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Journal articles on the topic 'Geometrical Probability'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Irvine, Richard. "A Geometrical Approach to Conflict Probability Estimation." Air Traffic Control Quarterly 10, no. 2 (2002): 85–113. http://dx.doi.org/10.2514/atcq.10.2.85.

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2

Avram, Florin, and Dimitris Bertsimas. "On Central Limit Theorems in Geometrical Probability." Annals of Applied Probability 3, no. 4 (1993): 1033–46. http://dx.doi.org/10.1214/aoap/1177005271.

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3

Ciaglia, Florio Maria, Alberto Ibort, and Giuseppe Marmo. "Geometrical structures for classical and quantum probability spaces." International Journal of Quantum Information 15, no. 08 (2017): 1740007. http://dx.doi.org/10.1142/s021974991740007x.

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On the affine space containing the space [Formula: see text] of quantum states of finite-dimensional systems, there are contravariant tensor fields by means of which it is possible to define Hamiltonian and gradient vector fields encoding the relevant geometrical properties of [Formula: see text]. Guided by Dirac’s analogy principle, we will use them as inspiration to define contravariant tensor fields, Hamiltonian and gradient vector fields on the affine space containing the space of fair probability distributions on a finite sample space and analyze their geometrical properties. Most of our

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4

Jia, W., and J. Wang. "Analysis of connectivity for sensor networks using geometrical probability." IEE Proceedings - Communications 153, no. 2 (2006): 305. http://dx.doi.org/10.1049/ip-com:20045176.

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5

Lindsay, Bruce G., Robert E. Kass, and Paul W. Vos. "Geometrical Foundations of Asymptotic Inference." Journal of the American Statistical Association 94, no. 446 (1999): 646. http://dx.doi.org/10.2307/2670184.

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6

Gzyl, H., and F. Nielsen. "Geometry of the probability simplex and its connection to the maximum entropy method." Journal of Applied Mathematics, Statistics and Informatics 16, no. 1 (2020): 25–35. http://dx.doi.org/10.2478/jamsi-2020-0003.

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AbstractThe use of geometrical methods in statistics has a long and rich history highlighting many different aspects. These methods are usually based on a Riemannian structure defined on the space of parameters that characterize a family of probabilities. In this paper, we consider the finite dimensional case but the basic ideas can be extended similarly to the infinite-dimensional case. Our aim is to understand exponential families of probabilities on a finite set from an intrinsic geometrical point of view and not through the parameters that characterize some given family of probabilities.Fo

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7

Mikov, Alexander. "Geometrical digraphs as models of heterogeneous computer networks." Informatization and communication 4 (November 2020): 50–59. http://dx.doi.org/10.34219/2078-8320-2020-11-4-50-59.

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New mathematical models of networks are considered — geometrical oriented graphs. Such models adequately reflect the structure of heterogeneous wireless computer, sensor and other networks. The strongly connected components of geometric digraphs, their dependence on the number of network nodes in a given area, on the distributions of the radii of the zones of reception and transmission of signals are investigated. The probabilistic characteristics of random geometric digraphs, the features of the dependences of the probability of strong connectivity on the number of nodes in the digraphs for v

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8

Itoh, Mitsuhiro, and Hiroyasu Satoh. "Information geometry of Busemann-barycenter for probability measures." International Journal of Mathematics 26, no. 06 (2015): 1541007. http://dx.doi.org/10.1142/s0129167x15410074.

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Using Busemann function of an Hadamard manifold X we define the barycenter map from the space 𝒫+(∂X, dθ) of probability measures having positive density on the ideal boundary ∂X to X. The space 𝒫+(∂X, dθ) admits geometrically a fiber space structure over X from Fisher information geometry. Following the arguments in [E. Douady and C. Earle, Conformally natural extension of homeomorphisms of the circle, Acta Math.157 (1986) 23–48; G. Besson, G. Courtois and S. Gallot, Entropies et rigidités des espaces localement symétriques de coubure strictement négative, Geom. Funct. Anal.5 (1995) 731–799; M

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9

Krapivsky, P. L., L. I. Nazarov, and M. V. Tamm. "Geometrical selection in growing needles." Journal of Statistical Mechanics: Theory and Experiment 2019, no. 7 (2019): 073206. http://dx.doi.org/10.1088/1742-5468/ab270c.

