We show how to reduce the general formulation of the mass-angular momentum-charge inequality, for axisymmetric initial data of the Einstein-Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. It is also shown that the same reduction argument applies to …
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48 results for “mass-angular momentum”
Establishes inequalities linking body size, mass, angular momentum, and charge.
problem Understanding the relationship between a body's size, mass, angular momentum, and charge.
method Analyzes axisymmetric initial data sets for the Einstein equations, using a computable notion of size.
result Provides black hole existence criteria even in the time-symmetric case.
In this paper, we proved the mass angular momentum inequality\cite{D1}\cite{ChrusLiWe}\cite{SZ} for axisymmetric, asymptotically flat, vacuum constraint data sets with small trace. Given an initial data set with small trace, we construct a boost evolution spacetime of the Einstein vacuum equations as \cite{ChOM}. Then …
In this paper, we extend the work in \cite{D}\cite{ChrusLiWe}\cite{ChrusCo}\cite{Co}. We weaken the asymptotic conditions on the second fundamental form, and we also give an norm bound for the difference between general data and Extreme Kerr data or Extreme Kerr-Newman data by proving convexity of the renormali…
Mass inequality for black ring spacetimes, showing extreme solutions.
problem Establishing mass-angular momentum relation for black ring spacetimes.
method Mathematical derivation of mass-angular momentum inequality.
result The inequality is saturated for extreme Pomeransky-Sen'kov black ring solutions.
We show that extreme Myers-Perry initial data realize the unique absolute minimum of the total mass in a physically relevant (Brill) class of maximal, asymptotically flat, bi-axisymmetric initial data for the Einstein equations with fixed angular momenta. As a consequence, we prove the relevant mass-angular momentum in…
We show how to reduce the general formulation of the mass-angular momentum inequality, for axisymmetric initial data of the Einstein equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. This procedure is based on a certain deformation of the initial data which p…
We prove a mass-angular momentum-charge inequality for a broad class of maximal, asymptotically flat, bi-axisymmetric initial data within the context of five-dimensional minimal supergravity. We further show that the charged Myers-Perry black hole initial data are the unique minimizers. In addition, we establish a rigi…
Establishes inequality for multiple black holes, proving mass lower bound.
problem Proving mass-angular momentum inequality for multiple black holes.
method Novel flow of singular harmonic maps with hyperbolic plane target.
result Mass lower bound for ADM mass and angular momentum.
Formulae for mass and angular momentum transformations under BMS transformations derived from curvature and metric.
problem Deriving transformation formulae for mass and angular momentum under BMS transformations.
method Two approaches: from curvature tensor and metric coefficients.
result Exact expressions for Drey-Streubel angular momentum of a general section.
We extend Brill's positive mass theorem to a large class of asymptotically flat, maximal, -invariant initial data sets on simply connected four dimensional manifolds . Moreover, we extend the local mass angular momenta inequality result Ref [1] for invariant black holes to the case with nonzero stre…
In this paper a lower bound for the ADM mass is given in terms of the angular momenta and charges of black holes present in axisymmetric initial data sets for the Einstein-Maxwell equations. This generalizes the mass-angular momentum-charge inequality obtained by Chrusciel and Costa to the case of multiple black holes.…
Transformations of Asymptotically AdS Hyperbolic Initial Data and Associated Geometric Inequalitiesgr-qc
Transforms hyperbolic to flat data, deriving geometric inequalities.
problem Deriving geometric inequalities in asymptotically AdS hyperbolic spacetimes.
method Constructs transformations preserving physical quantities to relate hyperbolic to flat spacetimes.
result Derives geometric inequalities from flat counterparts.
This paper proves a canonical foliation on null infinity for Kerr-like black holes.
problem Establishing well-defined physical quantities on null infinity for Kerr-like black holes.
method Existence and uniqueness results for GCM spheres by Klainerman-Szeftel.
result Existence of a canonical foliation on future null infinity with well-defined physical quantities.
This work removes logarithmic singularities from hyperboloidal initial data without creating new ones.
problem Logarithmic singularities in hyperboloidal initial data sets.
method Evolutionary framework of the constraint equations and generalization of Beyer and Ritchie's result.
result Generic solutions of the constraint equations are free of logarithmic singularities.
Study of harmonic maps with extreme Kerr-like singularities.
problem Analyzing harmonic maps with specific singularities.
method Asymptotic analysis of harmonic maps from 3D Euclidean space to hyperbolic plane.
result Existence and classification of tangent harmonic maps at extreme black hole horizons.
