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…
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48 results for “dominance condition”
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.
This study examines the space of initial values strictly satisfying the dominant energy condition.
problem The dominant energy condition on initial value pairs in spacetime.
method Introduced an index difference for initial value pairs and compared it to Riemannian metrics.
result The space of initial values has non-trivial homotopy groups.
Proves spacetime positive mass theorem with corners.
problem Proving a positive mass theorem for spacetime with corners.
method Deformation theorem with corner conditions, asymptotically flat initial data.
result Exterior end satisfies in every dimension .
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.
Portfolio Analysis Based on Markowitz Stochastic Dominance Criteria: A Behavioral Perspectiveq-fin.PM
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.
Study of Dirac-Witten operator on Lorentzian manifolds under dominant energy condition.
problem Detecting non-trivial homotopy groups in spaces of initial data under strict dominant energy condition.
method Use index theory and Lorentzian Hitchin's α-invariant to analyze Dirac-Witten operator.
result Kernel of Dirac-Witten operator is non-trivial only if fundamental group is virtually solvable of derived length at most 2.
Let and be two knots in 3-sphere. Say 1--dominates , if there is a proper degree 1 map $f\co E(k)\to E(k')$, between knot exterior of . Theorem: Suppose that any companion of is prime. If 1--dominates with the same Gromov volume, then can be obtained from by finitely many de-…
Positive energy theorem for asymptotically anti-de Sitter spacetimes with distributional curvaturegr-qc
The positive energy theorem is proven for certain spacetimes with irregular curvature.
problem Proving the positive energy theorem for spacetimes with irregular curvature.
method Weak asymptotically anti-de Sitter initial data sets with distributional curvature under weak dominant energy condition.
result Positive energy theorem established for weakly irregular spacetimes.
Nonexistence of spacelike foliations and the dominant energy condition in Lorentzian geometrymath.DG
We show that many Lorentzian manifolds of dimension >2 do not admit a spacelike codimension-one foliation, and that almost every manifold of dimension >2 which admits a Lorentzian metric at all admits one which satisfies the dominant energy condition and the timelike convergence condition. These two seemingly unrelated…
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.
The paper characterizes neural network landscapes for gradient dominance and regularity.
problem Understanding the landscape of neural network loss functions.
method Characterization of gradient dominance and regularity conditions for neural networks.
result Explicit characterization of global minimizers and landscape properties for different neural network types.
Gaussian-Dirichlet posterior dominance proven for sequential categorical data.
problem Sequential learning from categorical observations bounded in [0,1]
method Establishing an ordering between Dirichlet and Gaussian posteriors under N(0,1) noise
result Posterior mean of categorical distribution stochastically dominates Gaussian distribution
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.
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 for near initial data sets.
result Initial data sets with null ADM energy-momentum must embed into Minkowski space.
New study shows diversification can increase risk for heavy-tailed losses.
problem Diversification can increase tail risk for heavy-tailed losses.
method Comparison of diversified portfolio to a 'one-basket' benchmark.
result Diversified portfolio has larger tail probabilities than a 'one-basket' benchmark for all thresholds.
Investigates optimal investment strategies with non-dominated uncertainty.
problem Maximizing utility in a financial market with model uncertainty.
method Dynamic programming and measurable selection arguments.
result Optimal portfolios exist for unbounded utility functions.
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.
A closed 4-manifold (or, more generally, a finite -space) has a finitely dominated infinite regular covering space if and only if either its universal covering space is finitely dominated or it is finitely covered by the mapping torus of a self homotopy equivalence of a -complex.
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.
Paper establishes sufficient condition for comparing linear combinations of infinite-mean risks.
problem Comparing linear combinations of infinite-mean risks under stochastic dominance.
method Introduced a new class of distributions and used majorization order to compare weights.
result Linear combinations of random variables are stochastically larger when their weight vectors are smaller in majorization order.
The paper explores arbitrage opportunities in derivative markets under specific conditions.
problem Arbitrage opportunities in derivative markets under different conditions.
method Analyzes the relationship between pricing kernel monotonicity and stochastic arbitrage opportunities.
result Pricing kernel nonmonotonicity is equivalent to stochastic arbitrage opportunities under adequacy.
Affirms rigidity conjecture for spacetime positive mass theorem in dimensions less than eight.
problem Proving the rigidity conjecture for the spacetime positive mass theorem in dimensions less than eight.
method Analyzing asymptotically flat initial data sets with dominant energy condition and . Removing dimensional restriction with positive mass inequality assumption.
result Affirmation of the rigidity conjecture for spacetime positive mass theorem in dimensions less than eight.
We consider filtration consistent nonlinear expectations in probability spaces satisfying only the usual conditions and separability. Under a domination assumption, we demonstrate that these nonlinear expectations can be expressed as the solutions to Backward Stochastic Differential Equations with Lipschitz continuous …
On positive Lyapunov exponents along and non-uniformly expanding for partially hyperbolic systemsmath.DS
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.
This paper extends Kelly Criterion to include rebalancing frequency for optimal portfolio selection.
problem Optimizing a portfolio with multiple assets and varying rebalancing frequency.
method Using Kelly Criterion, the paper derives necessary and sufficient conditions for the frequency-based Kelly optimal portfolio.
result Proves the necessity and sufficiency of conditions for the frequency-based Kelly optimal portfolio.
