Related papers: Logarithmic Fulton--MacPherson configuration space…

We construct the universal Mumford curve of given genus as a family of Mumford curves over the deformation space of degenerate curves in the category of arithmetic formal geometry. Furthermore, we give explicit formulas of abelian…

Efficient tensor computation is a cornerstone of modern deep learning (DL) workloads, yet existing approaches struggle to achieve flexible and performant design and implementation of tensor layouts -- mappings between logical tensors and…

We prove the existence of a smoothing for a toroidal crossing space under mild assumptions. By linking log structures with infinitesimal deformations, the result receives a very compact form for normal crossing spaces. The main approach is…

We study the critical points over an algebraic variety of an optimization problem defined by a quadratic objective that is degenerate. This scenario arises in machine learning when the dataset size is small with respect to the model, and is…

We generalize the coset procedure of homogeneous spacetimes in (pseudo-)Riemannian geometry to non-Lorentzian geometries. These are manifolds endowed with nowhere vanishing invertible vielbeins that transform under local non-Lorentzian…

Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two of the central Hamiltonian systems encountered in…

Certain dissipative physical systems closely resemble Hamiltonian systems in $\mathbb{R}^{2n}$, but with the canonical equation for one of the variables in each conjugate pair rescaled by a real parameter. To generalise these dynamical…

Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables.…

This research explored a novel explicit total Lagrangian Fragile Points Method (FPM) for finite deformation of hyperelastic materials. In contrast to mesh-based methods, where mesh distortion may pose numerical challenges, meshless methods…

FPGAs provide a flexible and efficient platform to accelerate rapidly-changing algorithms for computer vision. The majority of existing work focuses on accelerating image classification, while other fundamental vision problems, including…

We introduce a unified elliptic extension of CL-type Clausen functions based on logarithmic primitives of the Jacobi theta function. The resulting elliptic Clausen family satisfies the same integral recursion as the classical circular case,…

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…

A novel approach to exploiting the log-convex structure present in many design problems is developed by modifying the classical Sequential Quadratic Programming (SQP) algorithm. The modified algorithm, Logspace Sequential Quadratic…

We construct a measure on the well-approximable numbers whose Fourier transform decays at a nearly optimal rate. This gives a logarithmic improvement on a previous construction of Kaufman.

In this paper, we classify the algebraic isomonodromic deformations that can be obtained through restriction to generic lines of logarithmic flat connections on the complex projective plane $\mathbb{P}^2_\mathbb{C}$ whose singular locus is…

A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…

Multi-fidelity modeling and calibration are data fusion tasks that ubiquitously arise in engineering design. In this paper, we introduce a novel approach based on latent-map Gaussian processes (LMGPs) that enables efficient and accurate…

In this note we study the convergence of monotone P1 finite element methods on unstructured meshes for fully non-linear Hamilton-Jacobi-Bellman equations arising from stochastic optimal control problems with possibly degenerate, isotropic…

In a previous work [J. Chem. Phys. 155, 244111 (2021)], we found counterexamples to the fundamental Hohenberg-Kohn theorem from density-functional theory in finite-lattice systems represented by graphs. Here, we demonstrate that this only…

We study a class of degenerate hyperbolic equations in a bounded domain whose degeneracy occurs at a boundary point. We first develop the weighted functional framework, prove well-posedness of the degenerate problem, and establish…