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The Denario project: Deep knowledge AI agents for scientific discovery

Francisco Villaescusa-Navarro, Boris Bolliet, Pablo Villanueva-Domingo, Adrian E. Bayer, Aidan Acquah, Chetana Amancharla, Almog Barzilay-Siegal, Pablo Bermejo, Camille Bilodeau, Pablo Cárdenas Ramírez, Miles Cranmer, Urbano L. França, ChangHoon Hahn, Yan-Fei Jiang, Raul Jimenez, Jun-Young Lee, Antonio Lerario, Osman Mamun, Thomas Meier, Anupam A. Ojha, Pavlos Protopapas, Shimanto Roy, David N. Spergel, Pedro Tarancón-Álvarez, Ujjwal Tiwari, Matteo Viel, Digvijay Wadekar, Chi Wang, Bonny Y. Wang, Licong Xu, Yossi Yovel, Shuwen Yue, Wen-Han Zhou, Qiyao Zhu, Jiajun Zou, Íñigo Zubeldia

arXiv:2510.26887v1cs.AIcs.CLcs.LGcs.MA

TL;DR

Scientific research involves time-consuming literature review, coding, and writing, motivating tools that assist across the discovery workflow. Denario is a modular multi-agent research assistant evaluated through papers generated across disciplines, with experts finding outputs comparable to good undergraduate or early graduate work produced in about 30 minutes for around $4.

  • Problem

    Scientific research requires extensive time for literature search, learning methods, debugging code, and writing, motivating AI assistance across these tasks.

  • Method

    Denario is a modular multi-agent system that generates ideas, checks literature, plans research, writes and executes code, creates plots, and drafts and reviews papers.

  • Results

    Expert evaluations found Denario-generated papers comparable to work by good undergraduate or early graduate students, produced in about 30 minutes at a cost of around $4 per paper.

  • Takeaways & Limitations

    Denario can rapidly explore broad scientific ideas, while human experts select promising directions and pursue them in greater depth.

  • Takeaways & Limitations

    Denario’s generated papers tend to provide shallower explanations than those written by experienced researchers.

Abstract

from arXiv · show

We present Denario, an AI multi-agent system designed to serve as a scientific research assistant. Denario can perform many different tasks, such as generating ideas, checking the literature, developing research plans, writing and executing code, making plots, and drafting and reviewing a scientific paper. The system has a modular architecture, allowing it to handle specific tasks, such as generating an idea, or carrying out end-to-end scientific analysis using Cmbagent as a deep-research backend. In this work, we describe in detail Denario and its modules, and illustrate its capabilities by presenting multiple AI-generated papers generated by it in many different scientific disciplines such as astrophysics, biology, biophysics, biomedical informatics, chemistry, material science, mathematical physics, medicine, neuroscience and planetary science. Denario also excels at combining ideas from different disciplines, and we illustrate this by showing a paper that applies methods from quantum physics and machine learning to astrophysical data. We report the evaluations performed on these papers by domain experts, who provided both numerical scores and review-like feedback. We then highlight the strengths, weaknesses, and limitations of the current system. Finally, we discuss the ethical implications of AI-driven research and reflect on how such technology relates to the philosophy of science. We publicly release the code at https://github.com/AstroPilot-AI/Denario. A Denario demo can also be run directly on the web at https://huggingface.co/spaces/astropilot-ai/Denario, and the full app will be deployed on the cloud.

1 Introduction

Denario is an AI multi-agent scientific research assistant that supports tasks from idea generation and literature checking through coding, analysis, plotting, and paper drafting and review. The paper evaluates its capabilities across disciplines, discusses limitations and ethical implications, and publicly releases the system.

  • AI assistance targets time-consuming research tasks such as literature search, learning methods, debugging code, and writing, which can otherwise make scientific paper generation take months to years.The intended benefit is enabling scientists to formulate and test hypotheses faster while retaining human involvement.
  • Denario supports end-to-end scientific research by generating ideas, checking literature, developing plans, writing and executing code, making plots, and drafting and reviewing papers.It is designed to accelerate scientific discovery rather than automate science, helping researchers explore broadly before investigating the most promising directions more deeply.
  • The system is evaluated through AI-generated paper drafts spanning disciplines from biology to astrophysics, with domain experts reporting positive and negative aspects.This evaluation is intended to characterize both Denario’s capabilities and limitations across diverse scientific contexts.
  • Denario is publicly released as a user-friendly research assistant intended to help the scientific community accelerate discovery.The paper describes public availability as part of its effort to make the system useful beyond the reported experiments.
  • Denario is positioned within earlier and recent research systems including Robot Scientist Adam, Eve, Automated Statistician, AI Scientist, Google co-scientist, and Agent laboratory.Related tools also address model selection, hypothesis generation, self-driving laboratories, virtual laboratories, multi-agent hypothesis testing, scientific software, algorithm discovery, graph-based agents, and learning from prior work [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21].
  • The paper treats validation standards, ethical considerations, and the relationship between AI-driven research and the philosophy of science as central issues for such systems.Debates about human standards for validating autonomous scientific discoveries motivate dedicated discussion of Denario’s ethical implications.

2 AI multi-agent systems

Denario is a modular AI multi-agent framework that supports specialized research tasks and sequential end-to-end scientific workflows. Its agents use configurable LLMs and coordinated orchestration, including Cmbagent’s Planning & Control strategy.

  • 2 AI multi-agent systems: Denario combines specialized modules and communicating agents to transform input text and data into one or more outputs for scientific research.Agents may operate autonomously or semi-autonomously, while orchestration controls task order, information flow, and coordination.
  • 2.1 Large Language Models: Most Denario agents call multimodal LLMs [24] through specialized prompts, and users can select models from OpenAI, Google, and Anthropic.The system is extensible to additional models, but current choices were selected by trial and error rather than systematic evaluation.
  • 2.2 Multi-Agent Orchestration and Strategy: Denario orchestrates agents with AG2 and LangGraph, with some modules implemented in both frameworks and others in only one.AG2-based modules can follow the Planning & Control strategy implemented in Cmbagent.
  • 2.2.1 Orchestration: AG2 unifies LLMs, tools, and human inputs through composable conversation patterns, while LangGraph represents agents, functions, and tools as graph nodes linked by computation-flow edges.LangGraph also supports shared graph state, static or dynamic graphs, loops, and interrupts.
  • 2.2.2 Planning and Control Strategy: Planning & Control decomposes complex research tasks into subtasks, assigns agents, and executes them under monitoring and adjustment without human-in-the-loop.Cmbagent’s planner and plan reviewer propose and refine the plan, after which a control agent tracks execution status and transfers between agents.
  • 2.2.2 Planning and Control Strategy: Planning is bounded by nsteps, typically producing 3 to 8 steps, while execution is bounded by nrounds = 500 and user-defined code-failure limits.Sessions can terminate positively after completing the plan or abort when failure thresholds or message limits are exceeded; additional failures can arise from provider API limits and unhandled errors.

