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.
Geometric approach uses Bäcklund transformations to create integrable discrete analogs of surface nets.
Legendre transformations link related integrable hierarchies.
The paper explores geometric aspects of Miura transformations in integrable systems.
We prove that second-order hyperbolic Monge-Ampere equations for one function of two variables are connected to the wave equation by a Backlund transformation if and only if they are integrable by the method of Darboux at second order. One direction of proof, proving Darboux integrability, follows the implications of t…
Proposes a new feature preprocessing method using kernel density integral transformation.
Develops support theorem for analytic transforms in tomography.
We give a new mechanism for constructing Backlund transformations by using symmetry reduction of differential systems. We then characterize a family of Backlund transformations between Darboux integrable systems where the Backlund transformation can be constructed by the proposed symmetry reduction method.
Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the approximation errors. Our aim is to design a method for moment transformation for …
New integral theorems improve density function estimations.
We introduce the Koenigs lattice, which is a new integrable reduction of the quadrilateral lattice (discrete conjugate net) and provides natural integrable discrete analogue of the Koenigs net. We construct the Darboux-type transformations of the Koenigs lattice and we show permutability of superpositions of such trans…
Transformers improve with Fourier integral attentions.
New integral transforms solve multilayer heat equations.
The paper discusses a new method for constructing two-step Darboux transforms of isothermic surfaces.
New method for curve comparison using iterated integrals and moving frames.
New method linearizes Darboux transformations of discrete curves.
New definition of Bäcklund transformation for surface isometric deformation.
DGPFM uses deep Gaussian processes to map functions accurately and quantify uncertainty.
GIT-Net uses neural networks to approximate PDE operators efficiently.
We study the asymptotic behaviour of doubly periodic instantons with square-integrable curvature. Then, we establish the equivalence given by the Nahm transform between the doubly periodic instantons with square integrable curvature and the wild harmonic bundles on the dual torus.
Derives integral formulae on weighted manifolds.
We establish a link between Archimedes' method of integration for calculating areas, volumes and centers of mass of segments of parabolas and quadrics of revolution by factorization via the moments of a balance and an integration technique for a particular integrable system, namely Bianchi's Bäcklund transformation for…
Bayesian quadrature improves integration efficiency with invariant priors.
This work integrates differentiation and integration in Physics-Informed Neural Networks.
We consider an application involving a financial quadratic portfolio of options, when the joint underlying log-returns changes with multivariate elliptic distribution. This motivates the needs for methods for the approximation of multiple integrals over hyperboloids. A transformation is used to reduce the hyperboloid i…
Study the Lax equation in infinite-dimensional Lie algebras and Lie groups.
We study the weighted light ray transform of integrating functions on a Lorentzian manifold over lightlike geodesics. We analyze as a Fourier Integral Operator and show that if there are no conjugate points, one can recover the spacelike singularities of a function from its the weighted light ray transform …
We study the dynamics of the discrete bicycle (Darboux, Backlund) transformation of polygons in n-dimensional Euclidean space. This transformation is a discretization of the continuous bicycle transformation, recently studied by Foote, Levi, and Tabachnikov. We prove that the respective monodromy is a Moebius transform…
The paper proves conditions for Darboux integrability in diagonal hydrodynamic systems.
The study provides a criterion for fractional-linear integrals of geodesics on surfaces.
We describe the gauge-theoretic approach to transformations in integrable geometry through discussion of two classical examples: surfaces of constant negative Gauss curvature and isothermic surfaces. These are purely expository notes written to accompany some lectures I gave in Fukuoka in May 2015.
One of the most challenging problems in the domain of 2-D image or 3-D shape is to handle the non-rigid deformation. From the perspective of transformation groups, the conformal transformation is a key part of the diffeomorphism. According to the Liouville Theorem, an important part of the conformal transformation is t…
Transformer-based method for causal discovery with prior knowledge integration.
New method calculates geometric Brownian motion with affine drift and its integral.
A general method for analytic inversion of geometric integral transforms is proposed
We discuss natural transformations in the context of Lie groupoids, and their infinitesimal counterpart. Our main result is an integration procedure that provides smooth natural transformations between Lie groupoid morphisms.
Study normal operators of double fibration transforms with conjugate points.
Inverts rank m symmetric tensor fields using line integrals.
The paper derives Pizzetti formulae and inverts the Radon transform on spheres.
We prove that any regular integral invariant of volume-preserving transformations is equivalent to the helicity. Specifically, given a functional defined on exact divergence-free vector fields of class on a compact 3-manifold that is associated with a well-behaved integral kernel, we prove that $\mat…
The paper analyzes how grid cells perform path integration and learns hexagon grid patterns.
The aim of this article is to design a moment transformation for Student- t distributed random variables, which is able to account for the error in the numerically computed mean. We employ Student-t process quadrature, an instance of Bayesian quadrature, which allows us to treat the integral itself as a random variable…
Simplified calculus for semimartingales makes complex transformations easier.
Study light ray transform in pseudo-Euclidean space, derive inversion formula, and prove stability.
In this paper we investigate overdetermined systems of scalar PDEs on the plane with one common characteristic, whose general solution depends on 1 function of 1 variable. We describe linearization of such systems and their integration via Laplace transformation, relating this to Lie's integration theorem and formal th…
Twistor correspondences for R-invariant indefinite self-dual conformal structures on R^4 are established explicitly. These correspondences are written down by using a natural integral transform from functions on a two dimensional cylinder to functions on the flat Lorentz space R^{1,2} which is related to the wave equat…
We study an analogue of the classical Bianchi-Darboux transformation for L-isothermic surfaces in Laguerre geometry, the Bianchi-Darboux transformation. We show how to construct the Bianchi-Darboux transforms of an L-isothermic surface by solving an integrable linear differential system. We then establish a permutabili…
Paper proposes integrating wavelet transform, channel attention, and LSTM for better stock price prediction.
In the article arXiv:1108.5443 we established a general group-theoretical approach to the construction of Bäcklund transformations. We then showed how this construction can be applied to construct Bäcklund transformation between equations which are Darboux integrable. Here we give a number of detailed examples and new …