Related papers: Norm functors and effective zero cycles

The aim of this book is to show that the use of f-analytic families of finite type cycles (cycles having finitely many irreducible components, but not compact in general) in a given complex space may be useful in complex geometry, despite…

The work in this article is concerned with two different types of families of finite sets: separating families and splitting families (they are also called "systems"). These families have applications in combinatorial search, coding theory,…

We characterize a family of number triangles whose production matrices are closely related to the original number triangle. We study a number of such triangles that are of combinatorial significance. For a specific subfamily, these…

This is primarily a survey of the developments in the theory of harmonic maps of finite uniton number (or unitons) which have taken place since the introduction of extended solutions by Uhlenbeck. Such maps include all harmonic maps from…

We characterize the full classes of M-estimators for semiparametric models of general functionals by formally connecting the theory of consistent loss functions from forecast evaluation with the theory of M-estimation. This novel…

We show that integration with respect to the Euler-Poincar\'e characteristic can be extended from the setting of definable sets to the setting of topological spaces homeomorphic to definable sets. We use that extension to generalize a…

Relative realizability toposes satisfy a universal property that involves regular functors to other categories. We use this universal property to define what relative realizability categories are, when based on other categories than of the…

This article is first in a series of papers where we reprove the statements in constructing the Enhanced Operation Map and the abstract six-functor formalism developed by Liu-Zheng. In this paper, we prove a theorem regarding constructing…

We forge connections between the theory of fractal sets obtained as attractors of iterated function systems and process calculi. To this end, we reinterpret Milner's expressions for processes as contraction operators on a complete metric…

We introduce Flux Matching, a new paradigm for generative modeling that generalizes existing score-based models to a broader family of vector fields that need not be conservative. Rather than requiring the model to equal the data score, the…

In this paper, we study a certain extension of Nori's fundamental group in the case where a base field is of characteristic 0 and give structure theorems about it. As a result, for a smooth projective curve with genus $g$>1, we prove that…

In continuous logic, there are plenty of examples of interesting stable metric structures. However, on the other side of the SOP line, there are only a few metric structures where order is relevant, and orders often appear in different…

Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…

Cycles, which can be found in many different kinds of networks, make the problems more intractable, especially when dealing with dynamical processes on networks. On the contrary, tree networks in which no cycle exists, are simplifications…

We introduce a reducibility on classes of structures, essentially a uniform enumeration reducibility. This reducibility is inspired by the Friedman-Stanley paper on using Borel reductions to compare classes of countable structures. This…

Functional dependencies are an integral part of database design. However, they are only defined when we exclude null markers. Yet we commonly use null markers in practice. To bridge this gap between theory and practice, researchers have…

We work with a generalization of knot theory, in which one diagram is reachable from another via a finite sequence of moves if a fixed condition, regarding the existence of certain morphisms in an associated category, is satisfied for every…

We define the zeta function of a finite category. And we propose a conjecture which states the relationship between the Euler characteristic of finite categories and the zeta function of finite categories. This conjecture is verified when…

Probability distributions supported on the simplex enjoy a wide range of applications across statistics and machine learning. Recently, a novel family of such distributions has been discovered: the continuous categorical. This family enjoys…

Monads are a useful tool for structuring effectful features of computation such as state, non-determinism, and continuations. In the last decade, several generalisations of monads have been suggested which provide a more fine-grained model…