Tootfinder

Primal-Dual Coordinate Descent for Nonconvex-Nonconcave Saddle Point Problems Under the Weak MVI Assumption
Iyad Walwil, Olivier Fercoq
https://arxiv.org/abs/2506.15597

Primal-Dual Coordinate Descent for Nonconvex-Nonconcave Saddle Point Problems Under the Weak MVI Assumption
We introduce two novel primal-dual algorithms for addressing nonconvex, nonconcave, and nonsmooth saddle point problems characterized by the weak Minty Variational Inequality (MVI). The first algorithm, Nonconvex-Nonconcave Primal-Dual Hybrid Gradient (NC-PDHG), extends the well-known Primal-Dual Hybrid Gradient (PDHG) method to this challenging problem class. The second algorithm, Nonconvex-Nonconcave Stochastic Primal-Dual Hybrid Gradient (NC-SPDHG), incorporates a randomly extrapolated prima…

Entanglement through high-energy scattering in noncommutative quantum electrodynamics
Carmelo P. Martin
https://arxiv.org/abs/2506.15350 https://

Entanglement through high-energy scattering in noncommutative quantum electrodynamics
We analyze the tree-level generation of entanglement through some key scattering processes in massless quantum electrodynamics on canonical noncomutative spacetime with space-space type of noncommutativity. The fermions in the noncommutative theory will be zero charge fermions. The scattering processes we shall study do not occur in ordinary Minkowski spacetime. We shall use the concurrence to characterize the amount of entanglement generated through a given scattering process. We shall show th…

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https://open.spotify.com/track/5ywoRjfVIlcJiSAxwPT3Pt

A Nonconforming Finite Element Method for Elliptic Interface Problems on Locally Anisotropic Meshes
Hua Wang, Qichen Zhang
https://arxiv.org/abs/2506.15077

A Nonconforming Finite Element Method for Elliptic Interface Problems on Locally Anisotropic Meshes
We propose a new nonconforming \(P_1\) finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of intersection points on an interface-unfitted background mesh, as introduced in \cite{Hu2021optimal}. We first establish interpolation error estimates on quadrilateral elements satisfying the regular decomposition property (RDP). Building on this, the main contributio…

Proximal Operators of Sorted Nonconvex Penalties
Anne Gagneux, Mathurin Massias, Emmanuel Soubies
https://arxiv.org/abs/2506.15315 https://

Proximal Operators of Sorted Nonconvex Penalties
This work studies the problem of sparse signal recovery with automatic grouping of variables. To this end, we investigate sorted nonsmooth penalties as a regularization approach for generalized linear models. We focus on a family of sorted nonconvex penalties which generalizes the Sorted L1 Norm (SLOPE). These penalties are designed to promote clustering of variables due to their sorted nature, while the nonconvexity reduces the shrinkage of coefficients. Our goal is to provide efficient ways t…

Almost uniform convergence for noncommutative Vilenkin-Fourier series
Yong Jiao, Sijie Luo, Tiantian Zhao, Dejian Zhou
https://arxiv.org/abs/2506.14431 htt…

Almost uniform convergence for noncommutative Vilenkin-Fourier series
In the present paper, we study almost uniform convergence for noncommutative Vilenkin-Fourier series. Precisely, we establish several noncommutative (asymmetric) maximal inequalities for the Cesàro means of the noncommutative Vilenkin-Fourier series, which in turn give the corresponding almost uniform convergence. The primary strategy in our proof is to explore a noncommutative generalization of Sunouchi square function operator, and the very recent advance of the noncommutative Calderón-Zygm…

A ringed-space-like structure on coalgebras for noncommutative algebraic geometry
So Nakamura
https://arxiv.org/abs/2506.14689 https://

A ringed-space-like structure on coalgebras for noncommutative algebraic geometry
Inspired by the perspective of Reyes' noncomutative spectral theory, we attempt to develop noncommutative algebraic geometry by introducing ringed coalgebras, which can be thought of as a noncommutative generalization of schemes over a field $k$. These objects arise from fully residually finite-dimensional(RFD) algebras introduced by Reyes and from schemes locally of finite type over $k$. The construction uses the Heyneman-Sweedler finite dual coalgebra and the Takeuchi underlying coalgebra. Wh…

Peak algebra in noncommuting variables
Farid Aliniaeifard, Shu Xiao Li
https://arxiv.org/abs/2506.12868 https://arxiv.org/pdf/2506.12…

Peak algebra in noncommuting variables
The well-known descent-to-peak map $Θ_{\mathrm{QSym}}$ for the Hopf algebra of quasisymmetric functions, $\mathrm{QSym}$, and the peak algebra $Π$ were originally defined by Stembridge in 1997. We define the labelled descent-to-peak map $Θ_{\mathrm{NCQSym}}$ and extend the notion of the peak algebra to noncommuting variables. Moreover, we define Schur $Q$-functions in noncommuting variables having properties analogous to the classical Schur $Q$-functions.

An investigation into the nonconformity of homogeneous gas limit for kinetic energy density of atomic systems
Priya, Anuvab Panda, Saswata Basu, Mainak Sadhukhan
https://arxiv.org/abs/2506.15393

An investigation into the nonconformity of homogeneous gas limit for kinetic energy density of atomic systems
Developing a reliable kinetic energy density functional within orbital-free density functional theory remains a long-standing challenge, particularly for atomic and molecular systems. A major difficulty lies in the absence of a systematic approach to accurately compute the kinetic energy density in such contexts. In our recent work, we introduced an analytical Green's function-based framework to address this issue. Majority of the existing efforts to construct an approximate kinetic energy dens…

Heavy Ball and Nesterov Accelerations with Hessian-driven Damping for Nonconvex Optimization
N. Hadjisavvas, F. Lara, R. T. Marcavillaca, P. T. Vuong
https://arxiv.org/abs/2506.15632

Heavy Ball and Nesterov Accelerations with Hessian-driven Damping for Nonconvex Optimization
In this work, we investigate a second-order dynamical system with Hessian-driven damping tailored for a class of nonconvex functions called strongly quasiconvex. Buil\-ding upon this continuous-time model, we derive two discrete-time gra\-dient-based algorithms through time discretizations. The first is a Heavy Ball method with Hessian correction, incorporating cur\-va\-tu\-re-dependent terms that arise from discretizing the Hessian damping component. The second is a Nesterov-type accelerated m…