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In this short note we present a generating function computing the compactly supported Euler characteristic $\chi_c(F(X, n), K^{\boxtimes n})$ of the configuration spaces on a topologically stratified space $X$, with $K$ a constructible…

Algebraic Topology · Mathematics 2023-04-21 Louis Hainaut

In this article, we study Euler characteristic techniques in topological data analysis. Pointwise computing the Euler characteristic of a family of simplicial complexes built from data gives rise to the so-called Euler characteristic…

Machine Learning · Computer Science 2024-07-25 Olympio Hacquard , Vadim Lebovici

We present an efficient algorithm to compute Euler characteristic curves of gray scale images of arbitrary dimension. In various applications the Euler characteristic curve is used as a descriptor of an image. Our algorithm is the first…

Computer Vision and Pattern Recognition · Computer Science 2018-10-18 Teresa Heiss , Hubert Wagner

In this paper we study the Kummer extensions of the power series field $K=k((X_1,...,X_n)$, where $k$ is an algebraically closed field of arbitrary characteristic.

Commutative Algebra · Mathematics 2007-05-23 J. M. Tornero

Modeling quantum thermal machines provides a practical approach to describing the thermodynamic properties of quantum technologies and devices. For this purpose, power-law potentials are often employed as working mediums of quantum…

Quantum Physics · Physics 2024-12-30 Vinicius Gomes de Paula , Wanisson S. Santana , Clebson Cruz , Mario Reis

Using the weak factorization theorem we give a simple presentation for the value group of the universal Euler characteristic with compact support for varieties of characteristic zero and describe the value group of the universal Euler…

Algebraic Geometry · Mathematics 2007-05-23 Franziska Bittner

We introduce a linearized version of group field theory. It can be viewed either as a group field theory over the additive group of a vector space or as an asymptotic expansion of any group field theory around the unit group element. We…

High Energy Physics - Theory · Physics 2014-11-20 Joseph Ben Geloun , Thomas Krajewski , Jacques Magnen , Vincent Rivasseau

A closed form formula (generating function) for the Euler characteristic of the configuration space of $\scriptstyle n$ particles in a simplicial complex is given.

General Topology · Mathematics 2010-03-15 S. R. Gal

We address the question of computing one selected term of an algebraic power series. In characteristic zero, the best algorithm currently known for computing the $N$th coefficient of an algebraic series uses differential equations and has…

Symbolic Computation · Computer Science 2016-05-19 Alin Bostan , Gilles Christol , Philippe Dumas

The commonest method of characterizing a cold field electron emitter is to measure its current-voltage characteristics, and the commonest method of analysing these characteristics is by means of a Fowler-Nordheim (FN) plot. This…

Mesoscale and Nanoscale Physics · Physics 2016-07-04 Richard G. Forbes , Jonathan H. B. Deane , Andreas Fischer , Marwan S. Mousa

These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…

High Energy Physics - Theory · Physics 2018-10-31 Edward Witten

For any given sequence of integers there exists a quantum field theory whose Feynman rules produce that sequence. An example is illustrated for the Stirling numbers. The method employed here offers a new direction in combinatorics and graph…

Quantum Physics · Physics 2013-09-13 Carl M. Bender , Dorje C. Brody , Bernhard K. Meister

We consider different generalizations of the Euler formula and discuss the properties of the associated trigonometric functions. The problem is analyzed from different points of view and it is shown that it can be formulated in a natural…

Classical Analysis and ODEs · Mathematics 2011-03-15 D. Babusci , G. Dattoli , E. Di Palma , E. Sabia

The notion of quantized characters is introduced in our previous paper as a natural quantization of characters in the context of asymptotic representation theory for compact quantum groups. As in the case of ordinary groups, the…

Operator Algebras · Mathematics 2019-08-13 Ryosuke Sato

For the quantum integer [n]_q = 1+q+q^2+... + q^{n-1} there is a natural polynomial multiplication such that [mn]_q = [m]_q \otimes_q [n]_q. This multiplication is given by the functional equation f_{mn}(q) = f_m(q) f_n(q^m), defined on a…

Number Theory · Mathematics 2016-12-30 Melvyn B. Nathanson

Via counting over finite fields, we derive explicit formulas for the E-polynomials and Euler characteristics of GL(d)- and PGL(d)-character varieties of free groups. We prove a positivity property for these polynomials and relate them to…

Algebraic Geometry · Mathematics 2014-02-28 Sergey Mozgovoy , Markus Reineke

We make explicit computations in the formal symplectic geometry of Kontsevich and determine the Euler characteristics of the three cases, namely commutative, Lie and associative ones, up to certain weights.From these, we obtain some…

Algebraic Topology · Mathematics 2015-04-14 Shigeyuki Morita , Takuya Sakasai , Masaaki Suzuki

The predictions of the standard model of particle physics are highly successful in spite of the fact that several parts of the underlying quantum field theoretical framework are analytically problematic. Indeed, it has long been suggested,…

Mathematical Physics · Physics 2021-05-05 David M. Jackson , Achim Kempf , Alejandro H. Morales

In this paper we investigate the properties of the Euler functions. By using the Fourier transform for the Euler function, we derive the interesting formula related to the infinite series. Finally we give some interesting identities between…

Number Theory · Mathematics 2008-08-14 Taekyun Kim

In classical thermodynamics the Euler relation is an expression for the internal energy as a sum of the products of canonical pairs of extensive and intensive variables. For quantum systems the situation is more intricate, since one has to…

Quantum Physics · Physics 2021-07-27 Akram Touil , Kevin Weber , Sebastian Deffner