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01.
medRxiv (Medicine) 2026-06-16

Preventing postpartum depression through mitigating breastfeeding grief: A convergent parallel mixed methods study

Background: Women who did not meet their breastfeeding goals often experience breastfeeding grief (BG) and may be likely to have postpartum depression (PD). Furthermore, PD is nearly twice as common in African American (AA) women as in Non-Hispanic White women. No research exists on BG and its role in PD. This study examined the BG experiences of AA women and its possible contributions to PD symptoms. Methods: A convergent parallel mixed methods design was used. A purposive sample of 16 AA women with children aged 6 months to 2 years with BG participated in individual semi-structured interviews about their experiences of BG and completed an online survey including the Edinburgh Postnatal Depression Scale (EPDS). Qualitative and quantitative data were analyzed using reflexive thematic analysis and descriptive statistics, respectively. Both data were integrated using joint display of data and side-by-side comparison. Results: The mean age of participants was 29.5 years. Four meaning-based themes about BG were generated including: We looked forward to breastfeeding, But it did not go as expected, So we grieve, and These would have helped. From quantitative results, 87.5% of participants reported a history of PD symptoms and almost 44% had EPDS scores >11. All participants reported that experiencing BG contributed to their PD symptoms. Findings suggest that BG influenced PD symptoms in AA women without prior diagnosis of depression. Conclusions: Qualitative and quantitative findings from this novel exploratory study revealed an overlap that AA women with BG report PD symptoms. Clinicians should support women to achieve their breastfeeding goals to prevent BG and PD. Keywords: African American; Breastfeeding grief; Mental health; Mixed methods; Postpartum depression

02.
arXiv (quant-ph) 2026-06-11

Diffusive Relaxation of Participation Entropy in U(1)-symmetric Dynamics

arXiv:2606.11561v1 Announce Type: new Abstract: Participation entropy (PE) quantifies the spread of a many-body wavefunction across configuration space. While PE relaxes rapidly in generic chaotic systems, we show that $\mathrm{U}(1)$ conservation laws slow it down by imprinting with the slow hydrodynamic modes. Using a cluster expansion around equilibrium, we show that, after local density inhomogeneities decay, the leading PE deficit is dominated by squared connected density correlations. The long time relaxation is therefore controlled by diffusive correlation spreading, giving $\Delta S(t)\sim t^{-1/2}$ in the hydrodynamic regime and crossing over to $\sim \exp[-O(t/L^2)]$ when $t\geq L^2$. We confirm this entropy correlation relation using exact computation and infinite system tensor network simulations in various quantum $\mathrm{U}(1)$ conserving circuits. Our results establish PE as a sensitive probe of hydrodynamic memory and suggest that slow relaxation is a generic consequence of conservation laws.

03.
arXiv (CS.LG) 2026-06-12

Allocating Human Oversight in AI-Enabled Analytics

arXiv:2604.12497v2 Announce Type: replace Abstract: Organizations increasingly deploy AI as a low-cost prediction layer in customer-facing decision processes, including demand sensing, service-quality monitoring, product testing, and market research, but AI-generated signals are unevenly reliable across tasks, products, and customer segments. Firms therefore still need scarce human validation (labels, audits, survey responses, or follow-up measurements) to anchor AI outputs to ground truth. Because human ground truth is itself noisy, varying across labelers and even across repeated judgments, the firm must collect and average several human labels per task, which makes human validation costly. We study how to allocate a limited human-validation budget across many AI-assisted tasks when reliability is heterogeneous and unknown before deployment. We cast this within tuned prediction-powered inference. Each human label both sharpens the AI-assisted estimate and reveals the task's rectification difficulty, the variance that remains after the AI prediction is optimally used as a control variate. If difficulties were known, the optimal allocation would follow a Neyman square-root rule; because they are unknown, we propose a policy based on upper confidence bounds that learns them online and steers validation toward tasks where AI is least reliable. We prove that the policy's terminal efficiency loss relative to the oracle allocation vanishes as the budget grows. In synthetic experiments and a real digital-twin survey with 68 tasks and over 2000 respondents, it closes most of the gap to the oracle when reliability is heterogeneous, outperforming uniform and epsilon-greedy allocation; on the survey data it also outperforms explore-then-commit pilot designs and cuts uniform's 10–12% gap to 2–6%. The value of AI depends not only on model accuracy but also on the operational policy that targets human oversight where AI errors matter most.

