We present an in-depth analysis of the orbital magnetism by means of the so-called modern theory based on the Berry phase across distinct classes of materials-d transition metals, sp metals, and transition metal dichalcogenides-highlighting the microscopic nature of band structure characteristics. We adopt a gauge-covariant formulation of the modern theory proposed in [Lopez et al. Phys. Rev. B 85, 014435 (2012)], which enables the calculation of orbital magnetism in a controlled manner in any chosen gauge of Wannier functions and gives the total contribution as a gauge-invariant measurable. This captures consistently the contributions due to the anomalous position, velocity, and orbital angular momentum of Wannier basis, as well as the contributions due to Hamiltonian such that their sum is gauge-invariant. For d transition metals, we find that the atom-centered approximation captures the majority of the total contribution given by modern theory, which we attribute to localized nature of d electrons. However, 5d metals tend to exhibit larger deviation between the two methods than 3d metals do, as 5d electrons are more delocalized than 3d electrons. On the other hand, sp metals exhibit a strong deviation between the two methods, where large kinetic energy of sp electrons is important. Finally, in 1H-MoS2, we find that the valley orbital moment far exceeds the atomic limit of d electrons due to coherent hybridization between valence and conduction bands in direct band gaps. Our work elucidates the interplay of the chemical nature of electronic orbitals and the effect of band structures in a consistent manner and highlights the role of Berry phase in orbital magnetism. The results suggest a promising direction of orbitronics beyond controlling atomic orbitals, in which the orbital magnetism can be greatly enhanced by exploiting Berry phase.

This study presents the first quantifications of ultrasound attenuation in oral soft tissues using validated standard techniques and serves as foundational step in advancing quantitative ultrasound (QUS) imaging in dentistry. Current standards of care in clinics for diagnosing periodontal diseases such as inflammation are limited by subjectivity, qualitive assessment, and late-stage indication. As a result, the application of ultrasonography is emerging as a surrogate for non-invasive and quantitative assessments and a relatively new research area with significant potential biomarkers to be explored. Many QUS analyses rely on quantifying ultrasound attenuation coefficient (UAC), as a confounding factor. Here, in a swine cohort (N=10), we characterized the high-frequency (24 MHz) UAC of healthy periodontal tissues (gingiva) in vivo. UAC were estimated using spectral difference method. Five interproximal oral sites were imaged from four oral quadrants: Premolar 3-Mesial, Premolar3-Distal, Premolar4-Distal, Molar1-Distal, and Molar2-Distal. A total of 162 oral sites were analyzed. The respective medians (1st-quartile|3rd-quartile) UACs for these oral sites were 1.66 (1.25|1.99), 1.37 (1.06|1.64), 0.99 (0.8|1.25), 1.08 (0.89|1.47), and 1.28 (0.94|1.24) dB/MHz.cm. The gingival attenuation mean at Premolar3-Mesial was significantly higher than any other oral sites while the rest of them showed non-significance difference in their means. Across all non-significant oral sites, the average UAC was 1.17 dB/MHz.cm with a standard deviation of 0.49 dB/MHz.cm. This work not only characterized an important acoustic property of oral tissues for the first time but also contributes to future development of a number of QUS biomarkers for periodontal/dental healthcare that rely on accurate attenuation knowledge.

We consider a tensor product of two spaces of holomorphic functions on a Hermitian symmetric space of tube type. Then generically this is decomposed into a direct sum of irreducible subrepresentations. In this manuscript, we construct the intertwining operator (holographic operator) from each irreducible summand to the tensor product as an integral operator. This gives a generalization of the result by Kobayashi--Pevzner (2020).

We investigate the superconducting gap structure in bilayer nickelates within a model in which conduction bands of dx2-y2 symmetry coexist with localized d3z2-r2 spins. Strong interlayer coupling drives the local moments into a singlet ground state, whose virtual singlet-triplet excitations ("triplons") mediate the pairing interaction. This mechanism yields interband s+- pairing, with opposite signs of the order parameter on the two (alpha and beta) bands. The calculated tunneling spectra naturally explain the key experimental features, including a larger gap on the alpha band despite its smaller density of states and a gap anisotropy induced by nonlocal Kondo coupling. The results support triplon-mediated pairing as the microscopic origin of superconductivity in bilayer nickelates.

