Proves a new Penrose inequality for static spacetimes.
problem Establishing a lower bound on mass using area and static references.
method Develops a new quasi-local Penrose inequality for spherically symmetric static spacetimes.
result Proves a quasi-local Penrose inequality for any spherically symmetric static spacetime.
This article considers the quasi-local energy in reference to a general static spacetime. We follow the approach developed by the authors in [19, 20, 7, 9] and define the quasi-local energy as a difference of surface Hamiltonians, which are derived from the Einstein-Hilbert action. The new quasi-local energy provides a…
Proposes a new framework to optimize portfolios with reduced estimation errors.
problem Estimation errors in multiperiod mean-variance portfolio optimization.
method Reference-regulated multiperiod mean-variance (RRMV) framework.
result Improves portfolio stability and out-of-sample Sharpe ratios.
Inspired by the work of Chen-Zhang \cite{Chen-Zhang}, we derive an evolution formula for the Wang-Yau quasi-local energy in reference to a static space, introduced by Chen-Wang-Wang-Yau \cite{CWWY}. If the reference static space represents a mass minimizing, static extension of the initial surface Σ, we observe that …
We review geometrical properties of a static spacetime (M,g), including geodesic completeness, causality, standard splittings, compact M, closed geodesics and geodesic connectedness. We pay special attention to the critical quadratic behavior at infinity of the coefficients β, β−1 (β=−g(K,K), being K a …
Proximal online gradient minimizes dynamic regret in evolving environments.
problem Optimizing dynamic regret in online learning where the optimal solution changes over time.
method Proximal online gradient method, showing it is optimal for dynamic regret.
result Proximal online gradient matches the lower bound for dynamic regret, proving its optimality.
CDLF predicts product life-cycles in cold-start phases with high accuracy.
problem Forecasting new products in early phases when data is scarce.
method Conditional Diffusion Life-cycle Forecaster (CDLF) combining static descriptors, reference trajectories, and new observations.
result CDLF outperforms classical models in accuracy and probabilistic forecasting.
Study of quasilocal mass using isometric embedding in various spacetimes.
problem Understanding quasilocal mass in different spacetimes.
method Application of isometric embedding theory to quasilocal mass.
result Recent progress in quasilocal mass calculations with specific spacetimes.
In this paper we provide a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a given group of translations and whose spatial factor is conformally flat, are charac…
A novel approach to computing barycenters on graph-supported probability measures.
problem Computing weighted averages of measures on graphs.
method Dynamic optimal transport formulation on the simplex, gradient descent on the probability simplex.
result Intrinsic gradient descent provides a coherent framework for synthesizing and analyzing measures on graphs.
Class-imbalance refers to classification problems in which many more instances are available for certain classes than for others. Such imbalanced datasets require special attention because traditional classifiers generally favor the majority class which has a large number of instances. Ensemble of classifiers have been…
Investigates fund separations and stability for long-term optimal investments.
problem Optimizing long-term investments in an incomplete market with risky and safe assets.
method Analyzes three market models with different state variable processes to find optimal portfolios and prove convergence stability.
result Dynamic optimal portfolios converge to static portfolios over time, with vanishing sensitivities in the long run.
Positive mass theorem for tori with scalar curvature bounds.
problem Proving positivity of static quasi-local mass for tori.
method Generalization of Shi-Tam result to 2-tori with specific curvature and scalar curvature bounds.
result Total weighted mean curvature of 2-tori is not greater than that of an isometric embedding into the Kottler manifold.
Proves mass-capacity inequalities for critical area-normalized capacitors, improving Schwarzschild metric uniqueness.
problem Proving mass-capacity inequalities for critical area-normalized capacitors.
method Analyzes asymptotically flat manifolds with boundary capacity potential satisfying an overdetermined problem.
result Improves Schwarzschild metric uniqueness and results for spin asymptotically flat spacetimes.
This paper analyzes dynamic ensemble selection and preprocessing for multi-class imbalanced datasets.
problem Class imbalance in multi-class datasets where majority classes have more instances.
method Examined dynamic selection techniques and data preprocessing methods for multi-class imbalanced problems.
result Dynamic ensemble improves AUC and G-mean compared to static ensemble.
