New stochastic algorithm improves on existing PRSM methods.
problem Improving performance of stochastic PRSM algorithms.
method Proposes SS-PRSM, a new stochastic algorithm based on PRSM.
result Demonstrates convergence rate, faster than ADMM.
On-device research index
arXiv research
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.
169,181 papers · 148 categories
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48 results for “Peaceman-Rachford splitting”
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…
New algorithm solves maximal monotone inclusion problems.
problem Solving maximal monotone inclusion problems.
method Bregman Douglas-Rachford splitting method and variants.
result Convergence of algorithms under certain assumptions.
A new optimization scheme tackles convex objectives with non-separable penalties.
problem Optimizing convex objectives with non-separable penalties.
method Expectation-consistent approximation and vector approximate message-passing (VAMP) algorithm.
result Faster convergence compared to state-of-the-art approaches in tasks like classification and reconstruction.
This paper performs the numerical analysis and the computation of a Spread option in a market with imperfect liquidity. The number of shares traded in the stock market has a direct impact on the stock's price. Thus, we consider a full-feedback model in which price impact is fully incorporated into the model. The price …
Efficient PDE method calibrates local volatility with stochastic interest rates.
problem Calibrating local volatility models with stochastic interest rates is time-consuming.
method Developed a PDE approach using ADI method to solve the forward equation.
result Effective and sufficient information for calibration and pricing is provided.
SPlit optimizes dataset splitting for better model performance.
problem Improving model performance through optimal dataset splitting.
method Adapting Support Points (SP) algorithm for subsampling and categorical variables in a sequential nearest neighbor approach.
result SPlit significantly improves worst-case testing performance compared to random splitting.
The paper extends keenness concept to bridge splittings and finds conditions for existence.
problem Extending keenness concept to bridge splittings and finding conditions for existence.
method Extending the concept of keenness to bridge splittings and proving existence conditions.
result Existence of strongly keen -splitting of a link with distance for certain integers , , and .
Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. Further it is shown that non-split structures appear in the first case as deformations of a split reduction and in the …
Study flippable Heegaard splittings in Seifert fibered spaces.
problem Identifying flippable Heegaard splittings in Seifert fibered spaces.
method Examining isotopies that interchange Heegaard splitting sides in Seifert fibered spaces.
result Characterized which Heegaard splittings are flippable in Seifert fibered spaces.
We study the self-dual Yang-Mills equations in split signature. We give a special solution, called the basic split instanton, and describe the ADHM construction in the split signature. Moreover a split version of t'Hooft ansatz is described.
Paper proposes a novel SVM method for creating survival trees.
problem Creating non-linear survival trees for right-censored data.
method L2-regularized dipole splitting criteria with kernel methods.
result Non-linear splits using polynomial and Gaussian kernels show similar predictive power but often smaller tree sizes.
New methods improve prediction regions for high-dimensional data.
problem Creating effective prediction regions for high-dimensional data.
method CD-split and HPD-split methods that combine split method and data-driven partition.
result CD-split and HPD-split converge to oracle highest predictive density set and satisfy local and asymptotic conditional validity.
New spheres can split a 4D link in ways not possible in 3D.
problem Exploring how splitting spheres behave in 4D space.
method Constructing specific 2-component surface-links in .
result Found non-isotopic splitting spheres in .
This paper studies properties of weak reducing pairs in critical Heegaard splittings.
problem Characterize weak reducing pairs in critical Heegaard splittings.
method Analyze the properties of weak reducing pairs in critical Heegaard splittings.
result Provide a necessary condition for a Heegaard surface to be critical.
The paper extends Lorentzian splitting theorems under curvature-dimension bounds.
problem Analyzing Lorentzian spacetimes with curvature-dimension bounds.
method Using Bakry-Émery-Ricci tensor, extending singularity and splitting theorems.
result Theorems hold for all synthetic dimensions, including negative and positive.
