The paper examines mass aspects at future null infinity and limits of quasilocal mass.
problem Understanding mass aspects and limits of quasilocal mass at future null infinity.
method Review and extension of Bondi mass and mass loss formula in Bondi-Sachs coordinate system.
result New results about the limit of quasilocal mass of unit spheres at null infinity.
New optimal transport method handles mass creation and destruction.
problem Optimal re-balancing of portfolios with mass creation or destruction.
method Formalizes an optimal transport problem with mass-change factor.
result Existence of optimal transport plans and maps established.
There are two important statements regarding the Trautman-Bondi mass at null infinity: one is the positivity, and the other is the Bondi mass loss formula, which are both global in nature. In this note, we compute the limit of the Wang-Yau quasi-local mass on unit spheres at null infinity of an asymptotically flat spac…
There are two important statements regarding the Trautman-Bondi mass [1,8,5] at null infinity: one is the positivity [7,6], and the other is the Bondi mass loss formula [1], which are both global in nature. The positivity of the quasi-local mass can potentially lead to a local description at null infinity. This is conf…
A censored transformed model for proportional outcomes with boundary mass and an application to loss given default modeling.
problem Modeling proportional outcomes with boundary mass in loss given default (LGD) modeling.
method Zero-one censored transformed normal (ZOC-TN) model.
result Captures a wider range of qualitative density shapes than benchmark models while being parsimonious, computationally efficient, and numerically stable.
Formulae track evolution of angular momentum and center of mass at null infinity.
problem Tracking the evolution of conserved quantities at null infinity.
method Evolution formulae in Bondi-Sachs coordinates, expressed in terms of shear and news tensors.
result Supertranslation invariance of fluxes, conservation law of angular momentum, duality paradigm.
Computer-aided breast cancer diagnosis in mammography is limited by inadequate data and the similarity between benign and cancerous masses. To address this, we propose a signed graph regularized deep neural network with adversarial augmentation, named \textsc{DiagNet}. Firstly, we use adversarial learning to generate p…
SPT predicts age and mass of red giants from spectra.
problem Challenges in age and mass estimation of red giants using traditional methods.
method SPT framework with Multi-head Hadamard Self-Attention and Mahalanobis distance-based loss function.
result Remarkable age and mass estimations with low errors and uncertainties.
AMORE uses neural operators to efficiently predict multiple thermochemical states in stiff chemical kinetics.
problem Efficiently integrating stiff chemical kinetics systems to reduce computational cost.
method Developed AMORE, a framework of adaptive multi-output operator network with two adaptive loss functions.
result Demonstrated improved accuracy and efficiency in predicting thermochemical states from initial conditions.
We study the Bondi-Sachs rockets with nonzero cosmological constant. We observe that the acceleration of the systems arises naturally in the asymptotic symmetries of (anti-) de Sitter spacetimes. Assuming the validity of the concepts of energy and mass previously introduced in asymptotically flat spacetimes, we find th…
In this article, we consider the limit of quasi-local conserved quantities [31,9] at the infinity of an asymptotically hyperbolic initial data set in general relativity. These give notions of total energy-momentum, angular momentum, and center of mass. Our assumption on the asymptotics is less stringent than any previo…
In this article we prove a family of local (in time) weighted Strichartz estimates with derivative losses for the Klein-Gordon equation on asymptotically de Sitter spaces and provide a heuristic argument for the non-existence of a global dispersive estimate on these spaces. The weights in the estimates depend on the ma…
The study examines correlations of logarithms of integers at different scalings.
problem Analyzing pair correlations of logarithms of integers at various scalings.
method Examined correlations of logarithms of positive integers at different scalings, proving the existence of pair correlation functions.
result Level repulsion at linear scaling, total loss of mass at superlinear scalings, and Poissonian behavior at sublinear scalings.