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10

Azaïs, Jean-Marc, José R. León, and Joaquín Ortega. "Geometrical characteristics of Gaussian sea waves." Journal of Applied Probability 42, no. 2 (2005): 407–25. http://dx.doi.org/10.1239/jap/1118777179.

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In this work, we study some geometrical properties of a stationary Gaussian field modeling the sea surface, using the energy spectrum. We consider the length of a crest and the mean speed of contours, which can be expressed as integrals over level sets. We also give central limit theorems for some of these quantities, using chaos expansions.

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11

Lapicki, Gregory. "Ionization probability for multiple ionization: An assessment of the geometrical model." Radiation Physics and Chemistry 76, no. 3 (2007): 475–82. http://dx.doi.org/10.1016/j.radphyschem.2006.01.038.

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12

Fundator, Michael. "Multidimensional Time Model for Probability Cumulative Function Applied to Geometrical Predictions." Applied and Computational Mathematics 7, no. 3 (2018): 89. http://dx.doi.org/10.11648/j.acm.20180703.13.

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13

Coronado, Eduardo A., and George C. Schatz. "Surface plasmon broadening for arbitrary shape nanoparticles: A geometrical probability approach." Journal of Chemical Physics 119, no. 7 (2003): 3926–34. http://dx.doi.org/10.1063/1.1587686.

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14

Zhang, Ruonan, Xiaoshen Song, Jianping Pan, and Jiajia Liu. "Stochastic Cooperative Communications Using a Geometrical Probability Approach for Wireless Networks." Mobile Networks and Applications 24, no. 5 (2019): 1437–51. http://dx.doi.org/10.1007/s11036-019-01266-y.

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15

Picco, M., R. Santachiara, and A. Sicilia. "Geometrical properties of parafermionic spin models." Journal of Statistical Mechanics: Theory and Experiment 2009, no. 04 (2009): P04013. http://dx.doi.org/10.1088/1742-5468/2009/04/p04013.

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16

Okamoto, Ichi, Shun-Ichi Amari, and Kei Takeuchi. "Asymptotic Theory of Sequential Estimation: Differential Geometrical Approach." Annals of Statistics 19, no. 2 (1991): 961–81. http://dx.doi.org/10.1214/aos/1176348131.

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17

Ingrassia, Salvatore. "Geometrical Aspects of Discrimination by Multilayer Perceptrons." Journal of Multivariate Analysis 68, no. 2 (1999): 226–34. http://dx.doi.org/10.1006/jmva.1998.1786.

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18

Le, Huiling. "Random spherical triangles I: Geometrical background." Advances in Applied Probability 21, no. 3 (1989): 570–80. http://dx.doi.org/10.2307/1427636.

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In this paper we identify the shape space Σ(S2, k) for k labelled points on the sphere S2 that gives a mathematical model applicable to data sets whose elements are, or can be represented by, configurations of labelled sequences of points on S2 and for which the fundamental properties of interest are the shapes of these configurations, and we examine the geometric structures on the space, especially the riemannian structure on Σ(S2, 3). In a companion paper (pp. 581–594) we investigate the statistical properties of such shapes when the k points are generated by a random mechanism.

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19

Sinha, Kishore. "C352. Geometrical configurations and pbib designs." Journal of Statistical Computation and Simulation 36, no. 1 (1990): 34–35. http://dx.doi.org/10.1080/00949659008811252.

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20

Zaitov, A. A. "Geometrical and Topological Properties of a Subspace Pf(X) of Probability Measures." Russian Mathematics 63, no. 10 (2019): 24–32. http://dx.doi.org/10.3103/s1066369x19100049.

