Journal of Theoretical Probability · 2005
Cited by 1
Ally Memedovich (4921123), Brian Steele (12709588), Taylor Orr (17050191) et al. · Figshare · 2025
Permutation variable importances for random forests.
Cited by 0Open access
Aaron E. Kornblith (8357226), Chandan Singh (503399), Gabriel Devlin (13215334) et al. · Figshare · 2022
Cited by 0Open access
William M. Kantor · DIMACS series in discrete mathematics and theoretical computer science · 1993
Cited by 2
Alexander Fracalossi (21376720), Jinhui Zhang (693741), Evelyn Lee (370749) et al. · Figshare · 2025
Expected length of stay in residential aged care facilities in Australia: Assessing the impact of dementia using machine learning
Cited by 0Open access
2016
Cited by 0
Ankur Chakravarthy · 2015
Cited by 0Open access