The study finds that factor momentum is significant only at short lags compared to stock momentum.
problem Investigating the relationship between factor momentum and stock momentum.
method Replicated earlier findings and conducted a spanning test controlling for stock momentum and factor exposure.
result Factor momentum is significant only at short lags after controlling for stock momentum and factor exposure.
We test the price momentum effect in the Korean stock markets under the momentum universe shrinkage to subuniverses of the KOSPI 200. Performance of the momentum strategy is not homogeneous with respect to change of the momentum universe. It is found that some submarkets generate the higher momentum returns than other …
Introduces homotopy momentum sections on multisymplectic manifolds.
problem No specific problem stated; focuses on introducing a new concept.
method Introduces a new concept of homotopy momentum sections on multisymplectic manifolds.
result Shows that a gauged nonlinear sigma model with Wess-Zumino term has homotopy momentum section structure.
Customer Momentumq-fin.PR
Customer momentum is a positive relationship between a firm's returns and past returns of its customers.
problem Understanding the relationship between a firm's returns and its customers' past returns.
method Examined customer momentum using a long-short equally-weighted decile portfolio and Fama-French factor models.
result Customer momentum generates significant monthly returns and is statistically significant.
This paper examines momentum spillover across multiple asset classes using only pricing data.
problem Challenges in studying momentum spillover across diverse asset classes due to lack of common characteristics.
method Utilised a linear and interpretable graph learning model to reveal momentum spillover network.
result Network momentum strategy yields a Sharpe ratio of 1.5 and an annual return of 22%.
The paper analyzes how hyperparameters affect SGD with momentum's convergence rate.
problem The role of hyperparameters in SGD with momentum's convergence rate.
method Theoretical analysis using a hyperparameters-dependent stochastic differential equation (hp-dependent SDE).
result The optimal linear rate of convergence depends on both the learning rate and the momentum coefficient.
This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to , the bundle of vertically adapted linear frames over the bundle of field configurations . Specifically, the generalized field momentum obs…
Momentum ResNets improve ResNets' memory efficiency.
problem Memory inefficiency in deep residual neural networks (ResNets).
method Adding a momentum term to the forward rule of ResNets to make them invertible.
result Momentum ResNets can learn any linear mapping up to a multiplicative factor, improving memory efficiency.
We give a detailed discussion about existence and uniqueness of Lu's momentum map. More precisely, we introduce the infinitesimal momentum map, and we study its properties. This allows us to describe the theory of reconstruction of the momentum map from the infinitesimal one. We provide the conditions for the uniquenes…
The paper analyzes how momentum affects convergence in stochastic gradient methods.
problem Lack of clear understanding of momentum's impact on convergence and performance.
method Unified analysis of several popular algorithms using the QHM formulation.
result Provides practical guidelines for setting learning rate and momentum parameters.
We introduce various quantitative and mathematical definitions for price momentum of financial instruments. The price momentum is quantified with velocity and mass concepts originated from the momentum in physics. By using the physical momentum of price as a selection criterion, the weekly contrarian strategies are imp…
DEAM optimizes momentum weights dynamically to improve deep learning model training.
problem Errors in momentum weights propagate errors in optimization algorithms like ADAM.
method DEAM computes adaptive momentum weights based on discriminative angles, reducing hyperparameters and introducing a backtrack term.
result DEAM achieves faster convergence rates in both convex and non-convex deep learning model training.
Sparse learning speeds up neural network training without sacrificing accuracy.
problem Training deep neural networks efficiently while maintaining performance.
method Sparse momentum algorithm that redistributes and grows weights based on momentum magnitude.
result State-of-the-art sparse performance on various datasets with up to 5.61x faster training.
Adapting momentum from optimization to reinforcement learning.
problem Improving the convergence and stability of reinforcement learning algorithms.
method Introducing Momentum Value Iteration (MoVI) by incorporating an average of consecutive state-action value functions, inspired by the concept of momentum in optimization.
result MoVI improves the convergence and stability of reinforcement learning algorithms, as demonstrated by experiments on Atari games.
Application of Langevin Dynamics to Advance the Quantum Natural Gradient Optimization Algorithmquant-ph
New algorithm Momentum-QNG improves optimization of quantum circuits.
problem Optimizing variational quantum circuits to avoid local minima.
method Applied Langevin dynamics to QNG, introducing momentum term.
result Momentum-QNG outperforms basic QNG and other optimizers.
Momentum speeds up evolutionary processes in machine learning.
problem Accelerating convergence in evolutionary dynamics.
method Combining momentum from machine learning with evolutionary dynamics using information divergences as Lyapunov functions.
result Momentum accelerates convergence of evolutionary dynamics, including the replicator equation and Euclidean gradient descent.
