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In this paper, we investigate the elastic scattering of an electron by a Yukawa potential within the framework of non-commutative (NC) geometry. We first derive the NC correction to the Yukawa potential at leading order in the NC parameter, resulting in a modified potential resembling a screened Kratzer potential. This potential reduces to the standard Kratzer form when considering the NC correction to the Coulomb potential. Subsequently, we calculate the NC correction to the electron scattering amplitude using the first-order Born approximation. We then analyze the effects of NC geometry on both the differential and total cross sections for elastic scattering. Our results indicate that non-commutativity enhances the differential cross section at small scattering angles and naturally gives rise to a Kratzer-like potential, reflecting the quantum nature of spacetime. Additionally, we establish a direct relationship between the system's energy level and the bound on the NC parameter. Specifically, for an ultra-relativistic incident electron scattering by a heavy molecule, we derive a new lower bound on $\Theta$ of the order of $10^{-28}\,\text{m}$.

In this work, we investigate the decoding of Low-Density Parity-Check (LDPC) codes using informed dynamic scheduling algorithms that require a reduced number of iterations. In particular, we devise the weighted residual layered belief propagation (WR-LBP) decoding algorithm, which exploits the residual within a structured layer framework to speed the number of required decoding iterations. The proposed WR-LBP algorithm is assessed against important LDPC decoding algorithms, in terms of the number of iterations required for convergence and the bit error rates., Comment: 5 figures, 7 pages

We present a coil system designed to generate a highly uniform magnetic field for the n2EDM experiment at the Paul Scherrer Institute. It consists of a main $B_0$ coil and a set of auxiliary coils mounted on a cubic structure with a side length of 273 cm, inside a large magnetically shielded room (MSR). We have assembled this system and characerized its performances with a mapping robot. The apparatus is able to generate a 1 $\mu$ T vertical field with a relative root mean square deviation $\sigma$ ($B_z$)/$B_z$ = 3 $\times$ $10^{-5}$ over the volume of interest, a cylinder of radius 40 cm and height 30 cm. This level of uniformity overcomes the n2EDM requirements, allowing a measurement of the neutron Electric Dipole Moment with a sensitivity better than 1 $\times$ $10^{-27}$ ecm., Comment: 20 pages, 13 figures

We construct initial data suitable for the Kerr stability conjecture, that is, solutions to the constraint equations on a spacelike hypersurface with boundary entering the black hole horizon that are arbitrarily decaying perturbations of a Kerr initial data set. This results from a more general perturbative construction on any asymptotically flat initial data set with the topology of $\mathbb{R}^3\setminus\{r<1\}$ enjoying some analyticity near and at the boundary. In particular, we design a suitable mixed boundary condition for the elliptic operator of the conformal method in order to exclude the Killing initial data sets (KIDS)., Comment: 26 pages

In this paper, we study the stability of geodesic motion for both massive and massless particles using Lyapunov exponents in the non-commutative (NC) Schwarzschild black hole (SBH) via the gauge theory of gravity. As a first step, we investigate the both time-like and null radial motion of particles, the mean result in NC geometry shows that the particles take infinity proper time to reach the NC singularity (infinite time affine parameter framework for photons). The proper/coordinate time of Lyapunov exponents and their ratio of time-like geodesic for the circular motion of this black hole shows a new behavior, which describes a new range of stable circular orbits between unstable ones. Then we analyze the circular motion of photons, where the result shows a new photon sphere near the event horizon which is not allowed in the commutative case, and the Lyapunov exponent is expressed in this geometry, where this confirms the instability of the outer photon sphere and the stability of the inner one. Finally, we check the effect of the non-commutativity on the shadow radius of the SBH, where we show the similarity between the non-commutativity and the black hole mass., Comment: 20 pages, 16 figures

Offline reinforcement learning algorithms have proven effective on datasets highly connected to the target downstream task. Yet, leveraging a novel testbed (MOOD) in which trajectories come from heterogeneous sources, we show that existing methods struggle with diverse data: their performance considerably deteriorates as data collected for related but different tasks is simply added to the offline buffer. In light of this finding, we conduct a large empirical study where we formulate and test several hypotheses to explain this failure. Surprisingly, we find that scale, more than algorithmic considerations, is the key factor influencing performance. We show that simple methods like AWAC and IQL with increased network size overcome the paradoxical failure modes from the inclusion of additional data in MOOD, and notably outperform prior state-of-the-art algorithms on the canonical D4RL benchmark.

