This paper presents a system design methodology for a large-scale static wireless mesh network for 155 commercial off-the-shelf (COTS) radio nodes at fixed infrastructure sites in a challenging island environment. The architecture consists of approximately ten 15-node clusters, each with designated primary and secondary gateway nodes to support inter-cluster communication. A structured, multi-stage planning methodology was developed to guide network design. Site-specific radio frequency (RF) path loss predictions were generated using Remcom's Wireless InSite ray-tracing platform, incorporating terrain, buildings, and dense foliage effects. To optimize connectivity under physical-layer and operational constraints, spectral embedding combined with balanced k-means clustering was applied to partition the nodes into clusters of comparable size. A link budget analysis determined the maximum tolerable path loss under waveform and hardware constraints, defining the connectivity threshold used in the clustering framework. This work integrates deterministic RF propagation modeling with constrained clustering optimization to provide a scalable framework for planning static wireless mesh networks in complex geographic environments. Node mobility and higher-layer networking protocols were outside the scope of this study.

In this paper, we investigate the nonlocal problem \begin{equation*}\left\lbrace \begin{aligned} &A_{s} u=(|x|^{-(n-2s)}\ast u^{2_{s}^{\sharp}-1-ε})u^{2_{s}^{\sharp}-2-ε} \quad\quad\hspace{3.5mm} \mbox{in}\hspace{2mm}Ω,\\ &u>0\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\hspace{2mm}\mbox{in}\hspace{2mm}Ω,\\ &u=0\quad \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\hspace{2mm}\mbox{on}\hspace{2mm}\mathbb{R}^n\setminusΩ, \end{aligned} \right.\end{equation*} where $Ω$ is a smooth bounded domain in $\mathbb{R}^n$, $0<s<1$, $n\in(2s,\min\{6s,n+2s\})$, $ε>0$ small, $2_{s}^{\sharp}-1=(n+2s)/(n-2s)$ and $A_{s}$ stands for the fractional Laplace operator $(-Δ)^{s}$ in $Ω$ with outside zero Dirichlet boundary condition. The above problem is reduced to the subcritical fractional system $$ A_{s}u=u^{2_{s}^{\sharp}-2-ε}v,\hspace{2mm}A_{s}v=u^{2_{s}^{\sharp}-1-ε},\hspace{2mm}u,v>0\hspace{2mm}\mbox{in}\hspace{2mm}Ω\hspace{2mm}\mbox{and}\hspace{2mm}u=(-Δ)^sv=0\hspace{2mm}\mbox{on}\hspace{2mm}\mathbb{R}^n\setminusΩ.$$ For a general domain $Ω$ or domains with convexity, we first prove a uniform $L^1$ bound away from the boundary and a uniform $L^{\infty}$ bound near the boundary for positive solutions to the general fractional Hartree-type PDEs by applying the moving planes method and integral estimates for the convolution term.Among these results, we study the asymptotic behavior of solutions as $ε\rightarrow0$.These solutions are shown to blow-up at exactly one point $x_0$ and location of this point is characterized. In addition, the shape and exact rates for blowing-up are studied.Finally,we also establish the corresponding main results for solutions of the fractional Brezis-Nirenberg problem involving critical Hartree-type nonlinearity.

This note presents AGDES, a tool for Automatic Generation of Dependent Event Sequences. Each event sequence is either generated as the output word of a deterministic finite automaton (DFA), or produced as the output word of a DFA called transducer that reads events from one or more input sequences, and produces an output sequence.

This paper presents a framework for assigning intrinsic geometric structures to topological groups using only the data provided by their topological and algebraic structure. The geometrisation spits into small-scale and large-scale components, formalised respectively through local Lipschitz and quasimetric categories that, in turn, are definable from the canonical left uniform and left coarse structures of the group. For Polish groups, the paper characterises metrisability of the left coarse structure in terms of local boundedness, countable coverings by bounded sets, and the existence of compatible coarsely proper left-invariant metrics. It then introduces minimal metrics, which determine local Lipschitz structure, and maximal metrics, which determine quasimetric structure, and provides intrinsic characterisations of both. When both structures exist, they combine into a single canonical Lipschitz structure. Our framework is subsequently applied to specific examples such as homeomorphism groups, non-Archimedean Polish groups and automorphism groups of Fraïssé limits.

