Papers

Repeated averaging on graphs is a natural prototype of local stochastic exchange, modeling consensus formation, information spreading, and wealth redistribution. Its convergence has attracted longstanding interest, from Bourgain's complete-graph $L^1$ cutoff question in the 80s (answered in recent years by Chatterjee, Diaconis, Sly, and Zhang) and the systematic study of Aldous and Lanoue. Addressing the still outstanding and widely asked $L^1$-cutoff question on general graphs, we establish a criterion based on size-biased sampling, and develop a general framework for sparse expanders. Specifically, we prove $L^1$ cutoff with a Gaussian profile on random $d$-regular graphs, for any $d\ge 3$ and uniformly over starting vertices. Remarkably, although the expected mass profile agrees exactly with the corresponding random-walk distribution, cutoff occurs strictly later than both the random walk cutoff time and the universal lower bound attained on complete graphs, revealing an unexpected entropy gap. The framework is robust, involving ideas of polymer representations, random geometry, universal-cover lifting, and adaptive revealing. Our companion work will extend it to Ramanujan graphs and bounded-degree configuration models.

Self-supervised learning for combinatorial optimization has emerged as a promising paradigm for solving discrete optimization problems with neural networks, but a central challenge remains: handling hard combinatorial constraints within continuous, gradient-based training. Continuously extending combinatorial objectives to convex domains is a powerful technique, yet existing approaches often require projection steps that constrain neural network outputs to lie inside the feasible polytope and rely on ad-hoc and problem-specific constructions. We propose a general framework in which the neural network is allowed to predict arbitrary continuous vectors that could potentially lie outside of the feasible polytope. These predictions are then approximated by sparse convex combinations of feasible solutions using a geometric decomposition algorithm based on Frank–Wolfe methods and approximate Caratheodory results. This decomposition induces an a.e.-differentiable, self-supervised loss defined as the expected value of the discrete objective. The same procedure provides an automatic rounding guarantee at inference time. We demonstrate strong empirical performance across multiple combinatorial problems, including the Quadratic Assignment Problem, Maximum Coverage, and the Traveling Salesperson Problem.

We prove that every sufficiently large finite planar point set contains either four collinear points or seven points with at most one non-visible pair. More generally, we show that for every fixed graph $H$ with chromatic number at most five, or with chromatic number six and a color-critical edge, the visibility graph of every sufficiently large finite planar point set with no four collinear points contains a copy of $H$. These results extend the recent breakthrough of Bonnet (2026), guaranteeing six pairwise visible points, and come within one visibility edge of the next open case of the big-line-big-clique conjecture.

We establish exact thresholds for the failure of simultaneous quantum typicality: three parties for mixed states and four for pure states. For the four-qubit Higuchi–Sudbery state, every sequence satisfying the expected purity bounds on three overlapping marginals, with sufficiently small fixed positive entropy slack, is asymptotically perfectly distinguishable from the tensor powers of the input: its trace distance from them tends to the maximum value $2$. This maximal separation persists, with a common positive slack, throughout an open neighborhood in the full four-qubit state space. Tracing out one party yields a mixed tripartite example. The proof connects simultaneous quantum smoothing with polynomial concentration on $\CP^1$. Symmetry reduces the problem to a frame inequality on $\Sym^n(\mathbb C^2)$, where a linear entropy deficit competes with a quadratic cost of polynomial concentration. Bernstein–Markov estimates and a subharmonic barrier control this cost, yielding an exponential obstruction to simultaneous typicality. These results disprove Dutil's multiparty quantum typicality conjecture, formulated in 2011, and the one-shot simultaneous min-entropy-smoothing conjectures of Drescher–Fawzi and Colomer–Winter. Together with the positive results for smaller systems, they determine the smallest numbers of parties at which simultaneous typicality can fail.

