Asynchronous messaging is a cornerstone of modern distributed systems, enabling decoupled communication for scalable and resilient applications. Today's message queue (MQ) ecosystem spans a wide range of designs, from high-throughput streaming platforms to lightweight protocols tailored for edge and IoT environments. Despite this diversity, choosing an appropriate MQ system remains difficult. Existing evaluations largely focus on throughput and latency on fixed hardware, while overlooking CPU and memory footprint and the effects of resource constraints, factors that are critical for edge and IoT deployments. In this paper, we present a systematic performance study of eight prominent message brokers: Mosquitto, EMQX, HiveMQ, RabbitMQ, ActiveMQ Artemis, NATS Server, Redis (Pub/Sub), and Zenoh Router. We introduce mq-bench, a unified benchmarking framework to evaluate these systems under identical conditions, scaling up to 10,000 concurrent client pairs across three VM configurations representative of edge hardware. This study reveals several interesting and sometimes counter-intuitive insights. Lightweight native brokers achieve sub-millisecond latency, while feature-rich enterprise platforms incur 2-3X higher overhead. Under high connection loads, multi-threaded brokers like NATS and Zenoh scale efficiently, whereas the widely-deployed Mosquitto saturates earlier due to its single-threaded architecture. We also find that Java-based brokers consume significantly more memory than native implementations, which has important implications for memory-constrained edge deployments. Based on these findings, we provide practical deployment guidelines that map workload requirements and resource constraints to appropriate broker choices for telemetry, streaming analytics, and IoT use cases.

In continuous-variable quantum computing, autonomous quantum error correction (QEC) can dissipatively steer a noisy quantum state into a target state or manifold, enabling robust quantum information processing without explicit syndrome measurements and feedback. Here, we propose a nullifier-based digital autonomous QEC enabled by conditional Gaussian operations. By designing jump operators for target nullifiers and compiling the resulting Lindbladian into a Trotterized sequence of elementary conditional Gaussian operations, we demonstrate two use cases: (i) deterministic preparation of non-Gaussian resource states for universal computation, including finitely squeezed cubic phase states and approximate trisqueezed states, and (ii) autonomous suppression of dephasing error for cat and squeezed cat states. We provide explicit gate decompositions for the required conditional Gaussian operations and numerically evaluate the performance under realistic imperfections, including photon loss in the bosonic mode and ancillary-qubit decoherence. Our results clarify the resource requirements and trade-offs, such as circuit depth, time-step choices, and the required set of conditional Gaussian operations, for scalable, gate-level implementations of autonomous state preparation and error suppression.

We consider the parabolic Lamé system on a bounded domain. We focus on two types of inequalities for higher-order derivatives of solutions. The first is related to an $L^p$-$L^p$ estimate locally in time in the Lebesgue space setting, which includes the endpoint cases $p=1$ and $p=\infty$. The second concerns an equivalent norm of Besov spaces by means of the solution of the parabolic Lamé system.

Battery state-of-health (SOH) reported by on-board battery management systems (BMS) is the primary metric available to electric vehicle (EV) owners and regulators, yet no study has validated its reliability across manufacturers against independent measurements. Here we show, through an epidemiological study of 1,114 EVs spanning five manufacturers and 375 days, that battery health reporting is fundamentally unreliable: real capacity differences of 12-25% exist within every model, but BMS SOH fails to track them, with correlations ranging from \r{ho} = 0.10 (non-significant) to \r{ho} = 0.62 only under restrictive filtering, while 384 vehicles do not expose SOH at all. A manufacturer-independent electrochemical marker achieves 74-89% degradation classification accuracy across all platforms without requiring BMS data, and a controlled laboratory validation on cells identical to those in the fleet confirms that partial-voltage-window charge measurements track reference capacity with \r{ho} > 0.80 across all 60 voltage windows (p < 0.001). These findings reveal a structural information asymmetry with direct implications for the EU Battery Regulation's 2027 SOH transparency mandate, California's Advanced Clean Cars (ACC) II durability requirements, warranty enforcement, used-vehicle valuation, right-to-repair legislation, and second-life battery markets.