In this paper we study the ergodic theory of the geodesic flow on negatively curved geometrically finite manifolds. We prove that the measure theoretic entropy is upper semicontinuous when there is no loss of mass. In case we are losing mass, the critical exponents of parabolic subgroups of the fundamental group have a…
We prove that for spacetimes solving the Einstein-Maxwell (EM) equations, the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In [5] D. Christodoulou showed that gravitational waves have a nonlinear memory. He discussed how this effect can be measured as a perma…
In [LW], we construct examples of two-dimensional Hamiltonian stationary self-shrinkers and self-expanders for Lagrangian mean curvature flows, which are asymptotic to the union of two Schoen-Wolfson cones. These self-shrinkers and self-expanders can be glued together to yield solutions of the Brakke flow - a weak form…
AI model identifies chemical agents in MCI with high accuracy.
problem Identifying chemical agents in mass casualty incidents.
method Reverse engineered signs/symptoms, trained using ANN, BDT, and WISER.
result WISER outperformed ANN and BDT in identifying chemical agents.
We explore geometric aspects of bubble convergence for harmonic maps. More precisely, we show that the formation of bubbles is characterised by the local excess of curvature on the target manifold. We give a universal estimate for curvature concentration masses at each bubble point and show that there is no curvature l…
Determining contributions by sub-portfolios or single exposures to portfolio-wide economic capital for credit risk is an important risk measurement task. Often economic capital is measured as Value-at-Risk (VaR) of the portfolio loss distribution. For many of the credit portfolio risk models used in practice, the VaR c…
NN-EVCLUS uses neural networks to cluster data with uncertainty.
problem Clustering data with uncertainty and handling outliers.
method NN-EVCLUS learns a neural network to map attributes to mass functions, minimizing discrepancy between dissimilarities and conflict.
result NN-EVCLUS outperforms existing methods in clustering tasks.
Study controlled contagion with state-dependent killing, proving a comparison principle.
problem Analyzing controlled McKean--Vlasov contagion with state-dependent killing.
method Proof of a comparison principle using Wasserstein smooth-gauge comparison and killing-jump absorption estimates.
result Established a comparison principle for the two-population killed-particle HJB.
The X-ADM mass is shown to be equivalent to the ADM mass, proving the X-positive mass theorem in all dimensions.
problem Proving the X-positive mass theorem for all dimensions.
method Conformal reduction argument.
result The X-ADM mass is equivalent to the ADM mass, proving the X-positive mass theorem in all dimensions.
The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce training data, overfitting is typically mitigated by adding regularization term…
The paper studies nonlinear mass concepts in 3-manifolds with nonnegative scalar curvature.
problem Nonlinear isocapacitary mass in 3-manifolds with nonnegative scalar curvature.
method Derives positive mass theorems and shows mass coincides with ADM mass under mild conditions.
result Nonlinear masses coincide with ADM mass and prove the Penrose inequality.
Equivalence proven for isocapacitary mass notions.
problem Proving equivalence of isocapacitary mass notions.
method Proof of equivalence for G. Huisken's and J. L. Jauregui's isocapacitary mass.
result Equivalence of isocapacitary mass notions proven.
The paper defines a new mass quantity for 3-manifolds and proves a positive mass theorem.
problem Proving the positive mass theorem for a new geometric quantity.
method Defining X-ADM mass and using a monotonicity formula. result Established a relative positive mass theorem for asymptotically flat 3-manifolds.
Introduce new boundary mass for asymptotically flat half-manifolds
problem Define boundary mass for asymptotically flat half-manifolds
method Introduce new boundary mass
result Define boundary mass for asymptotically flat half-manifolds
We prove directly without using a density theorem that (i) the ADM mass defined in the usual way on an asymptotically flat manifold is equal to the mass defined intrinsically using Ricci tensor; (ii) the Hamiltonian formulation of center of mass and the center of mass defined intrinsically using Ricci tensor are the sa…
Continuous metrics on R^3 with specific properties have non-negative harmonic mass.
problem Proving non-negativity of mass for continuous metrics.
method Defining harmonic mass and using properties of approximating smooth metrics.
result The harmonic mass of continuous metrics is non-negative.
Study the mass of flat 3-manifolds with boundary using specific methods.
problem Calculate the mass of asymptotically flat 3-manifolds with boundary.
method Use the method of Bray-Kazaras-Khuri-Stern to derive a mass formula.
result Derive sufficient conditions for the positivity of the mass.
Unified definition of mass aspect function for weakly regular hyperbolic manifolds.
problem Ambiguity in mass definition for asymptotically hyperbolic manifolds.
method Introduced an ADM-style mass aspect function for broad asymptotics and low regularity.
result Unified mass aspect function exhibits favorable covariance properties.