Agricultural robotics is advancing rapidly, yet progress remains constrained by limited field access, lack of control over field conditions, geographic variability, and seasonal crop cycles. These factors make it difficult and costly to acquire diverse agricultural datasets, resulting in limited evaluation and reduced system robustness. While other robotics domains have scaled learning and evaluation through high-fidelity simulation, agricultural robotics still lacks comparably capable tools. In this paper, we present a ROS-integrated framework, built on Isaac Sim, for large-scale procedural generation of agricultural environments. The framework supports photorealistic rendering, physics simulation, and domain randomization at scales relevant to robotics research, with built-in support for row crops, orchards, and vineyards and straightforward extensibility to additional crop categories. Project Page: https://baj31415.github.io/agrigen/

This paper present a spiral-cavity wheel for lunar regolith excavation and a sensor-light evaluation stack that jointly estimates fill ratio (vision), sinkage (vision), and specific energy from actuator logs. In benchtop tests (four revolutions at 5, 10, and 15~RPM) against two literature baselines, the proposed wheel achieved higher excavated mass and fill ratio, delivering 2.2-3.0 times higher excavation rate while reducing specific energy by 29 % relative to a bucket-drum baseline. Normalized sinkage (mm/kg) was also lower, indicating stable traction without bogging. Effort-time traces show a steady torque envelope with repeatable cut-carry-dump cycles across speeds. We provide a retention index $\eta$ that correlates with fill ratio and a DEM setup that reproduces experimental trends with low error. Results suggest spiral-cavity wheels can replace heavier multi-actuator diggers when mass, simplicity, and energy efficiency are mission drivers.

The LUX-ZEPLIN (LZ) experiment recently reported a nuclear-recoil-like candidate at $E_R=248\pm23_{\rm stat}\pm23_{\rm sys}$ keV. We show that such an energetic recoil can arise from the elastic form factor of composite dark matter, without invoking an inelastic mass splitting or a boosted population. A neutral baryon of $N$ dark quarks can have a charge form factor that is suppressed at low momentum transfer but recovers at higher momentum transfer, providing a momentum-space band-pass filter. Modeling the form factor with one Gaussian per charged constituent species, we prove that two terms cannot produce a hard recoil spectrum and find that three yield too few events in the LZ signal window, while four suffice. A confining $SU(4)_D\times U(1)_D$ gauge theory provides a concrete realization through a neutral bosonic baryon made of four dark quarks. For a 200 GeV benchmark normalized to one accepted event, we predict approximately 1.5 true recoils beyond the current LZ region of interest. The form factor also produces diffraction nodes at fixed momentum transfers, placing them at recoil energies that scale as $1/m_A$ across target nuclei.

Signed graphs arise in trust–distrust networks, financial correlation systems, biological interaction graphs, and many other domains in which edges can be positive or negative and may also be directed. While signed graph neural networks have improved task-specific learning, graph transfer learning on signed graphs remains underdeveloped. In this paper, we introduce TopoSIGN, a pioneer topology-guided graph pre-training and prompt learning framework for signed graphs. TopoSIGN combines a structural encoder built on the magnetic signed Laplacian with a novel persistent-homology branch that summarizes signed topology through Dowker-complex persistence images. The fused embeddings are then transferred to a prompt learning function. Experimental results on synthetic and real-world datasets demonstrate the efficacy of TopoSIGN in extracting useful structural information in signed graphs, as well as the adaptability and flexibility of the proposed general framework.

Language models are increasingly trained on the outputs of other models, forming chains that we call lineages, in which a trait present in one generation can pass to the next. Prior work on subliminal learning has shown that a teacher's trait can transmit to a student through filtered data carrying none of the trait's content. However, the evidence covers only a single training step. We study whether such a trait holds or fades across lineages. We instill the trait into three copies of Qwen2.5-7B-Instruct and iterate the training step to depth ten from each, reading every generation two ways on the same held-out prompts: a keyword screen that looks for expressions of the trait in the model's output, and an activation probe that projects each model's displacement from the base onto a direction built from the other lineages' teachers. We report two findings. First, the trait persists through ten generations across three lineages. The instilled models express it on every completion; the keyword-screen rate falls to 55.6% after the first step and to 21.1% by generation ten. The base itself matches the screen on none of its 300 completions. Second, the trait can be present internally while absent behaviorally. When the model's default system prompt is removed at evaluation, the generation-ten students' keyword-screen rate is zero on every prompt while the probe score stays positive on every prompt. Steering the untreated base with the displacement of a generation-ten student, which is trained and measured under the default system prompt, induces screened expression of the trait even with the system prompt removed, while that same student shows no expression of the trait with the system prompt removed.