04.
PLOS Medicine 2026-05-21

Semaglutide-associated risk of nonarteritic anterior ischemic optic neuropathy in patients with type 2 diabetes: A systematic review and meta-analysis of observational studies

by Jędrzej Chrzanowski, Magdalena Walicka, Jacek Burzyński, Małgorzata Zaraś, Arkadiusz Michalak, Wojciech Fendler Background Semaglutide, a glucagon-like peptide-1 receptor agonist, is widely used for the management of type 2 diabetes (T2DM). Recent case reports have raised concerns about a potential association between semaglutide use and the development of nonarteritic anterior ischemic optic neuropathy (NAION), a rare but vision-threatening condition. We aimed to evaluate whether semaglutide use is associated with an increased risk of NAION in patients with T2DM. Methods and findings We conducted a systematic review and meta-analysis of observational studies comparing patients with T2DM aged ≥12 years treated with semaglutide to those receiving other glucose-lowering therapies. We searched PubMed, Scopus, and Web of Science databases from January 2023 to November 2025. Two reviewers independently extracted data on study design, population characteristics, and outcomes. Risk of bias was assessed using the Newcastle–Ottawa Scale, and ROBINS-I v.2. Certainty of the evidence was graded according to the GRADE framework. Pooled hazard ratios (HRs) and 95% confidence intervals (CIs) were calculated using fixed-effects models; sensitivity analyses included crude and subgroup HRs, and overlapping study replacement. Leave-one-out analysis was conducted to assess small-study effects and publication bias. Results were contextualized within other meta-analyses, systematic reviews, consensus statements, and regulatory communications on the topic.Five eligible observational studies met the inclusion criteria, and 7 additional studies were included in the sensitivity analysis. Semaglutide use was associated with a significantly increased hazard of NAION compared with nonsemaglutide glucose-lowering regimens (HR 2.17, 95% CI [1.73, 2.74]; p 

05.
medRxiv (Medicine) 2026-06-16

Sleep regularity outweighs sleep duration as a predictor of disease

Sleep regularity, the consistency of sleep-wake timing from one day to the next, is more strongly associated with longevity than adequate sleep duration. Whether this relationship persists across common diseases is unknown. We compared sleep regularity vs. sleep duration as risk factors for 199 diseases and disorders, using ten million hours of objective sleep-wake data (N=60,998, age[mean{+/-}SD]=62.8{+/-}7.8, 55% female). Multivariable-adjusted risks of incident diseases/disorders for regular/irregular and short/adequate sleepers were compared across 9.5 years of follow-up. Irregular sleep predicted risks for 131 diseases/disorders, more than double the number predicted by short sleep duration (63). Irregular sleep was a superior predictor than short sleep duration for 90 diseases/disorders, including circulatory, metabolic, digestive, renal, infectious, neurological, and musculoskeletal conditions, and mental disorders, whereas short sleep duration was the superior predictor for only 9 diseases/disorders. For models where short sleep duration explained disease risks, 83% were improved by adding sleep regularity. Sleep regularity was a stronger predictor of diseases/disorders than sleep duration in this cohort and should be considered an essential dimension of sleep health.

06.
arXiv (CS.CL) 2026-06-18

Graph-ESBMC-PLC: Formal Verification of Graphical PLCopen XML Ladder Diagram Programs Using SMT-Based Model Checking

PLCopen XML defines two encoding formats for IEC 61131-3 Ladder Diagram programs: a textual encoding using elements, and a graphical encoding that represents rung logic as a directed graph of localId/refLocalId connections. ESBMC-PLC supported the textual format but parsed graphical exports from CONTROLLINO, Beremiz, and OpenPLC Editor into an empty GOTO intermediate representation, causing vacuous verification success. This paper presents Graph-ESBMC-PLC, which closes this gap with a DFS-based graphical LD resolver. The resolver traverses the connection graph from leftPowerRail to each coil, extracts rung paths as Boolean contact conjunctions, and applies a three-tier I/O inference scheme. Ordering coils by rightPowerRail connectionPointIn sequence ensures SET coils process before RESET coils, matching IEC scan-cycle semantics. The graphical-to-IR conversion leaves the ESBMC backend unchanged. Validation on 3 graphical LD programs from CONTROLLINO/OpenPLC Editor shows all produce full GOTO IR with nondeterministic inputs and rung logic, versus the empty IR previously. All 3 verify SAFE at k=2 under 70ms. The 11 textual LD benchmarks are fully preserved, with no regression. Two Beremiz examples with no LD content or unsupported timer semantics are reported as discovered limitations. Artifact at Zenodo (DantasCordeiro2026graphical, doi:10.5281/zenodo.20699856).