3 Architecture

This section describes Denario’s modular multi-agent architecture, including components for idea generation, research planning, methodology, analysis, paper drafting, keyword selection, and review. It also outlines the system’s iterative refinement, citation, error-checking, and human-review mechanisms, including the review module’s structured assessment of papers.

  • 3 Architecture: Denario’s modules support either standalone scientific tasks or sequential end-to-end research, with human input usable at any point.The architecture includes idea generation, literature checking, methodology development, analysis, paper writing, and review, with outputs passed through files between modules.
  • 3.1 Input Text: Detailed input text is critical: users should describe the data or problem, data location, desired plots, computational constraints, and relevant library instructions to guide reliable execution.Insufficient dataset structure can cause analysis failure, while vague plotting instructions may yield too few or redundant plots; Denario may also create synthetic data when it cannot read the intended data.
  • 3.2 Idea module: The idea module uses an idea maker and idea hater in an iterative propose–critique loop to produce creative, feasible, relevant, and better-refined research ideas.Denario offers a fast implementation and a more robust Planning & Control implementation; the latter takes about 4 minutes and ∼$1 per idea, versus about 15 seconds for the fast method.
  • 3.3 Literature module: The literature module evaluates novelty by combining the input text and idea with literature searches, returning a literature.md report while leaving final originality judgment to a human.Its Semantic Scholar workflow alternates novelty assessment and API-based retrieval until enough evidence is available or repeated searches find no relevant papers; an alternative uses FutureHouse’s Owl agent.
  • 3.4 Methods module: The methods module converts the input text and project idea into a detailed research plan saved as methods.md, with two implementations available in the current system.The plan specifies the methodology needed to carry out the proposed project.
  • 3.4 Methods module: The methods module offers a fast LangGraph mode and a Planning & Control mode that generate project-specific methodology descriptions without performing analyses.Fast mode uses the input text and idea.md, whereas Planning & Control clarifies hypotheses and assumptions, limits plans to four steps, and dedicates the final step to methodology writing.
  • 3.5 Analysis module: The analysis module uses Cmbagent’s Planning & Control strategy to execute methodologies, producing results.md and generated plots through engineer–researcher workflows.The engineer writes and executes analysis code, while the researcher reports quantitative results, plot interpretations, statistics, and insights for downstream paper writing.
  • 3.6 Paper module: The paper module sequentially drafts sections, integrates and captions plots, refines results, inserts citations, and outputs four LaTeX/PDF checkpoints because compilation errors can persist.It preprocesses inputs, writes the introduction, methods, results, and conclusions, batches figure insertion, retrieves arXiv BibTeX data when citations are enabled, and performs final LaTeX correction.
  • 3.6.1 Keyword Search module: The keyword-search module selects project keywords from UNESCO, AAAI, or AAS taxonomies, with UNESCO narrowing domains, subfields, and areas before choosing the requested number.UNESCO is broad across scientific domains but dates from 1988; AAAI is updated yearly and AI-focused, while AAS is intended for astrophysics papers.
  • 3.7 Review module: The review module converts each PDF page into an image for multimodal evaluation and produces referee.md identifying strengths, flaws, logical problems, and improvement suggestions.Its purpose is to help humans review and filter papers, while enabling human intervention or automatic refinement of generated manuscripts.
  • 3.7 Review module: The module identifies flaws, possible errors, needed revisions, and whether the paper’s conclusions have sufficient evidence.It also distinguishes genuinely surprising poor results from failures caused by an inappropriate strategy.
  • 3.7 Review module: It rates whether the paper merits publication on a scale from 0 (very bad) to 9 (amazing).Bad papers should receive low scores.
  • 3.7 Review module: The module requires its report inside a RE​​VIEW wrapper and can include referee images as embedded base64 PNG data.The prescribed output format is explicitly enforced.

4 Usage

Denario can be used through a Python API or graphical interface, either locally or through web applications. The API supports end-to-end research workflows, while the GUI exposes configurable modules, file handling, and multiple deployment options.

  • 4.1 Python API: The Python API supports an end-to-end workflow from data description and idea generation through novelty checking, method development, analysis, paper writing, and review.Users can execute the API in scripts, Jupyter notebooks, or Google Colab, and can provide ideas or methods themselves.
  • 4.1 Python API: The Python API lets users choose between the default fast LangGraph backend and the Cmbagent backend for idea and method generation.The API also accepts user-supplied ideas and methods from project files or input strings.
  • 4.2.1 Launch locally: The locally installed GUI lets users configure LLM API keys, upload inputs, download generated files, select modules, and tune module options.End-to-end research requires running the modules sequentially, with module inputs and outputs documented in Table 1.
  • 4.2.2 Web application: The web application provides installation-free access through a HuggingFace Spaces demo or deployment on general cloud platforms, but free online resources may be limited.Local use requires installation but can leverage resources such as GPUs or multiple CPUs.

5 End-to-end research examples

This section presents largely automated, end-to-end research examples generated by Denario across diverse scientific and interdisciplinary domains, including physics, astrophysics, biology, medicine, and biomedical data analysis. Together, the examples demonstrate the system’s analytical and manuscript-production capabilities while exposing limitations in contextual guidance, literature integration, methodological precision, interpretation, citation completeness, and scientific reliability.