Verification of probabilistic weather forecasts remains a crucial aspect of numerical weather prediction, as new AI-based models become more widely used alongside the more traditional physics-based ensemble forecasting systems that continue to be developed and improved. We present a first-of-its-kind idealized probabilistic dataset composed of one-dimensional cases aimed at analyzing the behavior and properties of verification methods for probabilistic forecasts and comparing their behavior. It covers a wide range of probabilistic cases, such as constant, localized events, gradients, fronts, noisy, bimodal, and limiting cases. Moreover, the code associated with the dataset provides great flexibility for customizing the experiments it covers. The dataset represents the first building block of the more extensive comparison dataset of the Bridging The Gap project, which aims to facilitate the development and comparison of spatial verification methods for probabilistic forecasts.

Audio watermarking is increasingly important for tracing generated speech. Several audio watermarking methods have been proposed to embed the watermark in various domains, such as waveform, timbre feature, or latent representations, for making the embedded watermark robust against traditional digital signal processing (DSP) attacks. On the other hand, modern neural codecs introduce a different threat from DSP attacks: they resynthesize speech through quantized acoustic representations and can remove the embedded watermark evi- dence that is not aligned with codec-preserved structure. In this paper, we propose NeuMark, a codec-latent audio watermarking framework that embeds watermark evidence into SpeechTok- enizer acoustic tokens to address this resynthesis threat. NeuMark uses cross-attention to inject a 16-bit message across residual vector quantization (RVQ) layers, distributing the watermark over codec-aligned latent structure. Experimental results show that NeuMark substantially improves robustness under neural- codec resynthesis while supporting both watermark detection and message recovery. We also analyze the trade-off between reconstruction-referenced transparency and original-referenced robustness.

In this article, we consider a general version of the classical group ring isomorphism problem, called the twisted group ring isomorphism problem (TGRIP), which determines an isomorphism between the twisted complex group algebras of finite groups. Although for isoclinic groups $G$ and $H$ their complex group algebras are isomorphic, i.e, $\mathbb C G \cong \mathbb C H$, their twisted complex group algebras need not be isomorphic. Continuing this line of investigation, we establish sufficient conditions under which two isoclinic groups have isomorphic twisted complex group algebras, thereby providing solutions to (TGRIP) for isoclinic groups. As applications, we study (TGRIP) for special $p$-groups of rank $2$, unicentral groups, and nilpotent groups of class $2$ with elementary abelian Schur multipliers, all considered up to isoclinism. We also present several examples illustrating the main results, including a complete solution of (TGRIP) for special $p$-groups of rank $2$ of order $p^6(p \ge 3)$

The first author and Dong \cite{DD} proposed three conjectures on antichain generating polynomials. Jiang \cite{Jiang} recently proved Conjectures 4.3 and 4.5, concerning real-rootedness and \(\gamma\)-positivity. We prove Conjecture 4.2 by adapting his method from \([k]\times [2] \times [n]\) to \([k]\times P_{n,s} \), where \(P_{n,s}\) is a two-row Ferrers shape. We establish real stability for a family of bivariate polynomials associated with adjacent shapes, then apply the Chudnovsky-Seymour compatibility criterion to obtain a common interleaver. As noted in \cite{DD}, Conjecture 4.2 also implies Conjecture 4.3.

Reference-based image quality assessment (IQA) metrics aim to reflect how humans perceive the perceptual distance between a pair of images. To learn how the human visual system (HVS) operates, recent reference-based IQA metrics heavily rely on human-annotated data. Mean opinion score (MOS)-based pointwise scoring, which assigns a scalar quality value per image, is preferable for annotation but is prohibitively expensive to collect at scale and is known to be noisy due to inconsistent human judgments. As an alternative, two-alternative forced choice (2AFC) pairwise labels have gained popularity due to their reliability and efficiency, but they capture only relative comparisons between pairs. In this paper, we propose a fully automated data generation pipeline that generates pointwise perceptual distance labels between image pairs without any human annotation. Our approach exploits the generative dynamics of diffusion models as a perceptual distance proxy, where the coarse structure of an image is generated in the early timesteps and the fine details are generated in the later timesteps. Images that fork early in the generation process share only coarse structure and are perceptually far apart; images that fork late differ only in fine detail. We demonstrate that the diffusion trajectory aligns well with the human visual system, and use this forking moment, FoMo, as a reference-grounded distance label to supervise the training of a reference-based IQA metric. The pointwise labels, which support universal comparison between arbitrary image pairs, enable an information-rich training objective. Extensive experiments across diverse backbone architectures confirm the effectiveness of our generation pipeline, outperforming human-annotated datasets in multiple benchmarks.

