arXiv research

The paper studies curves in surfaces using flow-spines and apparent contours.

Semi-supervised learning classifies cardiac pathology using motion features from cine MRI.

Study constructs solutions for evolving hypersurfaces using inverse spacetime mean curvature.

It is well-known that the LIE(Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of iso…

Paper studies apparent horizon dynamics and introduces a null comparison principle.

In this paper, we assume that the permanent market impact of metaorders is linear and that the price is a martingale. Those two hypotheses enable us to derive the evolution of the price from the dynamics of the flow of market orders. For example, if the market order flow is assumed to follow a nearly unstable Hawkes pr…

Penrose conjecture proven for specific initial data sets.

Paper proves a generalized Penrose conjecture for flat initial data.

Construct opers with apparent singularities from λ-connections on Riemann surfaces.

In this paper we characterize the intrinsic geometry of apparent horizons (outermost marginally outer trapped surfaces) in asymptotically flat spacetimes; that is, the Riemannian metrics on the two sphere which can arise. Furthermore we determine the minimal ADM mass of a spacetime containing such an apparent horizon. …

Investigate the local geometry of smooth surfaces in 4-space via contact with 2-planes and apparent contours.

Study metrics with specific spectral properties to compute Bartnik and Bartnik-Bray masses efficiently.

Solves Einstein constraint equations on compact manifolds with specified boundaries.

In this paper we find new examples of Riemannian manifolds with outermost apparent horizons with nonspherical topology, in dimensions four and above. More precisely, for any $n,m\ge1$, we construct asymptotically flat, scalar flat Riemannian manifolds containing smooth outermost minimal hypersurfaces with topology $S^n…

Paper analyzes blowup of regularized Jang solutions and constant expansion surfaces.

Causal autoregressive flows enable accurate causal inference and prediction.

This note shows surfaces in stable 3D data are bounded by area and diameter.

We study the long memory of order flow for each of three liquid currency pairs on a large electronic trading platform in the foreign exchange (FX) spot market. Due to the extremely high levels of market activity on the platform, and in contrast to existing empirical studies of other markets, our data enables us to perf…

We prove a conjecture of Tom Ilmanen's and Hubert Bray's regarding the existence of the outermost generalized apparent horizon in an initial data set and that it is outer area minimizing.

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

We establish a Positive Mass Theorem for initial data sets of the Einstein equations having generalized trapped surface boundary. In particular we answer a question posed by R. Wald concerning the existence of generalized apparent horizons in Minkowski space.

Gradient methods work well on overparameterized diagonal linear networks.

Given a submanifold $S \subset \mathbb R^n$ of codimension at least three, we construct an asymptotically Euclidean Riemannian metric on $\mathbb R^n$ with nonnegative scalar curvature for which the outermost apparent horizon is diffeomorphic to the unit normal bundle of $S$.

The paper shows how to create Schwarzschild initial data with degenerate apparent horizons.

Paper proves existence of anisotropic dynamical horizons in gravitational collapse.

For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the ADM mass and the area of an outermost apparent horizon, if the data are restricted suitably. We prove this by generalizing Geroch's proof of monotonicity of the Hawking mass…

Study shows formation of Kerr black holes with complete apparent horizons and proves Penrose inequalities.

Using a proprietary dataset of meta-orders and prediction signals, and assuming a quasi-linear impact model, we deconvolve market impact from past correlated trades and a predictable return component to elicit the temporal dependence of the market impact of a single daily meta-order, over a ten day horizon in various e…

This paper uses probability tensors for efficient path planning in complex scenarios.

This work originates from a heart's images tracking which is to generate an apparent continuous motion, observable through intensity variation from one starting image to an ending one both supposed segmented. Given two images p0 and p1, we calculate an evolution process p(t, \cdot) which transports p0 to p1 by using th…

Reducing volatility proxy improves apparent market correlation dynamics.

Paper introduces a method to assess liquidity risk in meme tokens using entity-linked address analysis.

We prove the Riemannian Penrose conjecture, an important case of a conjecture made by Roger Penrose in 1973, by defining a new flow of metrics. This flow of metrics stays inside the class of asymptotically flat Riemannian 3-manifolds with nonnegative scalar curvature which contain minimal spheres. In particular, if we …

Generalizes Rips' result on hyperbolic spaces to metric spaces, showing collapses for tree metrics.

Paper resolves apparent conflict between group and individual fairness.

New method proves instability of naked singularity and censors it.

Emulator speeds up landslide run-out modeling sensitivity analysis.

We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with an apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to generate such solutions. The method of proof is based on the barrier method used by Ise…

Background doesn't affect personality predictions in deep networks.

Survey of flow-based algorithms for improving clusters.

Rolling systems limit to billiard models with no-slip collisions.

New method transfers causal mechanisms for few-shot domain adaptation.

Bayesian method finds voids in galaxy surveys with deep neural networks.

Viewing a data set such as the clouds of Jupiter, coherence is readily apparent to human observers, especially the Great Red Spot, but also other great storms and persistent structures. There are now many different definitions and perspectives mathematically describing coherent structures, but we will take an image pro…

Bartnik mass is positive and non-decreasing for black holes

In a paper \cite{P} in 1973, R. Penrose made a physical argument that the total mass of a spacetime which contains black holes with event horizons of total area $A$ should be at least $\sqrt{A/16π}$. An important special case of this physical statement translates into a very beautiful mathematical inequality in Riemann…

Order-flow entropy predicts price magnitude without directionality.

The paper addresses causal estimation for text data with apparent overlap violations.