The paper proposes an implicit (i.e., machine-independent) complexity approach to studying computation by polynomial-size, constant-depth circuits with gates counting modulo a constant through the lens of discrete ordinary differential equations (ODEs). So far, recursion-theoretic characterizations have been provided for functions computed by circuits of constant depth, including gates counting modulo 2 and 6 only (i.e., for the classes FAC0[2] and FAC0[6], resp.). In this paper, it is shown that considering ODE schemas, rather than bounded recursion, allows for a more fine-grained analysis, leading to (uniform) characterizations for all classes FAC0[n] (n \in N), i.e. functions computed by circuits including counting modulo n gates. Inspired by the syntactic form of the ODE schemas, we go further in this direction and present first-order bounded theories for capturing provably total functions in each of these classes.

Modern audio-visual media rely on compact representations for efficient storage and transmission, whereas realistic digital touch still depends on high-resolution tactile recordings. Existing approaches for representing tactile signals constrain manipulation and limit the generation of new content. Here, we introduce two compact representations, spectral beta and spectral slope, that capture the temporal spectral structure of finger-surface friction signals while preserving perceptually relevant information. Spectral beta models spectral skewness using a two-parameter beta distribution, whereas spectral slope approximates the spectrum with an asymmetric bandpass filter defined by low- and high-pass orders. We evaluated these representations in a perceptual study with 14 participants using five virtual textures rendered on a friction-modulation display and compared them with physical textures and high-fidelity reproductions of recorded signals. Spectral beta achieved perceptual similarity ratings comparable to those of the original high-fidelity reproductions. Regression analysis further showed that matching spectral energy across nine critical frequency bands was the strongest predictor of perceived realism. Together, these findings suggest that tactile texture perception depends primarily on fundamental temporal spectral patterns and that modeling these patterns is sufficient for perceptually realistic rendering. These results establish an efficient and scalable framework for haptic compression, communication, and synthetic texture generation.

We study the Brownian dynamics and linear response of a particle with inertia moving in a 2-dimensional helical landscape imprinted on a cylindrical surface. In the harmonic well approximation, the deterministic motion separates into free propagation along the screw direction and harmonic motion in the transverse screw-normal direction. We show that for isotropic damping this simplification survives in the Langevin description, whereas anisotropic damping along the axial and angular directions couples the stochastic dynamics and destroys separability. The resulting anisotropic model is formulated as a linear Ornstein-Uhlenbeck process in phase space with a zero mode associated with diffusion along the screw coordinate, so that in an infinite system the full phase-space dynamics does not relax to a stationary distribution. To treat transport in this setting, we construct the stationary dynamics in the stable subspace obtained after projecting out the zero mode. This leads to a linear response theory for this system and yields closed analytical expressions for stationary time-correlation functions and the dynamical mobility tensor in both the time and frequency domains. The off-diagonal elements of the mobility tensor describe cross-response between axial forcing and angular motion, and between applied torque and axial transport. Consistent with time reversal symmetry, these cross mobilities are equal and provide a direct dynamical signature of the helical geometry. In addition, a simultaneous application of driving in both the axial and angular direction reveals asymmetry in energy dissipation rate due the helical landscape.