Mobile crowdsensing (MCS) is evolving from basic data collection to dynamic service provisioning, where platforms must maintain task completion, budget feasibility, and sensing quality under uncertain worker availability. Beyond raw-data and location privacy, workers' long-term intent traces, such as task-selection tendencies and participation histories, can be exploited by an honest-but-curious platform to infer private preferences from one or multiple allocation snapshots. Worker dropouts and execution uncertainty further destabilize sensing coverage, while frequent global re-optimization increases interaction overhead and observable exposure. To address these issues, we propose \textit{iParts}, an intent-preserving and risk-aware two-stage service provisioning framework for dynamic MCS. In the offline stage, workers report perturbed intent vectors through personalized local differential privacy with memoized permanent randomized response, suppressing frequency-based intent inference while retaining decision utility. The platform then builds a redundancy-aware quality model and performs risk-aware pre-planning under budget, quality-risk, and intent-mismatch constraints. This offline problem is formulated as an exact potential game with expected social welfare as the potential function, guaranteeing constrained equilibrium existence and finite-step convergence under feasible improvement dynamics. In the online stage, quality deficits are repaired through bounded-round temporary recruitment from idle or standby workers, enabling feasibility-preserving adjustment with limited exposure. Experiments show that iParts improves welfare and task completion while reducing redundancy and communication overhead against representative benchmarks.

We investigate the interplay between lattice symmetry, phonons, and magnetism in the quasi-one-dimensional ladder compound BaFe$_2$S$_3$ by combining polarized synchrotron infrared spectroscopy, hybrid-functional density functional theory calculations, and inelastic neutron scattering. Lattice-dynamics analysis reveals that the crystal symmetry is lower than previously proposed and is consistent with a $P1$ space group at low temperature. Several infrared-active phonon modes exhibit pronounced anomalies at both the structural transition temperature $T_S \approx 125$--$130$~K and the Néel temperature $T_N \approx 95$~K. First-principles calculations show that the modes affected at $T_S$ predominantly involve displacements that modulate magnetic exchange pathways. Neutron scattering demonstrates that below $T_N$ the magnetic order is three-dimensional, long-ranged, and static. Between $T_N$ and $T_S$, the system displays three-dimensional short-range dynamic magnetic correlations, which disappear above $T_S$. The structural transition thus coincides with the onset of magnetic fluctuations rather than with static magnetic order. Our results indicate that short-range, dynamical magnetic correlations are sufficient to drive a static structural instability, providing a magnetically driven mechanism reminiscent of the iron-pnictide 122 family, yet realized here in a quasi-one-dimensional Mott system. These findings highlight the central role of magnetoelastic coupling in iron-based superconductors beyond the itinerant regime.

Generative Search Engine (GSE) leverages the Retrieval-Augmented Generation (RAG) technique and the Large Language Model (LLM) to integrate multi-source information and provide users with accurate and comprehensive responses. Unlike traditional search engines that present results in ranked lists, GSE shifts users' attention from sequential browsing to content-driven subjective perception, not only driving a paradigm shift in information retrieval but also highlighting the importance of enhancing the subjective visibility of content in generative search. In this context, Generative Search Engine Optimization (G-SEO) methods have emerged as a new research focus. With the rapid advancement of Multimodal Retrieval-Augmented Generation (MRAG) techniques, GSE can now efficiently integrate text, images, audio, and video, producing richer responses that better satisfy complex information needs. Existing G-SEO methods, however, remain limited to text-based optimization and fail to fully exploit multimodal data. To address this gap, we propose Caption Injection, the first multimodal G-SEO approach, which extracts captions from images and injects them into textual content, integrating visual semantics to enhance the subjective visibility in generative search. We systematically evaluate Caption Injection on MRAMG, a benchmark for MRAG, under both unimodal and multimodal settings. Experimental results show that Caption Injection significantly outperforms text-only G-SEO baselines under the G-EVAL metric, effectively improving the subjective visibility of content perceived by users, and demonstrating the practical benefits of multimodal information in G-SEO. The source code for this work is openly available at https://github.com/GrayChan04/Caption-Injection.

