We explore log Manin's conjecture for integral points and its connections to $\mathbb A^1$-connectedness. We prove log Manin's conjecture for Campana rational curves and for $\mathbb A^1$-curves on split toric varieties. Our arguments combine the Cox ring description of the moduli space of rational curves with Batyrev's heuristic-type counting arguments. As our proofs are geometric in nature, they give a geometric explanation of the mysterious leading constant for Campana points proposed by Chow--Loughran--Takloo-Bighash--Tanimoto.

In this paper, we theoretically analyze and experimentally demonstrate the performance gains achievable by integrating an in-house built reconfigurable intelligent surface (RIS) with a 5G new radio (NR) system implemented using the OpenAirInterface (OAI) software stack. Unlike conventional RIS-assisted systems that rely on explicit channel state information (CSI) estimation followed by RIS phase configuration optimization, we adopt a low-complexity approach in which the RIS phase states are randomly switched among predefined configurations. The resulting channel fluctuations are opportunistically exploited by the inherent proportional fair (PF) scheduling mechanism of 5G NR. We develop a theoretical framework that characterizes the interaction between RIS switching dynamics and PF scheduling. Based on this framework and the associated analysis, we provide design guidelines for selecting the RIS switching time $T_s$ and the PF throughput averaging window $T_c$ that maximize the system throughput. Experimental evaluations on the 5G NR testbed demonstrate improvements in key performance metrics, including reference signal received power (RSRP), block error rate (BLER), modulation and coding scheme (MCS) index, and throughput. Our key takeaway is that randomly configured RIS operation with appropriately chosen system parameters can achieve performance comparable to optimized RIS designs, with no additional overhead compared to a conventional 5G NR system. More importantly, it requires no coordination between the RIS and the 5G NR system.

We have carried out a stacking analysis with the COSMOS-Web catalogue on one of the deepest ever SCUBA-2 images at 850 microns, allowing us to estimate the mean submillimetre flux density for samples of galaxies split by stellar mass and morphological class over the redshift range 0<z<12. For all morphological classes, the mean star-formation rate estimated from the dust emission increases with redshift, reaching a value for the most massive galaxies (~10^11 soar masses) of >~80 solar masses per year at 2 < z < 4.5. In this redshift range, the mean star-formation rate for these galaxies falls along the Hubble sequence from ~280 solar masses per year for irregular galaxies at one end to ~80 solar masses per year for spheroids at the other end, which shows that quenching was already happening shortly after the emergence of the Hubble sequence. The decrease in the star-formation rate for the spheroidal galaxies can be reproduced with a `starvation' quenching model with a depletion time of ~10^{8.2} years. We also show that the transformation of `submillimetre galaxies' can reproduce the growth in number-density of massive bulge-dominated and spheroidal galaxies over the redshift range 1.5 <z < 4. As a side-project, we have used our stacking results to show that the ratio of dust mass to stellar mass in galaxies increases with redshift out to z~8 and to determine the relationship between the mean density of dust and redshift in the range 0 < z <12. We show that a chemical evolution model based on the `star-formation history' of the universe, with a gas outflow rate equal to the star-formation rate, can explain the monotonic rise in the dust-to-stellar mass ratio and reproduce the relationship between mean dust density and redshift remarkably accurately.

The P-cubed Target Insertion Device (P$^3$-TID) is a research instrument dedicated to test novel positron source target configurations inside of the proof-of-principle PSI Positron Production (P-cubed or P$^3$) experiment at the Paul Scherrer Institute. The device allows an easy installation, positioning and replacement of different fixed targets. The present article describes its mechanical design at a detailed level.