07.
arXiv (CS.LG) 2026-06-18

Optimal scenario design for climate emulation

arXiv:2606.19302v1 Announce Type: cross Abstract: As deep learning for physical systems continues to grow in popularity, efforts to improve generalizability have primarily focused on designing architectures that embed physical constraints. However, for machine-learning surrogate climate models (emulators), we show that the low structural diversity in existing scenarios commonly used to generate training data places a ceiling on predictive skill. Here, we examine whether training datasets themselves can be optimized to improve generalization. We introduce a method to create datasets that produce emulators capable of generalizing to new, structurally different scenarios absent from the training data. We use a differentiable Simple Climate Model (SCM) to calculate the sensitivity of emulator loss to perturbations in the training data, iteratively updating the training data to maximize emulator skill. For an SCM, training on one scenario optimized in this fashion outperforms an emulator trained on six standard ScenarioMIP pathways. We achieve this higher predictive skill despite training on a smaller dataset, finding that our emulator successfully isolates distinct physical behaviors of different climate forcing agents (e.g., greenhouse gases vs. aerosols) without single-forcing runs. We then demonstrate that scenarios optimized using an SCM, when used to drive an intermediate-complexity climate model, produce a training dataset that yields a more skillful emulator than training on ScenarioMIP outputs. Our results suggest that, in the compute-constrained environment of running full-scale climate models, generating a small number of dynamically rich scenarios provides greater marginal value for emulation and characterizing system responses than expanding the suite of traditional emissions pathways.

08.
arXiv (quant-ph) 2026-06-15

Quantum geometrical description of hole spin qubits far away from the $\Gamma$-point

arXiv:2606.14683v1 Announce Type: cross Abstract: Hole spin qubits provide one of the leading platforms for spin-based quantum computing due to their large intrinsic spin-orbit interaction (SOI), which enables fast electrical manipulation. The SOI of planar quantum dots has mostly been investigated in theoretical studies by examining the SOI already present in the two-dimensional hole gas (2DHG). Here, we study the SOI created by the in-plane confinement by deriving non-perturbative effective Hamiltonians numerically for hole spin qubits. We find that the quantum geometry of the 2DHG naturally emerges, leading to a meaningful non-perturbative definition of pseudospin valid far away from the $\Gamma$-point. The SOI of the 2DHG and of the in-plane confinement have different forms; therefore, they cannot be turned off simultaneously, ruining the perfect spin-orbit switch functionality of spin qubits. We construct effective Hamiltonians using the symmetry approach for various low-dimensional hole systems: (i) a heavy-hole confined in a SiGe/Ge/SiGe heterostructure, (ii) a light-hole confined in SnGe/Ge, (iii) a gate-defined nanowire in SiGe/Ge/SiGe, and (iv) a hole confined in a Ge/Si core/shell nanowire. The non-perturbative effective Hamiltonians provide results with excellent agreement with the full Hamiltonians.

09.
arXiv (quant-ph) 2026-06-17

Kinematic properties of the Pauli equation

arXiv:2606.17548v1 Announce Type: new Abstract: Based on the Wigner-Vlasov formalism, this paper investigates the kinematic properties of the Pauli equation. It is shown that the probability current associated with the Pauli equation can be represented as a superposition of two currents with certain expansion coefficients. Each of these currents corresponds to a particular component of the spinor. The expansion coefficients effectively serve as weighting functions that determine the probability contribution of the corresponding spinor component. Therefore, each spin projection corresponds to its own probability flux. A new system of the Hamilton-Jacobi equations and also a system of motion equations in electromagnetic fields are obtained, taking into account the interaction between the spin and the magnetic field. To illustrate how these equations can be applied we have investigated the quantum system kinematics in detail using an exact solution of the Pauli equation in the presence of a uniform magnetic field and an asymmetric quadratic potential.