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21

Zaitov, Adilbek Atakhanovich. "Geometrical and topological properties of a subspace Pf (X) of probability measures." Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, no. 10 (2019): 28–37. http://dx.doi.org/10.26907/0021-3446-2019-10-28-37.

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22

Zaider, M., J. F. Dicello, and J. J. Coyne. "The effects of geometrical factors on microdosimetric probability distributions of energy deposition." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 40-41 (April 1989): 1261–65. http://dx.doi.org/10.1016/0168-583x(89)90634-4.

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23

Haddad, Abdolhosein, Danial Rezazadeh Eidgahee, and Hosein Naderpour. "A probabilistic study on the geometrical design of gravity retaining walls." World Journal of Engineering 14, no. 5 (2017): 414–22. http://dx.doi.org/10.1108/wje-07-2016-0034.

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Purpose The purpose of this study is to introduce a relatively simple method of probabilistic analysis on the dimensions of gravity retaining walls which might lead to a more accurate understanding of failure. Considering the wall geometries in the case of allowable stress design, the probability of wall failure is not clearly defined. The available factor of safety may or may not be sufficient for the designed structure because of the inherent uncertainties in the geotechnical parameters. Moreover, two cases of correlated and uncorrelated geotechnical variables are considered to show how they

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24

Rodríaguez, A. A., and E. Medina. "Geometrical and Transport Properties of Disordered Fibre Networks: Analytical Results." Modern Physics Letters B 11, no. 20 (1997): 867–75. http://dx.doi.org/10.1142/s0217984997001079.

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We study novel geometrical and transport properties of a 2D model of disordered fibre networks. To assess the geometrical structure we determine, analytically, the probability distribution for the number of fibre intersections and resulting segment sizes in the network as a function of fibre density and length. We also determine, numerically, the probability distribution of pore perimeters and areas. We find a non-monotonous behavior of the perimeter distribution whose main features can be explained by solving for two simplified models of the line network. Finally we formulate a mean field app

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25

David, François, and Michel Bauer. "Another derivation of the geometrical KPZ relations." Journal of Statistical Mechanics: Theory and Experiment 2009, no. 03 (2009): P03004. http://dx.doi.org/10.1088/1742-5468/2009/03/p03004.

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26

Hwang, Chii-Ruey, and Shuenn-Jyi Sheu. "On the Geometrical Convergence of Gibbs Sampler inRd." Journal of Multivariate Analysis 66, no. 1 (1998): 22–37. http://dx.doi.org/10.1006/jmva.1997.1735.

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27

Goodall, Colin R., and Kanti V. Mardia. "A geometrical derivation of the shape density." Advances in Applied Probability 23, no. 03 (1991): 496–514. http://dx.doi.org/10.1017/s0001867800023703.

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The density for the shapes of random configurations of N independent Gaussian-distributed landmarks in the plane with unequal means was first derived by Mardia and Dryden (1989a). Kendall (1984), (1989) describes a hierarchy of spaces for landmarks, including Euclidean figure space containing the original configuration, preform space (with location removed), preshape space (with location and scale removed), and shape space. We derive the joint density of the landmark points in each of these intermediate spaces, culminating in confirmation of the Mardia–Dryden result in shape space. This three-

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28

Goodall, Colin R., and Kanti V. Mardia. "A geometrical derivation of the shape density." Advances in Applied Probability 23, no. 3 (1991): 496–514. http://dx.doi.org/10.2307/1427619.

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The density for the shapes of random configurations of N independent Gaussian-distributed landmarks in the plane with unequal means was first derived by Mardia and Dryden (1989a). Kendall (1984), (1989) describes a hierarchy of spaces for landmarks, including Euclidean figure space containing the original configuration, preform space (with location removed), preshape space (with location and scale removed), and shape space. We derive the joint density of the landmark points in each of these intermediate spaces, culminating in confirmation of the Mardia–Dryden result in shape space. This three-

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29

Xu, Daming. "Differential geometrical structures related to forecasting error variance ratios." Annals of the Institute of Statistical Mathematics 43, no. 4 (1991): 621–46. http://dx.doi.org/10.1007/bf00121643.

