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Decentralized stochastic gradient descent (SGD) is a driving engine for decentralized federated learning (DFL). The performance of decentralized SGD is jointly influenced by inter-node communications and local updates. In this paper, we…
An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the…
The quantum antiferromagnetic spin-1/2 Ising model on a triangular lattice and analogous fully frustrated Ising model on a square lattice with quantum fluctuations induced by the application of the transverse magnetic field are studied at…
$L_0$-smoothness, which has been pivotal to advancing decentralized optimization theory, is often fairly restrictive for modern tasks like deep learning. The recent advent of relaxed $(L_0,L_1)$-smoothness condition enables improved…
We study the 2D Ising model on three different types of lattices that are topologically equivalent to spheres. The geometrical shapes are reminiscent of the surface of a pillow, a 3D cube and a sphere, respectively. Systems of volumes…
Interface undercooling is one of the most significant parameters in the solidification of colloidal suspensions. However, quantitative measurement of interface undercooling of colloidal suspensions is still a challenge. Here, a new…
The local structure of a solid-on-solid (SOS) interface in a two-dimensional kinetic Ising ferromagnet with single-spin-flip Glauber dynamics, which is driven far from equilibrium by an applied field, is studied by an analytic mean-field,…
There is no an accepted exact partition function (PF) for the two-dimensional (2D) Ising model with a non-zero external magnetic field to our knowledge. Here we infer an empirical PF for such an Ising model. We compare the PFs for two…
We map the ground-state ensemble of antiferromagnetic Ising model of spin-S on a triangular lattice to an interface model whose entropic fluctuations are proposed to be described by an effective Gaussian free energy, which enables us to…
In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in [Phys. Rev. Lett. 112, 070603] for the static inverse Ising problem, tries to…
We study the flux tube thickness of a generic Lattice Gauge Theory near the deconfining phase transition. It is well known that the effective string model predicts a logarithmic increase of the flux tube thickness as a function of the…
Finite-size scaling at fixed renormalization-group invariant is a powerful and flexible technique to analyze Monte Carlo data at a critical point. It consists in fixing a given renormalization-group invariant quantity to a given value,…
We investigate dynamics of the supersymmetric fermion lattice model defined by Hermann Nicolai. We provide its local fermionic constants of motion that exist infinitely many. These generate hidden local supersymmetries that the Nicolai…
We present and analyze a methodology for numerical homogenization of spatial networks, modelling e.g. diffusion processes and deformation of mechanical structures. The aim is to construct an accurate coarse model of the network. By solving…
We consider gradient models on the lattice $\mathbb{Z}^d$. These models serve as effective models for interfaces and are also known as continuous Ising models. The height of the interface is modelled by a random field with an energy which…
Extensive dynamical simulations of Restricted Solid on Solid models in $D=2+1$ dimensions have been done using parallel multisurface algorithms implemented on graphics cards. Numerical evidence is presented that these models exhibit KPZ…
We consider the quantum cat map - a toy model of a quantized chaotic system. We show that its eigenstates are fully delocalized on $\mathbb{T}^2$ in the semiclassical limit (or equivalently that each semiclassical measure is fully supported…
We develop a model for sheared gouge layers that accounts for the local increase in temperature at the grain contacts during sliding. We use the shear transformation zone (STZ) theory, a statistical thermodynamic theory, to describe…
This article studies descent theory in the setting of Berkovich spaces. We give sufficient conditions for a given fibered category over the category of k-affinoid algebras to be a stack for the Berkovich analogue of the faithfully-flat…
Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…