Though artificial intelligence (AI) increasingly transforms modern medicine, its integration into Traditional Chinese Medicine (TCM) has been relatively slow, primarily due to TCM's reliance on holistic, subjective diagnostic methods—namely Inspection, Auscultation and Olfaction, Inquiry, and Palpation(I-AOI-P)—which are difficult to align with quantitative, standardized medical systems. In this work, we introduce a Unification Framework for Multimodal Data (UFMD), which automatically processes tongue and pulse images into structured, clinically standard descriptions, integrating multi-source diagnostic information into a unified digital record of I-AOI-P process. Building on this structured data, we create LingLan-14B, a TCM-specific large language model fine-tuned via supervised learning to emulate the diagnostic logic and workflow of I-AOI-P process. Experimental results show that our method significantly enhances diagnostic accuracy, achieving a relative improvement of 103.5% over the baseline (62.72% vs. 30.82%) and reaching an F1-score of up to 82%.

The sensitivity of an atomic spin sensor is fundamentally constrained by the quantum Fisher information (QFI) of the probe state. The pinched state, $|{F,0}\rangle$, has an $(F+1)$-fold larger single-particle QFI for transverse-field sensing than the stretched state, $|{F,F}\rangle$, corresponding to a predicted $\sqrt{F+1}$ reduction in the spin-projection-noise-limited field uncertainty. We show that this advantage can be accessed in an rf sensing scheme by engineering a spectrum symmetric about $m=0$, yielding an ideal $(F+1)$-fold enhancement of magnetic-field response. For $^{87}\mathrm{Rb}$ with $F=2$, we observe up to 2.7-fold response enhancement. Implementing this approach in a compact $0.8~\mathrm{cm}^3$ anti-relaxation-coated multipass cell, we realize a single-beam, dual-axis, zero-field magnetometer, achieving $13$–$23$~$\mathrm{fT}/\sqrt{\mathrm{Hz}}$ over $3$–$100$~Hz at room temperature.

This study investigates the aerodynamic feasibility of high-speed evacuated tube transport (ETT) using an integrated CFD-machine learning framework for pod geometry optimization and a staged converging-diverging (CD) tube concept for supersonic operation. The pod geometry is parameterized using composite cubic Bezier curves with seven design variables. Latin Hypercube Sampling is used to generate 200 configurations across subsonic and supersonic regimes, which are evaluated using two-dimensional axisymmetric ANSYS Fluent simulations validated against published compressible-flow data. The resulting CFD dataset is used to train surrogate models for rapid drag prediction. XGBoost provides the best overall performance, achieving a test R^2 of 0.9524, and is coupled with Differential Evolution and Particle Swarm Optimization to identify low-drag geometries that are subsequently verified using CFD. The study further examines a staged CD tube architecture combining controlled area variation with gradual pressure reduction to mitigate choking during supersonic acceleration. In the idealized axisymmetric simulations, the proposed strategy enables transition from atmospheric entry at Mach 1.6 to near-vacuum cruise at Mach 2.5 and a blockage ratio of 0.50 without forming a choked annular flow region. Total drag decreases from 68,913.7 N under atmospheric supersonic conditions to 120.5 N in the final near-vacuum stage, associated with a transition from wave-drag-dominated to viscous-shear-dominated resistance. The results demonstrate the potential of combined pod-shape optimization and staged pressure-area management for reducing aerodynamic resistance in supersonic ETT systems.

Multi-source knowledge graphs (KGs) need query mechanisms that expose reliability and exploit domain structure. This paper presents TCMaster, a property-graph query substrate for confidence-aware traversal and workload-guided physical design over Traditional Chinese Medicine KGs. TCMaster integrates pharmacopoeias, prescriptions, molecular databases, and LLM-extracted micro-semantics into a KG with approximately 221K entities and 723K base edges. It annotates edges with provenance-level confidence, rewrites Cypher queries with confidence predicates, ranks multi-hop paths under PRODUCT, MIN, or weighted-average policies, and uses ontology skew through direction selection, herb-attribute bitmaps, and materialized shortcut edges. On Neo4j, direction selection improves attribute lookup by a factor of 1.47, shortcuts accelerate high-fanout target counting by a factor of 4.42, confidence filtering removes 39.3 percent of low-quality heterogeneous paths, and KG retrieval improves TCMbench QA accuracy by 20.0 percentage points.