We propose a constricting Control Barrier Function (CBF) framework for prescribed-time control of control-affine systems with input constraints. Given a system starting outside a target safe set, we construct a time-varying safety tube that shrinks from a relaxed set containing the initial condition to the target set at a user-specified deadline. Any controller rendering this tube forward invariant guarantees prescribed-time recovery by construction. The constriction schedule is bounded and tunable by design, in contrast to prescribed-time methods where control effort diverges near the deadline. Feasibilityå under input constraints reduces to a single verifiable condition on the constriction rate, yielding a closed-form minimum recovery time as a function of control authority and initial violation. The framework imposes a single affine constraint per timestep regardless of state dimension, scaling to settings where grid-based reachability methods are intractable. We validate on an 18-dimensional multi-agent system, demonstrating scalability and prescribed-time recovery with bounded control effort.

Nonlinear constrained optimization has a wide range of practical applications. The interior-point method is considered to be one of the most powerful algorithms for solving nonlinear inequality constrained optimization. In this paper, we consider optimization with general inequality constraints and propose an Adaptive Regularisation algorithm using Cubics Based on Interior-Point methods (ARCBIP). For solving the barrier problem, we construct ARC subproblem with linearized constraints and the well-known fraction to the boundary rule that prevents slack variables from approaching their lower bounds prematurely. We employ a composite-step approach and reduced Hessian methods to deal with linearized constraints, where the trial step is decomposed into a normal step and a tangential step. They are obtained by solving two ARC subproblems approximately with the fraction to the boundary rule. Requirements on normal steps and tangential steps are given to ensure global convergence. To determine whether the trial step is accepted, we use exact penalty function as the merit function in ARC framework. The updating of the barrier parameter is implemented by adaptive strategies. Global convergence is analyzed under mild assumptions. Preliminary numerical experiments and some comparison results are reported.

Ultra-compact X-ray binaries (UCXBs) are a subclass of low-mass X-ray binaries (LMXBs) characterized by ultra-short orbital periods, typically less than $60-80\,$min. They consist of a compact mass-accretor and a hydrogen-poor mass-donor, in which the mass-accretor could be a neuron star (NS) or even a black hole (BH). UCXBs play an important role in multiple areas of astrophysics. In particular, they are considered strong, continuous gravitational wave (GW) sources in the low-frequency band, making them key targets for future space-based GW observatories such as LISA, TianQin and Taiji. As the most compact binaries, the formation and evolution of UCXBs remain highly uncertain. In this article, we review four classic formation channels: the white dwarf donor channel, the He star donor channel, the evolved main-sequence donor channel, and the accretion-induced collapse channel. We also discuss recent progress in these channels, covering evolutionary scenarios, the initial parameter space for UCXB formation, and associated objects. A comparison between observed UCXBs and theoretical expectations is provided, along with a discussion on the observed BH-UCXB candidates. The origin of UCXBs can be constrained by the chemical composition of mass-donors and their locations in diagrams of mass-transfer rate and X-ray luminosity versus orbital period. We also examine the implications of UCXBs for several astrophysical fields, including GW astronomy, multi-messenger astronomy, binary evolution, and NS physics under extreme conditions. Further progress will depend on multi-wavelength observations, the discovery of more UCXB samples, and more detailed theoretical simulations.

We present efficient parallel algorithms for computing maximal matchings in hypergraphs. Our algorithm finds locally maximal edges in the hypergraph and adds them in parallel to the matching. In the CRCW PRAM models our algorithms achieve $O(\log{\logΔ}\log{m})$ time with $O(κ\log {m})$ work w.h.p. where $m$ is the number of hyperedges, and $κ$ is the sum and $Δ$ is the maximum of all vertex degrees. The CREW PRAM model algorithm has a running time of $O((\logΔ+\log{d})\log{m})$ and requires $O(κ\log {m})$ work w.h.p. It can be implemented work-optimal with $O(κ)$ work in $O((\log{m}+\log{n})\log{m})$ time. We prove a~$1/d$-approximation guarantee for our algorithms. We evaluate our algorithms experimentally by implementing and running the proposed algorithms on the GPU using CUDA and Kokkos. Our experimental evaluation demonstrates the practical efficiency of our approach on real-world hypergraph instances, yielding a speed up of up to 76 times compared to a single-core CPU algorithm.