We show that if a split link is obtained from a split link in by -Dehn surgery along a trivial knot , then the link is splittable. That is to say, it is impossible to obtain a split link from a split link via a non-trivial twisting. As its corollary, we completely determine when a trivial li…
Study evaluates when splitting classifiers can improve performance despite disparate treatment.
problem Impact of disparate treatment in classification models.
method Comparison of split classifiers and group-blind classifiers, quantifying performance improvement.
result Proves an equivalent expression for the benefit-of-splitting which can be efficiently computed.
New methods convert complex link presentations to simpler, recognizable forms.
problem Representing split and composite links in a clear, recognizable way.
method Pocket and flip moves to transform link presentations.
result Pocket moves are the only obstruction to representing split links by split plat presentations.
Powell's conjecture about Goeritz groups for genus 3 splittings is confirmed.
problem Determining the minimum set of elements needed to generate the Goeritz group of Heegaard splittings.
method Proof for splittings of genus 3 and a framework for higher genus splittings.
result Powell's conjecture is correct for splittings of genus 3.
Splitting numbers of linksmath.GT
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…
New proof of Lorentzian splitting theorems using elliptic operators.
problem Proving splitting theorems in Lorentzian geometry.
method Using a negative homogeneity elliptic p-d'Alembert operator to prove theorems.
result Lorentzian splitting theorems are proven in a framework similar to Riemannian geometry.
Little is known on the classification of Heegaard splittings for hyperbolic 3-manifolds. Although Kobayashi gave a complete classification of Heegaard splittings for the exteriors of 2-bridge knots, our knowledge of other classes is extremely limited. In particular, there are very few hyperbolic manifolds that are know…
New proof of Giroux Correspondence for tight contact 3-manifolds.
problem Proving the Giroux Correspondence for tight contact 3-manifolds.
method Introducing tight Heegaard splittings, using refinement process, and translating moves between splittings to moves between open books.
result Proves the tight Giroux Correspondence for contact 3-manifolds.
Paper generalizes splitting number to classify plane curve arrangements.
problem Distinguishing embedded topology of plane curves.
method Introduces splitting graph to generalize splitting number.
result Classifies embedded topology of specific plane curve arrangements.
Let M_1 and M_2 be compact, orientable 3-manifolds, and M the manifold obtained by gluing some component F of \bdy M_1 to some component of \bdy M_2 by a homeomorphism φ. We show that when φis "sufficiently complicated" then (1) the amalgamation of low genus, unstabilized, boundary-unstabilized Heegaard splittings of M…
Minimal splitting factors help study scalar curvature constraints.
problem Scalar curvature constraints in geometry.
method Introducing minimal splitting factors with positive scalar curvature.
result Minimal splitting factors have properties similar to area minimizing hypersurfaces.
Non-isotopic Heegaard splittings of non-minimal genus were known previously only for very special 3-manifolds. We show in this paper that they are in fact a wide spread phenomenon in 3-manifold theory: We exhibit a large class of knots and manifolds obtained by Dehn surgery on these knots which admit such splittings. M…
Paper strengthens splitting theorem using weak KAM theory.
problem Splitting theorem in warped product spaces.
method Weak KAM theory approach.
result Strengthened splitting theorem.
Introduces nonlinear splittings on fibre bundles for generalizing connections.
problem Generalizing connections on fibre bundles.
method Definition and properties of nonlinear splittings, including affine, homogeneous, and principal splittings.
result Curvature map defined for nonlinear splittings, linking to nonholonomic systems and magnetic Lagrangian systems.
We define a notion of Hempel distance for one-sided Heegaard splittings and show that the existence of alternate surfaces restricts distance for one-sided splittings in a manner similar to Hartshorn's and Scharlemann-Tomova's results for two-sided splittings. We also show that every geometrically compressible one-sided…
New method escapes local optima in neural architecture optimization.
problem Escaping local optima in neural architecture optimization.
method Signed neural splitting in steepest descent framework.
result Escapes local optima, leading to better performance.