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30

Yaitskova, Natalia. "Probability density cloud as a geometrical tool to describe statistics of scattered light." Journal of the Optical Society of America A 34, no. 4 (2017): 614. http://dx.doi.org/10.1364/josaa.34.000614.

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31

Stroom, Joep C., Hans C. J. de Boer, Henk Huizenga, and Andries G. Visser. "Inclusion of geometrical uncertainties in radiotherapy treatment planning by means of coverage probability." International Journal of Radiation Oncology*Biology*Physics 43, no. 4 (1999): 905–19. http://dx.doi.org/10.1016/s0360-3016(98)00468-4.

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32

Kaye, Brian H., Remi A. Trottier, and Garry G. Clark. "Characterizing the Fractal Structure of Fineparticle Profiles using the concepts of geometrical probability." Particle & Particle Systems Characterization 9, no. 1-4 (1992): 209–12. http://dx.doi.org/10.1002/ppsc.19920090129.

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33

Bhattacharyya, A. "On a Geometrical Representation of Probability Distributions and its use in Statistical Inference." Calcutta Statistical Association Bulletin 40, no. 1-4 (1990): 23–49. http://dx.doi.org/10.1177/0008068319900504.

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34

Hsu, Wu-ron, and Allan H. Murphy. "The attributes diagram A geometrical framework for assessing the quality of probability forecasts." International Journal of Forecasting 2, no. 3 (1986): 285–93. http://dx.doi.org/10.1016/0169-2070(86)90048-8.

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35

Langsrud, Øyvind. "The geometrical interpretation of statistical tests in multivariate linear regression." Statistical Papers 45, no. 1 (2004): 111–22. http://dx.doi.org/10.1007/bf02778273.

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36

Kopetzky, H. G., and F. J. Schnitzer. "A geometrical approach to approximations by continued fractions." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 43, no. 2 (1987): 176–86. http://dx.doi.org/10.1017/s1446788700029311.

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AbstractBy simple geometrical considerations new proofs for some classical results are given and also new theorems about approximation by continued fractions are derived. This geometrical approach presents an instructive visualisation of the nature of proximation theorems.

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37

Boulougouris, Georgios C. "On the geometrical representation of classical statistical mechanics." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 2 (2021): 023207. http://dx.doi.org/10.1088/1742-5468/abda36.

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38

Portesi, M., F. Pennini, and A. Plastino. "Geometrical aspects of a generalized statistical mechanics." Physica A: Statistical Mechanics and its Applications 373 (January 2007): 273–82. http://dx.doi.org/10.1016/j.physa.2006.05.024.

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39

Areia, Aníbal, Manuela M. Oliveira, and João T. Mexia. "Models for a series of studies based on geometrical representation." Statistical Methodology 5, no. 3 (2008): 277–88. http://dx.doi.org/10.1016/j.stamet.2007.09.001.

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40

Good, I. J. "C264. A geometrical approach to the amalgamation paradox." Journal of Statistical Computation and Simulation 26, no. 1-2 (1986): 129–32. http://dx.doi.org/10.1080/00949658608810954.

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41

Wu, Xian-Yuan, and Yu Zhang. "A geometrical structure for an infinite oriented cluster and its uniqueness." Annals of Probability 36, no. 3 (2008): 862–75. http://dx.doi.org/10.1214/07-aop339.

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42

Krauklis, P. V., and G. Kowalle. "Geometrical spreading andQ of the wavesP n." Journal of Mathematical Sciences 83, no. 2 (1997): 264–66. http://dx.doi.org/10.1007/bf02405820.

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43

Erickson, Timothy E. "Connecting Data and Geometry." Mathematics Teacher 94, no. 8 (2001): 710–14. http://dx.doi.org/10.5951/mt.94.8.0710.

