The emergence of cooperation in structured populations is fundamental to the success of human societies. Physical and online networks can drive behavioural change by altering who people interact with, thereby modifying social pressures. In this paper, we study imitation dynamics in a population of self-interested agents playing a continuous strategy Prisoner's Dilemma on a dynamically evolving weighted network. In the fast-network regime, we incorporate the edge weights into the strategy evolution before deriving and analysing the large population mean-field limit. Without noise, we establish well-posedness and show the solution collapses to a single Dirac mass. For initially separated clusters, we identify a payoff threshold and sufficient conditions for the overall level of cooperation to increase. We then introduce stochastic strategy updates, and obtain a non-local Fokker-Planck equation in the mean-field limit. We rigorously prove existence and uniqueness of stationary distributions, and show linear stability under sufficient noise. Numerics illustrate that noise can transform the deterministic consensus into stable cooperative stationary behaviour. These findings show that the fast adaptive interactions and stochastic exploration can jointly support the emergence of stable cooperation at a population level.

To meet the demands of 6G wireless systems operating in high-mobility scenarios, this paper presents a design of a random multiplexing (RM) communication system that is both storage-efficient and highly reliable. In principle, RM with cross-domain memory approximate message passing (CD-MAMP) can achieve replica maximum a posteriori (MAP)-optimal performance by constructing a fully dense equivalent channel matrix. However, its practical implementation is hindered by the large storage overhead of conventional interleavers and by performance degradation in severely ill-conditioned channels, which existing related work (focusing on interleaving and transform designs) fails to address simultaneously. To overcome these issues, we develop a storage-efficient and highly reliable system that integrates RM with CD-MAMP, referred to as RM-MAMP. Specifically, we propose a Logistic chaotic mapping interleaver with a quantitative parameter-selection criterion, and a dual-stage high-order permutation polynomial interleaver, both of which achieve nearly identical bit-error-rate (BER) as fully random interleavers while reducing the interleaver storage from O(N) to O(1) and significantly lowering interleaver signaling overhead. We further propose a highly reliable interleaved transform framework, comprising an interleaved phase perturbation transform and a multi-layer interleaved coupled transform, to enhance the incoherence and diversity of the equivalent channel matrix. Simulation results show that the proposed storage-efficient interleavers maintain BER performance comparable to fully random interleavers, while the highly reliable transforms provide over 4 dB gain in severely time-varying channels, confirming the dual benefits of reduced storage overhead and improved robustness for the enhanced RM-MAMP system.

We study the non-leptonic weak decays of doubly charmed baryons (${\cal B}_{cc}$) into singly charmed baryons (${\cal B}_c$) and vector mesons ($V$), denoted as ${\cal B}_{cc}\to{\cal B}_{c}V$. The short-distance contributions are calculated within the naive factorization hypothesis, while the long-distance final-state interaction effects are modeled via hadronic triangle diagrams. Unlike previous approaches, which compute only the imaginary part using the Cutkosky cutting rule, we evaluate the complete loop integrals to obtain both the real and imaginary parts of the amplitudes. These provide the nontrivial strong phases essential for CP violation. The model parameters are determined using experimental data. With this improved calculation method, we predict the branching ratios and decay asymmetry parameters for various decay channels, as well as $CP$ violations for short-distance dominated and singly Cabibbo-suppressed channels. This strengthens our theoretical framework for future study of doubly charmed baryons. Certain decays, primarily driven by long-distance effects, have been calculated; their observation in future experiments could help clarify the role of final-state interactions in charm baryon decays. Therefore, our calculation of ${\cal B}_{cc}\to{\cal B}_{c}V$ provides crucial predictions for branching ratios, decay asymmetry parameters, and $CP$ violation, which are essential for guiding experimental study at LHCb.

This work presents a new method for principal component analysis (PCA) of a mixed-type data consisting of continuous, binary, integer-valued and positive continuous variables. The data are assumed to come from a probability model, where the parameters of the exponential family distributions are determined by a set of shared Gaussian latent variables. The proposed method, MTPCA, is based on estimating the covariance matrix of these latent mixtures through the method of moments. A way to sparsify the component loadings is presented and aligns with the classical theory of sparse PCA. We propose a strategy for estimating the principal component scores and discuss the choice of the latent dimension. The method's performance is studied with a simulated mixed-type data and we illustrate the model on the Zoo data set consisting of binary animal characteristics.

