相关论文: Motivic measures

We prove a motivic enhancement of the classical Picard--Lefschetz formula. Our proof is completely motivic, and yields a description of the motivic nearby cycles at a quasi-homogeneous singularity, as well as its monodromy, in terms of an…

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

Let K be a field. A positive motivic measure on the Grothendieck ring K_0(Var_K) is a homomorphism from K_0(Var_K) to the real numbers assigning a nonnegative value to every variety. In this note we show that the only positive motivic…

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.

We develop the motivic integration theory over formal Deligne-Mumford stacks over a power series ring of arbitrary characteristic. This is a generalization of the corresponding theory for tame and smooth Deligne-Mumford stacks constructed…

Research on generative systems in music has seen considerable attention and growth in recent years. A variety of attempts have been made to systematically evaluate such systems. We present an interdisciplinary review of the common…

Some properties of integral averages of functions on intervals and their asymptotic behavior are investigated. The results are aimed at applications to entire and subharmonic functions.

For a formal scheme over a complete discrete valuation ring with a good action of a finite group, we define equivariant motivic integration, and we prove a change of variable formula for that.To do so, we construct and examine an induced…

We present a rational analysis of curiosity, proposing that people's curiosity is driven by seeking stimuli that maximize their ability to make appropriate responses in the future. This perspective offers a way to unify previous theories of…

It oftens occurs that Taylor coefficients of (dimensionally regularized) Feynman amplitudes $I$ with rational parameters, expanded at an integral dimension $D= D_0$, are not only periods (Belkale, Brosnan, Bogner, Weinzierl) but actually…

We introduce a generalization of symmetric functions and apply the resulting theory to compute the class in the Grothendieck ring of varieties of the space of geometrically irreducible hypersurfaces of a fixed degree in projective space.

This paper serves as a literature review of methodology concerning the (modern) causal inference methods to address the causal estimand with observational/survey data that have been or will be used in social science research. Mainly, this…

Making a survey of recent constructions of universal cohomologies we suggest a new framework for a theory of motives in algebraic geometry.

Integrating data from multiple heterogeneous sources has become increasingly popular to achieve a large sample size and diverse study population. This paper reviews development in causal inference methods that combines multiple datasets…

Measures of information transfer have become a popular approach to analyze interactions in complex systems such as the Earth or the human brain from measured time series. Recent work has focused on causal definitions of information transfer…

Some of the theoretical motivations and experimental developments leading to the discovery of charm are recalled.

We show that the motivic vanishing cycles introduced by J. Denef and F. Loeser give rise to a motivic measure on the Grothendieck ring of varieties over the affine line. We discuss the relation of this motivic measure to the motivic measure…

As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…

There are countless reasons cited in scientific studies to explain the difficulties in programming learning. The reasons range from the subject's complexity, the ineffective teaching and study methods, to psychological aspects such as…

Several different types of statistical interaction are defined and distinguished, primarily on the basis of the nature of the factors defining the interaction. Illustrative examples, mostly epidemiological, are given. The emphasis is…