Papers

What makes one quantum process more complex than another? We adopt an operational approach inspired by classical complexity science, which characterises structure through the memory required for causal generation. We develop a fully-quantum extension of computational mechanics for quantum space series: Correlated sequences of quantum outputs that do not return to interact with their generator. For stationary, memoryful quantum space series admitting finite-dimensional, primitive causal models, we show that any memory-minimal causal generator can be chosen to produce outputs isometrically, without a discarded environment. The resulting canonical matrix product state representation uniquely determines the irreducible memory required for generation. In particular, the minimum memory entropy is exactly the entanglement entropy across the past-future bipartition, giving entanglement a direct operational interpretation as irreducible memory for causal generation. The same structure determines the minimum memory dimension through the corresponding Schmidt rank. Within this class, we further show that the fundamental entropy rate vanishes, that causal generation is symmetric under time reversal, and that all memoryful processes possess infinite quantum Markov order with respect to arbitrary sharp measurements. These results establish an operational framework for quantifying intrinsic quantum structure, revealing deep connections between causal generation, complexity, memory, entropy, and entanglement.

Let $\mathcal{A}\to S$ be an abelian scheme over a normal quasi-projective variety over a number field, and let $\mathcal{X}\subseteq\mathcal{A}$ be a positive-dimensional subvariety. For every integer $t>0$, we prove that, outside the $t$-degeneracy locus of $\mathcal{X}$, at most finitely many points lie in flat group subschemes of relative dimension less than $t$. In particular, this intersection is not Zariski dense whenever $\mathcal{X}$ is $t$-nondegenerate. The proof combines a bounded height theorem with uniform large Galois orbit estimates, o-minimal point counting, and mixed Ax–Schanuel, following the Pila–Zannier strategy. The arithmetic input is an explicit bound for the complexity of endomorphism relations, obtained from geometry of numbers and height estimates for abelian varieties. As applications, we formulate a relative Mordell–Lang conjecture, prove it for section images in powers of certain abelian schemes, and establish injectivity of specialization of the group of sections outside a proper closed subset under variation and dimension hypotheses.

IoT encompasses diverse physical entities, from smart home devices to autonomous vehicles, creating a complex environment with heterogeneous security models. This heterogeneity makes IoT sub-systems vulnerable to various network attacks. Modern security systems must therefore be more robust to ensure security and privacy for IoT applications. A highly secure IoT system also demands real time insight, requiring data collection at the edge of the computing layer. This diversity calls for a unified security model applied at the foundational level. Edge intelligence offers a direct approach to handling device diversity. A key goal of edge intelligence in IoT is to extract insight from local data; security models can then use this data to build local node protections, and integrating AI models yields an advanced security solution. This research proposes a novel deep learning algorithm for effective intrusion detection at the edge, supported by a cloud-based IoT framework. We evaluate the proposed cross modal deep learning algorithm against baseline models. The contribution is a cross domain Deep Neural Network (DNN) algorithm for intrusion detection. The objective is to assess a multi-method deep learning model to detect intrusions in IoT systems at the edge via community detection with modeled attention. We evaluate GCT auto-encoder, a novel framework integrating edge intelligence to identify security flaws. The model significantly improves performance and efficiency. On a network intrusion IoT dataset covering multiple attack scenarios, it achieved 0.908 accuracy, reduced learning loss to 0.00156, and outperformed existing approaches.

While modern large language models (LLMs) have been trained to reason through verbalized chains-of-thought, the generation cost grows substantially due to suboptimal paths to reach the final answer. Furthermore, as new insights are discovered while observing various input queries (e.g. through self-reflection), limited mechanisms exist for carrying forward these findings to be applied to subsequent problems. One can view the list of such strategies or behaviors as a growing cheatsheet, with elements retrieved from this memory module at inference-time. In this work, we consider structured cheatsheets, with learned clusters of behaviors. We introduce a Hierarchical Dirichlet Process Gaussian Mixture Model (HDP-GMM) over behavior embeddings, which shares components across domains while allowing domain-specific mixing weights, and uses the posterior predictive to retrieve relevant behaviors for a query; we call this a $\textit{Bayesian Cheatsheet}$. This mechanism allows for cheap adaptation in an online test-time training (TTT) setting, softly updating the mixture's sufficient statistics following each sample and enabling the creation of new components when the synthesized behaviors are sufficiently novel. We demonstrate that Bayesian Cheatsheet achieves clear performance gains relative to existing memory modules across reasoning benchmarks such as AIME'25, Omni-MATH, and PhysReason, even in the cold-start setting. We show that the Bayesian Cheatsheet is an adaptively reorganizing memory module, as behaviors can be re-assigned to components through a single step of collapsed Gibbs sampling. Our findings highlight the value of Bayesian-inspired memory modules for effective test-time adaptation and the role of structure in metacognitive reasoning.

