相关论文: Construction of a specification from its singleton…

Reusable software components need expressive specifications. This paper outlines a rigorous foundation to model-based contracts, a method to equip classes with strong contracts that support accurate design, implementation, and formal…

We establish various forms of the following certainty principle: a set $S \subset \mathbb{R}^{n}$ contains a given finite linear pattern, provided that $S$ is a support of the Fourier transform of a sufficiently singular probability measure…

In this paper we establish a general framework in which the verification of support theorems for generalized convex functions acting between an algebraic structure and an ordered algebraic structure is still possible. As for the domain…

There are many research works devoted to Gibbs measure for models on Cayley trees. Among these works, there are some works in which the general results are identical, but the considered models are various. In this article, we present the…

The class of O-metric spaces generalize several existing metric-types in literature including metric spaces, b-metric spaces, and ultra metric spaces. In this paper, we discuss the properties of the topology induced by an O-metric and…

First-order optimization methods have attracted a lot of attention due to their practical success in many applications, including in machine learning. Obtaining convergence guarantees and worst-case performance certificates for first-order…

A bounded subset of a normed linear space is said to be (diametrically) complete if it cannot be enlarged without increasing the diameter. A complete super set of a bounded set $K$ having the same diameter as $K$ is called a completion of…

We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions…

We present a construction of a certain infinite complete partial order (CPO) that differs from the standard construction used in Scott's denotational semantics. In addition, we construct several other infinite CPO's. For some of those, we…

Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of…

We derive finite-dimensional quantum mechanics from a single ontological principle, that \emph{existence is constituted by distinguishability}, together with two structural commitments: finite capacity $N$ (parametric input) and…

Dependence on the parameter is continuous when perturbations of the parameter preserves strict preference for one alternative over another. We characterise this property via a utility function over alternatives that depends continuously on…

In a series of recent work, we have introduced a general framework for quantitative reasoning in specification theories. The contribution of this paper is to show how this framework can be applied to yield a robust specification theory for…

We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…

We develop the homotopy theory of semisimplicial sets constructively and without reference to point-set topology to obtain a constructive model for $\omega$-groupoids. Most of the development is folklore, but for a few results the author is…

We present a version of Krasnosel'skii fixed point theorem for operators acting on Cartesian products of normed linear spaces, under cone-compression and cone-expansion conditions of norm type. Our approach, based on the fixed point index…

Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…

We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice…

We study a notion of potential isomorphism, where two structures are said to be potentially isomorphic if they are isomorphic in some generic extension that preserves stationary sets and does not add new sets of cardinality less than the…

Protein structures in nature often exhibit a high degree of regularity (secondary structures, tertiary symmetries, etc.) absent in random compact conformations. We demonstrate in a simple lattice model of protein folding that structural…