Sound event detection (SED) methods are tasked with labeling segments of audio recordings by the presence of active sound sources. SED is typically posed as a supervised machine learning problem, requiring strong annotations for the presence or absence of each sound source at every time instant within the recording. Ho…
Sharp Minkowski inequality found for AdS-Melvin spacetime surfaces.
problem Proving a Minkowski-type inequality for surfaces in the AdS-Melvin space.
method Used weighted normal flow to prove inequality for general surfaces.
result Sharp Minkowski inequality holds for all surfaces in AdS-Melvin space.
Study classifies static potentials on 3-manifolds, proving one-dimensionality under specific conditions.
problem Classifying the dimension of static potentials on 3-manifolds.
method Analysis of relative zero sets of static potentials, using Miao and Tam's technique.
result Proves one-dimensionality of static potentials under specific conditions.
In general relativity, an IDEAL (Intrinsic, Deductive, Explicit, ALgorithmic) characterization of a reference spacetime metric g0 consists of a set of tensorial equations T[g]=0, constructed covariantly out of the metric g, its Riemann curvature and their derivatives, that are satisfied if and only if g is loc…
New static vacuum metrics confirmed for near Euclidean boundary data.
problem Establishing sufficient conditions for near Euclidean boundary data in static vacuum metrics.
method Using new arguments from studying the conjecture for arbitrary static vacuum metrics.
result Any hypersurface in a dense subfamily is static regular.
Extends static vacuum metrics with specific boundary conditions.
problem Proving the existence of static vacuum metrics with prescribed boundary data.
method Introducing static regular types (I) and (II), showing local well-posedness, and confirming Bartnik's conjecture.
result Confirms Bartnik's static vacuum extension conjecture for a broad range of boundary conditions.
Two neural network methods approximate conditional optimal transport for Bayesian inference.
problem Approximating conditional optimal transport for Bayesian inference in high dimensions.
method Neural network approximations of conditional optimal transport maps.
result Improved scalability and modeling choices for conditional sampling and density estimation.
We classify static manifolds which admit more than one static decomposition whenever a condition on the curvature is fullfilled. For this, we take a standard static vector field and analyze its associated one parameter family of projections onto the base. We show that the base itself is a static manifold and the warpin…
Study of 3D vacuum static spaces with specific curvature properties.
problem Classifying 3D vacuum static spaces with certain curvature conditions.
method Used generalized maximum principle to classify 3D spaces.
result Gave a complete classification of 3D complete vacuum static spaces.
Paper finds exact solutions for static fluids with symmetries.
problem Finding exact solutions for static fluids with symmetries.
method Utilized symmetries to solve Einstein's equation for a perfect fluid on a static manifold.
result Exact solutions found for static fluids with symmetries.
New rigidity theorem on static manifolds with boundary.
problem Static metrics on manifolds with boundary.
method Obata-type rigidity theorem, sufficient geometric conditions.
result Scalar curvature map can be locally surjective at static metrics on manifolds with boundary.
Geometric inequalities for static convex domains in hyperbolic space proved.
problem Proving geometric inequalities for static convex domains in hyperbolic space.
method Using static convexity of flow hypersurfaces, new inequalities are derived.
result New family of geometric inequalities for static convex domains in hyperbolic space.
The paper classifies vacuum static spaces with harmonic curvature.
problem Classifying vacuum static spaces with harmonic curvature.
method Extending the 4-dimensional work by Kim-Shin, the paper classifies n-dimensional spaces (n≥5). result New counterexamples to the Fischer-Marsden conjecture on compact vacuum static spaces.
The paper investigates geometrical aspects of static spacetime with almost gradient Ricci solitons.
problem Geometrical properties of static spacetime with almost gradient Ricci solitons.
method Analyzing conditions and properties of static spacetime with almost gradient Ricci solitons.
result Conditions and properties of static spacetime with almost gradient Ricci solitons are determined.
The study proves geometric inequalities for static convex domains in static rotationally symmetric spaces.
problem Proving geometric inequalities for static convex domains in static rotationally symmetric spaces.
method Locally constrained curvature flow in a static rotationally symmetric space Nn+1, proving graphical solutions and static convexity preservation. result Proves weighted geometric inequalities for static convex domains close to a slice of Nn+1. Proves equality in Minkowski inequality for static, flat manifolds.
problem Proving equality in Minkowski inequality for static, flat manifolds.
method Analyzes quasi-spherical metrics and static manifolds.
result Equality in Minkowski inequality achieved only by Schwarzschild space slices.
