arXiv research

New currents derived from Killing-Yano tensors for gravity.

In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so--called {\em conserved Noether currents}. It turns out that along any section of the relevant gauge--natural bundle this density is the divergence of a skew--symmetric (tenso…

It has been shown that for each Killing-Yano (KY)-form accepted by an $n$-dimensional (pseudo)Riemannian manifold of arbitrary signature, two basic gravitational currents can be defined. Conservation of the currents are explicitly proved by showing co-exactness of the one and co-closedness of the other. Some general ge…

Study connects surface classes to conservation laws.

We prove that under certain assumptions a partial differential equation can be derived from a variational principle. It is well-known from Noether's theorem that symmetries of a variational functional lead to conservation laws of the corresponding Euler-Lagrange equation. We reverse this statement and prove that a diff…

The paper explores symmetries and conserved charges on pre-symplectic manifolds.

RORL improves offline RL robustness with conservative smoothing.

New algorithms ensure policies perform at least as good as a baseline in reinforcement learning.

A gauged bi-differential calculus over an associative (and not necessarily commutative) algebra A is an N-graded left A-module with two covariant derivatives acting on it which, as a consequence of certain (e.g., nonlinear differential) equations, are flat and anticommute. As a consequence, there is an iterative constr…

A necessary and sufficient condition for energy-momentum conservation is proved within a topological, pre-metric approach to classical electrodynamics including magnetic as well as electric charges. The extended Lorentz force, consisting of mutual actions by F=(E, B) on the electric current and G=(H, D) on the magnetic…

We consider the second variational derivative of a given gauge-natural invariant Lagrangian taken with respect to (prolongations of) vertical parts of gauge-natural lifts of infinitesimal principal automorphisms. By requiring such a second variational derivative to vanish, {\em via} the Second Noether Theorem we find t…

When a gauge-natural invariant variational principle is assigned, to determine {\em canonical} covariant conservation laws, the vertical part of gauge-natural lifts of infinitesimal principal automorphisms -- defining infinitesimal variations of sections of gauge-natural bundles -- must satisfy generalized Jacobi equat…

BNRE improves simulation-based inference by producing more conservative posteriors.

Differential conservation laws in Lagrangian field theory are usually related to symmetries of a Lagrangian density and are obtained if the Lie derivative of a Lagrangian density by a certain class of vector fields on a fiber bundle vanishes. However, only two field models meet this property in fact. In gauge theory of…

Major internet companies routinely perform tens of thousands of A/B tests each year. Such large-scale sequential experimentation has resulted in a recent spurt of new algorithms that can provably control the false discovery rate (FDR) in a fully online fashion. However, current state-of-the-art adaptive algorithms can …

CQL learns conservative Q-functions to improve offline RL performance.

In this paper the dynamics of the classical chiral $QCD_{2}$ currents is studied. We describe how the dynamics of the theory can be summarized in an equation of the Lax form, thereby demonstrating the existence of an infinite set of conserved quantities. Next, the $r$ matrix of a fundamental Poisson relation is obtaine…

Study maps research streams in biodiversity finance, identifies key areas.

Homotopy momentum map extends Noether's theorem in general relativity.

This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious argume…

Dynamics of four-dimensional massless fields of all spins is formulated in the Siegel space of complex $4\times 4$ symmetric matrices. It is shown that the unfolded equations of free massless fields, that have a form of multidimensional Schrodinger equations, naturally distinguish between positive- and negative-frequen…

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

Auto-CEI improves LLM reasoning by balancing assertiveness and conservativeness.

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.

The extremely useful method of Malliavin calculus has not yet gained adequate popularity because of the complicated analytic apparatus of this method. The author attempts here to propose a simplified algebraic formalism similar to Malliavin calculus, but based on the notion of creation-annihilation operators instead of…

A new method for releasing AI workflows to avoid premature incorrect results.

This work connects symmetries and conserved quantities in machine learning.

Proposes a conservative exploration method for RL agents.

This study assesses risk concentration in MDB portfolios using Monte Carlo simulations.

Offline RL policies should adapt to unknown aspects of the environment.

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…

We study higher-order conservation laws of the non-linearizable elliptic Poisson equation $\frac{{\partial}^2 u}{\partial z \partial \bar{z}} = -f(u)$ 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.

This paper develops a model of reference-dependent assessment of subjective beliefs in which loss-averse people optimally choose the expectation as the reference point to balance the current felicity from the optimistic anticipation and the future disappointment from the realisation. The choice of over-optimism or over…

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 …

Develops higher-order Euler-Poincaré field equations for principal G-bundles.

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

The paper studies symmetries and conservation laws of non-diagonalisable hydrodynamic systems.

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.