Stability arises as the consistency criterion in a betting interpretation for hyperreal imprecise previsions, that is imprecise previsions (and probabilities) which may take infinitesimal values. The purpose of this work is to extend the notion of stable coherence introduced in [8] to conditional hyperreal imprecise probabilities. Our investigation extends the de Finetti-Walley operational char...

The paper applies some very elementary model theory to explain how Kenneth Arrow’s classical theory of collective choice sheds some light on the nature of mathematical structures arising in physics.

The chapter represents a comparison of ultrapower fields (loosely surreals, hyper-reals, long line) and number fields generated by infinite primes having a physical interpretation in Topological Geometrodynamics. Ultrapower fields are discussed in very physicist friendly manner in the articles of Elemer Rosinger and these articles are taken as a convenient starting point. The physical interpret...

Non-standard interactions (NSI) arise naturally when considering physics beyond the Standard Model. In particular, they can have an important influence in the solar neutrino analysis. The current status of NSI constraints will be discussed and the perspectives of future neutrino experiments will be briefly outlined.

this study was motivated by three factors, which also contribute to its significance for today’s academic writing. first, research articles are the significant means of communication between the writers all over the world. second, persuasion and organization are crucial notions in academic writing where the authors have to consider the academic audiences and their needs.  third, some writers ar...

A new construction is given of non-standard uniserial modules over certain valuation domains; the construction resembles that of a special Aronszajn tree in set theory. A consequence is the proof of a sufficient condition for the existence of non-standard uniserial modules; this is a theorem of ZFC which complements an earlier independence result.

In the classical theory of probability we start by a pair (Ω, ), with Ω set of elementary events and σ-algebra of subsets of Ω, called events. A probability on is defined as a countable additive and positive function p such that p(Ω)=1. If A and B are two events, the conditional probability p(A/B) is defined if and only if p(B) is not null, by considering the quotient p(AB)/p(B). In the theory ...

Machine learning has enjoyed astounding practical success in a wide range of applications in recent years—practical success that often hurries ahead of our theoretical understanding. The standard framework for machine learning theory assumes full supervision, that is, training data consists of correctly labeled i.i.d. examples from the same task that the learned classifier is supposed to be app...