A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New definitions of conserved quantities at null infinity resolve ambiguities in general relativity.
New neural network enforces mass conservation for better ice flow predictions.
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.
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…
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.
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…
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…
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…
USD algorithm transports distributions with or without mass conservation.
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…
CNFs learn on manifolds using PPD, improving likelihood and sample quality.
Charge measurements for instantons and gravitational perturbations.
LFlows model fluid densities and velocities using invertible maps that satisfy the continuity equation.
SSINNs learn Hamiltonian systems from data with interpretable, low-memory models.
New definition of angular momentum avoids supertranslation ambiguity.
We study the space of Killing fields on the four dimensional AdS spacetime . Two subsets and are identified: (the spinor Killing fields) is constructed from imaginary Killing spinors, and (the observer Killing fields) consists of all hypersurface orthog…
Closed and broken electromagnetic orbits in Kerr-Newman spacetime
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…
Diagonal Frog: High-order positivity-preserving FD schemes for anisotropic Fokker-Planck equations
Theoretical analysis confirms non-conservative algorithms can converge to optimal policies.
Study finds conserved quantities for two types of curves on conformal sphere.
Survey on conservation laws for geometric PDEs.
The article discusses conservation laws for polyharmonic maps and their applications.
Paper presents a reduction-based framework for conservative bandits and RL with improved lower and upper bounds.
I consider the existence and structure of conservation laws for the general class of evolutionary scalar second-order differential equations with parabolic symbol. First I calculate the linearized characteristic cohomology for such equations. This provides an auxiliary differential equation satisfied by the conservatio…
Non-trivial conservation law found for a specific system.
This work connects symmetries and conserved quantities in machine learning.
Proposes a conservative exploration method for RL agents.
Conservation law for weakly harmonic mappings in high dimensions.
The conservation laws of the third order quasilinear scalar evolution equations are considered via differential system and characteristic cohomology. We find a subspace of 2 forms in the infinite prolonged space in which every conservation law has a unique representative. The structure of this subspace naturally gives …
Given a vector field on a manifold M, we define a globally conserved quantity to be a differential form whose Lie derivative is exact. Integrals of conserved quantities over suitable submanifolds are constant under time evolution, the Kelvin circulation theorem being a well-known special case. More generally, conserved…
Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satisfied to obtain reliable results. However, standard machine learning algorithm…
We study higher-order conservation laws of the non-linearizable elliptic Poisson equation as elements of the characteristic cohomology of the associated exterior differential system. The theory of characteristic cohomology determines a normal form for diffe…
New conservation laws found for polyharmonic maps in critical dimension.
Calibration of stochastic local volatility (SLV) models to their underlying local volatility model is often performed by numerically solving a two-dimensional non-linear forward Kolmogorov equation. We propose a novel finite volume (FV) discretization in the numerical solution of general 1D and 2D forward Kolmogorov eq…
A challenging problem in complex networks is the network reconstruction problem from data. This work deals with a class of networks denoted as conserved networks, in which a flow associated with every edge and the flows are conserved at all non-source and non-sink nodes. We propose a novel polynomial time algorithm to …
A new MFG framework for evolving clusters from Gaussian mixtures.
The paper studies symmetries and conservation laws of non-diagonalisable hydrodynamic systems.
The X-ADM mass is shown to be equivalent to the ADM mass, proving the X-positive mass theorem in all dimensions.
We present a connection between the Killing fields that arise in the loop-group approach to integrable systems and conservation laws viewed as elements of the characteristic cohomology. We use the connection to generate the complete set of conservation laws (as elements of the characteristic cohomology) for the Tzitzei…
A new algorithm balances exploration and exploitation in online decision-making.
We obtain necessary and sufficient conditions for the existence of "conservation laws" on null hypersurfaces for the wave equation on general four-dimensional Lorentzian manifolds. Examples of null hypersurfaces exhibiting such conservation laws include the standard null cones of Minkowski spacetime and the degenerate …