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Social network analysis is pivotal for organizations aiming to leverage the vast amounts of data generated from user interactions on social media and other digital platforms. These interactions often reveal complex social structures, such as tightly-knit groups based on common interests, which are crucial for enhancing service personalization or fraud detection. Traditional methods like community detection and graph matching, while useful, often fall short of accurately identifying specific groups of users. This paper introduces a novel framework specifically designed to identify groups of users within transactional graphs by focusing on the contextual and structural nuances that define these groups.

We introduce VeloxQ, a fast and efficient solver for Quadratic Unconstrained Binary Optimization (QUBO) problems, which are central to numerous real-world optimization tasks. Unlike other physics-inspired approaches to optimization problems, such as quantum annealing and quantum computing, VeloxQ does not require substantial progress of technology to unlock its full potential. We benchmark VeloxQ against the state-of-the-art QUBO solvers based on emerging technologies. Our comparison includes quantum annealers, specifically D-Wave's Advantage, and Advantage2 prototype platforms, the digital-quantum algorithm designed to solve Higher-Order Unconstrained Binary Optimization (HUBO) developed by Kipu Quantum, physics-inspired algorithms: Simulated Bifurcation and Parallel Annealing and an algorithm based on tropical tensor networks. We also take into account modern developments of conventional algorithms: Branch and Bound algorithm, an optimal implementation of the brute-force algorithm and BEIT QUBO solver. Our results show that VeloxQ not only matches but often surpasses the mentioned solvers in solution quality and runtime. Additionally, VeloxQ demonstrates excellent scalability being the only solver capable of solving large-scale optimization problems, including up to $2\times 10^{8}$ sparsely connected variables, that are currently intractable for its competitors. These findings position VeloxQ as a powerful and practical tool for tackling large-scale QUBO and HUBO problems, offering a compelling alternative to existing quantum and classical optimization methods.

This paper explores ideas and provides a potential roadmap for the development and evaluation of physics-specific large-scale AI models, which we call Large Physics Models (LPMs). These models, based on foundation models such as Large Language Models (LLMs) - trained on broad data - are tailored to address the demands of physics research. LPMs can function independently or as part of an integrated framework. This framework can incorporate specialized tools, including symbolic reasoning modules for mathematical manipulations, frameworks to analyse specific experimental and simulated data, and mechanisms for synthesizing theories and scientific literature. We begin by examining whether the physics community should actively develop and refine dedicated models, rather than relying solely on commercial LLMs. We then outline how LPMs can be realized through interdisciplinary collaboration among experts in physics, computer science, and philosophy of science. To integrate these models effectively, we identify three key pillars: Development, Evaluation, and Philosophical Reflection. Development focuses on constructing models capable of processing physics texts, mathematical formulations, and diverse physical data. Evaluation assesses accuracy and reliability by testing and benchmarking. Finally, Philosophical Reflection encompasses the analysis of broader implications of LLMs in physics, including their potential to generate new scientific understanding and what novel collaboration dynamics might arise in research. Inspired by the organizational structure of experimental collaborations in particle physics, we propose a similarly interdisciplinary and collaborative approach to building and refining Large Physics Models. This roadmap provides specific objectives, defines pathways to achieve them, and identifies challenges that must be addressed to realise physics-specific large scale AI models.

We study transport in the spin chains by employing the Thouless approach based on the level sensitivity to the boundary conditions, $R$. Although spin transport in the integrable easy-axis XXZ model is diffusive, corresponding $R$ is much closer to ballistic chains than to chaotic diffusive systems. In the case of the grand canonical ensemble this observation can be rigorously justified, while in the case of the canonical ensemble it can be demonstrated by numerical calculations. Integrability breaking perturbation (IBP) strongly reduces $R$ which reveals a pronounced minimum at the crossover from anomalous diffusive to normal dissipative transport. This minimum coincides with the onset of the universality of the random matrix theory. Results for various IBP suggest a discontinuous jump of the spin conductivity in the thermodynamic limit, and moreover that its value universally decreases when the strength of IBP decreases., Comment: 8 pages, 8 figures (including Supplementary Material)

A significant part of the Milky Way (MW) dwarf galaxies orbit within a Vast POlar Structure (VPOS) that is perpendicular to the Galactic disk, whose origin has not yet been identified. It includes the Large Magellanic Cloud (LMC) and its six dynamically associated dwarf galaxies. Andromeda Galaxy (M31) experienced a major merger two to three billion years ago, and its accurate modelling predicts that an associated tidal tail is pointing toward the Galaxy. Here, we have tested a possible association between M31 tidal tail particles and MW dwarf galaxies, focusing first on the LMC and its associated dwarfs since they are less affected by ram pressure. We traced back these dwarf galaxy orbits by one billion years and calculated their association to the tidal tail particles in the 6D phase space, based on their proper motion from Gaia DR3. We find that for low-mass MW models (total mass smaller than 5 $\times 10^{11} M_{\odot}$), the separation in the 6D space can be less than 1$\sigma$ for most of the M31 modelling, while an important degree of freedom is provided by the still unknown proper motion of M31. We further discover that many other dwarfs could also be associated with the M31 tidal tails if their motions had been radially slowed down, as expected from the ram pressure exerted by the MW corona. This intriguing coincidence could explain the origin of the VPOS, which came from a matter exchange between M31 and MW., Comment: A&A, accepted 20th December 2024, 10 pages, 9 figures, and Appendix A, B, C, D & E