Tootfinder

Constrained Stein Variational Gradient Descent for Robot Perception, Planning, and Identification
Griffin Tabor, Tucker Hermans
https://arxiv.org/abs/2506.00589

Constrained Stein Variational Gradient Descent for Robot Perception, Planning, and Identification
Many core problems in robotics can be framed as constrained optimization problems. Often on these problems, the robotic system has uncertainty, or it would be advantageous to identify multiple high quality feasible solutions. To enable this, we present two novel frameworks for applying principles of constrained optimization to the new variational inference algorithm Stein variational gradient descent. Our general framework supports multiple types of constrained optimizers and can handle arbitra…

This https://arxiv.org/abs/2502.16492 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Convergence of Clipped SGD on Convex $(L_0,L_1)$-Smooth Functions
We study stochastic gradient descent (SGD) with gradient clipping on convex functions under a generalized smoothness assumption called $(L_0,L_1)$-smoothness. Using gradient clipping, we establish a high probability convergence rate that matches the SGD rate in the $L$ smooth case up to polylogarithmic factors and additive terms. We also propose a variation of adaptive SGD with gradient clipping, which achieves the same guarantee. We perform empirical experiments to examine our theory and algor…

more wind splitting the seconds/begonias in dappled morning sunlight
#photography #bloomScrolling #begonia #orange

The Grothendieck duality and sparse minimizing in spaces of Sobolev solutions to elliptic systems
Alexander Shlapunov, Alexander Polkovnikov, Kseniya Gagelgans
https://arxiv.org/abs/2506.23087

The Grothendieck duality and sparse minimizing in spaces of Sobolev solutions to elliptic systems
We present an instructive example of using Banach spaces of solutions to (linear, generally, non-scalar) elliptic operator $A$ to investigate variational inverse problems related to neural networks and/or to regularization of solutions to boundary value problems. More precisely, inspired by kernel's method for optimization problems in locally convex spaces, we prove the existence of the so-called sparse minimizers for the related variational problem and produce a representer theorem where a sui…

Low-dispersion low free-spectral-range Mach-Zehnder interferometer with long straight path lengths on silicon
Cael Warner
https://arxiv.org/abs/2507.01114 …

Low-dispersion low free-spectral-range Mach-Zehnder interferometer with long straight path lengths on silicon
Multiple Mach-Zehnder interferometers are constructed using fiber-Bragg grating couplers, y-branches, silicon waveguides, and/or broadband splitters in silicon on insulator strip waveguides to test the effect of variation in waveguide length between consecutive bends on the transmission gain spectrum, free-spectral range, group refractive index, and dispersion. Dispersion is mitigated by increasing the path length between consecutive bends of minimum radius. With long linear waveguide sections,…

This https://arxiv.org/abs/2505.13929 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Numerical analysis for the regularised total variation flow
We perform the numerical analysis of the regularised total variation flow using the gradient discretisation method (GDM). GDM is a unified convergence analysis framework that covers conforming and non-conforming numerical methods, for instance, conforming and non-conforming finite element, two-point flux approximation, etc.. In this paper, a fully discretised implicit scheme of the model is proposed, the existence and uniqueness of the solution to the scheme is proved, the stability and consist…

Viscosity variation in fluid flows across scale
Arjun Sharma, Ritabrata Thakur, Sharath Jose, Rama Govindarajan
https://arxiv.org/abs/2507.23532 https://ar…

Viscosity variation in fluid flows across scale
A wide range of natural and engineered fluid flows exhibit spatial or temporal viscosity variations, spanning scales from microbial locomotion to planetary mantle convection. These variations introduce qualitatively new physical mechanisms absent in constant-viscosity flows. This review surveys such phenomena across scales. In low Reynolds number (Stokes) flows, viscosity gradients couple translation and rotation, enabling novel particle responses to uniform forcing-- mechanisms that microorgan…

Beekeeping in progress #Uckermark #bees #beekeeping

What if each voxel were measured with a different diffusion protocol?
Santiago Coelho, Gregory Lemberskiy, Ante Zhu, Hong-Hsi Lee, Nastaren Abad, Thomas K. F. Foo, Els Fieremans, Dmitry S. Novikov
https://arxiv.org/abs/2506.22650

What if each voxel were measured with a different diffusion protocol?
Expansion of diffusion MRI (dMRI) both into the realm of strong gradients, and into accessible imaging with portable low-field devices, brings about the challenge of gradient nonlinearities. Spatial variations of the diffusion gradients make diffusion weightings and directions non-uniform across the field of view, and deform perfect shells in the q-space designed for isotropic directional coverage. Such imperfections hinder parameter estimation: Anisotropic shells hamper the deconvolution of fi…

An energy-stable parametric finite element method for the Willmore flow in three dimensions
Weizhu Bao, Yifei Li, Dongmin Wang
https://arxiv.org/abs/2506.21025

An energy-stable parametric finite element method for the Willmore flow in three dimensions
This work develops novel energy-stable parametric finite element methods (ES-PFEM) for the Willmore flow and curvature-dependent geometric gradient flows of surfaces in three dimensions. The key to achieving the energy stability lies in the use of two novel geometric identities: (i) a reformulated variational form of the normal velocity field, and (ii) incorporation of the temporal evolution of the mean curvature into the governing equations. These identities enable the derivation of a new vari…