A synthetic view is provided on scattered results which were never presented in this form in the literature. First we investigate precisely the oscillation length for periodic functions. Then, we establish the existence of a uniform oscillation lentgh for any scalar almost periodic function with mean-value 0. After that, we investigate upper bounds of the oscillation length for some almost periodic functions which appear in the study of continuum mechanics, and we show the existence of a finite oscillation length with respect to time in any open subset of some vibrating continuous media. The paper finally recalls a long standing open problem on the vibrations of a square membrane with fixed edge.

The growing adoption of large language model (LLM) agents creates a need for network administrators and security teams to audit agent behavior within organizational networks without inspecting private user content. Network traffic offers an observable source of evidence, but how much it reveals about agent tasks and operations remains unclear. Existing traffic datasets lack the joint task and stage annotations needed to evaluate this question. We introduce ANT (Agent Network Traffic), a dataset providing agent behavior information at risk, scenario, and behavior primitive granularities alongside network traffic. ANT contains 3,114 execution episodes across 20 tasks and five scenarios, comprising 276,417 bidirectional flows and 40,049 behavior primitive segments organized into 47 macro groups. We establish a benchmark for agent risk identification, scenario recognition, and behavior primitive classification using 13 representative traffic analysis baselines. The results show that existing methods recover useful but uneven behavioral signals. They struggle to identify risk when malicious workflows resemble benign tasks and to distinguish scenarios with similar traffic patterns. Primitive classification is more reliable for frequent macro groups and those with distinctive traffic patterns than for rare or semantically similar groups. ANT provides a common basis for developing more precise auditing and forensic analysis of agent behavior from network traffic. Our data and code are available at https://anonymous.4open.science/r/ant-main-suite-7BC0/.

Evaluating text generation requires measuring how well the generated distribution matches the data distribution. For autoregressive models, this is done by the perplexity. Diffusion and flow-based language models can only provide a likelihood bound, whose tightness differs between model families. Sample-based substitutes such as generative perplexity with entropy do not consider the distribution fit. We propose SOL, a distance between text distributions. Each sequence is represented by the empirical measure of its hidden states under a fixed transformer and the distributions of these measures are compared by the double sliced Wasserstein distance. We prove that SOL is a metric if the transformer is injective. Experiments show that SOL detects distributional failures, recovers expected model trends, and provides stable sample-based estimates. We put forward SOL to fill the gap in the current evaluation protocol used for non auto-regressive models. As a first step we use SOL to re-evaluate a variety of models trained on OpenWebText.

We identify a structural mechanism by which perfect play in a nonlocal game requires and self-tests a specific non-maximally entangled state. To this end, we construct a Flagged Magic-Square game by extending the standard Magic-Square game with an additional “flag” outcome and two additional questions for each player. The game admits a perfect strategy using a state with Schmidt coefficients proportional to $(1,\sqrt{2},\sqrt{2},\sqrt{2},\sqrt{2})$. We give a direct algebraic proof that maximally entangled strategies have winning probability bounded away from one, independently of dimension. Moreover, the game self-tests this state, providing an example of a two-party pseudo-telepathy game that certifies a specific non-maximally entangled state. Our construction illustrates how adding suitable constraints to a rigid measurement geometry can enforce specific Schmidt ratios and provides a modular route to further self-tests based on other rigid pseudo-telepathy games. We establish a general game-to-channel reduction that transfers separations in the game model to one-shot zero-error communication over classical channels. Applied to the Flagged Magic-Square game, it yields a classical channel for which entanglement permits the zero-error transmission of ten messages in a single use, whereas any finite-dimensional maximally entangled resource permits at most nine. Thus, maximally entangled states are not a universally optimal entanglement resource for zero-error communication over classical noisy channels.