We propose a nonlinear magnonic platform for bounded nonadiabatic parametric excitation in nanoscale ferrite structures. The approach is based on the algorithm, where the non-adiabaticity parameter is interpreted as a local measure of the spectral-flow rate associated with, while the nonlinear frequency regulator U represents the anharmonic spectral detuning of the medium. Using Co doped yttrium iron garnet YIG Co as a representative material system, we analyze how nonlinear detuning suppresses uncontrolled parametric growth and drives the system toward a dynamically localized low-occupancy magnonic state. Numerical verification in truncated Fock bases shows that a finite regulator U can suppress leakage into higher-order modes and preserve bounded dynamics under non-adiabatic excitation. The experimentally reported absorbed energy density for ultrafast switching in YIG Co corresponds to an estimated switching energy of approximately 22 aJ for a cell, providing a physically relevant scale for low-energy resonant state formation. We further discuss the role of magnetic damping, exchange-gap confinement, and phonon transparency in maintaining coherent magnonic dynamics over multiple operation cycles. These results suggest that nonlinear self-limited non-adiabatic dynamics in ferrite nanostructures may provide a physical basis for low-energy wave-based information processing.

We present an analysis of the time delay between the radio emission and the X-ray Compton luminosity during the 2010-2011 outburst of GX 339-4. Using the interpolated cross-correlation function (ICCF), we measure the time delay between the Compton luminosity and the radio luminosity, and find that during the rising hard state, the radio emission precedes the Compton luminosity by approximately 3 days. In contrast, in the decaying hard state, the radio emission lags behind the Compton luminosity by about 8 days. By estimating the mass accretion rate and the disk truncation radius, the calculated inner magnetic field can account for both the radio delay in the decaying hard state and the radio precedence in the rising hard state. The time delays observed in different outbursts across multiple sources are compared further, and the underlying physical mechanisms account for this difference are discussed. These results provide insights into the evolving coupling between the inner accretion flow and the jet in black hole X-ray binaries.

The explosive growth of AI-generated images has created a sustainability challenge for storage infrastructure. Platforms like Midjourney and Adobe Firefly already host billions of generative images, yet conventional object stores persist them as blobs with full-resolution pixels, consuming huge amounts of storage capacity and bandwidth. Unlike natural photos, however, AI-generated images can be deterministically reconstructed from compact, model-native latent tensors, making persistent image storage fundamentally redundant. This paper presents LatentBox, a latent-first storage system for AI-generated images. LatentBox treats compressed latents as durable storage objects and uses on-demand GPU reconstruction on the read path to trade inexpensive compute for large persistent storage savings. Our design is guided by the first large-scale analysis of AI-generated image access we are aware of, based on a 35-month, 2-billion-request production trace from a major generative-content platform. Motivated by the trace analysis, LatentBox keeps frequently accessed images in decoded pixel format for fast hits, stores less-active objects as compressed latents to expand effective cache capacity, and continuously adjusts the splits between the image and latent cache to optimize user-perceived access latency.We build a LatentBox prototype and evaluate it with the production trace. LatentBox reduces persistent storage by 78.7% with competitive or even lower mean and tail latency over a pure image-based storage.

We construct a family of non-invertible topological defects in two-dimensional theories of $n$ Weyl fermions. The construction relies on the existence of $G$-symmetric conformal boundary conditions for $n$ Dirac fermions. Upon unfolding, these boundary conditions become topological defects $\mathcal D$ of $n$ Weyl fermions that intertwine the two $G$-representations, and they are generically non-invertible. For $G=U(1)^n$, we show that $\mathcal D$ is a duality defect associated with gauging a finite Abelian group $Γ$, and we give an explicit algorithm for determining $Γ$ and its action on the fermions. We also show that the same finite-Abelian gauging description applies in certain restricted examples with non-Abelian $G$. By contrast, for certain non-Abelian symmetry structures, including the $G=SU(2)$ symmetry appearing in the $1$-$5$-$7$-$8$-$9$ problem, we prove that $\mathcal D$ cannot be realized as a duality defect for gauging any finite Abelian group. Finally, we explain how the duality-defect perspective gives a streamlined derivation of fermion scattering from a conformal boundary.