We present a homogeneous catalogue of fundamental astrophysical parameters -- age, metallicity ([Fe/H]), heliocentric distance, and colour excess $E(G_{\mathrm{BP}}-G_{\mathrm{RP}})$ -- for 5,056 open star clusters drawn from the Unified Cluster Catalogue (UCC). All parameters are derived uniformly from Gaia Data Release 3 (DR3) colour-magnitude diagrams via Bayesian Nested Sampling with PARSEC stellar isochrones, with no manual intervention on individual clusters. Initial metallicity $Z_{\mathrm{ini}}$ is treated as a free parameter throughout, yielding a photometric [Fe/H] estimate for every cluster. Physically motivated priors -- parallax-based distances from Gaia DR3 astrometry, spectrophotometric metallicity constraints from Gaia XP spectra where available, and interstellar reddening from the Schlegel-Finkbeiner-Davis dust map -- reduce CMD degeneracies without anchoring the fit to any external parameter catalogue. Of the 5,056 clusters, 3,766 (74.5\%) satisfy the fit-quality criterion $η_{\mathrm{fit}} \ge 0.80$. This high-quality subset spans ages 0.003-5.5~Gyr ($\log(\mathrm{Age/yr})$ median $8.33 \pm 0.34$~dex), heliocentric distances 88-19,011 pc (median 2,150~pc), metallicities $-1.17 \le \mathrm{[Fe/H]} \le +0.42$~dex (median $+0.002$ dex), and extinctions up to $A_G = 7.37$~mag (median 1.07~mag). The catalogue is made publicly available via CDS/VizieR; the complete nested-sampling posterior chains are archived on Zenodo.

The inner Galactic halo is a complex graveyard of the Milky Way's earliest accretion events, where severe orbital phase-mixing challenges traditional dynamical stream-finding techniques. We present a purely data-driven, 12-dimensional chemo-dynamical analysis of the inner halo using \textsl{SDSS-V Milky Way Mapper} (DR19) and \textsl{Gaia} DR3. Utilizing an unsupervised machine learning framework based on UMAP and HDBSCAN, we perform a blind search for clustered populations within a chemically selected \textit{ex-situ} sample of 2,185 stars without kinematic pre-selection. Our pipeline recovers nine kinematic groupings corresponding to seven known substructures (including \textsl{Gaia}-Enceladus/Sausage, the Helmi Streams, and Sequoia), validating the robustness of the high-dimensional feature space. We also report five new tightly bound candidate substructures, designated FO1--FO5 ($E_{\rm tot} \leq -1.8 \times 10^5~\mathrm{km^2~s^{-2}}$). Four candidates (FO1, FO3, FO4, FO5) are confirmed as robust chemo-dynamical overdensities, while FO2 exhibits a striking nitrogen enhancement ($[\mathrm{N/Fe}] = +0.83 \pm 0.16$) suggestive of tidal debris from a disrupted massive globular cluster. Finally, we demonstrate that high-dimensional chemical information is critical for resolving dynamical degeneracies in the crowded inner halo, differentiating structures sharing similar orbits but distinct chemistry (e.g., FO5 and Shiva), and the reverse (e.g., FO3 and the Helmi Streams). These findings confirm that the deepest regions of the Galactic potential preserve a rich record of the Galaxy's assembly history.

General equations are derived for slow viscous thin fluid film flows on curved surfaces through an extension of Leal's pedagogical approach, which leaves the characteristic velocity scale unspecified and employs a direct through-thickness integration of the continuity equation. The derivation neglects inertia, and includes gravitational, capillary, and Marangoni effects, the latter coupling the thickness dynamics to free-surface transport of a dilute, non-diffusing surfactant. The resulting general expression incorporates the leading order terms of each type, as well as additional terms that become leading order for nongeneric cases. A few examples are briefly presented and literature comparisons made. The importance of gradients in curvature is emphasized, and it is suggested that nondimensionalization of geometric features might lead to further useful generalizations. This relatively simple formulation is intended as a starting point for exploring interactions between geometry, gravity, and surface tension.

Let $\mathbb{P}$ be an algebraic number field. We provide a computational analog of the strong approximation theorem for finitely generated Zariski dense groups $H\leq \mathrm{SL}(n,\mathbb{P})$, $n$ prime. That is, we present algorithms to find the set of congruence quotients of $H$ modulo all maximal ideals of a finitely generated subring $R$ of $\mathbb{P}$ such that $H\leq \mathrm{SL}(n,R)$. The algorithms have been implemented in GAP. Potential applications are illustrated by a range of experiments in degree $2$, with a special focus on Bianchi groups.