10.
arXiv (CS.LG) 2026-06-19

A Hybrid GNN-FEM Framework for Phase-Field Fracture Simulation. Physics-Preserving Hybridization for Generalizable Surrogate Modeling

arXiv:2606.19378v1 Announce Type: new Abstract: Scientific machine learning (SciML) has emerged as a promising approach for accelerating simulations of complex physical systems, yet achieving physically consistent and generalizable predictions for nonlinear, history-dependent problems remains a central challenge. In this study, we propose a hybrid GNN–FEM framework for efficient and generalizable phase-field fracture modeling. While phase-field approaches provide a robust variational framework for simulating complex crack evolution, their high computational cost limits practical applications because they require solving coupled, nonlinear, and history-dependent systems within an incremental finite element procedure. To address this challenge, a graph neural network surrogate is integrated into the conventional staggered scheme, replacing the phase-field update at each load increment while retaining the FEM-based displacement solver to enforce mechanical equilibrium and boundary conditions. By preserving the incremental solution structure, the framework remains consistent with history-dependent fracture evolution without requiring the surrogate to approximate the full solution trajectory. This selective surrogate strategy emphasizes the identification of a physically meaningful and incrementally structured learning target, rather than relying on brute-force data generation to learn the full fracture process. The proposed framework achieves strong generalization across varying geometries, loading conditions, material properties, and discretizations through dimensionless feature design, a graph-based formulation on mesh-based domains, and a physics-informed loss derived from the governing phase-field equation. Numerical experiments demonstrate that the hybrid approach reduces computational cost while maintaining accuracy compared with conventional FEM, and exhibits robust predictive performance across diverse problem settings.

11.
arXiv (CS.CL) 2026-06-16

Beyond NL2Code: A Structured Survey of Multimodal Code Intelligence

While LLMs have substantially advanced text-to-code synthesis, many real programming tasks specify intent through visual artifacts such as screenshots, charts, documents, vector drawings, videos, and interactive states. These tasks require models to connect visual perception to executable programs, because correctness depends not only on syntax but also on layout, geometry, data semantics, editability, interaction behavior, and domain-specific constraints that apply after execution. This survey examines Multimodal Code Intelligence, covering systems that generate, edit, refine, execute, or reason with code under visually grounded inputs and outputs. We first formulate the field by the role that code plays in each task, distinguishing code as a rendered artifact, an editable symbolic structure, a scientific representation, an intermediate reasoning trace, or an executable policy or tool interface. We then organize benchmarks and methods into four domains: Graphical User Interface, Scientific Visualization, Structured Graphics, and Frontier Tasks and Frameworks. This taxonomy connects mature artifact-generation problems to emerging agentic and unified settings and allows us to compare how different tasks treat evidence of correctness. Looking ahead, we argue that future research may benefit from four verification-centered directions. Multi-signal validation can combine complementary evidence of correctness, multi-state verification can test behavior across execution trajectories, cross-task transfer testing can probe reusable visual-code skills, and verifiable agent traces can reveal whether agent actions are grounded in visual evidence. Together, these directions may move multimodal code generation from single-output imitation toward evidence-grounded executable systems.

12.
PLOS Medicine 2026-06-09

Prediction of hospitalisation in young children with pneumonia in Malawi: A machine learning-based approach