We characterize the quasi-stationary distribution (QSD) of the bond directed-percolation line of the Domany--Kinzel automaton using a matrix-product-state representation of the probability distribution, obtained by projecting out the absorbing state and iterating the transfer matrix. Unlike moment- or sampling-based methods, this yields the full conditional distribution and direct access to information-theoretic diagnostics. The spatial structure of the QSD changes sharply across the transition: the active phase is bulk-like with finite density, whereas in the inactive phase the surviving activity collapses into a single flock occupying a vanishing fraction of the chain, with an internal filling that ranges from a single cluster deep in the inactive phase to a loose, partially filled group near criticality. This picture carries a sharp information-theoretic signature: throughout the inactive phase the bipartite mutual information of the QSD equals the entropy of a single binary choice -- whether the flock lies to the left or right of the cut -- so the surviving clusters together encode just one bit of positional information, corresponding to a single effective cluster. The approach extends matrix-product-state techniques to the projected eigenvector defining a QSD, opening information-theoretic diagnostics for absorbing-state systems that bulk-observable methods cannot reach.

This manuscript addresses a hierarchical control system designed to suppress traffic congestion. The lower-layered controllers, implemented in each controlled vehicle, monitor microscopic vehicle behaviors and assist human drivers to ensure sufficient spacing for following vehicles. This spacing logic is designed based on the Control Barrier Function. Meanwhile, the upper-layered controller monitors the macroscopic traffic flow and activates the necessary lower-layered controllers, using a data-driven approach for the activation logic design. Furthermore, the effectiveness of the proposed control system is evaluated in a traffic flow simulation environment constructed using real-world traffic data.

Trace norms are fundamental to quantum information theory, yet in many-body systems their evaluation remains a major computational bottleneck, as it generally requires diagonalizing exponentially large operators. Here, we overcome this bottleneck by introducing a controlled tensor-network algorithm for estimating the trace norm of matrix product operators without full diagonalization. The key idea is to combine Zolotarev's rational approximation to the sign function with a variational formulation solved using a density-matrix-renormalization-group-like algorithm. The resulting approximation is systematically improvable, with its accuracy controlled by the rational approximation parameters and the spectral weight near zero. Beyond the reach of exact diagonalization, we demonstrate controlled trace-norm calculations for entanglement negativity, quantum fidelity and quantum Fisher information, achieving substantially improved accuracy over polynomial-based Lanczos approaches. Our results establish trace-norm-based quantities as practical tensor-network observables, opening a route toward tensor-network studies of quantum information in mixed states.

Thin films draining on top of curved surfaces occur in coating, manufacturing, and geophysical flows, where predicting accumulation and thinning is crucial. Unlike singularities associated with contact lines, boundaries, defects, a smooth saddle alone can produce a locally singular drainage thickness distribution. The singularity stems from competing converging and diverging flow and is regularized within a dynamically selected region where drainage, hydrostatic pressure, and capillarity balance. Saddles thus emerge as generic building blocks for thin-film drainage on complex topographies.

We investigate the impact of power amplifier (PA) nonlinearities on the sensing performance of affine filter bank modulation (AFBM). While AFBM offers several advantageous properties for integrated sensing and communications (ISAC) - including reduced out-of-band emission (OOBE), low peak-to-average power ratio (PAPR), and natural robustness to doubly-dispersive (DD) channel effects - mitigating waveform distortion typically requires highly linear PAs. This creates a fundamental contradiction with ISAC applications, which demand high transmit power for reliable sensing. Our analytical results reveal that the structure of the effective AFBM modulation matrix dictates how distortion propagates within the ambiguity function (AF). Furthermore, simulations demonstrate that both the AF and the overall sensing performance of AFBM remain remarkably insensitive to such nonlinearities. These findings highlight the robustness of AFBM, making it a highly viable candidate for practical ISAC deployments constrained by hardware impairments.