We propose a fully decoupled, structure-preserving relaxation Crank--Nicolson finite element method (FEM) for the coupled Gross--Pitaevskii--Poisson (GPP) system modeling ultracold plasmas. By introducing suitable auxiliary variables to reformulate the nonlinear interaction and charge density terms, the original system is recast into an equivalent form that enables a linear, fully decoupled numerical scheme. The proposed method preserves key physical invariants, including the mass of each component and a modified discrete energy, at the fully discrete level. We establish the well-posedness and uniqueness of the scheme and rigorously derive optimal error estimates, achieving second-order accuracy in time and optimal $(k+1)$-th order convergence in space for $P^k$ finite element approximations. Numerical experiments confirm the theoretical results and demonstrate the effectiveness of the method in preserving conservation properties and accurately capturing complex dynamical behaviors of the coupled GPP system.

The theory of polyptych lattices is a framework to obtain a family of toric degenerations whose polytopes are related by piecewise-linear transformations. It can be regarded as a generalization of toric degenerations arising from cluster algebras. In this paper, we study polyptych lattices consisting of transfer maps for marked chain-order polytopes, and obtain a family of toric degenerations of a projective variety to marked chain-order polytopes for the Gelfand-Tsetlin poset. We also compute the Cox ring of this projective variety.

Let $(R,\mathfrak{m})$ be a Cohen-Macaulay local ring with canonical module that is generically Gorenstein. In this paper, I prove isomorphisms relating the minimal MCM approximations and minimal FID hulls of modules constructed from a canonical ideal $\,ω\subset R$, including $\,ω/xR$, with $\,x \in ω\,$ a nonzerodivisor, $\,(ω/xR)^{\vee}:=\text{Ext}^1_R(ω/xR,ω)$, $\,R/ω^2$, and $\,ω/ω^2$. I also prove that if $R$ is not Gorenstein, then $δ_{R}\left(ω/xR \right)=δ_{R}\left(\left(ω/xR \right)^{\vee} \right)=0\,$ and $\,γ_{R}\left(Ω^{1}_{R}\left(ω/xR \right) \right)=γ_{R}\left(Ω^{1}_{R}\left(\left(ω/xR\right)^{\vee}\right) \right)=0$, where $δ_R$ is Auslander's $\,δ$-invariant and $γ_R$ is the dual $γ$-invariant.

Quantum Neural Networks (QNNs) are a promising class of quantum machine learning models with potential quantum advantages when implemented on scalable, error-corrected quantum computers. However, as system sizes increase, deploying QNNs becomes challenging. Similar to their classical counterparts, a key obstacle to their practical applications is that large-scale QNNs may not be easily deployed on smaller systems that have limited resources. Here, we tackle this challenge by compressing QNNs via knowledge distillation. We demonstrate how well-trained QNNs on large systems can be distilled into smaller architectures with similar configurations. We numerically show that knowledge distillation helps reduce the training cost of QNNs in terms of the number of qubits and circuit depth. Additionally, we find that a self-knowledge-distillation approach can accelerate training convergence. We believe our results offer new strategies for the efficient compression and practical deployment of QNNs.

We present an algorithm that computes the girth of the intersection graph of $n$ given line segments in the plane in $O(n^{1.483})$ expected time. This is the first such algorithm with $O(n^{3/2-\varepsilon})$ running time for a positive constant $\varepsilon$, and makes progress towards an open question posed by Chan (SODA 2023). The main techniques include (i)~the usage of recent subcubic algorithms for bounded-difference min-plus matrix multiplication, and (ii)~an interesting variant of the planar graph separator theorem. The result extends to intersection graphs of connected algebraic curves or semialgebraic sets of constant description complexity.

