Study vortex flows on Riemann surfaces, proving dominated splitting and Anosov properties.
problem Investigate flow properties on Riemann surfaces.
method Associate flow to vortex equations, investigate properties of flow.
result Show that flow always admits a dominated splitting and identify special cases of Anosov flow.
The paper proves conditions for non-uniform expansion in partially hyperbolic systems.
problem Conditions for non-uniform expansion in partially hyperbolic systems.
method Analysis of Lyapunov exponents and dominated splittings.
result Existence of physical SRB measure under specific conditions.
Global rigidity theorem for certain lattice actions on manifolds.
problem Volume-preserving actions of higher rank lattices on manifolds with dominated splitting.
method Proves standard conjugacy of actions with dominated splitting.
result Actions must be standard, manifold is flat torus with affine action.
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,…
We prove a finiteness result for the ∂-patterned guts decomposition of all 3-manifolds obtained by splitting a given orientable, irreducible and ∂-irreducible 3-manifold along a closed incompressible surface. Then using the Thurston norm, we deduce that the JSJ-pieces of all 3-manifolds dominated by a…
New split rules improve subpopulation targeting in policy-making.
problem Improving binary classification for subpopulation targeting in policy-making.
method MDFS, PFS, wEFS for maximizing distance and penalizing final splits.
result Proposed methods target more vulnerable subpopulations than classic CART/KD-CART.
The study proves how groups can be split with limited complexity.
problem Understanding the complexity of group splittings.
method Analyzing trees with finite stabilizers and their quotient structures.
result Deformation spaces of trees have maximal complexity.
Echo State Networks (ESNs) are known for their fast and precise one-shot learning of time series. But they often need good hyper-parameter tuning for best performance. For this good validation is key, but usually, a single validation split is used. In this rather practical contribution we suggest several schemes for cr…
Split conformal prediction provides finite-sample guarantees for black-box models without distributional assumptions.
problem Weak performance guarantees for modern predictive models under minimal assumptions.
method Develops finite-sample guarantees for split conformal prediction, a method that uses nested prediction sets and order statistics.
result The coverage of prediction sets based on order statistics stochastically dominates the Beta distribution.
Study homotopy motions of surfaces in 3-manifolds.
problem Understanding the behavior of surfaces under continuous deformations in 3-manifolds.
method Introduce and study homotopy motions of surfaces in closed orientable 3-manifolds.
result Systematic study of homotopy motions of surfaces in 3-manifolds.
Batch-splitting (data-parallelism) is the dominant distributed Deep Neural Network (DNN) training strategy, due to its universal applicability and its amenability to Single-Program-Multiple-Data (SPMD) programming. However, batch-splitting suffers from problems including the inability to train very large models (due to…
For every rational homology 3-sphere with 2-torsion only we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring), such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten-Reshetikhin-Turaev invariant at this root and at any even …
We introduce a new family of thermostat flows on the unit tangent bundle of an oriented Riemannian 2-manifold. Suitably reparametrised, these flows include the geodesic flow of metrics of negative Gauss curvature and the geodesic flow induced by the Hilbert metric on the quotient surface of divisible convex sets. We …
FREEtree improves tree-based methods for correlated longitudinal data.
problem Poor performance of Random Forests in high dimensional longitudinal data with correlated features.
method FREEtree uses a piecewise random effects model and clustering with WGCNA to select features and maintain interpretability.
result FREEtree outperforms other tree-based methods in prediction and feature selection accuracy.
Deep forecasting models show output heads significantly improve performance on fat-tailed financial returns.
problem Improving deep learning models for forecasting fat-tailed financial returns.
method Comparison of backbone architectures and output heads (point, Gaussian, Gaussian mixture) on S&P 500 monthly log-returns.
result Switching from point to Gaussian heads improves CRPS by about 1.3 percent, and from Gaussian to mixture adds another 2.4 percent.
Market portfolio decomposed into body and tail legs
problem Separation of market portfolio into body and tail legs
method Dynamic value-weighted body and tail legs
result Recombination identity holds for all models
Random forest performance depends on SNR and covariate characteristics.
problem Understanding when random forests perform well.
method Systematic analysis of out-of-sample MSE for different SNR scenarios.
result Randomization effectiveness depends on SNR and covariate characteristics.
