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01.
bioRxiv (Bioinfo) 2026-06-17

In silico characterization of lysis and host-recognition modules in Staphylococcus aureus bacteriophage genomes

Background/aim: Antimicrobial resistance in methicillin-resistant Staphylococcus aureus (MRSA) requires precision non-antibiotic therapeutics, yet phage lytic efficacy is poorly predicted by phenotypic assays, as shown by paradoxical biofilm responses. This study characterized the genomic architecture of lytic S. aureus bacteriophages, focusing on the conservation of the lysis module and the variability of host-recognition modules, to provide a rational basis for phage candidate selection. Materials and methods: Twenty-two complete S. aureus phage genomes were retrieved from NCBI GenBank. Genomic features were extracted with custom Biopython scripts. Lysis (endolysin, holin) and host-recognition (tail fiber/receptor-binding protein) modules were annotated and validated by InterPro domain analysis, with disrupted endolysins resolved by tBLASTn. Phylogeny was reconstructed from large terminase subunit (TerL) sequences using maximum likelihood. Results: Genome size spanned three classes, from 17.5 to 148.6 kb. The LysK-type endolysin (CHAP, Amidase, SH3b) was highly conserved, whereas tail fiber/RBP genes were detected in only 14 of 22 phages. Domain analysis reclassified two proteins annotated as endolysins as virion-associated peptidoglycan hydrolases, and identified two independent mechanisms, HNH endonuclease insertion and intron splitting, that interrupt lysis-module genes and confound automated annotation. Maximum likelihood analysis recovered a strongly supported, highly conserved core clade with EW and SA13 as divergent lineages. Conclusion: Lysis modules are conserved whereas host-recognition modules are variable, indicating that host recognition rather than the lytic enzyme is the principal determinant of host range and the more rational target for phage selection and engineering.

02.
medRxiv (Medicine) 2026-06-18

Biomedical Capacity, Governance, and Health Security: A Dominican Republic Research Analysis of Stakeholder Perspectives

The COVID-19 pandemic exposed critical vulnerabilities in globally concentrated biomedical supply chains and accelerated interest in nearshoring and hemispheric health-security strategies. The Dominican Republic, already the third-largest medical device exporter in Latin America, occupies a strategically significant but institutionally constrained position within this realignment. This study evaluates stakeholder perceptions of the principal opportunities and barriers affecting biomedical ecosystem development in the Dominican Republic, with particular attention to governance, workforce capacity, and value-chain upgrading pathways. Methods. A concurrent mixed-methods design was employed, integrating a cross-sectional electronic survey of 142 purposively sampled domain experts (administered September-December 2025) with a qualitative executive consultation with senior government and industry leaders. Survey analyses combined descriptive statistics, one-sample t-tests against the scale neutral midpoint, chi-square goodness-of-fit tests, Friedman non-parametric ranking, Spearman rank correlations, and exploratory linear and logistic multivariable regression. Qualitative responses were analyzed using a framework approach grounded in the Triple Helix model of innovation systems. Results. Perceived government support was significantly below neutral (mean = 2.67, SD = 1.12; p = 0.034). Workforce shortages (83.3%) and weak academia-industry collaboration (71.4%) were the most frequently endorsed barriers ({chi}2(5) = 18.7, p = 0.002). Regulatory modernization (88.1%) and workforce development (85.7%) ranked as the highest-priority policy levers (Friedman p = 0.005). Clinical trials and contract research organization services were the dominant sub-sector priority (76.2%, binomial p < 0.001). In multivariable analysis, perceived government support, talent availability, and confidence in IP protection jointly explained 46% of the variance in sector competitiveness (R2 = 0.46, p < 0.001). Strong majority support existed for a formal public-private biomedical coordination authority (73.8%, p < 0.001).Conclusion. Institutional credibility and advanced human capital–rather than geography or market access–are the perceived binding constraints on the Dominican Republics biomedical trajectory. Regulatory modernization, targeted workforce investment, and the establishment of a national biomedical coordination authority represent the highest-leverage interventions for positioning the country as a hemispheric hub for biomedical manufacturing, clinical research, and health security.

