Papers

We study the parabolic vectorial Allen–Cahn equation in two space dimensions for a fixed smooth potential with finitely many non-degenerate wells. Our result provides a parabolic extension of Bethuel's elliptic compactness theorem: at almost every positive time, the diffuse energy, potential energy, and gradient tensor converge to measures concentrated on a countably \(1\)-rectifiable interface and satisfy all the Bethuel-type relations. In the scalar case, the tangential defect vanishes and the usual mean-curvature-flow structure is recovered. For general vectorial potentials, the limiting stress and dissipation yield a two-mobility system: the normal energy flux balances weighted curvature, while a tangential internal mobility transports residual tangential energy. Thus the result extends the Allen–Cahn-to-Brakke framework of Ilmanen from scalar to vector-valued systems, with an additional non-negative dissipation defect in the localized energy inequality.

Wearable sensing enables intuitive hand gesture recognition for human–computer interaction, augmented reality, and prosthetic control, yet subject–independent recognition remains challenging because wearable signals provide only indirect and highly subject-specific observations of hand motion. Although visual information can improve wearable gesture recognition, requiring it during inference increases sensing complexity and limits practical deployment. We propose ViMoWear, a visual-motion-guided framework that leverages synchronized 3D hand motion as training-only supervision while requiring only wearable sensing for gesture classification at inference. Specifically, Motion-Guided Cross-Subject Contrastive Learning (MGCL) promotes subject-robust representations, and Thumb-Aware Masked Motion Reconstruction (TMMR) preserves fine-grained motion information. The leave-one-subject-out experiments on a synchronized sEMG–IMU–pose dataset demonstrate consistent improvements over supervised baselines across multiple sensing configurations, while the learned representations also support classifier-free retrieval. The proposed training-only visual motion supervision improves the generalization of wearable representations to unseen subjects.

We study the problem of computational efficiency for linear bandits in high-dimensional settings with a finite arm set. In linear bandits, the increase in the dimension $d$ of the feature vectors leads to growing computational costs of $O(d^2)$ at each round of update. Traditional sketching-based methods such as SOFUL reduce computation via fixed-size matrix sketching, yet run the risk of incurring vacuous linear regret when the spectral tail of the data is heavy and the sketch size is inadequately selected. To guarantee regret convergence and effectively reduce computational costs, we introduce a clustering mechanism and propose the Cluster Sketch Linear Bandit (CS-LB) algorithm. Our method preserves the full covariance information in each cluster to guarantee robust sublinear regret without spectral-tail vulnerabilities, performs cluster switching by assigning a sentinel for each cluster, and reduces per-round update computation to $O(l^2d)$ via a tunable sketch size $l<d$. Experiments on synthetic datasets demonstrate that our method consistently maintains a favorable trade-off between efficiency and regret.

Concept erasure methods that operate via linear projection assume that features occupy separable subspaces. We show this assumption fails under dense superposition: when two features are forced into an antipodal pair sharing a single subspace, state-of-the-art linear erasure destroys both, not just the target. Networks trained with gradient descent instead solve this problem non-linearly, but not uniformly: they converge to one of two distinct circuit-level solutions depending on initialization, which we call mirror and shadow solutions. We map this bifurcation as a function of feature entanglement, show it reflects a stable attractor structure rather than an artifact of our setup, and use targeted causal interventions to demonstrate that both solutions leave a substantial, measurable trace of the erased feature's representation intact, recoverable through a single scalar patch rather than requiring any further training. This mirrors a failure mode recently observed empirically in LLM unlearning, where suppression rather than deletion allows forgotten knowledge to resurface; our results offer a mechanistic, causally-validated account of why that failure mode occurs.

It has been shown recently that chiral dynamical multiferroicity can be generated on a ferroelectric lattice whose electric dipoles respond masslessly under chiral optical pumping. Here we demonstrate that, when driven by ultrafast electric pulses, chiral dynamical multiferroicity can also emerge even in situations where the external field is achiral. We reveal this striking phenomenon using a prototypical system of a BaTiO$_3$ moiré ferroelectric lattice, emphasizing the key factor that its chiral electric dipoles inevitably behave massively upon ultrafast driving. At a deeper level, the massive nature is attributed to the anisotropic and nonadiabatic dipolar responses, as captured by the phase difference between the faster longitudinal and slower transverse components of the ferroelectric polarization. Crucially, such a phase difference naturally also gives rise to dynamical magnetization, which exhibits chiral magnetic textures with monopole-like topology coexisting with the ferroelectric chirality. These findings establish the dipolar mass as an enabling and tunable degree of freedom in inducing chiral dynamical multiferroicity, offering new avenues for ultrafast, non-contact magnetic control using pure electric probes.

