Papers

As all generators are distributed in different areas among large scale power systems, the cooperative manipulation of the multi-generator system cannot be done well without consideration of the distance information of the generators, A distributed step-by-step finite-time consensus scheme for the heterogeneous Battery Energy Storage System (BESS) is proposed in this paper, where the coordinated consensus can be come into reality within a limited time, which is appealing for the electrical engineering community. To be concrete, at first, all BESSs are classified into several clusters according to their locations, and in each cluster, there is an active leader in charge of information receiving from outside. Then after, in order to coordinate the multi BESSs, five inputs, which are function oriented, were used to achieve energy level balancing, active/reactive power sharing, and voltage/frequency synchronization of the multi BESSs. To be further, the frequency and voltage restoration to the nominal values of the main grid was made possible by the introduction of a virtual leader, which is actually an external leader. Compared with the centralized methods, this control scheme is entirely distributed, and each BESS only utilizes the information of its own and its neighbors. Besides, this control is robust to the load perturbation and the plug-and-play of the communication topology. Finally, some simulation experiments are executed on the modified IEEE 57-bus system to verify the suggested scheme.

We study the unforced viscous Katz–Pavlović dyadic model with non-negative smooth initial data for two shell settings. For super-exponential scales $N_n=N_0^{b^n}$, with $N_0>1$ and $1<b<2$, we prove that $\alpha=1/(b+2)$ is the sharp dissipation threshold: every such datum produces a globally smooth solution at and above this value, whereas suitable compactly supported data lose regularity in finite time below it. For geometric scales $N_n=N_0\Lambda^n$, global regularity holds when $\alpha\geq1/3$ and $4\alpha-1>(\log2)/(2\log\Lambda)$. In particular, for $\Lambda>2^{3/2}$, the result reaches $\alpha=1/3$ and, together with the known classical blow-up theorem, identifies the sharp threshold in classical shell ratios.

We study what noisy data can justify before a manifold and its intrinsic dimension are assumed. For repeated observations with independent isotropic Gaussian errors of unknown variance, we compose a support confidence event with a sound geometric verifier to certify a nearby smooth witness of arbitrary compact latent support. Whole-support inference requires an external lower mass condition; independent validation instead certifies proximity of probability mass. Separate all-scale hypotheses yield true-support structure and dimension recovery: a credited Reifenberg–Dini criterion and positive continuous density give local $C^1$ structure and consistent dimension estimation, while two-sided Ahlfors regularity and positive reach give quantitative covariance separation under the stated sampling and observation-transfer conditions. An exact-arithmetic implementation verifies restricted witness families. A further matrix check certifies linear coordinates on a geometrically verified affine span containing the witness and propagates approximation and decoding errors. This restricted construction neither implements the general minimal-dimension Whitney theorem nor infers exact manifold support from finite approximation. Executed torus and Julia-set experiments test the observation-to-witness-to-coordinate route, including singular-support controls. Dynamical systems and chaos are the primary application context; state-identification and finite-horizon prediction results are conditional on observation embeddings and transition validation. Takens reconstruction is an optional scalar-delay application requiring additional smoothness, dynamics and observable conditions. Image comparisons are auxiliary reconstruction diagnostics. The finite-data verifier establishes neither those dynamical conditions nor the all-scale geometric premises for true-dimension recovery.

Two commuting channels yield the same composite channel in either fixed order, yet their quantum switch can alter information preservation. We study how this effect depends on the input state, retaining the joint output of the control and target. Exact Kraus commutator identities determine overlap and squared fidelity gaps. Fixed order preserves product inputs at least as well as the switch in fidelity. The reverse inequality holds for pure states of two qubits whose control Schmidt basis can be chosen to coincide with the order basis. A commutator matrix determines the target basis that maximizes the squared fidelity gap at fixed entanglement within this aligned family. For Pauli $X$ and $Y$ channels with equal error probabilities, the switch replaces a logical phase flip with an operator that stabilizes a joint code. At fixed noise, the switch preserves at least as much distinguishability and quantum Fisher information as fixed order for every state family in this code. For the pure encoded family studied here, exact formulas connect the phase information gain to the squared fidelity gap and quantify the reduction in information about the noise probability. Optimizing the probes yields equal maximal quantum Fisher information for noise estimation under both joint channels. These results connect commutator geometry and logical error structure to state preservation and the retention of encoded information.

