Results 21 to 30 of about 522,797 (308)
The Local Learning Coefficient: A Singularity-Aware Complexity Measure
, 2023 The Local Learning Coefficient (LLC) is introduced as a novel complexity measure for deep neural networks (DNNs). Recognizing the limitations of traditional complexity measures, the LLC leverages Singular Learning Theory (SLT), which has long recognized the significance of singularities in the loss landscape geometry.
Lau, Edmund +4 more
openaire +2 more sources
Multi-Fractality, Universality and Singularity in Turbulence
Fractal and Fractional, 2022 In most geophysical flows, vortices (or eddies) of all sizes are observed. In 1941, Kolmogorov devised a theory to describe the hierarchical organization of such vortices via a homogeneous self-similar process.
Bérengère Dubrulle
doaj +1 more source
Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization [PDF]
arXiv.org, 2017 In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries. Instead of the computational domain bounded by four B-spline curves, planar domains with high genus and more ...
Gang Xu +5 more
semanticscholar +1 more source
Complex powers for cone differential operators and the heat equation on manifolds with conical singularities [PDF]
, 2017 We obtain left and right continuous embeddings for the domains of the complex powers of sectorial $\mathbb{B}$-elliptic cone differential operators. We apply this result to the heat equation on manifolds with conical singularities and provide asymptotic ...
N. Roidos
semanticscholar +1 more source
Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case [PDF]
Communications in Mathematical Physics, 2018 For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue ...
L'aszl'o ErdHos +2 more
semanticscholar +1 more source
A universal form of localized complex potentials with spectral singularities
New Journal of Physics, 2020 Abstract We establish necessary and sufficient conditions for localized complex potentials in the Schrödinger equation to enable spectral singularities (SSs) and show that such potentials have the universal form U (
Dmitry A Zezyulin, Vladimir V Konotop
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Local polar varieties in the geometric study of singularities [PDF]
, 2016 This text presents several aspects of the theory of equisingularity of complex analytic spaces from the standpoint of Whitney conditions. The goal is to describe from the geometrical, topological, and algebraic viewpoints a canonical locally finite ...
A. G. Flores, B. Teissier
semanticscholar +1 more source
Journal of Fluid Mechanics, 2018 It is known that in steady-state potential flows, the separation of a gravity-driven free surface from a solid exhibits a number of peculiar characteristics.
Philippe H. Trinh, Thomas G. J. Chandler
semanticscholar +1 more source
Classification of phase singularities for complex scalar waves [PDF]
, 2006 Motivated by the importance and universal character of phase singularities which are clarified recently, we study the local structure of equi-phase loci near the dislocation locus of complex valued planar and spatial waves, from the viewpoint of ...
Adachi, Jiro, Ishikawa, Go-o
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Equivariant Hirzebruch class for singular varieties [PDF]
, 2015 The Hirzebruch $td_y(X)$ class of a complex manifold X is a formal combination of Chern characters of the sheaves of differential forms multiplied by the Todd class.
Weber, Andrzej
core +1 more source