We study joint oscillation conditions for commutators of bilinear rough singular integrals with bounded mean-zero angular kernels. For second-order commutators with two possibly distinct complex-valued symbols, we prove lower bounds under a geometric non-degeneracy assumption. These bounds distinguish the commutation positions: mixed commutators control the product of the separate quadratic oscillations, while repeated-position commutators of the partial transposes additionally control the quadratic average of the product of the centered symbols. We also establish sparse domination for iterated commutators, retaining the symbol oscillations inside the local averages. For each fixed commutator order, the sparse constant is $O(s/(s-1))$ as the averaging exponent $s$ decreases to $1$. The resulting joint oscillation conditions yield strong bounds in the Banach range and weak bounds in the quasi-Banach range. At the natural exponent triples, the necessary and sufficient conditions differ by an arbitrarily small increase in the oscillation exponents.

Long-context evaluations often test whether a model can recover distant evidence, but recoverability does not guarantee behavioral influence. We test the prediction that a distant discourse anchor can remain explicitly recoverable yet fail to change the locally preferred reading of a familiar multiword expression; such failures should concentrate when the model's no-anchor default conflicts with the anchor, while prior-correct decisions remain largely preserved. We introduce Multiword Expression Effective Context Length (MWE-ECL), a bilingual diagnostic whose matched anchor-retrieval, no-anchor prior, and interpretation prompts measure explicit recoverability, model-observed defaults, and anchor-conditioned decisions, respectively. Across eight English deployment panels on a shared 0-128K grid, retrieval-control accuracy on prior-conflict items is 0.989-1.000, prior-conflict override spans 0.806-1.000 (0.809-1.000 after conditioning on correct retrieval), and preservation of prior-correct decisions remains 0.977-1.000. A same-call control querying retrieval and interpretation in one prompt reproduces the gap for DeepSeek V4 Pro (1.000 retrieval versus 0.900-0.920 interpretation), showing that separate invocations are not its sole explanation; smaller or absent gaps in the other two models bound its generality. For DeepSeek V4 Flash, separate prompt-fit tests retain perfect retrieval with lower interpretation at 512K and 1M, while foil-consistent cues shift the no-anchor prior far more than retrieval; cross-model cue effects are heterogeneous. A separately reported 10-family Chinese subset shows similar descriptive gaps, but imperfect retrieval for some models prevents an integration-only attribution. MWE-ECL therefore evaluates whether explicitly recoverable distant context changes a competing local semantic decision.

This paper investigates a stochastic linear-quadratic (SLQ) control problem for a regime-switching jump-diffusion system. Unlike traditional regime-switching diffusion systems that couple a diffusion process with a Markov chain, we incorporate the jumps of the Markov chain into the state equation. This modeling methodology effectively captures potential gains or losses of the system during the regime transitions. It should be noted that the introduction of Markov chain jumps into the state equation leads to increased complexity in the corresponding coupled differential Riccati equations (CDREs), thereby rendering the solvability of the control problem more challenging. Under the assumption that the cost functional is uniformly convex, we establish the unique solvability of the corresponding CDREs. Building upon this foundation, we derive a closed-loop representation for the unique open-loop optimal control. Finally, we apply our theoretical results to the mean-variance portfolio selection problem in a regime-switching financial market with Markov chain jumps and obtain its efficient frontier.

Existing machine learning (ML) scaling laws relate predictive loss to compute, model parameters, and data. However, as models are increasingly deployed through agentic harnesses, loss alone is insufficient to characterize downstream performance: models with similar loss can exhibit different capabilities in reasoning, retrieval, planning, and adaptation. Yet, no unified framework connects such capabilities to the coupled resources available across the ML lifecycle. We bridge this gap by introducing a capability manifold, a multidimensional framework mapping downstream capabilities to pre-training, post-training, and test-time resources through bounded scaling functions. Analytical Jacobians quantify capability sensitivity to resource changes and interactions. As an initial application, we embed Kaplan- and Chinchilla-type scaling laws and test-time compute within the framework, demonstrating how existing scaling relationships can be unified as trajectories on a common capability manifold.