Recent advances in large language models (LLMs) have made significant progress across multiple biomedical tasks, including biomedical question answering, lay-language summarization of the biomedical literature, and clinical note summarization. These models have demonstrated strong capabilities in processing and synthesizing complex biomedical information and in generating fluent, human-like responses. Despite these advancements, hallucinations or confabulations remain key challenges when using LLMs in biomedical and other high-stakes domains. Inaccuracies may be particularly harmful in high-risk situations, such as medical question answering, making clinical decisions, or appraising biomedical research. Studies on the evaluation of the LLMs' abilities to ground generated statements in verifiable sources have shown that models perform significantly

The radius valley, a bimodal feature in the size distribution of close-in small exoplanets, is widely interpreted as a signature of atmospheric loss and therefore provides a key constraint on the formation and atmospheric evolution of these planets. We investigate its dependence on host-star properties using 769 planets orbiting 558 stars, for which we derive stellar ages, chromospheric activity, and Galactic birth radius, together with elemental abundances. We find that the radius valley is not fully established at ages $\sim 3$ Gyr and evolves over gigayear timescales, with its prominence strongly affected by stellar population mixing. The dependence on magnetic activity is non-monotonic: a clear valley is present even among magnetically quiet stars, while highly active systems do not show a systematically stronger depletion. The valley morphology also varies with stellar composition: the valley is strongest in metal-poor stars, weakens near solar metallicity, and partially strengthens again at the highest metallicities. In addition, the valley shows sensitivity to refractory element ratios such as [Mg/Si], while correlations with [C/O] are weaker, indicating a dependence on planetary interior structure. Our results are more consistent with a dominant role for core-powered atmospheric mass loss than with purely irradiation-driven photoevaporation. Finally, the radius valley also depends on the Galactic birth environment, with systems near the estimated solar birth radius $\sim 4.5$ kpc showing a high fraction of Earth-like planets and a well-defined bimodal structure, suggesting that the Solar System formed in a region with a well-developed Earth-sized planet population.

Determining the chemical structure for a single molecule on surface from spectroscopic data represents a challenging high-dimensional inverse problem. Tip-enhanced Raman spectroscopy (TERS) enables chemically specific imaging of single molecules with sub-nanometer spatial resolution, yet reconstructing complete molecular structures from TERS maps remains difficult owing to the ambiguous vibrational signatures and reliance on expert interpretation. Here, we introduce TERS-ABNet, a deep-learning framework that formulates single-molecule structure determination from spectroscopic images as an image-to-graph inference task. Using a "two-track" architecture, the model jointly predicts probabilistic atom and bond maps, enabling direct construction of explicit atom-bond graphs without relying on predefined chemical rules. Trained on simulated datasets, TERS-ABNet achieves about 94% atom-type classification accuracy (with a mean coordinate error of about 0.23 Å), enabling to reliably recovering molecular connectivity and fully reconstruct single-molecule structure from its TERS maps. The framework generalizes across varying spatial resolutions and structural complexity through transfer learning, and successfully reconstructs the atomic structure of a single porphyrin molecule from experimental TERS data. This work establishes a general deep-learning strategy for inferring explicit atom-bond graph representations from high-dimensional spectroscopic imaging data, providing a new pathway towards automated molecular structure determination in nanoscale characterization.

Garnet-type Li$_{6.25}$Al$_{0.25}$La$_3$Zr$_2$O$_{12}$ (Al-LLZO) solid electrolytes are promising for all-solid-state batteries but are limited by interfacial resistance. In this work, dense and graded tri-layer Al-LLZO electrolytes were fabricated and tested in Li/Al-LLZO/NMC(111) full cells. After 25 cycles, the tri-layer cell delivered discharge capacity of $\sim$55 mAhg$^{-1}$, nearly twice that of the dense Al-LLZO ($\sim$27 mAhg$^{-1}$). EIS showed lower initial interfacial resistance ($\sim$373 $Ω$) and improved stability. SEM confirmed a porous-dense-porous structure, while NRA revealed enhanced near-surface lithium ($\sim$75%) compared to dense Al-LLZO ($\sim$48%). These results highlight the role of microstructural grading in improving lithium distribution and cell performance.