Using holographic duality, we reveal a transition in vortex dipole dynamics below a critical dipole size in strongly interacting superfluids, characterized by a significant suppression of mutual friction. In the bulk, this transition is triggered by a topological reconnection of vortex tubes, which disconnects the boundary vortices from the black hole horizon and forms a \textit{U-pipe}. Consequently, the post-transition evolution is governed by the contraction of the bulk \textit{U-pipe} rather than the mutual friction associated with the horizon, revealing a scale-dependent dissipation mechanism. We further show that this reconnection persists over a broad temperature range, even when the transition becomes unobservable at high temperatures. Our results provide a dissipation-based interpretation for the anomalous critical dipole scale observed in strongly interacting cold-atom experiments, and suggest the existence of distinct dissipative regimes in strongly interacting superfluids.

We extend our previous analysis [Phys. Rev. D 109, 065005 (2024)] of CPT-odd electromagnetic response in tilted, anisotropic Weyl semimetals to the overtilted (type-II) regime, where electron and hole pockets coexist at the Fermi level. Starting from the minimal QED sector of the Standard-Model Extension matched to a lattice-motivated anisotropic Dirac Hamiltonian with tilt, we compute the zero-temperature finite-density effective action nonperturbatively from the vacuum polarization tensor, and corroborate the result using a complementary chiral kinetic theory formulation that consistently incorporates both Fermi-sea and Fermi-surface contributions. In the type-II regime the unbounded linear dispersion necessitates a physical ultraviolet regularization. Implementing a hard momentum cutoff tied to the lattice bandwidth, we show that the CPT-odd, axion-like response remains finite across the type-I to type-II Lifshitz transition, while acquiring tilt- and anisotropy-dependent renormalizations together with nonuniversal, cutoff-sensitive terms governed by the geometry of the electron and hole pockets. As a concrete application, we evaluate the anomalous Hall conductivity in the prototypical type-II Weyl semimetal WTe$_2$, using parameters extracted from first-principles calculations and experiments, and find that Fermi-sea and Fermi-surface contributions are comparable and partially cancel, yielding a finite and strongly anisotropic Hall response characteristic of the overtilted regime.

The gut-muscle axis has been proposed to link gut microbiota with skeletal muscle physiology, yet its universality across livestock species remains unclear. Using aged laying hens, a livestock model with a relatively short digestive tract, we examined the gut microbiota, faecal metabolome, and breast-muscle metabolome by integrative multi-omics analyses in hens fed a Caldifermentibacillus hisashii-containing fermented feed or a control diet. Non-metric multidimensional scaling revealed clear separation of the microbial community between groups (stress = 0.0097), characterised by a marked expansion of Lactobacillus with the administration of the fermented feed. Variance partitioning showed that the 16S microbiota shared substantial variance with both the faecal (shared R2 adj = 0.54) and muscle (shared R2 adj = 0.48) metabolomes, and partial dbRDA demonstrated that the faecal-to-muscle metabolite association was largely retained after controlling for 16S (direct R2 = 0.538, partial R2 = 0.485), consistent with faecal metabolites acting as an integral layer linking microbiota to muscle. Cliff's delta-based selection showed depletion of proteolytic taxa and faecal amino acids, and reduced muscle Ornithine and uric acid alongside elevated Hypoxanthine. Because both groups were processed identically post-slaughter, these differences reflect in vivo states: amino acid depletion despite reduced bacterial proteolytic capacity points to enhanced host utilisation, and reduced uric acid, a post-mortem-stable purine end-product in uricotelic chickens, indicates efficient nitrogen turnover rather than accumulation. Collectively, these findings support a putative tripartite model of the gut-muscle axis in aged laying hens, providing a statistically grounded framework for understanding microbial contributions to muscle physiology in aged livestock.