Many-core neuromorphic systems accelerate Spiking Neural Networks (SNNs), yet their packet-based spike communication can spend substantial traffic and energy repeatedly transmitting destination addresses. This overhead is amplified by the small payload of spike packets: in representative workloads, duplicate address transmissions account for up to 49% of the total traffic. This paper presents UniSpike, a hardware-software co-design that removes address redundancy by aggregating spikes destined for the same core into compact packets. UniSpike combines destination-centric spike scheduling, lightweight runtime packet assembly hardware, and destination-aware SNN partitioning. Across diverse SNN workloads, UniSpike reduces traffic by 1.93$\times$ on average, delivering 1.77$\times$ speedup and 1.50$\times$ energy efficiency improvement over state-of-the-art designs.

The accurate modeling of reflection coefficients is pivotal for developing reliable channel models in emerging terahertz (THz) communications. This study establishes a 300$\sim$400 GHz channel measurement platform to measure the reflection coefficients of various materials. Based on the analysis of measured data, we propose the single-layer interference with an extended-parameterized Lorentz/Drude (SLI-EPLD) reflection coefficient model. In this model, a sub-band modeling strategy is adopted to characterize the variation of reflection coefficients with frequency, while a parameterized mapping approach is employed to ensure the stability of model parameters. Furthermore, the weighted sub-band fitting for trend regression (WF-TREND) algorithm is introduced to achieve precise sub-band parameter fitting. Validation results demonstrate superior performance to existing models across multiple materials. The reflection coefficient model established in this work serves as a critical foundation for channel modeling in 300$\sim$400 GHz for high-THz communication.

Solar radius measurements and their variations -- if any -- are a difficult problem that has vexed researchers for decades. In this paper, we have attempted to clarify the various ways of expressing the definition ''solar diameter'', from a physical point of view. The concept of diameter is taken here in its broadest sense, leaving aside the issue concerning the oblateness caused by surface and internal angular velocity variations, as deviations from sphericity are negligible in our context. Astrometric time-series observations are still needed, and we advocate strengthening long-term metrological measures to achieve greater consensus on the subject. To date, modern observations of the solar diameter provide a frame of reference, and we give a new glossary. By comparing the best values obtained to date, it is shown that the ''seismic radius'' obtained from the Solar and Heliospheric Observatory (SOHO) and the Solar Dynamics Observatory (SDO) provides the best determination, a finding supported by observations made at the Calern (F) and Pic du Midi (F) observatories. The latest results on the leptocline show that it is more important than ever to consider at which layers of the Sun radius measurements are carried out. On this basis, we hope to converge on new standards.

Long-lived particles have emerged as a compelling signature of physics beyond the standard model, offering unique discovery opportunities at current and future colliders. We present an analysis of charged long-lived particles leading to signatures with kinked tracks and displaced vertices. Our study is motivated by the gauge mediated supersymmetry breaking model (GMSB) within the minimal supersymmetric standard model scenario, in which the lightest supersymmetric particle is a gravitino and the next-to-lightest supersymmetric particle is the stau, the superpartner of the tau lepton. The stau is predicted to be long-lived due to the small coupling between it and the gravitino. This work presents a phenomenological study of such long-lived staus with lifetimes between 20~cm and 20~m and explores their discovery prospects at the Future Circular Collider (FCC-ee), a proposed $e^{+}e^{-}$ collider. The results highlight the sensitivity to the GMSB model.

The precision and sensitivity achievable in quantum metrology are often compromised by the presence of noise. While quantum error correction has emerged as a promising strategy, it is ineffective in addressing noise that is indistinguishable from the signal. To address this challenge, virtual state purification was introduced as a complementary approach to quantum error correction. However, significant noise accumulation can impede its performance. To overcome this limitation, we propose a swap test-based method specifically designed to address indistinguishable noise, even under high noise levels. A systematic error-scaling analysis demonstrates that this method enables quantum-enhanced precision in certain scenarios. Furthermore, numerical simulations demonstrate that our method surpasses virtual state purification in both single- and multi-parameter estimation tasks. The significant improvements in precision across diverse settings underscore the robustness and practicality of our method for real-world applications.