Quasars,asextremelyluminousanddistantspecialcelestialbodiesintheuniverse,aredrivenbyacomplexsystemcomposedof supermassiveblackholesandsurroundingaccretiondisks.Thispaperadoptsatime-domainobservationstrategyandcombines the analysis of light curves with the construction of structure functions to indirectly reveal the physical essence of the central regionofquasarsfromtheperspectiveofvariability.Theresearchdataarederivedfromthelargesampleobservationdataofthe SloanDigitalSkySurvey(SDSS).Throughextensivedatastatisticsandcorrelationanalysis,aseriesofimportantfindingshave been obtained: the characteristic parameters of the structure function of quasars show significant correlations with luminosity, black hole mass, and Eddington ratio. That is, quasars with higher luminosity, larger black hole mass, and larger Eddington ratiohavelargerstructurefunctions.Forquasarsofthesameluminosity,thelargertheEddingtonratio,thesmallerthestructure function. However, the correlation between the structure function and redshift or rest wavelength is not significant, indicating that the variabilitycharacteristicsofquasars aremainly determined bytheir own physical propertiesandareminimallyaffected by the cosmologicalredshifteffect.

Recoil corrections, which appear at order $\mathcal{O}(\frac{1}{M})$, turn out to be crucial for the pentaquark molecules with heavy flavor. In the past, such corrections were typically regarded as negligible for the formation of heavy molecules. However, our research manifests the important impacts on the spectra of possible baryon-meson bound states. In certain cases, the binding energy sharply decreases after considering the recoil corrections. Using the one-boson-exchange (OBE) model, we have studied a series of double heavy and hidden heavy pentaquark states with an SU(3) anti-triplet baryon, including $Ξ_{c}\bar{D}^{(*)}$, $Λ_{c}\bar{D}^{(*)}$, $Ξ_{c}D^{(*)}$, $Λ_{c}D^{(*)}$, along with their bottom analogues. Considering both the $S$\--{}$D$ wave mixing effect and the recoil corrections, we find that recoil corrections, working against the stability of bound states in certain isospin-singlet channels, which cannot be ignored. For the $Ξ_{c}\bar{D}$ and $Ξ_{c}D$ systems with $I(J^P)=0(\frac{1}{2}^{-})$, the $Ξ_{c}\bar{D}^{*}$ and $Ξ_{c}D^{*}$ systems, as well as their bottom counterparts, with $I(J^P)=0(\frac{1}{2}^{-})$ and $0(\frac{3}{2}^{-})$, and the $Λ_{b}\bar{B}^{*}$ system with $I(J^P)=\frac{1}{2}(\frac{1}{2}^{-})$ and $\frac{1}{2}(\frac{3}{2}^{-})$, although the bound state solution can be found both with and without considering the recoil corrections, the inclusion of recoil corrections weakens the attraction of the molecules. This phenomenon arising from recoil corrections is especially prominent in the $Ξ_{c}\bar{D}^{*}$ and $Ξ_{c}D^{*}$ systems.