Any lossless compression algorithm (like gzip) may be converted into a machine learning method, via either Normalized Compression Distance or the Minimum Description Length principle. Any auto-regressive model may be converted into a lossless compression method via entropy coding. This seemingly circular dependence has unrealized potential in modern artificial intelligence and machine learning, and we survey and formalize the various strategies that have been used to leverage compression for machine learning. We introduce and empirically validate a design framework for compression-based ML, finding compression-based methods competitive with conventional baselines and decisively stronger on malware. We find that varying these design choices yields accuracy gains of up to 0.62.

Auto-bidding is a key component of modern advertising systems that provides a personalized bidding strategy for each advertiser. By characterizing each individual, profile-based methods achieve personalization and have proven effective in domains such as recommendation. However, despite the diverse bidding behavior of advertisers, their application to auto-bidding remains limited. A primary reason is that constructing and leveraging advertiser profiles face several challenges: extracting pure profiles is non-trivial, modeling common and private information simultaneously is difficult, and profile updating and cold-start adaptation remain challenging. To tackle these issues, we propose ADAPT, an \underline{A}uto-bidding framework with \underline{D}isentangled \underline{A}dvertiser \underline{P}rofiles and \underline{T}raining-free adaptation. ADAPT introduces a two-stage training paradigm and supports training-free adaptation. Specifically, (i) the stage 1 extracts pure static and dynamic profiles via contrastive learning over the advertiser memory bank; (ii) the stage 2 disentangles the dynamic profile into a common profile and a private profile, and combines them with the static profile to jointly condition the bidding strategy; (iii) once trained, ADAPT constructs profiles for new advertisers and updates profiles of existing advertisers without retraining. Our experiments on a large-scale auto-bidding benchmark demonstrate that ADAPT consistently achieves superior performance, and ablation studies further validate the effectiveness of each module. The source code will be released at https://github.com/YuzunoKawori/ADAPT.

Although conventional controllers and disturbance observers (DOBs) are the standard for precision tracking in manipulators, they suffer from parameter uncertainty, nonlinear friction, and compound disturbances. This study proposes a residual reinforcement learning DOB framework that pairs an analytical observer with an RL policy. The deterministic baseline operates within a reliable region, whereas the RL policy explicitly targets the residuals that the model cannot capture. To make this compensation disturbance-aware, an estimator network aligns the observation history with a privileged disturbance context, organizing the latent space by disturbance regime and enabling rapid adaptation across disturbance transitions. To guarantee stability, we derived and enforced a state-dependent action bound on the RL policy from an input-to-state stability (ISS) analysis such that the closed loop provably confines the tracking error to a certified envelope for arbitrary policy outputs. Experiments on a 6-DOF manipulator demonstrated consistent improvements in disturbance estimation and tracking, including a 27.8% tracking-error reduction on real hardware under zero-shot sim-to-real transfer and a 38.0% reduction under a base-vibration disturbance that was not observed during training.

A common requirement across organizations is to have a tool that can identify file types based on their contents, particularly in the cybersecurity domain where magic numbers and file extensions can not be trusted. While existing tools work well in practice, there is plenty of room for improvement either in terms of computational load and time for detection in the case of model based tools like Magika or in terms of accuracy of detection in the case of file parsing tools that use programming language constructs. In this study, we propose a neural network model for identification of types of text content files, especially source code, that is more accurate and faster than other available tools. Our experiments on open-source files indicate that it is not only more accurate on average for text-content file-type identification, but also approximately four times faster than Magika, while being 28% smaller in size.