Risk Comparisons in Linear Regression: Implicit Regularization Dominates Explicit Regularizationstat.ML
GD outperforms ridge regression and SGD in linear regression problems.
problem Comparing the risks of GD, ridge regression, and SGD in linear regression problems.
method Instance-wise finite-sample risk analysis of GD, ridge regression, and SGD.
result GD outperforms ridge regression and is incomparable with SGD in some cases.
Study shows certain spin manifolds can't meet DEC condition.
problem Non-existence of spin fill-ins meeting DEC condition.
method Analyzes spin Riemannian manifolds and generalized mean curvature functions.
result Closed spin manifolds cannot satisfy DEC if curvature is large.
Localized curvature bounds ensure harmonic maps are constant.
problem Ensuring harmonic maps are constant under localized curvature constraints.
method Localized Bochner-type rigidity theorem for harmonic maps with image-dependent curvature bounds.
result Harmonic maps are constant if minimal Ricci curvature dominates image-dependent curvature bounds.
New theorem for spacetime mass in noncompact regions.
problem Mass in noncompact spacetime regions.
method Developed mass type invariant and boundary conditions; proof based on spinors.
result Proved positive mass theorem for noncompact boundaries.
Optimal eigenvalue estimate for the Dirac-Witten operator on bounded domains with smooth boundarymath.DG
Eigenvalue estimate for the Dirac-Witten operator is given on bounded domains (with smooth boundary) of spacelike hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS, and chiral conditions). This result is a generalisation of Friedrich's inequality for …
This paper introduces new risk measures for systemic risk analysis.
problem Analyzing systemic risk in financial systems.
method Introducing conditional distortion risk measures and their properties.
result Presented sufficient conditions for ordering risk measures.
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.
Minimal surfaces connect to horizons and electrostatic systems.
problem Connecting minimal surfaces to horizons and electrostatic systems.
method One-parameter min-max problem for area functional, inequality relating area and charge.
result Minimal surfaces of index one are related to unstable horizons in electrostatic systems.
The Bartnik mass increases as spacetime evolves.
problem Understanding the evolution of the Bartnik mass in spacetime.
method Computing the derivative of the Bartnik mass along evolving surfaces under the assumption of the dominant energy condition.
result The Bartnik mass of evolving surfaces is monotone non-decreasing.
Building upon the work of Brendle, Marques and Neves on the construction of counterexamples to Min-Oo's conjecture, we exhibit deformations of the de Sitter-Schwarzschild space of dimension satisfying the dominant energy condition and agreeing with the standard metric along the event and cosmological horizons…
Paper proves Penrose inequality with a weaker late-time condition.
problem Penrose's inequality under the black hole final state conjecture.
method Developed a new late-time condition called quasi final state hypothesis and proved the inequality.
result Proved the spacetime Penrose inequality under the quasi final state hypothesis.
Unified view of label shift estimation methods.
problem Label distribution changes but class-conditional distributions remain the same.
method Unified view of two approaches: BBSE and MLLS.
result Unified framework and theoretical characterization of MLLS.
American options can be equivalent to European options under certain conditions.
problem Determining when American options can be simplified to European options.
method Using methods from Jourdain and Martini, Chrsitensen, and convex duality.
result A first step towards verifying representability of American options.
Investigates VaR behavior for sums of one-sided random variables, showing impossibilities and conditions for super-additivity.
problem Investigates the behavior of Value-at-Risk (VaR) for sums of one-sided random variables.
method Analyzes the extremal aggregation behavior of VaR, introduces structural conditions for super-additivity.
result Characterizes when VaR is fully super-additive and provides unified framework for various dependence structures.
Extends results on marginally outer trapped surfaces to general null expansion.
problem Analyzing geometry and topology of expanding horizons.
method Introduces -stability and proves conditions for positive Yamabe type and scalar curvature.
result Initial data sets with compact boundary of positive null expansion have positive mass.
Study on risk measures using distorted Choquet integrals with random distortions.
problem Developing risk measures under random distortions of capacities.
method Introducing and analyzing randomly distorted Choquet integrals with respect to a distorted capacity, establishing properties and providing representations.
result Representation of comonotonic additive conditional risk measures using G-randomly distorted Choquet integrals.
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.
Jackknife variance estimation validated for generalized U-statistics.
problem Uncertainty quantification for subsampling-based estimators.
method Jackknife variance estimation for generalized U-statistics with row-wise weak law.
result Jackknife and delete- variance estimators are ratio-consistent for generalized U-statistics.
Develops path integral for spiked tensor model dynamics.
problem Dynamics of spiked tensor model with random initial conditions.
method Path integral approach applied to partial differential equations.
result Large- saddle point equations dominated by melonic diagrams.
The paper defines almost strict domination for representations and connects it to anti-de Sitter 3-manifolds.
problem Defining and characterizing representations with specific properties.
method Using variational problems and harmonic maps to prove almost strict domination and construct representations.
result An almost strictly dominating pair of representations is equivalent to an anti-de Sitter 3-manifold with specific properties.
New algorithm identifies dominant arm with high probability.
problem Identifying the arm with the highest realized reward in multi-armed bandits.
method Dominance score criterion and joint mixing and recycling mechanism.
result Identifies the best dominant arm with nearly optimal sample complexity.
A new RL method using SSD compares action uncertainties to manage aleatoric uncertainty.
problem Managing aleatoric uncertainty in RL environments.
method Distributional RL based on SSD, mapping to Wasserstein gradient flow.
result Optimal particle-based algorithm for SSD policy demonstrates better uncertainty balancing.