Automating requirements quality analysis remains challenging because multiple, often conflicting quality attributes must be balanced while preserving stakeholder intent. Existing Large-Language-Model (LLM) approaches predominantly rely on task-oriented decomposition or implicit aggregation, limiting their ability to systematically surface and resolve cross-quality conflicts. We present QUARE (QUality-Aware REquirements Analysis), a multi-agent framework that takes a project description as input and formulates requirements quality analysis as structured negotiation among five quality-specialized agents: Safety, Efficiency, Green, Trustworthiness, and Responsibility, coordinated by a dedicated orchestrator. QUARE introduces a dialectical negotiation protocol that explicitly exposes inter-quality conflicts and resolves them through iterative proposal, critique, and synthesis. Negotiated outcomes are transformed into structurally sound KAOS goal models via topology validation and verified against industry standards through retrieval-augmented generation (RAG). We evaluate QUARE on five benchmark systems drawn from established RE benchmarks, MARE and iReDev, and an industrial autonomous-driving specification, spanning safety-critical, financial, and information-system domains. Results show that QUARE achieves 98.2% compliance coverage, a 105% improvement over both baselines; 94.9% semantic preservation, a 2.3 percentage-point improvement over the best baseline; and high verifiability, with a score of 4.96 out of 5.0, while generating 25-43% more requirements than existing multi-agent RE frameworks. These findings suggest that, when using capable instruction-tuned models, architectural choices such as quality-dimension decomposition, explicit negotiation, and automated verification may contribute more to output quality than model scale alone.

Quasi-one-dimensional transition-metal chalcogenide Ta$_2$PdSe$_6$ is a promising thermoelectric semimetal due to the strong electron-hole asymmetry in the carrier lifetime. However, the microscopic origin of such a strong asymmetry remains unclear. In this study, we theoretically investigate electron-phonon scattering in Ta$_2$PdSe$_6$. There is a soft phonon mode mainly consisting of atomic displacements in PdSe$_4$ chains. This soft mode is strongly coupled with the highest valence band at the $Γ$ point, which lies slightly below the Fermi energy, and causes strong electron-phonon scattering. The bottom of the electron pocket energetically overlapped with that band also suffers from strong intervalley scattering, by which the imaginary part of the electron self-energy exhibits a sharp change near the Fermi level. On the other hand, the imaginary part of the self-energy for carriers in the hole pocket shows a moderate energy dependence. Thus, we find that electron-phonon scattering is strongly valley-dependent. Our finding will help us to understand the distinctive transport properties observed in Ta$_2$PdSe$_6$.

Two-paths (wedges) are the elementary combinatorial objects behind clustering, triadic closure, redundancy, and brokerage. Motivated by a two-path formalism that links Burt's structural holes to node-centered ego networks, we develop an operator viewpoint in which wedge incidence induces a canonical ``two-walk'' matrix and a unique decomposition into an edge--supported (triadic) part and a nonedge-supported (open) part. We then study quotient/contraction constructions designed to compress collections of dominating ego networks together with selected ``traversing'' nodes, and we prove a two--walk transfer theorem under contraction, establishing an inequality with an explicit nonnegative error term and an equality characterization in terms of a wedge--equitable partition. Finally, we illustrate the theory on ten benchmark graphs and their ego-traversing contractions using table-driven diagnostics.

The exact solution of the two-dimensional (2D) Ising model at an external magnetic field is derived by a modified Clifford algebraic approach. At first, the transfer matrices are analyzed in three representations, i.e., Clifford algebraic representation, transfer tensor representation and schematic representation, to inspect nonlocal effects in this many-body interacting system. It is ensured that nontrivial topological structures exist in this system, which is analogous to (but different with) those in the three-dimensional (3D) Ising model at zero magnetic field. Therefore, the approaches developed for the 3D Ising models are modified to be appropriable for solving analytically the solution of the 2D Ising model at a magnetic field. An additional rotation, serving as a topological Lorentz transformation, is applied for dealing with the topological problems in the present system. The rotation angle for the transformation is determined by Yang-Baxter relations and a subsequent average of rotation angles treating the linear change of the topological actions. Application of a magnetic field increases the magnetization, shifting the critical point to higher temperatures. At the temperature above the critical point, the magnetization keeps zero until a critical field at which it jumps rapidly as a first-order magnetization process. The partition function and the magnetization obtained are helpful for understanding the physical properties, in particular, the magnetization processes of the 2D magnetic materials.

