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.
Study the evolution of the Lorenz strange set using Conley index theory.
Proves stability of Minkowski space-time in Einstein-Yang-Mills system.
Physics-constrained neural nets solve EM fields of charged particle beams.
New methods distill dynamical system equations from data.
New satellite knots counter a conjecture about Lorenz knots.
Stability of Minkowski space-time in higher dimensions proven for arbitrary small perturbations.
We describe the Williams zeta functions and the twist zeta functions of sub-Lorenz templates generated by renormalizable Lorenz maps, in terms of the corresponding zeta-functions of the sub-Lorenz templates generated by the renormalized map and by the map that determines the renormalization type.
Neural networks improve Lorenz trajectory prediction.
We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots code…
Twisted torus links are given by twisting a subset of strands on a closed braid representative of a torus link. T--links are a natural generalization, given by repeated positive twisting. We establish a one-to-one correspondence between positive braid representatives of Lorenz links and T--links, so Lorenz links and T-…
Stability of Minkowski space-time in Einstein-Yang-Mills system proven.
This is a review article on Lorenz knots.
The unknotting number of a positive braid with n strands and k intersections is known to be equal to (k-n+1)/2. We consider Lorenz knots (which are positive braids) and, using a different method, find their unknotting numbers in terms of their positions on the Lorenz attractor.
This article is a survey on Lorenz knots. We describe the original construction, prove several classical properties, in particular the fact that the closure of a positive braid is a fibered knot, and describe Ghys'correspondance between modular knots and Lorenz knots. We also prove two new properties, namely that follo…
We describe the Lorenz links generated by renormalizable Lorenz maps with reducible kneading invariant , in terms of the links corresponding to each factor. This gives one new kind of operation that permits us to generate new knots and links from old. Using this result we obtain explicit form…
Study of Lorenz links and T-links, showing equivalence and unique presentations.
We exhibit low-dilatation families of surface homeomorphisms among monodromies of Lorenz knots.
DD-SP uses ML to improve SP for Lorenz 96 systems, outperforming LR and DD-P.
In paper "A new twist on Lorenz links" (Journal of Topology 2(2009), 227-248) Joan Birman and Ilya Kofman prove the coincidence of the class of Lorenz links and the class of twisted links. The proof in that work is algebraic. We will identify this class in terms of grid diagrams and provide a transparent geometric argu…
Computed linking number of modular knots and Lorenz links.
Proves stability of Minkowski space-time for Einstein-Yang-Mills equations.
New findings on T-links derived from torus links.
Improved SINDy autoencoder for identifying noisy dynamical systems.
New satellite knots found that can't be represented by positive braids with full twists.
A new method predicts non-Markovian closure terms for complex systems.
During this last decades, several attempts to construct slow invariant manifold of the Lorenz-Krishnamurthy five-mode model of slow-fast interactions in the atmosphere have been made by various authors. Unfortunately, as in the case of many two-time scales singularly perturbed dynamical systems the various asymptotic p…
We show that the zeroes of the Alexander polynomial of a Lorenz knot all lie in some annulus whose width depends explicitly on the genus and the braid index of the considered knot.
Improved algorithm for modular links provides upper volume bounds.
Deep neural networks classify chaotic time series.
A universal rule-based self-learning approach using deep reinforcement learning (DRL) is proposed for the first time to solve nonlinear ordinary differential equations and partial differential equations. The solver consists of a deep neural network-structured actor that outputs candidate solutions, and a critic derived…
GANs improve stochastic parameterization of the Lorenz '96 model.
Proves energy estimates for tensorial wave equations, decoupling components for stability proof.
Deep learning models predict chaotic Lorenz 96 system accurately.
The study applies wealth thermalization hypothesis to social networks and explains inequality.
Deep networks infer parameters for chaotic dynamics in climate models.
We work on a 4-manifold equipped with Lorentzian metric and consider a volume-preserving diffeomorphism which is the unknown quantity of our mathematical model. The diffeomorphism defines a second Lorentzian metric , the pullback of . Motivated by elasticity theory, we introduce a Lagrangian expressed algebra…
New method learns chaotic dynamics from noisy, partial data.
The aim of this paper is to construct natural geometrical objects on the 1-jet space J^1(T,R^5), where , like a non-linear connection, a generalized Cartan connection, together with its d-torsions and d-curvatures, a jet electromagnetic d-field and a jet Yang-Mills energy, starting from the given Lorenz atm…
Using tax and census data, we demonstrate that the distribution of individual income in the USA is exponential. Our calculated Lorenz curve without fitting parameters and Gini coefficient 1/2 agree well with the data. From the individual income distribution, we derive the distribution function of income for families wi…
Unified four trade-off curves for assessing generative model proximity.
Deep density methods improve filtering in high-dimensional systems.
VSE estimates complex processes from noisy measurements without a model.
Paper simplifies link classification in 3-sphere using braids and templates.
We present here a general framework, expressed by a system of nonlinear differential equations, suitable for the modelling of taxation and redistribution in a closed (trading market) society. This framework allows to describe the evolution of the income distribution over the population and to explain the emergence of c…
Study proves global existence and decay for complex wave equations.
This work analyzes the Gompertz-Pareto distribution (GPD) of personal income, formed by the combination of the Gompertz curve, representing the overwhelming majority of the economically less favorable part of the population of a country, and the Pareto power law, which describes its tiny richest part. Equations for the…
Stochastic differential equations (SDEs) and the Kolmogorov partial differential equations (PDEs) associated to them have been widely used in models from engineering, finance, and the natural sciences. In particular, SDEs and Kolmogorov PDEs, respectively, are highly employed in models for the approximative pricing of …
We consider concepts and models for measuring inequality in the distribution of resources with a focus on how inequality varies as a function of covariates. Lorenz introduced a device for measuring inequality in the distribution of income that indicates how much the incomes below the u quantile fall short of the…