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.
Develops Poisson algebras for field theories using synthetic differential geometry.
Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construc…
We study scale invariant but not necessarily conformal invariant deformations of non-relativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when w…
The un-reduction procedure introduced previously in the context of Mechanics is extended to covariant Field Theory. The new covariant un-reduction procedure is applied to the problem of shape matching of images which depend on more than one independent variable (for instance, time and an additional labelling parameter)…
Two proofs of Kalman Theorem using flows of vector fields.
Abstract: Linking field theory to Floer theory via regularization.
Study modular surfaces in Lorentz-Minkowski 3-space, classifying and analyzing their curvature and applications.
Non linear sigma models are quantum field theories describing, in the large deviations sense, random fluctuations of harmonic maps between a Riemann surface and a Riemannian manifold. Via their formal renormalization group analysis, they provide a framework for possible generalizations of the Hamilton-Perelman Ricci fl…
In this lecture delivered at the Integrable and Quantum Field Theory at Peyresq sixth meeting, we review the Lychagin's Monge-Ampere operators theory and exhibit the link it establishes between the classical problem of local equivalence for non linear partial differential equations and the problem of integrability of s…
In this article we will show that the Macro-Economy and its growth can be modelled and explained exactly in principle by commonly known Field Theory from theoretical physics. We will show the main concepts and calculations needed and show that calculation and prediction of economic growth then gets indeed possible in D…
The paper explores how fields in higher dimensions are quantized.
To pave the way for the journey from geometry to conformal field theory (CFT), these notes present the background for some basic CFT constructions from Calabi-Yau geometry. Topics include the complex and Kaehler geometry of Calabi-Yau manifolds and their classification in low dimensions. I furthermore discuss CFT const…
We discuss in rather general terms quantum field theories dealing with spaces of maps between Riemannian manifolds. In particular we explore the well--known connection between the renormalization group flow for non--linear sigma models and the Ricci flow.
Reconstructing signature features from randomized vector fields in differential equations.
We study a new set of coupled field equations motivated by the non-linear supersymmetric sigma model of quantum field theory. These equations couple a map into a Riemannian manifold controlled by a harmonic map like action with a spinor field along that map. We study the solutions which we call Dirac-harmonic maps from…
The paper gauges non-linear sigma models using Lie algebroid actions.
Quantum Kerr learning shows enhancements in convergence and generalization for kernel-based methods.
The paper generalizes two-field α-attractor models using geometrically finite hyperbolic surfaces.
New method optimizes non-linear functionals over probability measures.
Unified Bayesian framework predicts cryptocurrency market dynamics and volatility.
New approach connects Finsler geometry's metric and connections.
Improved disability insurance model with collective health claims.
One 'problem' with the 21st century world, particularly the economic and business worlds, is the phenomenal and increasing number of interconnections between economic agents (consumers, firms, banks, markets, national economies). This implies that such agents are all interacting and consequently giving raise to enormou…
We discuss from a geometric point of view the connection between the renormalization group flow for non--linear sigma models and the Ricci flow. This offers new perspectives in providing a geometrical landscape for 2D quantum field theories. In particular we argue that the structure of Ricci flow singularities suggests…
The quantum field theory of two-dimensional sigma models with bulk and boundary couplings provides a natural framework to realize and unite different species of geometric flows that are of current interest in mathematics. In particular, the bulk renormalization group equation gives rise to the Ricci flow of target spac…
Starting from a relativistic phenomenology of anyons in crystals, we discuss the concept of relativistic interaction and the need to unify electromagnetism and gravitation within the Spencer cohomology of Lie equations. Then, from the sophisticated non-linear Spencer complex of the Poincaré and conformal Lie pseudogrou…
Researchers can retrieve Yang-Mills-Higgs fields from Minkowski space measurements.
Elliptic theory explains indicial weights for non-linear geometry problems.
Study proves cosmic no-hair conjecture for certain spacetimes.
This paper offers a precise analytical characterization of the distribution of returns for a portfolio constituted of assets whose returns are described by an arbitrary joint multivariate distribution. In this goal, we introduce a non-linear transformation that maps the returns onto gaussian variables whose covariance …
Study high-dimensional Bayesian linear regression using variational inference.
We use Vessiot theory and exterior calculus to solve partial differential equations(PDEs) of the type uyy = F(x, y,u,ux,uy,uxx,uxy) and associated evolution equations. These equations are represented by the Vessiot distribution of vector fields. We develop and apply an algorithm to find the largest integrable sub-distr…
New approach to ODEs using Gaussian processes and Bayesian filtering.
Diffeomorphism freedom induces a gauge dependence in the theory of spacetime perturbations. We derive a compact formula for gauge transformations of perturbations of arbitrary order. To this end, we develop the theory of Taylor expansions for one-parameter families (not necessarily groups) of diffeomorphisms. First, we…
Survey para-Hermitian geometry and its applications in physics.
Unified theory of -expectations derived from chaotic dynamics.
We develop a theory for solving continuous time optimal stopping problems for non-linear expectations. Our motivation is to consider problems in which the stopper uses risk measures to evaluate future rewards.
New model explains market dynamics with phase transitions and non-linear interactions.
New framework for analyzing games with multi-dimensional singular controls and non-linear jumps.
In arXiv:0805.2192, we set up a gauge-theoretic equation on symplectic 6-manifolds, which is a version of the Hermitian-Einstein equation perturbed by Higgs fields, and call Donaldson-Thomas equation, to analytically approach the Donaldson-Thomas invariants. In this article, we consider the equation on compact Kähler t…
New method reconstructs strain and lattice spacing from neutron data.
We show that generalised geometry gives a unified description of maximally supersymmetric consistent truncations of ten- and eleven-dimensional supergravity. In all cases the reduction manifold admits a "generalised parallelisation" with a frame algebra with constant coefficients. The consistent truncation then arises …
Researchers use quantum chaos and RMT to analyze turbulence, revealing unique scaling laws.
Neural ODEs provide a framework for studying the training dynamics of neural networks.
The study investigates how data variability impacts the generalization of neural networks.
Study improves understanding of network degree distributions using non-linear ERGs.
New black hole solutions found for specific conditions.
NON model improves tabular data classification accuracy.