Let $A\subset\mathbb{R}$ be a finite set. Combining the multiplicative slope estimate of Rudnev–Stevens, Cushman's higher-energy regularization, Shakan's $d^+$–$d^\times$ decomposition, and Solymosi's classical sum–product estimate, we prove \[ |AA|^{204}|A+A|^{301}\gtrsim |A|^{675}, \] where $\gtrsim$ suppresses a fixed polylogarithmic factor in $|A|$. Consequently, for every $\varepsilon>0$, \[ \max\{|A+A|,|AA|\}\gg_\varepsilon |A|^{135/101-\varepsilon}. \] The proof is organized around two intermediate estimates. For every nonempty finite set $B\subset\mathbb{R}_{>0}$, \[ d^\times(B)|BB|^{12}|B+B|^{16}\gtrsim |B|^{38}, \] whereas for every nonempty finite set $U\subset\mathbb{R}$, \[ d^+(U)^{17}|U+U|^{29}\gtrsim |U|^{46}. \]

The statistical accuracy of neural networks depends on both their approximation power and the complexity of the class fitted from data. While increasing network size is a natural way to improve approximation, parameter magnitude provides another resource whose role must be quantified in both respects. We establish a sharp width–magnitude tradeoff at fixed depth using one elementary bounded $1$-Lipschitz Dyadic–Triangular Activation. For the unit $\beta$-Hölder ball on $[0,1]^d$ with $0<\beta\leq1$, the optimal $L^p$ approximation error for $0<p<\infty$ is of order $[N^2\log(eNT)]^{-\beta/d}$ when the network width satisfies $N\geq2d+3$ and the parameter magnitudes are bounded by $T\geq1$. Matching lower bounds hold for every fixed globally Hölder activation; its Hölder exponent affects the constants but not the rate. Under bounded design densities and independent centered sub-Gaussian noise, approximate least squares over the full clipped class at depth $23$ attains the classical Hölder minimax risk $\mathcal{O}(M^{-\frac{2\beta}{2\beta+d}})$ without logarithmic loss whenever $N^2\log(eNT)\asymp M^{\frac{d}{2\beta+d}}$, where $M$ is the sample size. This yields a continuum of statistically optimal choices, ranging from unit parameter radius to fixed network size. At fixed size, four hidden layers with at most $8d+7$ nonzero parameters give a near-optimal radius, while six layers with at most $8d+27$ attain the optimal order $\log T=\mathcal{O}(\eta^{-d/\beta})$ at approximation error $\eta$. The same decoding method also yields fixed-size Transformer approximation.

Environmental reconnaissance needs mobile platforms that carry sensors, preserve measurement context, and return interpretable evidence under limited energy and communication. We present a literature-informed engineering design for Zephyron, a four-wheel rover with a front manipulator, environmental sensors, distributed computer vision, local recording, and a raised rear solar module. The design keeps the prototype layout but replaces unsupported numerical assumptions with an explicit component and geometry baseline. A reproducible search retrieved 5,000 records (4,858 unique) for screening, followed by targeted review of primary literature and manufacturer documentation. The baseline uses 165 mm wheels, a 12 kg mass budget, a 72 Wh battery-energy basis, and a 20 W photovoltaic module. With rolling-resistance coefficient 0.04, steady ascent of a 10 degree grade needs about 0.517 N m per wheel under equal load sharing. An illustrative 40 W motion load gives 1.44 h from 57.6 Wh usable energy, and a 25 percent driving duty gives 4.19 h without solar input; these are calculated scenarios, not measured performance. Sensor models show how integration time, calibration, temperature, and communication delay constrain interpretation, and a quality-aware stop-and-sample policy links these constraints to mission execution. Lightweight detectors, reference-based sensor learning, and executable data-integrity checks define a reproducible machine-learning evaluation pathway. The contribution is a traceable design and evaluation framework with editable 3D models, subsystem diagrams, and reproducible analytical data. Experimental validation is required before assigning payload, endurance, detection, or field-operating ratings.

