Related papers: Critical slowing down and the gradient flow coupli…
A foremost challenge in modern network science is the inverse problem of reconstruction (inference) of coupling equations and network topology from the measurements of the network dynamics. Of particular interest are the methods that can…
We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility $\chi_{\rm t}$ is measured directly, and by the slab method, which is based on the topological content of…
In simulations of a model with topological sectors, algorithms which proceed in small update steps tend to get stuck in one sector, especially on fine lattices. This distorts the numerical results; in particular it is not straightforward to…
We propose a new strategy for the determination of the step scaling function $\sigma(u)$ in finite size scaling studies using the Gradient Flow. In this approach the determination of $\sigma(u)$ is broken in two pieces: a change of the flow…
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…
In lattice gauge theories, the gradient flow has been used extensively both, for scale setting and for defining finite volume renormalization schemes for the gauge coupling. Unfortunately, rather large cutoff effects have been observed in…
We present first results of our study on the Euclidean topological charge density correlation function. In order to get a well defined topological charge density and to improve the signal of the correlation function at large separations we…
Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…
The gradient flow is a valuable tool for the lattice community, with applications from scale-setting to implementing chiral fermions. Here I focus on the gradient flow as a means to suppress power-divergent mixing. Power-divergent mixing…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…
The Schr\"odinger functional (SF) is a powerful and widely used tool for the treatment of a variety of problems in renormalization and related areas. Albeit offering many conceptual advantages, one major downside of the SF scheme is the…
We compute the one-loop running of the $SU(N)$ 't Hooft coupling in a finite volume gradient flow scheme using twisted boundary conditions. The coupling is defined in terms of the energy density of the gradient flow fields at a scale…
We consider the breakdown of conformal and scale invariance in random systems with strongly random critical points. Extending previous results on one-dimensional systems, we provide an example of a three-dimensional system which has a…
We discuss our present knowledge of $\alpha_s$, the fundamental running coupling or effective charge of Quantum Chromodynamics (QCD). A precise understanding of the running of $\alpha_s(Q^2) $ at high momentum transfer, $Q$, is necessary…
In contrast to perturbative QCD, the analytic QCD models have running coupling whose analytic properties correctly mirror those of spacelike observables. The discontinuity (spectral) function of such running coupling is expected to agree…
Convection is a well-studied topic in fluid dynamics, yet it is less understood in the context of networks flows. Here, we incorporate techniques from topological data analysis (namely, persistent homology) to automate the detection and…
This review paper provides an introduction of Markov chains and their convergence rates which is an important and interesting mathematical topic which also has important applications for very widely used Markov chain Monte Carlo (MCMC)…
On the universal bundle of unit spinors we study a natural energy functional whose critical points, if dim M \geq 3, are precisely the pairs (g, {\phi}) consisting of a Ricci-flat Riemannian metric g together with a parallel g-spinor…
We study the evolution of the coupling in SU(2) gauge field theory with $N_f=8$ fundamental fermion flavors on the lattice. This model is expected to have an infrared fixed point at high coupling. We use HEX-smeared Wilson-clover action,…
Conventional weak-coupling Rayleigh-Schr\"odinger perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale analysis, a powerful and sophisticated…