Animal experiments have provided many insights on auditory function, notably in cases of sensorineural hearing loss (SNHL). However, it is not always clear how these findings translate to the human auditory system in clinically relevant contexts. Cross-species computational models of the auditory periphery can help bridge the gap between non-invasive human diagnostics and experimental evidence from animal studies. In this work we adapted a 1-D nonlinear cochlear transmission-line model designed for the human auditory periphery to mouse and gerbil, enabling a single computational framework for cross-species research on SNHL. Species-specific anatomical and physiological parameters - including basilar membrane (BM) length and width, stapes area, middle-ear transfer functions, and frequency range - were adjusted to match each species' auditory periphery and hearing range. Other cochlear parameters were calibrated to reproduce realistic cochlear tuning and compression. The adapted mouse and gerbil models were validated against experimental BM velocity level-growth characteristics, auditory-nerve (AN) tuning curves, and DPOAEs. Simulated AN outputs reasonably matched empirical measurements, including realistic AN thresholds and frequency selectivity. However, the discrepancy between simulations and measurements became larger for cochlear sections closer to the base or apex. Simulations of cochlear synaptopathy reproduced observed differences in recorded auditory brainstem and envelope following responses from mice and gerbils with SNHL. OHC individualization of the mouse model based on DPOAEs failed to faithfully reproduce individual measurements, although intergroup differences in OHC damage were captured. Our findings demonstrate that biophysically grounded auditory models can be translated across species while preserving realistic sound-coding properties and pathophysiological alterations.

Small and medium enterprises (SMEs) face growing cyber threats but often lack the resources and expertise needed to adopt Zero Trust Architecture (ZTA). This pilot study examines the drivers and barriers shaping SME perceptions of ZTA necessity and proposes an exploratory staged adoption path. Survey data from 64 IT and security professionals in the Asia-Pacific region show that ZTA familiarity and cloud-computing needs are the strongest positive correlates of perceived necessity, whereas accumulated barriers show only a weak negative association. Identity and access management complexity and scalability emerge as the main implementation hurdles. Based on these findings, we propose a three-stage route for SMEs: strengthening identity governance, segmenting high-value assets, and introducing targeted monitoring in line with operational capacity. The study offers early evidence for more realistic Zero Trust transitions in resource-constrained firms.

We introduce Nested-GPT, a hierarchical autoregressive Transformer architecture for simulating the variable-multiplicity parton-shower histories. As a controlled benchmark, we study the leading-logarithmic resummation of non-global logarithms in the large-$N_c$ limit, utilizing a stochastic Monte Carlo dipole shower to generate reference training data. We systematically evaluate Nested-GPT against a Transformer flow-matching baseline. The flow-matching framework successfully parameterizes the joint distribution of emission kinematics at fixed multiplicity. Its phase-space representation, however, requires the final number of emissions to be specified externally rather than generated dynamically. Conversely, Nested-GPT strictly enforces the ordered Markovian branching structure, predicting emissions sequentially and dynamically evaluating a learned sequence-termination condition. We benchmark both approaches using gap fraction observables under two complementary training regimes: direct training on vetoed histories and inclusive training followed by an analysis-level veto. The resulting generated samples agree with the reference shower within statistical uncertainties for the observables considered. These results establish Nested-GPT as a physically consistent autoregressive surrogate for variable-multiplicity shower generator and motivate extensions to subleading-logarithmic resummation and finite-$N_c$ color evolution.

Higher dimensional permutations are tuples of d-1 permutations that can be identified with a point set in a d-dimensional grid. In N. Bonichon and P.-J. Morel, {\it J. Integer Sequences} 25 (2022), several conjectures regarding the enumeration of pattern avoiding d-permutations were stated. In this paper, we consider a mapping from d-permutations to $2^{d-1}-$ary trees that naturally generalizes the classical max-tree construction for permutations. We then show that, when restricted to d-permutations avoiding (21,12) and 231, this mapping yields a bijection with d-ary trees. This result resolves one of the conjectures of Bonichon and Morel.

The Toffoli gate is a fundamental building block for quantum arithmetic and reversible logic, yet its efficient realization remains a major challenge in both near-term and fault-tolerant quantum architectures. Recent advances in dynamic quantum circuit capabilities, including mid-circuit measurement and classical feedforward, provide new opportunities for reducing the resource overhead of non-Clifford operations. In this work, we propose a set of dynamic decomposition strategies for multi-controlled Toffoli gates that exploit adaptive circuit execution and ancilla-assisted constructions. Our methods systematically reduce entangling-gate count, T-count, and T-depth compared with conventional static decompositions, while preserving fault-tolerance guarantees. Through analytical cost models and experimental evaluation, we demonstrate that relative-phase primitives and measurement-conditioned corrections enable scalable implementations with improved depth and resource efficiency.