03.
arXiv (CS.LG) 2026-06-16

An Integrable Token Mixing Layer from the Generalized Yang Baxter Equation

arXiv:2606.15085v1 Announce Type: new Abstract: The YB Mixer is a sequence token mixing layer derived from free fermion and generalized Yang Baxter structures. It applies a core principle from integrable systems where a local algebraic constraint guarantees global computational stability. By using the Ising exchange algebra the mixer creates a free fermionic structure that acts as an exactly norm preserving orthogonal map. This algebra also produces commuting transfer matrices which allow inference to be order free and adaptable to any variable budget. To ensure the model can generalize to longer sequence lengths it uses a spectral circulant generator. This generator maintains the crucial orthogonal and commuting properties of the system. The result is a highly stable and mathematically grounded architecture for sequence processing.

04.
arXiv (quant-ph) 2026-06-16

Orbital-optimized spin-adapted multistate contracted VQE for excited states and properties on quantum hardware

arXiv:2606.15489v1 Announce Type: new Abstract: We introduce the orbital-optimized multistate contracted variational quantum eigensolver (oo-MC-VQE) method with spin-adapted operators for the computation of ground and excited states, as well as state-specific and transition properties. The use of spin-adapted operators ensures that the spin symmetry of the reference states is conserved throughout the VQE optimization. In multistate variational approaches, achieving a balanced description of an increasing number of electronic states places growing demands on the expressibility of the underlying ansatz, thereby introducing a fundamental trade-off between accuracy and circuit complexity. We consider the effects of this trade-off explicitly and find that the number of circuit parameters required to obtain accurate results is reported to scale approximately linearly in the number of states. We further present an explicit quantum-circuit implementation of the oo-MC-VQE method and demonstrate its integration with quantum error mitigation techniques. Finally, we execute the method on real quantum devices to compute absorption spectra for two benchmark molecular systems.

05.
arXiv (quant-ph) 2026-06-12

Effective Geometry and Position-Dependent Mass in Dual-$q$ Quantum Mechanics

arXiv:2606.12444v1 Announce Type: new Abstract: This work investigates the deformed-derivative formalism introduced by Borges, with emphasis on the relation between the linear operator $D_{(q)}$ and its nonlinear dual counterpart $D^{(q)}$. Directly inserting the dual derivative into the kinetic term leads to a nonlinear Schrödinger equation and obscures the usual interpretation of superposition and probability. We show that this nonlinearity can be removed by a simultaneous transformation of the coordinate and of the wave function. The transformed problem is an ordinary linear Schrödinger equation in a deformed coordinate, and its representation in the physical coordinate is equivalent to a Hermitian position-dependent-mass (PDM) Hamiltonian. In this formulation, the deformation parameter $q$ determines both the effective mass profile and the associated metric. The formalism is applied to the free particle, the infinite square well, the rectangular barrier, and the harmonic oscillator in the weak-deformation regime. Comparison with the nonadditive-translation approach of Costa Filho et al. shows that the Borges dual-$q$ framework provides an alternative route to the same effective geometric structure. For $q1$, the effective length is increased, which lowers the spectrum and suppresses tunneling relative to the undeformed limit $q=1$.

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

Multi-Granular Attention-Driven Reinforcement Learning Framework for Web Intelligent Enhancement Systems

arXiv:2606.19690v1 Announce Type: new Abstract: From the past few years, web intelligent enhancement systems increasingly rely on heterogeneous and dynamic web data to deliver personalized, context-aware services. However, traditional machine learning, deep learning, and reinforcement learning models often struggle with semantic understanding, adaptability, and scalability in continuously evolving web environments. In this research, a Multi-Granular Attention-based Reinforcement Web Intelligent Enhancement System (MGAR-WIES) is proposed to address the challenges by integrating semantic graph modeling, attention mechanisms, and adaptive reinforcement learning. Initially, heterogeneous web data comprising structured, semi-structured and unstructured sources are collected and preprocessed for generating unified feature representations. These representations are transformed into a dynamic semantic graph, where entities and their relationships are modeled by using graph embeddings enhanced by attention mechanisms for capturing both local relevance and global contextual dependencies. Subsequently, an adaptive multi-agent reinforcement learning strategy leverages the attention-aware semantic states to optimize personalized web actions like content recommendation, navigation optimization, and service adaptation. Finally, the continuous online feedback is further integrated to update graph representations and learning policies in real time by ensuring sustained adaptability and performance. The proposed MGAR-WIES acheived better results in terms of accuracy (80%) when compared with existing approaches.