  • 5 End-to-end research examples: Denario generates mostly hands-off research papers across astrophysics, biology, biophysics, biomedical informatics, chemistry, materials science, mathematical physics, medicine, neuroscience, and planetary science, including interdisciplinary work.Most human involvement consists of providing or adjusting prompts and data; one example uses iterative human feedback through Cmbagent.
  • 5.1 Mathematical Physics. High-level analysis and abstraction of complex structures: the physics of non-linear PDEs: Denario’s Burgers-equation study used PINNs to learn a latent solution space across viscosity values and initial or boundary conditions, enabling analysis of parameter dependence and inverse problems.PINNs minimize squared differential-equation residuals, while multihead training shares a body across parameter-specific heads to capture global solution properties.
  • 5.1.2 Multihead training: Multihead training separates a shared body that learns a high-dimensional latent representation from heads that project it into parameter-specific differential-equation solutions.Constraining the head response can expose the functional basis learned by the model.
  • 5.1.3 Latent space structure with Denario: 97.67% of the variance was described by nearly parallel viscosity-specific manifolds, with each solution represented by a 3-dimensional manifold translated along a 1-dimensional sub-manifold.The generated paper used PCA and subspace-similarity analyses; a misleading prompt caused viscosity variation to be mistaken for different initial conditions, but Denario followed the prompt rather than reproducing literature claims.
  • 5.2 Planetary Science. Mapping Size and Compositional Gradients in the Asteroid Belt: Denario mapped asteroid-belt size, composition, families, and resonance-related structure using density estimation, DBSCAN, GMM clustering, and predictive modeling, finding a shift from S-type asteroids inward to C-type asteroids outward.The clustering reproduced known asteroid families, while the paper’s findings were scientifically sound but not fundamentally new; increasing average size with solar distance was attributed likely to observational bias.
  • 5.2 Planetary Science. Mapping Size and Compositional Gradients in the Asteroid Belt: The asteroid example shows that Denario efficiently documents established knowledge but lacks domain intuition for recognizing subtle novel patterns, motivating human interpretation, validation, and iterative refinement.Predictive modeling based only on orbital data had limited success, and additional parameters such as albedo, spin state, or detailed spectral data could improve it.
  • 5.3 Medicine and Health Services Research. Assessment of Fertility Clinic Outcomes in the United States: For medicine and health-services research, Denario was given 2020–2022 U.S. National ART Surveillance System data covering clinic-level fertility-treatment utilization and success rates from approximately 98% of U.S. ART services.The data distinguish own-egg and donor-egg cycles, first and follow-up treatment, and cumulative or non-cumulative success measures.
  • 5.3 Medicine and Health Services Research. Assessment of Fertility Clinic Outcomes in the United States: Denario characterized overlooked year-to-year variability in U.S. ART clinic performance during COVID-19 using success and efficiency metrics stratified by age and egg source.The analysis used coefficients of variation, ordinary least squares regression, and Spearman correlation, but these standard methods would need reevaluation given the distributional properties of variability measures.
  • 5.4 Chemistry. Molecular dynamics simulations of self-assembling peptides: In peptide molecular-dynamics analysis, increasing contextual information progressed Denario from misidentifying 30 peptides and missing aggregation to routine self-assembly analyses and, with explicit hypotheses, novel multiscale graph analyses.The resulting study analyzed peptide aggregates with graph-theoretical methods and showed that detailed data descriptions and research-direction guidance were needed for Denario to reach its full capability.
  • 5.5 Astrophysics. Properties of recent high-mass binary black hole merger from gravitational wave data: Denario’s GW231123 study explored agreement and disagreement among five waveform-model posterior distributions for the most massive confident black-hole merger detected to date.The high-dimensional posteriors contained complex degeneracies, motivating analysis of robust statistical and astrophysical conclusions about the event.
  • 5.5 Astrophysics. Properties of recent high-mass binary black hole merger from gravitational wave data: Denario analyzed GW231123 posteriors with UMAP, finding consistent clustering among three time-domain models but isolated groups for two frequency-domain models.The analysis also found that physical explanations were independent of hyperparameters and used Jensen-Shannon divergences to compare parameter differences.
  • 5.6 Astrophysics. Impact of Convection and Radiation Pressure on the Dynamics of Roche Lobe Overflow in Binary Systems: Denario’s Roche-lobe-overflow paper quantitatively analyzed force components, captured convection’s importance, and efficiently examined flow streamlines in 3D radiation-hydrodynamic simulations.One generated plot was blank and required a small source-code modification to produce the intended figure.
  • 5.7.1 Input data: The malaria project supplied public single-cell gene-expression and metadata files spanning laboratory and field-derived Plasmodium falciparum parasites across asexual and sexual blood stages.The input invited comparisons between isolates and life stages and proposed identifying low-expression genes preceding coordinated transcriptional changes as candidate regulators.
  • 5.7.2 Description of research output: Denario produced four malaria manuscripts using standard scRNA-seq workflows, including preprocessing, UMAP, clustering, trajectory inference, pseudotime assignment, and varied regulator-identification strategies.Three manuscripts used SCANPY, one used Monocle 3, and some supplemented comparisons with differential-expression analysis using tradeSeq.
  • 5.7.3 Assessment of research output: The malaria manuscripts showed strong Plasmodium knowledge, reconstructed the intraerythrocytic development cycle, described laboratory–field differences, and generally used appropriate standard analysis methods.They also used specific genes as positive controls in some manuscripts and provided plausible explanations involving cell type and data quality.
  • 5.7.3 Assessment of research output: Denario completed the malaria analyses and manuscripts in less than a day, far faster than the multiple days or weeks expected for a human researcher.Open-ended regulator questions elicited four creative analytical approaches, but the resulting candidate-gene claims were not sufficiently supported by the expression changes and variance.
  • 5.7.3 Assessment of research output: The malaria manuscripts poorly connected claims to relevant literature: none cited the dataset’s original analysis, and only 2 of 30 references addressed malaria or Plasmodium.They often cited general reviews or methods instead of closely relevant studies, despite demonstrating substantial biological knowledge.
  • 5.7.3 Assessment of research output: Additional weaknesses included occasional factual errors, mutually exclusive methods presented without specifying the method used, and astrophysics papers that lacked broader literature context.The astrophysics examples were useful for rapid project ideas but were not yet publication-ready and required further refinement.
  • 5.7.3 Assessment of research output: Denario’s biological analyses were impressive in speed and field knowledge but concerning in presentation, interpretation, and comparison with other studies.The assessment also noted occasional missing tables and references, including unresolved question marks for some citations.
  • 5.8 Digital Health. Developing and evaluating step-counting algorithms from wrist- and hip-worn accelerometers: Denario processed the OxWalk dataset of 39 participants to develop or validate step-counting algorithms and compare wrist versus hip placement and 25 versus 100 Hz sampling.The dataset paired four accelerometers with foot-facing video annotations of heel strikes, while metadata enabled exploratory comparisons by age group and sex.
  • 5.8.1 Input data: The input comprised timestamped x-, y-, and z-axis accelerometer signals, heel-strike indicators, and participant age-band and sex metadata across four wrist/hip and frequency combinations.Participants wore synchronized triaxial accelerometers on the dominant wrist and hip, while belt-mounted video annotated purposeful steps during up to one hour of free living [67].

5. Participant sex and age range are provided in metadata.csv

This section evaluates Denario across interdisciplinary research tasks, examining its ability to frame questions, develop analyses, and interpret data in neuroscience, materials science, and astrophysics. It also assesses how prompt specificity and system support affect analytical rigor, reliability, and the need for human refinement.