The reuse of medico-administrative and synthetic spatial data may overcome some limitations of population-based registries, provided rigorous validation is performed. However, no tool exists to spatially validate a candidate-for-reuse database (CFRD) against a gold standard (GS). We propose a Bayesian framework for two-dimensional (global and local) map-to-map validation of spatial health-event databases. We consider an error-model family (random [REM] and structured [SEM]) in which the CFRD is modelled as a departure from the GS. Both are compared with a shared component model (SCM). Global disagreement is assessed using the database-specific intercept difference ($RR_{\mathrm{global}}$), while local disagreement is measured by the exceedance probability of the database-specific error term. Disturbance scenarios included null, uniform, clustered, and random perturbations in the CFRD. Sensitivity, specificity, false detection rate, and Matthews Correlation Coefficient assessed detection performance. $RR_{\mathrm{global}}$ accurately recovered map-wide shifts across all models and scenarios. REM and SEM behaved were both sensitive and specific to local discrepancies. SCM was more conservative. Applied to Crohn's disease data from the EPIMAD registry and a CFRD, all models reached the same conclusion: the CFRD reproduced global and local spatial structures with an overall signal about 7\% lower. Extensions to other outcome distributions, spatio-temporal models and calibration constitute natural next steps. \textit{Keywords:} data reuse; spatial database validation; Bayesian hierarchical models; disease mapping; shared component model.

Phase difference is central to classical coherence theory. With the advancement of various light-field modulation techniques, artificially generated pseudo-thermal light sources or random light beams can exhibit exotic wavefront correlation properties. However, such spatial wavefront correlations cannot be fully characterized using the phase difference alone. For instance, for a pair of conjugate pseudo-thermal beams, the spatial wavefronts exhibit a significant anti-correlation, meaning that the sum of their wavefronts tends to be constant. In this work, we propose the concept of degree of wavefront correlation $p^{(1)}$, ranging symmetrically from $-1$ to $+1$, for numerically calculating the wavefront correlation properties among various pseudo-thermal light sources, and the sign (positive or negative) can be used to determine the tendency-whether it leans toward wavefront-difference or wavefront-sum correlation. Numerical results demonstrate that the classical Siegert relation does not apply to pseudo-thermal light sources that exhibit wavefront-sum correlation properties. To address this, we propose a generalization valid for all Gaussian pseudo-thermal light. Experimentally, we introduce the measurable quantities of correlation visibility $\mathcal{V}_g$ and correlation background $μ_g$, which form a two-dimensional classification framework $\{μ_g,\mathcal{V}_g\}$ that enables the experimental characterization of diverse Gaussian pseudo-thermal light using a common-path interferometer and intensity correlation measurement. Furthermore, the correlation visibility $\mathcal{V}_g$ can serve as an observable criterion for a zero-mean, non-circularly symmetric, and jointly Gaussian distribution.

General-purpose LLMs are increasingly functioning as mental health infrastructure due to gaps in care left by provider shortages, inadequate insurance coverage, social isolation, and stigma around formal help-seeking. This shift poses a distinct problem for AI ethics: systems neither designed nor governed as care technologies are being used as such, while their dominant design incentives optimize for engagement rather than user well-being. We present findings from a qualitative, longitudinal study with 18 US-based participants who use general-purpose LLMs for socioemotional support and participated in one or more of our study phases, including initial interviews, a four-week diary study, focus groups, and exit interviews. Participants turned to LLMs because other forms of support were unavailable, unaffordable, socially costly, or inadequate. As they continued to use these systems, design features such as anthropomorphic cues, default validation, persistent responsiveness, and weak disengagement mechanisms shaped their ongoing reliance. Participants described meaningful support alongside dependency, epistemic distortion through one-sided validation, privacy expectations without corresponding legal protection, and continued use despite awareness of these risks. We argue these dynamics reflect a structurally unfair tradeoff: users accept risks because support is otherwise absent, while available systems are optimized to deepen engagement and lack care-based accountability. The paper makes three contributions: it traces the arc through which LLMs become care infrastructure and identifies distinct ethical tensions at each stage, shifts analysis from turn-based exchanges to longitudinal trajectories of use, and argues that accountability belongs at the design and incentive conditions through which these systems become care infrastructure rather than at the output or crisis-response layer.

