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arXiv2026

Strong existence for SDEs with singular drifts driven by fractional Brownian motion

Let $B^H$ be a $d$-dimensional fractional Brownian motion with Hurst parameter $H\in(0,1/2)$. We prove the existence of a strong solution to $$d X_t=b(t,X_t)d t+d B_t^H, X_0=x_0\in R^d,$$when $b\in L^q([0,T];L^p(\mathbb R^d;\mathbb R^d)),2\le p,q<\infty$ and the subcritical Ladyzhenskaya--Prodi--Serrin condition $\frac1q+\frac{Hd}{p}<1-H$ is satisfied. Thus, within the finite-exponent range $p,q\ge2$, the strong-existence result covers the full subcritical region, including the regime $p<2Hd$, where a uniform strong Novikov condition may fail. The proof is based on a compactness criterion for Wiener functionals. Its main ingredients are an exponentially quantitative derivative estimate for the finite-dimensional densities of fractional Brownian motion, a conditional moment estimate obtained through a martingale representation of fractional Brownian motion, and a frequency-localized truncation of the Cameron--Martin shift. These estimates yield uniform Malliavin--Sobolev bounds for smooth approximations of the equation.

math.PR↗
arXiv2026

New upper bounds for the period of a negative orientable sequence

Negative orientable sequences, i.e. periodic sequences with elements from a finite alphabet of size at least three in which an n-tuple or the negative of its reverse appears at most once in a period of the sequence, were introduced by Alhakim et al. in 2024. The main goal in defining them was as a means of generating orientable sequences, which have automatic position location applications, although they are potentially of interest in their own right. In this paper we develop new upper bounds on the period of negative orientable sequences which, for n>2, are significantly sharper than the previous known bound. The approach used to develop the new bounds involves examining the nodes in the subgraph of the de Bruijn graph corresponding to a negative orientable sequence, and to consider the implications of the fact that the in-degree of every vertex in this subgraph must equal the out-degree. However, despite improving the bounds, a gap remains between the largest known period for a negative orientable sequence and the corresponding bounds for every n>2.

math.CO↗
arXiv2026

SleepMaMi: A Universal Sleep Foundation Model for Integrating Macro- and Micro-structures

While the shift toward unified foundation models has revolutionized many deep learning domains, sleep medicine remains largely restricted to task-specific models that focus on localized micro-structure features. These approaches often neglect the rich, multi-modal context of Polysomnography (PSG) and fail to capture the global macro-structure of a full night's sleep. To address this, we introduce SleepMaMi , a Sleep Foundation Model engineered to master both hour-long sleep architectures and fine-grained signal morphologies. Our framework utilizes a hierarchical dual-encoder design: a Macro-Encoder to model full-night temporal dependencies and a Micro-Encoder to capture short-term characteristics from biosignals. Macro-Encoder is trained via Demographic-Guided Contrastive Learning, which aligns overnight sleep patterns with objective subject metadata, such as age, sex and BMI to refine global representations. Micro-Encoder is optimized via a hybrid Masked Autoencoder (MAE) and multi-modal contrastive objective. Pre-trained on a massive corpus of $>$20,000 PSG recordings (158K hours),SleepMaMi outperforms or matches state-of-the-art existing foundation models across a diverse suite of downstream tasks, demonstrating superior generalizability and label-efficient adaptation for clinical sleep analysis.

cs.AI↗
arXiv2026

Sinkhorn Distributionally Robust State Estimation via System Level Synthesis

In state estimation tasks, the usual assumption of an exactly known disturbance distribution is often unrealistic and renders the estimator fragile in practice. The recently emerging Wasserstein distributionally robust state estimation (DRSE) design can partially mitigate this fragility; however, its worst-case distribution is provably discrete, which deviates from the inherent continuity of real-world distributions and results in over-pessimism. In this work, we develop a new Sinkhorn DRSE design within the system level synthesis scheme with the aim of shaping the closed-loop errors under the unknown continuous disturbance distribution. For uncertainty description, we adopt the Sinkhorn ambiguity set that includes an entropic regularizer to penalize non-smooth and discrete distributions within a Wasserstein ball. We present the first result of finite-sample probabilistic guarantee of the Sinkhorn ambiguity set. Then we analyze the limiting properties of our Sinkhorn DRSE design, thereby highlighting its close connection with the generic $\mathcal{H}_2$ design and Wasserstein DRSE. To tackle the min-max optimization problem, we reformulate it as a finite-dimensional convex program through duality theory. By identifying a compact subset of the feasible set guaranteed to enclose the global optimum, we develop a tailored Frank-Wolfe solution algorithm and formally establish its convergence rate. The advantage of Sinkhorn DRSE over existing design schemes is verified through numerical case studies.