We consider anti-de Sitter flux vacua interpolated by flux-changing domain walls. Demanding that the tension of such a domain wall be above the ultraviolet cutoff of the effective description, we derive an upper bound on the anti-de Sitter radius, which we term domain wall bound. It translates into a lower bound on the gravitino mass, thus realizing the gravitino conjecture and the anti-de Sitter distance conjecture of the swampland program. We test the domain wall bound on several examples with a candidate hierarchy of scales: classical flux vacua, racetrack models, LVS and KKLT-like anti-de Sitter vacua. The classical flux vacua and LVS are found to be compatible with the bound. For racetrack and KKLT-like anti-de Sitter vacua, the bound poses a non-trivial constraint on achieving large hierarchies of scales.

By means of path integral- Monte Carlo, we study the finite-temperature behavior of the extended Bose-Hubbard model with cavity-mediated long-range interactions at unit filling. At zero temperature, the system supports superfluid, Mott-insulating, supersolid, and charge-density-wave phases, with a strongly first-order transition between superfluid and charge density wave states characterized by a broad coexistence region. Focusing on this coexistence regime, we explore how the dominant order evolves with temperature. When the system is initialized in a superfluid state, the superfluid density is progressively suppressed upon heating, and a normal fluid is stabilized. Upon further increasing the temperature, a thermally assisted emergence of crystalline order occurs which eventually melts into the normal fluid. In contrast, simulations initialized in a charge-density-wave configuration display a smooth thermal melting of density order, with no reemergence of superfluid coherence. Overall, our results show that metastability persists at low temperatures, but ultimately disappears at higher temperatures, where thermally induced crystallization takes place.

Recent progress in fault-tolerant quantum computing suggests that leveraging error-syndrome information at the logical layer can substantially improve performance, including the estimation of logical observables from noisy states. In this work, based on quantum estimation theory, we develop an information-theoretic framework to quantify the utility of error syndromes for noisy logical observable estimation. We distinguish two operational regimes of such syndrome-aware protocols: classical protocols, in which the logical measurement basis is fixed and syndrome information is used only in classical post-processing, and quantum protocols, in which the logical quantum control can be tailored to depend on the observed error syndrome. For classical syndrome-aware protocols, we prove a universal limitation: on average, syndrome information can improve the effective logical error rate by at most a factor of two, implying at most a quadratic reduction in sampling overhead. In contrast, once syndrome-conditioned quantum control is permitted, we demonstrate that the effective logical error rate decays exponentially with the number of code blocks. These findings provide fundamental guidance for designing future fault-tolerant architectures that actively exploit syndrome records rather than discarding them after decoding.

We develop potential-theoretic and \(L^p\)-regularity results for the fractional--logarithmic Laplacian \((-Δ)^{s+\ln}\) and its inhomogeneous counterpart \((λI-Δ)^{s+\ln}\), \(λ>1\). These operators lead to logarithmic analogues of the classical Riesz and Bessel potentials. For the associated logarithmic Bessel kernel \(K_{s+\ln}^λ\), we obtain representation formulas and sharp pointwise asymptotics at both the origin and infinity, including explicit leading constants. A key ingredient is a measure-level bridge between the homogeneous and inhomogeneous symbols. This allows us to pass between the equations $(λI-Δ)^{s+\ln}u=f$ and $(-Δ)^{s+\ln}u=f,$ and yields global \(L^p\) estimates, well-posedness for distributional solutions, and a natural scale of logarithmic Bessel spaces \(\mathcal L^p_{s+\ln,λ}\). We also discuss the dependence of these spaces on \(λ\), their relation to the classical Bessel spaces and with the logarithmic Bessel potential spaces introduced by Opic and Trebels. As applications, we prove endpoint embeddings and critical compactness results. On the critical line \(n=2sp\), we obtain embeddings with a logarithmic modulus of continuity, local compactness on bounded domains, and global compactness in the radial class. In the subcritical case \(n>2sp\), we prove compactness at the critical Sobolev exponent $p^*=\frac{np}{n-2sp},$ recovering compactness at the borderline Lebesgue threshold, a phenomenon absent from the classical Sobolev and Bessel scales.