To evaluate the frontier, we must measure models not by what they say, but by what they can engineer and build in grounded physical environments. We introduce ArtifactArena, an open-ended platform where models face a physically grounded hardware-software co-design challenge: engineering fully functional robots to compete in a simulated arena. We evaluate a frontier model's zero-shot, verifier guided refinement, and open-ended physical design capabilities through three harnesses that refine their bot artifacts based on text descriptions, physics simulator feedback, and gameplay data. We benchmark these capabilities with an Elo ranking of frontier models derived from head-to-head tournaments between their artifacts. By releasing this framework and tournament infrastructure for ongoing community submissions, we establish a living, non-saturating testbed to continuously measure the expanding limits of open-ended intelligence in the physical world. Please visit https://artifactarena.ai for more information.

When searching for an object, people choose their next move by considering both likely target locations and places already explored. The current view can cue place-associated memories, bringing target relevance and prior exploration into the same spatial context. In many zero-shot object navigation (ZSON) methods, however, vision-language models (VLMs) infer promising search areas from egocentric images, while exploration history is represented separately, e.g., as text or maps. This separation either requires an additional fusion step or leaves the correspondence between memory and route choices implicit for the VLM to recover. We instead make exploration memory directly visible on visual route choices. We propose MarvisNav, a ZSON framework that maintains a topological graph and projects candidate nodes together with their exploration states onto egocentric views as memory-bearing visual route choices. These states capture local exploration progress beyond binary visitation. By binding exploration state directly to each visual candidate, MarvisNav enables the VLM to jointly evaluate target relevance and exploration state without a separate post-hoc fusion or reranking stage. Without policy training, MarvisNav achieves state-of-the-art performance on HM3D (81.2% SR and 42.5% SPL), while remaining competitive on MP3D. It also outperforms representative VLM-based methods with far fewer VLM calls (e.g., 7.5% of WMNav). Real-robot experiments across diverse scenes further validate its practical deployability. Beyond MarvisNav, our study shows that memory representation shapes VLM decisions and ZSON performance, highlighting that effective memory use depends not only on its availability, but also on how it is represented. Code and project page will be available at \url{https://wangjincheng1998.github.io/MarvisNav/}.

Deep learning has revolutionised weather forecasting in recent years, especially through atmospheric foundation models, which offer competitive skill for a fraction of the computational costs of classic physics-based models. However, most existing foundation models are deterministic, limiting the generation of large ensembles for accurate uncertainty quantification, extreme weather risk assessment, and long-range weather forecasting. Furthermore, these models incur a large, often prohibitive, computational overhead to train from scratch. To address these shortcomings, we turn a pretrained deterministic prior model, namely the Aurora foundation model, into a generative ensemble-prediction model. To that end, we introduce a novel generative method, Denoising Stochastic Interpolants, combined with a replay buffer for Stochastic Differential Equation (SDE) rollout, enabling probabilistic training of SDE trajectories. Our stochastic foundation model, Xaurora, is finetuned from the small Aurora version, yet it approaches the state-of-the-art on global ensemble metrics and is competitive with the large version of Aurora. Our method is parameter and sample efficient, and generates skilful 15-day forecasts in 13 minutes. Our results demonstrate that deterministic foundation models can be efficiently extended into even stronger stochastic models.

Illuminant estimation is a fundamental problem in computational photography, as it enables the correction of color shifts induced by varying lighting conditions. While learning-based methods have demonstrated strong performance, their progress is hindered by the limited availability of large-scale datasets with accurate illuminant ground-truth. In this work, we propose a general and reusable pipeline to derive dense illuminant chromaticity maps from physically based 3D-rendered scenes. By repurposing an existing 3D scene collection, our approach enables the systematic generation of pixel-wise illuminant annotations under controlled lighting conditions, effectively lowering the barrier to data acquisition for learning-based illuminant estimation. Using this pipeline, we generate a large-scale synthetic set of 74,321 images, which we employ for pre-training both single- and multi-illuminant estimation models. Extensive experiments with state-of-the-art architectures show that synthetic pre-training consistently improves performance, with gains of up to 28% for single-illuminant estimation and up to 57% for multi-illuminant estimation, particularly in data-scarce regimes. These findings demonstrate that synthetic data generation pipelines offer an effective and scalable solution for the pre-training of illuminant estimation methods.