Given a generic solution $\mathbf{g}_0$ of the Einstein-null dusts system without restriction on the number of dusts, we construct families of solutions $(\mathbf{g}_\lambda)_{\lambda\in(0,1]}$ of the Einstein vacuum equations such that $\mathbf{g}_\lambda-\mathbf{g}_0$ and $\partial(\mathbf{g}_\lambda-\mathbf{g}_0)$ converges respectively strongly and weakly to 0 when $\lambda\to0$. Our construction, based on a multiphase geometric optics ansatz, thus extends the validity of the reverse Burnett conjecture without symmetry to a large class of massless kinetic spacetimes. In order to deal with the finite but arbitrary number of direction of oscillations we work in a generalised wave gauge and control precisely the self-interaction of each wave but also the interaction of waves propagating in different null directions, relying crucially on the non-linear structure of the Einstein vacuum equations. We also provide the construction of oscillating initial data solving the vacuum constraint equations and which are consistent with the spacetime ansatz., Comment: 67 pages

We construct and parametrize solutions to the constraint equations of general relativity in a neighborhood of Minkowski spacetime with arbitrary prescribed decay properties at infinity. We thus provide a large class of initial data for the results on stability of Minkowski which include a mass term in the asymptotics. Due to the symmetries of Minkowski, a naive linear perturbation fails. Our construction is based on a simplified conformal method, a reduction to transverse traceless perturbations and a nonlinear fixed point argument where we face linear obstructions coming from the cokernels of both the linearized constraint operator and the Laplace operator. To tackle these obstructions, we introduce a well-chosen truncated black hole around which to perturb. The control of the parameters of the truncated black hole is the most technical part of the proof, since its center of mass and angular momentum could be arbitrarily large., Comment: 86 pages

This paper presents a systematic design of an active disturbance rejection control (ADRC) system for unmanned tracked vehicles (UTVs) in leader-follow formation. Two ADRC controllers are designed for the lateral and the longitudinal channels of the UTV based on control errors in the cross-track and the along-track directions. Through simulations, the proposed ADRC approach is first shown to outperform the conventional PI/PID controllers in scenarios involving sudden changes in the leader motion dynamics, slippage disturbances, and measurement noise. Then, a comprehensive experimental validation of the proposed leader-follower control is performed using a laboratory UTV equipped with a camera and laser sensors (to enable the calculation of error signals). In order to provide more effective interaction between the human (leader) and the UTV (follower) during the leader-follower task, a camera-based subsystem for human pose recognition is developed and deployed. Finally, the experimental results obtained outdoors demonstrate that the proposed ADRC-based leader-follower UTV control system achieves high tracking capabilities, robustness against slippage disturbances, and adaptability to changing environmental conditions.

In this work, we investigate the phase transition of the Schwarzschild black hole (SBH) inside an isothermal spherical cavity in the context of the non-commutative (NC) gauge theory of gravity, by using the Seiberg-Witten (SW) map and the star product. Firstly, we compute the NC correction to the Hawking temperature and derive the logarithmic correction to the entropy, then we derive the local temperature and local energy of NC SBH in isothermal cavity. Our results show that the non-commutativity removes the commutative divergence behavior of temperature, and prevents the SBH from the complete evaporation, which leads to a remnant black hole, and this geometry has predicted a minimal length in the order of Planck scale $\Theta\sim l_{planck}$. Therefore, the thermodynamic stability and phase transition is studied by analyzing the behavior of the local heat capacity and the Helmholtz free energy in the NC spacetime, where the results show that, the NC SBH has a two second-order phase transition and one first-order phase transition, with two Hawking-Page phase transition in the NC gauge theory., Comment: 9 pages, 5 figures