CUDA collective operations often sit on security decision paths: votes accept batches, reductions aggregate evidence, shuffles select representatives, and barriers order checked state before use. Such decisions depend not only on computed values, but also on which lanes are represented, what evidence they contribute, which lane speaks for the group, and which checked state reaches commit. We identify this participation metadata as decision-making non-control data. We define Collective Semantic Corruption (CSC), a non-control-data attack family in which range-valid masks, predicates, source lanes, descriptors, group labels, or epochs cause a CUDA-conforming collective to authorize a decision over the wrong membership, contribution, role, or validation-to-use state. The kernel reaches the intended collective site and executes the expected primitive; the primitive represents the wrong authority set. We model CSC with a site-local participation-authority contract. A protected collective derives, recomputes, checks, or freezes membership, contribution, role, and temporal state before authorization. We evaluate CSC across NVIDIA CUDA collective primitives, trigger channels, compact workload-style kernels, reduced idiom bridges, and admission-guard harnesses. In a CUDA-defined contract-conformance suite spanning the four authority dimensions, corrupted participation metadata causes a trusted-reference mismatch in 102/102 instances, while hardened variants preserve that reference in 102/102. We report 13 synchronization-sensitive instances separately. We then introduce Collective Integrity Contracts (CIC), a wrapper discipline that binds participation metadata before collective use. For CUDA collective decisions, security depends on both the values computed and the participants represented.

The Network Data Analytics Function (NWDAF) is central to enabling zero-touch network management in fifth-generation (5G) networks by supporting real-time analytics and closed-loop automation. Despite its critical role, open-source NWDAF implementations remain limited in scope and accessibility. In this paper, we develop an open-source NWDAF, compatible with the open-source core network Free5GC, that collects network data via subscriptions to Network Functions (NFs), and also includes an integrated Large Language Model (LLM) interface that enables natural language interaction with human operators. The interface processes user intents, encodes them using a semantic embedding model, and maps them to one of seven predefined intent categories to trigger analytics queries or event subscription commands. This architecture abstracts the complexity of traditional interfaces, allowing non-expert users to manage network analytics and subscriptions with ease. The system supports Access and Management Function (AMF) and Session Management Function (SMF) event subscriptions, real-time monitoring, and analytics retrieval via Prometheus, all accessible through a conversational interface. By bridging AI-driven intent recognition with standardized network analytics, our implementation enhances operator usability and provides a foundation towards AI-native 6G networks. The source code and datasets generated during the current study are available in the github repository, https://github.com/HenokDanielbfg/testbed.

2D electrocatalysts that enable hydrogen evolution at low overpotentials offer an attractive alternative to expensive platinum-based systems. Here, we report the growth of Janus transition metal dichalcogenide (TMD) monolayers (MLs), SeMoS and SeWS, on Au foils using chemical vapor deposition, and systematically compare their catalytic properties in the context of hydrogen evolution reaction (HER) with those of their parent TMDs. The Janus MLs exhibited significantly enhanced catalytic performance relative to the parent TMDs. Furthermore, these MLs on Au foils were subjected to sonochemical treatment in polar and non-polar solvents, in which the treatment with polar solvents led to a substantial improvement in the HER activity of Janus MLs. In particular, SeMoS MLs treated with water showed a low overpotential of ~63 mV, a Tafel slope of ~42 mV/dec, and an exchange current density of ~10$^{-3}$ mA cm$^{- 2}$, approaching that of platinum. Analyses indicate that enhanced electrocatalytic activity is associated with tensile strain induced by Au surface restructuring and the formation of defects in Janus MLs, as shown by experimental observations and by density functional theory calculations. The enhancement in catalytic performance due to sonochemical treatment emphasizes the importance of our results for developing novel catalytic systems for HER based on Janus 2D materials.

