Related papers: Computing Euler characteristics using quantum fiel…
Quantum state wave functionals are constructed in exact form for the graviton-like field theory obtained by breaking down the topological symmetry of the string action related with the Euler characteristic of the world-surface; their…
A detailed analysis of the remainder obtained by truncating the Euler series up to the $n$th-order term is presented. In particular, by using an approach recently proposed by Weniger, asymptotic expansions of the remainder, both in inverse…
We introduce a diagrammatic quantum field formalism for the evaluation of normalized expectation values of operators, and suitable for systems with localized electrons. It is used to develop a convergent series expansion for the energy in…
We use Seiberg--Witten-like relations in the topological recursion framework to obtain virtual Euler characteristics for uni- and multicellular maps for ensembles of classic orthogonal polynomials and for ensembles related to nonorientable…
This study proposes a novel approach to extract topological properties, specifically the Euler characteristic, from input images using neural networks without relying on large pre-existing datasets but with a single geometric image.…
We propose a definition of an Euler characteristic for unbounded chain complexes by taking the (usual) Euler characteristics of successively longer parts of the complex, weighted inversely proportional to the length, and passing to the…
Computing the Euler genus of a graph is a fundamental problem in graph theory and topology. It has been shown to be NP-hard by [Thomassen '89] and a linear-time fixed-parameter algorithm has been obtained by [Mohar '99]. Despite extensive…
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…
We present an algorithm that computes Friedl and L\"uck's twisted $L^2$-Euler characteristic for a suitable regular CW complex, employing Oki's matrix expansion algorithm to indirectly evaluate the Dieudonn\'e determinant. The algorithm…
The form factor of a quantum graph is a function measuring correlations within the spectrum of the graph. It can be expressed as a double sum over the periodic orbits on the graph. We propose a scheme which allows one to evaluate the…
This work begins by establishing a mathematical formalization between different geometrical interpretations of Neural Networks, providing a first contribution. From this starting point, a new interpretation is explored, using the idea of…
This paper is a study of power series, where the coefficients are binomial expressions (iterated finite differences). Our results can be used for series summation, for series transformation, or for asymptotic expansions involving Stirling…
Traditionally, network analysis is based on local properties of vertices, like their degree or clustering, and their statistical behavior across the network in question. This paper develops an approach which is different in two respects. We…
We present an exact analytical solution of the spectral problem of quasi one-dimensional scaling quantum graphs. Strongly stochastic in the classical limit, these systems are frequently employed as models of quantum chaos. We show that…
We present and study a possible mechanism of extracting energies from the vacuum by external classical fields. Taking a constant magnetic field as an example, we discuss why and how the vacuum energy can be released in the context of…
We compute the Euler characteristics of the recently discovered series of Gothic Teichm\"{u}ller curves. The main tool is the construction of 'Gothic' Hilbert modular forms vanishing at the images of these Teichm\"{u}ller curves. Contrary…
We determine all the equivariant Euler characteristics of the building for the general unitary group over a finite field.
Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great…
Fault-tolerant quantum computers offer the promise of dramatically improving machine learning through speed-ups in computation or improved model scalability. In the near-term, however, the benefits of quantum machine learning are not so…
Quantum field theory is a powerful tool to describe the relevant physics governing complex quantum many-body systems. Here we develop a general pathway to extract the irreducible building blocks of quantum field theoretical descriptions and…