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 finds polynomial convergence rate for Farey sequences linked to Riemann hypothesis.
Hermite polynomials improve private data generation by reducing feature count.
New algorithm recovers sparse measures in polynomial time.
Bayesian neural networks learn efficiently at infinite width, matching polynomial-width performance.
Study shows polynomial-width neural networks can closely approximate infinite-width networks in polynomial time.
No regular algebraic hypersurfaces with non-zero constant mean curvature in Euclidean spaces are found.
New RL algorithms achieve optimal policies with polynomial sample complexity for mean-field problems.
Paper corrects a proof about biharmonic hypersurfaces with three distinct curvatures.
This paper studies a specific blow-up algorithm for sop polynomials and their RLCT.
We construct new invariant polynomial for long virtual knots. It is a generalization of Alexander polynomial. We designate it by meaning an analogy with -polynomial for virtual links. A degree of -polynomial estimates a virtual crossing number. We describe some application of -polynomial for the study of m…
We define a hierarchy of special classes of constrained Willmore surfaces by means of the existence of a polynomial conserved quantity of some type, filtered by an integer. Type 1 with parallel top term characterises parallel mean curvature surfaces and, in codimension 1, type 1 characterises constant mean curvature su…
Cryptocurrency prices predicted using LSTM, SVM, and polynomial regression.
In this short note we show the existence of an epimorphism between groups of -bridge knots by means of an elementary argument using the Riley polynomial. As a corollary, we give a classification of -bridge knots by Riley polynomials.
The paper studies random dynamical systems of polynomial automorphisms on C^2 and finds mean stability.
We show how Seifert surfaces, so useful for the understanding of the Alexander polynomial Δ_L(t), can be generalized in order to study the multivariable Alexander polynomial Δ_L(t_1,...,t_μ). In particular, we give an elementary and geometric proof of the Torres formula.
We derive the Do and Norbury recursion formula for the one-loop mean of an irregular spectral curve from a variant of replica method by Brezín and Hikami. We express this recursion in special times in which all terms of the genus expansion of the one-loop mean are polynomials. We find a generalization of th…
The study classifies polynomial relation tubular surfaces in 3-spaces.
Polynomial-time algorithm estimates mean with bounded covariance using differential privacy.
The Matérn covariance function is a popular choice for prediction in spatial statistics and uncertainty quantification literature. A key benefit of the Matérn class is that it is possible to get precise control over the degree of mean-square differentiability of the random process. However, the Matérn class possesses e…
In this article, we study properly immersed complete noncompact submanifolds in a complete shrinking gradient Ricci soliton with weighted mean curvature vector bounded in norm. We prove that such a submanifold must have polynomial volume growth under some mild assumption on the potential function. On the other hand, if…
New method for estimating sparse means in noisy data.
In this work we find all helicoidal surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is or and that the surface is ruled. If the generating curve is a Lorentzian ci…
New findings on computational limits for estimating hidden structures.
In this note we present a description of wave front evolving from an algebraic hypersurface by means of a pull-back of the discriminantal loci of a tame polynomial via a polynomial mapping. As an application we give examples of wave fronts which define free/almost free divisors near the focal point.
The Mishchenko-Fomenko conjecture says that for each real or complex finite-dimensional Lie algebra $\goth g$ there exists a complete set of commuting polynomials on its dual space $\goth g^*$. In terms of the theory of integrable Hamiltonian systems this means that the dual space $\goth g^*$ endowed with the standard …
Fuzzy clustering with similarity queries improves efficiency and accuracy.
Paper tackles non-stationary bandits with various examples.
We provide methods to compute the colored HOMFLY polynomials of knots and links with symmetric representations based on the linear skein theory. By using diagrammatic calculations, several formulae for the colored HOMFLY polynomials are obtained. As an application, we calculate some examples for hyperbolic knots and li…
In this paper we present a sequence of link invariants, defined from twisted Alexander polynomials, and discuss their effectiveness in distinguish knots. In particular, we recast and extend by geometric means a recent result of Silver and Williams on the nontriviality of twisted Alexander polynomials for nontrivial kno…
New method uses Hermite polynomials for American option valuation.
I prove that if markets are weak-form efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how we can "progr…
In this survey we summarize results regarding the Kauffman bracket, HOMFLYPT, Kauffman 2-variable and Dubrovnik skein modules, and the Alexander polynomial of links in lens spaces, which we represent as mixed link diagrams. These invariants generalize the corresponding knot polynomials in the classical case. We compare…
New algorithms improve privacy in statistical estimation by making them robust.
Polynomial-time algorithm for clustering mixtures with separation Δ=Ω(√(log k)).
Algorithm distinguishes Gaussian mixtures from pure Gaussians in quasi-polynomial time.
Polynomial-time private algorithm for robust estimation of mean and covariance in the presence of outliers.
Efficiently estimates mean in contaminated Gaussian data with near-optimal sample complexity.
The aim of this paper is to state and prove polynomial analogues of the classical Manning inequality relating the topological entropy of a geodesic flow with the growth rate of the volume of balls in the universal covering. To this aim we use two numerical conjugacy invariants, the {\em strong polynomial entropy $h_{po…
We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an -fraction of our samples were chosen by an adversary. We give robust estimators that achieve estimation error in the total variation distance, which is optimal up…
New algorithm estimates Gaussian means and covariances efficiently and privately.
The paper certifies projective rigidity for once-punctured torus bundles using twisted Alexander polynomials.
We consider regular surfaces that are given as the zeros of a polynomial function , where the gradient of vanishes nowhere. We assume that has non-zero mean curvature and prove that there exist only two examples of such surfaces, namely the sphere and the circular cylinder.
We compute the Kauffman bracket polynomial of the three-lead Turk's head, the chain sinnet and the figure-eight chain shadow diagrams. Each of these knots can in fact be constructed by repeatedly concatenating the same 3-tangle, respectively, then taking the closure. The bracket is then evaluated by expressing the stat…
From analysis of a big variety of different knots we conclude that at q which is an root of unity, q^{2m}=1, HOMFLY polynomials in symmetric representations [r] satisfy recursion identity: H_{r+m} = H_r H_m for any A, which is a generalization of the property H_r = (H_1)^r for special polynomials at q=1. We conjecture …
Proves subgaussian distributions are SoS-certifiably subgaussian, enabling efficient algorithms for various statistical tasks.
New connection found between complex polynomials and surface homeomorphisms.
The paper constructs solutions with infinite-time singularities in Lagrangian mean curvature flow.
Deep Gaussian Processes with polynomial kernels can collapse rapidly without proper hyperparameter tuning.