by Patrick Staunton, Mohammad Adib Makrooni, Master Chisale, Billy Nyambolo, Joseph Wu, Damien McCarthy, Mark Ledwidge, Yasir Bin Nisar, Chris Watson, Balwani Mbakaya, Cathal Seoighe, Joe Gallagher Background Globally, pneumonia remains the single biggest cause of mortality in children under 5 years of age. This study sought to train and test a prediction model for hospitalisation within 7 days after initial presentation in 2- to 59-month-old Malawian children with WHO-defined pneumonia in primary care and compare its performance to existing risk prediction models. Methods and findings BIOTOPE is a cohort study of children with pneumonia in a primary healthcare setting in Malawi. The training cohort involved nine primary care centres and the testing cohort involved two primary care centres in Northern Malawi. The training cohort was recruited between December 2022 and April 2023 while the testing cohort was recruited in 2016. Participants were consecutive children aged 2–59 months presenting with cough and/or difficulty breathing and who were diagnosed as WHO-defined pneumonia in primary care of any severity. The training cohort was used to train and validate a machine learning model with a prespecified primary outcome defined as hospitalisation and/or death within 7 days as the outcome. This model was then further evaluated in the testing cohort.Median age was 15 months (interquartile range 8−27) in the training and 17 months (interquartile range 9−29) in the external testing cohort (52.1% and 54.4% male, respectively). Hospitalisation occurred in 14.3% (294) of the training cohort and 12.1% (55) of the testing cohort. There was one death in the training cohort only. WHO danger signs were present in 17.6% (360) and 15.9% (70) of children in the training and testing cohorts, respectively. The optimal machine learning model achieved an area under the receiver operating characteristic and precision recall curves of 0.87 and 0.57, respectively, in the testing cohort outperforming existing risk prediction models; furthermore, this model produced an expected calibration error of 0.16 (a logistic regression model using severity status as the response variable and the log odds of the machine learning model’s calibrated probabilities produced an intercept estimate of −0.32 and a slope estimate of 1.13). Key limitations include the use of hospitalisation and/or death as a severity outcome, which may reflect health system factors rather than true disease severity, that mortality-based comparisons were not possible due to low mortality in these primary care cohorts, and that comparator tools were developed for hospital populations rather than primary care populations. Conclusion This machine learning score outperformed traditional pneumonia risk scores in predicting hospitalisation within 7 days in Malawian children presenting to primary care. Traditional pneumonia risk scores diminish in performance when externally applied to new datasets suggesting they may not generalise well beyond their original derivation settings. Mortality-related findings are not applicable as there was only one death in this cohort. Overall these findings support the potential of machine learning to meaningfully improve early identification of children at risk of severe pneumonia in low-resource primary care settings. Further external validation and clinical impact studies are needed to confirm these results.

13.
arXiv (math.PR) 2026-06-16

The optimal sub-Gaussian normalisation for randomised monotone functions

arXiv:2312.01265v5 Announce Type: replace Abstract: Let $\mathcal{M}$ denote the class of randomised monotone functions on $\mathbb{R}$ with values in $[0,1]$, and let $U_{\mathcal{M}}\colon \mathbb{R}_+\to \mathbb{R}_+$ be the minimal function for which $$ \mathbb{P}\left\{ \sqrt{\eta_f}\, \sup_{t\in\mathbb{R}} \left| f_Z(t) - \Exf{f_Z(t)} \right| \ge \varepsilon\sqrt{U_{\mathcal{M}}(\eta_f)} \right\} \le 2\e^{-2\varepsilon^2} $$ holds for every member $f_Z$ of $\mathcal{M}$ with finite effective sample size $\eta_f$ and every positive $\varepsilon$. We prove that for every $x> 1$, $$ \left| \sqrt{U_{\mathcal{M}}(x)} - \sqrt{\log_4 x} \right| \le 2 \min\!\left\{ 1,\, \frac{2 \ln(\e + \ln x)}{\sqrt{\ln x}} \right\}\,. $$ The optimal adjustment $\sqrt{U_{\mathcal{M}}(x)}$ matches $\frac{1}{\sqrt{2\ln 2}}\sqrt{\ln x}$ for all $x>1$, with residuals bounded as above.

14.
arXiv (CS.CV) 2026-06-11

XPR: An Extensible Cross-Platform Point-Based Differentiable Renderer

Point-based differentiable rendering underpins modern 3D reconstruction, novel-view synthesis, and learning-based graphics pipelines, but developing new rendering methods often requires extensive low-level implementation, hardware-specific kernels, and manually written backward passes. This limits rapid prototyping, reproducibility, exploration, and deployment, especially across diverse hardware platforms. This paper presents XPR, an extensible cross-platform framework for point-based differentiable rendering. XPR introduces a high-level programming interface that separates method-specific logic from the shared rendering pipeline, allowing users to implement new methods in a few lines of code. Its pipeline decomposes rendering into modular, statically shaped parallel operations that can be lowered by a cross-platform compiler to GPUs, TPUs, CPUs, and other ML accelerators. We demonstrate implementations of 3DGS, 3DGUT, and LinPrim, with only a few 100s lines of Python code, each of which can be compiled to a range of hardware platforms with the XLA compiler. These results show that XPR enables fast experimentation and portable execution for emerging point-based differentiable rendering systems.

