Related papers: Integration with respect to the Lefschetz number
We obtain an equivariant index theorem, or Lefschetz fixed-point formula, for isometries from complete Riemannian manifolds to themselves. The fixed-point set of such an isometry may be noncompact. We build on techniques developed by Roe.…
Humans are able to learn to recognize new objects even from a few examples. In contrast, training deep-learning-based object detectors requires huge amounts of annotated data. To avoid the need to acquire and annotate these huge amounts of…
We introduce a model category of spaces based on the definable sets of an o-minimal expansion of a real closed field. As a model category, it resembles the category of topological spaces, but its underlying category is a coherent topos. We…
Localization of a set of nodes is an important and a thoroughly researched problem in robotics and sensor networks. This paper is concerned with the theory of localization from inner-angle measurements. We focus on the challenging case…
In this paper, we give the explicit bounds for the data of objects involved in some basic theorems of Singularity theory: the Inverse, Implicit and Rank Theorems for Lipschitz mappings, Splitting Lemma and Morse Lemma, the density and…
We develop aspects of functional analysis in an abstract axiomatic setting, through monoidal and enriched category theory. We work in a given closed category, whose objects we call spaces, and we study R-module objects therein (or algebras…
The main purpose of this paper is to apply the theory of vector lattices and the related abstract modular convergence to the context of Mellin-type kernels and (non)linear vector lattice-valued operators, following the construction of an…
We study subgradient sequences of locally Lipschitz functions definable in a polynomially bounded o-minimal structure. We show that the diameter of any subgradient sequence is related to the variation in function values, with error terms…
The purpose of this survey is to present analytic versions of the injectivity theorem and their applications. The proof of our injectivity theorems is based on a combination of the L^2-method for the dbar-equation and the theory of harmonic…
This text grew out of notes I have used in teaching a one quarter course on integration at the advanced undergraduate level. My intent is to introduce the Lebesgue integral in a quick, and hopefully painless, way and then go on to…
We address the problem of one dimensional segment detection and estimation, in a regression setup. At each point of a fixed or random design, one observes whether that point belongs to the unknown segment or not, up to some additional…
Methods for object detection and segmentation often require abundant instance-level annotations for training, which are time-consuming and expensive to collect. To address this, the task of zero-shot object detection (or segmentation) aims…
We survey several non-absolutely convergent integrals, including the Henstock-Kurzweil and Pfeffer integrals, and use ideas from these theories to investigate the problem of multidimensional Young integration. We further present results on…
It is shown that the approximating functions used to define the Bochner integral can be formed using geometrically nice sets, such as balls, from a differentiation basis. Moreover, every appropriate sum of this form will be within a…
We extend the frozen density embedding theory to non-integer subsystems' particles numbers. Different features of this formulation are discussed, with special concern for approximate embedding calculations. In particular, we highlight the…
This paper addresses the task of zero-shot image classification. The key contribution of the proposed approach is to control the semantic embedding of images -- one of the main ingredients of zero-shot learning -- by formulating it as a…
A brief survey of the author and collaborators' work in compressive sensing applications to continuous imaging models.
In this paper, we analyze the subspace migration that occurs in limited-view inverse scattering problems. Based on the structure of singular vectors associated with the nonzero singular values of the multi-static response matrix, we…
We develop category-theoretic framework for universal homogeneous objects, with some applications in the theory of Banach spaces, linear orderings, and in topology of compact spaces.
The Lefschetz hyperplane section theorem asserts that an affine variety is homotopy equivalent to a space obtained from its generic hyperplane section by attaching some cells. The purpose of this paper is to describe attaching maps of these…