arXiv research

The paper extends a theorem about momentum maps to singular symplectic spaces.

SPI-Optimizer separates momentum term to eliminate oscillation in stochastic optimization.

Integrates momentum into RNNs to improve training.

Inverts rank m symmetric tensor fields using line integrals.

Paper extends Noether's Theorem to nonholonomic systems, proving conserved momentum.

Researchers prove CWY angular momentum is supertranslation invariant in double null gauge.

Unified approach to constructing integrable systems using Stäckel lifts.

New approach to QFT divergences uses curved momentum space.

Characterizes the range of a tensor field transform in Schwartz space.

This paper analyzes momentum Q-learning with finite-sample guarantees.

Integrates momentum into SMoE for improved stability and robustness.

In this paper we prove rigidity theorems for Poisson Lie group actions on Poisson manifolds. In particular, we prove that close infinitesimal momentum maps associated to Poisson Lie group actions are equivalent using a normal form theorem for SCI spaces. When the Poisson structure of the acted manifold is integrable, t…

Unified AdaGrad with momentum accelerates stochastic optimization in non-convex settings.

The article constructs a new map for fluid dynamics and reinterprets linking numbers.

Introduces group-valued momentum maps for symplectic fiber bundles.

Investigates integrable systems with linear periodic integral for e(3) Lie algebra.

Dyna optimizes momentum for stochastic optimization of neural networks.

This paper optimizes cryptocurrency portfolios by integrating sentiment analysis with technical indicators.

In this paper, we propose a geometric integrator for nonholonomic mechanical systems. It can be applied to discrete Lagrangian systems specified through a discrete Lagrangian defined on QxQ, where Q is the configuration manifold, and a (generally nonintegrable) distribution in TQ. In the proposed method, a discretizati…

The classical notion of center of mass for an isolated system in general relativity is derived from the Hamiltonian formulation and represented by a flux integral at infinity. In contrast to mass and linear momentum which are well-defined for asymptotically flat manifolds, center of mass and angular momentum seem less …

Study accelerates optimization methods in non-convex problems, but doesn't improve the algorithm's performance.

In these lecture notes, we give a quick account of the theory of Poisson groupoids and Lie bialgebroids. In particular, we discuss the universal lifting theorem and its applications including integration of quasi-Lie bialgebroids, integration of Poisson Nijenhuis structures and Alekseev and Kosmann-Schwarzbach's theory…

New HMC method uses asymmetrical momentum distributions and improves performance.

Boosts adversarial attacks with momentum to improve model robustness.

Study norm-squared of momentum map in infinite dimensions with applications to symplectic geometry.

Study on sub-Riemannian structures in low dimensions, proving non-integrability in some cases.

AdamS uses momentum as a denominator to optimize LLMs efficiently.

Joachimsthal integrals characterize conics in various geometries.

The paper studies a natural $n$-dimensional generalization of the classical nonholonomic Chaplygin sphere problem. We prove that for a specific choice of the inertia operator, the restriction of the generalized problem onto zero value of the SO(n-1)-momentum mapping becomes an integrable Hamiltonian system after an app…

A new method uses trivialized momentum to generate data on Lie groups.

INO learns physical models with momentum conservation laws.

By using variational calculus and exterior derivative formalism, we proposed in two previous joint papers with S. Siparov a new geometric approach for electromagnetism in pseudo-Finsler spaces. In the present paper, we provide more details, especially regarding generalized currents, the domain of integration and gauge …

The eigenvalue problem for the Sen--Witten operator on closed spacelike hypersurfaces is investigated. The (square of its) eigenvalues are shown to be given exactly by the 3-surface integral appearing in the expression of the total energy-momentum of the matter+gravity systems in Witten's energy positivity proof. A sha…

We prove the universal lifting theorem: for an $α$-simply connected and $α$-connected Lie groupoid $\gm$ with Lie algebroid $A$, the graded Lie algebra of multi-differentials on $A$ is isomorphic to that of multiplicative multi-vector fields on $\gm$. As a consequence, we obtain the integration theorem for a quasi-Lie …

Novel method for solving ODEs on k-polysymplectic manifolds.

Zero-energy orbits in the Kepler-Heisenberg problem are self-similar and stratify into three families.

The paper defines and studies almost complex structures on product manifolds and their integrability.

CoolMomentum combines momentum and Simulated Annealing for deep learning optimization.

We study coordinate-invariance of some asymptotic invariants such as the ADM mass or the Chruściel-Herzlich momentum, given by an integral over a "boundary at infinity". When changing the coordinates at infinity, some terms in the change of integrand do not decay fast enough to have a vanishing integral at infinity; bu…

Novel approach to dissipative prolongations of multipeakons in Camassa-Holm equation.

In this paper we study Poisson actions of complete Poisson groups, without any connectivity assumption or requiring the existence of a momentum map. For any complete Poisson group $G$ with dual $G^\star$ we obtain a suitably connected integrating symplectic double groupoid $\calS$. As a consequence, the cotangent lift …

MiM-StocR combines momentum indicators and adaptive ranking loss for better stock recommendation.

New minibatching strategy reduces stochastic gradient bias in optimisation.

The study finds that factor momentum is significant only at short lags compared to stock momentum.

Study focuses on classifying special geometric structures.

Integrates uncertainty of loss landscape into stochastic optimization.

We test the price momentum effect in the Korean stock markets under the momentum universe shrinkage to subuniverses of the KOSPI 200. Performance of the momentum strategy is not homogeneous with respect to change of the momentum universe. It is found that some submarkets generate the higher momentum returns than other …

Quantizes area of surfaces in loop quantum gravity.