Computer vision services delivered through Web interfaces and APIs process textual requests for image-resource acquisition, inference-task configuration, and result management, making Web attack-payload analysis relevant to their deployment security. Large language models (LLMs) can identify payload types and explain attack intent. However, existing studies generally treat payload analysis as a single-layer classification task and lack both a systematic assessment of how deeply LLMs understand payloads and an evaluation benchmark dedicated to the depth of semantic understanding of Web attack payloads. We construct PayloadSemBench, a four-layer semantic evaluation benchmark that operationalizes payload understanding across measurable tasks and comprises 240 payloads. Its ground truth was established through two rounds of anchor calibration and re-verified by a fourth independent expert. Two experiments, a semantic-understanding benchmark and an analysis mapping semantic understanding to detection performance, yielded three main findings: (1) type identification and intent understanding were generally strong, whereas severity assessment was the principal weakness; (2) the effects of obfuscation varied across models and layers, with intent explanation and reconstruction of specific obfuscation techniques more susceptible to degradation, while performance did not degrade synchronously across all layers; and (3) semantic understanding and detection decisions were partially decoupled, with only 12.5% to 50% of missed detections attributable to semantic-understanding failures. External re-evaluation on an independent 180-record dataset comprising production WAF alert streams and real application requests reproduced the non-uniform four-layer capability profile and the layer-specific differences on obfuscated payloads.

We present an AI-based web-oriented tool designed to support formative feedback for oral presentation slides in higher education: AISSA. It allows students to upload their slides before presentation and automatically receive rubric-based quantitative scores and qualitative feedback generated by large language models (LLMs). The tool analyses slide-level features and content using a teacher-defined rubric and delivers feedback through interactive Learning Analytics dashboards. These dashboards enable students to visualize performance indicators, inspect feedback in context, and reflect on strengths and areas for improvement, while teachers can review automated assessments, provide their own evaluations, and monitor student engagement with feedback.

Proactive AI assistants continuously observe a user's activity and decide whether to provide new guidance or remain silent. They should provide appropriate guidance for the task, determine when to provide the next guidance based on task progress, and adjust the guidance level to the user's expertise and needs. Supporting these capabilities requires training and evaluation data that reflect procedural structure and capture how guidance should adapt to task progress and user needs. However, existing datasets either focus on detection-based proactive understanding or provide procedural guidance at a fixed granularity. Fixed-granularity guidance provides limited information about fine-grained progress and broader procedural context, making it difficult to determine completion and adapt guidance granularity. To address these limitations, we introduce the ProactiveCoach suite, comprising ProactiveCoach-Instruct for training, ProactiveCoachBench for evaluation, and fine-tuned VLMs with an adaptive guidance system. ProactiveCoach-Instruct provides hierarchically structured guidance at the phase, step, and action levels for learning task progress and procedural context. ProactiveCoachBench evaluates whether models provide appropriate guidance at the right time across different guidance levels and adapt when the requested level changes. We fine-tune pretrained VLMs on ProactiveCoach-Instruct and demonstrate its effectiveness across backbones. Compared with fixed-granularity supervision, hierarchical supervision improves overall performance across backbones by up to 9.6%p. We further build an adaptive guidance system by combining our fine-tuned model with a lightweight guidance router. Without additional fine-tuning, our system outperforms the in-context adaptation baseline by 57.1%p across four guidance-level transitions. Our project page is available at https://jinsuby.github.io/ProactiveCoach/.

