A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Framework optimizes expensive manufacturing processes efficiently.
In this paper we construct the differential equations of the stream lines that characterize plasma regarded as a non-isotropic medium geometrized by a jet rheonomic time-invariant Berwald-Moor metric. Section 1 contains historical notes regarding the Plasma Physics and its geometrical description. Section 2 analyzes th…
In this paper, using Riemann-Lagrange geometrical methods, we construct a geometrical model on 1-jet spaces for the study of multi-time relativistic magnetized non-viscous plasma, characterized by a given energy-stress-momentum distinguished (d-) tensor. In that arena, we give the conservation laws and the continuity e…
Deep learning compares turbulence models in plasma physics.
Inhomogeneous plasmas filaments instabilities are investigated by using the techniques of classical differential geometry of curves where Frenet torsion and curvature describe completely the motion of curves. In our case the Frenet frame changes in time and also depends upon the other coordinates taking into account th…
The paper studies sprays on Hamel-Funk functions and their properties.
Physics-informed ML models improve turbulence understanding in fusion plasmas.
Study shows zero Pontrjagin classes for sprays.
New sprays of constant curvature introduced; conditions for metrizability given.
Defines projective Ricci curvature and proves rigidity for sprays.
This paper classifies geodesics of projectively flat sprays and introduces a method to determine sprays based on geodesics.
Sprays with vanishing X-curvature are studied in this paper.
Geodesic orbit and weakly symmetric properties in spray geometry.
Neural surrogates speed up 5D gyrokinetic simulations of plasma turbulence.
Analysis of Vlasov plasma dynamics using matched pair Lie-Poisson formulation.
Study left invariant spray structures on Lie groups, calculating curvature and geodesics.
The paper studies Jacobi fields and conjugate points in projective sprays.
Study predicts turbulent electric fields in fusion plasmas using deep learning.
Sprays get Hamiltonian description using Dirac structures.
Sprays on Frechet manifolds connect connections and tangent structures.
Introduces submersion in spray geometry and defines key components.
GyroSwin models plasma turbulence with neural nets, reducing costs and capturing neglected nonlinearities.
The paper classifies spherically symmetric sprays and their curvature properties.
The multi-scale, mutli-physics nature of fusion plasmas makes predicting plasma events challenging. Recent advances in deep convolutional neural network architectures (CNN) utilizing dilated convolutions enable accurate predictions on sequences which have long-range, multi-scale characteristics, such as the time-series…
Deep learning is having a profound impact in many fields, especially those that involve some form of image processing. Deep neural networks excel in turning an input image into a set of high-level features. On the other hand, tomography deals with the inverse problem of recreating an image from a number of projections.…
Study reformulates Finsler metrizability problems using geodesic invariance.
Plasma toroidal metric singularities in helical devices and tokamaks, giving rise to magnetic surfaces inside the plasma devices are investigated in two cases. In the first we consider the case of a rotational plasma on an helical device with circular cross-section and dissipation. In this case singularities are shown …
Predicting unscheduled breakdowns of plasma etching equipment can reduce maintenance costs and production losses in the semiconductor industry. However, plasma etching is a complex procedure and it is hard to capture all relevant equipment properties and behaviors in a single physical model. Machine learning offers an …
The main purposes of this article are to extend our previous results on homogeneous sprays to arbitrary (generalized) sprays, to show that locally diffeomorphic exponential maps can be defined for any (generalized) spray, and to give a (possibly nonlinear) covariant derivative for any (possibly nonlinear) connection. I…
Spray-invariant sets maintain geodesics on infinite-dimensional manifolds.
Study left invariant spray geometry on Lie groups using parallel translations.
In this paper, we introduce the notion of one form deformation of sprays. The metrizability of the new spray, when the background spray is flat, is characterized. Therefore, we obtain new projectively flat metrics of constant flag curvature . Moreover, these new metrics are not, generally, isometric to the Klein met…
The pseudoconvex and disprisoning conditions for geodesics of linear connections are extended to the solution curves of general homogeneous sprays. The main result is that pseudoconvexity and disprisonment are jointly stable in the fine topology on the space of all homogeneous sprays of any degree of homogeneity.
INNs improve acceptance rates in electron spectra analysis.
In this work we show that for the geodesic spray of a Finsler function the most natural projective deformation leads to a non-Finsler metrizable spray, for almost every value of . This result shows how rigid is the metrizablility property with respect to certain …
A fast method learns plasma collision kernels from simulations, improving kinetic models.
New method uses neural networks to interpolate stellar atmospheres with high precision.
The projective metrizability problem can be formulated as follows: under what conditions the geodesics of a given spray coincide with the geodesics of some Finsler space, as oriented curves. In Theorem 3.8 we reformulate the projective metrizability problem for a spray in terms of a first-order partial differential ope…
The projective Finsler metrizability problem deals with the question whether a projective-equivalence class of sprays is the geodesic class of a (locally or globally defined) Finsler function. In this paper we use Hilbert-type forms to state a number of different ways of specifying necessary and sufficient conditions f…
In the previous work, the notion of the Finsleroid--Finsler space have been formulated and the necessary and sufficient conditions for the space to be of the Landsberg type have been found. In the present paper, starting with particular spray coefficients, we demonstrate how the Landsberg condition can explicitly appea…
In this paper we are investigating variational homogeneous second order differential equations by considering the questions of how many different variational principles exist for a given spray. We focus our attention on h(2)-variationality; that is, the regular Lagrange function is homogeneous of degree two in the dire…
In this paper we study the invariant metrizability and projective metrizability problems for the special case of the geodesic spray associated to the canonical connection of a Lie group. We prove that such canonical spray is projectively Finsler metrizable if and only if it is Riemann metrizable. This result means that…
In his book "Differential Geometry of Spray and Finsler spaces", page 177, Zhongmin Shen asks "wether or not there always exist non-trivial Funk functions on a spray space". In this note, we will prove that the answer is negative for the geodesic spray of a finslerian function of non-vanishing scalar flag curvature.
Neural nets improve plasma equilibrium modeling for NSTX-U.
Riemannian geometrical tools, such as Ricci collineations and Killing symmetries, so often used in Einstein general theory of gravitation are here applied to plasma physics to build magnetic surfaces from Einstein plasma metrics used in tokamak devices. It is shown that the Killing symmetries are constrains the Einstei…
The paper establishes conditions for Riemannian connections and semi-simplicity of Lie algebras using spray structures.
In 2001, Zhongmin Shen asked if it is possible for two projectively related Finsler metrics to have the same Riemann curvature tensor, [14, page 184]. In this paper, we provide an answer to this question, within the class of Finsler metrics of scalar flag curvature. In Theorem 3.1, we show that the answer is negative, …
Considering prolongation of a Lie algebroid equipped with a spray, defining some classical tensors, we show that a Lie symmetry of a spray is a curvature collineation for these tensors.