arXiv research

The paper studies deformations of Kundt metrics using nil-Killing vector fields.

New spaces at infinity identified for Minkowski spacetime.

SPI uses synthetic data to improve predictive inference efficiency.

To overcome the oscillation problem in the classical momentum-based optimizer, recent work associates it with the proportional-integral (PI) controller, and artificially adds D term producing a PID controller. It suppresses oscillation with the sacrifice of introducing extra hyper-parameter. In this paper, we start by …

Proves the Kundt conjecture in arbitrary dimensions, confirming its validity.

Study predicts droughts using ANN models and hydro-meteorological data.

Batch Reinforcement Learning (Batch RL) consists in training a policy using trajectories collected with another policy, called the behavioural policy. Safe policy improvement (SPI) provides guarantees with high probability that the trained policy performs better than the behavioural policy, also called baseline in this…

This paper considers Safe Policy Improvement (SPI) in Batch Reinforcement Learning (Batch RL): from a fixed dataset and without direct access to the true environment, train a policy that is guaranteed to perform at least as well as the baseline policy used to collect the data. Our approach, called SPI with Baseline Boo…

New method uses small perturbations to improve representation learning from few labels.

New model solves complex SDEs with high-dimensional spatial and stochastic spaces.

We introduce a new unsupervised anomaly detection ensemble called SPI which can harness privileged information - data available only for training examples but not for (future) test examples. Our ideas build on the Learning Using Privileged Information (LUPI) paradigm pioneered by Vapnik et al. [19,17], which we extend …

Surface mount technology (SMT) is a process for producing printed circuit boards. Solder paste printer (SPP), package mounter, and solder reflow oven are used for SMT. The board on which the solder paste is deposited from the SPP is monitored by solder paste inspector (SPI). If SPP malfunctions due to the printer defec…

We describe Venture, an interactive virtual machine for probabilistic programming that aims to be sufficiently expressive, extensible, and efficient for general-purpose use. Like Church, probabilistic models and inference problems in Venture are specified via a Turing-complete, higher-order probabilistic language desce…

Study of charged scalar fields on Reissner-Nordström spacetimes via energy estimates.

The paper generalizes Alexandrov theorems for null hypersurfaces with integral curvature conditions.

Proves a positive mass theorem for static causal fermion systems.

Paper proves exponential lower bounds for policy iteration in MDPs.

The paper estimates area and volume for spacetimes with integral mean curvature bounds.

Starting with the most general four-dimensional spacetime possessing two commuting Killing vectors and a nontrivial Killing tensor, we analytically integrate Einstein-Yang-Mills equations for a completely arbitrary gauge group. It is assumed that the gauge field inherits the symmetries of the background and is aligned …

Classifies left invariant Kundt structures on 3D Lie groups.

The integral of the energy density function $\mathfrak m$ of a closed Robertson-Walker (RW) spacetime with source a perfect fluid and cosmological constant $Λ$ gives rise to an action functional on the space of scale functions of RW spacetime metrics. This paper studies closed RW spacetimes which are critical for this …

The null distance for Lorentzian manifolds was recently introduced by Sormani and Vega. Under mild assumptions on the time function of the spacetime, the null distance gives rise to an intrinsic, conformally invariant metric that induces the manifold topology. We show when warped products of low regularity and globally…

The `observer space' of a Lorentzian spacetime is the space of future-timelike unit tangent vectors. Using Cartan geometry, we first study the structure a given spacetime induces on its observer space, then use this to define abstract observer space geometries for which no underlying spacetime is assumed. We propose ta…

The paper proposes extensions of the usual notions of Finslerian volume to time orientable Finsler spacetime manifolds. The basic idea is to replace, in the classical Busemann-Hausdorff and Holmes-Thompson definitions, integration on the indicatrices of the given metric (which are, in Lorentzian signature, non-compact,…

New inequality shows all special submanifolds in light cone are totally umbilical spheres.

New approach to Kundt spacetimes using $G$-structures.

We prove nonexistence of a nontrivial integral that is polynomial in momenta of degree less than 7 for the Zipoy-Voorhees spacetime with the parameter $δ=2$

A characterization of the foliation by spacelike slices of an $(n+1)$-dimensional spatially closed Generalized Robertson-Walker spacetime is given by means of studying a natural mean curvature type equation on spacelike graphs. Under some natural assumptions, of physical or geometric nature, all the entire solutions of…

The paper proves a spacetime positive mass theorem for singular initial data sets.

We classify all spacetimes with a closed rank-2 conformal Killing-Yano tensor. They give a generalization of Kerr-NUT-de Sitter spacetimes. The Einstein condition is explicitly solved and written as an indefinite integral. It is characterized by a polynomial in the integrand. We briefly discuss the smoothness condition…

Study Godbillon-Vey invariants in non-Lorentzian spacetimes and fluid dynamics.

Formula for Hadamard coefficients from Green's operators on spacetimes.

Geometric approach to Dirac operator evolution on spacetimes.

Survey on stability of Minkowski spacetime in relativity.

Study of $k$-almost Yamabe solitons in perfect fluid spacetimes.

Study axisymmetric waves on extremal Kerr spacetime using physical-space estimates.

Formula for index in Lorentzian spacetimes.

We show that the index of a lightlike geodesic in a conformally standard stationary spacetime is equal to the index of its spatial projection as a geodesic of a Finsler metric associated to the spacetime. Moreover we obtain the Morse relations of lightlike geodesics connecting a point to an integral line of the standar…

We reinterpret special relativity, or more precisely its de Sitter deformation, in terms of 3d conformal geometry, as opposed to (3+1)d spacetime geometry. An inertial observer, usually described by a geodesic in spacetime, becomes instead a choice of ways to reverse the conformal compactification of a Euclidean vector…

Wave propagator constructed on globally hyperbolic spacetimes.

A relation between the conformal anomaly and the logarithmic term in the entanglement entropy is known to exist for CFT's in even dimensions. In odd dimensions the local anomaly and the logarithmic term in the entropy are absent. As was observed recently, there exists a non-trivial integrated anomaly if an odd-dimensio…

Study shows no hidden symmetries in specific spacetime metrics.

In this work we construct and analyze exact solutions describing Ricci flows and nonholonomic deformations of four dimensional (4D) Taub-NUT spacetimes. It is outlined a new geometric techniques of constructing Ricci flow solutions. Some conceptual issues on spacetimes provided with generic off-diagonal metrics and ass…

New mass inequalities and proofs for causal variational principles.

Study shows nonextendibility of warped spacelike singularities in specific spacetimes.

Using techniques of integrable systems, we study a Weierstrass representation formula for timelike surfaces with prescribed mean curvature in Minkowski 3-space. It is shown that timelike minimal surfaces are obtained by integrating a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in Minkowski 3-spa…

Proposes a new quasi-local mass for timelike 2-surfaces in spacetimes.

We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical …