Papers

We show that, for a second-countable locally compact Hausdorff étale minimal groupoid with compact unit space, simplicity of the reduced groupoid C*-algebra implies the existence of a comeager set of unit points with C*-simple isotropy group. Combining this result with work of Christensen and Neshveyev on exotic completions of isotropy group algebras, we show that the converse implication is also true. Finally, we construct a Hausdorff étale minimal groupoid with an isotropy group whose induced exotic completion differs from its reduced group C*-algebra, answering a question of Christensen and Neshveyev.

We study local convergence to the dynamical $\Phi^4_3$ model under a vanishing quintic perturbation. More precisely, on the three-dimensional torus we consider $$\partial_tu_\varepsilon=\Delta u_\varepsilon-\varepsilon^\alpha u_\varepsilon^5+\xi_\varepsilon+C_\varepsilon u_\varepsilon+\widetilde C_\varepsilon u_\varepsilon^3$$ for $\alpha\in(\frac56,1)$, where $\xi_\varepsilon$ is a spatial mollification of space-time white noise. Although the quintic coefficient vanishes, its contractions generate divergent linear and cubic contributions. We identify suitable mass and cubic counterterms that compensate these divergences. Using paracontrolled calculus, we construct the required enhanced stochastic data and prove that their renormalized higher-order components vanish, while the remaining coordinates converge to the enhanced data of the dynamical $\Phi^4_3(\lambda)$ model. We further establish local well-posedness and stability of the associated deterministic solution map. Consequently, for well-prepared initial conditions, $u_\varepsilon$ converges in probability, as a random local solution germ, to the renormalized dynamical $\Phi^4_3(\lambda)$ solution. In particular, the cubic counterterm allows convergence strictly below the threshold $\alpha=1$ arising when only linear renormalization is allowed.

Orbital transport in light transition metals has emerged as a promising route toward angular-momentum electronics, with Hanle magnetoresistance (HMR) providing a direct electrical probe of the orbital Hall effect (OHE) in non-magnetic conductors. Here we report magnetoresistance signatures consistent with orbital HMR in epitaxial SrVO$*3$ (SVO), a narrow-band $d^1$ oxide grown on (001)-oriented (LaAlO$*3$)$*{0.3}$(Sr$*2$TaAlO$*6$)$*{0.7}$ substrates. In films of different thickness and longitudinal resistivity, field-dependent measurements reveal a reproducible positive, even-in-field, and approximately quadratic $\Delta\rho*{x-y}$ response, as expected for HMR. Angular measurements characterize the corresponding magnetoresistance anisotropy and reveal an additional non-Hanle contribution. Density functional theory (DFT) calculations yield an intrinsic orbital Hall conductivity $\sigma*{\mathrm{OH}}^{\mathrm{DFT}} = 390,(\hbar/e),\Omega^{-1}\mathrm{cm}^{-1}$ and a spin Hall conductivity $\sigma_{\mathrm{SH}}^{\mathrm{DFT}} = -12,(\hbar/e),\Omega^{-1}\mathrm{cm}^{-1}$ at the Fermi level, corresponding to $|\sigma_{\mathrm{OH}}^{\mathrm{DFT}}/\sigma_{\mathrm{SH}}^{\mathrm{DFT}}| \approx 33$, thus indicating a predominantly orbital response. Using the diffusive HMR framework with $\lambda_{\mathrm{OD}} = 2$ nm as a reference value, the 20.8 nm film gives conservative saturation-limit lower-bound (LB) estimates $\theta_{\mathrm{OH,LB}} = 0.0144 \pm 0.0004$ and $\sigma_{\mathrm{OH,LB}} = (460 \pm 11),(\hbar/e),\Omega^{-1}\mathrm{cm}^{-1}$, comparable to the DFT value. Across the series, lower-bound estimates obtained with the same $\lambda_{\mathrm{OD}}$ increase overall with longitudinal conductivity. These results suggest that narrow-band $d^1$ metallic oxides are a promising platform for orbital transport.

Auto-bidding is central to computational advertising, where strategies must maximize advertisers' conversion value under economic constraints. It has evolved from rule-based controllers to reinforcement learning and generative methods such as Decision Transformer (DT). Yet these methods increasingly mismatch the prevailing optimized cost-per-X (oCPX) paradigm, which spans heterogeneous scenarios (e.g., registration, purchase), each served by a separate model, leading to fragmented pipelines and underexploring cross-scenario modeling. Inspired by foundation models like LLMs, unifying these oCPX scenarios into one model raises three challenges: multi-objective control, scalable capacity under strict latency, and safe offline policy improvement. We present OneBid, a unified auto-bidding foundation model that learns a reusable backbone from heterogeneous oCPX logs and adapts it to scenario-specific deployments via offline post-training. Building on DT, OneBid extends single Return-to-Go conditioning to two atomic signals, Return-to-Go for conversion value and Cost-to-Go for cost ratio, plus value-aware regularization on next-action prediction. To absorb distributional heterogeneity, we design a sequence-level Mixture-of-Experts architecture, where shared experts encode cross-scenario knowledge and sparsely-routed experts capture scenario-specific patterns at low latency, yielding consistent scaling with model size and data. During post-training, we align the backbone with scenario preferences via Critic-guided Relative Offline Policy optimization (CROP): a learned critic scores candidate actions group-relatively, avoiding the unsafe online exploration of GRPO-style fine-tuning while constraining policy shift to reduce OOD risk. Validated via online A/B tests and fully deployed at Kuaishou, OneBid delivers an overall +2.2% ADVV gain on oCPX Ads, peaking at +13.1% in the ROAS scenario.

This paper addresses the problem of parameter estimation and model-based imputation for multivariate circular data lying on a $p$-dimensional torus in the presence of missing values. Actually, the periodic nature of the sample space invalidates conventional imputation techniques designed for Euclidean data. Then, we propose a general framework for maximum likelihood estimation under the wrapped elliptically symmetric family of distributions, with particular interest in the multivariate wrapped normal distribution, when the missing data mechanism is ignorable. The methodology leverages the conditional properties of the elliptically symmetric distributions on the unwrapped space, embedding the imputation of missing torus data into an Expectation-Maximization algorithm that treats both the wrapping coefficients and the missing entries as latent variables. Derivation of both the E and M steps is detailed and a working algorithm is discussed. Imputation methods are also taken into account.

Sequential recommendation aims to predict the next item a user will interact with based on their historical behavior. Advances in Transformers have significantly improved sequential recommendation but are still limited by cost efficiency. Although State Space Models (SSMs) have recently enabled efficient long-range modeling, most existing methods encode each item with a single static contextual role, overlooking the phenomenon of item polysemy. In fact, the same item often plays different semantic roles depending on user context, and existing methods are limited in capturing dynamic behavior across different temporal granularities. In this work, we propose DSRec, a novel dual-interest cross-SSM model that explicitly disentangles item roles across long-term and short-term semantic context. Sequential items are encoded into long-term interest embeddings that capture stable preferences via historical aggregation, and a short-term interest branch that emphasizes local session intent modulated by inter-click time intervals. These interest embeddings are processed through distinct SSM encoders: a full-sequence Mamba for long-term modeling, and a time-modulated SSM that dynamically adjusts state evolution based on temporal gaps. To enable effective cross-granularity alignment, we adopt a residual cross-fusion mechanism that exchanges contextual information between the two branches while preserving semantic independence. Experiments on public benchmarks demonstrate that DSRec outperforms other state-of-the-art methods.

Research on explainability in recommender systems largely centers on end users, overlooking the perspectives of those who build and maintain these systems and their potential use cases such as model debugging. In this study, we examine how news engineers and related technical stakeholders perceive and implement personalization and explainability in practice. We conducted 15 semi-structured interviews across nine news organizations, spanning diverse regions in both public and private sectors, to investigate the challenges and motivations shaping their approaches. Our findings reveal that personalization is not always a straightforward or desirable choice for news organizations, as concerns around user tracking, editorial control, and resource constraints often limit its adoption. Even among organizations implementing personalized news recommender systems in production, explainability is rarely prioritized, with day-to-day operational demands frequently taking precedence over longer-term transparency goals. Definitions of explainability vary widely across organizations, though some demonstrate promising internal practices and visualization tools that facilitate communication between engineering teams and newsrooms. Based on our analysis, we provide actionable and practical guidelines for news engineers and researchers on how to adopt explainability methods within a news personalization pipeline.

Long-baseline nulling interferometry suppresses the on-axis light of a star, enabling high-contrast observations of faint circumstellar emission and exoplanets at high angular resolution. The Nulling Observations of dusT and PlaneTs (NOTT) instrument is the L'-band nulling interferometer of the Asgard instrument suite and will be the first nuller installed at the Very Large Telescope Interferometer (VLTI). Its main scientific goals are to characterise hot/warm exozodiacal dust and young Jupiter-like exoplanets at close (<10 AU) orbital separations, where indirect detection methods are most sensitive. NOTT uses a four-telescope integrated-optics photonic beam combiner operating over 3.5-4.0 micrometres. The photonic chip produces photometric, bright, and nulled outputs that are polarization-split, spectrally dispersed, and imaged onto a 5-micrometre-cutoff HAWAII-2RG detector by the NOTT cold nulling camera. The cold optical assembly includes the photonic-chip interface, injection optics, collimator, Wollaston prism, dispersive element, imager, and cryogenic detector stage. The mechanical implementation is designed for operation near 90 K using aluminium support structures, spring-loaded optical mounts, and cryogenic-compatible mechanisms to preserve alignment during cooldown. We present the current status and performance of the NOTT cold nulling camera and cryostat assembly. The system is undergoing assembly, integration, and verification to validate thermal stability, detector operation, vacuum performance, and opto-mechanical repeatability. Initial cryogenic tests have demonstrated operation near 100 K for the cold optics and 30 K for the detector, cryogenic validation of the filter wheel, and a vacuum pressure of 8 x 10^-8 mbar. These activities represent a key step toward deploying NOTT as the first nulling interferometer at the VLTI.

Identifying defects responsible for non-radiative recombination in metal-halide perovskites remains challenging, with no common defect signatures established across compositions. Here, we combine fluence-dependent time-resolved photoluminescence, full Shockley–Read–Hall modelling and Bayesian posterior inference across an FA$_{1-x}$Cs$_x$PbI$_3$ compositional series. We show that trap occupation governs carrier dynamics and defect-parameter identifiability in semiconducting materials: weakly occupied states exhibit electron-capture-coefficient–trap-density degeneracies, whereas trap filling lifts them. In our perovskite systems, a non-degenerate signature $T\beta$, characterized by a strongly asymmetric $\beta_p/\beta_n$ capture-coefficient ratio, occurs across all compositions, suggesting substantial trap filling is a general feature of perovskite carrier dynamics. We further identify $T\alpha$ as a shared, device-performance-limiting non-radiative recombination channel, while a shallow $T\epsilon$ signature unique to FAPbI$_3$ produces the largest steady-state non-radiative recombination rate and is consistent with the previously observed high stacking-fault density of this composition. This framework therefore provides a basis for comparing trapping signatures across different semiconducting materials at room temperature.

Cross-platform mobile frameworks promise code reuse, shorter delivery cycles, and lower implementation effort, but their trade-offs relative to native development remain difficult to assess objectively. Many comparisons rely on simplified applications, inconsistent feature sets, or a narrow set of metrics. This paper compares five implementations of the same plant-management application: native iOS, native Android, Flutter, React Native, and Kotlin Multiplatform. The shared approaches target both Android and iOS, yielding eight executable variants. Guided by ISO/IEC 25010, the study examines time behavior, implementation footprint, source-code organization, and observable rendering responsiveness. All implementations share the same domain, backend services, functional requirements, and benchmark contract. The supplied dataset contains 2,000 completed runs per variant and covers authenticated and cached retrieval, image transfer and decoding, list rendering and scrolling, local synchronization, and media upload. Backend preparation and framework-specific UI drivers are analyzed separately from the primary client workflow. Native records the lowest non-UI client subtotal on both operating systems, with Kotlin Multiplatform the closest cross-platform implementation, while operation and UI-wrapper rankings vary by task. The shared approaches contain less authored mobile source than the native applications combined, and the source inventory shows different patterns of file size, organization, and dependency use. Rather than identifying a universally superior technology, the study shows that each approach's advantages and costs depend on the quality attribute, workload, platform, and measurement boundary.

Does a general vision–language model acquire specialized OCR ability by developing a new reading circuit or by reusing an existing mechanism? We address this question in the setting of full-sequence OCR, rather than local-answer retrieval. Using an evidence-grounded protocol with held-out causal interventions, we identify sparse and stable OCR-head sets in GLM-OCR, MinerU2.5, and PaddleOCR-VL-1.6. We then investigate the mechanistic origin of these OCR heads by comparing them with independently identified textual retrieval/copy heads in general VLMs. Across two general VLMs, visual OCR heads strongly overlap independently identified textual retrieval/copy heads, yielding untuned top-20 intersections of 73.3% and all-head Spearman correlations of 0.677-0.886. The overlap and causal interventions suggest that full-sequence OCR operates as dense sequential multimodal copy-and-paste, repeatedly retrieving visual evidence and routing it to the current output position. Finally, we examine how this shared circuit changes as a general VLM becomes an OCR specialist. Matched base-to-specialized comparisons show that OCR specialization largely preserves head identity, retaining 17-20 of the top 20 heads per task with all-head rank correlations of 0.874-0.942, while redistributing their functional and causal strengths.

Raman spectroscopy is widely used for molecular identification in biological samples, but spectral congestion often obscures key molecular fingerprints. Strategies to enrich vibrational spectra with additional controllable features are therefore desirable. We theoretically show that vibrational strong coupling (VSC) can reshape Raman spectra by reorganizing vibrational energies and intensities. Near-resonant coupling enables the resolution of quasi-degenerate vibrational modes and redistributes Raman activity among molecular vibrations, brightening otherwise Raman-inactive modes. Off-resonant coupling mediates effective interactions between vibrations, leading to tunable intensity reorganizations and spectral shifts via cavity-controlled vibrational mixing. Using a microscopic theory of Raman scattering, we show that observing Raman signals from collective VSC polaritons requires appropriate geometries for the scattering setup, the sample, and the cavity environment, helping to explain why polaritonic Raman signatures have remained challenging to observe experimentally.

Multi-label few-shot learning (MLFSL) remains a significant challenge in medical image analysis (MIA). Current metric-based meta-learning methods face two critical limitations in MIA. First, conventional prototype generation often entangles irrelevant disease information, leading to contaminated prototypes and degraded performance. Second, prior studies typically enforce inter-class separability in embedding space, largely neglecting the inherent correlations among diseases. To overcome these challenges, we propose Prototype Purification and Regulation (PPR), a novel MLFSL framework for MIA. PPR first performs prototype purification by leveraging sample-level comorbidity scores to emphasize disease-specific features, producing purified prototypes that better characterize each disease. Building upon these purified prototypes, PPR further addresses the underexplored problem of inter-class prototype distance in MIA by incorporating disease-level comorbidity statistics to adaptively regulate inter-class similarity, forming a comorbidity-aware embedding space. Overall, PPR sequentially enables the model to capture pure disease features and inter-class relationships for reliable MLFSL in MIA. Extensive experiments across four chest X-ray benchmark datasets, including cross-domain evaluation, show that PPR consistently outperforms state-of-the-art methods, significantly improving disease detection while demonstrating robust generalization and clinical applicability.

This paper studies the element-wise convergence behavior of subspace iteration. All results are established for both \(\mathbb{F}=\mathbb{R}\) and \(\mathbb{F}=\mathbb{C}\). For a diagonal matrix \(\Lambda=\mathrm{diag}(\lambda_1,\ldots,\lambda_n)\) with \(|\lambda_1|>\cdots>|\lambda_n|>0\), we analyze the modulus of each entry of the iterative matrix sequence generated by subspace iteration, both without and with the Rayleigh–Ritz procedure. Under mild assumptions on the initial matrix \(X\in\mathbb{F}^{n\times m}\), we first derive exact asymptotic expressions for \(|Q_k(i,j)|\) in the subspace iteration without the Rayleigh–Ritz procedure: entries with \(i\neq j\) decay as \(|\lambda_{\max\{i,j\}}/\lambda_{\min\{i,j\}}|^k\), and the deviation of \(|Q_k(j,j)|\) from \(1\) decays as \(\max\{|\lambda_j/\lambda_{j-1}|,|\lambda_{j+1}/\lambda_j|\}^{2k}\), with explicit coefficients determined by the LU factorization of \(X\). Similar conclusions could also be established for upper triangular matrices. For the Rayleigh–Ritz variant, we obtain element-wise asymptotic formulas for the normalized Ritz vectors \(Z_k\). Specifically, for \(|Z_k(i,j)|\), off-diagonal entries with \(i\geq m+1\) decay as \(|\lambda_i/\lambda_j|^k\), off-diagonal entries with \(i\leq m\) decay as \(|\lambda_{m+1}^2/(\lambda_i\lambda_j)|^k\), and the deviation of \(|Z_k(j,j)|\) from \(1\) decays as \(|\lambda_{m+1}/\lambda_j|^{2k}\). These results give an element-wise description of the convergence behavior of subspace iteration. After an orthogonal or unitary change of basis, the results could be further generalized.

Suppose an economy moves continuously along a closed path of fundamentals and returns exactly to its initial state. A regular Walrasian equilibrium price followed continuously along that path need not return to itself. For every number of commodities $L\ge3$, we construct a closed one-parameter family of pure-exchange economies in which all preferences are fixed, only three individual endowments vary, and aggregate resources remain constant. Along the loop, two regular equilibrium-price branches are exchanged while a third returns to itself; at the end, every economic primitive is exactly as it was initially. The construction uses at most $2L+2$ consumers. We also provide an exact realization with at most $2L$ consumers in which all endowments are fixed and only one preference varies; the two families generate identical aggregate excess demand. The key realization problem is parametric: classical aggregate-realization results guarantee an economy at each fixed parameter value, but not a continuous loop of realizing primitives. We construct such a loop explicitly. The resulting monodromy is structurally stable under sufficiently small $C^1$ perturbations. It is impossible with one or two commodities, making three commodities the sharp threshold. Thus local regularity guarantees local continuation but not a globally path-independent identity of an equilibrium branch, with implications for global comparative statics under multiplicity and for equilibrium selection based on continuation.

This paper proposes fuzzy entropic triple k-means (FE3KM), an entropy-regularized fuzzy partitioning method for three-way data arrays that simultaneously clusters objects, variables, and occasions. The method combines three row-stochastic fuzzy membership matrices and a full array of block centroids through a product-weighted squared-distance criterion with mode-specific entropy regularization to represent uncertainty in cluster assignments. With normalized product membership weights and weighted-mean block centroids, the ordinary total sum of squares decomposes exactly into within- and between-block components, further attributable to each mode and to individual clusters within each. This identity supports cluster-level descriptive summaries and conditional assessments of the gain associated with each way's partition. We derive a block-coordinate descent algorithm with weighted-mean centroid updates and entropy-based membership updates, and clarify the relationship with tandem procedures, independent partitioning, hard three-way partitioning, and Tucker reconstruction. An accelerated variant is also proposed for large arrays. A simulation study examines partition and centroid recovery under different noise levels and array sizes, sensitivity to the entropy regularization parameters, and a comparison with tandem and independent procedures. An application to a benchmark three-way TV ratings dataset shows how FE3KM illustrates interpretable object-variable-occasion structures and quantifies the contribution of each cluster and mode to overall data variability.

Although memristor-based in-memory computing (IMC) has been widely investigated for brain-inspired neuromorphic workloads, systematic evaluations of its energy, latency, and signal-to-noise ratio (SNR) trade-offs across diverse system parameters remain scarce for classical digital signal processing (DSP). To address this gap, this paper introduces a comprehensive hardware-aware design framework for systematically mapping algorithmic workloads onto IMC architectures, using the discrete Fourier transform (DFT) as a case study. Tailored to the stringent performance requirements of a DFT accelerator for 5G orthogonal frequency-division multiplexing (OFDM) systems, we propose a novel mapping scheme that reduces energy consumption per computation by 53% compared with conventional mapping techniques. Additionally, we present a comparative study of resistive random-access memory (RRAM) and ferroelectric tunnel junction (FTJ) technologies with identical numbers of programmable states but distinct conductance ranges, demonstrating the importance of device-informed architectural co-design. By bridging the gap between emerging IMC architectures and rigid DSP constraints, this work provides a pathway toward energy-efficient edge accelerators for future wireless communication systems.

We propose a framework for incorporating quantum-computing-based electronic-structure calculations into universal machine-learning interatomic potentials (uMLIPs). Rather than constructing an interatomic potential from scratch, we refine a pretrained DFT-based uMLIP using a small set of accurate reference energies obtained from quantum computing. We demonstrate the approach for three chemically distinct applications: the Menshutkin reaction, water adsorption in the metal-organic framework HKUST-1, and CO hopping on a high-entropy-alloy nanoparticle. For the Menshutkin reaction, fine-tuning on gas-phase configurations improves the transition-state energy inside a carbon nanotube but not the product energy. For water adsorption in HKUST-1, fine-tuning with only 14 reference configurations brings adsorption thermodynamics obtained from millions of configurations sampled by Widom insertion into closer agreement with reference values. For CO hopping on an IrPdPtRhRu nanoparticle, the preference for on-top over bridge adsorption is recovered in the finite-temperature free-energy profile obtained from enhanced-sampling molecular dynamics, even though the reference data contain only energies. These results demonstrate that the proposed framework provides a practical route for incorporating quantum-computing calculations into realistic atomistic simulations and that quantum-computing reference data can improve pretrained uMLIPs.

We prove that, for every positive integer $r$, the positive normalized diameters of isometric quotients of simply connected irreducible compact Riemannian symmetric spaces of rank $r$ have a uniform positive lower bound. The bound is independent of the dimension and of the acting group, which need not be connected. For the higher-dimensional Grassmannian families, we obtain an explicit bound for positive-dimensional acting groups by constructing nonconstant invariant functions of bounded trigonometric degree. The real and complex cases use moment maps. The quaternionic case follows from a quartic rigidity theorem proved by means of invariant four-forms and the classification of compact quaternionic symmetric spaces. We also give examples showing why the rank and the relative scales of product factors must be controlled.

We study Bousfield–Kan completions through the interaction of free simplicial resolutions, their filtration spectral sequences, and a noncommutative arithmetic square. For every free discrete simplicial group of finite type, we express its integral pronilpotent completion as the homotopy pullback of its rational prounipotent completion and the product of its pro-$p$ completions over an explicit adelic simplicial group. The adelic entry is formed by taking restricted products at finite nilpotent stages and then their inverse limit; no nilpotency assumption on the original group of components is required. Finite subpresentations of contractible presentations provide an explicit application of this construction. Independence of the specified relators makes the positive-degree terms of the rational and mod-$p$ filtration spectral sequences vanish, with convergence verified on the quotient towers. Continuous comparison of free simplicial resolutions then realizes, in characteristic zero, the equivalence with a constant free prounipotent group by morphisms and homotopies in that category. For the corresponding presentation complex $K$ we obtain $R_\infty K\simeq K(F_R(Z),1)$ for $R=\mathbb Q,\mathbb F_p,\mathbb Z$, where $Z$ indexes a complementary basis and $F_R(Z)$ denotes, respectively, the rational points of a free prounipotent group, a free pro-$p$ group, or a free pronilpotent group. Compatible contractions at the nilpotent stages identify all four entries of the arithmetic square in this case.

LLM-based multi-agent systems generate collaboration traces that record how agents plan tasks, verify intermediate results, and repair failures. Reusing these procedures requires preserving an action's prerequisites and the outputs needed by subsequent agents. Our empirical studies show that grouping these dependencies into functional memory units improves their retention, while connecting units increases retrieval of the units and links jointly required by a task. The preferred combination of units also changes between instructions and checklists, even when each combination's content is fixed across formats. Updating choices from the outcomes of each combination and format pairing outperforms scoring combinations and formats separately. These findings motivate MACE, a memory-agent co-evolution framework that adapts memory organization and agent memory use through execution feedback. Its MemGoG structure represents functional units as subgraphs of related conditions, actions, and outputs, connecting them through support, conflict, and repair relations. MACE Loop selects task-relevant units and relations within a memory budget and provides each agent with instructions or checklists for its current operation. It records the selected units, presentation formats, agent outputs, and task outcomes to update unit scores and relations for retrieval and inform subsequent presentation choices. Across eight benchmarks, MACE outperforms ten baselines with an average score of 81.11%, compared with 78.97% for the strongest baseline, SAGE.

In cryptography, critical sets of Latin squares have particularly been implemented to design secret sharing schemes. A main problem in these cryptographic protocols arises from absent holders of pieces of information that are common to different critical sets, because they become indispensable to recover the secret. This paper solves this problem by making use of the orbits of entries described by the autoparatopism group of the Latin square under consideration. To this end, we introduce the more general problem of computing critical sets of Latin squares having a given paratopism in their autoparatopism group. These critical sets depend only on the conjugacy class of the autoparatopism and the main class of the Latin square under consideration. Based on this fact, as an illustrative example, we determine the smallest and largest sizes of critical sets associated with autoparatopisms of Latin squares of order up to six. We implement this approach in the design of a new secret sharing scheme.

Granular packings undergo intermittent rearrangements, known as precursors, before avalanche onset. Using grain-scale tracking in an inclined granular layer, we show experimentally that the number and recurrence of precursors change with the compatibility between the anisotropic structure inherited from preparation and the subsequent loading direction. Preparation also modifies the propagation of the mobility front, defined as the region in which the packing undergo measurable displacement: frequent precursors produce small progressive advances, whereas rare precursors involve larger extensions. By contrast, several features remain unchanged across protocols. The ensemble-averaged displacement always decays exponentially with depth over approximately four grain diameters, while the local shear-strain variance follows a common quadratic scaling with the mean strain. A two-state model suggests that, regardless of the packing structure, local strain heterogeneities affect approximately one quarter of the elementary cells, superimposed on the exponential strain profile. The reported results separate preparation-dependent precursor activity from the robust spatial features of the deformation preceding avalanches.

WiFi-based human activity recognition has achieved high accuracy under the single-user scene. Recognizing activities performed by multiple concurrent users remains challenging, because their body-reflected propagation paths superimpose in the channel state information (CSI) measurement. Existing multi-user methods either decompose the signal before classification, suffering from error propagation, or predict activities jointly without reliably associating each prediction with the correct user. Moreover, attention mechanisms that have proven effective for single-user sensing compute a single user-agnostic attention map, blending patterns from different users and providing no mechanism to associate features with specific user slots. This paper proposes a user-conditioned spatial attention (UCSA) module that generates per-user spatial attention maps by conditioning multi-scale spatial attention on learnable user-ID embeddings via feature-wise linear modulation (FiLM). UCSA creates a deep coupling between spatial feature enhancement and user differentiation: the attention module itself becomes user-aware, producing distinct attention maps for each user slot rather than relying on a late-fusion embedding addition. Combined with a shareable multi-semantic spatial attention (SMSA) module for multi-scale spatial enhancement, the proposed framework addresses both feature quality and user differentiation in a unified architecture. Experiments on the WiMANS benchmark across three indoor environments and up to five concurrent users show that the proposed method outperforms nine baselines in all settings, achieving an average accuracy of over 93% across three environments even with five users. Ablation studies confirm that both SMSA and UCSA contribute substantially to recognition accuracy, with UCSA providing the critical link between shared features and per-user predictions.

Let $k\ge 3$ and let $n=km$. A $K_k$-factor in an $n$-vertex graph is a collection of $m$ vertex-disjoint copies of $K_k$ that covers the entire vertex set. We determine the maximum adjacency spectral radius of an $n$-vertex graph containing no $K_k$-factor when $m\ge 2k-1$. More precisely, we prove that every such graph $G$ satisfies \[ \rho(G)\le \rho(H_{n,k}), \qquad H_{n,k}=K_{k-2}\vee\bigl(K_{n-k+1}\cup K_1\bigr), \] with equality if and only if $G\cong H_{n,k}$. Equivalently, the unique extremal graph is obtained from $K_{n-1}$ by adding one vertex adjacent to exactly $k-2$ vertices of the clique. Our proof combines a decomposition lemma for sparse complements, derived from the Hajnal–Szemerédi theorem, with the Motzkin–Straus inequality and spectral estimates based on quotient matrices and the Rayleigh quotient.