In the current era, in which an unprecedented wealth of data is available for the study of the Milky Way, the Gaia Benchmark Stars (GBS) have become an established reference and calibration sample. Studies of stellar structure and evolution, as well as the chemical history of our Galaxy, largely rely on large spectroscopic surveys and their output catalogs. In this context, deriving precise and accurate stellar parameters and chemical abundances is of paramount importance. This study provides the determination of neutron(n)-capture element abundances, extending the set of chemical abundances available for the third GBS release (GBSv3). Based on the compilation of high-resolution spectra assembled for GBSv3 and consistently with the spectral analysis adopted for the chemical abundances of GBSv3, we used the iSpec code to derive heavy-element abundances. We infer homogeneous abundances of n-capture elements across the GBSv3 sample using an in-depth line assessment tailored to different groups identified through a clustering algorithm that accounts for the diversity in stellar parameters and metallicities. This approach addresses key challenges in the spectral analysis of these elements, including the paucity of usable lines, weak line strengths, saturation effects, and sensitivity to atomic data. It yields reliable measurements, establishing an extended and robust reference scale in good agreement with the literature. This compilation of these abundances is based on the GBS's robust and accurate atmospheric parameters, together with the analysis of a large sample of stellar spectra per star, which provides a reliable and homogeneous spectral analysis. It supports the use of chemical abundances as precise tracers of the Milky Way's star formation history and chemical evolution, and constitutes a legacy sample for the calibration of current and future spectroscopic surveys.

We present an FPGA-based study of matrix-element acceleration for Monte Carlo event generation, using MadGraph5_aMC@NLO as a benchmark framework. Two complementary scenarios are considered. First, we implement the full matrix-element workflow on an AMD Alveo U250 accelerator for the benchmark process $e^+e^- \to μ^+μ^-$, enabling an end-to-end evaluation of FPGA acceleration for a simple process. Second, for the more complex $gg \to t\bar{t}+X$ processes with increasing jet multiplicity, we investigate FPGA acceleration of the color-algebra kernels as a structured and scalable entry point for selective acceleration. In this second case, the reported speedups correspond to the isolated color-reduction kernel operating on precomputed amplitudes, rather than to the full matrix-element evaluation or the complete event-generation workflow. The proposed implementations are developed using High-Level Synthesis and are evaluated in terms of numerical accuracy, performance, energy efficiency, resource utilization, and scalability. Compared with CPU and GPU implementations available within the MG5aMC framework, the FPGA solutions achieve substantial speedups and significantly improved energy efficiency. For the considered benchmarks, the numerical results remain in close agreement with the corresponding CPU reference calculations, while the resource analysis highlights the importance of numerical representation in determining scalability on FPGA devices. These results support the use of FPGAs as a competitive architecture for selected Monte Carlo event-generation workloads in high-energy physics.

We investigate phaseless inverse scattering problem for the Schrödinger equation and develop reconstruction methods based on the inverse Born series (IBS). We consider three types of phaseless data: the far-field total field, the total field and the far-field scattered field. For phaseless total-field data, we extend the IBS framework and analyze its radius of convergence. In the far-field setting, we propose a Fourier-based reconstruction method that exploits the scattering reciprocity between incident and observation directions to recover Fourier coefficients of the scattering potential. For phaseless scattered-field data, we employ a polarization-based approach to recover phase information and enable IBS reconstruction. Numerical experiments are conducted to validate the proposed methods.