In causal analysis, understanding the causal mechanisms through which an intervention or treatment affects an outcome is often of central interest. We propose a test to evaluate (i) whether the causal effect of a treatment that is randomly assigned conditional on covariates is fully mediated by, or operates exclusively through, observed intermediate outcomes (referred to as mediators or surrogate outcomes), and (ii) whether the various causal mechanisms operating through different mediators are identifiable conditional on covariates. We demonstrate that if both full mediation and identification of causal mechanisms hold, then the conditionally random treatment is conditionally independent of the outcome given the mediators and covariates. Furthermore, we extend our framework to settings with non-randomly assigned treatments. We show that, in this case, full mediation remains testable, while identification of causal mechanisms is no longer guaranteed. We propose a double machine learning framework for implementing the test that can incorporate high-dimensional covariates and is root-n consistent and asymptotically normal under specific regularity conditions. We also present a simulation study demonstrating good finite-sample performance of our method, along with two empirical applications revisiting randomized experiments on maternal mental health and social norms.

In recent years, knowledge graphs (KGs) - in particular in the form of labeled property graphs (LPGs) - have become essential components in a broad range of applications. Although the absence of strict schemas for KGs facilitates structural issues that lead to redundancies and subsequently to inconsistencies and anomalies, the problem of KG quality has so far received only little attention. Inspired by normalization using functional dependencies for relational data, a first approach exploiting dependencies within nodes has been proposed. However, real-world KGs also expose functional dependencies involving edges. In this paper, we therefore propose graph-native normalization, which considers dependencies within nodes, edges, and their combination. We define a range of graph-native normal forms and graph object functional dependencies and propose algorithms for transforming graphs accordingly. We evaluate our contributions using a broad range of synthetic and native graph datasets.

Satellite-terrestrial communications are severely constrained by high path loss, limited spectrum resources, and time-varying channel conditions, rendering conventional bit-level transmission schemes inefficient and fragile, particularly in low signal-to-noise ratio (SNR) regimes. Semantic communication has emerged as a promising paradigm to address these challenges by prioritizing task-relevant information over exact bit recovery. In this paper, we propose a semantic forwarding-based semantic communication (SFSC) framework optimized for satellite-terrestrial networks. Specifically, we develop a vector-quantized joint semantic coding and modulation scheme, in which the semantic encoder and semantic codebook are jointly optimized to shape the constellation symbol distribution, improving channel adaptability and semantic compression efficiency. To mitigate noise accumulation and reduce on-board computational burden, we introduce a satellite semantic forwarding mechanism, enabling relay satellites to forward signals directly at the semantic level without full decoding and re-encoding. Furthermore, we design a channel-aware semantic reconstruction scheme based on feature-wise linear modulation (FiLM) to fuse the received SNR with semantic features, enhancing robustness under dynamic channel conditions. To support multi-user access, we further propose a codebook split-enhanced model division multiple access (CS-MDMA) method to improve spectral efficiency. Simulation results show that the proposed SFSC framework achieves a peak signal-to-noise ratio (PSNR) gain of approximately 7.9 dB over existing benchmarks in the low-SNR regime, demonstrating its effectiveness for robust and spectrum-efficient semantic transmission in satellite-terrestrial networks.

We explore the relationship between quantum Fisher information (QFI) and the negative of the second derivative of concurrence with respect to the coupling between two qubits, referred to as the curvature of entanglement (CoE). The two-qubit system serves as a minimal model to study the connection between QFI and dynamically generated entanglement in scenarios where the measured quantity is a two- or many-body coupling strength. We analyze in detail the pure-state lossless case for which general results can be inferred and we also consider a simple interaction Hamiltonian in the case of one form of loss applied to the qubits. For a two-qubit quantum probe used to estimate the coupling constant appearing in the interaction Hamiltonian we show, for certain initial conditions, that there are times such that CoE = QFI. These times can be associated with the concurrence, viewed as a function of the coupling parameter, being a maximum. We examine the time evolution of the concurrence of the eigenstates of the symmetric logarithmic derivative (SLD). Measurements using the SLD eigenstates as basis are optimal for saturating the quantum Cramer bound. We show that, for several families of initially separable and initially entangled states, the SLD eigenstates are simple product states when CoE = QFI.