We give a proof, that does not rely on analytic determinacy, of the existence of an idealistic analytic equivalence relation with Borel classes that is not classwise Borel isomorphic to an orbit equivalence relation. This result answers a question of Becker, and Calderoni and Motto Ros. Our proof proceeds through an analysis of Borel complexity of certain sets of countable rooted trees defined via the notion of the Lusin derivative.

Reliable plant-level information from unmanned aerial vehicle (UAV) imagery is important for automated crop monitoring. However, in dense crop canopies, adjacent plants frequently overlap and are detected as a single object, reducing the reliability of plant-level measurements. This study presents a geometry-aware post-detection framework for resolving overlapping plant instances using standard RGB UAV imagery. The framework combines object detection with geometric clustering of plant components. Leaves or branches detected within each bush-level region are represented using two complementary geometric features: component centroids and radial intersection points (RIPs) derived from detected plant structures. K-means and Gaussian mixture models determine whether a detected region contains a single plant or two overlapping plants. Density filtering suppresses spurious radial intersections, and a post-pipeline ensemble combines spatial and directional geometric information. The framework was evaluated using UAV imagery of eggplant and tomato crops under field conditions. Centroid-based clustering achieved an F1-score of 0.89 for eggplant, while the combined centroid-RIP approach achieved the best tomato performance, with an accuracy of 0.80, precision of 1.00, and F1-score of 0.75 using K-means. Density filtering substantially improved RIP-based clustering for tomato. The proposed approach provides a lightweight, modular engineering solution that can be integrated with existing RGB UAV monitoring pipelines without additional depth sensors, pixel-level segmentation, three-dimensional reconstruction, or retraining of the primary bush detector. The results demonstrate that geometric reasoning applied to existing detector outputs can complement deep-learning-based object detection and improve plant-level interpretation in dense agricultural canopies.

Product abuse is an individually rare, but growing, problem across the SaaS industry. Highly sophisticated threat actors can misuse security platforms within customer environments or conduct bypass experiments on the product itself. Threat actors can leverage living-off-the-land (LOTL) attacks to avoid using cumbersome, frequently detected malware. Remediating this threat requires collecting multiple data modalities across different types of databases, addressing a cold-start problem in the intrinsic rarity of such sophisticated but dangerous events, and designing within the constraints of real-world deployment (e.g., cost, user behavior, performance, etc). To wit, we provide the first study of such a whole-system defense, especially with respect to a deployed and operational capability. Our results show an increase in product abuse coverage by 35%, a 30% reduction in monthly alerts, and adaptability to changes in malicious actors' behavior. We review both the constraints we considered in designing the system to meet operational requirements and a retrospective evaluation of the value of explainable features and counterfactual performance on previously identified attacks.

The network virtualization (NV) technology has enabled the sharing of multiple resources among virtual networks (VNs) in cloud data centers. One of the key challenges is to allocate resources in real-time for virtual network request (VNR), which is known as online virtual network embedding (VNE). However, the existing online VNE methods do not exploit the multi-dimensional complementary relationship among diverse VNRs, resulting in the fragmentation and waste of substrate resources. In this paper, we propose the pattern matching based online VNE approach by constructing appropriate matching rules among observed patterns to maximize resources utilization. We devise the clustering based VNRs quantization method and conduct rigorous study on the pattern combination filtering problem. Then, we utilize the column generation to solve it and construct the pattern matching rules. Based on the rules, we propose an online pattern matching VNE algorithm with linear worst-case complexity. Evaluation on a 106-server testbed using Alibaba production cluster trace dataset shows that our algorithm achieves close-to-offline performance and more accepted workloads that outperforms traditional designs by 25%-30%.