15.
arXiv (CS.CV) 2026-06-11

TopoHR: Hierarchical Centerline Representation for Cyclic Topology Reasoning in Driving Scenes with Point-to-Instance Relations

Topology reasoning is crucial for autonomous driving. Current methods primarily focus on instance-level learning for centerline detection, followed by a sequential module for topology reasoning that relies on simplified MLP layers. Moreover, they often neglect the importance of point-to-instance (P2I) relationships in topology reasoning. To address these limitations, we present TopoHR (Topological Hierarchical Representation), a novel end-to-end framework that establishes cyclic interaction between centerline detection and topology reasoning, allowing them to iteratively enhance each other. Specifically, we introduce a hierarchical centerline representation including point queries, instance queries, and semantic representations. These multi-level features are seamlessly integrated and fused within a hierarchical centerline decoder. Furthermore, we design a hierarchical topology reasoning module that captures both fine-grained P2I relationships and global instance-to-instance (I2I) connections within a unified architecture. With these novel components, TopoHR ensures accurate and robust topology reasoning. On the OpenLane-V2 benchmark, TopoHR refreshes state-of-the-art performance with significant improvements. Notably, compared with previous best results, TopoHR achieves +3.8 in $\mathrm{DET}_{l}$, +5.4 in $\mathrm{TOP}_{ll}$ on $subset_A$ and +11.0 in $\mathrm{DET}_{l}$, +7.9 in $\mathrm{TOP}_{ll}$ on $subset_B$, validating the effectiveness of the proposed components. The code will be shared publicly at https://github.com/Yifeng-Bai/TopoHR.git.

16.
arXiv (CS.CL) 2026-06-19

A BART-based approach with hierarchical strategy for Vietnamese abstractive multi-document summarization

In this technical report, we focus on solving the challenge of Vietnamese multi-document abstractive summarization, introduced in the International Workshop on Vietnamese Language and Speech Processing (VLSP) 2022. We choose to follow the popular hierarchical approach, i.e. condensing each document followed by aggregation and summarization. We propose a novel yet simple strategy to shorten documents that is driven by the golden summary, thus ensuring high correlation between stages of the hierarchical approach. Our method achieves a ROUGE2-F1 score of 0.2468 on the VLSP's public test set, and can produce fluent and concise summaries. Additionally, we utilize external sources for extra data, which greatly enhances the quantity of data for Vietnamese multi-document summarization. The additional data is made available for the community.

17.
arXiv (CS.AI) 2026-06-16

Automated ultrasound doppler angle estimation using deep learning

arXiv:2508.04243v2 Announce Type: replace-cross Abstract: Angle estimation is an important step in the Doppler ultrasound clinical workflow to measure blood velocity. It is widely recognized that incorrect angle estimation is a leading cause of error in Doppler-based blood velocity measurements. In this paper, we propose a deep learning-based approach for automated Doppler angle estimation. The approach was developed using 2100 human carotid ultrasound images including image augmentation. Five pre-trained models were used to extract images features, and these features were passed to a custom shallow network for Doppler angle estimation. Independently, measurements were obtained by a human observer reviewing the images for comparison. The mean absolute error (MAE) between the automated and manual angle estimates ranged from 3.9{\deg} to 9.4{\deg} for the models evaluated. Furthermore, the MAE for the best performing model was less than the acceptable clinical Doppler angle error threshold thus avoiding misclassification of normal velocity values as a stenosis. The results demonstrate potential for applying a deep-learning based technique for automated ultrasound Doppler angle estimation. Such a technique could potentially be implemented within the imaging software on commercial ultrasound scanners.