A coherent radar observes sea clutter through a non-injective multiplicative combination of latent texture and coherence variables. We study a class of partially observed slow–fast diffusions for which the projected quadratic covariance has the form \(Q=S+qyy^\top\), using Field's sea-clutter diffusion as a solvable benchmark. For fixed-shape fast covariance, we derive an exact generalized spectral-gap criterion for recovery of the latent slow coordinate and a stability bound. When the fast covariance changes shape, we obtain an invariant scale–shape decomposition and exact conditions for reinforcement or cancellation of the latent quadratic signature. We then quantify the loss of resolvability caused by finite sampling and receiver noise. Controlled CIR–OU simulations verify the analytic identities and exhibit regimes in which structural observability does not yield stable reconstruction.

A topological pump transports a conserved quantity. Yet temporal modulation exchanges energy with the field, so the transported quantity must be identified from Maxwell's equations. Here we connect band topology to the temporal displacement of conserved Maxwell wave action in a photonic time crystal. The temporal Wannier function of an isolated positive-action band carries unit action with zero net energy flux, and its temporal center is a Berry polarization. Over one adiabatic cycle, that center shifts by the band Chern number: one cell for a rigid translation and two for a two-tone cycle within a single band.

LLM coding agents increasingly operate inside game-engine repositories, where application logic is inseparable from serialized assets: a single gameplay change may span C\# scripts, prefabs, scenes, and ScriptableObjects wired together by Unity GUIDs. The retrieval tools agents carry today—shell utilities and code-only indexes—cannot answer basic cross-file questions, because these relationships live in .meta files and YAML assets rather than in code. We present Unity Insight, to our knowledge the first persistent, LLM-facing, agent-integrated cross-file code–asset index for Unity projects, shipping in production with Tuanjie Codely, the agent CLI of Tuanjie Engine, since its public launch on 2026-07-28. In a paired experiment—28 project-specific questions on two Unity games, same model and harness, one run per arm per question—the index-backed agent spent 53% fewer tokens and 52% less wall-clock time than a general-purpose exploration agent (exact paired sign tests, $p{<}0.004$), using only its typed index-query tools.

We study generalized Volterra companion operators on Bergman spaces over smoothly bounded convex domains of finite type. A derivative Carleson embedding gives boundedness and compactness criteria between reflexive Bergman spaces. When the target exponent is smaller than the source exponent, boundedness already implies compactness. In the other range, we also obtain an essential-norm formula. Local masses on McNeal polydiscs describe these criteria. Their norm estimates require an extra weight because radial derivatives vanish at the origin. On the Hilbert Bergman space, we characterize Schatten-class membership at and above the Hilbert–Schmidt threshold and prove a sufficient condition below it. We also give a Hilbert–Schmidt kernel test. For bounded symbols and self-maps with relatively compact image, singular values decay exponentially in a power of their index. An ellipsoid example gives a sharp power law governed by boundary type and dimension. The results extend to positive radial shifts.

A de Bruijn sequence packs all $n$-bit binary words into a cycle of length $2^n$. A de Bruijn torus is the two-dimensional analogue in which each word appears exactly once in a rectangular window. Here we consider the natural analogue for permutations using their shorthand representation (i.e., each permutation's final redundant value is omitted from the window). We show that these tori exist when $n = 2m + 1$ is odd and the torus and windows have two rows (i.e., the torus is a "tworus"). These twori can be constructed with a high degree of symmetry. More specifically, there are twori that can be partitioned into $2^{m-1}$ matching blocks where each block contains the same sequence of unordered columns. Furthermore, given one such block we can generate each successive column of a tworus in amortized $\mathcal{O}(1)$-time. We also prove non-existence results for certain sizes of tori and provide algorithms for constructing multiversal cycles (perfect necklaces) of unlabeled binary words.

Let $\Ga$ be a connected prime-valent $X$-arc-transitive Cayley graph of a finite characteristically simple group $G\cong T^k$, where $k\geqslant2$. We obtain a precise structural characterization of such graphs and their arc-transitive automorphism groups. In the cubic case, every connected symmetric Cayley graph of $T^k$, where $T$ is a finite nonabelian simple group, is normal.