The standard Euler discretization schemes for numerical option pricing under stochastic volatility models are known to exhibit high biases and potential unreliability. The alternative use of the exact (unbiased) simulation approach invariably involves numerical evaluation of integrated variance (and / or volatility) conditional on terminal variance (volatility) value. To resolve the technical challenge, most simulation schemes either employ the tedious Fourier inversion of conditional characteristic function or numerical approximation by moment matched distribution. We propose a general framework of constructing efficient and reliable simulation schemes for stochastic volatility models via the Strang operator splitting approximation. The simulation procedure completely circumvents the necessity of evaluation of conditional integrated variance (and / or) volatility. Our simulation schemes compete favorably well with most existing exact simulation schemes and the biased Euler schemes in terms of accuracy, efficiency, reliability and ease of implementation. Extensive numerical tests were conducted to illustrate the versatility and success of our operator splitting approach for most common stochastic volatility models, such as the Heston-type models, lifted Heston model, Hull-White model, and Barndorff-Nielsen and Shephard model. We also establish the proof of second-order convergence of the operator splitting schemes.

Orbital angular momentum (OAM) is a promising degree of freedom for low-dissipation transport and magnetization control, yet its relaxation mechanisms remain controversial, with atomcentered approximations (ACA) predicting much shorter OAM diffusion lengths than experiments. We address this discrepancy using first-principles Lindbladian density-matrix dynamics, capturing electron-phonon scattering and itinerant OAM contributions, together with a first-principles parameterized tight-binding approach that separates the ACA and itinerant components. In MoS2,a strong-spin-orbit-coupling (SOC) system, orbital relaxation is multi-timescale, with fast intervalley redistribution followed by slower decay coupled to the spin. In weak-SOC silicene, spin and orbital dynamics decouple; an electric field tunes spin relaxation while leaving orbital lifetimes unchanged. In both materials, ACA orbital lifetimes are at least one order of magnitude shorter than itinerant ones, due to ultrafast precession driven by crystal-field splitting, absent from the itinerant component. These results demonstrate that going beyond atom-centered models is essential for describing orbital relaxation and diffusion.

Contemporary cloud and distributed systems expose control through resource-centric abstractions: services, deployments, network flows, execution graphs. Agentic and tool-augmented systems have meanwhile shifted application logic toward intent-driven, adaptive execution. Existing control planes, workflow engines and service meshes lack abstractions for intent-level decision governance: they cannot represent high-level goals as first-class control objects, cannot enforce policy over the mapping from intent to execution plan, and cannot produce auditable records of why one execution path was chosen over its alternatives. Control logic is therefore embedded in application code, leaving systems brittle, opaque and hard to govern. We propose Brain API, an intent-aware control plane for policy-governed agentic systems. Its central contribution is the decision artifact: a durable, versioned, auditable record of how an intent became an executable plan, capturing which policies applied, which capabilities were evaluated, which alternatives were rejected, and why. A motivating use case is agentic datasets: datasets participating as policy-governed capabilities under residency, compliance and cost constraints. We evaluate a prototype of the decision layer against two external policy corpora we did not author. On the OPA Gatekeeper constraint library it agrees with the library's own published verdicts on 42 of 42 encodable cases, 19 admit and 23 deny. On Cedar example policies, labeled by differential testing against its reference implementation, a deliberately dissimilar domain exposed three defects in our model, including a default-allow assumption that would have inverted every authorization policy. The evaluation covers policy filtering and selection; candidate generation, context signals, ranking and plan synthesis are not measured, nor is decision latency under load.