math.OC↗
arXiv2026

The Game-Theoretic Katětov Order and Idealised Effective Subtoposes

This paper addresses the longstanding problem of determining the structure of the $\leq_{\mathrm{LT}}$-order in the Effective Topos, known to effectively embed the Turing degrees. In a surprising discovery, we show that the $\leq_{\mathrm{LT}}$-order is in fact tightly controlled by the combinatorics of filters on $ω$, raising deep questions about how combinatorial and computable complexity interact, both within this order and beyond it. To make the connection precise, we introduce a game-theoretic (''gamified'') variant of the Katětov order on filters over $ω$, which turns out to exhibit a striking mix of coarseness and subtlety. For one, it is strictly coarser than the classical Rudin-Keisler order and, when viewed dually on ideals, collapses all MAD families to a single equivalence class. On the other hand, the order also supports a rich internal structure, including an infinite strictly ascending chain of ideal classes, which we identify by way of a new separation technique. From the computability-theoretic perspective, we show that a computable (and extended) variant of the gamified Katětov order is isomorphic to the original $\leq_{\mathrm{LT}}$-order. Moreover, our work brings into focus a new degree-spectrum invariant for filters $\mathcal{F}$, $$\mathcal{D}_{\mathrm{T}}(\mathcal{F}):=\{\,[f\colonω\toω] \mid f\leq_{\mathrm{LT}} \mathcal{F} \},$$ which is shown to always determine a proper initial segment of the Turing degrees. Extending this, given any non-principal $Δ^1_1$ filter $\mathcal{F}$, we show that $\mathcal{D}_{\mathrm{T}}(\mathcal{F})$ is precisely the class of hyperarithmetic degrees. This significantly generalises previous results obtained by van Oosten \cite{vO14} and Kihara \cite{Kih23}. The proofs draw on ideas from general topology, descriptive set theory, and computability theory.

math.LO↗
arXiv2026

Are Two LLMs Better Than One? A Student-Teacher Dual-Head LLMs Architecture for Pharmaceutical Content Optimization

Large Language Models (LLMs) are increasingly used for content creation in regulated domains such as pharmaceuticals, where content must be medical accurate and legally compliant. Traditional manual quality control (QC) is slow, error-prone, and create publication bottlenecks. To address this, we introduce a modular, LLM/VLMs-driven QC architecture, LRBTC (Language, Regulatory, Brand, Technical, Content Structure), implemented through a Student Teacher HITL architecture and Waterfall rule filtering logic for scalable, verifiable content validation. This architecture is designed to provide verifiable, traceable, and scalable content optimization. Our methods achieve 83.0% F1 and 97.5% recall on AIReg Bench, reducing missed violations five fold compared with Gemini 2.5 Pro. On CSpelling, it improves mean accuracy by +26.7 %. Our error analysis further reveals that while current models are strong at detecting misspellings (92.5% recall), they fail to identify complex grammatical (25.0% recall) and punctuation (41.7% recall) errors, highlighting a key area for future work. This work provides a practical, plug-and-play solution for reliable, transparent quality control of content in high-stakes, compliance-critical industries. We also provide demo access.

cs.LG↗
arXiv2026

Artificial intelligence is creating a new global linguistic hierarchy

Artificial intelligence (AI) has the potential to transform healthcare, education, governance and socioeconomic equity, but its benefits remain concentrated in a small number of languages (Bender, 2019; Blasi et al., 2022; Joshi et al., 2020; Ranathunga and de Silva, 2022; Young, 2015). Language AI - the technologies that underpin widely-used conversational systems such as ChatGPT - could provide major benefits if available in people's native languages, yet most of the world's 7,000+ linguistic communities currently lack access and face persistent digital marginalization. Here we present a global longitudinal analysis of social, economic and infrastructural conditions across languages to assess systemic inequalities in language AI. We first analyze the existence of AI resources for 6003 languages. We find that despite efforts of the community to broaden the reach of language technologies (Bapna et al., 2022; Costa-Jussà et al., 2022), the dominance of a handful of languages is exacerbating disparities on an unprecedented scale, with divides widening exponentially rather than narrowing. Further, we contrast the longitudinal diffusion of AI with that of earlier IT technologies, revealing a distinctive hype-driven pattern of spread. To translate our findings into practical insights and guide prioritization efforts, we introduce the Language AI Readiness Index (EQUATE), which maps the state of technological, socio-economic, and infrastructural prerequisites for AI deployment across languages. The index highlights communities where capacity exists but remains underutilized, and provides a framework for accelerating more equitable diffusion of language AI. Our work contributes to setting the baseline for a transition towards more sustainable and equitable language technologies.