07.
arXiv (CS.AI) 2026-06-16

No One-Size-Fits-All Neurons: Task-based Neurons for Artificial Neural Networks

arXiv:2405.02369v2 Announce Type: replace-cross Abstract: In the past decade, many successful networks are on novel architectures, which almost exclusively use the same type of neurons. Recently, more and more deep learning studies have been inspired by the idea of NeuroAI and the neuronal diversity observed in human brains, leading to the proposal of novel artificial neuron designs. Designing well-performing neurons represents a new dimension relative to designing well-performing neural architectures. Biologically, the brain does not rely on a single type of neuron that universally functions in all aspects. Instead, in our brain, neurons are often task-based. In this study, we address the following question: since the human brain is a task-based neuron user, can the artificial network design go from the task-based architecture design to the task-based neuron design? Since methodologically there are no one-size-fits-all neurons, given the same structure, task-based neurons can enhance the feature representation ability relative to the existing universal neurons due to the intrinsic inductive bias for the task. Specifically, we propose a two-step framework for prototyping task-based neurons. As the initial step, we evaluate the proposed framework using polynomials as base functions. Empirically, systematic experimental results on synthetic data, classic benchmarks, and real-world applications show that the proposed task-based neuron design is not only feasible but also delivers competitive performance over other state-of-the-art models.

08.
arXiv (CS.AI) 2026-06-12

A Zero-shot Generalized Graph Anomaly Detection Framework via Node Reconstruction

arXiv:2606.12673v1 Announce Type: cross Abstract: Cross-domain graph anomaly detection (GAD) aims to identify abnormal nodes in unseen target graphs, showing strong potential in real-world applications with heterogeneous graph data. However, existing methods often depend on dataset-specific feature semantics and structural patterns, which limits their ability to generalize across different domains. To address this challenge, we propose AlignGAD, a zero-shot generalized graph anomaly detection framework. Our framework is built upon three key components: a Global Unification Module that aligns heterogeneous node features and normalizes graph signals in the spectral domain; a Clustering Module that constructs cluster-aware graph views to capture group-level abnormal patterns; and a Node Discrepancy Scoring Module that measures reconstruction discrepancy and aggregates anomaly evidence from different graph views. Experiments on multiple real-world datasets demonstrate the effectiveness of AlignGAD under the zero-shot GAD setting.

09.
arXiv (CS.CV) 2026-06-18

Clinically Aligned Geometry Constraints for Robust IVUS Vessel Boundary Segmentation

Intravascular ultrasound (IVUS) lumen and external elastic membrane (EEM) segmentation is important for quantitative coronary plaque burden assessment. Errors in lumen or EEM delineation directly propagate to plaque area, plaque burden and geometric measurements. However, standard methods prioritising overlap scores often suffer from boundary drift and topology errors, leading to inaccurate clinical measurements. We present GeoCat, a geometry-consistent network that processes 5-frame IVUS clips using dual Cartesian-polar encoders with cross-domain attention and temporal fusion. A differentiable geometry consistency loss directly supervises clinically relevant descriptors including diameters, orientations, and cross-sectional areas. The model is trained on 12,242 annotated frames from 146 patients acquired with two commercial IVUS systems. We evaluate performance using both segmentation accuracy and plaque-relevant clinical metrics, including Dice/IoU, boundary measures(95HD (mm), ASSD), topology violation rate, and clinical geometry errors (dmax/dmin, angles, and areas). On our dataset, GeoCat achieves a Dice of 0.93, reduces 95HD to 0.14 mm, and lowers topology violations to 1.0%. Importantly, it significantly improves geometric fidelity, yielding diameter errors of 0.13-0.16 mm and angular errors of ~8 degrees, supporting reliable plaque burden quantification.