We prove that on a compact locally flat HKT manifold the quaternionic Monge–Ampère equation always has a unique continuous solution. This provides new evidence for the Conjecture of Alesker and Verbitsky.

Graph-enhanced multi-agent systems (G-MAS) coordinate large language model agents through communication graphs and role assignments, which determine how agents exchange information and divide responsibilities. However, final-score comparisons across systems combine differences in models, communication patterns, roles, and computation costs, making performance differences difficult to attribute to specific communication structures, role assignments, and information flows. To address this evaluation attribution problem, we introduce OpenMAS-GCom, a benchmark for diagnosing how these components affect G-MAS performance through controlled interventions. We represent systems through collaboration units, communication links, shared intermediate information, and execution rules. OpenMAS-GCom compares original systems with versions modified by changing one component while keeping tasks, models, prompts, and budget limits fixed. We rewire communication edges, remove specialist or critic agents, replace intermediate messages with incorrect content, and disable workers during execution. The benchmark evaluates 17 single-agent, ordinary multi-agent, and graph-enhanced configurations on 29 datasets across six domains. We add 400 G-MAS-Complex tasks requiring agents to combine information from multiple documents, resolve conflicting records, and return specified values with source identifiers. Experiments show larger mean losses after specialist removal than after critic removal, different performance degradation under incorrect messages and worker failures despite similar original scores, and different configurations achieving the highest accuracy and accuracy per token on G-MAS-Complex.

Introduction Risk modelling (RM) and treatment effect modelling (EM) are two approaches to build models to estimate heterogeneous treatment effects from randomized control trials (RCT). RM is a two-stage approach; it estimates a predicted baseline risk at the first stage and then includes it as the only effect modifier in a regression model in the second stage. EM is a full treatment interaction multivariable model. Both approaches have theoretical advantages and limitations, but a thorough comparison including a simulation study is missing. Methods In a theoretical review of the two approaches, we present their underlying assumptions and theoretical advantages and disadvantages. Based on our theoretical review, we design simulation scenarios for RCTs with a dichotomous outcome and evaluate the performance of both approaches with respect to the root mean square error and the bias in the predicted risk difference. Results In the theoretical part we argue that baseline risk is a treatment effect modifier in many clinical situations. RM is a dimensionality reduction approach which, however, makes strong assumptions about the role of prognostic factors modifying the treatment effect. EM's greater flexibility is a possible advantage when the sample size is large. In most simulated scenarios RM performs better than EM, even when the assumptions underlying RM are not fully met. The advantage of RM diminishes as sample size increases. Conclusion When choosing between RM and EM the available sample size and the plausibility of their underlying assumptions should be considered.

Preference-based reward shaping can guide reinforcement learning, but adding preference signals to the reward may unintentionally change the task being optimized. We address this problem with IncentRL, a framework that introduces preference guidance while explicitly characterizing its effect on external-task performance. IncentRL adds a Kullback–Leibler (KL) penalty between a specified outcome distribution and a preferred distribution. For finite discounted Markov decision processes with bounded shaping costs, we derive an external-value perturbation bound, establish a sufficient strict-action-gap condition for preserving the original optimal policy, and characterize the large-weight regime through discounted cumulative preference cost. Exact examples clarify the limits of these guarantees, including tied optima and support mismatch. We study a practical implementation using a hand-designed, distance-based outcome proxy, a fixed preference distribution, and score-weighted coefficient search. On MiniGrid DoorKey-8x8, the reported three-seed mean success rate after two million training steps reaches 98% with coefficient 0.01, compared with 90.5% for the reported zero-coefficient baseline, while the search progressively shifts toward smaller coefficients. Together, these results provide a principled view of the central trade-off in preference-based RL: using additional guidance to improve learning without excessively distorting the original task objective. The current experiments remain descriptive and do not yet isolate KL shaping from simpler alternatives.

In this article we claim that we are going to give a priori and a posteriori error estimates for a Crank Nicolson type scheme. The problem is discretized by the finite elements in space. The main result of this paper consists in establishing two types of error indicators, the first one linked to the time discretization and the second one to the space discretization.