arXiv research

Study shows instability of certain MOTSs with continuous symmetry.

Study examines stability of MOTS in symmetric initial data sets.

Enhances MOT with causality constraints for better option pricing.

Area-charge inequalities and local rigidity of free boundary MOTS in charged initial data sets

We prove in this paper that, under suitable coinditions on an initial data set, we can obtain Area and Curvature Estimates for simple marginally outer trapped surfaces (or MOTS). Using this estimates, we derive a Compactness Theorem for MOTS. Moreover, the Compactness Theorem will allow us to adapt the recent Degree Th…

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. This result requires that the MOTS be generic in a suitable sense. In the same spirit…

Study shows how charged MOTS restrict spacetime configurations.

The study examines the index of MOTS in Kerr-Newman-de Sitter spacetime and its relation to mass and charge.

New method to find surfaces in null cones with constant curvature near black hole indicators.

In recent work, the notion of Double Convexity for a foliation of a conical null hypersurface was introduced to give a proof, if satisfied, of the Null Penrose Inequality. Double Convexity constrains the geometry of a Marginally Outer Trapped Surface (MOTS), called a quasi-round MOTS. In the first part of this paper, f…

Paper proves rigidity of initial data sets with boundary and capillary MOTS.

Study of mean curvature flow on null hypersurfaces leading to MOTS.

Proves properties of free boundary stable MOTS in spacetimes.

Hybrid Bayesian MOT uses neural networks to improve model aspects, achieving state-of-the-art performance.

The aim of this paper is to collect some facts about the blowup of Jang's equation. First, we discuss how to construct solutions that blow up at an outermost MOTS. Second, we exclude the possibility that there are extra blowup surfaces in data sets with non-positive mean curvature. Then we investigate the rate of conve…

A new relaxed framework for pricing illiquid derivatives using bid-ask spreads.

MOT uses RL with OT to adapt to different market conditions for algorithmic trading.

Improved neural framework for scaling entropic MOT with significant computational gains.

We study the evolution of hypersurfaces in spacetime initial data sets by their null mean curvature. A theory of weak solutions is developed using the level-set approach. Starting from an arbitrary mean convex, outer untapped hypersurface $\partialΩ_0$, we show that there exists a weak solution to the null mean curvatu…

Study stability of surfaces in spacetimes, proving new estimates and theorems.

Small deformations of marginally outer trapped surfaces (MOTS) are studied by using the stability operator introduced by Andersson-Mars-Simon. Novel formulae for the principal eigenvalue are presented. A characterization of the many marginally outer trapped tubes (MOTT) passing through a given MOTS is given, and the po…

TreeDSB solves mOT problems on tree-structured costs for Wasserstein barycenters.

MOTS improves Thompson sampling to match minimax bounds for bandit problems.

Vacuum gravity shows black holes can form without collapse.

We prove dual attainment for multi-asset financial derivatives pricing.

The problem of Multiple Object Tracking (MOT) consists in following the trajectory of different objects in a sequence, usually a video. In recent years, with the rise of Deep Learning, the algorithms that provide a solution to this problem have benefited from the representational power of deep models. This paper provid…

Study stability and rigidity of axisymmetric marginally outer trapped surfaces.

We study the complexity of approximating the multimarginal optimal transport (MOT) distance, a generalization of the classical optimal transport distance, considered here between $m$ discrete probability distributions supported each on $n$ support points. First, we show that the standard linear programming (LP) represe…

A drone-based MOT algorithm tracks vehicles using neural network detections and TPMBM filter.

We introduce a new geometric evolution equation for hypersurfaces in asymptotically flat spacetime initial data sets, that unites the theory of marginally outer trapped surfaces (MOTS) with the study of inverse mean curvature flow in asymptotically flat Riemannian manifolds. A theory of weak solutions is developed usin…

New groupoids generalize classical motion and mapping classes.

New algorithms compute robustness bounds for multiclass classification models.

Constructs initial data leading to apparent horizons and tests Penrose Inequality.

In [5], a rigidity result was obtained for outermost marginally outer trapped surfaces (MOTSs) that do not admit metrics of positive scalar curvature. This allowed one to treat the "borderline case" in the author's work with R. Schoen concerning the topology of higher dimensional black holes [8]. The proof of this rigi…

Unified Kantorovich duality for multimarginal optimal transport on Polish spaces.

We prove some related results concerning blow-up solutions for the Jang equation. First: it has been shown that, given an outermost marginally outer trapped surface (MOTS) Σ, there exists a solution to Jang's equation which blows up at Σ. Here we show that in addition, large classes of spherically symmetric initial dat…

Online Multi-Object Tracking (MOT) from videos is a challenging computer vision task which has been extensively studied for decades. Most of the existing MOT algorithms are based on the Tracking-by-Detection (TBD) paradigm combined with popular machine learning approaches which largely reduce the human effort to tune a…

For an admissible class of smooth compact initial data sets with boundary, we prove a comparison theorem between the Wang/Liu-Yau quasi-local mass of the boundary and the Hawking mass of strictly minimizing hulls in the Jang graphs of the domain. Using this, we prove a quasi-local Penrose inequality that involves these…

We solve Einstein vacuum equations in a spacetime region up to the "center" of gravitational collapse. Within this region, we construct a sequence of marginally outer trapped surfaces (MOTS) with areas going to zero. These MOTS form a marginally outer trapped tube (apparent horizon). It emerges from a point and is smoo…

Study of null mean curvature flow on de Sitter lightcone, related to 2d-Ricci flow.

The paper proves density and positive mass theorems for incomplete manifolds.

Study bounds financial path expectations using martingale distributions.

Study rigidity in Penrose's singularity theorem with weakly trapped surfaces.

New positive mass theorems for ALH manifolds with toroidal ends.

New security patch for object tracking in self-driving cars mitigates vulnerabilities.

Obstructs complete metrics with positive scalar curvature on non-compact manifolds.

We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be approximated using linear programming (LP) problems which result from a discretisa…

Develops a new duality between entropy martingale optimal transport and nonlinear pricing-hedging.