Study decomposes market portfolio into body and tail legs, revealing systematic differences.
problem Understanding the relationship between body and tail components in market portfolios.
method Decomposes CRSP market portfolio into body and tail legs, analyzes their recombination identity.
result Recombination identity holds for all models but not for all, indicating systematic differences.
Paper speeds up GP inference by reducing precision matrix computation.
problem High computational complexity in computing kernel precision matrices.
method Splitting precision matrix into Hankel-Toeplitz matrices and computing only unique entries.
result Precision matrix computation reduced from O(NM2) to O(NM). Connected domination numbers found for plane triangulations up to 13 vertices.
problem Finding connected domination numbers for plane triangulations.
method Analyzing triangulations of up to 13 vertices and proving the difference between connected and regular domination numbers can be arbitrarily large.
result Connected domination numbers for triangulations up to 13 vertices and upper bound for larger triangulations.
New benchmark predicts cardiometabolic risk from accelerometer data, with varying accuracy.
problem Lack of accurate tabular benchmarks for cardiometabolic risk from accelerometer data.
method Tabular learning methods (ridge regression, XGBoost, TabPFN v2) applied to NHANES data.
result TabPFN v2 achieves best performance, but triglycerides remain largely unpredictable.
The Gauss-Bonnet inequality holds for certain non-aspherical manifolds up to dimension five.
problem Proving the Gauss-Bonnet inequality for non-aspherical manifolds.
method Analyzing the universal covering space and scalar curvature properties.
result The Gauss-Bonnet quantity is bounded and equality implies specific geometric structures.
Regression Trees analyze stock returns, revealing market excess return as the most informative factor.
problem Understanding informational content of three factors in stock returns.
method Joint regression tree analysis of daily stock return data for 5 major US corporations.
result The market excess return factor is always the most informative in all cases (solo and joint).
Manifolds can be dominated by hypersurfaces in a sphere.
problem Dominating manifolds with hypersurfaces.
method Proving any smooth, closed, oriented manifold can be dominated by a codimension 1 submanifold of the sphere.
result Any smooth, closed, oriented manifold can be dominated by a codimension 1 submanifold of the sphere.
HRF enhances tree diversity in random forests to improve performance.
problem Selection bias and lack of diversity in random forests.
method Introducing heterogeneity during tree construction by assigning lower weights to features used in previous trees.
result HRF outperforms other ensemble methods in accuracy across 52 datasets.
New method ranks multivariate distributions in SMOOP using q-dominance.
problem Lack of reliable methods to rank multivariate distributions in SMOOP.
method Introduces center-outward q-dominance and develops empirical test procedures.
result Proves q-dominance implies FSD and establishes a sample size threshold.
The paper develops techniques to study dynamical systems with Carnot metrics.
problem Understanding smooth dynamical systems in the presence of Carnot metrics.
method Employing techniques from Margulis-Mostow, Métivier, Mitchell, and Pansu on tangent cones, the paper establishes resonances between Lyapunov exponents.
result Local rigidity properties of higher hyperbolic rank metrics and uniform lattice actions on quaternionic and octonionic symmetric spaces.
Decomposes financial networks to reveal cause-effect hierarchies during crises.
problem Complex financial networks are hard to interpret due to Granger causality.
method Helmholtz-Hodge-Kodaira decomposition to separate networks into rotational and gradient components.
result Precious metals and pharmaceutical products are identified as causal drivers during crises.
We show that non-domination results for targets that are not dominated by products are stable under Cartesian products.
New framework for ranking distributions using variable fractional parameters.
problem Ordering distributions with varying steepness and local non-concavities.
method Introducing a function γ:Ro[0,1] to replace the fixed parameter in fractional SD. result Enables ranking of a broader range of distributions and incorporates dynamic greediness.
Research examines when 4-manifolds are dominated by geometric ones.
problem When is an orientable closed 4-manifold dominated by another?
method Focuses on geometric or fibred cases.
result Characterizes conditions for domination.
3-manifolds can virtually dominate others with positive simplicial volume.
problem Domination of 3-manifolds with positive simplicial volume.
method Proving existence of finite covers with degree-1 maps.
result Virtual domination of 3-manifolds with positive simplicial volume.
Study domination between non-Fuchsian surface group representations and anti-de Sitter geometry.
problem Domination problem between non-Fuchsian representations of closed surface groups.
method Analysis of branched harmonic immersions and construction of anti-de Sitter 3-manifolds.
result Found that representations admitting branched harmonic immersions dominate other representations, and constructed large families of branched anti-de Sitter 3-manifolds.
Dominant knots have isomorphic Seifert and Tait graphs.
problem Understanding knot dominance through graph isomorphism.
method Examined alternating knots and their Seifert and Tait graphs.
result Isomorphic Seifert and Tait graphs indicate dominant knots.
New homology theory connects graph domination to subtle algebraic structures.
problem Understanding graph domination through algebraic homology.
method Interpreting überhomology as poset homology and showing its functorial properties.
result The Euler characteristic of bold homology equals the evaluation of the connected domination polynomial.
3-manifolds can be virtually dominated by maps of degree 8.
problem Understanding virtual domination of 3-manifolds.
method Proving existence of finite covers with specific map properties.
result Virtual 8-dominance of 3-manifolds.
Odd-dimensional manifolds have contact maps of non-zero degree.
problem Contact domination in odd-dimensional manifolds.
method Proving existence of maps from tight contact manifolds.
result Existence of non-zero degree maps from Liouville-fillable but not Weinstein-fillable contact manifolds.
Unified framework for efficient Frank-Wolfe optimization of Dominant Set Clustering.
problem Optimizing Dominant Set Clustering with various Frank-Wolfe algorithms.
method Unified framework for pairwise, standard, and away-steps Frank-Wolfe algorithms, with explicit convergence rates.
result Explicit convergence rates for Frank-Wolfe methods in Dominant Set Clustering.
New EI strategies using OWA and SSD for excess return.
problem Selecting EI portfolios that stochastically dominate a benchmark.
method Proposes a new OWA-based EI model and introduces a new SSD criterion.
result OWA-based EI portfolios stochastically dominate a benchmark and generate excess return.
We study a generalized family of stochastic orders, semiparametrized by a distortion function H, namely H-distorted stochastic dominance, which may determine a continuum of dominance relations from the first- to the second-order stochastic dominance (and beyond). Such a family is especially suitable for representing a …
The paper analyzes how behavioral investors make portfolio decisions using Markowitz Stochastic Dominance criteria.
problem Understanding how behavioral investors make portfolio decisions.
method Developed stochastic optimization problems and MILP models to capture subjective decision weights and probability weighting functions.
result The developed models can be used to formulate computationally tractable portfolio analysis problems.
New framework for distributed nonparametric estimation under slow communication.
problem Efficiently estimate nonparametric models across multiple nodes with limited communication.
method Developed a general framework for nonparametric estimation under communication constraints.
result Derived minimax lower and upper bounds for various models.
Finite simplicial complexes dominate certain manifolds with a bounded number of simplices.
problem Understanding the finite domination of manifolds by simplicial complexes.
method Proving that a manifold can be dominated by the n-skeleton of a finite simplicial complex with a bounded number of simplices. result The total number of simplices in the n-skeleton is bounded above by a constant depending only on n and the embolic volume of the manifold. Solves risk minimization problem with SSD constraints.
problem Finding SSD-minimal quantile function under mixed constraints.
method Explicitly works out SSD-minimal solution and relates to Skorokhod problem.
result Explicit solution to risk minimizing problem.
Develops a new solver for optimizing with stochastic dominance constraints.
problem Optimizing with stochastic dominance constraints is computationally expensive and impractical.
method Introduces Light Stochastic Dominance Solver (light-SD) that uses Lagrangian properties and surrogate approximation.
result The light-SD solver demonstrates superior performance on various problems.
Proposes new rule for ranking investment prospects over long horizons.
problem Ranking investment prospects over long horizons considering bounded risk aversion.
method Introduces asymptotic fractional-order stochastic dominance with bounded relative risk aversion.
result Establishes equivalent conditions for the new rule under lognormal returns without mean non-negativity constraint.
Paper extends stochastic dominance for compound binomial distributions.
problem Stochastic dominance for infinite-mean random variables.
method Investigates properties and inclusion relationships of distribution classes, extends results to compound binomial distributions.
result Establishes necessary and sufficient conditions for first-order stochastic dominance preservation.
The study shows how energy density of harmonic maps dominates in n-Fuchsian fibers, leading to unique minimal surfaces.
problem Understanding energy density and topological invariants in n-Fuchsian fibers of Higgs bundles. method Establishing an algebraic inequality generalizing a GIT theorem to prove energy density domination.
result Energy density of harmonic maps dominates in n-Fuchsian fibers, leading to unique minimal surfaces.