相关论文: Second-order properties for planar Mondrian tessel…

This paper presents asymptotic covariance formulae and central limit theorems for geometric functionals, including volume, surface area, and all Minkowski functionals and translation invariant Minkowski tensors as prominent examples, of…

A random planar quadrangulation process is introduced as an approximation for certain cellular automata in terms of random growth of rays from a given set of points. This model turns out to be a particular (rectangular) case of the…

In this second part of the paper, dedicated to theories with extra dimensions, a new physical notion about the "tensor length scale" is introduced, based on the gravitational theories with covariant and contravariant metric tensor…

Permutations can be viewed as pairs of linear orders, or more formally as models over a signature consisting of two binary relation symbols. This approach was adopted by Albert, Bouvel and F\'eray, who studied the expressibility of…

Applications of machine learning tools to problems of physical interest are often criticized for producing sensitivity at the expense of transparency. To address this concern, we explore a data planing procedure for identifying combinations…

Recent studies of gradient descent with large step sizes have shown that there is often a regime with an initial increase in the largest eigenvalue of the loss Hessian (progressive sharpening), followed by a stabilization of the eigenvalue…

We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the…

Machine learning (ML) is rapidly transforming the way molecular dynamics simulations are performed and analyzed, from materials modeling to studies of protein folding and function. ML algorithms are often employed to learn low-dimensional…

The increasing size of neural networks has led to a growing demand for methods of efficient fine-tuning. Recently, an orthogonal fine-tuning paradigm was introduced that uses orthogonal matrices for adapting the weights of a pretrained…

The interest in machine learning with tensor networks has been growing rapidly in recent years. We show that tensor-based methods developed for learning the governing equations of dynamical systems from data can, in the same way, be used…

We investigate the galaxy bispectrum induced by the nonlinear gravitational evolution as a possible probe to constrain degenerate higher-order scalar tensor (DHOST) theories. We find that the signal obtained from the leading kernel of…

Simple hidden Markov models are proposed for predicting secondary structure of a protein from its amino acid sequence. Since the length of protein conformation segments varies in a narrow range, we ignore the duration effect of length…

In this second paper on the method of deriving linearizing transformations for nonlinear ODEs, we extend the method to a set of two coupled second order nonlinear ODEs. We show that besides the conventional point, Sundman and generalized…

This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian…

High-dimensional tensor models are notoriously computationally expensive to train. We present a meta-learning algorithm, MMT, that can significantly speed up the process for spatial tensor models. MMT leverages the property that spatial…

The mechanical properties are essential for structural materials. The analyzed 360 data on four mechanical properties of steels, viz. fatigue strength, tensile strength, fracture strength, and hardness, are selected from the NIMS database,…

This report is concerned with the Mondrian process and its applications in machine learning. The Mondrian process is a guillotine-partition-valued stochastic process that possesses an elegant self-consistency property. The first part of the…

We present the second-order general relativistic description of the observed galaxy number density in a cosmological framework. The observed galaxy number density is affected by the volume and the source effects, both of which arise due to…

We introduce a new coarse-graining algorithm, tensor network skeletonization, for the numerical computation of tensor networks. This approach utilizes a structure-preserving skeletonization procedure to remove short-range correlations…

Manufactured metallic components often contain non-uniformly distributed pores of complex morphologies. Since such porosity defects have significant influence on material behaviors and affect the usage in high-performance applications, it…