Results 61 to 70 of about 7,293 (133)

Combinatorial Hopf algebraic description of the multiscale renormalization in quantum field theory [PDF]

, 2013
We define in this paper several Hopf algebras describing the combinatorics of the so-called multi-scale renormalization in quantum field theory. After a brief recall of the main mathematical features of multi-scale renormalization, we define assigned ...
Krajewski, Thomas, Rivasseau, Vincent, Tanasa, Adrian   +2 more
core   +1 more source

Siegel–Veech constants for cyclic covers of generic translation surfaces

Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.
Abstract We compute the asymptotic number of cylinders, weighted by their area to any nonnegative power, on any cyclic branched cover of any generic translation surface in any stratum. Our formulae depend only on topological invariants of the cover and number‐theoretic properties of the degree: in particular, the ratio of the related Siegel–Veech ...
David Aulicino, Aaron Calderon, Carlos Matheus, Nick Salter, Martin Schmoll   +4 more
wiley   +1 more source

Polynomial realizations of some combinatorial Hopf algebras

Journal of Noncommutative Geometry, 2014
We construct explicit polynomial realizations of some combinatorial Hopf algebras based on various kinds of trees or forests, and some more general classes of graphs, ranging from the Connes–Kreimer algebra to an algebra of labelled forests isomorphic to the Hopf algebra of parking functions and to a new noncommutative algebra based on endofunctions ...
Foissy, Loïc, Novelli, Jean-Christophe, Thibon, Jean-Yves   +2 more
openaire   +5 more sources

Relative Chaoticity of Natural Languages

Complexity, Volume 2026, Issue 1, 2026.
This paper presents a novel approach to analyzing and grouping natural languages based on the degree of their chaoticity. It clusters 52 languages from 18 language families, according to the value of the entropy–complexity pair, to reveal the chaotic properties of semantic trajectories.
Assel S. Yerbolova, Korney K. Tomashchuk, Alexandra S. Kogan, Nhu Q. Dang, Inna V. Skrynnikova, Vasilii A. Gromov, Tao Zhou   +6 more
wiley   +1 more source

Exploring Stability Landscapes and Complex Dynamics in a Discrete Holling–Tanner Predator–Prey Model via Bifurcation Theory and Machine Learning

Journal of Mathematics, Volume 2026, Issue 1, 2026.
Discretization of continuous models can do more than approximate their dynamics; it can fundamentally transform their dynamical behavior, such as the complex dynamical behavior that translates the system to a chaotic state. In this study we investigated the discrete‐time Holling–Tanner predator–prey model.
Muhammad Rafaqat, Magda Abd El-Rehman, Abubakar Masha, Tayyaba Mehmood, Anila Bibi, Feyisa Edosa Merga, Smritijit Sen   +6 more
wiley   +1 more source

Rota-Baxter Algebras in Renormalization of Perturbative Quantum Field Theory

, 2006
Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras.
Ebrahimi-Fard, Kurusch, Guo, Li
core   +1 more source

Continuation‐Enhanced Harmonic Balance Method for Nonlinear Dynamics in Rotating Machinery

Shock and Vibration, Volume 2026, Issue 1, 2026.
Nonlinear response conception in rotating machinery, particularly in systems with squeeze film dampers (SFDs), pose significant challenges for established time‐domain numerical methods due to bifurcations and critical points along the response trajectories.
Muhammad Umar, Charles Nutakor, Jussi Sopanen, Yan Niu   +3 more
wiley   +1 more source

A Combinatorial Overview of the Hopf Algebra of MacMahon Symmetric Functions [PDF]

Annals of Combinatorics, 2002
A MacMahon symmetric function is a formal power series in a finite number of alphabets that is invariant under the diagonal action of the symmetric group. In this article, we give a combinatorial overview of the Hopf algebra structure of the MacMahon symmetric functions relying on the construction of a Hopf algebra from any alphabet of neutral letters ...
Rosas Celis, Mercedes Helena, Rota, Gian-Carlo, Stein, Joel   +2 more
openaire   +4 more sources

Toward Useful Quantum Kernels

Advanced Quantum Technologies, Volume 8, Issue 12, December 2025.
The hybrid approach to Quantum Supervised Machine Learning is compatible with Noisy Intermediate Scale Quantum (NISQ) devices but hardly useful. Pure quantum kernels requiring fault‐tolerant quantum computers are more promising. Examples are kernels computed by means of the Quantum Fourier Transform (QFT) and kernels defined via the calculation of ...
Massimiliano Incudini, Francesco Martini, Alessandra Di Pierro   +2 more
wiley   +1 more source

Boundary representations of locally compact hyperbolic groups

Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.
Abstract We develop the theory of Patterson–Sullivan measures for locally compact hyperbolic groups. This theory associates to certain left‐invariant metrics on the group measures on its boundary. Next, we establish irreducibility of the resulting (unitary) Koopman representations for second countable, nonelementary, unimodular locally compact ...
Michael Glasner
wiley   +1 more source