Results 41 to 50 of about 51,414 (229)
Advanced Science, EarlyView.Geometry and connectivity are complementary structures, which have demonstrated their ability to represent the brain's functional activity. This study evaluates geometric and connectome eigenmodes as biologically informed constraints for EEG source localization.
Pok Him Siu +6 more
wiley +1 more source
Symmetry and convexity of level sets of solutions to infinity Laplace's equation
Electronic Journal of Differential Equations, 1998 We consider the Dirichlet problem $$displaylines{ -Delta_infty u=f(u) quad hbox{in }Omega,,cr u=0quad hbox{on }partialOmega,,} $$ where $Delta_infty u=u_{x_i}u_{x_j}u_{x_ix_j}$ and $f$ is a nonnegative continuous function.
Edi Rosset
doaj
A Laplace transform approach to the quantum harmonic oscillator
, 2012 The one-dimensional quantum harmonic oscillator problem is examined via the Laplace transform method. The stationary states are determined by requiring definite parity and good behaviour of the eigenfunction at the origin and at ...
de Castro, Antonio S. +1 more
core +1 more source
Linearizing and Forecasting: A Reservoir Computing Route to Digital Twins of the Brain
Advanced Science, EarlyView.A new approach uses simple neural networks to create digital twins of brain activity, capturing how different patterns unfold over time. The method generates and recovers key dynamics even from noisy data. When applied to fMRI, it predicts brain signals and reveals distinctive activity patterns across regions and individuals, opening possibilities for ...
Gabriele Di Antonio +3 more
wiley +1 more source
On the boundary H��lder regularity for the infinity Laplace equation
, 2019 In this note, we prove the boundary H lder regularity for the infinity Laplace equation under a proper geometric condition. This geometric condition is quite general, and the exterior cone condition, the Reifenberg flat domains, and the corkscrew domains (including the non-tangentially accessible domains) are special cases. The key idea, following [3],
Wu, Leyun, Lian, Yuanyuan, Zhang, Kai
openaire +2 more sources
Advanced Intelligent Discovery, EarlyView.This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley +1 more source
Advanced Intelligent Discovery, EarlyView.We propose a residual‐based adversarial‐gradient moving sample (RAMS) method for scientific machine learning that treats samples as trainable variables and updates them to maximize the physics residual, thereby effectively concentrating samples in inadequately learned regions.
Weihang Ouyang +4 more
wiley +1 more source
Вісник Харківського національного університету імені В.Н. Каразіна. Серія: Математичне моделювання, інформаційні технології, автоматизовані системи управління, 2019 The method for simulating forced vibrations of structure elements, which interact with water medium during service is developed. Harmonic, impulse and seismic loadings are accounted for.
Degtyarev Kirill +3 more
doaj +1 more source
Discontinuous gradient constraints and the infinity Laplacian [PDF]
, 2012 Motivated by tug-of-war games and asymptotic analysis of certain variational problems, we consider a gradient constraint problem involving the infinity Laplace operator.
D. Rossi +3 more
core
Notes on the Infinity-Laplace Equation
, 2014 These notes are written up after my lectures at the University of Pittsburgh in March 2014 and at Tsinghua University in May 2014. My objective is the $\infty$-Laplace Equation, a marvellous kin to the ordinary Laplace Equation. The $\infty$-Laplace Equation has delightful counterparts to the Dirichlet integral, the Mean Value Theorem, the Brownian ...
openaire +2 more sources