Chinese stock market shows time series momentum and contrarian effects over different periods.
problem Analyzing momentum and contrarian effects in Chinese stock market performance.
method Examined time series momentum and contrarian strategies applied to major indices in China.
result Time series momentum effect in short run, contrarian effect in long run, performance dependent on look-back and holding periods.
Unified model learns from both time-series and cross-sectional momentum features.
problem Separate time-series and cross-sectional momentum strategies do not consider concurrent relationships.
method Spatio-Temporal Momentum strategies using neural networks to combine both types of momentum.
result Simple neural network with single fully connected layer generates trading signals for all assets.
SMG combines shuffling and momentum for non-convex optimization.
problem Non-convex finite-sum optimization problems.
method Shuffling Gradient-based method with momentum.
result Established state-of-the-art convergence rates for SMG.
Contact manifolds' momentum polytopes are convex.
problem Understanding the structure of contact manifolds.
method Using isomorphism to toric varieties.
result Momentum polytopes of contact manifolds are convex.
ADINE uses adaptive higher momentum to speed up convergence.
problem Optimization of deep neural networks.
method Adaptive higher momentum in stochastic gradient descent.
result ADINE helps converge faster without increasing generalization error.
GMC uses global momentum for sparse communication in distributed learning.
problem Latency and bandwidth limitations in network communication for large-scale deep learning models.
method GMC utilizes global momentum for sparse communication in DMSGD, improving convergence and accuracy.
result GMC and GMC+ achieve higher test accuracy and faster convergence compared to local momentum methods.
The paper analyzes momentum variants of various stochastic optimization methods.
problem Improving the convergence rates of stochastic optimization methods.
method Stochastic gradient descent, Newton, proximal point, and subspace ascent methods with momentum.
result Global linear convergence rates for various measures of success.
New method shows stochastic momentum can converge quickly on optimization problems.
problem Improving convergence of stochastic optimization methods.
method Stochastic heavy ball momentum with minibatching.
result Stochastic heavy ball momentum retains fast linear rate on quadratic problems.
The paper analyzes dynamics of momentum in high dimensions with sparse updates.
problem Theoretical analysis of momentum dynamics in high-dimensional sparse settings.
method Theoretical analysis of two models: least squares with sparse inputs and logistic regression with a rare class.
result Characterization of high-dimensional limits of momentum dynamics and phase structure.
The paper investigates momentum and liquidity in crypto markets.
problem Exploring the relationship between momentum effects and liquidity in cryptocurrency markets.
method Formed and rebalanced portfolios based on momentum-liquidity bivariate sorts across various cryptocurrencies over time.
result Strong momentum effect in the most liquid cryptocurrencies supports herding behavior theories.
One has not any conventional energy-momentum conservation law in Lagrangian field theory, but relations involving different stress-energy-momentum tensors associated with different connections. It is not obvious how to choose the true energy-momentum tensor. This problem is solved in the framework of the multimomentum …
Constructibility of momentum maps and linear variation for singular symplectic reduced spacesmath.SG
The paper extends a theorem about momentum maps to singular symplectic spaces.
problem Extending a theorem about momentum maps to singular symplectic spaces.
method Using integral affine stratification and equivariant locally trivial fibrations, the paper extends the linear variation theorem to singular values of the momentum map.
result Cohomology classes of symplectic forms on reduced spaces vary linearly within strata.
This paper analyzes momentum Q-learning with finite-sample guarantees.
problem Improving Q-learning performance with momentum schemes.
method Proposes MomentumQ algorithm integrating Nesterov and Polyak's momentum schemes, analyzes convergence for function approximations.
result Establishes finite-sample convergence rates for MomentumQ, demonstrating better performance than vanilla Q-learning.
Momentum improves deep learning generalization by stabilizing noise and learning features.
problem Improving generalization in deep learning models.
method Empirical and theoretical analysis of gradient descent with momentum (GD+M) vs. gradient descent (GD) in binary classification tasks.
result GD+M outperforms GD in generalization, especially in datasets with shared features and varying margins.
Generalizes momentum sections to higher-dimensional gauged sigma models.
problem Understanding momentum sections in Hamiltonian mechanics and sigma models.
method Introduces a generalization of momentum sections on pre-multisymplectic manifolds.
result Shows a connection between constrained Hamiltonian systems and gauged sigma models.
Generalizes momentum map to Courant algebroid for constrained mechanics.
problem Generalizing momentum map to new geometric structures.
method Generalized momentum section on Lie algebroid to Courant algebroid, constructed cohomological formulations.
result Identified momentum section in constrained Hamiltonian mechanics with Courant algebroid symmetry.