Recent advancements in vehicle autonomy have drawn interest in understanding the impact of autonomous vehicles on traffic systems. In this paper, we study a traffic assignment problem in a mixed-autonomy setting where both human-driven and autonomous vehicles coexist. We model the interaction as a simultaneous routing game where human drivers are self-interested and aim to minimize their own travel times, while autonomous agents are altruistic and aim to minimize the total social cost. The standard nonatomic congestion game analysis establishes the existence of equilibrium to this game under convex cost functions, and does not have any implication of its uniqueness. In this work, we formulate the equilibrium as a variational inequality (VI), which enables us to establish the equilibrium existence without convexity assumption, and guarantees the uniqueness of the aggregated link flow and social cost at equilibrium under a specific class of cost functions. Leveraging this VI framework, we provide sufficient conditions under which including autonomous agents improves, deteriorates, or has no effect on social cost. While the possibility of deterioration has been established in prior work, our results complement existing worst-case bounds by explicitly characterizing sufficient conditions under which each outcome occurs, thereby providing a deeper understanding of mixed-autonomy traffic systems. Furthermore, we consider a centralized scenario where a social planner optimizes the routing of autonomous agents, and show that the same equilibrium is achieved as in the decentralized scenario when assuming convex costs.Finally, we conduct numerical experiments that illustrate how social cost changes with the amount of autonomous vehicles under different system parameters.

Non-equilibrium systems display memory, a dependence not merely on their present environment but on previously applied fields. Multistable systems such as spin glasses, martensites and granular matter have exponentially many microstates consistent with an applied field, making their rich dynamics difficult to control. Control and order can be achieved through the concept of partial ordering, which we here generalize to systems subject to multiple control fields. We demonstrate, within the model system of the zero-temperature Ising model, that this leads to return-point memory, in which an applied sequence of fields restores the hysteretic system not only to a previous magnetization, but to a previous exact microstate. The multiplicity of fields grants more precise and complex control of the system, with different classes of operations displaying commutative and noncommutative behavior. This grants new insight into how physical systems can remember, learn, and be trained.

The deployment of Extremely Large-Scale Antenna Arrays for 6G enables radiative near-field sensing but poses significant challenges in terms of hardware complexity and interference. Stacked Intelligent Metasurfaces (SIMs) address these limitations by enabling wave-domain dimensionality reduction. This paper proposes a rigorous SIM-aided framework for near-field channel and localization estimation based on Multiport Network Theory, which provides an electromagnetically consistent characterization accounting for mutual coupling and non-unilateral inter-layer propagation effects. An indirect estimation approach is adopted, where the SIM is optimized to perform analog spatial filtering by projecting the received signal onto a relevant subspace identified through coarse prior location information. Within this realistic setting, we analytically characterize the impact of SIM approximation errors on channel estimation and quantify the resulting effects on localization performance. The results show that the proposed architecture preserves the essential wavefront curvature information required for accurate near-field localization, achieving performance comparable to fully digital solutions while drastically reducing the number of radio-frequency chains.

Stratospheric aerosol injection (SAI), a possible climate engineering strategy where reflective particles are injected into the stratosphere, has been explored to mitigate global warming and its associated risks, such as the intensification of extreme precipitation events. However, current Earth system models (ESMs) often used to simulate SAI and other climate change scenarios are too coarse to properly assess such risks. Traditional statistical downscaling methods, used to project higher resolution impacts, may be biased and unrealistic. To address this, we train a deep learning diffusion downscaler to generate 0.25° contiguous United States (CONUS) daily precipitation using historical and future climate simulations from the Mesoscale Atmosphere-Ocean Interaction in Seasonal-to-Decadal Climate Prediction (MESACLIP) project, then apply the diffusion downscaler to out-of-distribution CESM2 simulations with and without SAI. The diffusion model generates realistic downscaled precipitation using either MESACLIP or CESM2 inputs. It also faithfully recreates the climate change projections of extreme precipitation in MESACLIP. Diffusion-downscaled projections of the future CESM2 SAI scenarios suggest that SAI could nearly cut in half the CONUS-average increase in yearly max precipitation, compared to the non-SAI scenario. However, there is considerable regional variation and internal variability, with SAI modeled to only slightly reduce increases in extreme precipitation frequency in the Mid Atlantic and the Pacific Northwest, but mitigating most intensification in other regions. Future application of diffusion downscaling to a wider variety of SAI scenarios would provide valuable insight into how proposed SAI strategies may affect precipitation variability on fine spatial scales for regional impact assessments.

