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.
New algorithm for recognizing 3-spheres using Groebner basis methods.
A deformation of the Orlik-Solomon algebra of a matroid M is defined as a quotient of the free associative algebra over a commutative ring R with 1. It is shown that the given generators form a Groebner basis and that after suitable homogenization the deformation and the Orlik-Solomon have the same Hilbert series as R-…
This paper has been withdrawn by the author, due to errors in Groebner basis calculations in the cases of five and six dimensional groups.
We describe a Groebner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and other special cases. We also investigate the connection to generali…
In "The {G}el'fand-{K}alinin-{F}uks class and characteristic classes of transversely symplectic foliations" arXiv:0910.3414, Kotschick and Morita showed that the Gel'fand-Kalinin-Fuks class in $\ds\HGF{7}{2}{}{8}$ is decomposed as a product of some leaf cohomology class and a transverse symplectic class…
We propose a new point of view on quantum cohomology, strongly motivated by the work of Givental and Dubrovin, but closer to differential geometry than the existing approaches. The central object is the D-module which "quantizes" a commutative algebra associated to the (uncompactified) space of rational curves. A stand…
Rosso and Jones gave a formula for the colored Jones polynomial of a torus knot, colored by an irreducible representation of a simple Lie algebra. The Rosso-Jones formula involves a plethysm function, unknown in general. We provide an explicit formula for the second plethysm of an arbitrary representation of $\fsl_3$, …
Automatically explores geometric loci of curves using software networking.
We classify SIC-POVMs of rank one in CP^2, or equivalently sets of nine equally-spaced points in CP^2, without the assumption of group covariance. If two points are fixed, the remaining seven must lie on a pinched torus that a standard moment mapping projects to a circle in R^3. We use this approach to prove that any S…
In this paper we prove that the only algebraic constant mean curvature (cmc) surfaces in R^3 of order less than four are the planes, the spheres and the cylinders. The method used heavily depends on the efficiency of algorithms to compute Groebner Bases and also on the memory capacity of the computer used to do the com…
We propose a purely algebraic approach to construct invariants of transversal links in the standard contact structure on the 3-sphere generalizing Jones' approach to invariant of usual links. The only geometry used is the analogue of Alexander and Markov theorems. More precisely, we construct a trace on a certain cubic…
We provide a scheme for inferring causal relations from uncontrolled statistical data based on tools from computational algebraic geometry, in particular, the computation of Groebner bases. We focus on causal structures containing just two observed variables, each of which is binary. We consider the consequences of imp…
Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, we considered the definition of orthonormal basis in Minkows…
New basis confirms Thurston's conjecture and reveals knot configurations.
Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, I considered the definition of orthonormal basis in Minkowsk…
We study a novel spline-like basis, which we name the "falling factorial basis", bearing many similarities to the classic truncated power basis. The advantage of the falling factorial basis is that it enables rapid, linear-time computations in basis matrix multiplication and basis matrix inversion. The falling factoria…
Study optimal dynamic basis trading strategies with stochastic basis model.
We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so called chamber basis. We consider structure constants of the Orlik-Solomon algebra with respect to the chamber basis and prove that these structure constants recover D. Cohen's minimal complex from the Aomoto complex.
New framework models complex spatial data with basis functions and graphical vectors.
Machine learning model predicts DFT total energy to complete basis set limit.
The paper explains the fair basis in bond-CDS trading during financial crises.
Researchers found a special basis for cycles on a K3 surface.
Optimizes basis for density-based atomic representations to enhance compactness and accuracy.
This study tackles basis risk in weather parametric insurance using Monte Carlo simulations.
We show that the twisted SL(2) skein algebra of a surface has a natural basis (the bracelets basis) that is positive, in the sense that the structure constants for multiplication are positive integers.
New basis for permutation equivariant layers reduces computation costs.
Investigates smoothness of specific algebra structures.
Harmonic basis vector fields on surfaces
Proves log-concavity of cluster algebra coefficients for type .
Defines tensor eigenvalues and singular values without basis, simplifying analysis.
The study explores various localized bases and their duals for scattered data approximation.
Study transitions between tableau and spider bases for Specht modules.
T-Basis represents neural network tensors with fewer parameters.
A graph connects Specht and web bases; matrix is unipotent with vanishing entries.
New method estimates density functionals using polynomial basis without full distribution knowledge.
This paper optimizes PCE for efficient surrogate modeling in engineering.
New algorithm improves asset pricing model for high-dimensional financial data.
Paper tackles spurious vanishing problem in approximate vanishing ideals.
In this paper we study a symmetry group of vector space. Basis manifold is a homogeneous space of a symmetry group. This concept leads us to the definition of active and passive transformations on basis manifold. Active transformation can be expressed as a transformation of vector space. Passive transformation gives ab…
Sparse principal component analysis (sparse PCA) aims at finding a sparse basis to improve the interpretability over the dense basis of PCA, meanwhile the sparse basis should cover the data subspace as much as possible. In contrast to most of existing work which deal with the problem by adding some sparsity penalties o…
A neural network predicts coarse-scale basis functions for efficient uncertainty quantification.
A new kernel improves statistical surrogates for stochastic manifolds with diverse data.
A new density model using Fourier basis achieves better approximations and compression.
BASIS improves LLM reasoning by sharing batchwise rollout info, reducing MSE by 69%.
Alternative basis for Kauffman bracket skein module of solid torus found using braids.
Derives representations invariant under crystallographic groups for functions.
We give an explicit graded cellular basis of the -web algebra . In order to do this, we identify Kuperberg's basis for the -web space with a version of Leclerc-Toffin's intermediate crystal basis and we identify Brundan, Kleshchev and Wang's degree of tableaux with the weigh…
Given a simple algebraic group , a web is a directed trivalent graph with edges labelled by dominant minuscule weights. There is a natural surjection of webs onto the invariant space of tensor products of minuscule representations. Following the work of Westbury, we produce a set of webs for $\SL_n$ which form a bas…