We study the ground-state density patterns of a population-imbalanced two-component dipolar Bose-Einstein condensate confined in a circular quasi-two-dimensional box. Using a mean-field model, we map out phase diagrams as functions of the axial confinement, interaction imbalance, and population ratio. The system supports a rich sequence of stationary morphologies, including a nearly uniform pancake state, pancake-droplet and ring-droplet coexistence states, droplet arrays, and concentric rings. These patterns show a close structural correspondence to microphase-separated morphologies in diblock-copolymer systems, with the population imbalance acting as an effective volume fraction that selects the pattern topology. Analysis of the density profiles and structure factors reveals that the modulated states possess an intrinsic nonzero characteristic wave vector, which remains essentially unchanged when the box size is varied. We also find that the characteristic pattern spacing scales linearly with the axial confinement length, indicating that the transverse thickness of the condensate controls the effective in-plane length scale. In a finite circular box, this smooth scaling is interrupted by discrete steps, reflecting geometric frustration and the integer locking of the number of rings or droplets. Our results show that box-trapped dipolar mixtures provide a controllable platform for studying finite-size pattern selection and nonlocal microphase formation in quantum fluids.

This work investigates the impact of seasonal variations in seismic noise on the low-frequency performance of the Einstein Telescope (ET) at the Sardinia candidate site, focusing on implications for compact binary coalescence observations. Using seismic data collected between 2022 and 2025 in deep boreholes, we characterize monthly noise variations and identify representative best and worst case scenarios, corresponding to July and December. The measured seismic spectra are used to estimate the Newtonian noise contribution in the 2-10 Hz band and to derive modified ET sensitivity curves. These are implemented in a simulation framework to evaluate their effect on the signal-to-noise ratio (SNR) of binary neutron star and intermediate mass black hole signals, assuming the triangular ET configuration. We find that the low seismic noise of the Sardinia site results in only minor seasonal variations in detector sensitivity. The corresponding impact on SNR is limited to a few percent, even without including Newtonian noise mitigation. These results indicate that seasonal environmental fluctuation have a minor effect on the early inspired detectability of compact binaries, confirming the suitability of the Sardinia site for achieving ET low-frequency sensitivity goals.

Rapid electric vehicle (EV) expansion necessitates optimized charging infrastructure to bridge the persistent gaps between vehicle growth and charger availability. This study develops a demand-driven framework for city-scale EV charging demand assessment and charging pile capacity planning. It employs a bottom-up estimation approach to quantify electricity demand and a Harris Hawks Optimization algorithm to solve capacity planning challenges, capturing spatiotemporal demand variations across powertrain types and guiding allocation over 2022-2030 in Chongqing, China. The results show that (1) compared with June 2022, monthly EV electricity consumption tripled to 57.5 gigawatt-hours by the end of 2024, characterized by significant seasonal volatility and a structural shift in which the combined share of plug-in hybrid electric vehicles and extended-range electric vehicles reached 57.6%, necessitating a transition toward technology-specific infrastructure planning; (2) historical evaluations reveal a marked spatial mismatch, with actual deployment heavily concentrated in the urban core while public charging capacity consistently lagging behind demand, whereas the proposed optimized configuration achieved a superior comprehensive performance score of 0.28, compared to 0.65 for actual deployment, in balancing service adequacy across the "Core-Suburban-Exurban" hierarchy; and (3) by 2030, Chongqing is projected to require approximately 1.8 million charging units to sustain a stable 9:1 private-to-public ratio, a synergetic strategy expects to significantly mitigate urban-rural service disparities and enhance overall system resilience and grid compatibility. Ultimately, this study provides a versatile, spatially explicit tool for policymakers to support sustainable and cost-effective EV infrastructure deployment aligned with long-term electrification targets.

