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.
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.
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.
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.
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.
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…
Proves positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.
problem Proving the positive mass theorem for spin initial data sets with various ends and energy shields.
method Modification of Witten's approach involving an additional independent timelike direction in the spinor bundle.
result Positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.
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.
New insights into Bartnik mass from improvability of dominant energy scalar.
problem Characterizing Bartnik mass minimizing initial data sets.
method Introducing improvability concept, proving non-improvability consequences, and analyzing pp-wave counterexamples.
result Bartnik mass minimizing initial data sets are characterized, advancing conjectures.
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.
Smooth dec initial data sets may not extend to smooth spacetimes.
problem Whether every dec initial data set can be extended to a smooth spacetime.
method Examined the converse of the dominant energy condition for initial data sets and spacelike hypersurfaces.
result Not all dec initial data sets can be extended to smooth spacetimes.
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.
Proves density and mass theorems for specific initial data sets.
problem Initial data sets with boundary in spacetime.
method Harmonic asymptotics and dominant energy condition.
result Spacetime positive mass theorem for initial data sets with apparent horizon boundary.
We derive properties of the cdf of random variables defined as saddle-type points of real valued continuous stochastic processes. This facilitates the derivation of the first-order asymptotic properties of tests for stochastic spanning given some stochastic dominance relation. We define the concept of Markowitz stochas…
Paper proposes a new method to compare classifiers across multiple datasets.
problem Comparing classifiers over multiple datasets with multiple criteria.
method Adopting decision theory, the paper introduces generalized stochastic dominance for ranking classifiers.
result Generalized stochastic dominance can be used to rank classifiers and statistically tested.
New proof shows equality in spacetime mass theorem.
problem Proving the equality case of spacetime positive mass theorem.
method Uses a new approach requiring only E≥∣P∣ for near initial data sets. result Initial data sets with null ADM energy-momentum must embed into Minkowski space.
Investigates the effects of nondominated sets of probability measures in robust models of finance.
problem Uncertainty in financial models due to multiple possible probability measures.
method Analyzes various results from mathematical finance literature under the assumption of nondominated sets of probability measures.
result Many classical results in robust models do not hold when the set of measures is nondominated.
This note removes technical assumptions and characterizes relatively dominated representations.
problem Geometrically finiteness and Anosov conditions in higher-rank settings.
method Characterization using eigenvalue gaps and limit maps.
result Relatively dominated representations are characterized using eigenvalue gaps and limit maps.
We introduce a new paradigm that is important for community detection in the realm of network analysis. Networks contain a set of strong, dominant communities, which interfere with the detection of weak, natural community structure. When most of the members of the weak communities also belong to stronger communities, t…
The paper calculates extreme measures in continuous time conic finance.
problem Determining valuation bounds for financial claims.
method Using dynamic spectral risk measures and estimating extreme measures from market data.
result Explicit formulas for extreme measures' Radon-Nykodim derivatives and estimation methods.
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…
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.
In this work, we develop a novel framework to measure the similarity between dynamic financial networks, i.e., time-varying financial networks. Particularly, we explore whether the proposed similarity measure can be employed to understand the structural evolution of the financial networks with time. For a set of time-v…
A new algorithm for competing agents in a two-sided market setting.
problem Decentralized competition between agents in a two-sided market with unknown valuations.
method UCB-D3 algorithm for UCB with Decentralized Dominant-arm Deletion.
result UCB-D3 is order optimal and achieves a new regret lower bound.
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.
Study harmonic maps and anti-de Sitter 3-manifolds.
problem Existence and uniqueness of harmonic maps in infinite energy settings.
method Generalization of Corlette's result to infinite energy, analysis of asymptotic behavior, use of CAT(-1) Hadamard manifolds.
result Existence of new anti-de Sitter 3-manifolds.
We consider the question of efficient estimation in the tails of Gaussian copulas. Our special focus is estimating expectations over multi-dimensional constrained sets that have a small implied measure under the Gaussian copula. We propose three estimators, all of which rely on a simple idea: identify certain \emph{dom…
We show that non-domination results for targets that are not dominated by products are stable under Cartesian products.
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.
Local SGD outperforms minibatch SGD for quadratic objectives.
problem Theoretical foundations of local SGD are lacking.
method Proved local SGD strictly dominates minibatch SGD for quadratic objectives and accelerated local SGD is minimax optimal.
result Local SGD does not dominate minibatch SGD in general convex objectives.
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.
Study geometric manifolds in arbitrary dimensions, focusing on maps and diffeomorphisms.
problem Existence and properties of maps and diffeomorphisms in geometric manifolds.
method Analysis of geometric structures and homotopy invariants in arbitrary dimensions.
result Existence of Anosov diffeomorphisms and monotonicity of homotopy invariants.
SRRM improves recursive transport surrogates in the small-discrepancy regime.
problem Insufficient understanding of recursive partitioning methods' statistical behavior and resolution in the small-discrepancy regime.
method Introduced Selective Recursive Rank Matching (SRRM) to improve the resolution of Recursive Rank Matching (RRM).
result SRRM yields a higher-fidelity practical surrogate for the Wasserstein distance at moderate additional computational cost.
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.
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.
Diversification improves profits for heavy-tailed investments.
problem Investment portfolios of Pareto-distributed returns.
method Stochastic dominance and majorization order.
result Diversification increases first-order stochastic dominance for heavy-tailed returns.
We establish the positive energy theorem for weak asymptotically anti-de Sitter initial data sets with distributional curvature under the weak dominant energy condition.
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.
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. 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.
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.
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.
We develop a new statistical test for comparing variables with varying scales.
problem Comparing variables with different scales in multidimensional spaces.
method Order based on expectations of random variables, generalized stochastic dominance (GSD) order, regularized statistical test, linear optimization, imprecise probability models.
result Validated through multidimensional data from various fields.
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.