Swarical, a Swarm-based hierarchical localization technique, enables miniature drones, known as Flying Light Specks (FLSs), to accurately and efficiently localize and illuminate complex 2D and 3D shapes. Its accuracy depends on the physical hardware (sensors) of FLSs, which are used to track neighboring FLSs in order to localize themselves. It uses the hardware specification to convert mesh files into point clouds that enable a swarm of FLSs to localize at the highest accuracy afforded by their hardware. Swarical considers a heterogeneous mix of FLSs with different orientations for their tracking sensors, ensuring a line of sight between a localizing FLS and its anchor FLS. We present an implementation using Raspberry cameras and ArUco markers. A comparison of Swarical with a state of the art decentralized localization technique shows that it is as accurate and more than 2x faster.

We prove that, among rectangular grid graphs with a fixed number of vertices, the number of spanning trees increases when the side lengths are made more balanced. In particular, among all rectangular grid graphs with $n^2$ vertices, the square $n\times n$ grid has the largest number of spanning trees. The proof starts with the Laplacian product formula, passes to hyperbolic coordinates, and compares logarithms by separating a discrete-concavity term from a positive decreasing residual term.

We show that a sliding spatial modulation of the on-site Hubbard interaction realizes a many-body Thouless pump whose boundary spectral flow is reconstructed by correlations. For a period-three Hubbard chain at filling $ρ=2/3$, density-matrix renormalization group (DMRG) calculations identify a correlated insulator with many-body Chern number $C=+2$, corresponding to two units of charge pumped per cycle. Its excitation spectrum separates the charge gap from the lowest neutral spin gap, revealing an interacting bulk response beyond a simple spin-degenerate band pump. Under open boundary conditions, this contrast becomes even more pronounced. A spin-degenerate Hartree/Aubry-André-Harper reference pump exhibits simultaneous edge flow in the two spin channels, whereas the full modulated Hubbard model suppresses the boundary doublon channel and splits the spectral flow into two distinct edge events. Between these events, the boundary charge is neutralized while a neutral, spinful triplet-like excitation is localized at the edge. The global $μ-U$ phase diagram reveals filling-dependent topology: the $ρ=2/3$ regime remains in the $C=+2$ sector, while $ρ=4/3$ regime undergoes a spin-gap-closing transition from a $C=-2$ pump to a distinct $C=+1$ topological Mott pump.

With the growing subset of magnetic massive stars, it is now possible to conduct a systematic survey of radio emission from magnetic hot stars to better understand the underlying emission mechanisms. Previous surveys of radio emission from hot star magnetospheres have focused on high frequencies ($>$2 GHz). At lower frequencies, additional emission and absorption mechanisms are expected, increasing the complexity of the observed emission. In this work, we survey towards lower frequencies while also increasing the sample size. We report the study of 28 magnetic hot stars with the Giant Metrewave Radio Telescope (GMRT) during cycles 27 and 28 of its operation. Among these, we found 11 detections and 17 non-detections. We also include 16 additional targets observed with GMRT from the literature. We investigated the dependence of low-frequency radio luminosity on different stellar parameters and searched for a scaling relationship at low frequencies. We further test the centrifugal breakout model for gyrosynchrotron emission. The observed low-frequency radio luminosities show a clear dependence of radio emission on magnetic field strength and rotation period, consistent with high-frequency studies. We observe a trend in scaling relationships with frequency and comment on the statistical behavior of gyrosynchrotron spectra. The observed low-frequency behavior likely reflects a combination of free-free absorption and the location of the low-frequency turnover in the gyrosynchrotron spectrum, which may vary among stars depending on their magnetospheric properties and can suppress detectable sub-GHz emission. One of the detected stars, HD 37742, is the first magnetic O-type star detected at sub-GHz frequencies.