cs.CY↗
arXiv2026

Sci-CoE: Co-evolving Scientific Reasoning LLMs via Geometric Consensus with Sparse Supervision

Large language models (LLMs) have demonstrated exceptional reasoning capabilities, and co-evolving paradigms have shown promising results in domains with verifiable reward signals, such as code and math. However, in unverifiable domains, such as scientific reasoning, these methods remain fragile due to unreliable solution evaluation and limited diversity in verification strategies. In this work, we propose Sci-CoE, a two-stage co-evolving framework for domains without verifiable feedback. The framework enables models to self-evolve as both solvers and verifiers by transitioning from sparse supervision to unsupervised learning. In the first stage, the model uses a small set of annotated data to establish fundamental correctness judgment anchors for the Verifier. In the second stage, we introduce a geometric reward mechanism that jointly considers consensus, reliability, and diversity, driving large-scale self-iteration on unlabeled data. Experiments on several general scientific benchmarks demonstrate that Sci-CoE enhances complex reasoning capabilities and exhibits strong scalability, facilitating the construction of more robust and diverse evaluation systems. Codes are available at https://github.com/InternScience/Sci-CoE.

cs.AI↗
arXiv2026

Modeling of Therapist-Client Dynamics in Psychotherapy Using LLM-Based Assessments: An Empirical Study

This study aimed to develop and validate a computational framework for modeling therapist--client interaction processes and to examine how therapist behaviors and relational qualities relate to client self-disclosure and emotional expression in psychotherapy sessions. We developed automated assessment pipelines using large language models (LLMs) to measure therapist behaviors (empathy, exploration), relational quality (rapport), and client outcomes (self-disclosure, self-directed negative emotion, outward-directed negative emotion). Model-generated scores were validated against human annotations. We then applied these measures to approximately 2,000 hours of psychotherapy transcripts from the Alexander Street corpus. This yielded an estimation sample of 119,233 client utterances from 1,573 sessions and 37 clients. Automated measures showed good to excellent agreement with human annotations (ICC = 0.60 - 0.81), with rapport (ICC = 0.81), self-disclosure (ICC = 0.78), empathy components (ICC = 0.60 - 0.75), and emotion measurements (ICC = 0.66 - 0.80). SEM analyses revealed that therapist empathy and exploration were each associated with increased client disclosure and increased expression of self-directed negative emotions. Both behaviors were also associated with reduced expressions of enjoyment. Surprisingly, rapport in the prior session showed no association with client self-disclosure or negative emotion expression. This study demonstrates that LLM-based measurement combined with structural modeling can capture core therapeutic processes at scale.

cs.CY↗
arXiv2026

Beyond Imitation: Reinforcement Learning-Based Sim-Real Co-Training for VLA Models

Simulation offers a scalable and low-cost way to enrich vision-language-action (VLA) training, reducing reliance on expensive real-robot demonstrations. However, most sim-real co-training methods rely on supervised fine-tuning (SFT), which treats simulation as a static source of demonstrations and does not exploit large-scale closed-loop interaction. Consequently, real-world gains and generalization are often limited. In this paper, we propose an RL-based sim-real Co-training (RL-Co) framework that leverages interactive simulation while preserving real-world capabilities. Our method follows a generic two-stage design: we first warm-start the policy with SFT on a mixture of real and simulated demonstrations, then fine-tune it with reinforcement learning in simulation while adding an auxiliary supervised loss on real-world data to anchor the policy and mitigate catastrophic forgetting. We evaluate our framework on four real-world tabletop manipulation tasks using two representative VLA architectures, OpenVLA and $π_{0.5}$, and observe consistent improvements over real-only fine-tuning and SFT-based co-training, including +24% real-world success on OpenVLA and +20% on $π_{0.5}$. Beyond higher success rates, RL co-training yields stronger generalization to unseen task variations and substantially improved real-world data efficiency, providing a practical and scalable pathway for leveraging simulation to enhance real-robot deployment.

cs.RO↗
arXiv2026

Electrostatic edge effects versus edge doping in graphene nanoribbons: a scanning gate microscopy and modelling study