10.
medRxiv (Medicine) 2026-06-22

Development and validation of a risk prediction algorithm to estimate all-cause mortality among community-dwelling Canadians: the Mortality Population Risk Tool (MPoRT)

BACKGROUND: The risk of all-cause mortality can inform decision-making for chronic disease prevention. We developed a predictive algorithm to estimate the 5-year risk of death among community-dwelling adults. METHODS: We derived and validated the Mortality Population Risk Tool (MPoRT) using data from population health surveys in Canada (the Canadian Community Health Survey) and the United States (the National Health Interview Survey), survey years 2001 to 2011, linked to vital statistics. The outcome was death within five years of the survey response. The algorithm was developed using data from Ontario respondents using a Cox proportional hazards model, then modified and re-estimated to allow cross-national assessment in Canada and the United States. Twenty-three prespecified predictors were assessed: seven sociodemographic, six behavioural, and ten general health and chronic disease. RESULTS: 527,369 respondents aged 20 to 105 years were included in the Canadian and United States development and validation cohorts, with 43,758 deaths during 3.68 million person-years follow-up. The final sex-specific MPoRT algorithms each contained 21 variables, showing strong discrimination (C-statistic: females 0.874 [0.871–0.877]; males 0.867 [0.865–0.871]) and good calibration overall and in 246 of 247 subgroups. Discrimination was modestly attenuated (0.01 decrease in C-statistic) in cross-national validation between Canada and the United States, with good calibration across all 71 subgroups. INTERPRETATION: MPoRT accurately discriminated all-cause mortality using only self-reported data, enabling broad application without clinical measures. While validation outside North America is needed to confirm broader applicability, MPoRT is designed for straightforward recalibration using routinely available national mortality data. This supports targeted chronic disease prevention strategies at both the population and individual levels, though the limitations inherent to self-reported predictors should be considered when interpreting predictions.

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

SPARK: Spatial Policy-driven Adaptive Reinforcement learning for Knowledge distillation

Low-bit quantization enables deployment of image restoration (IR) networks on resource-constrained devices, but introduces rounding noise that disproportionately degrades high-frequency regions such as edges and fine textures. Existing knowledge distillation (KD) methods apply distillation signals uniformly across all spatial locations, overlooking the varying reconstruction difficulty across image regions. To address this, we propose SPARK (Spatial Policy-driven Adaptive Reinforcement Learning for Knowledge Distillation), a framework that adaptively allocates distillation effort using a lightweight reinforcement learning (RL) policy network. At each training step, a difficulty feature extractor computes four signals, namely Laplacian variance, pixel variance, student reconstruction error, and teacher-student knowledge gap, which are fed into a compact policy CNN that produces a stochastic spatial weight map to modulate the KD loss during quantization-aware training (QAT). SPARK is IR task-agnostic, adds no inference cost, and integrates into any existing QAT pipeline without architectural changes. Experiments on benchmark datasets demonstrate that SPARK consistently outperforms PTQ, QAT, and state-of-the-art (SOTA) KD approaches across multiple student architectures, achieving reconstruction quality closest to the full-precision teacher under significant computational constraints.

12.
arXiv (math.PR) 2026-06-16

Joint convergence in Wiener chaos via transport hierarchy and Malliavin covariances

arXiv:2606.14812v1 Announce Type: new Abstract: We study the joint convergence in distribution of a sequence $X_N = I_p(f_N)$ of multiple Wiener–Itô integrals of order $p\geq 2$ that converges to a Gaussian limit $Z\sim N(0,\sigma^2)$, together with another sequence $Y_N = I_q(g_N)$ converging in law. The central finding is that the joint convergence of $(X_N, Y_N)$ is completely governed by the asymptotic behavior of the iterated Malliavin covariances $Y_{r+1,N} = \langle DX_N, DY_{r,N}\rangle_H$, $r\geq 0$: joint convergence holds as soon as these covariances converge jointly with $Y_N$, and the structure of the limiting distribution is then explicitly determined by their limits. Moreover, the convergence of the Malliavin covariances is necessary for joint convergence, as shown by a counterexample. When $q

13.
arXiv (quant-ph) 2026-06-16

Towards Quantum Limited Spatial Resolution of NV-Diamond Magnetometry

arXiv:2508.13438v2 Announce Type: replace Abstract: Optically addressable ensembles of solid-state defects, such as nitrogen vacancy (NV) centers, are a leading modality for imaging-based magnetometry, thermometry and strain sensing. However, monitoring the fluorescence of individual defects within a sub-diffraction ensemble remains an outstanding challenge that currently limits access to atomic-scale features and dynamics. For compact clusters of NVs, we formulate imaging-based atomic sensing as a low-dimensional multiparameter estimation task in which one seeks to localize each defect and quantify the field strength in its immediate vicinity. In this work, we employ optical spatial mode demultiplexing (SPADE) to enhance localization and brightness estimation accuracy at sub-diffraction scales. Specifically, we develop a two-stage sensing protocol that augments direct imaging by projecting the incoming optical field onto point spread function (PSF)-adapted, i.e., PAD spatial modes and Yuen-Kennedy-Lax (YKL) spatial modes enabling efficient extraction of emitter positions and brightnesses. The YKL-SPADE measurement employed for brightness estimation is shown to be quantum-optimal in the case of two emitters and establishes a new connection between quantum detection and estimation theories. We numerically evaluate the statistical performance of our protocol for sub-diffraction optically detected magnetic resonance (ODMR) and Rabi sensing experiments. Compared to conventional focal plane intensity measurements, our protocol improves emitter localization accuracy by 6$\times$ and brightness estimation accuracy by 2$\times$ for tightly confined ensembles, residing well below the diffraction limit.

14.
arXiv (math.PR) 2026-06-16

Hua-Chen New Theory of Economic Optimization

arXiv:2504.19134v4 Announce Type: replace-cross Abstract: Between 1957-1985, Chinese mathematician Loo-Keng Hua pioneered economic optimization theory through three key contributions: establishing economic stability's fundamental theorem, proving the uniqueness of equilibrium solutions in economic systems, and developing a consumption-integrated model 50 days before his death. Since 1988, Mu-Fa Chen has been working on Hua's theory. He introduced stochastics, namely Markov chains, to economic optimization theory. He updated and developed Hua's model and came up with a new model (Chen's model) which has become the starting point of a new economic optimization theory. Chen's theory can be applied to economic stability test, bankruptcy prediction, product ranking and classification, economic prediction and adjustment, economic structure optimization. Chen's theory can also provide efficient algorithms that are programmable and intelligent. {Stochastics} is the cornerstone of Chen's theory. There is no overlap between Chen's theory, and the existing mathematical economy theory and the economics developments that were awarded Nobel Prizes in Economics between 1969 and 2024. The distinguished features of Chen's theory from the existing theories are quantitative, calculable, predictable, optimizable, programmable and can be intelligent. This survey provides a theoretical overview of the newly published monograph [5rw24]. Specifically, the invariant of the economic structure matrix, also known as the Chen's invariant, was first published in this survey.

15.
arXiv (quant-ph) 2026-06-16

Measuring Non-Stabilizerness in an SU(2) Lattice Gauge Theory

arXiv:2606.14842v1 Announce Type: new Abstract: One of the goals of quantum simulation is to provide novel insights into quantum systems, such as the gauge theories that are relevant for high-energy and nuclear physics. Recent years have seen rapid improvements in both the hardware and software necessary for these simulations. A central consideration in the design of such simulations is the quantum complexity of a given quantum state. This work takes a step towards studying a specific kind of complexity, namely the non-stabilizerness, in a simple yet non-trivial system: SU(2) lattice gauge theory of two plaquettes. The non-stabilizerness of low-energy eigenstates is studied and the implications for quantum simulations are discussed. The real-time evolution of this system is simulated on ibm_marrakesh and the non-stabilizerness is measured using a random measurement protocol. New techniques enhancing the efficiency of this protocol are developed, including both a new way to calculate the estimator for non-stabilizerness and a flexible error mitigation technique called Bit String Decoherence Renormalization. This mitigation method is central to accurately resolving the experimental time dependence of non-stabilizerness, and is anticipated to have broad applicability in digital quantum simulations.