Strategic multi-agent systems are fundamentally characterized by decentralization, uncertainty, and ambiguity. Agents operating under limited observations will often need to make decisions based on simplified internal models of the environment, reflecting bounded rationality in both computational capacity and environmental knowledge. The Empirical Evidence Equilibrium (EEE) framework explicitly accounts for these limitations by modeling each agent as forming a potentially misspecified belief derived from signals obtained through partial observations of the environment. The resulting equilibrium concept captures the system's steady state under bounded rationality and decentralization. In this work, we study games in which the environment dynamics are driven jointly by exogenous factors and agents' actions. We analyze agent behavior under Q-value iteration where each agent independently forms a belief model, computes Q-values, and derives a greedy strategy, yet the collective actions of all agents jointly shape the environment each agent faces at the next stage. We prove that despite this decentralization, an EEE emerges from the joint dynamics when the coupling between agents' actions and the environment is sufficiently weak. We further extend this result to softmax policies, establishing a contraction result under a sufficient coupling condition.

Kerr quasinormal modes near algebraically special frequencies exhibit anomalous behavior, including apparent bifurcation, disappearance, and a nonsmooth connection to the Schwarzschild limit, which has remained puzzling for decades. Tracking poles and zeros of Green-function building blocks across different Riemann sheets, we show that the bifurcation is due to an avoided crossing accompanied by resonant excitation, while the disappearance is due to pole skipping caused by cancellation of a quasinormal-mode pole by a Matsubara-mode zero. This resolves the physical origin of these long-standing anomalies.

On a mixed-frustration 12-qubit Ising instance run on two D-Wave generations, Advantage2 Zephyr and Advantage_system6.4 Pegasus, the late-time subsystem autocorrelation under cycled reverse annealing sits strictly between two equilibrium reference processes at the device-calibrated effective temperature: localized parallel tempering, and delocalized equilibrated path-integral simulated quantum annealing at a fixed Advantage2 pause-point transverse-field scale. The bracket holds on all three tested schedules and at both hardware calibrations. We obtain this result through two ingredients: a cycled reverse-anneal protocol (reinitialize_state=False, 50 cycles per submission) used as a Markov-chain probe of the device's pause-point dynamics, and a parallel-tempering falsification framework with bias-corrected and accelerated bootstrap 95% confidence intervals. Of eighteen tested (instance, schedule) combinations on Advantage2, three are PT-unmatched and correspond to two distinct Ising instances; an independent native-graph control with no minor embedding on a third mixed-frustration instance reproduces the same direction of mismatch. Among twenty random training instances, schedule shape modulates basin occupation on six of the thirteen multi-basin-in-readout instances, with dominant-configuration shifts of up to 38 percentage points including changes of the dominant configuration. A pre-registered linear predictor of schedule sensitivity from exhaustively computable landscape features fails on ten held-out instances, indicating that schedule sensitivity is not captured by simple linear functions of the tested landscape moments. The bracketing result revises an earlier two-pause-enhancement claim and reframes reverse-anneal schedules as instance-specific basin-occupation probes rather than universal quantum-enhancement knobs.

In cuprates, electron doping yields a much lower superconducting $T_c$ than hole doping. For recently discovered nickelate superconductors, the analogous doping strategies become more challenging. Consequently, while hole-doped Ruddlesden-Popper (RP) nickelates have been extensively studied, electron-doped RP nickelates remain rarely explored both experimentally and theoretically. Here we fill this gap by systematically investigating the two-orbital bilayer model for three representative systems: bulk La$_3$Ni$_2$O$_7$ at ambient pressure and 15\,GPa, and a heterostructure La$_3$Ni$_2$O$_7$:La$_3$Al$_2$O$_7$ that provides a feasible experimental route to electron doping. Using first-principle calculations and large-scale dynamical cluster quantum Monte Carlo simulations, we find that electron doping generically enhances $s^\pm$-wave pairing superconductivity (SC) in all three cases, with the heterostructure showing the highest $T_c$ in the underdoped regime. Furthermore, our results suggest an inter-orbital cooperative mechanism that the pairing on the $d_{x^2-y^2}$ orbital, induced by that on the $d_{z^2}$ orbital, plays a vital role in the SC. This work provides the theoretical prediction of enhanced SC in electron-doped RP nickelates and calls for future experimental verification.

