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.
The splitting number of a link is the minimal number of crossing changes between different components required, on any diagram, to convert it to a split link. We introduce new techniques to compute the splitting number, involving covering links and Alexander invariants. As an application, we completely determine the sp…
It was shown by Bonahon-Otal and Hodgson-Rubinstein that any two genus-one Heegaard splittings of the same 3-manifold (typically a lens space) are isotopic. On the other hand, it was shown by Boileau, Collins and Zieschang that certain Seifert manifolds have distinct genus-two Heegaard splittings. In an earlier paper, …
Paper shows idempotents in tangle categories split naturally.
New optimization algorithms for neural networks using operator splitting.
The paper proves normal forms for Dirac-Jacobi bundles and splitting theorems for Jacobi structures.
Low regularity spacetimes split into simpler structures.
Split learning preserves privacy in 1D CNN models for detecting heart abnormalities.
The splitting number of a link is the minimal number of crossing changes between different components required to convert it into a split link. We obtain a lower bound on the splitting number in terms of the (multivariable) signature and nullity. Although very elementary and easy to compute, this bound turns out to be …
New proof of Giroux Correspondence for tight contact 3-manifolds.
When a Dehn filled link manifold contains a geometrically incompressible one-sided surface, it is shown there is a unique boundary incompressible position that the surface can take in the link space. The proof uses a version of the sweep-out technique from two-sided Heegaard splitting theory. When applied to one-sided …
SBSS uses similarity to split data for better classifier training.
We use a new geometric construction, grope splitting, to give a sharp bound for separation of surfaces in 4-manifolds. We also describe applications of this technique in link-homotopy theory, and to the problem of locating pi_1-null surfaces in 4-manifolds. In our applications to link-homotopy, grope splitting serves a…
The study examines how altering impurity functions influences optimal splits in binary classification trees.
Study shows that splitting links requires an arbitrarily large number of extra crossings.
Novel methods for splitting Gaussian mixtures improve uncertainty propagation in nonlinear systems.
A new method for causal inference in high-dimensional data using machine learning.
The paper develops and tests operator splitting schemes for American options in a complex model.
A specific set of 4g+1 elements is shown to generate the Goeritz group of the genus g+1 Heegaard splitting of a genus g handlebody. These generators are consistent with Powell's proposed generating set for the Goeritz group of the genus g+1 splitting of S^3. There are two proofs: one using purely classical techniques a…
Study shows splitting schemes can approximate WFR flows faster than the exact flow.
SplitEasy trains ML models on mobile devices without server data transfer.
Our main result is a generalization of Cappell's 5-dimensional splitting theorem. As an application, we analyze, up to internal s-cobordism, the smoothable splitting and fibering problems for certain 5-manifolds mapping to the circle. For example, these maps may have homotopy fibers which are in the class of finite con…
Develops Frank-Wolfe Augmented Lagrangian for convex optimization.
New minibatching strategy reduces stochastic gradient bias in optimisation.
Study robustness of split conformal prediction in data contamination setting.
Introduces semistability in geometric group theory and provides techniques to prove it.
We generalize the Bartsch-Li's splitting lemma at infinity for -functionals in [2] and some later variants of it to a class of continuously directional differentiable functionals on Hilbert spaces. Different from the previous flow methods our proof is to combine the ideas of the Morse-Palais lemma due to Duc-Hung-…
Online and stochastic learning has emerged as powerful tool in large scale optimization. In this work, we generalize the Douglas-Rachford splitting (DRs) method for minimizing composite functions to online and stochastic settings (to our best knowledge this is the first time DRs been generalized to sequential version).…
New technique reduces verification time for neural networks.
Assigning significance in high-dimensional regression is challenging. Most computationally efficient selection algorithms cannot guard against inclusion of noise variables. Asymptotically valid p-values are not available. An exception is a recent proposal by Wasserman and Roeder (2008) which splits the data into two pa…
Proves effective linear volume growth for 3-manifolds with positive scalar curvature.
Data structure for Heegaard splittings reduces complexity.
New random forest variants achieve optimal performance in high dimensions.
We propose a pricing technique based on coherent risk measures, which enables one to get finer price intervals than in the No Good Deals pricing. The main idea consists in splitting a liability into several parts and selling these parts to different agents. The technique is closely connected with the convolution of coh…
New algorithm samples from log concave distributions efficiently.
Random Forests (RFs) are strong machine learning tools for classification and regression. However, they remain supervised algorithms, and no extension of RFs to the one-class setting has been proposed, except for techniques based on second-class sampling. This work fills this gap by proposing a natural methodology to e…
Proves cosmetic surgery conjecture for strongly invertible knots.
Our aim in this note is to extend the semi discrete technique by combine it with the split step method. We apply our new method to the Ait-Sahalia model and propose an explicit and positivity preserving numerical scheme.
We show that if two 3-manifolds with toroidal boundary are glued via a `sufficiently complicated' map then every Heegaard splitting of the resulting 3-manifold is weakly reducible. Additionally, if Z is a manifold obtained by gluing X and Y, two connected small manifolds with incompressible boundary, along a closed sur…
Split-BN improves SSL by separating BN stats for unlabeled data.
We develop techniques for computing the integer valued SU(3) Casson invariant. Our method involves resolving the singularities in the flat moduli space using a twisting perturbation and analyzing its effect on the topology of the perturbed flat moduli space. These techniques, together with Bott-Morse theory and the spl…
Unified proof of smooth fibration theorems for collapsed manifolds.
The usual Gromoll-Meyer's generalized Morse lemma near degenerate critical points on Hilbert spaces, so called splitting lemma, is stated for at least -smooth functionals. In this paper we establish a splitting theorem and a shifting theorem for a class of continuously directional differentiable functionals (lower…
Decision tree classifiers are a widely used tool in data stream mining. The use of confidence intervals to estimate the gain associated with each split leads to very effective methods, like the popular Hoeffding tree algorithm. From a statistical viewpoint, the analysis of decision tree classifiers in a streaming setti…
New MCMC method speeds up inference for complex models.
We give a distance estimate for the metric on the disk complex and show that it is Gromov hyperbolic. As another application of our techniques, we find an algorithm which computes the Hempel distance of a Heegaard splitting, up to an error depending only on the genus.
Develops variance-reduced methods for solving generalized equations.
Improves predictive performance of nested dichotomies.
Study confirms Chern's conjecture on compact Hessian manifolds and classifies their topologies.