The evolution toward next-generation mobile communication systems demands intelligence-native networks capable of autonomously adapting to user intent, yet the prevailing 3GPP protocol-driven device-network-cloud (DNC) architecture imposes three structural bottlenecks: protocol-constrained decision spaces confining optimization to predefined parameter subsets, cascaded information asymmetry from lossy interface compression that strips semantic context and causes intent miscalibration, and inherently reactive coordination mechanisms that trigger actions only after performance degradation. This paper proposes an autonomous agentic AI paradigm named Agentic Synergy for Telecommunication Resource Autonomy (ASTRA), which introduces a three-tier agent layer, including device agent, network agent, and cloud agent, decoupling network intelligence from the underlying hardware infrastructure. These agents collaborate through bidirectional semantic channels, including semantic intent messages, capability abstraction messages, global directives, and peer coordination, executing a six-phase cycle of perceive, reason and predict, communicate, decide, act, and learn that transforms reactive protocol-driven operations into proactive, intent-calibrated optimization over the full decision space. Validated through system-level simulations in two representative scenarios, ASTRA achieves a 13.1% average throughput gain in dense-crowd cell selection by redistributing UEs from congested cells via semantic load exchange, and an 18.2% passive handover reduction in high-speed mobility through predictive trajectory-aware coordination, providing initial evidence that the proposed agentic framework accesses solution regions structurally inaccessible under protocol-constrained architectures.

Dense granular flows are commonly investigated using the soft-sphere Discrete Element Method (DEM), whereas large-scale applications generally require continuum models. Granular temperature, defined as the variance of particle velocity fluctuations, is a relevant variable to collapse rheological scaling. However, experimental forcing approaches used to control temperature also affects other aspects of the granular state. An alternative is to use a thermostat algorithm to control the fluctuation energy directly. Although thermostat algorithms are well established in Molecular Dynamics (MD), their behaviour in dissipative DEM systems has received comparatively little attention. We show that conventional Langevin and Nosé-Hoover thermostats exhibit complementary limitations: Langevin control requires strong coupling to offset collisional dissipation, thereby damping particle dynamics, whereas Nosé-Hoover does not independently disrupt the correlations and segregation generated by repeated inelastic collisions, leading to non-ergodic and numerically unstable states. To address these limitations, we introduce two pairwise hybrid formulations combining deterministic temperature regulation with stochastic decorrelation. Both enforce the prescribed temperature, while variation of the stochastic decorrelation timescale modifies velocity statistics and associated mesoscopic properties such as diffusivity. Finally, application to pressure-controlled simple shear shows that increasing granular temperature at fixed inertial number reduces the apparent friction, consistent with previously reported trends. The framework therefore provides controlled reference states for comparing differently forced granular systems and identifying the variables required for temperature-dependent constitutive models.

Fairness research on language models involves measuring bias, applying mitigation methods, and examining the evidence on which an evaluation rests. Existing tools offer complementary functionality through different interfaces, so combining them requires reconciling model interfaces, evidence formats, access constraints, and result types before applicability can be checked or methods compared. We introduce FairLMs, a Python library that connects these activities through explicit declarations of model capabilities and input requirements. It provides 33 intrinsic and extrinsic metrics, 14 mitigation components spanning four intervention categories, 14 dataset and scoring-instrument diagnostics, adapters for the three Transformer architectures and supported hosted completion APIs, and benchmark loaders. Declarations are checked before execution and results carry the configuration under which they were obtained, so that compatible components can be combined, methods compared under a common protocol, and workflows extended to new models and datasets. The source code is available at: https://github.com/FairLMs/FairLMs.

A unified kernel-free boundary integral (KFBI) framework is proposed for the Allen-Cahn and Cahn Hilliard equations with homogeneous no-flux boundary conditions on two- and three-dimensional irregular domains. With a stabilized first-order implici-explicit (IMEX) discretization, the Allen-Cahn update reduces to a Neumann modified Helmholtz problem. An auxiliary-variable reformulation reduces the Cahn-Hilliard update to subproblems of the same type without evaluating the Laplacian of the nonlinear source. The Cahn-Hilliard update requires two sequential solves for real shifts, while complex-conjugate shifts allow the real-valued solution to be reconstructed from a single complex solve. All subproblems are handled by the same KFBI solver that indirectly evaluates potentials through equivalent interface problems. To correct discrete mass defects in the Cahn-Hilliard update, a geometry-weighted discrete $L\v{s}$ mass projection is constructed tailored to the KFBI treatment of irregular boundaries. Exterior overlap weights are redistributed to physical nodes, excluding auxiliary KFBI extension values from the mass calculation. Numerical experiments demonstrate second-order spatial convergence, first order convergence of paired temporal-error indicators, and preservation of the prescribed discrete mass. The reported source-free simulations exhibit energy decay, with cumulative projection-induced energy perturbations remaining small relative to the observed dissipation.