Hamiltonian Monte Carlo (HMC) generates efficient Markov transitions by combining Hamiltonian dynamics with a Metropolis correction. This paper develops a geometric \(q\)-analogue of HMC by replacing classical Hamiltonian dynamics with a \(q\)-deformed Hamiltonian system arising from \(q\)-calculus. Starting from a Lagrangian formulation, we derive the corresponding \(q\)-Hamiltonian equations and prove the formal invariance of the associated \(q\)-symplectic form within the \(q\)-deformed differential calculus. To obtain a computable sampler, we introduce a Jackson-derivative realization and construct a Metropolis-corrected \(q\)-HMC algorithm. The proposal reduces to classical HMC as \(q\to1\), while for \(q\neq1\) it replaces ordinary derivatives by \(q\)-Jackson finite differences. We establish detailed balance, which ensures that the resulting Markov transition preserves the target distribution. Numerical experiments examine the computational behavior of the proposed method. For positive-scale black-box targets, the \(q\)-Jackson force has a scale-consistent interpretation: multiplicative perturbations of \(s>0\) correspond to centered finite differences in \(y=\log s\). In such examples, \(q\)-HMC closely tracks log-coordinate finite-difference HMC and the exact-gradient benchmark, whereas raw additive finite differences may produce large force and Hamiltonian errors. These results suggest that the proposed \(q\)-analogue provides a valid HMC-type sampling framework with a visible advantage for positive and multiplicative black-box targets.

Given an elliptic curve $E$ defined over $\mathbb{Q}$ without complex multiplication, we provide an explicit sharp bound on the index of the image of the adelic representation $ρ_E$. In particular, if $\operatorname{h}_{\mathcal{F}}(E)$ is the stable Faltings height of $E$, we show that $[\operatorname{GL}_2(\widehat{\mathbb{Z}}) : \operatorname{Im}ρ_E]$ is bounded above by $10^{21} (\operatorname{h}_{\mathcal{F}}(E)+40)^{4.42}$, and, for $\operatorname{h}_{\mathcal{F}}(E)$ tending to infinity, by $\operatorname{h}_{\mathcal{F}}(E)^{3+o(1)}$. We also classify the possible (conjecturally non-existent) images of the representations $ρ_{E,p^n}$ whenever $\operatorname{Im}ρ_{E,p}$ is contained in the normaliser of a non-split Cartan. This result improves previous work of Zywina and Lombardo.

Heralding the advent of autonomous vehicles and mobile robots that interact with humans, responsibility in spatial interaction is burgeoning as a research topic. Even though metrics of responsibility tailored to spatial interactions have been proposed, they are mostly focused on the responsibility of individual agents. Metrics of causal responsibility focusing on individuals fail in cases of causal overdeterminism - when many actors simultaneously cause an outcome. To fill the gaps in causal responsibility left by individual-focused metrics, we formulate a metric for the causal responsibility of groups. To identify assertive agents that are causally responsible for the trajectory of an affected agent, we further formalise the types of assertive influences and propose a tiering algorithm for systematically identifying assertive agents. Finally, we use scenario-based simulations to illustrate the benefits of considering groups and how the emergence of group effects vary with interaction dynamics and the proximity of agents.

A new Richardson number formulation, Ri_new, is introduced to improve the diagnosis of turbulence in the stratified free atmosphere. The formulation is derived from the turbulent kinetic energy budget and accounts for both vertical wind shear and horizontal shear (deformation and divergence), weighted by the ratio of horizontal to vertical eddy viscosities (K_mh/K_mv). This extends the classical Richardson number Ri_old, which accounts only for vertical shear. The diagnostics Ri_new , Ri_old ,and the widely used Turbulence Index 1 (TI1), computed from ERA5 reanalysis, are evaluated using more than 247 million automated turbulence reports from commercial aircraft (2017--2024). Across various turbulence intensity thresholds, Ri_new consistently outperforms the other diagnostics, resulting in higher AUC values and improved probability of detection at operationally relevant false-alarm rates. The highest skill is obtained for K_mh/K_mv approximately 5000. Seasonal and regional evaluations indicate that the added value of Ri_new is largest where turbulence generation involves both vertical and horizontal shear, such as over the contiguous United States and during summer. Ri_new remains the best-performing diagnostic in all regions and seasons. Spatial case studies show that Ri_new identifies 83--98% of observed moderate-or-greater turbulence events compared with 54--85% for Ri_old. This substantial improvement in detection comes with a much smaller increase in false alarms, confirming that Ri_new provides a more physically realistic representation of turbulence-prone regions. These results demonstrate that incorporating horizontal wind shear into the Richardson number yields a physically consistent and statistically robust improvement in turbulence diagnostics, with relevance for research and operational applications.

