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Probability and science
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Description: A collection of research and pedagogic material in physics, mathematics, other sciences, and the probability calculus
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Geometry of maximum-entropy proofs: stationary points, convexity, Legendre transforms, exponential families
This note is a geometric commentary on maximum-entropy proofs. Its purpose is to illustrate the geometric structures involved in such proofs, to expla...
Maximum-entropy from the probability calculus: exchangeability, sufficiency
Maximum-entropy distributions are shown to appear in the probability calculus as approximations of a model by exchangeability or a model by sufficienc...
Unlearning and Seyab's theorem: a dialogue about updating probability
This dialogue explores the possibility of updating a probability as a consequence of unlearning, reversing the role of prior and posterior probabiliti...
Conjectures and questions in convex geometry: of interest for quantum theory and other physical statistical theories
Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance for quantum theory and generic...
Inferring health conditions from fMRI-graph data
Automated classification methods for disease diagnosis are currently in the limelight, especially for imaging data. Classification does not fully meet...
Force, inertia, metric in Newtonian relativity and general relativity
[Draft:] This note is an exploration of some notions around kinematics, dynamics, matter, inertia, and force in Newtonian- and general-relativistic co...
"Eppur ruota": modelling the ocean as a fluid with spin
[Draft:] This note presents and motivates the idea of modelling the ocean on eddy-permitting and coarser scales as a continuum with spin.
Quantum theory within the probability calculus: a there-you-go theorem and partially exchangeable models
"Ever since the advent of modern quantum mechanics in the late 1920's, the idea has been prevalent that the classical laws of probability cease, in so...
Maximum-entropy and representative samples of neuronal activity: a dilemma
The present work shows that the maximum-entropy method can be applied to a sample of neuronal recordings along two different routes: (1) apply to the ...
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