Related papers: Integration with respect to the Lefschetz number
In a former paper the first and third authors introduced the notion of direction set for a subset of R^n, and showed that the dimension of the common direction set of two subanalytic subsets, called directional dimension, is preserved by a…
We offer streamlined proofs of fundamental theorems regarding the index theory for partial self-maps of an infinite set that are bijective between cofinite subsets.
Semantic Embeddings are a popular way to represent knowledge in the field of zero-shot learning. We observe their interpretability and discuss their potential utility in a safety-critical context. Concretely, we propose to use them to add…
The statistical convergence is defined for sequences with the asymptotic density on the natural numbers, in general. In this paper, we introduce the statistical convergence for nets in Riesz spaces by using the finite additive measures on…
In this paper consisting of two parts, we study the integral of a logarithmic differential form on a compact semi-algebraic set in R^n or C^n. In Part I, we prove the convergence of the integral when the semi-algebraic set satisfies…
In this contribution we summarize our recent progress in understanding the relation between ${\cal N} = 1$ superconformal indices and relativistic elliptic integrable models. We start briefly reviewing the emergence of such models in…
Given a surface of infinite topological type, there are several Teichm\"uller spaces associated with it, depending on the basepoint and on the point of view that one uses to compare different complex structures. This paper is about the…
We suggest a simple definition for categorification of modules over rings and illustrate it by categorifying integral Specht modules over the symmetric group and its Hecke algebra via the action of translation functors on some subcategories…
This paper investigates functional inequalities involving Besov spaces and functions of bounded variation, when the underlying metric measure space displays different local and global structures. Particular focus is put on the $L^1$ theory…
Dimensions of objects in fusion categories are cyclotomic integers, hence number theoretic results have implications in the study of fusion categories and finite depth subfactors. We give two such applications. The first application is…
A transfer-matrix algorithm is presented herein as a beginning to study the transmission characteristics of coherent light through three-dimensional periodic microstructures, in which the structures are treated as two-dimensional-layer…
Recent approaches have shown that training deep neural networks directly on large-scale image-text pair collections enables zero-shot transfer on various recognition tasks. One central issue is how this can be generalized to object…
Object detection has achieved a huge breakthrough with deep neural networks and massive annotated data. However, current detection methods cannot be directly transferred to the scenario where the annotated data is scarce due to the severe…
We give sufficient conditions for a metric space to bilipschitz embed in L_1. In particular, if X is a length space and there is a Lipschitz map u:X--->R such that for every interval I in R, the connected components of the inverse image…
Let A, B, S be categories, let F:A-->S and G:B-->S be functors. We assume that for "many" objects a in A, there exists an object b in B such that F(a) is isomorphic to G(b). We establish a general framework under which it is possible to…
Based on tiles and on the Coven-Meyerowitz property, we present some examples and some general constructions of spectral subsets of integers.
Context is important for accurate visual recognition. In this work we propose an object detection algorithm that not only considers object visual appearance, but also makes use of two kinds of context including scene contextual information…
We present in this survey some results regarding Riemann_Lebesgue integrability with respect to arbitrary non-additive set functions.
One of the most important statistics in studying the zeros of L-functions is the 1-level density, which measures the concentration of zeros near the central point. Fouvry and Iwaniec [FI] proved that the 1-level density for L-functions…
As a core problem in computer vision, the performance of object detection has improved drastically in the past few years. Despite their impressive performance, object detectors suffer from a lack of interpretability. Visualization…