Byzantine Agreement (BA) considers a setting of $n$ parties out of which up to $t$ can be byzantine (malicious), and requires the honest parties to agree on an input subject to a condition called \emph{validity}: if all honest parties have input $v$, the output agreed upon must be $v$. Convex Agreement (CA) strengthens BA by requiring the output agreed upon to lie in the convex hull of the honest parties' inputs. This validity condition captures aggregation tasks, such as robust learning and sensor fusion, where honest inputs may differ but should still constrain the final decision. Existing protocols for CA over general convexity spaces require at least $O(L \cdot n^2)$ bits of communication for $L$-bit inputs, leaving a gap with BA's $Ω(L \cdot n)$ lower bound. We investigate this gap, and we present deterministic synchronous CA protocols with near-optimal communication complexity in the long-message regime. When $L=Ω(n\cdotκ)$, where $κ$ is a security parameter, our protocols use $\mathcal{O}(L\cdot n\log n)$ bits of communication for finite convexity spaces and $\mathcal{O}(L\cdot n^{1+o(1)})$ communication for Euclidean spaces $\mathbb{R}^d$. Our protocols also have asymptotically optimal round complexity $\mathcal{O}(n)$. If an upper bound $L$ on the honest inputs' length in bits is known in advance, we achieve near-optimal resilience $t<n/(ω+\varepsilon)$ for any constant $\varepsilon>0$, where $ω$ is the Helly number of the convexity space. When no such bound is known, we achieve resilience $t<n/(ω+\varepsilon+1)$. As a sample application, we show how our protocols can be used to obtain efficient solutions for parallel instances of BA. Our main technical contribution is the use of extractor graphs to obtain a deterministic assignment of parties to committees, which is robust against adaptive adversaries.

High-dimensional datasets are frequently subject to contamination by outliers and heavy-tailed noise, which can severely bias standard regularized estimators like the Lasso. While Maximum Mean Discrepancy (MMD) has recently been introduced as a ``universal'' framework for robust regression, its application to high-dimensional Generalized Linear Models (GLMs) remains largely unexplored, particularly regarding variable selection. In this paper, we propose a penalized MMD framework for robust estimation and feature selection in GLMs. We introduce an $\ell_1$-penalized MMD objective and develop two versions of the estimator: a full $O(n^2)$ version and a computationally efficient $O(n)$ approximation. To solve the resulting non-convex optimization problem, we employ an algorithm based on the Alternating Direction Method of Multipliers (ADMM) combined with AdaGrad. Through extensive simulation studies involving Gaussian linear regression and binary logistic regression, we demonstrate that our proposed methods are highly competitive with classical penalized GLMs and existing robust benchmarks. Our approach shows particular resilience in maintaining a balance between estimation accuracy and variable selection across diverse contamination scenarios, especially in handling high-leverage points and heavy-tailed error distributions where traditional methods may fluctuate in performance.

Semantic communication can significantly improve bandwidth utilization in wireless systems by exploiting the meaning behind raw data. However, the advancements achieved through semantic communication are closely dependent on the development of deep learning (DL) models for joint source-channel coding (JSCC) encoder/decoder techniques, which require a large amount of data for training. To address this data-intensive nature of DL models, federated learning (FL) has been proposed to train a model in a distributed manner, where the server broadcasts the DL model to clients in the network for training with their local data. However, the conventional FL approaches suffer from catastrophic degradation when client data are from different domains. In contrast, in this paper, a novel FL framework is proposed to address this domain shift by constructing the global representation, which aligns with the local features of the clients to preserve the semantics of different data domains. In addition, the dominance problem of client domains with a large number of samples is identified and, then, addressed with a domain-aware aggregation approach. This work is the first to consider the domain shift in training the semantic communication system for the image reconstruction task. Finally, simulation results demonstrate that the proposed approach outperforms the model-contrastive FL (MOON) framework by 0.5 for PSNR values under three domains at an SNR of 1 dB, and this gap continues to widen as the channel quality improves.