The rotational velocity of interstellar gas in the Milky Way, and other galaxies, has been taken to represent the circular velocity of a test particle in the Galaxy gravitational field, and hence an indicator of the Galaxy mass. The derived circular velocity is found to be too high for the gas to be gravitationally bound to the galaxy given the observed Galaxy mass in stars and gas, and consequently an extra component of mass in the Milky Way and other galaxies, namely dark matter, has been postulated. However recently the observational satellite Gaia, has been carrying out ground-breaking astrometric observations to accurately measure, inter alia, the three dimensional velocities of stars in the vicinity of the Sun and beyond. This has revealed that the circular velocity derived from the stellar population is much less than that of the gas, and the rotation curve, circular velocity versus radius, is distinctly declining with radius, whereas the gas rotation curve is not declining. By combining results from multiple observations of the gas velocity, averaging the velocities in radial bins, we establish that there is a grand average rotation curve. This can be compared directly with a grand average of the published Gaia rotation curves, and the confidence level in the difference between the two estimated by statistical analysis. The difference is shown to have a high degree of confidence, and increases with galactocentric radius. The lower circular rotation curve from the stellar velocities has resulted in significantly reduced estimates of the dark matter mass fraction of the Milky Way. The higher rotation of the gas lacks an explanation, but it is unlikely to be an accurate indicator of the kinematic mass of the Galaxy. This also has significant consequences for the mass of external galaxies based on gas rotation curves.

Recent CUDA exploitation work shows that GPU memory bugs can escalate into device-side control-flow corruption, as kernels later consume corrupted return continuations, function pointers, dispatch-table entries, or branch targets. For deployed CUDA binaries, the relevant security boundary is executed NVIDIA SASS, after PTX lowering, inlining, ABI decisions, register allocation, spills, predication, and SIMT execution; source- or PTX-level policies do not capture this boundary. We present WarpGuard, to our knowledge the first protected-site CFI system for CUDA device binaries operating on executed SASS. WarpGuard enforces at protected sites: recovered SASS instructions or sequences that consume control-flow state, provide sufficient binary evidence to derive policy, are checked before release, and fail closed on violation. It authenticates backward-edge continuation state for instrumented returns, validates recoverable forward targets per site, and reports fixed-edge, unsupported, profile-excluded, fallback, and no-surface outcomes outside the protected denominator. On 77 CUDA artifacts, WarpGuard classifies 51,621 SASS control-flow sites, including 1,343 returns and 154 supported forward target-set entries, and records 52.2 million dynamic checks. In representative backward- and forward-edge corruption attacks, native execution reaches attacker-selected behavior, detect-only mode records the expected violation, and enforcement fails closed before releasing the invalid protected transfer. Public-code evidence shows that the same SASS consumption patterns occur in real CUDA systems, including runtime dispatch tables, cuFFT callbacks, generated callable tables, and uploaded device-function pointers. WarpGuard delivers auditable protected-site CFI for CUDA SASS and separates dynamic-instrumentation enforcement from callback-free SASS timing and patch-cache feasibility.

Mixture-of-Experts (MoE) and reinforcement learning (RL) post-training now dominate large language model (LLM) development, yet expert load imbalance remains a critical challenge. Existing load-balancing systems target pre-training by relying on historical step-level statistics. However, these methods fail under the unique workload dynamics of RL post-training: the step-level load is stable, but the tiny batch sizes processed during micro-steps cause severe, high-frequency load fluctuations. We introduce ForeMoE, a micro-step-level load balancing system for MoE RL post-training. Instead of relying on historical statistics, ForeMoE exploits the multi-stage RL pipeline (rollout, recompute, policy update) by using foreseeable routing information from the rollout stage to proactively guide load balancing in the remaining stages. To support frequent per-micro-step reconfiguration, ForeMoE employs a hierarchical planner that decomposes the NP-hard load balancing problem into tractable sub-components, alongside a transfer engine that leverages complementary hardware paths (CPU-assisted and GPU-direct) for overlapped expert transfer. Evaluations on 64 GPUs demonstrate that ForeMoE achieves up to a 1.45$\times$ speedup over state-of-the-art RL post-training systems.

Some rocky planets orbit so close to their host stars that stellar heating melts their surfaces. They offer a rare glimpse of planets in a magma-ocean state, providing an observable analogue to processes that likely shaped the early Earth and other terrestrial planets during their infancy. Recent JWST observations of five eclipses of the prototypical lava planet 55 Cnc e have confirmed earlier hints that it exhibits highly variable thermal emission, with low-resolution spectroscopy pointing to a possible volatile-rich atmosphere likely rich in CO and CO2. Here we report on an analysis of the same JWST datasets but at their native spectral resolution, utilizing cross-correlation techniques. An unambiguously strong ~8 sigma signal from CO in emission is recovered during one out of five epochs, with potential ~3 sigma detections during two others. The strongest observed cross-correlation signal is difficult to reconcile with a hydrostatic atmosphere, requiring a steep and strong thermal inversion at the right pressure level (~1-10 mbar) and a relative abundance of CO2 that is at least 3 orders of magnitude lower which would otherwise mask the CO signal. Self-consistent atmospheric modelling indicates that this is most readily achieved in a hydrogen-rich atmosphere, which produces the steepest inversions and highest CO/CO2 ratios. The pronounced epoch-to-epoch variability suggests that the CO signal does not trace a static atmosphere alone, but may reveal a transient, dynamically active component, potentially linked to variable atmospheric outflow.