This article studies a retirement planning problem from a new perspective in which a retiree delegates an initial lump sum to a professional fund manager. The fund is managed dynamically to deliver lifelong benefits while satisfying a guarantee that, at all times, wealth remains above a prescribed solvency level and the benefit rate remains above a minimum level. We formulate this problem as a continuous-time stochastic control model, in which the controls are the benefit rate and the portfolio allocation, and the objective incorporates general utility functions over benefits, management fees, and terminal bequest. Conventional approaches such as standard viscosity solution and martingale methods are not immediately applicable here due to the simultaneous influence of (i) the control variable nature of the benefit rate; (ii) the guarantee constraints; and (iii) the running wealth-dependent utility. We develop a new approach that deals directly with the associated fully nonlinear Hamilton-Jacobi-Bellman equation and establish the unique existence of a classical solution. One particular trick for resolving this equation is to apply an intricate transform that diverts the former to a semilinear auxiliary equation. A major contribution is to establish the existence of the solution to the auxiliary equation and characterize its precise growth, derivative, and boundary behavior. These results are crucial for establishing the verification theorems and deriving the optimal strategy. Besides, numerical experiments indicate that guarantee constraints induce more conservative policies, particularly at low wealth levels, while providing effective downside protection for both wealth and benefits. The associated well-being loss relative to the unconstrained framework remains small, suggesting that incorporating guarantees into retirement products is practically appealing.

Text-to-image generative models can produce highly realistic imagery but also raise concerns about harmful misuse. While safety mechanisms exist, systematic evaluations of their effectiveness against realistic attacks remain limited. We present a systematic evaluation of harmful content generation across five open text-to-image models using an automated pipeline that transforms legitimate news captions into unsafe prompts targeting sexually explicit content, violence/gore, harmful stereotypes, self-harm, and hate speech. We evaluate both standard models with built-in safety mechanisms and community fine-tuned variants that bypass content restrictions. A human evaluation of 1,500 generated images shows high harmful-content generation rates: 89.2% for gore-related prompts, 47.6% for sexually explicit content, 43.6% for harmful stereotypes, 46.0% for hate speech, and 34.5% for self-harm, predominantly through graphic violence. Models show substantial capability for generating violent and stereotypical content, while community fine-tuned variants are particularly vulnerable to sexually explicit prompts. Generation quality is largely preserved under harmful prompting, producing imagery of sufficient fidelity to pose risks for disinformation and abuse; FLUX.1-dev produces clearly realistic harmful images in 30.9% of cases. We further evaluate automated moderation systems and find substantial detection gaps that allow unsafe images to evade filtering. Finally, we assess synthetic image detectors and show that models trained only on benign datasets perform worse on explicit content, while more diverse training data improves detection, highlighting semantic distribution gaps in current approaches. These findings expose limitations in current generation safeguards, moderation systems, and synthetic image detection, highlighting the need for stronger defenses against misuse at scale.

Content-based image retrieval (CBIR) in neuroimaging enables the identification of structurally similar brain scans, supporting diagnosis, prognosis, and treatment planning; however, existing methods are often limited to small datasets, single brain regions, or coarse class labels, thereby restricting their clinical utility and generalizability. Here, we present NeuroCBIR, a framework for fast and flexible retrieval of both whole-brain and region-specific 3D T1w MRI scans. A total of 103 cortical and subcortical regions are extracted to enable both whole-brain and region-level queries. NeuroCBIR leverages latent representations learned by a variational autoencoder (VAE) combined with contrastive learning, producing scan-specific embeddings that capture anatomical patterns. These embeddings were evaluated for subject re-identification, zero-shot age prediction, and zero-shot multi-class pathology stratification. Re-identification performance was high across both whole-brain and brain-region levels (mean average precision across the top-5 retrieved images (mAP@5) >= 98.4%), with robust generalization across datasets and acquisition conditions. While NeuroCBIR is not trained for age prediction or pathology stratification, zero-shot evaluations for these two tasks demonstrate that the embeddings encode meaningful information for downstream tasks. Embedding extraction on a 4-core CPU required approximately 18.7 s per scan, whereas similarity search was effectively instantaneous (less than 0.01 s). NeuroCBIR is publicly available for brain MRI with more than 26,000 precomputed T1w MRI embeddings. It supports reproducible research, region-specific flexibility, and clinically meaningful personalized diagnostic support. The software is available at https://github.com/minnelab/NeuroCBIR.