16.
arXiv (quant-ph) 2026-06-17

Microwave-free vector magnetometry and crystal orientation determination with Nitrogen-Vacancy centers using Bayesian inference

arXiv:2512.13835v2 Announce Type: replace Abstract: Nitrogen-vacancy (NV) centers in diamond provide a solid-state platform for quantum sensing. While optically detected magnetic resonance techniques offer high sensitivity, their reliance on microwaves introduces heating and stray electromagnetic fields that can perturb nearby samples. Optical approaches based on cross-relaxation between differently oriented NV centers remove this constraint but have so far required stringent alignment of the external field with crystallographic axes, restricting their practicality. Here we introduce a general framework for microwave-free vector magnetometry at near-zero field that leverages Bayesian inference to extract both the magnetic field vector and the NV orientation directly from photoluminescence maps. An analytical model of cross-relaxation resonances enables efficient inference under arbitrary field and orientation configurations, while naturally incorporating the discrete degeneracies of the NV symmetry. We experimentally demonstrate robust orientation determination and vector-field reconstruction, establishing a general route toward compact and alignment-free NV magnetometers for practical sensing applications.

17.
arXiv (CS.CV) 2026-06-11

Cross-Modal Benchmarking for Robotic Perception in Natural Environments

Natural environments present a complex challenge to robotics perception systems. Current models, particularly vision foundation models, are largely trained on structured, urban environments leading to weaknesses in their perception for field robotics tasks. We showcase the limitations of current models using our recently released WildCross benchmark, a new cross-modal benchmark for place recognition and metric depth estimation in large-scale natural environments. WildCross comprises over 476K sequential RGB frames with semi-dense depth and surface normal annotations, each aligned with accurate 6DoF pose and synchronized dense lidar submaps. In this work, we provide an expanded analysis of the benchmark results from the recent WildCross benchmark, with particular emphasis on expanded metric depth estimation experiments. Access to the code repository and dataset for this work can be found at https://csiro-robotics.github.io/WildCross.

18.
bioRxiv (Bioinfo) 2026-06-11

STITCH links cellular morphology and gene expression in spatial transcriptomics

In situ spatial (ISS) sequencing can uncover co-variation between cellular morphology and gene expression in vivo. However, a principled and interpretable mathematical representation of morphology has not yet been applied in this context. In particular, current deep learning-based representations of cell images confound a cell's shape with its size. We present an interpretable representation of cellular boundary contours, based on tangent principal component analysis (TPCA) in a Kendall shape manifold, that captures size-independent contour shape features. This approach successfully recovers shape-perturbing genes in an RNAi screen than a previous metric geometry-based approach. We build on TPCA to develop STITCH (Shape-TranscriptomIc Correlation and Harmonization), an approach to reveal covariation between cell morphology with gene expression in ISS datasets. In a Xenium dataset, STITCH outperforms a deep learning-based approach in both recovering the layered organization of keratinocytes and a spatial gradient in nuclear eccentricity. Across samples in a melanoma CosMx dataset, STITCH reproducibly associates elongated and triangular fibroblasts with proximity to malignant cells and myofibroblast-like transcriptional program. Finally, STITCH independently recovers a known link between mesenchymal-like malignant cell states and increased cell area in two melanoma cohorts. STITCH can thus yield interpretable morphology-transcriptome relationships across cell types, patients, and spatial transcriptomics platforms.