Code retrieval is becoming central to coding agents, but agentic coding requires more than matching a natural-language query to an isolated snippet. Given a user request, a coding agent needs to navigate a concrete repository state, locate relevant files and functions, gather supporting context, and filter similar in-repository distractors. Existing code retrieval benchmarks mainly evaluate docstring-to-function or snippet-level matching, thereby missing this requirement-driven repository search problem. To address this gap, we introduce CORE-Bench, a comprehensive benchmark for code retrieval in the era of agentic coding. CORE-Bench evaluates code retrieval ability at three levels: code understanding, issue-to-edit localization, and broader context retrieval. Built from curated code-search tasks and SWE-bench-series instances, CORE-Bench contains over 180K queries and 106K broader-context relevance labels. Experiments with representative embedding models show a sharp drop from traditional code search to code retrieval in agentic coding settings. Simple supervised fine-tuning of existing embedding models significantly improves performance in this setting, suggesting substantial room for further progress.

Large language models (LLMs) have shown great promise for automated code translation, yet existing approaches often rely on token-level statistical patterns rather than sufficient understanding of program semantics. As a result, translated programs may still contain logical and semantic errors. Although high-quality semantic guidance, such as functional descriptions and test cases, can help mitigate these errors, such resources are often unavailable in real-world scenarios. This raises two key challenges: how to construct rich semantic information directly from source code, and how to ensure that such semantics are accurate and reliable enough to guide translation.To address these challenges, we propose Multisage, a multi-semantic augmentation and self-calibration framework for LLM-based code translation. Multisage consists of three modules. First, a semantic representation parsing module extracts structured base semantics from source code, including data-flow graphs, type constraints, and external API information. Second, a multi-semantic augmentation module builds on these representations to generate diverse augmented semantics, including code summaries, function-level test cases, and API-oriented descriptions and tests. Third, a semantic consistency calibration module uses semantics-preserving mutations and cross-semantic consistency verification to filter, calibrate, and refine the generated semantics.Experiments on the HumanEval-X code translation benchmark show that Multisage improves translation success rates by up to 2.22 times across diverse backbone models. It consistently outperforms vanilla prompting, instruction-tuned LLMs, and Chain-of-Thought reasoning, with the largest gains observed on smaller models. These results demonstrate that explicit semantic augmentation can substantially improve the reliability of LLM-based code translation.

The quantum anomalous Hall effect in altermagnets is difficult to realize because spin-up and spin-down states remain degenerate at the $Γ$ point in the nonrelativistic limit. We start from the Bernevig-Hughes-Zhang model to incorporate nontrivial band topology. We demonstrate that the combined effects of an external magnetic field, spin canting, and ferroelectric orbital hybridization lift the degeneracy at the $Γ$ point, enabling electric-field control of the Chern number. A minimal two-dimensional d-wave altermagnetic model with band inversion then realizes a ferroelectrically tunable Chern insulator with spontaneous spin canting. The ferroelectric polarization controls the topological phase and the orbital angular momentum, enabling a rich phase diagram with C = $\pm 1$ and C = $\pm 2$ through a Berry-curvature reorganization linked to the spin canting response and ferroelectricity. Our results establish a symmetry-consistent route to electrically tunable Chern insulating phases in altermagnetic materials, opening opportunities for low-power topological and orbitronic devices.

