arXiv research

Classifies conformal transformations in spacetimes without observer horizons.

Study of isometries in spacetimes without observer horizons.

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…

A correct description of the past and the future event horizons for timelike geodesics in de Sitter space-time of the first kind is given.

Paper proves existence of anisotropic dynamical horizons in gravitational collapse.

We consider generic static spacetimes with Killing horizons and study properties of curvature tensors in the horizon limit. It is determined that the Weyl, Ricci, Riemann and Einstein tensors are algebraically special and mutually aligned on the horizon. It is also pointed out that results obtained in the tetrad adjust…

The study reveals distinct patterns in retail investors' holding periods affecting stock returns.

This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do…

We review a resent {\em time-dependent} performance measure for economical time series -- the (optimal) investment horizon approach. For stock indices, the approach shows a pronounced gain-loss asymmetry that is {\em not} observed for the individual stocks that comprise the index. This difference may hint towards an sy…

In this paper we present Horizon, Facebook's open source applied reinforcement learning (RL) platform. Horizon is an end-to-end platform designed to solve industry applied RL problems where datasets are large (millions to billions of observations), the feedback loop is slow (vs. a simulator), and experiments must be do…

Many robotic applications require the agent to perform long-horizon tasks in partially observable environments. In such applications, decision making at any step can depend on observations received far in the past. Hence, being able to properly memorize and utilize the long-term history is crucial. In this work, we pro…

We investigate whether fractal markets hypothesis and its focus on liquidity and invest- ment horizons give reasonable predictions about dynamics of the financial markets during the turbulences such as the Global Financial Crisis of late 2000s. Compared to the mainstream efficient markets hypothesis, fractal markets hy…

We consider solutions to the linear wave equation $\Box_gφ=0$ on a non-extremal maximally extended Schwarzschild-de Sitter spacetime arising from arbitrary smooth initial data prescribed on an arbitrary Cauchy hypersurface. (In particular, no symmetry is assumed on initial data, and the support of the solutions may con…

The capitalization-weighted total relative variation $\sum_{i=1}^d \int_0^\cdot μ_i (t) \mathrm{d} \langle \log μ_i \rangle (t)$ in an equity market consisting of a fixed number $d$ of assets with capitalization weights $μ_i (\cdot)$ is an observable and nondecreasing function of time. If this observable of the market …

Study optimal policy regret in partially observable Markov games with adaptive opponents.

Firms miscount their customers who stop buying without saying goodbye.

Microgrids (MGs) are small, local power grids that can operate independently from the larger utility grid. Combined with the Internet of Things (IoT), a smart MG can leverage the sensory data and machine learning techniques for intelligent energy management. This paper focuses on deep reinforcement learning (DRL)-based…

Optimizes investment under uncertain time horizons with non-concave utility.

Past lightcones of certain points in globally hyperbolic spacetimes determine the entire spacetime.

Logarithmic regret achieved in continuous-time linear-quadratic reinforcement learning.

Minimal TIP and TIF found in compact spacetimes, impacting spacetime splitting.

Investment horizon approach has been used to analyze indexes of Polish stock market.Optimal time horizon for each return value is evaluated by fitting appropriate function form of the distribution. Strong asymmetry of gain-loss curves is observed for WIG index, whereas gain and loss curves look similar for WIG20 and fo…

Using high frequency data, we have studied empirically the change of volatility, also called volatility derivative, for various time horizons. In particular, the correlation between the volatility derivative and the volatility realized in the next time period is a measure of the response function of the market particip…

Scalar-tensor gravitation theories, such as the Brans-Dicke family of theories, are commonly partly described by a modified Einstein equation in which the Ricci tensor is replaced by the Bakry-Émery-Ricci tensor of a Lorentzian metric and scalar field. In physics this formulation is sometimes referred to as the "Jordan…

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

SurvFM-RMST converts survival outcomes into pseudo-observation targets for tabular models.

Study optimal stopping problems with finite-time horizon and proves continuity and strict monotonicity of the boundary.

Efficient RL in large POMDPs with latent determinism and embeddings.

We compare some methods recently used in the literature to detect the existence of a certain degree of common behavior of stock returns belonging to the same economic sector. Specifically, we discuss methods based on random matrix theory and hierarchical clustering techniques. We apply these methods to a portfolio of s…

This work tackles long-term visual planning by goal-conditioned hierarchical predictors.

The inverse statistics is the distribution of waiting times needed to achieve a predefined level of return obtained from (detrended) historic asset prices \cite{optihori,gainloss}. Such a distribution typically goes through a maximum at a time coined the {\em optimal investment horizon}, $τ^*_ρ$, which defines the most…

Study tackles OPE in confounded settings, estimating policy value from proxies.

We establish the conjectured area-angular momentum-charge inequality for stable apparent horizons in the presence of a positive cosmological constant, and show that it is saturated precisely for extreme Kerr-Newman-de Sitter horizons. As with previous inequalities of this type, the proof is reduced to minimizing an `ar…

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

Off-policy evaluation of sequential decision policies from observational data is necessary in applications of batch reinforcement learning such as education and healthcare. In such settings, however, unobserved variables confound observed actions, rendering exact evaluation of new policies impossible, i.e., unidentifia…

We show that the Brill-Lindquist initial data provides a counterexample to a Riemannian Penrose inequality with charge conjectured by G. Gibbons. The observation illustrates a sub-additive characteristic of the area radii for the individual connected components of an outermost horizon as a lower bound of the ADM mass.

Study on cryptocurrency market correlations at various time scales.

Study learns state representations from observations for control, proving guarantees.

In the seminal work [9], several macroscopic market observables have been introduced, in an attempt to find characteristics capturing the diversity of a financial market. Despite the crucial importance of such observables for investment decisions, a concise mathematical description of their dynamics has been missing. W…

Transformers improve Alzheimer's disease progression prediction by accounting for irregular biomarker histories.

Continuous Glucose Monitoring (CGM) has enabled important opportunities for diabetes management. This study explores the use of CGM data as input for digital decision support tools. We investigate how Recurrent Neural Networks (RNNs) can be used for Short Term Blood Glucose (STBG) prediction and compare the RNNs to con…

We study the problem of regret minimization in partially observable linear quadratic control systems when the model dynamics are unknown a priori. We propose ExpCommit, an explore-then-commit algorithm that learns the model Markov parameters and then follows the principle of optimism in the face of uncertainty to desig…

Develops anytime-valid stopping rules for SGD based on observed trajectory.

ETC learns minimal representations for reinforcement learning in POMDPs.

We compare our results on empirical analysis of financial data with simulations of two stochastic models of the dynamics of stock market prices. The two models are (i) the truncated Lévy flight recently introduced by us and (ii) the ARCH(1) and GARCH(1,1) processes. We find that the TLF well describes the scaling and i…

We study the online estimation of the optimal policy of a Markov decision process (MDP). We propose a class of Stochastic Primal-Dual (SPD) methods which exploit the inherent minimax duality of Bellman equations. The SPD methods update a few coordinates of the value and policy estimates as a new state transition is obs…

A proof is given that the maximal Fermi coordinate chart for any comoving observer in a broad class of Robertson-Walker spacetimes consists of all events within the cosmological event horizon, if there is one, or is otherwise global. Exact formulas for the metric coefficients in Fermi coordinates are derived. Sharp uni…

A new method learns to stop with minimal data, outperforming traditional approaches.