We explicitly compute the lower algebraic K-theory of the split three-dimensional crystallographic groups; i.e., the groups G that act properly and cocompactly on three-dimensional Euclidean space by isometries, such that the natural map from G to O(3) is a split injection onto its image. There are 73 split three-dimen…
We describe an example of a closed orientable 3-manifold with distinct distance three genus two Heegaard splittings. This demonstrates that the constructions of alternate genus two Heegaard splittings of closed orientable 3-manifolds described by Rubinstein and Scharlemann in their 1998 paper Genus Two Heegaard Splitti…
New approach connects stochastic gradient descent to ODE splitting schemes.
problem Improving convergence in stochastic optimization.
method Connection between stochastic gradient descent and ODE splitting schemes.
result Derive a new upper bound on global splitting error.
Casson and Gordon gave the rectangle condition for strong irreducibility of Heegaard splittings [1]. We give a parity condition for irreducibility of Heegaard splittings of irreducible manifolds. As an application, we give examples of non-stabilized Heegaard splittings by doing a single Dehn twist.
Using basic properties of one-sided Heegaard splittings, a direct proof that geometrically compressible one-sided splittings of RP^3 are stabilised is given. The argument is modelled on that used by Waldhausen to show that two-sided splittings of S^3 are standard.
Let M be a totally orientable graph manifold with characteristic submanifold T and let M = V cup_S W be a Heegaard splitting. We prove that S is standard. In particular, S is the amalgamation of strongly irreducible Heegaard splittings. The splitting surfaces S_i of these strongly irreducible Heegaard splittings have t…
The splitting number of a link is the minimum number of crossing changes between distinct components that is required to convert the link into a split link. We provide a bound on the splitting number in terms of the four-genus of related knots.
A new method for kernel tests without data splitting increases power.
problem Lack of power in kernel-based tests due to data splitting.
method Selective inference framework to learn hyperparameters and test on full sample.
result Empirically larger test power without data splitting, regardless of split proportion.
Extend Kauffman bracket skein module to homology theory using Heegaard splittings
problem Extend Kauffman bracket skein module to homology theory
method Combinatorial approach using Heegaard splittings
result Homology theory depends on Heegaard splittings
This paper studies Heegaard splittings of surface bundles via the curve complex of the fibre. The translation distance of the monodromy is the smallest distance it moves any vertex of the curve complex. We prove that the translation distance is bounded above in terms of the genus of any strongly irreducible Heegaard sp…
We show that if a Heegaard splitting is obtained by gluing a splitting of Hempel distance at least 4 and the genus-1 splitting of , then the Goeritz group of the splitting is finitely generated. To show this, we first provide a sufficient condition for a full subcomplex of the arc complex for a compact …
Data Twinningstat.ML
Twinning splits data into fast, statistically similar sets.
problem Creating statistically similar data splits for Big Data.
method Twinning is a method based on SPlit for fast, model-independent dataset splitting.
result Twinning is orders of magnitude faster than SPlit.
Stabilizations of Heegaard splittings of sufficiently complicated 3-manifolds (Preliminary Report)math.GT
We construct families of manifolds that have pairs of genus Heegaard splittings that must be stabilized roughly times to become equivalent. We also show that when two unstabilized, boundary-unstabilized Heegaard splittings are amalgamated by a "sufficiently complicated" map, the resulting splitting is unstabili…
The study examines stock splits and their effects on companies, managers, and shareholders.
problem Misunderstandings and confounding factors around stock splits and their impacts.
method Selected database analysis of nine recent events, examining market impact, trading volume, and shareholder base.
result Stock splits enhance trading volume, increase shareholder base, and improve market liquidity.
New algebraic structures for Lie 2-algebroids and their connections.
problem Characterizing and understanding Lie 2-algebroids and their structures.
method Construction of homotopy Poisson algebra and introduction of Dirac structures.
result One-to-one correspondence between Manin triples and Lie 2-bialgebroids.
Split learning preserves privacy in 1D CNN models for detecting heart abnormalities.
problem Privacy leakage in 1D CNN models under split learning.
method Implemented and validated an 1D CNN model under split learning, applied privacy leakage mitigation techniques.
result Split learning alone is insufficient to maintain raw data privacy in 1D CNN models.