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.
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. The study of Chern numbers on vector bundles uses combinatorial methods to establish bounds and ordering.
problem Establishing bounds and ordering for Chern numbers on vector bundles.
method Combinatorial ideas to study Chern numbers on ample and numerically effective vector bundles.
result An effective lower bound for Chern numbers of ample vector bundles and reverse dominance ordering for nef vector bundles.
Graphs and their complements are intrinsically knotted.
problem Characterizing maximal linklessly embeddable graphs and their complements.
method Analyzing maximal linklessly embeddable graphs, deriving connected domination numbers, and proving intrinsic knotting properties.
result Complements of maximal linklessly embeddable graphs of order 12 and 15 are intrinsically knotted.
Deep Neural Networks, and specifically fully-connected convolutional neural networks are achieving remarkable results across a wide variety of domains. They have been trained to achieve state-of-the-art performance when applied to problems such as speech recognition, image classification, natural language processing an…
We consider the partial observability model for multi-armed bandits, introduced by Mannor and Shamir. Our main result is a characterization of regret in the directed observability model in terms of the dominating and independence numbers of the observability graph. We also show that in the undirected case, the learner …
In a system containing a large number of interacting stochastic processes, there will typically be many non-zero correlation coefficients. This makes it difficult to either visualize the system's inter-dependencies, or identify its dominant elements. Such a situation arises in Foreign Exchange (FX) which is the world's…
Characterizes causal structure dominance for latent variables.
problem Determining dominance relations between causal structures with latent variables.
method Complete characterization for three visible variables, partial for four; uses nontrivial inequality constraints.
result Equivalence classes with nontrivial inequality constraints become ubiquitous as the number of visible variables increases.
We employ random geometric digraphs to construct semi-parametric classifiers. These data-random digraphs are from parametrized random digraph families called proximity catch digraphs (PCDs). A related geometric digraph family, class cover catch digraph (CCCD), has been used to solve the class cover problem by using its…
For any symmetric collection of natural numbers h^{p,q} with p+q=k, we construct a smooth complex projective variety whose weight k Hodge structure has these Hodge numbers; if k=2m is even, then we have to impose that h^{m,m} is bigger than some quadratic bound in m. Combining these results for different weights, we so…
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.
New graph feedback model for bandits with improved regret bounds.
problem Understanding how graph structure affects regret in bandit problems.
method Introduced fractional weak domination number and k-packing independence number to capture upper and lower bounds on regret. Used strong duality theorem to derive upper and lower bounds. result Proved general upper and lower bounds on regret for various graph structures, showing tightness up to a logarithmic factor.
We define a large class of abstract Coxeter groups, that we call ∞--spanned, and for which the word growth rate and the geodesic growth rate appear to be Perron numbers. This class contains a fair amount of Coxeter groups acting on hyperbolic spaces, thus corroborating a conjecture by Kellerhals and Perren. We a…
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.
A new decomposition explains over-parameterized models' counterintuitive behaviors.
problem Understanding predictive error in over-parameterized models.
method Introducing the Generalized Aliasing Decomposition (GAD) to explain predictive performance.
result The GAD decomposes predictive error into three parts: model insufficiency, data insufficiency, and generalized aliasing.
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.
The CAPM's market returns are endogenously determined, affecting all assets' expected returns.
problem The standard CAPM's market return assumption is not endogenously consistent.
method Demonstrates the impact of endogenously determined market returns on asset returns and the range of feasible market returns.
result Expected returns are influenced by all assets' risks, and market returns are limited by asset distribution.
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.
Given a rational homology 3-sphere M with the first integral homology of rank b and a link L inside M, colored by odd numbers, we construct a unified invariant I_{M,L} belonging to a modification of the Habiro ring where b is inverted. Our unified invariant dominates the whole set of the SO(3) Witten-Reshetikhin-Turaev…
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.
This work analyzes Adam's preconditioning effect on quadratic functions and quantifies its impact on condition number.
problem Understanding and quantifying the preconditioning effect of Adam to alleviate ill-conditioning in gradient descent.
method Detailed analysis of Adam's preconditioning effect for quadratic functions, including empirical evidence.
result Adam can mitigate the condition number but at a dimension-dependent cost, with specific bounds for different types of Hessians.
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. Unexpectedly, weighted Pareto variables are stochastically dominant.
problem Understanding stochastic dominance in Pareto distributions.
method Analyzing weighted averages of Pareto random variables with infinite mean.
result The weighted average of Pareto variables is stochastically dominant.
We consider localized deformation for initial data sets of the Einstein field equations with the dominant energy condition. Deformation results with the weak inequality need to be handled delicately. We introduce a modified constraint operator to absorb the first order change of the metric in the dominant energy condit…
New class of heavy-tailed distributions shows weighted averages dominate individual variables.
problem Understanding and comparing risks in heavy-tailed distributions.
method Introducing a new class of heavy-tailed distributions and proving stochastic dominance relations.
result Weighted averages of random variables in this class are stochastically larger than individual variables.
In this work we apply variations of ResNet architecture to the task of atrial fibrillation classification. Variations differ in number of filter after first convolution, ResNet block layout, number of filters in block convolutions and number of ResNet blocks between downsampling operations. We have found a range of mod…
Proves rigidity for specific initial data sets under the dominant energy condition.
problem Rigidity of initial data sets with boundary and convex polytopes.
method Solution of boundary value problems for Dirac operators and approximations by manifolds with smooth boundary.
result Proves rigidity for compact smooth spin manifolds and convex polytopes under the dominant energy condition.
Banking system crises are complex events that in a short span of time can inflict extensive damage to banks themselves and to the external economy. The crisis literature has so far identified a number of distinct effects or channels that can propagate distress contagiously both directly within the banking network itsel…
New method assesses multivariate stochastic dominance using Optimal Transport.
problem Benchmarking models across multiple metrics considering dependencies.
method Characterization of multivariate first stochastic dominance via couplings, entropic regularization, and Optimal Transport.
result Established CLT and consistency for the empirical statistic, enabling hypothesis testing.
We present the alternative topological twisting of N=4 Yang-Mills, in which the path integral is dominated not by instantons, but by flat connections of the COMPLEXIFIED gauge group. The theory is nontrivial on compact orientable four-manifolds with nonpositive Euler number, which are necessarily not simply connected. …
This study finds a special class of representations that dominate others in a complex hyperbolic group.
problem Domination of surface-group representations in complex hyperbolic groups.
method Analysis of T-bent representations and their domination by discrete and faithful representations. result A discrete and faithful representation exists that dominates a given T-bent representation in the Bergman translation length spectrum. Dominant representations found via Fock-Goncharov coordinates.
problem Finding dominant representations of surface groups.
method Linear-algebraic approach using Fock-Goncharov coordinates.
result Explicit description of dominating representations.
The paper connects higher order risk measures and stochastic dominance, showing their equivalence and integrating them with optimization.
problem Comparing and characterizing random outcomes in risk assessment.
method Exploring the equivalence between higher order risk measures and stochastic dominance, using stochastic optimization and expectiles as examples.
result Higher order risk measures and stochastic dominance are equivalent and can be used to characterize random outcomes.
We determine which three-manifolds are dominated by products. The result is that a closed, oriented, connected three-manifold is dominated by a product if and only if it is finitely covered either by a product or by a connected sum of copies of the product of the two-sphere and the circle. This characterization can als…