18.
arXiv (math.PR) 2026-06-12

The Lov\'{a}sz Local Lemma: Foundations and Applications

Authors:

arXiv:2603.07245v5 Announce Type: replace-cross Abstract: The Lov\'{a}sz Local Lemma (LLL) is a central tool in probabilistic combinatorics, providing a sufficient condition under which a finite collection of undesirable events with limited dependencies can be simultaneously avoided with positive probability. This paper offers a self-contained expository treatment of the lemma and its strengthened versions, emphasizing mathematical foundations, conceptual clarity, and applications. We begin with a pedagogically motivated proof of the LLL based entirely on unconditional probability inequalities. Particular attention is given to the symmetric form of the lemma and several subsequent strengthenings. The paper also discusses a variety of classical applications of both the symmetric and asymmetric forms of the LLL in combinatorics and graph theory, including bounds for the edge-disjoint paths problem, satisfiability of Boolean formulas in conjunctive normal form, lower bounds on diagonal and off-diagonal Ramsey numbers, hypergraph coloring results, structural properties of directed graphs, and acyclic graph colorings. Additional observations and refinements are provided throughout. We also introduce the algorithmic framework of Moser and Tardos, highlighting its constructive counterpart to the LLL, together with an introduction to the entropy-compression principle. The lopsided LLL, a refinement of the LLL, is presented along with an application to the Latin transversal problem. We further discuss the cluster-expansion lemma and its relation to the LLL, and present an alternative treatment of the Latin transversal problem from the cluster-expansion perspective that yields an improved result. The paper concludes with a high-level overview of the iterated LLL, also known as the semi-random method.

19.
medRxiv (Medicine) 2026-06-10

Healthy Heart Actions Right Time (HHART): Co-design priorities to connect Aboriginal and Torres Strait Islander community and clinic activities for healthy hearts

Aim: Healthy Heart Actions Right Time (HHART) is a multi-phased research project that seeks to identify, implement and evaluate strategies to connect community and clinical activities to reduce the burden of heart disease for Aboriginal and Torres Strait Islander people. The aim in Phase One was to identify priority activities for two participating services. Background: The ongoing effects of colonisation drive a disproportionate burden of heart disease for Aboriginal and Torres Strait Islander people. Clinical and community groups both have established strengths in reducing the risk of heart disease, but these are not always well connected. Methods: Using a case study methodology in two locations we partnered in a 12-month co-design process to identify priority activities to connect clinical and community activities. Findings: Three priorities emerged from the Phase One co-design process: (i) community-led gardening as a strategy to promote heart health through connection and healthy lifestyles; (ii) community days to increase engagement in heart checks and strengthen community-clinic relationship; and (iii) clinic-led development of culturally relevant education resources to promote clinician confidence and community heart health knowledge.

20.
arXiv (CS.AI) 2026-06-12

Two-Layer Linear Auto-Regressive Models Estimate Latent States

arXiv:2606.12691v1 Announce Type: cross Abstract: Auto-regressive models have emerged as powerful tools for sequential data, from language to video. Understanding how and why these models learn latent representations remains an open theoretical question. In this work, we demonstrate that when trained by empirical risk minimization on data from partially observed linear dynamical systems, two-layer linear auto-regressive models naturally learn to approximate Kalman filtering. In particular, we show that the learned hidden representation coincides, up to a similarity transformation, with the state estimates produced by the optimal (Kalman) filter, even though the model has no explicit knowledge of the underlying dynamics or state. The result follows from three main insights. First, we establish that the Kalman filter is well approximated by an auto-regressive model with bounded truncation error. Second, we show that despite non-convexity, the two-layer optimization landscape is benign, i.e., all stationary points are either strict saddles or global minima. Finally, as our main contributions, we provide finite-sample guarantees on prediction error, parameter estimation error, and latent state recovery. Numerical simulations support the theoretical results and demonstrate that the latent representations of auto-regressive models recover state estimates.

21.
arXiv (CS.AI) 2026-06-11

When Poison Fails After Retrieval: Revisiting Corpus Poisoning under Chunking and Reranking Pipelines