This paper investigates the spectral structure, numerical dispersion, and observability of fully discrete approximations of the one-dimensional wave equation by $P^k$ (local) discontinuous Galerkin methods. Characterizing the coupled space-time numerical dispersion reveals a trapping mechanism that forces the group velocities of both physical and spurious modes to vanish at selected frequencies. We then establish an exponential blow-up of order $\exp(h^{-(1-\varepsilon)})$ for the observability constant under this trapping mechanism. To overcome this divergence for arbitrary $k$, we propose a spectral filtering strategy to restore uniform observability. Theoretical analysis and numerical experiments indicate that higher-order methods may facilitate this recovery by preserving a larger genuine physical frequency band, thereby reducing filtering cost and observation time.

As emerging attacks increasingly target Industrial Control Systems (ICS), the security of Programmable Logic Controllers (PLCs) has become a critical concern. Binary Code Analysis (BCA), which enables analysts to understand compiled programs without source code, is essential for ICS security tasks such as post-attack digital forensics and incident response. However, automated BCA for PLC binaries remains challenging due to three key issues: heterogeneous binary formats across PLC platforms, entangled program semantics caused by the mixture of control logic with runtime code, and limited semantic representations for interpretable and learning-based downstream analysis. In this paper, we present PLC-BinX, a BCA workflow for cross-platform PLC binary understanding. PLC-BinX analyzes PLC binaries from four platforms: CODESYS v3, GEB, OpenPLC v2, and OpenPLC v3, and recovers function-level information through cross-platform reverse engineering, core-function extraction, and function-level semantic representation construction. Based on the recovered semantic representations, we further study two downstream tasks: toolchain prediction and functionality prediction. Under ten-fold program-level evaluation, PLC-BinX achieves 100.00% precision, recall, and F1 in toolchain prediction, and 51.43% precision, 49.38% recall, and 49.18% F1 in functionality prediction over 22 labels. The results demonstrate that PLC-BinX provides an effective and interpretable approach to cross-platform PLC binary understanding by exposing task-relevant function-level semantics from heterogeneous PLC binaries.

Alternating projections and their variants are classical tools for computing points in intersections of sets. Existing analyses for smooth manifolds mainly focus on local convergence rates under transversality or related regularity conditions. In this work, we develop a unified framework for a broad class of (possibly inexact) alternating-projection-type methods on intersections of smooth manifolds. Specifically, under the assumption that two $C^{2,1}$ embedded submanifolds $\mathcal{M}_1, \mathcal{M}_2 \subset \mathbb{R}^n$ intersect cleanly, we show that the associated alternating mapping admits a well-defined local limiting map $ψ$ on the intersection manifold $\mathcal{M}=\mathcal{M}_1\cap \mathcal{M}_2$, and that $ψ$ is a retraction on $\mathcal{M}$. If, in addition, $\mathcal{M}_1$ and $\mathcal{M}_2$ are $C^{3,1}$, then $ψ$ is a second-order retraction. Furthermore, the standard NewtonSLRA scheme, which exhibits quadratic local behavior under transversality, can be understood as inducing a second-order retraction on \(\M\). This framework thus provides new retraction-based optimization tools for problems constrained to the intersection manifold.

In this paper, we study the uncertainty principle for Schrödinger equations with a bounded time-independent potentials on certain Cartan-Hadamard manifolds endowed with an asymptotic hyperbolic metric in dimensions $n\geq2$. The classical Hardy uncertainty principle in Euclidean space, as developed in the works of Escauriaza-Kenig-Ponce-Vega (JEMS, 2008; Duke Math. J., 2010), reveals a rigidity phenomenon for solution $u$ to Schrödinger equations: sufficiently strong Gaussian decay at two distinct times yields $u\equiv0$. In this work, we show that a similar rigidity persists in the setting of hyperbolic geometry, despite the absence of translation invariance and Fourier representation. Our approach follows a general strategy of Escauriaza-Kenig-Ponce-Vega, where the underlying geometry brings an essential change. This enables us to establish new Carleman estimates and logarithmic convexity. Unlike the Euclidean setting, the hyperbolic geometry exhibits exponential volume growth and nontrivial geodesic escape at infinity, which fundamentally alters the propagation mechanism of Schrödinger evolutions. Based on the newly-built virial identities and an approximation argument, we derive the logarithmic convexity. The main difficulty in proving the logarithmic convexity is the lack of convolution structure on general manifolds. By making use of the exponential map and Jacobi field, we define a new mollifier on curved geometry. Meanwhile, to establish the Carleman estimate adapted to hyperbolic space, we introduce a new weight function adapted to the curved manifold. Our results highlight the role of curvature in shaping quantitative uniqueness properties for dispersive equations.

