Related papers: On Generalized Metric Spaces for the Simply Typed …
We give Ramsey expansions of classes of generalised metric spaces where distances come from a linearly ordered commutative monoid. This complements results of Conant about the extension property for partial automorphisms and extends an…
Log-Euclidean distances are commonly used to quantify the similarity between positive definite matrices using geometric considerations. This paper analyzes the behavior of this distance when it is used to measure closeness between…
Enriched Lawvere theories are a generalization of Lawvere theories that allow us to describe the operational semantics of formal systems. For example, a graph enriched Lawvere theory describes structures that have a graph of operations of…
The objective of this manuscript is to introduce and develop the concept of a generalized $\theta$-parametric metric space-a novel extension that enriches the modern metric fixed point theory. We study of its fundamental properties,…
We introduce the notion of scale to generalize and compare different invariants of metric spaces and their measures. Several versions of scales are introduced such as Hausdorff, packing, box, local and quantization. They moreover are…
In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying…
In the present work, metrics which lead to projected closed orbits are found by comparing the relativistic differential equation of orbits with the corresponding classical differential equation. Physical and geometrical properties of these…
We advocate the use of de Bruijn's universal abstraction $\lambda^\infty$ for the quantification of schematic variables in the predicative setting and we present a typed $\lambda$-calculus featuring the quantifier $\lambda^\infty$…
We generalize the measurement using an expanded concept of cover, in order to provide a new approach to size of set other than cardinality. The generalized measurement has application backgrounds such as a generalized problem in dimension…
Numerous models for grounded language understanding have been recently proposed, including (i) generic models that can be easily adapted to any given task and (ii) intuitively appealing modular models that require background knowledge to be…
We present a conceptual framework that unifies a variety of evaluation metrics for different structured prediction tasks (e.g. event and relation extraction, syntactic and semantic parsing). Our framework requires representing the outputs…
Canonical extension has proven to be a powerful tool in algebraic study of propositional logics. In this paper we describe a generalization of the theory of canonical extension to the setting of first order logic. We define a notion of…
We prove the equivalence of two seemingly very different ways of generalising Rademacher's theorem to metric measure spaces. One such generalisation is based upon the notion of forming partial derivatives along a very rich structure of…
This paper is a review of concepts from graded commutative algebra with specific attention given to length and multiplicity. The author's motivation for this paper comes from the study of equivariant cohomology in algebraic topology where…
By using the metric projection onto a closed self-dual cone of the Euclidean space, M. S. Gowda, R. Sznajder and J. Tao have defined generalized lattice operations, which in the particular case of the nonnegative orthant of a Cartesian…
{Researchers recently introduced interpolative metric spaces and established fixed-point theorems in this setting. We demonstrate that these metrics are a special case of b-metrics. On the other hand, suprametrics and b-suprametrics have…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
In this paper, we take a pervasively effectful (in the style of ML) typed lambda calculus, and show how to extend it to permit capturing pure expressions with types. Our key observation is that, just as the pure simply-typed lambda calculus…
Vector fields with components which are generalized zero-forms are constructed. Inner products with generalized forms, Lie derivatives and Lie brackets are computed. The results are shown to generalize previously reported results for…
Categories and categorical structures are increasingly recognized as useful abstractions for modeling in science and engineering. To uniformly implement category-theoretic mathematical models in software, we introduce GATlab, a…