  • 5.8.3 Assessment of research output: Prompt iteration improved adherence to task requirements, while Denario also reused field practices and proposed novel machine-learning approaches for wearable data.The system followed revised prompts more successfully, applied published models and standard wearable-monitoring metrics or segmentation, and generated ideas retained for future fellowship applications.
  • 5.8.3 Assessment of research output: Denario’s wearable manuscripts exhibited limitations including irrelevant jargon, formatting problems, data-handling errors, and a tendency to build walking classifiers instead of step counters.Novel research questions also produced poorer methods and results, reflecting a trade-off between novelty and manuscript quality.
  • 5.8.3 Assessment of research output: Denario generated useful wearable-monitoring research questions and analyses, but reliable manuscript quality remained limited, favoring exploratory research use.Across seven manuscripts, models examined age, sex, device location, and sampling frequency using F1/AUC for walking detection and MAPE for step counting.
  • 5.9.1 Data generation: The NTL9 study used a 10 µs, 300 K molecular-dynamics trajectory and compared conventional variables, PCA, tICA, and diffusion maps within a hierarchical MSM workflow.The requested pipeline targeted dimensionality reduction, state partitioning, free-energy landscapes, kinetics, mechanistic analysis, and scalability without PyEMMA.
  • 5.9.3 Assessment of research output: The generated NTL9 manuscript identified folded, intermediate, and unfolded states across approaches and linked unfolding to loss of hydrogen bonds and native contacts.It reported successful PCA, tICA, and diffusion-map MSM construction, free-energy minima, and implied-timescale and Chapman–Kolmogorov validation.
  • 5.9.3 Assessment of research output: The NTL9 manuscript lacked sufficient theoretical motivation, literature context, uncertainty estimates, and visible supporting figures despite claims of quantitative kinetic agreement.It omitted error bars or confidence intervals for free-energy, kinetic, and MFPT estimates and did not discuss force-field or sampling limitations.
  • 5.9.3 Assessment of research output: The NTL9 output demonstrated a logical conventional workflow but limited novelty and required considerable manual refinement, contextual analysis, and validation.The assessment characterizes it as a proof of concept for LLM-generated scientific content rather than a sufficiently communicated scientific manuscript.
  • 5.10 Neuroscience. Behavioral Cognitive Decline in Egyptian Fruit-Bats.: The neuroscience study used approximately 40 Egyptian fruit bats with paired behavioral and diffusion-tensor MRI measures, methylome-based ages, and a three-phase foraging-box memory protocol.Each phase lasted three hours; correct food-box locations were changed to assess learning, short-term memory, and long-term memory, with behavior video recorded and coded from per-bat spreadsheets.
  • Behavioral Data collection and analysis: The bat MRI protocol used 7T DTI with 30 noncollinear directions, b = 1000s/mm2, 3 b = 0 images, and 0.5X0.5mm2 in-plane resolution across 34 1mm slices.Scans used an EPI sequence with TR/TE = 4000/19ms and covered the entire bat brain.
  • Bats as an aging model: Denario identified age-related declines in some spatial-cognition parameters and a significant correlation between brain volume and one cognitive measure, but did not perform outlier removal or model comparison.The generated study used mixed-effect generalized linear models, residual QQ plots, and comparisons of age-only versus age-plus-brain-volume models.
  • Bats as an aging model: Brain-volume analysis found no significant correlation with age and was limited by nonoptimal mean-diffusivity contrast images and the absence of voxel-level regional analysis.The analysis therefore tested a relatively naive whole-brain-volume hypothesis rather than regional structural changes.
  • 5.11 Materials Science. Confined Water Dynamics at Functionalized Graphene Interfaces: Across 91 molecular-dynamics trajectories, polar -COOH and -OH groups produced structured interfaces with suppressed diffusion of 0.65-1.30 × 10−5 cm2/s, whereas =O and -CH3 yielded 1.15-1.35 × 10−5 cm2/s.Surface coverage amplified effect intensity without changing its fundamental chemistry-dependent pattern across electrolyte concentrations.
  • 5.11 Materials Science. Confined Water Dynamics at Functionalized Graphene Interfaces: The graphene analysis combined precomputed diffusion, radial-distribution, and density-profile data with MSD, diffusion, RDF, heatmap, ranking, and summary-table analyses across functionalization, coverage, and salt concentration.The planned outputs included comparisons at fixed coverage, salt effects, top and bottom systems, and statistical summaries.
  • 5.11.1 Assessment of Strengths: Denario achieved 100% context understanding and identified analytical methods correctly in 75% of cases, but generated only basic novel insights across successful prompts.Performance degraded systematically from context understanding toward novel insight generation, with complete failures on prompts 4 and 8.
  • 5.11.1 Assessment of Strengths: Denario recognized confined-water dynamics, surface-functionalization effects, nanofluidic applications, and the multi-parameter roles of functional groups, coverage, and concentration.This contextual recognition was universal across all 8 successful prompts.
  • 5.11.1 Assessment of Strengths: Denario identified MSD, density-profile, hydrogen-bond, and radial-distribution analyses, recognized qualitative mobility trends, and processed all 91 trajectories when functioning properly.It associated hydrophilic groups (-COOH, -OH) with enhanced structuring and reduced mobility, and hydrophobic (-CH3) or weakly polar (=O) groups with minimal impact.
  • 5.11.2 Assessment of Weaknesses: Denario exhibited order-of-magnitude diffusion errors, inconsistent numerical precision, systematic omissions of CH3 and =O groups, and incomplete coverage–concentration exploration.CH3 and =O groups were analyzed in only 60% of cases, despite their importance for the hydrophobic–hydrophilic spectrum.
  • 5.11.2 Assessment of Weaknesses: Denario failed completely on 20% of prompts and showed context overflow, missing computational libraries, formatting errors, and evidence of relying on memorized information instead of supplied data.Prompts 4 and 8 produced total failures with five distinct failure modes identified.
  • 5.11.2 Assessment of Weaknesses: Denario often missed that functional-group chemistry is primary while coverage is a secondary amplifier, and did not consistently recognize concentration-independent structure–property relationships.These omissions prevented reliable identification of key design principles in the published work.
  • 5.11.2 Assessment of Weaknesses: Broad prompting produced partial, basic analyses lacking quantitative rigor, systematic completeness, advanced computational methods, and creative follow-up hypotheses for materials-science discovery.Successful prompts generated only standard statistical tests, while omitting methods such as free-energy calculations, transition-state analysis, machine learning, and proposals for new functional groups.
  • 5.11.2 Assessment of Weaknesses: Detailed prompts enabled Denario to analyze 91 systems across functionalization, coverage, and salt concentration, quantify interactions, and derive mechanistic design principles using advanced analyses.The resulting work included SHAP feature-importance analysis, interfacial-water structure–dynamics correlations, and explicit separation of interfacial and bulk regions to identify finite-size effects.
  • 5.12 Astrophysics. Impact of feedback on stellar mass - black-hole mass relation.: The astrophysics dataset description was insufficient because galaxy-property variation ranges were unspecified, potentially hindering highly specific research design by downstream methods agents.The dataset comprised 1,000 CAMELS galaxy catalogs, with stellar mass, black-hole mass, star-formation rate, and six cosmological or feedback parameters [77].
  • 5.12 Astrophysics. Impact of feedback on stellar mass - black-hole mass relation.: Without human-in-the-loop intervention, Cmbagent reorganized the 1,000-catalog dataset into galaxies full optimal.parquet and catalog params optimal.parquet with an accompanying usage guide.The generated organization provided a full galaxy DataFrame with one row per galaxy, 17 galaxy features, catalog number, and six cosmological or astrophysical parameters.