We present chemical abundance ratios of 8 nitrogen-rich ([N/O]$>0.3$) galaxies at $z\sim 6-12$ identified by the first 4 years of the JWST observations, and compare these ratios with chemical evolution models. We reanalyze the JWST/NIRSpec data of these galaxies in the self-consistent manner for line fluxes and upper limits including those previously unconstrained. We derive the abundance ratios and constraints of [N/O], [C/O], [Ne/O], [Ne/C], [Ar/O], [S/O] and [Fe/O], characterizing the nebulae in the galaxies with the electron temperatures and densities measured with {\sc[Oiii]}$\lambda4363$ and {\sc[Oii]}$λ\lambda3727, 3729$ lines, respectively. We develop the chemical evolution models for the three major scenarios, Wolf-Rayet stars, supermassive stars, and tidal disruption events (TDEs) with the AGB star contribution, integrating the ejecta of the stars and core-collapse supernovae (CCSNe) over the age with yields calculated by numerical simulations. We compare the models with the [N/O] measurements and stellar ages, and find that all of the scenarios reproduce [N/O] as high as those of our galaxies. However, the time-scales of the high [N/O] ratios are too short to explain our galaxies in any of the scenarios, suggestive of very frequent failed supernovae that do not increase oxygen against nitrogen. We find that the three scenarios are distinguished in the plane of [Ne/C] vs. [N/O] due to Ne production outside CNO cycle, and that the observed abundance ratios are explained by the Wolf-Rayet models better than supermassive-star and TDE models. We argue that abundance ratios of various elements and time scales are clues for understanding nitrogen-rich galaxies.

While the numbers of superspecial curves of genus at most 3 are well understood, and several computational approaches have been developed to count superspecial curves of genus 4 with large automorphism groups, much less is known in higher genera. In this paper, we construct a feasible algorithm to enumerate superspecial hyperelliptic curves of genus 5 whose automorphism groups contain $(\mathbb{Z}/2\mathbb{Z})^3$. We implement and executing our algorithm in Magma, we succeeded in enumerating such superspecial curves in every characteristic $11 < p < 1000$.

We introduce a numerical invariant $ζ(Σ)$ measuring the end-complexity of $Σ$ and use it to organize coarse-geometric features of Map($Σ$). Our main tool is the \emph{non-peripheral curve graph} $C_{\rm np}(Σ)$, whose vertices are those essential simple closed curves that cannot be pushed out of every compact subsurface, with edges given by disjointness. Assuming Map($Σ$) is CB-generated and $ζ(Σ)\ge 5$, we prove that $C_{\rm np}(Σ)$ is connected, has infinite diameter, is Gromov hyperbolic, and that the Map($Σ$)-action has unbounded orbits. As applications, we show that if $ζ(Σ)\ge 4$ then Map($Σ$) has infinite coarse rank, and if $ζ(Σ)\ge 5$ then Map($Σ$) has at most quadratic divergence, hence is one-ended.

Developers rely on online tutorials to learn web application security, but tutorial quality varies. We reviewed 132 free security tutorials to examine topic coverage, authorship, and technical depth. Our analysis shows that most tutorials come from vendors and emphasize high-level explanations over concrete implementation guidance. Few tutorials provide complete runnable code examples or direct links to authoritative security resources such as the Open Web Application Security Project (OWASP), Common Weakness Enumeration (CWE), or Common Vulnerabilities and Exposures (CVE). We found that two visible signals help identify more useful tutorials: the presence of runnable code and direct links to official resources. These signals can help developers distinguish broad awareness material from tutorials that better support secure implementation.

The secondary zeta function is defined as a generalized zeta series over the imaginary parts of non-trivial zeros assuming (RH). This function admits Laurent series expansion at the double pole at $s=1$. In this article, we derive a new formula for the expansion coefficients of the regular part, which is similar to the Stieltjes constants formula for the Riemann zeta function. We also numerically verify and compute the new formula to high precision for several test cases. Lastly, we also apply the Brent's (BPT) Theorem for improving convergence of the main formula.

Vector quantile regression (VQR) is an optimal transport (OT)-based framework that extends linear quantile regression to vector-valued response variables and can be formulated as an OT problem with a mean-independence constraint. In this paper, we study two Sinkhorn-type algorithms for VQR with entropic regularization, building on our previous work on its duality theory. The first is a direct adaptation of the classical Sinkhorn iteration based on solving the full Schrödinger-type system characterizing the dual potentials, which requires solving an implicit functional equation at each iteration. The second algorithm, which is new in the literature, replaces the implicit update with a projected gradient step, resulting in a modified scheme that is computationally more practical. For both algorithms, and for general compactly supported marginals, we establish linear convergence in both the dual objective value and the iterates. A key innovation in our analysis is the derivation of explicit quantitative bounds on the dual potentials and Sinkhorn iterates.