We report ground-based coherent VHF radar observations of extreme turbulent field-structures detected in coincidence with a magnetospheric substorm-associated magnetotail dipolarization. The field-structures are observed by the ICEBEAR radar, in the form of Farley-Buneman (FB) waves in the auroral electrojets, and the field-structures themselves move an order of magnitude faster than the saturation speed of the underlying FB waves, implying transient electric field sources up to 330 mV/m in strength. The field-structures are identified and automatically tracked using an unsupervised clustering & tracking algorithm, applied to clutters of ICEBEAR radar backscatter targets, a method that turns the Doppler radar into a tracking radar capable of measuring the ionospheric ExB-drift by proxy. We place this finding in a coordinated multi-instrument context. Three THEMIS spacecraft observed the dipolarization event in-situ in the near-Earth plasma sheet. In the ionosphere, Swarm A, crossing through the guilty auroral arc at the onset of the dipolarization event, recorded clear signatures of propagating Alfvén waves threading the relevant flux tube. We interpret the ICEBEAR transients as the natural ionospheric foot signature of a shear Alfvén pulse launched by the bipolar space-charge (Hall) electric field of the thinned current sheet, with amplification along the converging flux tube, partial reflection at the ionospheric boundary, and spatial sharpening by precipitation-produced Pedersen-conductance gradients on the auroral arc edges. A one-dimensional wave-transmission analysis recovers the observations. Our results elucidate a tightly controlled coupling between magnetotail processes and meter-scale auroral plasma turbulence, and demonstrate the capability of ICEBEAR to resolve extreme, transient electric-field enhancements in the ionosphere.

Generating stochastic trajectories for asset classes is an increasingly relevant task in quantitative finance. Traditional approaches, such as the stationary bootstrap, preserve by construction the empirical distribution of asset-class returns, but do not ensure that each individual simulated path is economically realistic: scenarios may be valid in distribution while single trajectories fail to represent plausible states of the world. To address this limitation, we review semiparametric simulation methodologies that combine a parametric structure, which enforces realistic dynamics, with the resampling of model residuals, which preserves the stochastic component observed in historical data. The issue is particularly acute for interest rates, where direct resampling of rate changes may produce implausible yield-curve evolutions despite correct distributional properties. Our empirical analysis shows the effectiveness of semiparametric bootstrap methods based on autoregressive or mean-reverting specifications. In the fixed-income setting, combining these methods with fully parametric term-structure models yields more coherent and realistic simulations of yield-curve dynamics.

This paper investigates an analytical Koopman-based nonlinear model predictive control (K-NMPC) approach for tracking control of virtually coupled train systems. A nonlinear train movement model incorporating train dynamics, speed and control input limits, passenger comfort constraints, and collision avoidance is systematically lifted into a finite-dimensional Koopman space through closed-form observable functions. After freezing the affine parameter-varying lifted predictor along the shifted predicted trajectory, the online optimal control problem is solved as a quadratic program that can be solved efficiently. The proposed KNMPC is benchmarked against a time-discrete NMPC scheme, demonstrating comparable control performance with significantly reduced online computation time and strong potential for real-time implementation in practical virtually coupled train control systems.

In this article, we study some classes of solutions for a stationary Navier-Stokes equation where we consider a rough drift given by a singular integral operator which does not belong to the classical Calder{ó}n-Zygmund family of singular integral operators. Given a small external force, we will construct solutions to this system in the framework of weighted Morrey-Sobolev spaces. The use of Morrey-based Sobolev spaces provides a more general setting than the usual Lebesgue-based Sobolev spaces, and the presence of Muckenhoupt weights will allow us to present some existence and uniqueness results from several points of view.

In this paper, we introduce a class of preference robust risk measures-\emph{robust optimized certainty equivalents} (ROCE)-which encompasses several widely used measures, including Conditional Value-at-Risk and expectiles, as special cases. Motivated by recent developments in distributionally robust optimal reinsurance (DROR), we investigate DROR problems under the ROCE risk measure and consider two prominent uncertainty sets: the mean-variance uncertainty set and the Wasserstein uncertainty set. For the mean-variance uncertainty set, we reformulate the infinite-dimensional optimization problem into a finite-dimensional one by showing that it suffices to consider three-point distributions. This leads to a unified and explicit formulation for a broad class of ROCE risk measures and offers a simplified framework that also recovers earlier results for Conditional Value-at-Risk and expectiles. For the Wasserstein uncertainty set, we also derive a tractable finite-dimensional formulation. The resulting data-driven models enable efficient computation and facilitate a systematic comparison between moment-based and Wasserstein-based uncertainty sets in the optimal deductible design. Numerical experiments are exhibited to illustrate the performance of our reformulated programs.