Offline Goal-Conditioned Reinforcement Learning (GCRL) is tasked with learning to achieve multiple goals in an environment purely from offline datasets using sparse reward functions. Offline GCRL is pivotal for developing generalist agents capable of leveraging pre-existing datasets to learn diverse and reusable skills without hand-engineering reward functions. However, contemporary approaches to GCRL based on supervised learning and contrastive learning are often suboptimal in the offline setting. An alternative perspective on GCRL optimizes for occupancy matching, but necessitates learning a discriminator, which subsequently serves as a pseudo-reward for downstream RL. Inaccuracies in the learned discriminator can cascade, negatively influencing the resulting policy. We present a novel approach to GCRL under a new lens of mixture-distribution matching, leading to our discriminator-free method: SMORe. The key insight is combining the occupancy matching perspective of GCRL with a convex dual formulation to derive a learning objective that can better leverage suboptimal offline data. SMORe learns scores or unnormalized densities representing the importance of taking an action at a state for reaching a particular goal. SMORe is principled and our extensive experiments on the fully offline GCRL benchmark composed of robot manipulation and locomotion tasks, including high-dimensional observations, show that SMORe can outperform state-of-the-art baselines by a significant margin., Comment: Published at International Conference of Learning Representations (ICLR) 2024. 26 pages

In this Letter, we present the first study of the Hawking radiation as a tunneling process in the noncommutative (NC) gauge theory of gravity. First, we reconstruct the non-commutative Schwarzschild black hole in the gauge theory of gravity, using the Seiberg-Witten map and the star product. Then, we calculate the emission spectrum of the outgoing massless particles, using the quantum tunneling mechanism. In first case, we calculate the tunneling rate of massless particles across the event horizon of the non-commutative Schwarzschild black hole with lower frequency, where the obtained results show a pure thermal radiation, where we find that the Hawking temperature is the same in the two approaches; the classical thermodynamics and the quantum tunneling approach which indicate the equivalence between these two in the NC spacetime. However, in the case of masseless particles emission with large frequency we take into account the conservation of energy.The tunneling rate deviates from the pure thermal radiation, but it's consistent with an underlying unitary quantum theory, then we find it related to the change in the black hole entropy, where this relation show a logarithmic correction to the entropy in this geometry. Moreover, we obtain the NC density number of the particles emission and finally, we discuss the results., Comment: 7 pages, 5 figures

This paper introduces constrained correlated equilibrium, a solution concept combining correlation and coupled constraints in finite non-cooperative games. In the general case of an arbitrary correlation device and coupled constraints in the extended game, we study the conditions for equilibrium. In the particular case of constraints induced by a feasible set of probability distributions over action profiles, we first show that canonical correlation devices are sufficient to characterize the set of constrained correlated equilibrium distributions and provide conditions of their existence. Second, it is shown that constrained correlated equilibria of the mixed extension of the game do not lead to additional equilibrium distributions. Third, we show that the constrained correlated equilibrium distributions may not belong to the polytope of correlated equilibrium distributions. Finally, we illustrate these results through numerical examples.

A common setting in multitask reinforcement learning (RL) demands that an agent rapidly adapt to various stationary reward functions randomly sampled from a fixed distribution. In such situations, the successor representation (SR) is a popular framework which supports rapid policy evaluation by decoupling a policy's expected discounted, cumulative state occupancies from a specific reward function. However, in the natural world, sequential tasks are rarely independent, and instead reflect shifting priorities based on the availability and subjective perception of rewarding stimuli. Reflecting this disjunction, in this paper we study the phenomenon of diminishing marginal utility and introduce a novel state representation, the $\lambda$ representation ($\lambda$R) which, surprisingly, is required for policy evaluation in this setting and which generalizes the SR as well as several other state representations from the literature. We establish the $\lambda$R's formal properties and examine its normative advantages in the context of machine learning, as well as its usefulness for studying natural behaviors, particularly foraging.