Step Law gives power-law formulas for the optimal peak learning rate eta* and batch size B* when pre-training language models. It was calibrated on models between 59M and 1B parameters; the small-model regime N < 59M was never tested empirically by its authors. This regime matters for single-GPU training, interpretability research, educational experiments, and settings where larger models are infeasible on memory or cost grounds. We test whether Step Law transfers to small language models. We consider three outcomes: H1, the original coefficients work directly; H2, the power-law form holds but with different coefficients; and H3, a power law does not describe the optima in this regime. All experiments use a single nanoGPT/TinyStories pipeline with a 2048-token BPE vocabulary, AdamW, and a warmup-cosine schedule. The optimum for each (N, D) cell is extracted from the loss surface L(eta, B) via a local quadratic approximation in log-log coordinates over the smoothed training loss. The final dataset contains 29 unique (N, D) cells and 935 analysis-ready runs. The main refit uses 25 cells (815 runs) in the working range 4 <= D/N <= 600. On the pooled data we accept H2: the functional form is preserved, but the coefficients differ from the original. We obtain eta*(N, D) = 0.0985 N^(-0.508) D^(0.238) (R^2 = 0.834) and B*(D) = 3.6 x 10^(-4) D^(0.931) (R^2 = 0.950). Step Law's structural claim that B* is independent of N is reproduced (p = 0.87), but the growth of B* with D is nearly twice as steep as in the original work. Direct transfer of Step Law systematically overestimates the optimal learning rate: the median ratio eta_SL / eta* is approximately 4.0x, with a range of 2.4x to 6.6x.

Distributed intelligence concerns systems in which semi-autonomous components with local dynamics and partial observations coordinate through information exchange to maintain a shared function. This paper proposes an operational way to study such systems: measure information at the interface where a message changes a receiving action, then connect that measure to function by intervention and disturbance evaluation. We instantiate this proposal in DI-Walker, a two-dimensional four-limb embodied plant controlled by frozen Cross-Entropy-Method policies. We compare a controller using each limb's own realized-force sensor with one using the realized-force sensors of peer limbs. Under limb loss, limb slip, and weak central-control dropout, Peer-Sensor has lower late tracking error in several conditions. A corrected finite-history action-predictive estimator shows a substantially larger peer-message gain under compound failure. A future scalar functional-prediction estimator does not show the same stable advantage. We interpret this discrepancy as a methodological result: information useful for an intermediate control action can be hidden by later plant dynamics, redundancy, and context. The paper relates this result to Predictive Information, Transfer Entropy, Directed Information, information-to-go/IT-PAC ideas, empowerment, and the robust control data-rate perspective, while explicitly distinguishing operational predictive gains from exact Directed Information, channel capacity, and a formal data-rate theorem.

The efficient operation of accelerator facilities increas- ingly relies on rapid access to heterogeneous operational knowledge, including logbooks, interlock reports, machine parameters, and historical archive data. At ELBE, we pro- posed a Retrieval-Augmented Generation (RAG) frame- work that integrates facility documentation and operational records into a unified AI-assisted support tool for operators. The system is expected to index electronic logbooks, ma- chine archive time-series data, and subsystem manuals using domain-adapted embeddings stored in a vector database. User queries will be expected to be processed through a large language model that retrieves the most relevant oper- ational context and generates structured, operator-oriented responses with traceable source references. This contribu- tion presents the system architecture, data integration strat- egy, and challenges toward real-time AI-assisted accelerator operation

In this paper, we introduce fractional Cesàro–Morrey function spaces over $p$-adic fields and investigate their fundamental properties. We first study the behavior of dilation operators on these spaces and establish a Minkowski-type integral inequality. We then prove the boundedness of $p$-adic Hardy–Hilbert–type integral operators on fractional Cesàro–Morrey function spaces. As an applications, we derive the $p$-adic Hardy inequality, the Hilbert inequality, and the Hardy–Littlewood–Pólya inequality. Finally, we establish the boundedness of the Erdélyi–Kober fractional integral operator and the Hadamard fractional integral operator on these spaces.

