Related papers: Fonctions constructibles et int\'egration motiviqu…

We give an elementary characterization of rational functions among meromorphic functions in the complex plane.

In this paper we generalize notions of iterated integral with regard to an unpredictable process. We establish a formula of integration by parts, the existence of a continuous modification and give an expression of the increasing process.

Extending G\"odel's \emph{Dialectica} interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite…

We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.

An informal discussion of how the construction problem in algebraic geometry motivates the search for formal proof methods. Also includes a brief discussion of my own progress up to now, which concerns the formalization of category theory…

In this paper, we generally describe a method of taking an abstract six functors formalism in the sense of Khan or Cisinski-D\'{e}glise, and outputting a derived motivic measure in the sense of Campbell-Wolfson-Zakharevich. In particular,…

Given a group, we construct a fundamental additive functor on its orbit category. We prove that any isomorphism conjecture valid for this fundamental isomorphism functor holds for all additive functors, like K-theory, cyclic homology,…

The notion of constructible functions in the setting of tame real geometry has been introduced by Cluckers and Dan Miller in their work on parametric integration of globally subanalytic functions. A function on a globally subanalytic set is…

We construct a functor from the triangulated category of Voevodsky motives to a certain derived category of mixed Hodge structures enriched with integral weight filtration. We use this construction to prove a strong integral version of the…

Some sorts of generalized morphisms are defined from very basic mathematical objects such as sets, functions, and partial functions. A wide range of mathematical notions such as continuous functions between topological spaces, ring…

We study projective functions. We prove that projective functions generalise lower and upper-semianalytic ones while being stable by composition and difference. We show that the class of projective functions is closed under sums,…

Integration of Hamiltonian systems by reduction to action-angle variables has proven to be a successful approach. However, when the solution depends on elliptic functions the transformation to action-angle variables may need to remain in…

There are several physically motivated density matrix functionals in the literature, built from the knowledge of the natural orbitals and the occupation numbers of the one-body reduced density matrix. With the help of the equivalent…

We present a factorized compositional distributional semantics model for the representation of transitive verb constructions. Our model first produces (subject, verb) and (verb, object) vector representations based on the similarity of the…

A series of physically motivated operations appearing in the study of composite materials are interpreted in terms of elementary continued fraction transforms of matrix valued, rational Stieltjes functions.

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…

The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…

To understand changes in physical systems and facilitate decisions, explaining how model predictions are made is crucial. We use model-based interpretability, where models of physical systems are constructed by composing basic constructs…

We propose a new definition of actual cause, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for…

We explore a functionalist approach to emotion by employing an ansatz -- an initial set of assumptions -- that a hypothetical concept generation model incorporates unproven but biologically plausible traits. From these traits, we…