A fundamental question in nonequilibrium statistical physics is whether effective equilibrium behavior can emerge at coarse-grained scales in strongly driven systems. Here, we investigate this question in the context of human mobility by analyzing five years of intercity flow data covering millions of travelers. While short-term flows are highly asymmetric, temporal coarse-graining reveals that over half of all city pairs converge toward effective flow balance, with normalized directional imbalance decaying as a power law. The remaining pairs either exhibit persistent drift-dominated currents or a crossover between these two extremes. A stochastic model decomposing mobility into directional drift and correlated fluctuations quantitatively captures the coexistence of all three regimes. Directly measured variance scaling of the fluctuation process confirms near-diffusive behavior with regime-dependent deviations. These results demonstrate that large-scale mobility networks exhibit a scale-dependent transition from broken to restored flow symmetry, with direct implications for modeling transport and spreading dynamics.

We report the detection of a molecular cloud, CO+40.05-2.40, positionally coincident with the "heartbeating" GeV source Fermi J1913+0515 at the northern boundary of the SS 433/W50 system. Millimeter and submillimeter spectroscopy with the Nobeyama 45 m telescope and the James Clerk Maxwell Telescope shows that the cloud has physical properties typical of quiescent dark clouds in the Galactic disk, with no evidence of shock heating or enhanced excitation. We examine possible high-energy emission mechanisms and find that the observed GeV luminosity cannot be accounted for by electron bremsstrahlung or hadronic interactions driven by relativistic particles originating from SS 433 under reasonable energetic assumptions. As an alternative, we propose that the gamma-rays may arise from a compact object embedded within the cloud and powered by Bondi-type accretion. In this framework, the reported heartbeat-like variability may reflect periodic modulation of the accretion flow by density waves induced by the precessing equatorial outflow of SS 433.

Ordinary differential equation (ODE) models are widely used to describe systems in many areas of science. To ensure these models provide accurate and interpretable representations of real-world dynamics, it is often necessary to infer parameters from data, which involves specifying the form of the ODE system as well as a statistical model describing the observational process. A popular and convenient choice for the error model is a Gaussian distribution with constant variance. However, the choice may not be realistic in many systems, since the variance of the observational error may vary over time or have some dependence on the system state (heteroscedastic), reflecting changes in measurement conditions, environmental fluctuations, or intrinsic system variability. Misspecification of the error model can lead to substantial inaccuracies of the posterior estimates of the ODE model parameters and predictions. More elaborate parametric error models could be specified, but this would increase computational cost because additional parameters would need to be estimated within the MCMC procedure and may still be misspecified. In this work we propose a two-step semi-parametric framework for Bayesian parameter estimation of ODE model parameters when there exists heteroscedasticity in the error process. The first step applies a heteroscedastic Gaussian process to estimate the time-dependent error, and the second step performs Bayesian inference for the ODE model parameters using the estimated time-dependent error estimated from step one in the likelihood function. Through a simulation study and two real-world applications, we demonstrate that the proposed approach yields more reliable posterior inference and predictive uncertainty compared to the standard homoscedastic models. Although our focus is on heteroscedasticity, the framework could be applied to handle more complex error processes.

The inclusion of internship courses in Software Engineering (SE) programs is essential for closing knowledge gaps and improving graduates' readiness for the software industry. Our study focuses on year-long internships at RMIT University (Melbourne, Australia), which offers in-depth industry engagement. We analysed how the course evolved over the last 10 years to incorporate students' needs and summarised the lessons learned that can be helpful for other educators supporting internship courses. Our qualitative analysis of internship data based on 91 reports during 2023-2024 identified three challenge themes the students faced, and which courses were found by students to be particularly beneficial during their internships. On this basis, we proposed recommendations for educators and companies to help interns overcome challenges and maximise their learning experience.