Multimodal joint training often suffers from modality imbalance, where a dominant modality suppresses the optimization of others. Existing methods mainly balance modality learning by modulating gradient magnitudes or directions, modifying optimization objectives, or adjusting training strategies, with most interventions focusing on the current update. However, when combined with widely used momentum-based optimizers, the update also incorporates accumulated information from previous gradients, which is not explicitly addressed by current-step modulation alone. To address this issue, we propose Variance-Calibrated MomentuM (VCMM), which adapts gradient memory to modality-specific gradient dynamics. Specifically, VCMM estimates minibatch noise and temporal drift online and uses their relative strength to determine modality-specific momentum through a Kalman-inspired controller. We further center the control signal across modalities and apply exact bias correction for the time-varying first moment, enabling adaptive gradient memory without extra network passes or explicit learning-rate scaling. Experiments on four multimodal benchmarks demonstrate consistent improvements with modest training overhead.

Bi4Ti3O12-based ceramics are promising candidates for high-temperature piezoelectric devices owing to their high Curie temperature (> 600 {\deg}C). However, their low piezoelectric constants and poor mechanical reliability hinder their use in some engineering applications. Here, we fabricate nacre-like <00l>-textured (f_00l > 94%) Bi3.96Ce0.04Ti2.965W0.0175Nb0.0175O12 (NL-BCWNT) ceramics via a scalable magnetic-assisted slip casting (MASC) self-assembly process. In addition to crystallographic texture, the final material presents a brick-and-mortar microstructure with micro-sized grains with a median aspect ratio of 15. NL-BCWNT exhibits a high fracture toughness for piezoceramics, with both $K_{IC}$ and $K_J$ reaching 2.2 $\pm$ 0.4 $MPa \cdot m^{0.5}$ and 4.2 $\pm$ 0.4 $MPa \cdot m^{0.5}$, respectively. The toughening originates from deflection and stable crack propagation within the nacre-like structure. The $d_{33}$ is 30 $\pm$ 3 $pC/N$ with a Curie temperature of 661${\deg}C$, and $d_{33}^*$ reaches 46 $\pm$ 3 $pm/V$ at 160 ${\deg} C$ with less remanent strain than random BCWNT. The improvements are attributed to aligned domain along spontaneous polarization direction <h00> with better mobility. NL-BCWNT exhibited excellent ferroelectricity fatigue resistance with higher than 106 cycles without degradation. Furthermore, similar improvements are observed in pure BiT, suggesting the general applicability of this strategy to other BiT-based systems. The nacre-like architecture thus provides a promising addition to the design toolbox for high-performance electromechanical materials.

In the ultrastrong light-matter coupling regime, the ability to confine the electric field to subwavelength scales and define an electromagnetic mode is essential. This task is typically achieved through dedicated cavities, such as THz metal resonators. Here, we instead introduce ultrastrong coupling directly between distinct magnetoplasmon excitations, leveraging solely the spatial symmetry of a confined electronic medium in the presence of a magnetic field. By patterning an AlGaN/GaN single quantum well hosting a two-dimensional electron gas into micrometer-scale patches, we tailor the mutual interactions between topologically protected edge and bulk magnetoplasmons, achieving coupling strengths of up to 0.1. The progressive breaking of rotational symmetry determines the coupling rules and leads to the emergence of energy gaps and unique chiral-mode hybridization. Our results highlight a path towards exploiting the symmetry class and topology of the magnetoplasmon wavefunction as a new parameter space for ultrastrong light-matter interaction without a dedicated cavity.

To each modular knot, we attach a weight $2$ modular integral for $\mathrm{SL}_2(\mathbb{Z})$ whose homogenized cycle integrals recover its linking numbers with other modular knots in $S^3$. This construction answers Choie-Zagier's question of explicitly constructing modular integrals with prescribed rational period functions in weight $2$. Our formula applies to individual modular knots without symmetrization, thereby realizing an approach discussed but not pursued by Duke-Imamoḡlu-Tóth. This gives an answer to Ghys' question on pairwise linking numbers in terms of modular integrals, as sought by Simon.