We derive a thermodynamically-consistent model of fluid flow through a poroelastic medium. Starting from elastic and fluid free-energy densities, an energy-dissipation rate, and a kinematic constraint, the force-balance equations are derived using variational principles, with the pressure–density constitutive relation emerging as a direct consequence of the variational structure; the same kinematic constraint also supplies the total-flux transport structure. In the ideal-gas limit, the model linearization recovers the classical linear Biot equations. For power-law fluid energies, it yields isentropic pressure–density relations. A key advantage of the variational formulation is that extensions to richer physics, such as thermal effects, chemical reactions, or multi-component fluids, can be incorporated systematically by augmenting the energy and dissipation functionals without redesigning the force-balance or transport closure. We support the model with an energy-compatible two-field discretization and study consolidation under a surface load with three lateral-boundary treatments and three fluid-compressibility exponents.

Autonomous software generation (ASG) aims to turn human requirements into executable applications, but delivering these applications does not necessarily establish that their interacting components satisfy the specified behavioral requirements. We introduce GameASG-Bench, a benchmark that makes behavioral testability part of the generation task for game development. Our design declares an evaluation interface specification before generation, fixing legal starting scenarios, player-level actions, stable snapshots, rejection behavior, and invariants while leaving private implementations open. Concretely, we include: (i) static L1 checks that assess source-level compliance; and (ii) browser-executed L2 checks that combine semantic observations with real input and runtime evidence. We implement this protocol as 47 browser-native game-generation tasks spanning 12 primary genres and both 2D and 3D interaction, each with executable checks and an independently verified reference implementation. Our experiments answer four key questions about end-to-end agent performance, tool access and nominal turn budget, reasoning effort, and harness choice. Across nine agent stacks, the highest observed mean L2 check pass rate is 93.2%, yet the highest observed strict task success rate, requiring all L1 and applicable L2 prerequisite and core requirement checks, is only 55.3% (26/47 tasks). For DeepSeek-V4-Flash, full tool access and larger nominal turn budgets yield more strict task successes, while the strict task success rate is not monotonic in reasoning effort. Both tested harnesses achieve 18 strict task successes, but only ten tasks succeed under both. These results expose task-level compliance gaps that high average check pass rates actually obscure.

Anycast allows for providing services from multiple, geographically distant Points of Presence (PoPs), using a single IP address, to, e.g., improve resilience. Due to its opaqueness, it is often unknown which addresses are provisioned using anycast and, if so, where the PoPs are located. As anycast is widely used for critical Internet infrastructures (e.g., the DNS) efforts have been made to map anycast deployments. The current state-of-the-art mapping technique, iGreedy, relies on latency-based measurements, and is adversely affected by noise caused by, e.g., network processing delays. Previous work has shown that traceroute can alternatively be used to detect anycast. As traceroute reveals the hops a packet traverses, it may also be used to locate sites using geolocation data for hops near the anycast PoPs. This paper is the first to assess the performance of the traceroute-based approach at scale, by targeting 14k prefixes from an anycast census. Using ground truth we show traceroute achieves a slight increase in enumeration and geolocation precision over iGreedy. However, it suffers from overestimating the number of PoPs and incurs a 4 times increase in probing cost, making it unattractive for anycast censuses.

