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The conformal symmetry SO(d,2) of the massless particle in d dimensions, or superconformal symmetry OSp(N|4), SU(2,2|N), OSp(8|N) of the superparticle in d=3,4,6 dimensions respectively, had been previously understood as the global Lorentz…
We consider the 2D quasi-periodic scattering problem in optics, which has been modelled by a boundary value problem governed by Helmholtz equation with transparent boundary conditions. A spectral collocation method and a tensor product…
Tensor network methods provide a scalable solution to represent high-dimensional data. However, their efficacy is often limited by static, expert-defined structures that fail to adapt to evolving data correlations. We address this…
Ultra-thin MoS2 has recently emerged as a promising two-dimensional semiconductor for electronic and optoelectronic applications. Here, we report high mobility (>60 cm2/Vs at room temperature) field-effect transistors that employ…
Transformers have achieved state-of-the-art performance in numerous tasks. In this paper, we propose a continuous-time formulation of transformers. Specifically, we consider a dynamical system whose governing equation is parametrized by…
In this paper, we introduce a neural network-based method to address the high-dimensional dynamic unbalanced optimal transport (UOT) problem. Dynamic UOT focuses on the optimal transportation between two densities with unequal total mass,…
We investigate a two-component reaction-diffusion system with a slow-fast structure and spatially varying coefficients $f_1$ and $f_2$ appearing in the slow equation. Under mild boundedness and regularity conditions on $f_1$ and $f_2$ the…
We present version 2 of SModelS, a program package for the fast reinterpretation of LHC searches for new physics on the basis of simplified model results. The major novelty of the SModelS v2 series is an extended topology description with a…
We study the energy landscape of the Traveling Salesperson problem (TSP) using exact ground states and a novel linear programming approach to generate excited states with closely defined properties. We look at four different ensembles,…
Spatio-temporal traffic forecasting is challenging due to complex temporal patterns, dynamic spatial structures, and diverse input formats. Although Transformer-based models offer strong global modeling, they often struggle with rigid…
The radiative transport equation accurately describes light transport in participating media such as biological tissues, though analytic solutions are known only for simple geometries. We present a pseudospectral technique to efficiently…
By utilizing the gauge symmetries of Two-Time Physics (2T-physics), a superstring with linearly realized global SU(2,2|4) supersymmetry in 4+2 dimensions (plus internal degrees of freedom) is constructed. It is shown that the dynamics of…
In this paper, we aim at the problem of tensor data completion. Tensor-train decomposition is adopted because of its powerful representation ability and linear scalability to tensor order. We propose an algorithm named Sparse Tensor-train…
In pattern classification, polynomial classifiers are well-studied methods as they are capable of generating complex decision surfaces. Unfortunately, the use of multivariate polynomials is limited to kernels as in support vector machines,…
Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…
We develop both first and second order numerical optimization methods to solve non-smooth optimization problems featuring a shared sparsity penalty, constrained by differential equations with uncertainty. To alleviate the curse of…
Understanding charge transport in strongly correlated systems remains a central challenge in condensed matter physics, particularly in light of the ubiquitous linear-in-$T$ resistivity observed in strange metals across many platforms from…
We comparatively use some classical spectral collocation methods as well as highly performing Chebfun algorithms in order to compute the eigenpairs of second order singular Sturm-Liouville problems with separated self-adjoint boundary…
Tensor robust principal component analysis (TRPCA) is a fundamental model in machine learning and computer vision. Recently, tensor train (TT) decomposition has been verified effective to capture the global low-rank correlation for tensor…
The transport of energetic particles in a spatially varying magnetic field is described by the focused transport equation. In the past two versions of this equation were investigated. The more commonly used standard form described a…