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

We extend known existence and uniqueness results of weak measure solutions for systems of non-local continuity equations beyond the usual Lipschitz regularity. Existence of weak measure solutions holds for uniformly continuous vector fields…

This work builds a unified framework for the study of quadratic form distance measures as they are used in assessing the goodness of fit of models. Many important procedures have this structure, but the theory for these methods is dispersed…

Helton, Lasserre, and Putinar (2008, Ann. Probability; arXiv:math/0702314) expose the relationship between three properties of a measure: the conditional triangularity property of the associated orthogonal polynomials, the zeros in the…

Proteins contain a large fraction of regular, repeating conformations, called secondary structure. A simple, generic definition of secondary structure is presented which consists of measuring local correlations along the protein chain.…

The main result of this paper, Theorem 1.5, establishes a conjecture of Lyons and Peres: for a determinantal point process governed by a reproducing kernel, the system of kernels sampled at the particles of a random configuration is…

We present a new strictification method for type-theoretic structures that are only weakly stable under substitution. Given weakly stable structures over some model of type theory, we construct equivalent strictly stable structures by…

Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.

In this paper, we address the problem of constructing a uniform probability measure on $\mathbb{N}$. Of course, this is not possible within the bounds of the Kolmogorov axioms and we have to violate at least one axiom. We define a…

We establish a general structure theorem for the singular part of ${\mathscr A}$-free Radon measures, where ${\mathscr A}$ is a linear PDE operator. By applying the theorem to suitably chosen differential operators ${\mathscr A}$, we obtain…

The test of homogeneity for normal mixtures has been conducted in diverse research areas, but constructing a theory of the test of homogeneity is challenging because the parameter set for the null hypothesis corresponds to singular points…

For a fixed set $X$, an arbitrary \textit{weight structure} $d \in [0,\infty]^{X \times X}$ can be interpreted as a distance assignment between pairs of points on $X$. Restrictions (i.e. \textit{metric axioms}) on the behaviour of any such…

Even when a system is proven to be correct with respect to a specification, there is still a question of how complete the specification is, and whether it really covers all the behaviors of the system. Coverage metrics attempt to check…

We describe the Dedekind cuts explicitly in terms of non-standard rational numbers. This leads to another construction of a Dedekind complete totally ordered field or, equivalently, to another proof of the consistency of the axioms of the…

This paper studies axioms for nonmonotonic consequences from a semantics-based point of view, focusing on a class of mathematical structures for reasoning about partial information without a predefined syntax/logic. This structure is called…

We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our…

We develop a constructive theory of continuous domains from the perspective of program extraction. Our goal that programs represent (provably correct) computation without witnesses of correctness is achieved by formulating correctness…

Bell non-local correlations cannot be naturally explained in a fixed causal structure. This serves as a motivation for considering models where no global assumption is made beyond logical consistency. The assumption of a fixed causal order…

The motivation of this note is to show how singular values affect local uniqueness. More precisely, Theorem 3.1 shows how to construct a neighborhood (a ball) of a regular equilibrium whose diameter represents an estimate of local…

A fundamental question in system design is to decide how much of the design of one component must be known in order to successfully design another component of the system. We study this question in the setting of reactive synthesis, where…

Models like support vector machines or Gaussian process regression often require positive semi-definite kernels. These kernels may be based on distance functions. While definiteness is proven for common distances and kernels, a proof for a…