We develop an efficient Monte Carlo simulation scheme for pricing options under the Ornstein-Uhlenbeck driven stochastic volatility model via the operator splitting approach. With an ingenious splitting of the governing stochastic differential equations, our operator splitting scheme admits analytic solutions in all sub-steps, so its implementation is simplified to require simulation of a few normal variates. This resolves the two typical numerical challenges in other simulation schemes, namely, sampling of conditional integrated variance and pathwise inverse integral transform of characteristic functions. There are three pioneering simulation schemes that attempt to overcome the above two numerical challenges. These include the Hilbert interpolation scheme of Zeng et al. (2023), Karhunen-Lo`eve expansion scheme of Choi (2025) and moment matching scheme based on the Inverse Gaussian distribution of Brignone and Sgarra (2026). We performed numerical tests to compare accuracy-speed performance of pricing options using our operator splitting scheme with these three pioneering schemes. We found that our scheme competes favorably well in terms of accuracy-speed tradeoff among all these schemes, in particular for pricing path dependent options with a large number of monitoring instants. The performance of our scheme can be well enhanced by martingale-preserving control variates and variance reduction via conditioning.

Matrix product operator (MPO) serves as a fundamental component in tensor network simulations of quantum many-body dynamics. We employ an MPO construction that introduces additional propagation channels to embed both periodic boundary conditions and finite-range couplings directly into an open boundary MPO. We apply this construction within the time-dependent variational principle (TDVP) framework to simulate quench dynamics in a spin-1/2 chain with finite-range interactions, and benchmark the results numerically against the fourth-order Runge-Kutta method, finding excellent agreement for both single-body and two-body observables. The approach offers a practical route for tensor network simulations of many-body dynamics in periodic finite-range systems.

Spin space groups provide the natural symmetry framework for magnetic crystals with weak spin-orbit coupling, but extracting their physical consequences requires a general theory of irreducible representations. The central difficulty is that spin space groups are represented projectively: their factor systems can render lattice translations noncommuting, induce nonsymmorphic actions in momentum space, and modify the projective structure of little cogroups. These effects lie beyond conventional space-group and double-group representation theory. Here, using Mackey's theory of group extensions, we develop a unified constructive framework for all collinear, coplanar, and noncoplanar spin space groups, including antiunitary symmetries and general factor systems. A central technical result is a canonical decomposition of the relevant factor system $\nu$ into a translational factor $\sigma$, a mixed factor $\gamma$ coupling translations to point-group operations, and a point-group factor $\alpha$. This decomposition makes transparent how ordinary representation theory is modified: $\sigma$ determines the projective translation algebra and the appropriate Brillouin zone, $\gamma$ controls the momentum-space group action and can make it nonsymmorphic, and $\alpha$ contributes to the factor systems of little cogroups. On this basis, we construct all projective irreducible corepresentations by induction over momentum-space orbits. The framework identifies which nonsymmorphic momentum-space symmetries can be realized by spin space groups and reveals Brillouin spaces that are compact flat manifolds rather than tori, symmetry-enforced Zak phases, reconstructed high-symmetry momenta and band degeneracies, and new types of quasiparticles. Our results establish the representation-theoretic foundation for systematic studies of weak-spin-orbit-coupled magnetic materials.

Surface electromyography (sEMG)-based silent speech interfaces are limited by cross-user variability and calibration burden. We study a limited-data setting in which each of 27 speech-typical participants contributed less than 0.5 h of data (21.3 min on average) across Aloud and Mimed speech. Within a closed 50-sentence corpus, we used leave-one-subject-out evaluation, initializing from a released single-subject checkpoint, pretraining on non-held-out participants, and fine-tuning on the target participant. This pipeline achieved 21.7% character error rate (CER) and 31.9% word error rate (WER), compared with 49.3% CER without target-subject calibration and 68.0% CER for direct checkpoint fine-tuning. Multi-subject pretraining from random initialization followed by fine-tuning reached 44.9% CER and did not converge under the fixed schedule in 5 of 27 folds, indicating substantial optimization and accuracy benefits from checkpoint initialization. Macro-averaged CER declined from 74.4% with one pretraining participant to 21.7% with 26. Three minutes of target-subject calibration achieved 20.5% CER and 31.7% WER, with no statistically significant difference from the full approximately 13-min pool (21.7% CER and 31.9% WER). A subject-specific adapter provided no detectable benefit. Excluding the five evaluation sentences from all sEMG model-training data increased CER and WER to 78.6% and 99.9%. These results support short-calibration personalization in a standardized-montage, closed-corpus setting.

