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 limits of adjoint orbits for Lie groups, describing nilpotent orbits.
Study convex hulls of orbits for compact groups, defining new invariants related to polynomial degrees.
New method reduces bias in incomplete data using deliberate missingness.
Paper analyzes \FedAvg's convergence and introduces a new algorithm to reduce bias.
Paper analyzes LSA algorithm bias and error bounds with RR extrapolation.
Generalized Schouten, Froelicher-Nijenhuis and Froelicher-Richardson brackets are defined for an arbitrary Lie algebroid. Tangent and cotangent lifts of Lie algebroids are introduced and discussed and the behaviour of the related graded Lie brackets under these lifts is studied. In the case of the canonical Lie algebro…
Paper proposes a new algorithm to reduce derivative pricing computation time.
Quantized Variational Inference improves ELBO optimization with fast convergence.
This is an expository paper in which we explain how basic, standard, results about simple Lie algebras can be obtained by geometric arguments, following ideas of Cartan, Richardson and others.
The paper analyzes SGD with Richardson-Romberg extrapolation for convex optimization problems.
For a connected abelian Lie group T acting on a Poisson manifold (Y,π) by Poisson isomorphisms, the T-leaves of π in Y are, by definition, the orbits of the symplectic leaves of π under T, and the leaf stabilizer of a T-leaf is the subspace of the Lie algebra of T that is everywhere tangent to all the symplectic leaves…
We demonstrate the use of several tools from Algebraic Combinatorics such as Young tableaux, symmetry operators, the Littlewood-Richardson rule and discrete Fourier transforms of symmetric groups in investigations of algebraic curvature tensors.
Paper examines constant stepsize in LSA for Markovian data inference.
The problem of classifying, upto isometry (or similarity), the orientable spherical, Euclidean and hyperbolic 3-manifolds that arise by identifying the faces of a Platonic solid is formulated in the language of Coxeter groups. In the spherical and hyperbolic cases, this allows us to complete the classification begun by…
Study on bias of constant-step stochastic approximation with Markovian noise.
Paper traces origins of graded Lie brackets theory.
The coupled system, where one is a degenerate parabolic equation and the other has not a diffusion term arises in the modeling of European options with liquidity shocks. Two implicit-explicit (IMEX) schemes that preserve the positivity of the differential problem solution are constructed and analyzed. Numerical experim…
Improves numerical solution of ill-conditioned linear systems for machine learning.
Study Q-learning with constant stepsize, proving convergence and bias, and applying extrapolation.
New estimators for intrinsic dimension and Wasserstein distance improve OT accuracy.
For the numerical solution of the American option valuation problem, we provide a script written in MATLAB implementing an explicit finite difference scheme. Our main contribute is the definition of a posteriori error estimator for the American options pricing which is based on Richardson's extrapolation theory. This e…
New method uses Wasserstein loss for data unfolding, offering better accuracy than classical techniques.
Study on bias and extrapolation in LSA with Markovian data, showing bias reduction with Richardson-Romberg extrapolation.
In this paper we review the recently proposed path-integral counterpart of the Koopman-von Neumann operatorial approach to classical Hamiltonian mechanics. We identify in particular the geometrical variables entering this formulation and show that they are essentially a basis of the cotangent bundle to the tangent bund…
Study of braid varieties and their Legendrian isotopy.
We define the notion of the orbit group of a quandle via its connectivity and compute the orbit groups for some basic quandles. We also show that the orbit group counts the number of orbits of certain quandles.
For a positive definite fundamental tensor all known examples of Osserman algebraic curvature tensors have a typical structure. They can be produced from a metric tensor and a finite set of skew-symmetric matrices which fulfil Clifford commutation relations. We show by means of Young symmetrizers and a theorem of S. A.…
The paper finds linked periodic orbits in disc homeomorphisms using braids.
New insights into pseudo-Anosov flows with special periodic orbits.
The study counts periodic orbits on smooth manifolds, adding ghost orbits for completeness.
This paper develops a model of liquidity provision in financial markets by adapting the Madhavan, Richardson, and Roomans (1997) price formation model to realistic order books with quote discretization and liquidity rebates. We postulate that liquidity providers observe a fundamental price which is continuous, efficien…
Study properties of orbits of Hermann actions without commutability assumptions.
Smooth approximations for continuous functions on orbit spaces.
A quandle orbit's orientation is problematic when reversed.
Minimal orbits of semi-simple Lie groups are studied and related to invariant subspaces.
A geodesic orbit manifold is a complete Riemannian manifold all of whose geodesics are orbits of one-parameter groups of isometries. We give both a geometric and an algebraic characterization of geodesic orbit manifolds that are diffeomorphic to . Along the way, we establish various structural properties …
Given a compact Riemannian manifold together with a group of isometries, we discuss MCF of the orbits and some applications: eg, finding minimal orbits. We then specialize to Lagrangian orbits in Kaehler manifolds. In particular, in the Kaehler-Einstein case we find a relation between MCF and moment maps which, for exa…
New Frobenius manifold structures found on Dicyclic group orbits.
Study orbits in right triangles, deducing periodic billiard paths and classifying orbit closures.
The use of machine learning algorithms to address classification problems is on the rise in many research areas. The current study is aimed at testing the potential of using such algorithms to auto-select the best solvers for transport problems in uniform slabs. Three solvers are used in this work: Richardson, diffusio…
Study orbit spaces of equivariant ANEs for proper actions of metrizable groups.
We produce infinitely many examples of Anosov flows in closed 3-manifolds where the set of periodic orbits is partitioned into two infinite subsets. In one subset every closed orbit is freely homotopic to infinitely other closed orbits of the flow. In the other subset every closed orbit is freely homotopic to only one …
The classification of G-spaces by Palais is refined for the case where the orbit space satisfies certain mild topological hypotheses. It is shown that when a sequence of such orbit spaces is "close" to a limit orbit space, in some suitable sense, within a larger ambient orbit space, the G-spaces in the tail of the sequ…
We list up all the possible local orbit types of hyperbolic or elliptic orbits for the isotropy representations of semisimple pseudo-Riemannian symmetric spaces. It is key to give a recipe to determine the local orbit types of hyperbolic principal orbits by using three kind of restricted root systems and Satake diagram…
Study of adjoint orbits in simplest non-trivial Lie algebra case.
Geodesic graphs for special Finsler metrics on spheres are studied.
We consider the minimization of an objective function given access to unbiased estimates of its gradient through stochastic gradient descent (SGD) with constant step-size. While the detailed analysis was only performed for quadratic functions, we provide an explicit asymptotic expansion of the moments of the averaged S…
Classifies finite orbits of mapping class group action on character varieties.