2. Catalog-level DataFrame (‘catalog params optimal.parquet’)

The catalog-level data contain one row per simulation catalog, with cosmological, astrophysical, and derived galaxy properties stored in a compressed Parquet file. Denario used these data and merger-tree inputs to generate analyses spanning feedback effects, quantum-inspired tensor compression, and cosmological-parameter estimation.

  • 2. Catalog-level DataFrame (‘catalog params optimal.parquet’): Each row represents one simulation catalog, and the DataFrame includes a catalog number plus six cosmological or astrophysical parameters.The catalog-level file is stored in gzip-compressed Parquet format.
  • 2. Catalog-level DataFrame (‘catalog params optimal.parquet’): The MBH−M∗ analysis models log10(MBH) = α + β log10(M∗) across low-, intermediate-, and high-stellar-mass bins, using XGBoost, SHAP values, and Huber-loss regression.The second pass replaced the initial linear-regression and random-forest approach with more sophisticated methods while retaining the core analysis.
  • 2. Catalog-level DataFrame (‘catalog params optimal.parquet’): Supernova feedback most strongly affects the MBH−M∗ relation in low-mass galaxies, whereas AGN feedback dominates in massive galaxies, with cosmological parameters remaining important secondary factors.The study identifies this as a new result in CAMELS data with potentially important theoretical implications.
  • 5.13 Quantum physics, machine learning & cosmology. Cosmological parameters from merger trees: QITT compresses each merger tree’s 60-substructure, 74-feature tensor into a latent representation whose optimal reduced dimensionality is 202.The representation combines physical substructure properties with graph-neural-network topological embeddings before tensor-train compression.
  • 5.13 Quantum physics, machine learning & cosmology. Cosmological parameters from merger trees: Linear regression with global merger-tree features slightly outperforms QITT features while accurately constraining both Ωm and σ8, suggesting simple tree-level features may suffice.The comparison used physical substructure features, global tree features, and topological substructure features without QITT compression as baselines.
  • 5.13 Quantum physics, machine learning & cosmology. Cosmological parameters from merger trees: The workflow decomposes merger trees into substructures, trains graph neural networks unsupervised, and compresses the resulting data with quantum-inspired tensor trains.Node features include halo mass, concentration, Vmax, and scale factor, targeting Ωm and σ8; each simulation has 25 randomly chosen merger trees.
  • 5.13 Quantum physics, machine learning & cosmology. Cosmological parameters from merger trees: The quantum-inspired merger-tree paper was accepted at Agents4Science 2025, receiving the maximum score among 48 acceptances from approximately 250 submissions.Only five fully AI-generated papers were accepted, including this one.

6 Discussion

Denario shows substantial promise for rapid, transparent, interdisciplinary research assistance, but its outputs can fail scientifically and require rigorous human verification. The authors identify shortcomings in mathematical reasoning, citations, depth, coding, and workflow robustness, alongside concrete plans for improvement.

  • 6.1.1 Cylic peptide generation: Denario hallucinated a cyclic-peptide paper and plots despite missing the numerical solver, while implementations produced geometrically flawed structures even with detailed requirements.The case underscores the need to verify source code and raw data, since plausible strategies did not translate into valid solutions.
  • 6.1.2 Pure Mathematics: Five papers on an open pure-mathematics problem mimicked mathematical form but lacked formal logic, proofs, coherent development, and mathematically meaningful results.They also showed decorative or misused citations, template-like prose, and vacuous definitions, illustrating that stylistic imitation does not reproduce mathematical practice.
  • 6.2 Validation and Evaluation: Validation requires checking whether claims are true and whether code and results provide sufficient evidence, with human experts ultimately responsible despite Denario’s checking agents.In one astrophysics case, independent code reproduced very similar correlation metrics and supported the same conclusion without access to Denario’s code.
  • 6.2 Validation and Evaluation: Expert scores from 0 to 10 placed most generated papers above average, with some scoring 8 or 9, but the subjective ratings only indicate generative capability rather than rigorous quality.Figure 11 shows the distribution, with three papers below the average score of 5.
  • 6.3 Advantages and limitations: Denario can expand researchers’ ideas, perform shallow analyses quickly, support interdisciplinary connections, expose risky ideas, and free scientists to focus on higher-level research under supervision.Its generated text, plots, and code also provide transparency and support reproducibility.
  • 6.3 Advantages and limitations: Current limitations include shallow explanations, less-relevant citations, LaTeX and figure-label errors, and coding failures caused by package changes or parallel execution.The authors suggest improving task-specific agents, reasoning, and error-checking agents to address these problems.
  • 6.4 Future directions: Future work will add asynchronous execution, feedback agents, parallelized and adaptive workflows, richer paper-writing context, local-model support, easier interfaces, and systematic benchmark-based evaluation.These changes target speed, cost, robustness, planning, user control, accessibility, and research-assistance quality.

7 Ethical implications and scientific challenges

The section argues that Denario and similar AI agents could improve scientific work but raise substantial ethical, epistemic, and institutional challenges. Their use may reshape scientific knowledge, legitimacy, innovation, and responsibility, requiring validation, accountability, democratized access, and renewed philosophical reflection.