This paper deals with the generic modeling of systems of systems (SoSs) using agent-based modeling. SoSs are large-scale systems, including numerous-possibly heterogeneous-interacting component systems evolving in a dynamic environment. The aim of this paper is to provide generic formalism allowing to represent and control the whole complexity of a SoS using agent-based simulations. In particular, organizational aspects of SoSs are managed with the Agent-Group-Role model. Functional aspects, guiding SoSs to accomplish their global goals, are handled via a functional specification. Multilevel aspects are modeled with the Influence Reaction Model for Multilevel Simulation (IRM4MLS) agent-based meta-model. Models generated using this formalism encompass static and dynamic aspects of SoSs. They consider reorganization of SoSs caused by changes of goals or subsystem capacity. All these elements are illustrated in this paper using a SoS case study of Intelligent Autonomous Vehicles initiated by the Intelligent Transportation for Dynamic Environment (InTraDE) European project to automate the port container logistic.

Reinforcement learning (RL) has emerged as a key paradigm for improving the reasoning capabilities of large language models (LLMs). However, existing reward systems, such as rule-based and reward-model-based, often exhibit issues such as unstable optimization and reward hacking. In this work, we revisit the general reasoning of LLMs from a geometric perspective, conceptualizing it as a coupled manifold composed of three interdependent sub-manifolds: logical deduction, evaluation, and representation. Based on this perspective, response generation in RL can be interpreted as a decoupling process from the evaluation manifold, while reward estimation corresponds to a decoupling process from the logical deduction manifold. The limitations of rule-based and reward-model RL systems can be geometrically interpreted as the mismatch of policy-reward manifolds during RL process. To address the aforementioned misalignment, we propose Decoupling and Coupling Reinforcement Learning (DCRL) framework, which incorporates two key components: (1) a syllogistic logic-based prompt evolution mechanism that dynamically refines reward rubrics to enhance the expressiveness of the reward manifold; and (2) a policy-reward re-coupling mechanism that jointly updates the reward and policy models, ensuring consistent evaluation and mitigating manifold mismatch during training. Theoretical analysis and extensive experiments across multiple reasoning domains demonstrate that DCRL consistently outperforms both rule-based and reward-model baselines. Notably, a Qwen3-4B model trained under DCRL surpasses a Qwen3-32B baseline and approaches the performance of a Qwen3-235B model, highlighting superior effectiveness and generalization in RL.

Deployment requires an agent to turn application code into a running system whose services connect, become ready, and remain observable. FDE-Bench evaluates this capability with 136 deployment-configuration tasks spanning Docker images, multi-service Compose stacks, and Kubernetes, in greenfield and diagnose-and-repair modes. Agents submit declarative artifacts that are collected, rebuilt, and redeployed in a pristine environment. Four gated binary check layers measure build, readiness, behavior, and conformance to the deployment specification, using programmatic checks without an LLM judge. A four-arm release gate requires a resolving reference solution and rejects tasks solved by do-nothing, specification-transcription, or generic-stub submissions. The released check annotations expose the link between 2,145 checks and their specifications, including seven documented gaps. Three additional adversarial strategies test shortcuts in the grading signals; none resolves any of the 135 tasks they cover, while a vacuous health probe passes readiness and exposes the need for downstream checks. On the 136-task evaluation grid, seven language models from four providers use the same four-tool scaffold and resolve 52.9-75.0 percent of tasks. The three zero-intelligence floors resolve none and reach a mean Deployment Score of at most 0.44. Readiness is the largest failure stage, accounting for 110 of 313 unresolved episodes. Mean resolution rate is 30.7 percentage points higher on the repair task group than on the disjoint greenfield group, with a positive gap for every model; ten tasks resist all seven. In a 25-task case study, one practicing engineer directing Claude-Sonnet-5 resolves 92 percent against 72 percent for the autonomous baseline. FDE-Bench links deployment success and failure to artifacts that can be inspected and replayed.

Consider the space of $C^\infty$-functions on the two-dimensional sphere $S^2$ and its decomposition $\oplus\mathcal H_n$ into a direct sum of minimal rotation-invariant spaces. We consider elements of $\oplus\mathcal H_n$ as functions of two variables, a nonnegative integer variable $n$ and a complex variable $u$ (a restriction of such function to the set $n=k$ is a polynomial in $u$ of degree $\le 2k$). For operators of multiplication by $x_1$, $x_2$, $x_3$ in $C^\infty(S^2)$ we obtain the corresponding operators in $\oplus\mathcal H_n$, they are differential-difference operators in the variables $u$, $n$ (including second derivatives in $u$ and shifts $n\mapsto n\pm1$). We obtain the similar correspondence for operators of differentiation along conformal vector fields on $S^2$.

