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 proof of timelike minimal surfaces using split-harmonic maps.
New approach connects stochastic gradient descent to ODE splitting schemes.
Study Loday algebroids, prove splitting theorem, and linearize problems.
SPlit optimizes dataset splitting for better model performance.
Optimizes decision-making with uncertain variables using auxiliary observations.
Novel methods for splitting Gaussian mixtures improve uncertainty propagation in nonlinear systems.
In this work, we propose a novel node splitting method for regression trees and incorporate it into the regression forest framework. Unlike traditional binary splitting, where the splitting rule is selected from a predefined set of binary splitting rules via trial-and-error, the proposed node splitting method first fin…
The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range constraints. Split feasibility generalizes important inverse problems including con…
Twinning splits data into fast, statistically similar sets.
New algorithm solves maximal monotone inclusion problems.
Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or multidimensional parabolic problems of the convection-diffusion type and generaliz…
C. Gordon conjectured that a connected sum of two Heegaard splittings is stabilized if and only if one of the two factors is stabilized (Problem 3.91 in Kirby's problem list). In this paper, we shall prove this conjecture.
It is a classical result that any complex analytic Lie supergroup is split \cite{kosz}, that is its structure sheaf is isomorphic to the structure sheaf of a certain vector bundle. However, there do exist non-split complex analytic homogeneous supermanifolds. We study the question how to find out whether …
Develops formal moduli theory for splitting complex supermanifolds.
Novel approach for creating interpretable classifiers using bilevel optimization of split-rules in NLDTs.
Explains historical connections between vector bundle splitting and Riemann-Hilbert problems.
The long standing classification problem in the theory of Heegaard splittings of 3-manifolds is to exhibit for each closed 3-manifold a complete list, without duplication, of all its irreducible Heegaard surfaces, up to isotopy. We solve this problem for non Haken hyperbolic 3-manifolds.
Study evaluates when splitting classifiers can improve performance despite disparate treatment.
These are problems on Heegaard splittings, that were raised at the Workshop, listed according to their contributors: David Bachman, Mario Eudave-Munoz, John Hempel, Tao Li, Yair Minsky, Yoav Moriah and Richard Weidmann. On pages 285-298 of this monograph (arxiv:0904.0017) Hyam Rubinstein gives a personal collection of …
Study rigidity of spectral gap on Finsler manifolds with specific curvature bounds.
We address a special case of the Stabilization Problem for Heegaard splittings, establishing an upper bound on the number of stabilizations required to make a Heegaard splitting of a Haken 3-manifold isotopic to an amalgamation along an essential surface. As a consequence we show that for any positive integer there…
An updated proof of a 1933 theorem of Goeritz, exhibiting a finite set of generators for the group of automorphisms of the 3-sphere that preserve a genus two Heegaard splitting. The group is analyzed via its action on a certain connected 2-complex. (The analogous problem for higher genus Heegaard splittings appears to …
New split rules improve subpopulation targeting in policy-making.
Extends branch and bound for probabilistic neural network verification.
Optimizes data splitting for shorter conformal prediction intervals.
Study non-split supermanifolds from complex manifolds.
A method to split a data point into two parts that individually cannot reconstruct the whole, but together can.
Geroch's theorem about the splitting of globally hyperbolic spacetimes is a central result in global Lorentzian Geometry. Nevertheless, this result was obtained at a topological level, and the possibility to obtain a metric (or, at least, smooth) version has been controversial since its publication in 1970. In fact, th…
In-network learning outperforms Federated and Split learning in wireless networks.
High order splitting schemes with complex timesteps are applied to Kolmogorov backward equations stemming from stochastic differential equations in Stratonovich form. In the setting of weighted spaces, the necessary analyticity of the split semigroups can be easily proved. A numerical example from interest rate theory,…
The split Bregman (SB) method [T. Goldstein and S. Osher, SIAM J. Imaging Sci., 2 (2009), pp. 323-43] is a fast splitting-based algorithm that solves image reconstruction problems with general l1, e.g., total-variation (TV) and compressed sensing (CS), regularizations by introducing a single variable split to decouple …
This paper optimizes high-dimensional oblique splits for decision trees, enhancing performance and computational efficiency.
Study shows that splitting links requires an arbitrarily large number of extra crossings.
Develops a new inference method for split-sample estimators using multiple splits.
Develops variance-reduced methods for solving generalized equations.
We enhance the analogy between field extensions and covering spaces by introducing the concept of splitting covering which correspondences to the splitting field in Galois theory. We define semi-topological Galois groups for Weierstrass polynomials and prove the existence of a Galois correspondence. This new tool enabl…
This paper deals with the numerical approximation of American-style option values governed by partial differential complementarity problems. For a variety of one- and two-asset American options we investigate by ample numerical experiments the temporal convergence behaviour of three modern splitting methods: the explic…
We adapt the Douglas-Rachford (DR) splitting method to solve nonconvex feasibility problems by studying this method for a class of nonconvex optimization problem. While the convergence properties of the method for convex problems have been well studied, far less is known in the nonconvex setting. In this paper, for the…
We survey the problem of separation under conjugacy and malnormality of the abelian peripheral subgroups of an orientable, irreducible -manifold . We shall focus on the relation between this problem and the existence of acylindrical splittings of as an amalgamated product or HNN-extension along the abeli…
Within the unmanageably large class of nonconvex optimization, we consider the rich subclass of nonsmooth problems that have composite objectives---this already includes the extensively studied convex, composite objective problems as a special case. For this subclass, we introduce a powerful, new framework that permits…
The problem of splitting a homotopy equivalence along a submanifold is closely related to the surgery exact sequence and to the problem of surgery of manifold pairs. In classical surgery theory there exist two approaches to surgery in the category of manifolds with boundaries. In the case the surgery on…
One purpose of this article is to draw attention to the seminal work of J. Mealy in 1989 on calibrations in semi-riemannian geometry where split SLAG geometry was first introduced. The natural setting is provided by doing geometry with the complex numbers C replaced by the double numbers D, where i with i^2 = -1 is rep…
We consider the problem of estimating the inverse covariance matrix by maximizing the likelihood function with a penalty added to encourage the sparsity of the resulting matrix. We propose a new approach based on the split Bregman method to solve the regularized maximum likelihood estimation problem. We show that our m…
Let M_1 and M_2 be closed, orientable 3-manifolds. Let H_i denote a Heegaard surface in M_i. We prove that if H_1 # H_2 comes from stabilizing a lower genus splitting of M_1 # M_2 then either H_1 or H_2 comes from stabilizing a lower genus splitting. If H_i and G_i are non-isotopic Heegaard surfaces in M_i, and H_i is …
New algorithms accelerate value function convergence in MDPs.
To reduce the label complexity in Agnostic Active Learning (A^2 algorithm), volume-splitting splits the hypothesis edges to reduce the Vapnik-Chervonenkis (VC) dimension in version space. However, the effectiveness of volume-splitting critically depends on the initial hypothesis and this problem is also known as target…
We investigate a generalization of the so-called metric splitting of globally hyperbolic space-times to non-smooth Lorentzian manifolds and show the existence of this metric splitting for a class of wave-type space-times. Our approach is based on smooth approximations of non-smooth space-times by families (or sequences…
Co-Clustering, the problem of simultaneously identifying clusters across multiple aspects of a data set, is a natural generalization of clustering to higher-order structured data. Recent convex formulations of bi-clustering and tensor co-clustering, which shrink estimated centroids together using a convex fusion penalt…