For a set $X$ of integer points, the relaxation complexity $\operatorname{rc}(X)$ is the smallest number of facets of any polyhedron $P$ such that $P \cap \mathbb{Z}^d = X$. In this paper, we focus on the case where $X$ is the discrete standard simplex $Δ_d = \{\mathbf{0}, \mathbf{e}_1, \dots, \mathbf{e}_d\}$. We show that $\operatorname{rc}(Δ_d) = O(\log d)$ by an explicit, elementary construction. This improves upon the previously best-known upper bound $\operatorname{rc}(Δ_d) = O(d / \sqrt{\log d})$ due to Aprile, Averkov, Di Summa, and Hojny (2024) and matches an asymptotic lower bound by Averkov and Schymura (2022).

Cells dynamically generate, transmit, and dissipate stress. Central to these processes is the actomyosin cortex, an active contractile material that drives cellular mechanical behavior. While prior studies have focused on freely contracting actomyosin systems, the role of mechanical constraints such as adhesion to boundaries remains less explored. To address this, we employ reconstituted actomyosin gels to investigate cellular contractility. We study contraction dynamics under pinned boundary conditions, where the gel is adhered transversely to two opposing surfaces, mimicking supracellular actomyosin networks in tissues and embryos. We find that pinned contraction leads to stress buildup, delaying contraction, producing intermittent dynamics, and generating spatially nonuniform strain fields. Stress is relieved through several pathways, including active-stress-driven symmetric constriction and defect-driven processes such as boundary detachment and internal rupture. We develop a hydrodynamic model incorporating elastic, viscous, and active stress contributions that distinguishes between stress-accumulation and stress-release phases and links variations in active stress to the observed intermittent dynamics. The model predicts distinct energy relaxation rates before and after detachment events, providing insight into stress dissipation. We compare experiments with numerical simulations, which reproduce the observed behavior and reveal how internal energy is generated and dissipated during stress buildup and relaxation. Together, our results demonstrate how boundary conditions and spatial heterogeneity govern the mechanical behavior of contractile active gels. These findings provide insight into stress regulation in cellular and tissue-scale systems and may inform the design of adaptive soft materials and bioinspired robotic systems.

Earthquakes propagating faster than the shear wave-speed are commonly thought to undergo a super-shear transition upon which they discontinuously jump from the sub-Rayleigh regime to the super-shear one. The super-Rayleigh regime, i.e., the range of propagation speeds between the Rayleigh and shear wave-speeds, is regarded as "forbidden" by the two-dimensional classical rupture theory. Here, we revisit the assumptions underlying the classical theory and develop a rupture theory that takes into account the dependence of the fault strength (frictional resistance) on the slip rate. The theory quantitatively agrees with numerical simulations nearly up to the Rayleigh wave-speed. Yet, very close to the latter, two-dimensional rupture solutions change their character due to frictional rate nonlinearity and rupture continuously propagates through the "forbidden" super-Rayleigh range into the super-shear regime, without a sharp super-shear transition. These results demonstrate that frictional rate dependence, generically observed in experiments, can have profound implications for fast earthquake propagation.

The second solar spectrum is the spectrum of the Stokes parameter Q (linear polarization) close to the solar limb. It is made of a few polarized lines with Q/I of about 1% (such as CaI, SrI, or BaII), but most lines exhibit weaker polarization. This paper presents processing of unpublished observations made in 2008 with the Meudon solar tower spectropolarimeter, which are of interest for weak and turbulent unresolved magnetic field measurements in the quiet Sun, through the Hanle effect.

In this work we consider tensor train varieties. These are varieties of tensors arising in a range of fields, including quantum many-body physics and machine learning. Using methods from integral geometry, we obtain a combinatorial expression for their degrees. We provide the ready-to-use julia package TTVarietyDegree$.$jl$.$

We revisit the large population limit of our epidemic model with infection age dependent infectivity and progressive immunity waning, under the assumption that the supremum in $t$ of the random infectivity function has a finite expectation, while the previous proofs assumed that this supremum admits a deterministic upper bound.