  • 7.1 Ethics: AI-driven research may produce low-quality or malicious publication floods, distort incentives, obscure authorship and responsibility, restrict access, and consume unsustainable resources.These risks include inflated output and citations, unclear professional credit and accountability, unequal participation, environmental costs, and agenda-driven claims entering scientific corpora.
  • 7.1 Ethics: Responsible use could improve research quality by freeing researchers’ time for deeper thinking, whereas generating papers with little validation would degrade quality.The authors favor Denario as an assistant for tasks such as idea development, writing, debugging, and exploration, while emphasizing that quality depends on how it is used.
  • 7.2.1 The nature of scientific knowledge in AI-driven science: LLMs challenge traditional scientific knowledge by potentially constituting research programmes grounded in probabilistic linguistic modeling rather than human-understandable causal or explanatory theories.Their outputs can generate predictions and connections that are not always interpretable or falsifiable in Lakatosian terms, raising questions about whether progress requires a theoretical core.
  • 7.2.2 The nature of scientific legitimacy, quality, and purpose in AI-driven science: LLMs act as opaque epistemic agents whose performance-based outputs reshape scientific legitimacy, evidence, explanation, and the balance between human understanding and statistical utility.Their infrastructural influence can determine what is written, cited, or ignored, while their lack of causal understanding creates challenges for judging knowledge produced without experiential or semantic grounding.
  • 7.3.1 AI agent-driven science as an enabler of innovation: By generating hypotheses, synthesizing literature, and recombining cross-disciplinary knowledge beyond individual human scale, LLMs could catalyze a paradigm shift in scientific practice.Their participation may challenge the centrality of singular human cognition, creativity, and interpretive judgment, while enabling epistemic pluralism and unexpected analogies.
  • 7.3.2 AI agent-driven science as a stifling, homogenizing force: AI agent-driven science could instead produce perpetual normal science by extending training-set knowledge, reinforcing institutional biases, and accelerating feedback loops from AI-generated literature.Convergence on similar data, architectures, and desired outcomes could reduce paradigm-shifting work and create a form of scientific homogenization or monism.
  • 7.3.2 AI agent-driven science as a stifling, homogenizing force: Reducing homogenization requires architectures that preserve human involvement, deliberate training-data practices, democratized access, and changes to scientific incentives and funding.The proposed response spans agent design, computer science, career evaluation, funding mechanisms, and access to tools, skills, and infrastructure.
  • 7.4 Conclusions from philosophy of science: The philosophical conclusion is that AI agents may outsource scientific judgment and meaning, making coherence and plausibility substitutes for theoretical depth, causal understanding, and validation.The section therefore calls for reevaluating what counts as knowledge, explanation, progress, and responsible scientific practice in an AI-mediated epistemic environment.

8 Summary and Conclusions … C. State Partitioning and Clustering

This section synthesizes Denario’s capabilities, evaluations, and limitations alongside AI-generated analyses spanning astrophysics, biology, biophysics, biomedical informatics, and molecular dynamics. Across these studies, it summarizes methods and findings involving scientific modeling, clustering, dynamic systems, biological trajectories, sensor-based prediction, and conformational-state analysis.