While unconditional uniqueness for the cubic nonlinear Schrödinger equation (NLS) on $\Bbb R^3$ is known in the scaling-subcritical Sobolev spaces $\dot H^s(\Bbb R^3)$ for $1/2<s<1$, the critical case $s=1/2$ has remained open. We resolve this problem by adapting Kato's bootstrap argument to the critical space $\dot B^{-1}_{\infty,\infty}$. The main difficulty at this endpoint is that the natural solution class does not provide the coefficient regularity required to close the bootstrap in $\dot B^{-1}_{\infty,\infty}$. To overcome this issue, we perform a second Duhamel iteration of Born type and estimate the resulting double Duhamel integral as a whole. This yields improved estimates that allow the bootstrap to close in $\dot B^{-1}_{\infty,\infty}$ using only the available regularity of the coefficients.

Plastic scintillators remain attractive for large-area particle detectors because of their fast response, mechanical flexibility, and relatively simple fabrication. Motivated by future applications including the ALICE~3 Muon Identifier (MID) and the upgrade of the ALICE Fast Interaction Trigger (FIT), this work investigates polyurethane (PU)-based plastic scintillators doped with 2,5-diphenyloxazole (PPO) and 1,4-bis(5-phenyloxazol-2-yl)benzene (POPOP). Systematic information on the optimization and radiation response of this material system remains limited. A series of compositions was therefore fabricated and characterized using minimum-ionizing particles (MIP), optical spectroscopy, and time-correlated single-photon counting. The measurements show that the scintillation response is governed primarily by the PPO concentration, while POPOP mainly modifies the spectral response, and fast effective decay times of approximately 1.6–1.75~ns are maintained across the doped samples. The best-performing formulation was subsequently scaled to 20-$cm$ and 1-m scintillator bars and successfully operated with a single embedded wavelength-shifting fiber and SiPM readout, demonstrating its suitability for meter-scale light collection. Proton-irradiation measurements at the CERN IRRAD facility further revealed systematic degradation of the optical and scintillation responses with increasing exposure, together with substantial recovery after approximately two months. These results demonstrate that optimized PU–PPO–POPOP scintillators can combine fast timing, high light output, scalable detector geometry, and recoverable radiation response, supporting their further development for future large-area particle-detector systems.

We study probability distributions on independent sets of uniform hypergraphs with local constraints. For a positive vertex-weight function $w$ on an $(r+1)$-uniform hypergraph, define the weighted degree of vertex $v$ by \[ d_w(v):= \sum_{e\ni v} \left( \prod_{u\in e\setminus\{v\}}\dfrac{w(u)}{w(v)} \right)^{1/r}. \] For each fixed $r\geq1$, our first result gives, in every triangle-free $(r+1)$-uniform hypergraph (without a linearity assumption), a random independent set $I$ satisfying \[ \mathbb P(v\in I)\geq \left( \frac{r}{r+1}(r(r+1))^{-1/r}+o_r(1) \right) \left(\frac{\log d_w(v)}{d_w(v)}\right)^{1/r}, \qquad d_w(v)\to+\infty. \] The same result also implies that every $d$-degenerate triangle-free $(r+1)$-uniform hypergraph satisfies \[ \chi_f(G)\leq \left( \dfrac{r+1}{r}(r(r+1))^{1/r}+o_r(1) \right) \left(\dfrac{d}{\log d}\right)^{1/r}, \qquad d\to+\infty. \] Our second result concerns linear Berge-$C_4$-free hypergraphs which allow Berge triangles. In this setting, for every sufficiently large threshold $D$, there exists a random independent set $I$ such that, uniformly over all vertices with $d_w(v)\geq D$, \[ \mathbb P(v\in I)\geq (1-o_r(1)) \left(\frac{\log d_w(v)}{r\,d_w(v)}\right)^{1/r}, \qquad D\to+\infty. \] It also yields \[ \chi_f(G)\leq (1+o_r(1)) \left(\frac{rd}{\log d}\right)^{1/r} \] for $d$-degenerate linear Berge-$C_4$-free $(r+1)$-uniform hypergraphs. Both results are based on the ordered random pick process originated from Martinsson and Steiner. By choosing different selection functions and iteration, we prove the output of the random process gives the required random independent set.