The Jupiter Icy Moons Explorer (Juice) embarked in 2023 on a 8-year interplanetary journey to Jupiter and its icy moons. The Submillimetre Wave Instrument (SWI) is one of the ten science instruments aboard the spacecraft. SWI is a sophisticated and first-of-its-kind payload visiting the outer solar system, featuring dual-band tunable receivers, two independent pointing mechanisms, and spectrometers capable of high resolution (up to a resolving power of 10^{7}). It is designed to support the diverse science objectives of the Juice mission targeting Jupiter's middle atmosphere, icy-moon's exospheres as well as near sub-surface thermophysical properties. For this purpose the Juice mission adopts a complex trajectory tour within the Jovian system, which further necessitates a sophisticated, mission-driven operations concept for SWI. This presents significant planning, operations and commanding challenges which are described in this paper in the context of the Lunar and Earth Gravity Assist (LEGA). After the development and ground calibration of the instrument, the SWI Team has designed a comprehensive calibration strategy applicable during the Cruise Phase of Juice. Among the various opportunities for calibration, including the Near-Earth Commissioning Phase and more than ten Payload Checkout Windows, the LEGA offers the means not only to improve the calibration of the instrument, but also to validate the operational strategy of future icy moon flybys.

We use direct numerical simulations to study the turbulent transonic flow over a supercritical airfoil, spanning the transition from stable conditions to fully developed buffet at chord-based Reynolds numbers of $3\times10^5$ and $6\times10^5$. The Reynolds number determines the incoming boundary-layer state, thereby affecting the separation behaviour. Spectral proper orthogonal decomposition reveals a single dominant mode that emerges below onset and persists across the transition to buffet. The energy of this mode increases with the angle of attack while its spatial structure and fundamental frequency remain nearly unchanged, consistent with a global instability that saturates into a nonlinear limit cycle. Geometrical acoustics provides a first-order description of the global mode propagation and identifies two paths connecting the acoustic source, located in the near wake, to the shock. A shorter path impinges on the shock from behind, while a longer one circumvents the shock tip before reaching it from the front. Linearised shock–acoustic interaction theory predicts a stronger shock response to low-frequency, front-impinging acoustic disturbances. Space–time correlations link the establishment of a downstream path to complete boundary-layer separation, which is induced intermittently by the upstream motion of the shock. The sum of the upstream acoustic time along the front-impinging path and the downstream convective time is compatible with the measured buffet period at both Reynolds numbers. Together, these results are consistent with a unified picture of buffet, where an aeroacoustic feedback mechanism provides the physical pathways through which perturbations can sustain the global dynamics.

Standardised, machine-readable cybersecurity playbooks provide a basis for portable, shareable, and reusable incident-response logic. OASIS CACAO provides a vendor-neutral representation for such playbooks, but not the product-specific integration artefacts needed to invoke external products and services. We introduce the Common CACAO Registry (CCR), an open, provenance-aware registry of CACAO HTTP-API connector envelopes. Each envelope captures an API operation's command, inputs, target, authentication-related information, provenance, validation evidence, and maturity metadata. CCR is quality-gated, with acceptance requiring both CACAO v2 schema validity and a mean back-validation score of at least 0.8 against the source OpenAPI operation, while a six-level maturity model records progressively stronger evidence and distinguishes gate acceptance from operational readiness. To seed CCR, we develop a hybrid OpenAPI-to-CACAO pipeline. Deterministic code extracts source-derived interface facts, generates identifiers, wires cross-references, and validates structure, while a constrained LLM provides bounded semantic enrichment, including action naming, authentication interpretation, and CACAO activity annotation. Evaluation across eight security APIs yields 713 CACAO-schema-valid envelopes with a mean back-validation score of 91.5%, of which 675 produce well-formed, dispatchable HTTP requests in a local harness. Comparison with a deterministic rule-based baseline shows that mechanical API structure is preserved more reliably through rule-based translation, while the LLM contributes bounded semantic enrichment, most notably CACAO activity annotation. Together, these results support CCR as reusable integration infrastructure for CACAO action steps and as an initial foundation for a broader common European registry.