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Heavy flavored hydrogen molecule systems
Hui-Min Yang, Yao Ma, Shi-Lin Zhu
https://arxiv.org/abs/2507.21498 https://arxiv.org/pdf/2507.21498 https://arxiv.org/html/2507.21498
arXiv:2507.21498v1 Announce Type: new
Abstract: This study provides a comprehensive analysis of $S$-wave exotic hydrogen-like three-body systems ($pp\mu^-$, $pp\tau^-$, $\mu^-\mu^-p$, $\tau^-\tau^-p$, $p\mu^-\tau^-$) with spin-parity $J^P = 1/2^ $ and $3/2^ $, and four-body systems ($pp\mu^-\mu^-$, $pp\tau^-\tau^-$) with $J^P = 0^ $, $1^ $, and $2^ $. We use complex scaling and Gaussian expansion methods to solve the complex-scaled Schr\"{o}dinger equation and obtain possible bound and quasi-bound states. The resulting binding energies range from $-33.8$~keV to $-340$~eV. Notably, we present the first theoretical estimation of the bound-state energy levels of $pp\mu^-\mu^-$ and $pp\tau^-\tau^-$, which is of significant importance for understanding exotic few-body Coulomb systems. We further analyze spin configurations and root-mean-square radii to elucidate the spatial structure of these bound and quasi-bound states. Our results reveal that $K$-type spatial configurations play a crucial role in accurately describing bound and quasi-bound states in the hydrogen-molecule-like systems $pp\mu^-\mu^-$ and $pp\tau^-\tau^-$. Incorporating $K$-type configurations significantly alters the mass spectra of these states. Future muon colliders and muon facilities may offer promising platforms for the possible copious production of such heavy flavored hydrogen molecules and molecular ions. For instance, scattering processes such as $2\mu^- \mathrm{H_2} \to \mathrm{H_{2\mu}} 2e^-$, $\mu^- \mathrm{H_2} \to \mathrm{H_{\mu e}} e^-$, and $\mu^- \mathrm{H_2^ } \to \mathrm{H_{2\mu}^ } e^-$ could be utilized, facilitating detailed studies of intriguing states such as $\mathrm{H_{2\mu}}$, $\mathrm{H_{\mu e}}$, and $\mathrm{H_{2\mu}^ }$.
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Systematic Hazard Analysis for Frontier AI using STPA
Simon Mylius
https://arxiv.org/abs/2506.01782 https://arxiv.org/pdf/2506.01782

Systematic Hazard Analysis for Frontier AI using STPA
All of the frontier AI companies have published safety frameworks where they define capability thresholds and risk mitigations that determine how they will safely develop and deploy their models. Adoption of systematic approaches to risk modelling, based on established practices used in safety-critical industries, has been recommended, however frontier AI companies currently do not describe in detail any structured approach to identifying and analysing hazards. STPA (Systems-Theoretic Process A…

This https://arxiv.org/abs/2407.13257 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Predictive control for nonlinear stochastic systems: Closed-loop guarantees with unbounded noise
We present a stochastic model predictive control framework for nonlinear systems subject to unbounded process noise with closed-loop guarantees. First, we provide a conceptual shrinking-horizon framework that utilizes general probabilistic reachable sets and minimizes the expected cost. Then, we provide a tractable receding-horizon formulation that uses a nominal state to minimize a deterministic quadratic cost and satisfy tightened constraints. Our theoretical analysis demonstrates recursive f…

This https://arxiv.org/abs/2411.06564 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_ees…

Distributionally Robust Adaptive Beamforming
As a fundamental technique in array signal processing, beamforming plays a crucial role in amplifying signals of interest (SoI) while mitigating interference plus noise (IPN). When uncertainties exist in the signal model or the data size of snapshots is limited, the performance of beamformers significantly degrades. In this article, we comprehensively study the conceptual system, theoretical analysis, and algorithmic design for robust beamforming against uncertainties in the assumed snapshot or…

Memory-Driven Bounded Confidence Opinion Dynamics: A Hegselmann-Krause Model Based on Fractional-Order Methods
Meiru Jiang, Wei Su, Guojian Ren, Yongguang Yu
https://arxiv.org/abs/2506.04701

Memory-Driven Bounded Confidence Opinion Dynamics: A Hegselmann-Krause Model Based on Fractional-Order Methods
Memory effects play a crucial role in social interactions and decision-making processes. This paper proposes a novel fractional-order bounded confidence opinion dynamics model to characterize the memory effects in system states. Building upon the Hegselmann-Krause framework and fractional-order difference, a comprehensive model is established that captures the persistent influence of historical information. Through rigorous theoretical analysis, the fundamental properties including convergence …