arXiv research

New definitions of conserved quantities at null infinity resolve ambiguities in general relativity.

New neural network enforces mass conservation for better ice flow predictions.

CNFs learn on manifolds using PPD, improving likelihood and sample quality.

MC-LSTM extends LSTM to conserve mass in neural networks.

Formulae track evolution of angular momentum and center of mass at null infinity.

The study extends conserved quantities theory to non-compact boundary initial data sets.

Given a three dimensional pseudo-Einstein CR manifold $(M,T^{1,0}M,θ)$, we study the existence of a contact structure conformal to $θ$ for which the logarithmic Hardy-Littlewood-Sobolev (LHLS) inequality holds. Our approach closely follows \cite{Ok1} in the Riemannian setting. For this purpose, we introduce the notion …

We define quasi-local conserved quantities in general relativity by using the optimal isometric embedding in [26] to transplant Killing fields in the Minkowski spacetime back to the 2-surface of interest in a physical spacetime. To each optimal isometric embedding, a dual element of the Lie algebra of the Lorentz group…

In this article, we consider the limit of quasi-local conserved quantities [31,9] at the infinity of an asymptotically hyperbolic initial data set in general relativity. These give notions of total energy-momentum, angular momentum, and center of mass. Our assumption on the asymptotics is less stringent than any previo…

For a closed surface M with metric g, the Robin mass m(p) at the point p is the value of the Green function G(p,q) at p=q after the logarithmic singularity has been removed. The Laplacian-mass is the average value of the Robin mass, minus the value of the Robin mass for the round sphere of the same area. The Laplacian-…

DJIA is tested whether it can be described as a mechanical system conserving total energy with K (=v*v/2) + U, where U is calculated as the negative of work done by force obtained in terms of the second derivative of price, assuming unit mass.

New optimal transport method handles mass creation and destruction.

This work removes logarithmic singularities from hyperboloidal initial data without creating new ones.

Through the main example of the Ornstein-Uhlenbeck semigroup, the Bakry-Emery criterion is presented as a main tool to get functional inequalities as Poincaré or logarithmic Sobolev inequalities. Moreover an alternative method using the optimal mass transportation, is also given to obtain the logarithmic Sobolev inequa…

In the first half of this article, we survey the new quasi-local and total angular momentum and center of mass defined in [9] and summarize the important properties of these definitions. To compute these conserved quantities involves solving a nonlinear PDE system (the optimal isometric embedding equation), which is ra…

The study examines correlations of logarithms of integers at different scalings.

We introduce Minimal Achievable Sufficient Statistic (MASS) Learning, a training method for machine learning models that attempts to produce minimal sufficient statistics with respect to a class of functions (e.g. deep networks) being optimized over. In deriving MASS Learning, we also introduce Conserved Differential I…

For a spacelike 2-surface in spacetime, we propose a new definition of quasi-local angular momentum and quasi-local center of mass, as an element in the dual space of the Lie algebra of the Lorentz group. Together with previous defined quasi-local energy-momentum, this completes the definition of conserved quantities i…

We define the "sum of squares of the wavelengths" of a Riemannian surface (M,g) to be the regularized trace of the inverse of the Laplacian. We normalize by scaling and adding a constant, to obtain a "mass", which is scale invariant and vanishes at the round sphere. This is an anlaog for closed surfaces of the ADM mass…

New method improves long-term forecasting of stochastic dynamical systems.

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…

Local mass perspective on Bayesian inference

Sharp $L^p$-logarithmic-Sobolev inequalities on submanifolds with applications to hypercontractivity.

USD algorithm transports distributions with or without mass conservation.

Study revisits Bondi mass and discusses memory effect in polyhomogeneous spacetimes.

The paper finds that circles and logarithmic spirals are the only constant-speed ramps for a specific force field.

Honest traders can outperform insiders in a Black-Scholes market with positive probability.

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equatio…

Research examines correlations of complex logarithms of lattice points, showing level repulsion and Poissonian behavior.

Charge measurements for instantons and gravitational perturbations.

LFlows model fluid densities and velocities using invertible maps that satisfy the continuity equation.

Estimates missing mass in Markovian sequences with linear runtime and near-optimal risk.

New formulas for geodesics on Stiefel and flag manifolds using trust-region method.

SSINNs learn Hamiltonian systems from data with interpretable, low-memory models.

An efficient algorithm for Riemannian logarithm on Stiefel manifold family.

New definition of angular momentum avoids supertranslation ambiguity.

Sharp bounds on heat kernel derivatives on incomplete manifolds.

The paper studies Kähler metrics from finite Monge-Ampère mass exhaustion functions.

New algorithm reduces pricing error by a factor of T^2/3.

We study the space of Killing fields on the four dimensional AdS spacetime $AdS^{3,1}$. Two subsets $\mathcal{S}$ and $\mathcal{O}$ are identified: $\mathcal{S}$ (the spinor Killing fields) is constructed from imaginary Killing spinors, and $\mathcal{O}$ (the observer Killing fields) consists of all hypersurface orthog…

Prove rigidity and classification results for quasilinear Liouville equation on manifolds with nonnegative Ricci curvature.

Closed and broken electromagnetic orbits in Kerr-Newman spacetime

The space C of conservative vertex colorings (over a field F) of a countable, locally finite graph G is introduced. The subspace of based colorings is shown to be isomorphic to the bicycle space of the graph. For graphs G with a free Z^d-action by automorphisms, C is a finitely generated module over the polynomial ring…

The z-transform technique is used to investigate the model for distribution of high-tax payers, which is proposed by two of the authors (K. Y and S. M) and others. Our analysis shows an asymptotic power-law of this model with the exponent -5/2 when a total ``mass'' has a certain critical value. Below the critical value…

A new method calculates fractional moments using the moment-generating function.

Quadratic memory is essential for optimal convex optimization queries.

Study explores warped geometries of tensor manifolds, finding non-geodesic connections for some parameters.

Diagonal Frog: High-order positivity-preserving FD schemes for anisotropic Fokker-Planck equations