Related papers: Vop\v{e}nka's Alternative Set Theory as a framewor…
Turing machines and spin models share a notion of universality according to which some simulate all others. Is there a theory of universality that captures this notion? We set up a categorical framework for universality which includes as…
We extend de Finetti's [Ann. Inst. H. Poincar\'{e} 7 (1937) 1--68] notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than…
Little effort has been devoted to studying generalised notions or models of (un)predictability, yet is an important concept throughout physics and plays a central role in quantum information theory, where key results rely on the supposed…
We consider the task of forecasting an infinite sequence of future observations based on some number of past observations, where the probability measure generating the observations is "suspected" to satisfy one or more of a set of…
This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…
The past decades have seen increasing interest in modelling uncertainty by heterogeneous methods, combining probability and interval analysis, especially for assessing parameter uncertainty in engineering models. A unifying mathematical…
We establish new uniform height inequalities for rational points on higher-dimensional varieties, extending the classical Roth-Schmidt-Subspace paradigm to the Arakelov-theoretic setting. Our main result provides sharp bounds for heights…
A class of subsets designated as very thin subsets of natural numbers has been studied and seen that theory of convergence may be rediscovered if very thin sets are given to play main role instead of thin or finite sets which removes some…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…
Within the possibilistic approach to uncertainty modeling, the paper presents a modal logical system to reason about qualitative (comparative) statements of the possibility (and necessity) of fuzzy propositions. We relate this qualitative…
This article discusses completeness of Boolean Algebra as First Order Theory in Goedel's meaning. If Theory is complete then any possible transformation is equivalent to some transformation using axioms, predicates etc. defined for this…
We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coefficients which allow us to characterize transport problems in a gradient flow setting, and form the basis of our…
We consider a system of weak* closed sets of finite-dimensional distributions. We show that a corresponding system of random variables can be defined on a probability space with a probability measure determined up to some set of measures,…
The construction of weak solutions to compressible Navier-Stokes equations via a numerical method (including a rigorous proof of the convergence) is in a short supply, and so far, available only for one sole numerical scheme suggested in…
This paper develops a new divergence that generalizes relative entropy and can be used to compare probability measures without a requirement of absolute continuity. We establish properties of the divergence, and in particular derive and…
We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles,…
Homological algebra of modules over posets is developed, as closely parallel as possible to that of finitely generated modules over noetherian commutative rings, in the direction of finite presentations and resolutions. Centrally at issue…
Many practical optimization problems involve uncertain parameters that are strictly positive. However, the most common uncertainty sets used in robust optimization are the box and the ellipsoidal sets, which may include non-positive values…
The topic of this paper is the subtle interplay between countability and representations. In particular, we establish that the definition of countability of a certain set $X$ crucially hinges on the associated equivalence relation $=_{X}$.…