相关论文: Linear representations of probabilistic transforma…

The probabilities of point events in space 3 + 1 obey an equation of Dirac type. Masses, moments, energies, spins, etc. are the parameters of the probability distribution of such events. The terms and equations of quark-gluon theories turn…

Probabilistic circuits compute multilinear polynomials that represent multivariate probability distributions. They are tractable models that support efficient marginal inference. However, various polynomial semantics have been considered in…

The ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables. This goal is, however, seldom achieved because most established regression models only…

The probabilistic description of the time evolution of a physical system can take two conceptually distinct forms: a trajectory of probabilities, which specifies how probabilities evolve over time, and a probability on trajectories, which…

We introduce a framework to describe probabilistic models in Bell experiments, and more generally in contextuality scenarios. Such a scenario is a hypergraph whose vertices represent elementary events and hyperedges correspond to…

We review some of our recent results (with collaborators) on information processing in an ordered linear spaces framework for probabilistic theories. These include demonstrations that many "inherently quantum" phenomena are in reality quite…

Numerical simulations are widely used to predict the behavior of physical systems, with Bayesian approaches being particularly well suited for this purpose. However, experimental observations are necessary to calibrate certain simulator…

One may ask whether an extended group of invariance can naturally be attributed to the space of associative commutative Quadrahyperbolic Numbers? To search for a rigorous and positive answer to the question, we shall focus on the method of…

We constructed the representation of contextual probabilistic dynamics in the complex Hilbert space. Thus dynamics of the wave function can be considered as Hilbert space projections of realistic dynamics in a ``prespace''. The basic…

Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models…

Max Born's statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. While the latter always result from an…

We develop a transitional geometry, that is, a family of geometries of constant curvatures which makes a continuous connec-tion between the hyperbolic, Euclidean and spherical geometries. In this transitional setting, several geometric…

Non-commutative propositions are characteristic of both quantum and non-quantum (sociological, biological, psychological) situations. In a Hilbert space model states, understood as correlations between all the possible propositions, are…

These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…

We establish large deviation formulas for linear statistics on the $N$ transmission eigenvalues $\{T_i\}$ of a chaotic cavity, in the framework of Random Matrix Theory. Given any linear statistics of interest $A=\sum_{i=1}^N a(T_i)$, the…

A theorem of McCann shows that for any two absolutely continuous probability measures on R^d there exists a monotone transformation sending one probability measure to the other. A consequence of this theorem, relevant to statistics, is that…

Logistic models are studied as a tool to convert output from numerical weather forecasting systems (deterministic and ensemble) into probability forecasts for binary events. A logistic model obtains by putting the logarithmic odds ratio…

We study a nonlinear recombination model from population genetics as a combinatorial version of the Kac-Boltzmann equation from kinetic theory. Following Kac's approach, the nonlinear model is approximated by a mean field linear evolution…

This paper introduces the concept of random context representations for the transition probabilities of a finite-alphabet stochastic process. Processes with these representations generalize context tree processes (a.k.a. variable length…

Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given…