Related papers: Corrections to universal scaling in real maps
We argue that the optimization plays a crucial role in generalization of deep learning models through implicit regularization. We do this by demonstrating that generalization ability is not controlled by network size but rather by some…
We investigate scaling and universality in nonequilibrium spin correlation functions in the presence of uncorrelated noise. In the absence of noise, spin correlation functions exhibit a crossover from monotonic decay at fast sweep…
The empirical spectral distribution of Hermitian $K \times K$-block random matrices converges to a deterministic density on the real line with a potential atom at the origin as the dimension of the blocks tends to infinity. In this model…
Quantum graphs have recently emerged as models of nonlinear optical, quantum confined systems with exquisite topological sensitivity and the potential for predicting structures with an intrinsic, off-resonance response approaching the…
The parallel orbital-updating approach is an orbital/eigenfunction iteration based approach for solving eigenvalue problems when many eigenpairs are required. It has been proven to be efficient, for instance, in electronic structure…
The spin-1 XY chain in a transverse field is studied using finite-size scaling. The ground state phase diagram displays a paramagnetic, an ordered ferromagnetic and an ordered oscillatory phase. The paramagnetic-ferromagnetic transition…
Neural scaling laws describe how the performance of deep neural networks scales with key factors such as training data size, model complexity, and training time, often following power-law behaviors over multiple orders of magnitude. Despite…
Phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method. A general formula for phase diffusion coefficients is…
An integral domain $R$ is \emph{perinormal} if every local going-down overring is a localization of $R$ and \emph{globally perinormal} if every going-down overring is a localization of $R$. In this paper, I introduce notions of graded…
Percolation is a cornerstone concept in physics, providing crucial insights into critical phenomena and phase transitions. In this study, we adopt a kinetic perspective to reveal the scaling behaviors of higher-order gaps in the largest…
In this work we study the renormalization operator acting on piecewise smooth homeomorphisms on the circle, that turns out to be essentially the study of Rauzy-Veech renormalizations of generalized interval exchanges maps with genus one. In…
We study straight-line drawings of planar graphs with prescribed face areas. A plane graph is 'area-universal' if for every area assignment on the inner faces, there exists a straight-line drawing realizing the prescribed areas. For…
We prove existence results for optimization problems for the $k$th Laplace eigenvalue on closed Riemannian manifolds of dimension $m \geq 3$, depending on the choice of normalization. One such normalization leads to eigenvalue optimization…
We investigate multicritical phenomena in O(N)+O(M)-models by means of nonperturbative renormalization group equations. This constitutes an elementary building block for the study of competing orders in a variety of physical systems. To…
Using Wilson renormalization group, we show that if no integrated vector operator of scaling dimension $-1$ exists, then scale invariance implies conformal invariance. By using the Lebowitz inequalities, we prove that this necessary…
Frames for Hilbert spaces are interesting for mathematicians but also important for applications e.g. in signal analysis and in physics. Both in mathematics and physics it is natural to consider a full scale of spaces, and not only a single…
The article is devoted to the study of mappings with finite distortion in metric spaces. Analogues of results relating to equicontinuity and normality of families of quasiregular mappings are obtained. It is proved that the indicated…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
Area-preserving maps have been observed to undergo a universal period-doubling cascade, analogous to the famous Feigenbaum-Coullet-Tresser period doubling cascade in one-dimensional dynamics. A renormalization approach has been used by…
In this work a symmetry of universal finite-size scaling functions under a certain anisotropic scale transformation is postulated. This transformation connects the properties of a finite two-dimensional system at criticality with…