  • 8 Summary and Conclusions: Denario supports idea generation, literature checking, research planning, coding, plotting, paper drafting, and paper review through modular agents.The system can also execute these modules sequentially in end-to-end mode from general instructions.
  • 8 Summary and Conclusions: Denario is intended to accelerate scientific discovery rather than automate science, with AI scanning broadly for promising directions and human experts selecting and pursuing ideas in depth.The authors characterize these broad AI explorations and focused human investigations as complementary approaches.
  • 8 Summary and Conclusions: Expert evaluations found Denario’s generated papers comparable to work by a good undergraduate or early graduate student, taking around 30 minutes per paper at a cost of around $4.The authors also report discussing failure modes, validation, evaluation, advantages, limitations, ethics, and philosophy of science.
  • 8 Summary and Conclusions: The authors note that Denario’s current papers lack the breadth and reach of those written by experienced researchers, while benchmarking and risk assessment remain unaddressed active research areas [99].Whether future LLMs or more specialized multi-agent systems can close this gap remains an open question.
  • Initial Condition Encoding: The PINN latent representation occupies an effectively 6-dimensional global subspace capturing over 99% of variance, while each of 25 initial conditions forms a distinct approximately 3-dimensional affine manifold.The study analyzes latent vectors from a 10-dimensional representation of a PINN solving the 2D Burger’s equation using PCA and subspace similarity measures.
  • Initial Condition Encoding: Changing the initial condition primarily translates these approximately 3-dimensional manifolds along a nearly one-dimensional path aligned with the dominant global principal component, and their average subspace similarity exceeds 0.98.The manifolds are therefore nearly parallel, with only subtle low-dimensional orientation changes, indicating an efficient and structured encoding.
  • 3.2. Intrinsic dimensionality of per initial condition manifolds: 97.48% of per-initial-condition variance is captured by exactly three principal components across all 25 initial conditions, with the fourth component contributing below 2% on average.The resulting 3D affine manifolds are consistent within the 10D latent space and show limited nonlinear deviations.
  • 3.3. Geometric arrangement of manifold centroids: 99.86% of centroid variance lies along the first centroid principal component, with initial conditions 0–24 forming an almost linear sequence in that direction.Changing the initial condition therefore primarily translates each 3D latent manifold along a nearly one-dimensional path.
  • 3.4. Comparison of manifold orientations: 0.986 is the average pairwise subspace similarity across initial conditions, with a 0.014 standard deviation and 0.954 minimum, indicating nearly parallel 3D manifolds.Orientation differences are systematic: the first PCA components of the vector sets explain 85.45%, 80.04%, and 97.67% of the variance for the first, second, and third principal vectors, respectively.
  • 3.5. Relationship between per initial condition structures and global structure: 99.66% of each initial condition’s intrinsic variance is captured by the global 6D subspace on average, with a 99.24% minimum, while centroid position tracks Global PC1.The latent organization is hierarchical: each initial condition selects a 3D affine manifold within a common 6D subspace, translating it along a nearly one-dimensional path.
  • 3.6. Synthesis and interpretation: The PINN learns a disentangled representation in which intrinsic spatiotemporal dynamics occupy a common 3D structure, while initial conditions primarily induce translation and minor orientation adjustments.This organized geometry avoids 25 unrelated high-dimensional representations and suggests an efficient, potentially interpretable encoding of the essential physics.
  • 3.7. Limitations and future directions: The PINN conclusions are limited by reliance on linear PCA, fixed viscosity, 25 initial conditions, and one PDE and architecture, motivating nonlinear methods and broader parameter, dataset, PDE, and architecture studies.Future work also includes relating initial-condition properties to centroid positions and manifold orientations to clarify their physical meaning.
  • 4. CONCLUSIONS: The conclusion reports a 6D global representation, consistent approximately 3D per-initial-condition affine manifolds, nearly one-dimensional centroid translation, and average inter-manifold similarity exceeding 0.98.These results support a structured, efficient separation between initial-condition effects and intrinsic dynamics in the PINN latent space.
  • A.2 Planetary science: 35,623 main-belt asteroids reveal increasing size with semimajor axis, S-type inner-belt to C-type outer-belt zoning, clustered dynamical groups, and resonance-driven depletion of smaller asteroids.Predictive modeling finds that orbital location captures population-level trends but has limited power for individual asteroid properties, consistent with stochastic collisional effects.
  • 3.1. Global properties and bivariate correlations of the main-belt population: The refined sample contains 35,623 asteroids, dominated by S-types (44.8%), followed by C-types (17.8%), X-types (12.0%), V-types (7.0%), and B-types (4.6%).The sample requires complete diameter, semimajor-axis, eccentricity, inclination, and spectral-type data and is restricted to 2.0 < a < 3.5 AU, e < 0.4, and i < 30°.
  • 3.1. Global properties and bivariate correlations of the main-belt population: The bivariate analysis finds r = 0.427 between log10(diameter_km) and semimajor axis and r = 0.251 between semimajor axis and inclination, while scatter plots show Kirkwood-gap voids.S-types concentrate in the inner belt, C- and X-types in the outer belt, and V-types form a compact semimajor-axis–inclination distribution characteristic of a collisional family.
  • 3.2.1. One-dimensional gradients along the semimajor axis: Mean log10(diameter_km) rises from approximately 0.56 (∼3.6 km) at 2.1–2.4 AU to over 0.88 (∼7.6 km) at 3.1–3.2 AU, with differences across bins highly significant (p ≈0).The Kruskal-Wallis H-test confirmed the size gradient, which may reflect disk conditions or stronger collisional grinding in the inner belt.
  • 3.2.1. One-dimensional gradients along the semimajor axis: S-types decline from ∼75% at 2.2 AU to less than 10% at 3.2 AU, whereas C-types increase from below 5% to ∼47%, with a distinct V-type peak near 2.3–2.4 AU.A chi-squared test found the spectral-type variation with orbital distance highly significant (p ≈0); the pattern is interpreted in relation to the protoplanetary disk’s thermal structure and the Vesta family.
  • 3.2.2. Two-dimensional distribution in orbital space: Two-dimensional heatmaps confirm increasing asteroid size with semimajor axis across eccentricities and inclinations, with S-types concentrated inward and C-types prevalent in the outer belt, especially at higher inclinations.These maps extend the one-dimensional gradients across the full orbital-parameter range.
  • 3.3.1. Kernel density estimation of orbital space: KDE maps place the highest asteroid concentrations at 2.2–2.8 AU with e < 0.2 and i < 10°, where small-to-intermediate bodies dominate, while the largest asteroids are sparser and preferentially outer-belt.The KDE provides a smooth orbital-density representation and is consistent with the observed outward size gradient; the broader workflow also standardizes orbital elements for clustering and evaluates diameter and spectral-type prediction models.
  • 3.3.2. Unsupervised clustering: identifying dynamical groupings: DBSCAN identified 38 dense asteroid clusters and classified 14.25% of asteroids as noise, supporting a belt composed of compact families embedded in diffuse background material.The neighborhood radius was selected from the k-distance plot’s elbow.
  • 3.3.2. Unsupervised clustering: identifying dynamical groupings: GMM selected 10 components using BIC, aligning with known dynamical regions and families, including Vesta-associated Cluster 7 and C-type-rich outer-belt Clusters 6 and 9.Cluster 7 contained 25% V-types; Clusters 6 and 9 contained 55% and 43% C-types, respectively.
  • 3.3.3. Predictive modeling: the limits of location: Orbital location predicts population-level patterns but poorly predicts individual asteroid properties: XGBoost diameter regression reached R2 = 0.22, while Random Forest spectral classification achieved 53% accuracy.Semimajor axis dominated spectral-type prediction; S-types reached an F1-score of 0.70, whereas macro-averaged F1-score was 0.16.
  • 3.4. The influence of mean-motion resonances: Kirkwood gaps significantly deplete asteroid density and alter size distributions, with mean log10(diameter_km) of 0.722 inside and 0.739 adjacent to gaps versus 0.670 in the background.The Kruskal-Wallis test gave p ≈ 10^-174, consistent with preferential removal of smaller bodies by size-dependent dynamical drift.
  • 3.4. The influence of mean-motion resonances: Resonances also modify composition: X-types comprise 18.2% inside gaps versus 9.8% in the background, while S-types are slightly depleted.A chi-squared test yielded p ≈ 10^-129, indicating compositionally non-neutral dynamical clearing.
  • 3.5. Synthesis: The synthesis identifies asteroid-belt architecture as the combined result of primordial composition and size gradients, collisional evolution, asteroid families, planetary resonances, and non-gravitational forces.Population-level trends are statistically clear, but stochastic collisional histories limit prediction of individual asteroid properties.
