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541“…From the perspective of the probability theory, SG is considered as an implicit probability distribution estimation under the assumption that there exists a true contextual distribution among words. …”
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542por Gentili, Pier Luigi“…Human interaction with the world is dominated by uncertainty. Probability theory is a valuable tool to face such uncertainty. …”
Publicado 2021
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543“…We study three convolutions of polynomials in the context of free probability theory. We prove that these convolutions can be written as the expected characteristic polynomials of sums and products of unitarily invariant random matrices. …”
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544por Al-Dayel, Ibrahim, Alshahrani, Mohammed N., Elbatal, Ibrahim, Alotaibi, Naif, Shawki, A. W., Elgarhy, Mohammed“…This article extends to probability theory by developing a unique two-parameter statistical distribution called the half-logistic inverse moment exponential (HLIMExp). …”
Publicado 2022
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545por Otto, Sarah P., 1967-Tabla de Contenidos: “…Ch. 1: Mathematical Modeling in Biology -- Ch. 2: How to Construct a Model -- Ch. 3: Deriving Classic Models in Ecology and Evolutionary Biology -- Primer 1: Functions and Approximations -- Ch. 4: Numerical and Graphical Techniques-Developing a Feeling for Your Model -- Ch. 5: Equilibria and Stability Analyses-One-Variable Models -- Ch. 6: General Solutions and Transformations-One-Variable Models -- Primer 2: Linear Algebra -- Ch. 7: Equilibria and Stability Analyses-Linear Models with Multiple Variables -- Ch. 8: Equilibria and Stability Analyses-Nonlinear Models with Multiple Variables -- Ch. 9: General Solutions and Transformations-Models with Multiple Variables -- Ch. 10: Dynamics of Class-Structured Populations -- Ch. 11: Techniques for Analyzing Models with Periodic Behavior -- Ch. 12: Evolutionary Invasion Analysis -- Primer 3: Probability Theory -- Ch. 13: Probabilistic Models -- Ch. 14: Analyzing Discrete Stochastic Models -- Ch. 15: Analyzing Continuous Stochastic Models-Diffusion in Time and Space -- Appendix 1: Commonly Used Mathematical Rules -- Appendix 2: Some Important Rules from Calculus -- Appendix 3: The Perron-Frobenius Theorem -- Appendix 4: Finding Maxima and Minima of Functions -- Appendix 5: Moment-Generating Functions -- Index of Definitions, Recipes, and Rules -- General Index.…”
Publicado 2007
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546por Kyprianou, Andreas E“…Andreas Kyprianou has a degree in Mathematics from the University of Oxford and a Ph.D. in Probability Theory from The University of Sheffield. He is currently a Professor of Probability at the University of Bath, having held academic positions in Mathematics and Statistics Departments at the London School of Economics, Edinburgh University, Utrecht University and Heriot-Watt University, besides working for nearly two years as a research mathematician in the oil industry. …”
Publicado 2014
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547“…Though the structure remains unchanged, the new edition also explores recent advances in the use of distances and metrics for e.g. generalized distances, probability theory, graph theory, coding theory, data analysis. …”
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548“…Readers should have completed introductory courses in analysis and probability theory. .…”
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549“…Earlier work on the RH based on supersymmetric QM, whose potential was related to the Gauss-Jacobi theta series, allows to provide the proper framework to construct the well defined algorithm to compute the probability to find a zero (an infinity of zeros) in the critical line. Geometric probability theory furnishes the answer to the very difficult question whether the probability that the RH is true is indeed equal to unity or not. …”
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550por Yu, Shoujun, Yue, Wenji, Guo, Tianruo, Liu, Yonghong, Zhang, Yapeng, Khademi, Sara, Zhou, Tian, Xu, Zhen, Song, Bing, Wu, Tianzhun, Liu, Fenglin, Tai, Yanlong, Yu, Xuefei, Wang, Hao“…This study proposes a new method based on a Circuit-Probability theory (C-P theory) to reveal the interlinkages between the subthreshold oscillation induced by neurons' resonance and ES-dependent instability of neural response. …”
Publicado 2023
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551“…The history and mechanism of molecular evolution in DNA have been greatly elucidated by contributions from genetics, probability theory and bioinformatics—indeed, mathematical developments such as Kimura's neutral theory, Kingman's coalescent theory and efficient software such as BLAST, ClustalW, Phylip, etc., provide the foundation for modern population genetics. …”
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552“…A proportion of these mutational events can create new immunogenic epitopes that, if processed and presented by an MHC allele, may be recognized by the adaptive immune system. Here, we use probability theory to analyze the mutational and epitope composition of a tumor mass in successive division cycles and create a double Pölya model for calculating the number of truly tumor-specific MHC I epitopes in a human tumor. …”
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553“…Knowledge of some basic linear algebra and probability theory should make the review easier to follow, although it may still have something to offer to those readers whose mathematics may be more limited.…”
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554“…Our findings sharpen and advance existing analysis on conceptual combinations, revealing systematic deviations from classical (fuzzy set) logic and probability theory. And, more important, our results give further considerable evidence to the validity of our quantum-theoretic framework for the combination of two concepts. …”
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555“…We show that Surprise, a recently proposed fitness function based on probability theory, does not suffer from these limitations. …”
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556“…The results obtained show that the proposed quantum Bayesian Network is a general method that can accommodate violations of the laws of classical probability theory and make accurate predictions regarding human decision-making in these scenarios.…”
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557“…Assisted by related probability theory and binomial distribution, we analyzed historical accident statistics in detail to reveal hidden laws. …”
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558“…Moreover, by adapting a construction from the study of exchangeable processes in probability theory, we prove that the corresponding [Formula: see text] -body OT problem is well approximated by the infinite-body problem. …”
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559“…Fokker–Planck PDEs (including diffusions) for stable Lévy processes (including Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image analysis, directional statistics and probability theory. Exact analytic designs and solutions are known in the 2D case, where they have been obtained using Fourier transform on [Formula: see text]. …”
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560“…Also, as a matter of fact that Shannon entropy is an intersection of information, probability theory, (non)linear dynamical systems and statistical physics, the proposed model in this study can be further calibrated to fit much better on COVID-19 observational data, using the above formalisms.…”
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