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

Connect the Dots: Training LLMs for Long-Lifecycle Agents with Cross-Domain Generalization Via Reinforcement Learning

This work presents a general framework for training large language models (LLMs) to "Connect the Dots" (CoD), a meta-capability required by long-lifecycle agents: as an LLM-based AI agent gets deployed in an environment, it solves a long sequence of tasks while continuously exploring the environment, learning from its own experiences, and iteratively self-updating its context about the environment, thereby achieving progressively better performance on future tasks conditioned on the updated context. Major components of the CoD framework include: (1) algorithm design and infrastructure for end-to-end reinforcement learning (RL) with long rollout sequences interleaving solve-task and update-context episodes; (2) tasks and environments for incentivizing and eliciting the targeted meta-capability in LLMs during training, as well as for faithfully measuring progress during evaluation. We present proof-of-concept implementations of the CoD framework, including a GRPO-style RL algorithm with fine-grained credit assignment, as well as tasks and environments tailored to the targeted meta-capability (rather than domain-specific LLM capabilities or standard task-by-task RL). Empirical results validate the efficacy of end-to-end RL training in the CoD setting, and demonstrate the potential for out-of-distribution generalization – within the training domains, across different domains, and from CoD to Ralph-loop settings – of the elicited meta-capability. Our investigation of CoD connects several lines of prior works, and opens up new opportunities for advancing LLMs and AI agents. To facilitate further research and applications, we release our implementations at \url{https://github.com/agentscope-ai/Trinity-RFT/tree/research/cod/examples/research_cod}.

20.
arXiv (CS.CL) 2026-06-11

Geometry of Reason: Spectral Signatures of Valid Mathematical Reasoning

Verifying whether a language model is genuinely reasoning or pattern-matching remains an open problem: learned verifiers are expensive, and output-based heuristics are brittle. We show that valid mathematical reasoning induces a measurable, training-free spectral signature in transformer attention. By treating each attention matrix as a weighted token graph, we extract four diagnostics: Fiedler value, High-Frequency Energy Ratio (HFER), spectral entropy, and smoothness, that require no learned parameters. Experiments across seven models from four architectural families yield effect sizes up to Cohen's $d = 3.30$ ($p < 10^{-116}$), enabling $85$–$96\%$ single-threshold classification accuracy. Two findings sharpen the interpretation. First, Platonic validity: the spectral signal tracks logical coherence rather than compiler acceptance, proofs rejected for timeouts or missing imports are correctly classified as valid, a distinction confirmed by a manual audit ($\kappa = 0.82$, $n = 51$). Second, architectural determinism: Sliding Window Attention shifts the discriminative feature from HFER to smoothness ($d = 2.09$, $p < 10^{-48}$), showing that attention design governs which spectral channel encodes reasoning quality. Causal ablation confirms the signature traces induction-head circuits. The method generalises to informal chain-of-thought ($d = 0.78$, $p < 10^{-3}$), and in proof search, HFER reranking improves Best-of-16 Pass@1 by $+4.4$–$6.6$\%, matching $98\%$ of the AUC of fully supervised probes with zero labels. Spectral graph analysis is a principled, architecture-aware primitive for reasoning verification.

21.
arXiv (CS.CL) 2026-06-15

The Linguistics Olympiads: Towards a New Corpus for Linguistics Research?

Linguistics olympiad problems (LOPs) are a category of self-sufficient puzzles consisting of a scaled-down corpus representative of certain linguistic phenomena, from which the solver must deduce a primitive set of rules of the language and then translate a new set of elements. The linguistics olympiads (LOs) have become a worldwide phenomenon with 43 different territories taking part in the International Linguistics Olympiad (IOL) 2025. While the typology and solving strategies of LOPs have been analysed, their scientific facet and connections to academic linguistics have yet to be explored. LOPs are directly connected to many linguistic fields, e.g., linguistic typology, linguistic relativity, and linguistics fieldwork. Recently, LOPs have become a research focus as benchmarks for large language models, thus highlighting their usefulness in computational linguistics. Nevertheless, they have not yet been integrated into mainstream linguistics research. This paper attempts to open new directions of including this particular type of puzzle in academic research by offering a structured evaluation of LOPs as linguistic data sources and proposes criteria for their responsible use in academic research. Starting from a set of over 1800 LOPs, this study critically examines the potential of LOPs as a novel corpus for linguistics research by discussing their strengths and limitations as tools, as well as the areas of linguistics into which these problems could fit. This work forms the foundation for a broader initiative aimed at bridging the gap between LOs and academic linguistics, by establishing a robust theoretical framework for LOPs.