A group of individuals wishes to classify $m$ objects into $n$ categories in such a way that no class is left empty, a condition known as surjectivity. The opinions of the individuals are aggregated separately for each object using an aggregation function that can depend on the object. Maniquet and Mongin showed that if the aggregation functions are unanimous and the outcome must always be surjective, then the aggregation mechanism is dictatorial. Cailloux et al. showed that the same holds even if unanimity is relaxed to citizen sovereignty (each object can be classified into any category). We show that similar results hold even if we only require the outcome to be surjective with probability $1-ε$ (with respect to an arbitrary symmetric i.i.d. distribution), provided that the aggregation functions are far from being constant. On the way, we characterize all aggregation mechanisms whose outcome is always surjective without any assumptions on the aggregation functions. Our approach uses a general result of Alekseev and Filmus which has wider applicability. We illustrate this by proving a similar impossibility result for aggregating equivalence relations.

We carry out a Bayesian model comparison analysis to determine the dark matter model that best describes the Milky Way rotation curve, using four recent compilations of rotation-curve velocities with the Gaia data. We compare these data using three different baryonic models along with seven different dark matter models. Within the adopted modeling framework and Gaia-based rotation curve datasets, we find that the Einasto profile provides the preferred phenomenological fit compared to the NFW profile} across most combinations of datasets and baryonic models. We also find that the cored dark profiles are preferred over the (cuspy) NFW profile. We also test MOND using three different interpolating functions and find that, within the implementations considered, the models provide poorer fits than the preferred dark matter profiles. Finally, among the different baryonic models considered, none is decisively favored over the others.

We present the second data release (DR2) of Spectra and Polarisation in Cutouts of Extragalactic sources from RACS (SPICE-RACS). SPICE-RACS DR2 is derived from the third low-band epoch of the Rapid ASKAP Continuum Survey (RACS-low3) and covers the entire sky from the South celestial pole up to a declination of $+49^\circ$; approximately 87.5% of the celestial sphere. We produce 'cutout' spectral cubes in Stokes $I$, $Q$, $U$ around 4 million radio sources and extract spectra towards 5 million radio components. Across our observed band of 799.5--1087.5 MHz we find an $rms$ noise of $\sim200μ\mathrm{Jy/PSF}$, an angular resolution of $\sim15''$, and residual wide-field instrumental polarisation on the order of 0.1%. After de-duplication, our polarisation catalogue contains the detection of $2.5\times10^5$ ($3.4\times10^5$) Faraday rotation measures (RM) for components with a linearly polarised signal above $8σ$ ($6σ$). This places SPICE-RACS DR2 as the largest single RM catalogue ever produced by nearly an order of magnitude; the number of RMs in our catalogue alone is $\sim5$ times larger than every previous RM catalogue combined. Our resulting RM grid has an areal density of $6.7^{+1.8}_{-1.7}\mathrm{deg}^{-2}$, providing an effective 'resolution' of $\sim23'$, and reveals striking features across the sky. The broad-band RMs have a median uncertainty of $\sim2\ \mathrm{rad\ m}^{-2}$, and include complexity metrics and information from the time domain. The breadth and quality of the SPICE-RACS DR2 dataset will enable a new generation of RM science. Further, SPICE-RACS will provide an ideal reference for forthcoming deep polarisation surveys such as the ASKAP POSSUM survey. All of our data products are publicly available on the CSIRO Data Access Portal (DAP) and the CSIRO ASKAP Science Data Archive (CASDA).