The charge neutrality point (CNP) of graphene nanoribbons (GNRs) patterned by oxygen plasma etching moves towards zero as the ribbon narrows and, on 300 nm SiO2, changes sign below a crossover width of ~ 50 nm: an observation previously attributed to n-type edges surrounding a p-type bulk. We test this edge-doping hypothesis in three ways. First, finite element modelling of complete GNR transistors with uniform doping shows that fringing of the gate field at the edges reproduces the trend of the measured CNP with width down to ~ 50nm without any edge doping, while producing a bias-dependent inversion of the carrier type at the edges that mimics n-type edges in scanned-probe measurements. Second, fitting the CNP of ribbons on 90 nm and 300 nm SiO2 with the gate capacitance of a finite strip, which fixes the electrostatic contribution with no adjustable parameter other than the bulk doping, shows that fringing accounts for most of the width dependence and isolates the remainder as an edge charge. This is acceptor-like (0.24 e/nm per edge) in the present ribbons, which therefore have no n-type edges, and donor-like but small in devices on 300 nm SiO2; no single edge-charge, field-coupled or contact-doping mechanism describes both. Third, scanning gate microscopy finds no edge contrast of the sign expected for n-type edges. The width dependence of the CNP is therefore predominantly electrostatic, and n-type edges are not an intrinsic consequence of oxygen-plasma etching. A design map shows that fringing dominates the width dependence whenever the gate dielectric is thicker than 30-50 nm, whereas in scaled high-K transistors, edge charge dominates and would shift the threshold voltage of a 10 nm ribbon by ~ 0.1-0.15 V. Fitting the CNP versus width with the strip capacitance provides a simple test for edge doping in any gated two-dimensional nanostructure

cond-mat.mes-hall↗
arXiv2026

The Influence of Code Smells in Efferent Neighbors on Class Stability

Understanding what drives code instability is essential for effective software maintenance, as unstable classes require larger or more frequent edits and increase the risk of unintended side effects. Although code smells are widely believed to harm maintainability, most prior stability studies examine only the smells within the class being modified. In practice, however, a class can change because its efferent neighbors (i.e., the classes it depends on) are modified due to ripple effects that propagate along static dependencies, even if the class itself is clean. Such ripple effects may be more severe when efferent neighbors exhibit code smells. Therefore, this study investigates whether code smells in a class's efferent neighbors affect its stability. We mined one year of commit history from 152 top-starred GitHub Java projects, detected code smells and static dependencies, and modeled their associations with class stability. Our results challenge the practice of examining code smells only within the class being maintained by showing that this provides an incomplete view of stability risk. Specifically, considering code smells in efferent neighbors reveals stability risks that are not observed when examining code smells in the class itself. Moreover, considering smells in both the class and its efferent neighbors, as well as their relationships across dependencies, reveals further stability risks that are not observed when smells at these two locations are analyzed separately. Consequently, these findings suggest that code smell analysis for class maintenance should extend beyond the class being maintained to the classes on which it depends.

cs.SE↗
arXiv2026

RG-Invariant Symmetry Ratio for QCD: A Study of $U(1)_A$ and Chiral Symmetry Restoration

We introduce a renormalization-group-invariant (RGI), scheme-independent symmetry ratio $κ_{AB}$, for the quantitative characterization of symmetry breaking in QCD. As a first application, we employ $κ_{AB}$ to investigate the relative strength of $SU(2)_L \times SU(2)_R$ chiral symmetry and $U(1)_A$ axial symmetry breaking in $N_f=2+1+1$ lattice QCD using optimal domain-wall fermions at the physical point. Our study covers three lattice spacings and twelve temperatures in the range 164--385~MeV. We examine three independent symmetry-breaking channels in the nonsinglet sector with quark-connected correlators: the $U(1)_A$-sensitive scalar--pseudoscalar channel ($κ_{PS}$), probing the $π$--$δ$ system; the $SU(2)_L \times SU(2)_R$-sensitive vector--axial-vector channel ($κ_{VA}$), probing the $ρ$--$a_1$ system; and an additional $U(1)_A$-sensitive tensor vector--axial-tensor vector channel ($κ_{TX}$), probing the $ρ_T$--$b_1$ system. At each lattice spacing we observe a clear hierarchy $κ_{PS} > κ_{VA} > κ_{TX}$. Since temperature and lattice spacing are not varied independently in the present ensembles, the lattice-spacing dependence of the hierarchy cannot be isolated, and a controlled continuum extrapolation is deferred to future work.