Researchers found specific conformal groups for Einstein static universe models.
problem Understanding conformal groups of Einstein static universe models.
method Constructed explicit models for restricted conformal groups and universal covering groups.
result Determined all conformal Lorentz manifolds with maximal restricted conformal group dimension.
Geometric flow method finds static extensions for axisymmetric data.
problem Bartnik's static metric extension conjecture under axisymmetry.
method Geometric flow coupled with Weyl-Papapetrou formalism.
result Axisymmetric static extensions found for various data.
We consider Killing vector fields on standard static space-times and obtain equations for a vector field on a standard static space-time to be Killing. We also provide a characterization of Killing vector fields on standard static space-times with compact Riemannian parts.
Proves existence of static vacuum metrics with specific boundary data.
problem Existence of static vacuum metrics with prescribed boundary data.
method Proves existence and local uniqueness of static vacuum metrics close to the Euclidean metric.
result Existence of static vacuum metrics with prescribed Bartnik boundary data.
Analyzing static solutions in Finsler gravity, extending known results.
problem Extending the analyticity of static vacuum solutions to Finsler spacetimes.
method Examining Finsler spacetimes with properties similar to static Lorentzian spacetimes.
result Finsler spacetimes with vanishing Ricci scalar are analytic.
Adaptive ensemble improves flu forecasts with minimal data.
problem Accurate flu forecasts to help public health.
method Adaptive stacking of ensembles, changing model weights weekly.
result Adaptive ensemble outperforms static ensembles in flu forecasts.
Paper derives Riccati equation for static spaces and proves its applications.
problem Deriving Riccati equation for static spaces.
method Proving splitting theorem and connectivity of conformal boundary.
result Establishes compactness of universal covering for static triples.
We consider a continuous-time financial market that consists of securities available for dynamic trading, and securities only available for static trading. We work in a robust framework where a set of non-dominated models is given. The concept of semi-static completeness is introduced: it corresponds to having exact re…
This paper completes the classification of S1-symmetric static vacuum black holes.
problem Identifying all S1-symmetric static vacuum black hole solutions.
method Analyzing and constructing known solutions and proving their completeness.
result Proves that the Schwarzschild, Boost, and Weyl-Korotkin-Nicolai families exhaust all S1-symmetric static vacuum black hole solutions.
In this paper, we study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions of the Einstein vacuum equations with negative cosmological constant. For a static vacuum…
Paper proves static triples with specific curvature are standard hemispheres.
problem Proving rigidity of static triples with half harmonic Weyl curvature.
method Analyzes static triples with positive scalar curvature and half harmonic Weyl curvature.
result Proves static triples with half harmonic Weyl curvature and positive scalar curvature are standard hemispheres.
New gravitational solitons and infinite topological manifolds found.
problem Finding new gravitational solitons and Riemannian manifolds.
method Space-periodic solutions of Einstein equations, quotients, Wick rotation.
result Complete Ricci flat Riemannian manifolds of infinite topological type.
Study on stellar models' topology and mass using minimal surfaces.
problem Investigating the topology and mass of static stellar models.
method Analyzing stable free boundary minimal surfaces in static perfect fluid spaces.
result Proved non-existence of stable free boundary minimal surfaces and derived upper bounds for Hawking mass.
Classifies vacuum static spaces with harmonic curvature.
problem Classifying vacuum static spaces with harmonic curvature.
method Thorough classification through geometric analysis.
result Spaces are locally isometric to four types.
Paper proves a rigidity result for static perfect fluids.
problem Proving a rigidity result for static perfect fluids.
method Robinson's divergence formula and boundary conditions.
result Rigidity result for static perfect fluids.
The paper redefines semi-static hedging as derivatives and calculates hedging errors.
problem The costs of maintaining hedging portfolios and the limitations of semi-static hedging.
method New integral representations, approximations, and efficient numerical methods for calculating Wiener-Hopf factors and Laplace-Fourier inversion.
result The hedging error of static hedging portfolios can be larger than variance-minimizing portfolios.
Existence proved for static vacuum extensions near Schwarzschild spheres.
problem Proving existence of static vacuum extensions near Schwarzschild spheres.
method Existence and local uniqueness of static vacuum extensions for Bartnik data on a sphere near a Schwarzschild sphere.
result Existence of static vacuum extensions near Schwarzschild spheres.