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Geometrical ideas and representations often help us understand other areas of mathematics. For example, we might use area models for multiplying polynomials, for summing series, or for conditional probability calculations. But we can also use other areas of mathematics to help us understand a geometrical situation. This article describes an activity that was adapted from Erickson (2000, pp. 111–13), in which students use data analysis and mathematical modeling to obtain insight into a geometrical question. This activity explores a simple case of what is called the isoperimetric inequality. A W

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44

Kuipers, H. P. C. E., H. C. E. Van Leuven, and W. M. Visser. "The characterization of heterogeneous catalysts by XPS based on geometrical probability 1: Monometallic catalysts." Surface and Interface Analysis 8, no. 6 (1986): 235–42. http://dx.doi.org/10.1002/sia.740080603.

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45

Mora, Thierry, and Marc Mézard. "Geometrical organization of solutions to random linear Boolean equations." Journal of Statistical Mechanics: Theory and Experiment 2006, no. 10 (2006): P10007. http://dx.doi.org/10.1088/1742-5468/2006/10/p10007.

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46

Han, Chun Xiu, Dong Hua Zhou, Wen Yuan Liao, Xu Chen, Long Qi Li, and Kai Cheng Yao. "Probability Statistical Model and Network Simulation Technology of Random Fractured Rock Mass." Applied Mechanics and Materials 580-583 (July 2014): 679–83. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.679.

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Based on field investigation of random fractured rock mass, the sample parameters are put to statistical analysis, and 2-D fracture network model is established with probability-statistics theory and Monte-Carlo simulation technique. Finally, 2-D fracture network model is formed, which gain fracture distributed regularity in statistical sense, and is of important meaning to describe the fracture geometrical characteristics.

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47

DEBBASCH, F., and M. MOREAU. "Diffusion on a curved surface: a geometrical approach." Physica A: Statistical Mechanics and its Applications 343 (November 15, 2004): 81–104. http://dx.doi.org/10.1016/s0378-4371(04)00864-7.

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48

Debbasch, F., and M. Moreau. "Diffusion on a curved surface: a geometrical approach." Physica A: Statistical Mechanics and its Applications 343 (November 2004): 81–104. http://dx.doi.org/10.1016/j.physa.2004.06.159.

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49

Hindia, MHD Nour, Faizan Qamar, Talib Abbas, Kaharudin Dimyati, Mohamad Sofian Abu Talip, and Iraj Sadegh Amiri. "Interference cancelation for high-density fifth-generation relaying network using stochastic geometrical approach." International Journal of Distributed Sensor Networks 15, no. 7 (2019): 155014771985587. http://dx.doi.org/10.1177/1550147719855879.

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In order to resolve the issue of coverage limitation for the future fifth-generation network, deploying a relay node within a cell is one of the most capable and cost-effective solution, which not only enhances the coverage but also improves the spectral efficiency. However, this solution leads to the undesired interferences from nearby base station and relay nodes that affects user’s signal-to-interference-plus-noise ratio and can cause the ambiguous received signal at the user end. In this article, we have analyzed a relay-based interference-limited network at millimeter wave frequency and p

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50

Wei, Xin Xin, and Yi Bin Wu. "Analysis and Design of Strengthened Hyperbolic Cooling Tower by Using PDS Module in ANSYS." Advanced Materials Research 446-449 (January 2012): 3436–40. http://dx.doi.org/10.4028/www.scientific.net/amr.446-449.3436.

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In consideration of the uncertain factors, a hyperbolic cooling tower with initial geometrical imperfections is studied by the PDS module in ANSYS. Contrastive analysis is made on stress, internal force, displacement and failure probability of cooling tower shell. It is indicated that the value of Mx and Ty is sensitive to the initial geometrical imperfections, and the failure of shell in imperfections increase in large. On top of this, the non-local cooling tower shell strengthened with FRP is found to solve the insufficient capacity, which is proved to be feasible. Lastly, the reliability an

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