hep-lat↗
arXiv2026

Integer Cantor Sets: Arithmetic Combinatorial Properties

Cantor sets of integers have a rich set of arithmetic combinatorial properties. We consider classical Cantor sets, with a base and a fixed set of allowed digits. For such sets, we (a) give examples of such sets that satisfy the intersective property with power savings (b) characterize uniform distribution, (c) establish polynomial mean ergodic theorems and (d) study metric pair correlation of Cantor sets.

math.DS↗
arXiv2026

Learning to Drive in New Cities Without Human Demonstrations

While autonomous vehicles have achieved reliable performance within specific operating regions, their deployment to new cities remains costly and slow. A key bottleneck is the need to collect many human demonstration trajectories when adapting driving policies to new cities that differ from those seen in training in terms of road geometry, traffic rules, and interaction patterns. In this paper, we show that self-play multi-agent reinforcement learning can adapt a driving policy to a substantially different target city using only the map and meta-information, without requiring any human demonstrations from that city. We introduce NO data Map-based self-play for Autonomous Driving (NOMAD), which enables policy adaptation in a simulator constructed based on the target-city map. Using a simple reward function, NOMAD substantially improves both task success rate and trajectory realism in target cities, demonstrating an effective and scalable alternative to data-intensive city-transfer methods. Project page: https://zerlinwang.github.io/NOMAD/

cs.RO↗
arXiv2026

Structured Unitary Tensor Network Representations for Circuit-Efficient Quantum Data Encoding

Encoding classical data into quantum states is a central bottleneck in quantum machine learning: many widely used encodings are circuit-inefficient, requiring deep circuits and substantial quantum resources, which limits scalability on quantum hardware. In this work, we propose tensor network-based quantum data encoding (TNQE), a circuit-efficient framework built on structured unitary tensor network (TN) representations. TNQE first represents each classical input via a TN decomposition and then compiles the resulting tensor cores into an encoding circuit through two complementary core-to-circuit strategies. To make this compilation trainable while respecting the unitary nature of quantum operations, we introduce a unitary-aware constraint that parameterizes TN cores as learnable block unitaries, enabling them to be directly optimized and directly encoded as quantum operators. The proposed TNQE framework enables explicit control over circuit depth and qubit resources, allowing the construction of shallow, resource-efficient circuits. Across a range of benchmarks, TNQE achieves encoding circuits as shallow as $0.04\times$ the depth of amplitude encoding, while naturally scaling to high-resolution images ($256 \times 256$) and demonstrating practical feasibility on real quantum hardware.

quant-ph↗
arXiv2026

TabAgent: Distilling LLM Agent Components into Cheap Classifiers

Agentic systems, AI architectures that autonomously execute multi-step workflows to achieve complex goals, are often built using repeated large language model (LLM) calls for closed-set decision tasks such as routing, shortlisting, gating, and verification. While convenient, this design makes deployments slow and expensive due to cumulative latency and token usage. We propose TabAgent, a framework for replacing generative decision components in closed-set selection tasks with a compact textual-tabular classifier trained on execution traces. TabAgent (i) extracts structured schema, state, and dependency features from trajectories (TabSchema), (ii) augments coverage with schema-aligned synthetic supervision (TabSynth), and (iii) scores candidates with a lightweight classifier (TabHead). On the long-horizon AppWorld benchmark, TabAgent maintains task-level success while eliminating shortlist-time LLM calls, reducing latency by approximately 95% and inference cost by 85-91%. Beyond tool shortlisting, TabAgent generalizes to other agentic decision heads, establishing a paradigm for learned discriminative replacements of generative bottlenecks in production agent architectures.

cs.CL↗
arXiv2026

Dissipative Time Crystals as Passively Protected Oscillating Qubits

Passive error correction schemes have so far been limited to static memories rather than dynamical qubits. We demonstrate that a driven-dissipative bosonic system, the Bose-Hubbard dimer (BHD), can encode a persistently oscillating qubit within a dynamical noiseless subsystem (DNS). The strong parity symmetry of the system leads to degenerate stationary states, whose mutual coherence breaks the time translation symmetry, giving rise to a time crystal in the thermodynamic limit. This time crystal undergoes a dissipative phase transition controlled by the driving force, with the DNS present above the transition point. This noiseless subsystem, and hence the qubit, is resilient to collective loss and at most quadratically affected when the strong symmetry condition is weakened. The decoherence from collective dephasing also cancels in the leading order, with the cancellation being exact at a specific drive strength, set by the photon-number difference between the two logical states. Tuning the drive extends this cancellation to unbalanced dephasing. These results establish dissipative time crystals as a medium for autonomously stabilized oscillating qubits.

quant-ph↗

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