For a vector bundle $E$ on a smooth projective curve $C$, one defines the Quot scheme $Q:=Q_d(E,C)$ parametrizing subsheaves of $E$ having length $d$ torsion quotients. We describe the indecomposable components of the tangent bundle $T_Q$ of $Q$, thus characterizing when $T_Q$ is indecomposable. We also characterize when $T_Q$ is simple; in fact, we completely describe the endomorphism rings of the indecomposable components of $T_Q$. As an application, we determine when two products of such Quot schemes can be isomorphic.

Let $G$ be a Borel digraph with maximum out-degree $d \in \mathbb{N}$. We show that $G$ admits a random Borel $(2d+1)$-coloring for which every edge is almost surely not monochromatic. This gives a simpler proof of a recent result of Pelayo-Gómez: such a graph $G$ admits a measurable proper $(2d+1)$-coloring with respect to any Borel probability measure on $V(G)$. Our proof is an adaptation of Pelayo-Gómez's proof to the randomized Borel setting.

Generative User Interfaces (GenUIs) enable applications to generate interfaces on demand from user needs and context. Like conventional UIs, they must still reflect designers' intent and conform to requirements such as brand identity. Unlike conventional UIs, designers cannot directly specify or see every interface a GenUI may produce, making design intent harder to enforce. We introduce GUIDE (GenUI Development Environment), a system that lets designers continuously inspect and refine GenUI behavior as they create and edit interfaces. GUIDE uses designers' modifications and interactions to adapt GenUIs through prompt optimization and a novel adaptive conformance scoring model. We validate GUIDE's scoring model and system. The scoring model matched or outperformed proprietary LLM baselines on held-out comparisons of real and synthetic application screens. In a study with 12 UI/UX practitioners, participants found GUIDE effective and usable and significantly preferred aligned outputs over a strong baseline using exemplars and a model-generated design.md.

Long-running AI agents outlive initiating processes through credentials, delegated tasks, queues, callbacks, reservations, and provider-side operations. Cancellation, process exit, and credential revocation neither close every pre-cut carrier nor distinguish independently authorized shared work. We define root-scoped authorization quiescence: for each manifested sink, a certificate accounts for every cut-relevant acceptance under the retired root-epoch atom that precedes its local fence and excludes protected acceptance under that atom after the fence, while permitting exact rebind to a current, independently sufficient support. The root-scoped quiescence protocol linearizes a root cut, fences old-root expansion and protected sinks, represents alternative and conjunctive authority as antichains of minimal sufficient root sets, and composes provider-frontier certificates into a cutset over registered old-root paths. Exact channel-token accounting reconciles transfers; missing or conflicting evidence remains indeterminate. Under stated assumptions, we prove post-cut issuer non-expansion, support-sound projection, compositional soundness under exact channel conservation, independent-support preservation, merge-order independence, and crash/replay stability. A provider-free late-effect test suite matches 17/17 registered outcomes. Two cancellation-only and one cut-only execution accept the same class of already scheduled late effect; two cut-plus-fence executions, one restart, and one stale-process execution reject it. A separately implemented checker verifies 17/17 traces and rejects 44/44 consistently rehashed semantic regressions. The certificate establishes root-relative authorization quiescence within its bound manifest and configuration, not global idleness, rollback, or business completion.