Related papers: Log motivic exceptional direct image functors
The purpose of this note is to report, in narrative rather than rigorous style, about the nice geometry of $6$-division points on the Fermat cubic $F$ and various conics naturally attached to them. Most facts presented here were derived by…
We present a simple and accessible method which uses contour integration methods to derive formulae for functional determinants. To make the presentation as clear as possible, the general idea is first illustrated on the simplest case: a…
This article is the second one of a series of three articles devoted to direct images of isocrystals: here we consider convergent isocrystals with Frobenius structure. Let V be a complete discrete valuation ring, with residue field k = V/m…
One of the key advantages of Inductive Logic Programming systems is the ability of the domain experts to provide background knowledge as modes that allow for efficient search through the space of hypotheses. However, there is an inherent…
A new type of an integrable mapping is presented. This map is equipped with fractional difference and possesses an exact solution, which can be regarded as a discrete analogue of the Mittag-Leffler function.
The derivation of a function is a fundamental tool for solving problems in calculus. Consequently, the motivations for investigating physical systems capable of performing this task are numerous. Furthermore, the potential to develop an…
In this paper we define a class of polynomial functors suited for constructing coalgebras representing processes in which uncertainty plays an important role. In these polynomial functors we include upper and lower probability measures,…
We present a system for the automatic differentiation of a higher-order functional array-processing language. The core functional language underlying this system simultaneously supports both source-to-source automatic differentiation and…
We apply some methods and technique of complex dynamics to study the set of symmetries of attractors of holomorphic Iterated Function Systems (IFS), as well as relations between IFS sharing the same attractor.
In this note we consider different versions of coinduction functors between categories of comodules for corings induced by a morphism of corings. In particular we introduce a new version of the coinduction functor in the case of locally…
We use the theory of motivic integration in order to give a geometric explanation of the behavior of some p-adic integrals.
We define an operation of evaluation at a point for motivic constructible (exponential) functions from the Cluckers-Loeser framework of motivic integration and show that two such motivic functions are abstractly equal if and only if their…
Neuromorphic photonic accelerators are becoming increasingly popular, since they can significantly improve computation speed and energy efficiency, leading to femtojoule per MAC efficiency. However, deploying existing DL models on such…
Motivic local systems over a curve in finite characteristic form a countable set endowed with an action of the absolute Galois group of rational numbers commuting with the Frobenius map. I will discuss three series of conjectures about such…
The logarithmic slope of the diffractive structure function is a potential observable scanning the hard and soft contributions in diffraction, allowing to disentangle the QCD dynamics. We report our calculations concerning this quantity, in…
We develop a theory of modulus triples, for future motivic applications.
Reflexive functors of modules naturally appear in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in "duality theories". In this paper we study and determine reflexive functors and we give many…
We define a fundamental group for digital images. Namely, we construct a functor from digital images to groups, which closely resembles the ordinary fundamental group from algebraic topology. Our construction differs in several basic ways…
In nature, there are many phenomena with both irregularity and uncertainty. Therefore, a fuzzy-valued fractal interpolation is more useful for modeling them than fuzzy interpolation or fractal interpolation. We construct fractal…
We show that for quasi-compact quasi-separated schemes of finite dimension, the constructibility condition in real \'etale cohomology agrees with a notion of constructibility arising naturally from topology. As application we prove that the…