Related papers: Integration with respect to the Lefschetz number
We extend Donaldson's asymptotically holomorphic techniques to symplectic orbifolds. More precisely, given a symplectic orbifold such that the symplectic form defines an integer cohomology class, we prove that there exist sections of large…
Satellite image analysis has important implications for land use, urbanization, and ecosystem monitoring. Deep learning methods can facilitate the analysis of different satellite modalities, such as electro-optical (EO) and synthetic…
In recent years, Teichm\"uller theory, which is the study of moduli spaces of marked Riemann surfaces, has come to be considered more and more from the point of view of actions of surface groups inside certain semi-simple Lie groups. In…
Object detection aims to identify instances of semantic objects of a certain class in images or videos. The success of state-of-the-art approaches is attributed to the significant progress of object proposal and convolutional neural…
In this paper we study singular integrals on small (that is, measure zero and lower than full dimensional) subsets of metric groups. The main examples of the groups we have in mind are Euclidean spaces and Heisenberg groups. In addition to…
We propose to grok Lipschitz stratifications from a non-archimedean point of view and thereby show that they exist for closed definable sets in any power-bounded o-minimal structure on a real closed field. Unlike the previous approaches in…
Zero-shot learning has gained popularity due to its potential to scale recognition models without requiring additional training data. This is usually achieved by associating categories with their semantic information like attributes.…
In this work a combinatorial approach towards the weak Lefschetz property is developed that relates this property to enumerations of signed perfect matchings as well as to enumerations of signed families of non-intersecting lattice paths in…
Foundation models are a strong trend in deep learning and computer vision. These models serve as a base for applications as they require minor or no further fine-tuning by developers to integrate into their applications. Foundation models…
In this work, we develop Extraction Theorems for classes of geometric objects with small extraction numbers. These classes include intervals, axis-parallel segments, axis-parallel rays, and octants. We investigate these classes of objects…
continuum-robots, prosthetic devices and wearable body-shape sensors. A miniaturised one-degree-of-freedom joint-angle sensor is devised, using a single light emitting/receiving optical fibre with a coupler connected to a Keyence (FS-N11MN,…
As lensing of coherent astrophysical sources e.g. pulsars, fast radio bursts, and gravitational waves becomes observationally relevant, the mathematical framework of Picard-Lefschetz theory has recently been introduced to fully account for…
We use the theory of motivic integration for singular spaces to give a characterization of minimal log discrepencies in terms of the codimension of certain subsets of spaces of arcs. This is done for arbitrary pairs $(X,Y)$, with $X$ normal…
We give criteria for Morin singularities for germs of maps into lower dimensions. As an application, we study the bifurcation of Lefschetz singularities.
We are going to widen the scope of the previously defined Hausdorff-integral in two ways. First, in the sense, that we develop the theory of the integral on some naturally generalized measure spaces. Second, we extend it to functions taking…
Current Zero-Shot Learning (ZSL) approaches are restricted to recognition of a single dominant unseen object category in a test image. We hypothesize that this setting is ill-suited for real-world applications where unseen objects appear…
This study investigates the applicability of Kirchhoff migration (KM) for a fast identification of unknown objects in a real-world limited-aperture inverse scattering problem. To demonstrate the theoretical basis for the applicability…
The segmentation of transparent objects can be very useful in computer vision applications. However, because they borrow texture from their background and have a similar appearance to their surroundings, transparent objects are not handled…
Let N be an o-minimal expansion of a real closed field. We develop cohomology theory for the category of N-definable manifolds and N-definable maps, and use this to solve the Peterzil-Steinhorn problem on the existence of torsion points on…
In this paper, we consider a question of sum-keeping about a multiplicative subsemigroup and its generator subsets in a semiring, and develop some elementary (collapse) process of the sum-keeping retraction through subsets until one minimal…