arXiv research

New approach confirms Kruskal-Szekeres extension for Schwarzschild spacetime.

WSqD extends learning rate schedules for large model training without fixed horizons.

Proves conditions for Cauchy horizons in low-regularity spacetimes.

The paper extends Hawking--Page solutions to various spacetimes with singularities.

Proves symmetries of extremal horizons in spacetimes.

We revisit the problem of extension of a Killing vector field in a spacetime which is solution to the Einstein-Maxwell equation. This extension has been proved to be unique in the case of a Killing vector field which is normal to a bifurcate horizon by Yu. Here we generalize the extension of the vector field to a stron…

In this paper we investigate the extension of the charged Riemannian Penrose inequality to the case where charges are present outside the horizon. We prove a positive result when the charge densities are compactly supported, and present a counterexample when the charges extend to infinity. We also discuss additional ex…

This paper is devoted to the study of the Reissner-Nordstrøm-de Sitter black holes and their maximal analytic extensions. In particular, we study some of their properties that lays the groundwork for separate papers where we obtain decay results and construct conformal scattering theories for test fields on such spacet…

We prove that any compact Cauchy horizon with constant non-zero surface gravity in a smooth vacuum spacetime is a smooth Killing horizon. The novelty here is that the Killing vector field is shown to exist on both sides of the horizon. This generalises classical results by Moncrief and Isenberg, by dropping the assumpt…

Improved algorithm for optimal stopping problems reduces runtime.

Study optimal consumption with drawdown limits over a fixed time frame.

Paper proves existence of anisotropic dynamical horizons in gravitational collapse.

ForecastGAN improves multi-horizon time series forecasting by integrating numerical and categorical features.

The horizon and geodesic structure of static configurations generated by anisotropic conformal transforms of the Schwarzschild metric is analyzed. We construct the maximal analytic extension of such off--diagonal vacuum metrics and conclude that for small deformations there are different classes of vacuum solutions of …

Null geodesics in Kerr spacetimes cannot be closed or bounded.

nGPT learns to transfer learning rates across model dimensions and token horizons.

We analyze the horizon and geodesic structure of a class of 4D off--diagonal metrics with deformed spherical symmetries, which are exact solutions of the vacuum Einstein equations with anholonomic variables. The maximal analytic extension of the ellipsoid type metrics are constructed and the Penrose diagrams are analyz…

A new Bayesian method optimizes time-dependent expensive functions with lookahead.

The paper analyzes risk measures and optimal reserve allocation strategies.

The study shows black hole horizons at low temperatures have limited topology.

Study shows nonextendibility of warped spacelike singularities in specific spacetimes.

Bartnik mass is positive and non-decreasing for black holes

No closed timelike geodesics in Kerr spacetimes, proving absence of closed causal geodesics.

In many finite horizon episodic reinforcement learning (RL) settings, it is desirable to optimize for the undiscounted return - in settings like Atari, for instance, the goal is to collect the most points while staying alive in the long run. Yet, it may be difficult (or even intractable) mathematically to learn with th…

UCRL2-VTR achieves nearly optimal regret for learning MDPs with linear function approximation.

LLapDiff models irregular multivariate time series without step-by-step integration.

The study introduces anytime learning schedules for large language models without fixed horizons.

Paper identifies reductive MDPs, solving them in polynomial time.

Upper bound derived for informed traders' gains in a model, akin to thermodynamics.

We consider off-policy policy evaluation when the trajectory data are generated by multiple behavior policies. Recent work has shown the key role played by the state or state-action stationary distribution corrections in the infinite horizon context for off-policy policy evaluation. We propose estimated mixture policy …

Reinforcement learning algorithms such as the deep deterministic policy gradient algorithm (DDPG) has been widely used in continuous control tasks. However, the model-free DDPG algorithm suffers from high sample complexity. In this paper we consider the deterministic value gradients to improve the sample efficiency of …

Bayesian filtering optimizes portfolio weights over time with uncertain parameters.

We construct a time-symmetric asymptotically flat initial data set to the Einstein-Maxwell Equations which satisfies the inequality: m - 1/2(R + Q^2/R) < 0, where m is the total mass, R=sqrt(A/4) is the area radius of the outermost horizon and Q is the total charge. This yields a counter-example to a natural extension …

Study extends binary omniprediction to multiclass setting with improved sample complexity.

The paper proves that certain FLRW spacetimes cannot be extended past the big bang.

Study on unique spacetime extensions in 1+1 dimensions with applications to weak null singularities.

We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate framework to account simultaneously for correlations across times scales and bet…

Temporal aggregation reveals latent default correlation from monthly data.

In a recent paper, Eichmair, Galloway and Pollack have proved a Gannon-Lee-type singularity theorem based on the existence of marginally outer trapped surfaces (MOTS) on noncompact initial data sets for globally hyperbolic spacetimes. However, one might wonder whether the corresponding incomplete geodesics could still …

Proves rigidity of extremal Kerr-Newman horizons.

Temporal coarse-graining of latent default paths explains effective correlation in corporate defaults.

Develops a formalism for studying general horizons and derives a near-horizon equation.

We estimate risk measures in Markov cost processes with lower and upper bounds.

We consider axisymmetric stationary dirty black holes with regular non-extremal or extremal horizons, and compute their on-horizon Petrov types. The Petrov type (PT) in the frame of the observer crossing the horizon can be different from that formally obtained in the usual (but singular in the horizon limit) frame of a…

We construct asymptotically flat, scalar flat extensions of Bartnik data $(Σ, γ, H)$, where $γ$ is a metric of positive Gauss curvature on a two-sphere $Σ$, and $H$ is a function that is either positive or identically zero on $Σ$, such that the mass of the extension can be made arbitrarily close to the half area radius…

Proposes pT-Learning for optimal dynamic treatment regimes in mHealth.

New insights into black hole horizons from asymptotic expansions.

Given a Riemannian 3-ball $(\bar B, g)$ of non-negative scalar curvature, Bartnik conjectured that $(\bar B, g)$ admits an asymptotically flat (AF) extension (without horizons) of the least possible ADM mass, and that such a mass-minimizer is an AF solution to the static vacuum Einstein equations, uniquely determined b…