Topological entanglements are central to understanding and predicting the properties of polymer melts. Yet, they make equilibrium sampling computationally challenging, as decorrelation times grow rapidly with chain length. Here, we introduce a Monte Carlo scheme that bypasses typical computational bottlenecks by working in a self-assembly ensemble rather than at fixed composition. Strictly local moves efficiently propagate backbone reconnections across scales while conserving the number of linear chains, achieving near-linear scaling of decorrelation time with system size, $\tau_{\rm eq}\sim V^{1.0}$. With this method, formulated for a fully-packed lattice, we equilibrate periodic systems totalling up to $\simeq 1.1\times 10^9$ monomers, accessing a universal melt regime insensitive to lattice details. We analyze intra- and inter-chain entanglements for chains of up to $N\simeq 5 \times 10^5$ monomers, revealing that they manifest as localized knots and links rather than as global tangles. Finally, we show that the magnitude of the Gauss linking integral between neighbouring chains grows only as $N^{1/4}$.

We classify the regularity of the origin for the $p$-parabolic equation in the soda-can domains $$\Theta_{l,\theta}=\{(x,t)\in\mathbb{R}^n\times\mathbb{R}:0 < -t < \theta |x|^l < \theta\},\text{ where }l,\theta>0.$$ The classification covers every $p>1$ in dimensions $n\ge2$. At the endpoint $l=p$, the origin is regular if and only if $p\ge2n/(n+1)$. We also prove that the origin admits a traditional barrier for every $p>2$ and $l>0$. When $2 < p < n$ and $l < p$, the origin is nevertheless irregular. This answers negatively the well-known open question whether one barrier suffices to characterize boundary regularity in the degenerate range $p>2$.

When a large language model handles a multi-turn task and a user proposes a change but ultimately rejects it, the model should continue as if nothing changed. We find a surprising failure: merely mentioning a rejected change can derail task execution, even when the user's final intent remains unchanged. To systematically study language model behavior under evolving user intent, we introduce Intent-Eval, a controlled benchmark spanning tool actions, code, databases, and mathematics. Across diverse tasks, models are vulnerable to both rejected proposals and superseded requirements, consistent with mentioned-as-in-effect confusion: conversational content is treated as active requirements even after it has been rejected or replaced. Accuracy degradation can deepen or persist as interaction continues, highlighting the need to distinguish what has been mentioned from what remains in effect. Building on this insight, we propose Intent-OPSD, a decision-conditioned on-policy self-distillation framework with Teacher and Student initialized from the same model. The frozen Teacher provides active-intent supervision from the complete task matching the user's decision, training the Student on the full dialogue to follow active requirements reflecting user intent.

We develop a posteriori primal-dual bounds for numerical approximations of European option prices in the Uncertain Volatility Model. Given a smooth candidate approximation of the value function, a feedback control induced by its Hessian yields a primal lower bound. On the dual side, we derive a representation based on a matrix-valued Gamma field, which provides an upper bound through a nonnegative Hamiltonian penalty. We further show that, when the dual field is generated by the candidate itself, this upper bound admits an equivalent representation in terms of the residual of the associated Black-Scholes-Barenblatt equation. We then study discrete-time approximations of these primal and dual quantities and quantify the corresponding discretization errors. Finally, we investigate their numerical evaluation for candidates obtained by stochastic policy-gradient and physics-informed neural-network methods, and compare the resulting estimates with a martingale dual approach from the stochastic-control literature. The numerical experiments highlight the importance of derivative accuracy, and in particular of second-order information, for obtaining tight a posteriori bounds.

Multi-structure segmentation of the uterus is important for computer-assisted screening, diagnosis, and treatment planning of uterine diseases, where ultrasound and MRI provide complementary clinical information. However, developing a unified model across these modalities is challenging due to their substantially different image appearances, anatomical contexts, spatial resolutions, and label spaces. Moreover, existing datasets often define different segmentation targets, making joint learning challenging and potentially leading to negative transfer across heterogeneous tasks. To this end, we propose a Topology-informed Prompt-conditioned Universal Segmentation (TPUS) framework for segmenting multiple uterine structures across ultrasound and MRI. TPUS introduces a graph-based multi-dataset backbone comprising modality-specific stems and a modality-shared graph-based encoder-decoder to support modality-sensitive input adaptation, structural feature reasoning, and joint representation learning across heterogeneous uterine segmentation tasks. In addition, TPUS uses task-aware class prompts to condition the segmentation process for different datasets and label spaces, a dynamic convolutional adaptation module to generate task-specific output responses, and a topology-informed loss to encourage anatomically consistent predictions. Experiments on a uterine ultrasound dataset and a T2-weighted uterine myoma MRI dataset demonstrate that TPUS achieves Dice scores of 0.898 and 0.693 on the two held-out test sets, respectively, outperforming several generic and universal segmentation baselines. Source code can be accessed at https://github.com/YonghengSun1997/TPUS.

