Related papers: A transfer principle for second-order arithmetic, …
This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or "toy" model of quantum mechanics over sets (QM/sets). There…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…
Preparation and measurement of physical systems are the operational building blocks of any physical experiment, and to describe them is the first purpose of any physical theory. It is remarkable that, in some situations, even when only…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
The Subspace Theorem is a powerful tool in number theory. It has appeared in various forms and been adapted and improved over time. It's applications include diophantine approximation, results about integral points on algebraic curves and…
In reverse mathematics, is is possible to have a curious situation where we know that an implication does not reverse, but appear to have no information on on how to weaken the assumption while preserving the conclusion. A main cause of…
In this short note, we introduce a generalization of the canonical base property, called transfer of internality on quotients. A structural study of groups definable in theories with this property yields as a consequence infinitely many new…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
A generalization of fluctuation theorems in stochastic processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via the Bayes theorem. In usual fluctuation theorems, a forward path and its…
We present a new proof of the classical divergence theorem in bounded domains. Our proof is based on a nonlocal analog of the divergence theorem and a rescaling argument. Main ingredients in the proof are nonlocal versions of the divergence…
In this paper, we intend to generalize the classical set theory as much as possible. we will do this by freeing sets from the regular properties of classical sets; e.g., the law of excluded middle, the law of non-contradiction, the…
Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…
Semi-algebraic priors are ubiquitous in signal processing and machine learning. Prevalent examples include a) linear models where the signal lies in a low-dimensional subspace; b) sparse models where the signal can be represented by only a…
In this paper, we introduce a new class of implicit function to prove common fixed point theorems in fuzzy metric space. Moreover we define a new altering distance in terms of integral and utilize the same to deduce integral type…
We suggest an interpretation of quantum mechanics, inspired by the ideas of Aharonov et al. of a time-symmetric description of quantum theory. We show that a special final boundary condition for the Universe, may be consistently defined as…
We define a game semantics for second order classical arithmetic PA2 (with quantifiers over predicates on integers and full comprehension axiom). Our semantics is effective: moves are described by a finite amount of information and whenever…
We provide a version of the celebrated theorem of Koml\'os in which, rather then random quantities, a sequence of finitely additive measures is considered. We obtain a form of the subsequence principle and some applications.
Recent analysis of classical algorithms resulted in their axiomatization as transition systems satisfying some simple postulates, and in the formulation of the Abstract State Machine Theorem, which assures us that any classical algorithm…
Our aim in this paper is to look at some transfer results in model theory (mainly in the context of o-minimal structures) from the category theory viewpoint.