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.
Curve shortening flow shrinks curves to points under certain conditions.
Study foliations on Riemannian manifolds with specific vector fields, focusing on geometric properties.
Improved CG force-field learning from all-atom data.
New method uses normalizing flows to improve force fields for coarse-grained molecular dynamics.
The paper finds that circles and logarithmic spirals are the only constant-speed ramps for a specific force field.
In this paper, we study the evolution of submannifold moving by mean curvature minus a external force field. We prove that the flow has a long-time smooth solution for all time under almost optimal conditions. Those conditions are that the second fundamental form on the initial submanifolds is not too large, the extern…
The paper establishes a connection between force-free fields and conformally geodesic fields.
Machine learning generates coarse-grained force fields for molecular dynamics.
Neural network models colloidal particle dynamics in non-equilibrium systems.
The Giroux correspondence and the notion of a near force-free magnetic field are used to topologically characterize near force-free magnetic fields which describe a variety of physical processes, including plasma equilibrium. As a byproduct, the topological characterization of force-free magnetic fields associated with…
Proposes linking energy and force uncertainty in deep learning potentials.
The mean curvature flow describes the parabolic deformation of embedded branes in Riemannian geometry driven by their extrinsic mean curvature vector, which is typically associated to surface tension forces. It is the gradient flow of the area functional, and, as such, it is naturally identified with the boundary renor…
Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwell's equations, we derive and present a Bayesian non-parametric probabilistic modeling approach for interpolation and extrapolation of the magnetic field. We model the magnetic field components jointly by…
Develops Hamiltonian Score Matching and Generative Flows for machine learning.
BoostMD accelerates molecular dynamics simulations by 8x with ML force fields.
Study active nematic forces on curved surfaces, revealing new coupling mechanisms.
Study physical work done by isotropic vector forces along isotropic curves.
New method speeds up kernel-based machine learning for force field reconstruction.
AniDS improves molecular force field modeling by learning anisotropic noise.
MACE uses higher-order messages to create fast, accurate force fields.
Given a real vector space V of finite dimension, together with a particular homogeneous field of bivectors that we call a "field of projective forces", we define a law of dynamics such that the position of the particle is a "ray" i.e. a half-line drawn from the origin of V. The impulsion is a bivector whose support is …
Flow of curves with curvature and forcing vector field exists.
Nearly all field theories suffer from singularities when particles are introduced. This is true in both classical and quantum physics. Classical field singularities result in the notorious self-force problem, where it is unknown how the dynamics of a particle change when the particle interacts with its own (self) field…
Given a complete hypersurface isometrically immersed in an ambient manifold, in this paper we provide a lower bound for the norm of the mean curvature vector field of the immersion assuming that: 1) The ambient manifold admits a Killing submersion with unit-length Killing vector field. 2)The projection of the image of …
New method proves rigidity of minimal hypersurfaces in curved 4-manifolds.
CAMEL embeds data into a manifold using curvature-augmented forces.
Paper introduces a PDE-free method for decomposing forces in any dimension.
In this article we present a natural generalization of Newton's Second Law valid in field theory, i.e., when the parameterized curves are replaced by parameterized submanifolds of higher dimension. For it we introduce what we have called the geodesic -vector field, analogous to the ordinary geodesic field and which …
We consider the dynamics of vector fields on three-manifolds which are constrained to lie within a plane field, such as occurs in nonholonomic dynamics. On compact manifolds, such vector fields force dynamics beyond that of a gradient flow, except in cases where the underlying manifold is topologically simple. Furtherm…
GDML learns effective CG models from all-atom data.
The Lorentz force equations provide a partial description of the geodesic motion of a charged particle on a four-manifold. Under the hypothesis that Maxwell's equations express symmetry properties of the Ricci tensor, the full electromagnetic connection is determined. From this connection, the fourth equation of the ge…
Given a generic 2-plane field on a 5-dimensional manifold we consider its (3,2)-signature conformal metric [g] as defined in math.DG/0406400. Every conformal class [g] obtained in this way has very special conformal holonomy: it must be contained in the split-real-form of the exceptional group G_2. In this note we show…
MACE architecture outperforms alternatives in various molecular and materials science tasks.
We prove existence and uniqueness of weighted ambient metric for manifolds with density.
New method to determine parabolic surfaces invariant under Killing fields.
We provide a self-contained treatment of set-theoretic subsolutions to flow by mean curvature, or, more generally, to flow by mean curvature plus an ambient vector field. The ambient space can be any smooth Riemannian manifold. Most importantly, we show that if two such set-theoretic subsolutions are initially disjoint…
The dynamics defined by a force field which is positively homogeneous of degree can always be reduced, by simply constraining it. The dimension of the phase space is reduced by two dimensions, while it may only be reduced by one dimension if the degree of homogeneity is different from . This remark is an elega…
The holonomy of the ambient metrics of Nurowski's conformal structures associated to generic real-analytic 2-plane fields on 5-manifolds is investigated. It is shown that the holonomy is always contained in the split real form G_2 of the exceptional Lie group, and is equal to G_2 for an open dense set of 2-plane fields…
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form of flows of a given geodesic curvature is proposed. For illustration, the proble…
We present a novel learning framework that consistently embeds underlying physics while bypassing a significant drawback of most modern, data-driven coarse-grained approaches in the context of molecular dynamics (MD), i.e., the availability of big data. The generation of a sufficiently large training dataset poses a co…
Study calculates indices and nullities of focal manifolds in spheres.
We provide a benchmark dataset for hand gesture recognition using force myography.
This work discovers latent field effects governing interacting dynamical systems.
We study the motion of a particle in the hyperbolic plane (embedded in Minkowski space), under the action of a potential that depends only on one variable. This problem is the analogous to the spherical pendulum in a unidirectional force field. However, for the discussion of the hyperbolic plane one has to distinguish …
A new framework for generative modeling using controlled vector fields.
This paper continues the study of decompositions of a smooth 4-manifold into two handlebodies with handles of index . Part I gave existence results in terms of spines and chain complexes over the fundamental group of the ambient manifold. Here we assume that one side of a decomposition has larger fundamental gro…
Flow deforms curves to match an embedded target.
Tractor Calculus is a powerful tool for analyzing Weyl invariance; although fundamentally linked to the Cartan connection, it may also be arrived at geometrically by viewing a conformal manifold as the space of null rays in a Lorentzian ambient space. For dimension d conformally flat manifolds we show that the (d+2)-di…