Maslov's class K is a decidable fragment of equality-free first-order logic. It subsumes numerous classical decidable fragments, including the equality-free monadic fragment, the equality-free two-variable fragment, and the Gödel class. Introduced over 50 years ago, the class K has been studied in automated deduction, primarily through resolution-based methods. Despite this long history, the precise complexity of the satisfiability problem for K remained open until recently, when NExpTime-completeness was finally established. The two main contributions of this work are as follows. 1. The recent proofs of NExpTime-completeness and the finite model property for K are highly non-trivial and technically sophisticated. We present considerably simpler proofs of both results. Our approach combines a novel reduction from K to the class of solvable Skolem sentences with a randomised construction of finite models. 2. We introduce the class K+E by allowing sentences in K to contain one distinguished binary predicate E whose interpretation is constrained to be an equivalence relation. By leveraging our approach to this extended class, we prove that K+E has the finite model property and that its satisfiability problem is 2-NExpTime-complete.

Pinching-antenna systems (PASSs) offer a great degree of flexibility for integrated sensing and communications (ISAC) by adapting the pinching locations for both communication channel reshaping and sensing-beam steering. Despite that, direct location optimization in PASSs is high-dimensional and non-convex, making their fast reconfiguration difficult in practice. This work proposes a low-complexity PASS-assisted ISAC design based on user clustering. Instead of direct optimization of pinching locations, the elements on each waveguide are distributed over multiple segments, where each segment serves a cluster of users or targets. This alternative configuration reduces the location tuning problem to a low-dimensional weight allocation task, which can be efficiently addressed via a gradient based method. We propose a low-complexity iterative algorithm, in which the digital precoder is updated via an equivalent weighted mean squared error minimization, and pinching locations are updated via weight allocation and projection. Our numerical experiments show that the proposed design can significantly enhance the communication-sensing trade-off of ISAC systems over the benchmark designs with modest computational cost. The results highlight the potential gain of deploying PASS-assisted transceiver in practical ISAC systems.

Multi-view learning jointly exploits multiple complementary representations of the same data and has become increasingly important in machine learning. However, the Python ecosystem lacks actively maintained, unified tooling for end-to-end multi-view workflows. In this paper, we present polyview, a Python package that provides tools for multi-view embedding, clustering, fusion, and view augmentation, as well as for handling incomplete views, all compatible with scikit-learn. The library offers a unified interface for composing heterogeneous multi-view workflows, including seamless transitions between multi-view and single-view stages. It is built around a core set of classes and utilities that enable composition of different methods and straightforward implementation of new ones. We illustrate the package on five real multi-view datasets and compare its components based on canonical correlation analysis with those of two established libraries. polyview aims to be both a practical toolkit for benchmarking and prototyping multi-view methods and a foundation for future research and development in this area.

We study upper large deviations of the free energy of mixed $p$-spin Ising spin glasses through the generalized TAP free energy $F_{\mathrm{TAP}}$ of Chen, Panchenko and Subag. For every mixture with radius of convergence greater than one, $\max F_{\mathrm{TAP}}$ and $\log Z_N$ have the same large deviations at speed $N$; the proof combines their band theorem with Ramsey's theorem. For convex mixtures with $\sum_p 2^p\beta_p^2<\infty$, upper deviations at level $f$ are carried by generalized TAP critical points, which exist at the free-energy rate without Boursier's strict Plefka condition. Outside an event of smaller exponential order, near-maximizers at level $f$ lie near the contact set of a constrained Parisi obstacle, follow the Auffinger-Chen field law, and have Hessian bulk near a reflected Pastur law whose edge is nonpositive and vanishes exactly at contacts where the obstacle is flat to second order. Where every contact is of this kind, a fixed stability margin costs rate.