arXiv:2606.11265v1 Announce Type: cross Abstract: Retrieval-Augmented Generation (RAG) systems are vulnerable to corpus poisoning attacks that manipulate downstream model outputs through malicious knowledge injection. Existing studies mainly evaluate poisoning under simplified retrieval settings, overlooking practical RAG pipelines involving document chunking, dense retrieval, reranking, and grounded generation. In this paper, we revisit corpus poisoning under realistic multi-stage retrieval pipelines and show that many existing attacks substantially degrade after reranking despite achieving high retrieval-stage relevance. We identify retrieval granularity mismatch as a key reason for this failure: document-level adversarial signals are often fragmented during chunking, while rerankers favor locally coherent and answer-bearing passages rather than globally optimized semantic similarity. Based on this observation, we propose Chunk-aware and Rerank-Consistent Poisoning (CRCP), a poisoning framework that jointly optimizes retrieval relevance, reranker consistency, and chunk-boundary robustness. CRCP explicitly models chunking transformations during optimization to generate locally self-contained adversarial passages that remain effective under varying chunking configurations. Experiments on standard RAG benchmarks with multiple retrievers and rerankers show that existing poisoning methods are highly sensitive to chunk size and reranking strategies, whereas CRCP achieves substantially higher attack success rates and stronger robustness across realistic retrieval pipelines. Our findings highlight an important realism gap in current RAG security evaluation and suggest that poisoning in modern RAG systems should be studied as a multi-stage retrieval consistency problem rather than a retrieval-only problem.

22.
arXiv (math.PR) 2026-06-11

Continuous stochastic flows driven by white noise and their duals

Authors:

arXiv:2606.12143v1 Announce Type: new Abstract: We study a class of continuous stochastic flows driven by a space-time white noise and characterize their dual flows by explicit stochastic differential equations. A key ingredient of the proof is the convergence of solutions under coefficient approximations. As an application, we derive the dual flows in two illustrative examples, the squared Bessel flow and the Jacobi flow. We also introduce a new model of polynomially self-repelling (PSR) flow and show that it enjoys a self-duality property.

23.
arXiv (CS.LG) 2026-06-17

Can Vision Foundation Models Navigate? Zero-Shot Real-World Evaluation and Lessons Learned

arXiv:2603.25937v2 Announce Type: replace-cross Abstract: Visual Navigation Models (VNMs) promise generalizable, robot navigation by learning from large-scale visual demonstrations. Despite growing real-world deployment, existing evaluations rely almost exclusively on success rate, whether the robot reaches its goal, which conceals trajectory quality, collision behavior, and robustness to environmental change. We present a real-world evaluation of five state-of-the-art VNMs (GNM, ViNT, NoMaD, NaviBridger, and CrossFormer) across two robot platforms and five environments spanning indoor and outdoor settings. Beyond success rate, we combine path-based metrics with vision-based goal-recognition scores and assess robustness through controlled image perturbations (motion blur, sunflare). Our analysis uncovers three systematic limitations: (a) even architecturally sophisticated diffusion and transformer-based models exhibit frequent collisions, indicating limited geometric understanding; (b) models fail to discriminate between different locations that are perceptually similar, however some semantics differences are present, causing goal prediction errors in repetitive environments; and (c) performance degrades under distribution shift. We will publicly release our evaluation codebase and dataset to facilitate reproducible benchmarking of VNMs.

24.
arXiv (quant-ph) 2026-06-11

Fun with Graph States: Nonlocal Bell Pairs and the Arf Invariant

arXiv:2606.06582v2 Announce Type: replace Abstract: We study inner products and partial amplitudes of graph states–a commonly employed class of quantum states, which are specified by graphs. We find that the magnitudes of these quantities are simply related to the rank of the adjacency matrix of the graph over F_2 while the phase is determined by the Arf invariant of its quadratic refinement. These facts motivate a nonlocal tensor factorization of the Hilbert space, with respect to which all graph states are products of Bell pairs with unentangled ancillae. These results may illuminate the quantum advantage in the framework of Measurement-Based Quantum Computation and suggest that graph states can be usefully visualized in the language of algebraic topology. In addition, we develop a specialized technique for computing expectation values of qubit-wise permutations in graph states, which is useful for calculating multi-invariants.

25.
arXiv (CS.LG) 2026-06-18

Stochastic Adaptive Gradient Descent Without Descent

arXiv:2509.14969v2 Announce Type: replace Abstract: We introduce a new adaptive step-size strategy for convex optimization with stochastic gradient that exploits the local geometry of the objective function only by means of a first-order stochastic oracle and without any hyper-parameter tuning. The method comes from a theoretically-grounded adaptation of the Adaptive Gradient Descent Without Descent method to the stochastic setting. We prove the convergence of stochastic gradient descent with our step-size under various assumptions, and we show that it empirically competes against tuned baselines.