Intrigued by the response of T cell receptors to the presence of a few agonist ligands, we propose a minimal model that can achieve similar performance. The model consists of a small cluster of immobile receptors that bind reversibly to two types (correct/incorrect) of ligands in the environment, with slightly weaker binding strength for the incorrect one. It features binding-state coupling between nearest-neighbor receptors, and receptors in the bound/free states are activated/deactivated by specific enzymes, with rates that allow kinetic proofreading. It is found that, for a range of binding-state coupling strength, incorrect ligands alone cannot activate the receptors, but the binding of merely one correct ligand to a receptor is sufficient to promote the activation of other receptors via induced binding to incorrect ligands. Both response time and signal amplification increase as the receptor binding-state coupling strength increases until it reaches an optimal range to achieve the most rapid and sensitive response. These results suggest a possible mechanism for a speedy and specific response of receptors to very few correct ligands in biological and artificial systems at the subcellular scale.

Dynamic speaking style adaptation in multi-turn multimodal interaction remains a major challenge for text-to-speech (TTS) systems. Existing context-aware TTS (CTTS) methods typically map dialogue context to speech in an end-to-end manner. Such implicit modeling makes contextual style decisions difficult to supervise, while the entanglement of style, timbre, and content often leads to weak instruction-following and severe timbre drift across turns. To overcome these limitations, we propose Interactive TTS, a dynamic, style-adaptive framework for contextually appropriate and speaker-consistent speech generation. Interactive TTS decouples the process by explicitly modeling contextual style decisions as executable instructions. To bridge the gap between style decisions and speech generation, we introduce Iterative Rejection Sampling Fine-Tuning (Iterative RSFT) and Context-Aware Direct Preference Optimization (CADPO), which significantly enhance instruction-following and align the generated speech with conversational contexts. Extensive experiments demonstrate that Interactive TTS outperforms state-of-the-art models on VStyle and SpeechParaling-Bench. Demo is available at https://wjtian-wonderful.github.io/InteractiveTTS/

Understanding the sources of ENSO prediction skill and error is essential for improving long-range climate prediction. Here we examine ENSO precursors in CESM2 Seasonal-to-Multiyear Large Ensemble (SMYLE) hindcasts initialized in February and August during 1970-2019, using ensemble sensitivity analysis and an extended nonlinear recharge oscillator (XRO) benchmark. SMYLE exhibits meaningful long-lead skill, with February-initialized predictions remaining skillful through the following winter, and August-initialized predictions retaining useful skill at the December target sixteen months ahead. However, the predictions are under-dispersive in a state-dependent manner. Rank histograms reveal overconfidence issues for strong ENSO events and a warm bias for weak events. February predictability arises from canonical Bjerknes feedback dynamics reinforced by subtropical-tropical interactions resembling the North Pacific Meridional Mode (NPMM). The best February-initialized predictions feature warm western Pacific subsurface anomalies and La Nina anomalies at initialization, with equatorially confined anomalies and relatively weak sensitivities to extratropical influences thereafter. Second-year ENSO predictability in August-initialized predictions instead emerges through a delayed pathway characterized by cross-basin preconditioning. Skillful cases begin with a cold tropical equatorial South Atlantic and a warmer tropical western Indian Ocean, while Pacific processes play a reduced role until the following year. SMYLE matches the skill of the cross-validated XRO at both December targets, and its sensitivities agree with the observationally fitted benchmark, though the Atlantic couplings appear misrepresented. These findings suggest that improving the initial Pacific state and cross-basin coupling fidelity in GCMs may help improve ENSO prediction.

Federated learning (FL) is intrinsically heterogeneous: honest clients may have different data-generating models. On top of that, adversarial clients can make heterogeneity even more pronounced by sharing arbitrary updates. Existing analyses typically control the interaction between statistical heterogeneity and adversarial behavior through gradient-dissimilarity conditions. However, the underlying bound is imposed a priori and may yield conservative guarantees even for least-squares regression. We instead derive the gradient heterogeneity from the statistical model of linear and nonlinear regression with fresh data samples at every round. Our bounds separate heterogeneity among the honest clients' ground-truth model parameters, finite-sample label noise, and initialization. We then demonstrate that, for any $(f,\kappa)$-robust aggregator with coefficient $\kappa = O(f/n)$, where $f$ is the number of adversarial clients and $n$ the total number of clients (with $f/n < 1/2$), convergence holds after an explicit sample burn-in.

