Results 11 to 20 of about 4,391 (253)
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.
Edmund Lau +4 more
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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
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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 invariants of singular surfaces in an almost complex four-manifold [PDF]
Annals of Global Analysis and Geometry, 1993 Let \(f: S^2\to (M^4, J)\) be a generic mapping, that is, \(f\) is a finite cover of an almost everywhere immersion (except for a finite number of points) which has only finite complex points. To such a mapping \(f\) the authors assign local invariants \(i(x)\) and \(m(x)\) at every point \(x\in f (S^2)\). The invariant \(i(x)\) is defined as the local
Ishikawa, Goo, Ohmoto, Toru
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Regular Solutions in Higher-Derivative Gravity
Universe, 2018 Local gravitational theories with more than four derivatives can have remarkable quantum properties. Namely, they can be super-renormalizable and may be unitary in the Lee-Wick sense, if the massive poles of the propagator are complex.
Breno L. Giacchini +1 more
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On Generation, Motions, and Collisions of Dowsons
Frontiers in Physics, 2020 Dowsons are ±2π point singularities of the unitary complex order parameter eiφ characterizing the so-called dowser texture in a thin nematic layer with homeotropic boundary conditions.
Pawel Pieranski, Maria Helena Godinho
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Complex-time singularity and locality estimates for quantum lattice systems [PDF]
Journal of Mathematical Physics, 2015 We present and prove a well-known locality bound for the complex-time dynamics of a general class of one-dimensional quantum spin systems. Then we discuss how one might hope to extend this same procedure to higher dimensions using ideas related to the Eden growth process and lattice trees. Finally, we demonstrate with a specific family of lattice trees
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Nonlocal vertices and analyticity: Landau equations and general Cutkosky rule
Journal of High Energy Physics, 2018 We study the analyticity properties of amplitudes in theories with nonlocal vertices of the type occurring in string field theory and a wide class of nonlocal field theory models.
Paokuan Chin, E. T. Tomboulis
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The local analytical triviality of a complex analytic singular foliation
Hokkaido Mathematical Journal, 2004 The authors investigate complex analytic singular foliations defined on the complex analytic manifold \(M\) of dimension \(n\). After recalling basic notions of the theory of singular foliations they prove a theorem about local analytic triviality along the leaves. The main tool of the proof is the Whitney stratification of the singular locus. The last
MITERA, Yoshiki, YOSHIZAKI, Junya
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Frontiers in Physics, 2022 Atomic gases tightly trapped near the focus of an electromagnetic wave interact with photons that exhibit a complex structure, displaying strong gradients of field amplitude and local polarization that can lead to topological phase singularities.
R. Gutiérrez-Jáuregui, R. Jáuregui
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