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We use a simple relational framework to develop the key notions and results on hidden variables and non-locality. The extensive literature on these topics in the foundations of quantum mechanics is couched in terms of probabilistic models,…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
Within the Kolmogorov theory of probability, Bayes' rule allows one to perform statistical inference by relating conditional probabilities to unconditional probabilities. As we show here, however, there is a continuous set of alternative…
First the crucial but very confidential fact is brought into evidence that, as Kolmogorov himself repeatedly claimed, there exists no abstract theory of probabilities, simply because the factual concept of probability is itself unachieved:…
The separately continuity topology is considered and some its properties are investigated. With help of these properties a generalization of Sierpinski theorem on determination of real separately continuous function by its values on an…
Recently, [{arXiv:0810.3134}] is accepted and published. We present ultimate version of no-hidden-variables theorem. We derive a proposition concerning the quantum theory under the existence of the Bloch sphere in a single spin-1/2 system.…
The notion of monogenic (or regular) functions, which is a correspondence of holomorphic functions, has been studied extensively in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. Recently, the concept of…
The study of stochastic variational principles involves the problem of constructing fixed-endpoint and adapted variations of semimartingales. We provide a detailed construction of variations of semimartingales that are not only fixed at…
This paper defines a new notion of bounded computable randomness for certain classes of sub-computable functions which lack a universal machine. In particular, we define such versions of randomness for primitive recursive functions and for…
Using the ideas of abstract algebra, we introduce the basic concepts of abstract probability theory that generalize the Kolmogorov's probability theory, possibility theory and other theories that deal with uncertainty. Based on abstract…
The class of convex sets that admit approximations as Minkowski sum of a compact convex set and a closed convex cone in the Hausdorff distance is introduced. These sets are called approximately Motzkin-decomposable and generalize the notion…
Some years ago Szab\'o and Fine proposed a {\it local} hidden variable theory for the GHZ experiment based on the assumption that "the detection efficiency is not (only) the effect of random errors in the detector equipment, but it is a…
It was shown in the early Seventies that, in Local Quantum Theory (that is the most general formulation of Quantum Field Theory, if we leave out only the unknown scenario of Quantum Gravity) the notion of Statistics can be grounded solely…
Constant (naive) imputation is still widely used in practice as this is a first easy-to-use technique to deal with missing data. Yet, this simple method could be expected to induce a large bias for prediction purposes, as the imputed input…
We provide a test for the specification of a structural model without identifying assumptions. We show the equivalence of several natural formulations of correct specification, which we take as our null hypothesis. From a natural empirical…
Scaling in the dynamical properties of complex many-body systems has been of strong interest since turbulence phenomena became the subject of systematic mathematical studies. In this article, dynamical critical phenomena far from…
We provide an algebraic perspective on Nielsen--Ninomiya-type no-go theorems arising from group cohomological anomalies, revisiting in particular the version proved by Kapustin and Sopenko. Departing from their analytic proof, our approach…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
In this short note we describe an alternative global version of the twisting procedure used by Dolgushev to prove formality theorems. This allows us to describe the maps of Fedosov resolutions, which are key factors of the formality…
We introduce notions of absolutely continuous functionals and representations on the non-commutative disk algebra $A_n$. Absolutely continuous functionals are used to help identify the type L part of the free semigroup algebra associated to…