22.
arXiv (CS.LG) 2026-06-11

Hierarchical Probabilistic Conformal Prediction for Distributed Energy Resources Adoption

arXiv:2411.12193v4 Announce Type: replace-cross Abstract: The rapid growth of distributed energy resources (DERs) presents both opportunities and operational challenges for electric grid management. Accurately predicting DER adoption is critical for proactive infrastructure planning, but the inherent uncertainty and spatial disparity of DER growth complicate traditional forecasting approaches. Moreover, the hierarchical structure of distribution grids demands that predictions satisfy statistical guarantees at both the circuit and substation levels, a non-trivial requirement for reliable decision-making. In this paper, we propose a novel uncertainty quantification framework for DER adoption predictions that ensures validity across hierarchical grid structures. Leveraging a multivariate Hawkes process to model DER adoption dynamics and a tailored split conformal prediction algorithm, we introduce a new nonconformity score that preserves statistical guarantees under aggregation while maintaining prediction efficiency. We establish theoretical validity under mild conditions and demonstrate through empirical evaluation on customer-level solar panel installation data from Indianapolis, Indiana that our method consistently outperforms existing baselines in both predictive accuracy and uncertainty calibration.

23.
arXiv (math.PR) 2026-06-18

Multi-floor generalization of TASEP

arXiv:2603.13610v2 Announce Type: replace Abstract: We consider an interacting particle system, which generalizes the classical totally asymmetric simple exclusion process (TASEP), in that each site can contain up to a fixed finite number of particles, and the particle movement is governed by a back-pressure (BP) algorithm (also often called MaxWeight). There are $N$ sites (with $N$ finite or infinite), each may contain at most $c$ particles, $1 \le c < \infty$. New particles enter the system at the left-most site $1$ as a Poisson process of rate $\alpha\le 1$, unless site $1$ has $c$ particles. Particles (if any) are removed from the right-most site $N$ as a Poisson process of rate $\beta \le 1$. The left-to-right movement of particles between neighboring sites is governed by the BP rule: one particle moves from site $n$ to $n+1$ at epochs of a rate $1$ Poisson process, as long as the former site has strictly more particles than the latter. When $c=1$, this is the standard TASEP. Our main results address the asymptotics of the stationary distribution of a finite system, and especially the limit of the flux (current) as $N\to\infty$. In particular, we prove that interesting non-trivial phase transitions take place in a system with $c>1$. For example, if $c>1$ and $1/2 \le \beta \le 1$, the maximum limiting flux $1/4$ is achieved as long as $\alpha \ge \alpha_c^*$, where $\alpha_c^* < 1/2$ is some non-trivial threshold. (For the standard TASEP the threshold is $1/2$.) We also put forward a general conjecture about the stationary distribution asymptotics under an arbitrary parameter setting. We illustrate our formal results and the conjecture by simulations, and identify interesting directions for further research.

24.
arXiv (CS.CL) 2026-06-12

Detect, Remask, Repair: Diffusion Editing for Faithful Summarization of Evolving Contexts

Summaries of real-world events can become outdated as contexts evolve and new information arrives. A common response is to generate a new summary from the updated context, but full regeneration discards the previous draft, can obscure what changed, and may be unnecessary when only a few claims are unsupported. We study localized faithfulness repair: updating outdated spans in an existing summary while preserving supported content. We propose DETECT-REMASK-REPAIR, a diffusion-based framework that identifies, remasks, and repairs outdated regions with masked diffusion language models. To evaluate evolving-context summarization, we introduce StreamSum, a benchmark of synthetic event timelines. Experiments on DialogSum and StreamSum show that localized diffusion repair provides a controllable alternative to full rewriting: faithfulness-steered repair improves early drafts, one-step repair reduces repair cost to under half a second, with the framework enabling faithfulness-speed-preservation tradeoffs across datasets. We also find that the framework can provide a post-hoc correction step that improves faithfulness for autoregressive systems.