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Quantum Set Theory Extending the Standard Probabilistic Interpretation of Quantum Theory (Extended Abstract) [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of equality relation ...
Masanao Ozawa
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Remarks on the Maximum Entropy Principle with Application to the Maximum Entropy Theory of Ecology [PDF]
Entropy, 2017 In the first part of the paper we work out the consequences of the fact that Jaynes’ Maximum Entropy Principle, when translated in mathematical terms, is a constrained extremum problem for an entropy function H ( p ) expressing the uncertainty ...
Marco Favretti
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Algorithmic Information Theory and Foundations of Probability [PDF]
, 2009 The use of algorithmic information theory (Kolmogorov complexity theory) to explain the relation between mathematical probability theory and `real world' is discussed.
G. Polya, O. Goldreich, V. Uspensky
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Foundational Problems of Quantum Theory: Novel Approach to Temporal Probability Density
Journal of Physics: Theories and Applications, 2022 Present study focuses on some foundational problems of quantum theory specifically deals with the concept of probability density and relating introductory problems.
Mustafa Erol, M. Emre Kuzucu
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Construction of Fuzzy Numbers via Cumulative Distribution Function
Mathematics, 2022 The first person to introduce possibility theory was Lotfi A. Zadeh, in 1977. It was, of course, of no coincidence that he directly combined it with the theory of fuzzy sets.
Georgios Souliotis +2 more
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New extreme value theory for maxima of maxima
Statistical Theory and Related Fields, 2021 Although advanced statistical models have been proposed to fit complex data better, the advances of science and technology have generated more complex data, e.g., Big Data, in which existing probability theory and statistical models find their ...
Wenzhi Cao, Zhengjun Zhang
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Random Fields in Physics, Biology and Data Science
Frontiers in Physics, 2021 A random field is the representation of the joint probability distribution for a set of random variables. Markov fields, in particular, have a long standing tradition as the theoretical foundation of many applications in statistical physics and ...
Enrique Hernández-Lemus +1 more
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Logical perspectives on the foundations of probability
Open Mathematics, 2023 We illustrate how a variety of logical methods and techniques provide useful, though currently underappreciated, tools in the foundations and applications of reasoning under uncertainty.
Hosni Hykel, Landes Jürgen
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How Quantum Mechanics Requires Non-Additive Measures
Entropy, 2023 Measure theory is used in physics, not just to capture classical probability, but also to quantify the number of states. In previous works, we found that state quantification plays a foundational role in classical mechanics, and, therefore, we set ...
Gabriele Carcassi, Christine A. Aidala
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Response to Johnson: A random sample versus the radical event
Finance and Society, 2016 Timothy Johnson's working hypothesis in his review of my latest book, The Medium of Contingency, is that I (as well as the ‘quants’ involved in the derivative pricing industry) do not understand the foundations of abstract probability theory.
Elie Ayache
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