相关论文: Motivic measures

This work is motivated by the need to assess the degree of agreement between two independent groups of raters. It proposes two new methods.

This position paper describes an experiment conducted to understand the relationships between different physiological measures including pupil Diameter, Blinking Rate, Heart Rate, and Heart Rate Variability in order to develop an estimation…

We show that closed subsets of the character variety of a complex variety with negatively weighted homology, which are $p$-adically integral and Galois invariant, are motivic. Final version: Cambridge Journal of Mathematics

These are notes for my talk at ICCM 2010, Beijing. We survey some results, obtained jointly with Pavlo Pylyavskyy, concerning the ring of loop symmetric functions. Motivations from networks on surfaces, total positivity, crystal graphs, and…

In recent years, cross-modal reasoning (CMR), the process of understanding and reasoning across different modalities, has emerged as a pivotal area with applications spanning from multimedia analysis to healthcare diagnostics. As the…

This short note is an "elementary'' introduction to the conjectural theory of motives.

The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…

We study the moduli space of rank 0 semistable sheaves on some rational surfaces. We show the irreducibility and stable rationality of them under some conditions. We also compute several (virtual) Betti numbers of those moduli spaces by…

We present the statistical approach to the combining of signal significances.

A summary is given of recent exact results concerning the functional integration measure in Regge gravity.

We develop the theory of multiple polylogarithms from analytic, Hodge and motivic point of view. Define the category of mixed Tate motives over a ring of integers in a number field. Describe explicitly the multiple polylogarithm Hopf…

In this article we determine the implicational fragments of most of the known subintuitionistic logics.

Observational studies are a key resource for causal inference but are often affected by systematic biases. Prior work has focused mainly on detecting these biases, via sensitivity analyses and comparisons with randomized controlled trials,…

This is a pedagogical review on polarized structure functions .

The main results of this paper are a Cell Decomposition Theorem for Henselian valued fields with analytic structure in an analytic Denef-Pas language, and its application to analytic motivic integrals and analytic integrals over…

The paper is an introduction to intuitionistic mathematics.

We compute the motivic nearby cycles of functions obtained by composition of two functions with distinct sets of variables with a two variable function

Estimates of some integrals related to variations of smooth functions are presented.

Some notes and observations on analytic functions defined on an annulus

This text was published in the Gazette de la Soci\'et\'e Math\'ematique de France in October 2023. It is an introduction to the theory of motives, from its sources to its more modern developments.