“…We compare two approaches to embedding joint distributions of random variables recorded under different conditions (such as spins of entangled particles for different settings) into the framework of classical, Kolmogorovian probability theory. In the contextualization approach each random variable is “automatically” labeled by all conditions under which it is recorded, and the random variables across a set of mutually exclusive conditions are probabilistically coupled (imposed a joint distribution upon). …”
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“…Correspondingly, the conflict relationships of streams are built using probability theory. Furthermore, the entry capacity model of roundabouts is built, and sensitivity analysis is conducted on the model parameters. …”
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“…The iceLogo web server and SOAP service implement the previously published iceLogo algorithm. iceLogo builds on probability theory to visualize protein consensus sequences in a format resembling sequence logos. …”
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“…The formulation of the forward and backward variables in profile HMMs is made under statistical independence assumption of the probability theory. We propose a fuzzy profile HMM to overcome the limitations of that assumption and to achieve an improved alignment for protein sequences belonging to a given family. …”
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“…Here we use a statistical mechanical approach to show that the allosteric coupling between two collective variables is not a single number, but instead a two-dimensional thermodynamic coupling function that is directly related to the mutual information from information theory and the copula density function from probability theory. On this basis, we demonstrate how to quantify the contribution of specific energy terms to this thermodynamic coupling function, enabling an approximate decomposition that reveals the mechanism of allostery. …”
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“…Moreover, the advances in our understanding are also attributable to the development of new computational methods based on a phylogenetic analysis of influenza virus strains and mathematical (integro-differential equations, statistical methods, probability-theory-based methods) and simulation modeling. …”
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“…Using this empirical example and the principles of probability theory, the derivation of the equations describing this treatment failure is carried out. …”
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“…Using results from probability theory, we show analytically and using examples that averaged trajectories will be more symmetric as the number of averaged trajectories increases, even if none of the original trajectories they were derived from is symmetric. …”
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“…A large number of studies in cognitive science have revealed that probabilistic outcomes of certain human decisions do not agree with the axioms of classical probability theory. The field of Quantum Cognition provides an alternative probabilistic model to explain such paradoxical findings. …”
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“…It has important applications in cybernetics, probability theory, astrophysics, life sciences and other fields. …”
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“…We employ a Markov model, stochastically simulated via an adapted Gillespie algorithm, and further improved through probability theory. The stochastic algorithm produces a simulated dataset for comparison with experimental clonal data by inspecting quantifiable properties. …”
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“…Bayesian approaches presuppose that following the coherence conditions of probability theory makes probabilistic judgments more accurate. …”
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“…This theory is based on the synthesis of the fuzzy sets theory with perception-based information and the probability theory. The book is self containing and represents in a systematic way the decision theory with imperfect information into the educational systems. …”
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“…Ito: Semigroups in probability theory.- T. Kato: Abstract evolution equations, linear and quasilinear, revisited.- J.L. …”
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“…This updated and revised third edition of the leading reference volume on distance metrics includes new items from very active research areas in the use of distances and metrics such as geometry, graph theory, probability theory and analysis. Among the new topics included are, for example, polyhedral metric space, nearness matrix problems, distances between belief assignments, distance-related animal settings, diamond-cutting distances, natural units of length, Heidegger’s de-severance distance, and brain distances. …”
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“…As one of the key parts of Calder6n-Zygmund's real method which first appeared in the 50's, Calder6n-Zygmund Decomposition is exactly the so-called stopping time argument in nature which already existed in the Probability Theory early in the 30's, although such a close relationship between Calder6n-Zygmund De­ composition and the stopping time argument perhaps was not realized consciously at that time. …”
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“…The reader is assumed to be familiar with some of the concepts of probability theory, but no particular knowledge of branching processes is required. …”
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“…This volume is a completely revised and enlarged second edition which comprises recently obtained research results of topical interest, and has been extended to include a new section on the basic concepts of probability theory. A completely new chapter on fully developed turbulence presents the successes of chaos theory, its limitations as well as future trends in the development of complex spatio-temporal structures.   …”
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“…No measure theory is used and only a small amount of linear algebra is required. All necessary probability theory is developed in several chapters throughout the book, on a "need-to-know" basis. …”
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“…ourishing and rapidly growing subject of probability theory as well. These developments have been triggered to a large part by the mathem- ical understanding gained on the fascinating and previously mysterious “Parisi solution” of the Sherrington–Kirkpatrick mean ?…”
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