Related papers: Rank-Preserving Index-Dependent Matrix Transformat…
We study a class of superstring models compactified in the 3-generation Calabi-Yau manifold of Tian and Yau. Our analysis includes the complete $E_6$-singlet sector, which has been recently evaluated using techniques of spectral and exact…
In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p \times p$ matrices, subject to rank constraints on $L$. However, existing first-order methods for solving such problems either are too…
We show that the N-patch functional renormalization group (pFRG), a theoretical method commonly applied for correlated electron systems, is unable to implement consistently the matrix element interference arising from strong momentum…
We address the problem of efficient sparse fixed-rank (S-FR) matrix decomposition, i.e., splitting a corrupted matrix $M$ into an uncorrupted matrix $L$ of rank $r$ and a sparse matrix of outliers $S$. Fixed-rank constraints are usually…
We present a novel machine learning architecture that uses the exponential of a single input-dependent matrix as its only nonlinearity. The mathematical simplicity of this architecture allows a detailed analysis of its behaviour, providing…
In a previous work, Optics Communications 284 (2011) 2460--2465, we considered a dielectric medium with an anti-reflection coating and a spatially uniform index of refraction illuminated at normal incidence by a quasimonochromatic field.…
This work presents a novel formulation and numerical strategy for the simulation of geometrically nonlinear structures. First, a non-canonical Hamiltonian (Poisson) formulation is introduced by including the dynamics of the stress tensor.…
We present a coherent and consistent framework for explicit time-dependence in non-Hermitian quantum mechanics. The area of non-Hermitian quantum mechanics has been growing rapidly over the past twenty years. This has been driven by the…
We derive a localization formula for the refined index of gauged quantum mechanics with four supercharges. Our answer takes the form of a residue integral on the complexified Cartan subalgebra of the gauge group. The formula captures the…
In this article, we discuss new models for static nonlinear deformations via scale-invariant conformal energy functionals based on the linear distortion. In particular, we give examples to show that, despite equicontinuity estimates giving…
We consider the task of building compact deep learning pipelines suitable for deployment on storage and power constrained mobile devices. We propose a unified framework to learn a broad family of structured parameter matrices that are…
A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation…
High-dimensional time series has diverse applications in econometrics and finance. Recent models for capturing temporal dependence have employed a bilinear representation for matrix time series, or the Tucker-decomposition based…
We study the question of approximability for the inverse of the FEM stiffness matrix for (scalar) second order elliptic boundary value problems by blockwise low rank matrices such as those given by the H-matrix format. We show that…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
Any effort to localise an event in the vicinity of the Planck length scale, only where the quantum gravitational effects are predicted to be observed, will invariably result in gravitational collapse. One must postulate noncommutative (NC)…
With the advent of the big data era, generative models of complex networks are becoming elusive from direct computational simulation. We present an exact, linear-algebraic reduction scheme of generative models of networks. By exploiting the…
We present a computationally efficient approach to solve the time-dependent Kohn-Sham equations in real-time using higher-order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this…
Accurately depicting multiphysics interactions in interfacial systems requires computational frameworks capable of reconciling geometric adaptability with strict conservation fidelity. However, traditional spatiotemporal discretisation…
This paper studies how to sketch element-wise functions of low-rank matrices. Formally, given low-rank matrix A = [Aij] and scalar non-linear function f, we aim for finding an approximated low-rank representation of the (possibly high-rank)…