Neural network controllers trained via behavior cloning are increasingly deployed in cyber-physical systems (CPS), yet practitioners lack tools to trace controller failures back to training data. Existing data attribution methods assume i.i.d.\ data and standard loss targets, ignoring CPS-specific properties: closed-loop dynamics, safety constraints, and temporal trajectory structure. We propose IF-CPS, a modular influence function framework with three CPS-adapted variants: safety influence (attributing constraint violations), trajectory influence (temporal discounting over trajectories), and propagated influence (tracing effects through plant dynamics). We evaluate IF-CPS on six benchmarks across diagnosis, curation, and safety attribution tasks. IF-CPS improves over standard influence functions in the majority of settings, achieving AUROC $1.00$ in Pendulum (5-10\% poisoning), $0.92$ vs.\ $0.50$ in HVAC (10\%), and the strongest constraint-boundary correlation (Spearman $ρ= 0.55$ in Pendulum).

The human brain achieves its remarkable computational prowess not despite its inherent non-ideal factors noise, heterogeneity, structural irregularities, decentralized plasticity, systematic errors, and chaotic dynamics but precisely because of them. This paper systematically demonstrates that these traits, long dismissed as imperfections in classical neuroscience and eliminated in digital engineering, are evolutionary design principles that endow the brain with robustness, adaptability, and creativity.

Model-based controllers learned from data have the biases and noise of their training trajectories, making it important to know which trajectories help or hurt closed-loop performance. Influence functions, widely used in machine learning for data attribution, approximate this effect through first-order parameter-shift surrogates, avoiding costly retraining. Applying them to stochastic LQR, however, is nontrivial because the cost depends on the learned dynamics through the Riccati equation, and the process-noise covariance is estimated from the same residuals. We develop a three-level influence hierarchy that accounts for both channels.

In this article, we derive a series expansion of the prime zeta function about the $s=1$ logarithmic singularity and prove general formula for its expansion coefficients, which is similar to the Stieltjes expansion coefficients for the Riemann zeta function. These results can also be viewed as a generalization of Mertens's Theorems to higher order. We also numerically verify and compute the presented formulas to high precision for several test cases.

Online contention resolution schemes (OCRSs) are a central tool in Bayesian online selection and resource allocation: they convert fractional ex-ante relaxations into feasible online policies while preserving each marginal probability up to a constant factor. Despite their importance, designing (near) optimal OCRSs is often technically challenging, and many existing constructions rely on indirect reductions to prophet inequalities and LP duality, resulting in algorithms that are difficult to interpret or implement. In this paper, we introduce "stationary online contention resolution schemes (S-OCRSs)," a permutation-invariant class of OCRSs in which the distribution of the selected feasible set is independent of arrival order. We show that S-OCRSs admit an exact distributional characterization together with a universal online implementation. We then develop a general `maximum-entropy' approach to construct and analyze S-OCRSs, reducing the design of online policies to constructing suitable distributions over feasible sets. This yields a new technical framework for designing simple and possibly improved OCRSs. We demonstrate the power of this framework across several canonical feasibility environments. In particular, we obtain an improved $(3-\sqrt{5})/2$-selectable OCRS for bipartite matchings, attaining the independence benchmark conjectured to be optimal and yielding the best known prophet inequality for this setting. We also obtain a $1-\sqrt{2/(πk)} + O(1/k)$-selectable OCRS for $k$-uniform matroids and a simple, explicit $1/2$-selectable OCRS for weakly Rayleigh matroids (including all $\mathbb{C}$-representable matroids such as graphic and laminar). While these guarantees match the best known bounds, our framework also yields concrete and systematic constructions, providing transparent algorithms in settings where previous OCRSs were implicit or technically involved.