Related papers: Identity-Preserving Lax Extensions and Where to Fi…
Latent fibrations are an adaptation, appropriate for categories of partial maps (as presented by restriction categories), of the usual notion of fibration. The paper initiates the development of the basic theory of latent fibrations and…
The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…
We study the approximation of arbitrary distributions $P$ on $d$-dimensional space by distributions with log-concave density. Approximation means minimizing a Kullback--Leibler-type functional. We show that such an approximation exists if…
We discuss the existence of pullback attractors for multivalued dynamical systems on metric spaces. Such attractors are shown to exist without any assumptions in terms of continuity of the solution maps, based only on minimality properties…
We consider inference procedures, conditional on an observed ancillary statistic, for regression coefficients under a linear regression setup where the unknown error distribution is specified nonparametrically. We establish conditional…
This paper studies the behavior of Grobner bases with respect to extensions of scalars. We prove that an extension of scalars commutes with taking Grobner bases iff the extension is flat. We consider what information can be deduced about…
Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability…
We introduce normal cores, as well as the more general action cores, in the context of a semi-abelian category, and further generalise those to split extension cores in the context of a homological category. We prove that, if the category…
We prove that if a separable II$_1$ factor $M$ is existentially closed, then every $M$-bimodule is weakly contained in the trivial $M$-bimodule, $\text{L}^2(M)$, and, equivalently, every normal completely positive map on $M$ is a pointwise…
In this paper, we study the evolution of smooth, closed planar curves under a fourth order biharmonic flow with an external forcing term. Such flows arise naturally in the theory of biharmonic maps and geometric variational problems…
The question of whether classically conformal modifications of the standard model are consistent with experimental obervations has recently been subject to renewed interest. The method of Gildener and Weinberg provides a natural framework…
Process tomography, the experimental characterization of physical processes, is a central task in science and engineering. Here we investigate the axiomatic requirements that guarantee the in-principle feasibility of process tomography in…
In the context of a linear model with a sparse coefficient vector, exponential weights methods have been shown to be achieve oracle inequalities for prediction. We show that such methods also succeed at variable selection and estimation…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
This article establishes a rigorous spectral framework for the mathematical analysis of SHAP values. We show that any predictive model defined on a discrete or multi-valued input space admits a generalized Fourier expansion with respect to…
Given a double category D such that D_0 has pushouts, we characterize oplax/lax adjunctions between D and Cospan(D_0) such that the right adjoint is normal and restricts to the identity on D_0, where Cospan(D_0) denotes the double category…
Much like admissibility is the key concept underlying preferred semantics, strong admissibility is the key concept underlying grounded semantics, as membership of a strongly admissible set is sufficient to show membership of the grounded…
Real numbers do not admit an extensional procedure for observing discrete information, such as the first digit of its decimal expansion, because every extensional, computable map from the reals to the integers is constant, as is well known.…
The goal of this survey is to describe some recent results concerning the L 2 extension of holomorphic sections or cohomology classes with values in vector bundles satisfying weak semi-positivity properties. The results presented here are…
We consider the most common variants of linear regression, including Ridge, Lasso and Support-vector regression, in a setting where the learner is allowed to observe only a fixed number of attributes of each example at training time. We…