Many statistical procedures compute an entire solution path rather than a single estimator. For one class the path is piecewise linear, traced corner to corner by an active-set homotopy. Two of its members coincide exactly: under $\Sigma=X^\top X$ and $\mu=X^\top y$ the gross-exposure-constrained mean–variance program and the constrained LASSO trace the same piecewise-linear curve, and they keep doing so under arbitrary linear equality and inequality constraints. Which parameter is swept, a leverage budget or a return tilt, is not a choice the curve notices: under a homogeneous mandate the two sweeps differ by a scalar. A mandate that holds the portfolio invested costs a radial rescaling instead, and the efficient frontier is that curve rescaled; its corners pass unnoticed because the frontier is continuously differentiable where they fall. We give the map between the two parametrisations and the single way it degenerates. That mean–variance selection and the LASSO instantiate one parametric quadratic program is prior art (Gärtner, Jaggi and Maria, 2012). The Critical Line Algorithm itself lies off that route, and the correspondence established here is new. The identity is one of curves, not of statistical experiments. The map between the parametrisations is computed from the data, so the geometry of the path transfers while quantities averaged over the response do not. We cross that boundary deliberately and give the degrees of freedom of the constrained fit under arbitrary linear constraints. In the long-only, fully invested case it is the expected number of holdings away from a bound, less one.

We prove an $S$-integrality theorem for special divisors on GSpin Shimura varieties in positive characteristic. Let $C$ be a generically ordinary curve in such a Shimura variety not contained in any special divisor. Then, for any increasing sequence of prime-to-$p$ positive integers $m_i$ and any finite set of closed points $S\subset C$, we prove that $C\setminus S$ meets the special divisor $Z(m_i)$ for all but finitely many $i$. The key new input is an algebraicity theorem for formal special endomorphisms which allows us to use techniques from Diophantine approximation. We prove this algebraicity theorem using a punctual monodromy theorem and a positive-characteristic analogue of the Mumford–Tate conjecture.

Despite its physical importance, the stability of Prandtl boundary layers under wall suction remains relatively unexplored in rigorous PDE analysis. In this paper, we establish the global-in-$x$ asymptotic stability of a suction profile. For any prescribed algebraic decay rate in $x$, we prove that sufficiently small inflow perturbations with sufficiently rapid spatial decay yield downstream decay at that rate. The von Mises transformation reduces the Prandtl system to a degenerate parabolic equation with a favorably directed convection term. We first identify the downstream decay mechanism in an associated uniformly parabolic problem, then control the boundary degeneracy using a sharp Hardy-type estimate. Together, these arguments yield stability and decay for the original Prandtl system.

We study distributed Byzantine-resilient actor-critic multi-agent reinforcement learning (AC-MARL), where agents collectively learn policies through local interactions. Existing methods guarantee convergence of the agents' parameters only to a neighborhood of the attack-free limit points, resulting in degraded performance. We propose Fully Resilient AC-MARL (FRAC-MARL), a decentralized method in which each agent leverages redundancy in two-hop messages to identify reliable messages. Under linear parameterizations of the value and team-reward functions and Byzantine edge attacks, where adversarial behavior is confined to the communication layer, we prove that agents' parameters converge almost surely to the same limit points as in the attack-free case over time-varying communication graphs. We introduce a novel topological condition for the convergence of our method, present a systematic method to construct such networks, and prove that this condition can be verified in polynomial time. Finally, we demonstrate our method on cooperative multi-robot formation control tasks.

Despite the emergence of large language models (LLMs) for visual data storytelling workflows, there are open questions about how authors decide what activities or tasks to entrust to them and what should be "protected" or maintained under human control. To investigate this, we interviewed a cohort of 12 expert visual data storytellers. Our analysis shows that participants rarely treated LLMs as autonomous storytellers. Instead, they tend to selectively delegate execution-oriented tasks to LLMs while retaining control over activities that shape narrative intent and story meaning. Our findings show that LLM assistance is most productive after human seeding and constraint-setting, and that it shifts labor from production to verification. We discuss design implications for boundary-aware authoring tools, data-grounded generation, low-fidelity ideation, and reporting practices for LLM-based visualization research. Supplemental materials for this paper are available at https://osf.io/hcnp6.