Local mass perspective on Bayesian inference
problem Measuring distributional discrepancy in Bayesian inference
method Introducing Mass Index and Regularised Extended KL
result Proving inequalities for comparing local small-ball masses
On asymptotically flat and asymptotically hyperbolic manifolds, by evaluating the total mass via the Ricci tensor, we show that the limits of certain Brown-York type and Hawking type quasi-local mass integrals equal the total mass of the manifold in all dimensions.
Simple proof for sphere mass calculation.
problem Computing the ADM mass of static sphere extensions.
method Uses mass formula for static asymptotically flat manifolds.
result Validated mass formula for small spheres.
New ADM mass definition for weakly regular manifolds.
problem Defining ADM mass for non-smooth manifolds.
method Proposed a new definition for metrics with local Sobolev regularity.
result Finite mass, invariance under coordinate changes, and agreement with smooth case.
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.
Huisken's isoperimetric mass is always nonnegative.
problem Understanding the nonnegativity of Huisken's isoperimetric mass.
method Simple reasoning based on basic properties.
result Huisken's isoperimetric mass is nonnegative.
Study on residual Monge-Ampère mass for symmetric plurisubharmonic functions.
problem Estimating the residual Monge-Ampère mass of symmetric plurisubharmonic functions with isolated singularities.
method Utilized Sasakian geometry to derive estimates on the residual mass in relation to Lelong numbers.
result Partially resolved the zero mass conjecture by Guedj and Rashkovskii.
Study on residual Monge-Ampère mass for symmetric plurisubharmonic functions.
problem Analyzing the residual Monge-Ampère mass of symmetric plurisubharmonic functions.
method Proved zero mass for functions with zero Lelong number at origin and S1-invariance. result Zero mass conjecture answered for symmetric functions.
Surveying mass in 2D hyperbolic geometry, overcoming challenges via minimisation.
problem Defining mass in 2D hyperbolic geometry.
method Minimisation using positive energy theorem and gluing theorems.
result Construction of novel initial data sets with controlled mass.
New mass definition linked to ADM mass for general metrics.
problem Defining mass for metrics with low regularity.
method Using isocapacitary inequality to define total mass.
result Inequality between new mass and ADM mass proved.
The paper connects mass, harmonic functions, and capacity in asymptotically flat 3-manifolds.
problem Connections among ADM mass, harmonic functions, and capacity in asymptotically flat 3-manifolds.
method New formulae for ADM mass via harmonic functions, monotone quantities, and geometric inequalities.
result The mass-to-capacity ratio is bounded below by 1 - sqrt(normalized Willmore functional of the boundary).
Mass in relativity linked to polyhedra geometry.
problem Understanding ADM mass in general relativity.
method Relating ADM mass to the total mean curvature and defect of dihedral angles of Riemannian polyhedra.
result Expressed n-dimensional mass as an integral of geometric quantities. Refines geometric center of mass analysis for Einstein field equations.
problem Analyzing the geometric center of mass of Willmore surfaces in initial data for Einstein field equations.
method Refined Lyapunov-Schmidt analysis to study geometric center of mass of area-constrained Willmore surfaces.
result The geometric center of mass agrees with the Hamiltonian center of mass under specific conditions.
Proves spacetime positive mass theorem in all dimensions.
problem Proving the spacetime positive mass theorem in arbitrary dimensions.
method Using Brendle--Wang's Riemannian positive mass theorem approach.
result Proves the spacetime positive mass theorem for all dimensions.
New mass inequalities and proofs for causal variational principles.
problem Proving new mass inequalities for causal variational principles.
method Proved a new inequality for minimizers of causal variational principles and applied it to prove the positive mass theorem.
result Introduced a positive quasilocal mass and proved new mass inequalities.
Defines mass for non-smooth hyperbolic spaces using a modified flow.
problem Defining mass for non-smooth, asymptotically hyperbolic spaces.
method Normalized Ricci-DeTurck flow with scalar curvature lower bound.
result Mass function well-defined for continuous metrics.
New solutions found with negative mass in general relativity.
problem Finding metrics with negative mass in general relativity.
method Constructing families of metrics with specific properties.
result Obtained new classes of solutions with negative mass.