  • 4. CONCLUSIONS: The conclusion analyzes 35,623 main-belt asteroids with binning, KDE, DBSCAN, GMM, regression, classification, and resonance analyses to quantify orbital, compositional, and size structure.It maps inner-belt S-type dominance, outer-belt C-type dominance, increasing size with semimajor axis, and family-level dynamical organization.
  • A.3 Medicine and Health Services Research: The ART study uses 2020–2022 NASS clinic-level data to quantify year-to-year success and efficiency variability by egg source and age, using CV, SD, correlations, and regression.It reports substantial variability, higher volume-associated variability in some success rates, state-specific but non-uniform associations, and modest explanatory power of clinic volume and state.
  • 2.6. Computational Environment: Analyses used Python 3.9 with pandas, NumPy, SciPy, and statsmodels, with parallel processing where applicable and code plus intermediate data managed for reproducibility.The statistical workflow included descriptive summaries, Spearman correlations, Kruskal–Wallis tests, and OLS regression across egg-source and age strata.
  • 3.1. Data cohort and preparation: The dataset contained 6,800 clinic-year-stratum combinations from 510 clinics, with highly right-skewed clinic volumes and uneven geographic coverage across states.Data were stratified by egg source and age group, and clinic volume was represented by the maximum cycle count for each clinic-year-stratum.
  • 3.2. Descriptive analysis of ART metrics (2020-2022): ART metrics showed marked age-related and inter-clinic differences: own-egg success rates decreased with age, while Avg_IntendedRetrievals_LB increased and Avg_Transfers_IntendedRetrieval generally remained below 1.0.In 2020, mean Perc_LB_IntendedRetrieval ranged from 15.9% for patients <35 to 1.3% for patients >40; the 2022 mean for ages 35–37 rose to 27.2%.
  • 3.5. Data limitations and noteworthy observations: Donor_Egg_LB_Rate was 3.2% in 2020 and 3.9% in 2021 but 0.0% for all 457 available 2022 clinic-year-stratum instances, making 2022 comparisons unreliable.The anomaly also produced median SD and CV values of 0.0% for this metric, while analyses involving 2022 require caution.
  • 3.3. Variability in ART clinic performance (2020-2022): Year-to-year variability was substantial, including a median SD of 3.70 and median CV of 86.6% for own-egg Perc_LB_IntendedRetrieval, with CVs generally higher in older age groups.Other medians included SD/CV values of 3.56/25.1% for Perc_LB_ActualRetrieval, 0.25/53.9% for Avg_Transfers_IntendedRetrieval, and 1.62/92.9% for Avg_IntendedRetrievals_LB.
  • 3.4.2. Association with geographic location (state): State-level differences in variability were generally limited and inconsistent, with only isolated significant Kruskal–Wallis results and some adjusted state effects for specific metrics and strata.After adjustment, Nevada and Virginia exceeded California for CV_Perc_LB_IntendedRetrieval among patients <35, while North Carolina exceeded California for CV_Donor_Egg_LB_Rate.
  • 3.4.3. Multivariable OLS regression analysis: OLS models explained only a modest share of variability, with typical R-squared values below 0.10 to around 0.19, and some CV models violating normality or homoscedasticity assumptions.These diagnostics require caution when interpreting the linear associations, particularly for CV outcomes.
  • 3.4. Correlates of performance variability: Higher clinic volume was associated with greater success-rate variability but lower efficiency-metric variability, consistently in correlations, volume-quartile tests, and adjusted regressions.For example, SD_Perc_LB_ActualRetrieval had a volume coefficient of 0.0041 (p < 0.001), whereas CV_Avg_Transfers_IntendedRetrieval had a coefficient of -0.0235 (p < 0.001).
  • 3.5. Data limitations and noteworthy observations: NASS limitations included exclusion of percentage live birth per transfer, anomalous 2022 donor-egg live birth rates of 0.0% for all clinics, and incomplete measures of pandemic effects.Clinic volume based on stratum cycle counts was treated as a reasonable but potentially nuanced proxy.
  • 4. CONCLUSIONS: Higher clinic volume was associated with greater variability in own-egg and donor-egg success rates but lower variability in some efficiency metrics, while volume and state explained only modest variance.Geographic associations were less consistent than clinic-volume associations.
  • 4. CONCLUSIONS: ART clinic performance and efficiency metrics showed substantial year-to-year variability from 2020 to 2022, highlighting instability during a period of potential external stress.The analysis used CV and SD across success and efficiency metrics stratified by egg source and age group.
  • 1. INTRODUCTION: The KYFIL study represented peptide aggregates as dynamic coarse-grained peptide graphs and fine-grained amino-acid graphs to quantify evolving structure during equilibrium molecular dynamics.The framework analyzed connectivity, density, centrality, clustering, and spectral properties at both scales.
  • 2.6. Development of a Stable Aggregation Order Parameter: A composite order parameter combining largest-aggregate size with internal fine-grained density improved stability compared with aggregate size alone.Candidate parameters also incorporated fine-grained Fiedler value or clustering coefficient, with stability compared primarily using coefficient of variation.
  • and Splitting: Aggregates preceding splitting exhibited lower density and spectral connectivity at both peptide and amino-acid levels, identifying multiscale structural signatures of fragmentation risk.The study tracked aggregate histories and compared pre-split properties with stable aggregates.
  • 3.1. System equilibration and simulation setup: The framework represented peptide aggregates as evolving coarse-grained peptide networks and fine-grained amino-acid networks throughout the 100–500 ns equilibrium trajectory.Graphs used a 4.0 Å heavy-atom contact cutoff; coarse-grained nodes were peptides, while fine-grained nodes were amino acids within aggregates.
  • 3.3.1. Coarse-grained peptide network properties: The coarse-grained network remained moderately connected, with mean edge count 35.392 and density 0.081, while its dominant aggregate averaged 24.196 of 30 peptides and fluctuated substantially.The LCC’s mean Fiedler value was 0.107 with high variability, indicating changing structural robustness and susceptibility to partitioning.
  • 3.3.2. Fine-grained amino acid network properties (within the LCC): Fine-grained networks within the largest aggregates were sparse, averaging density 0.026, and their near-zero Fiedler value indicated loosely connected or fragmented amino-acid contact subgraphs.Despite sparse overall connectivity, the average fine-grained clustering coefficient was 0.559, indicating localized dense contacts within the fragmented network.
  • 3.4. Development and validation of stable aggregation order parameters: The composite OP_Size_x_FG_Density was the most stable tested order parameter, with mean 0.585 and CoV 7.07%, compared with 22.85% for LCC_Size alone.OP_Size × FG_Fiedler was uninformative because FG Fiedler values were near zero, while OP_Size_x_FG_Clustering had CoV 23.75%.
  • 3.5. Relationship between multiscale graph features and aggregate dynamics: Tracking identified 2832 aggregate instances, 2830 formation events, 2831 dissolution events, and 48 potential splitting events, demonstrating continuous aggregate rearrangement.These events enabled comparison of structural properties before splitting with those of stable aggregates.
  • 3.5.1. Correlation of aggregate longevity with graph properties: Aggregate longevity showed only weak correlations with average graph properties, including negative correlations with CG density (r = −0.228) and FG density (r = −0.233).The weak relationships indicate that persistence depends on multiple factors beyond simple time-averaged structural properties.
  • 3.5.2. Structural signatures of aggregate splitting events: Pre-split aggregates had lower CG density (0.1259 vs 0.2833), CG Fiedler value (0.0758 vs 0.2524), and FG density (0.0307 vs 0.0715) than stable aggregates.FG Fiedler values remained near zero in both groups, so they did not discriminate splitting; reduced connectivity and packing across scales characterized instability.
  • 4. CONCLUSIONS: Overall, aggregate stability depended on multiscale contact networks rather than size or compactness alone, with reduced connectivity and packing density predisposing aggregates to fragmentation.The conclusions present dynamic multiscale graph analysis as a quantitative tool for understanding peptide self-assembly and guiding sequence design for enhanced aggregate stability.
  • Physics-Informed Discrepancy Decomposition and Robust Astrophysical Inference for GW231123: No key astrophysical parameter for GW231123 is robustly constrained across all five waveform models, so waveform-model systematics can exceed statistical uncertainties.The study concludes that firm astrophysical interpretation requires accounting for model-dependent biases, especially for high-mass, precessing mergers.
  • 2.3. High-Dimensional Degeneracy and Discrepancy Analysis: UMAP embeddings separate the five waveform models into distinct clusters in the high-dimensional parameter space, revealing systematic model-dependent posterior structure.The analysis combines all 13 physical parameters after standardization and projects them into two dimensions for visualization of degeneracies and separation.
  • 2.4.3. Correlation of Discrepancies with Model Physics: The individual spin and orientation subspace shows the most severe model dependence, linked to differing treatments of spin precession, while remnant properties are sensitive to merger-ringdown modeling.The individual-spin subspace contrasts full precessional dynamics with simplified twisting-up formalisms; remnant properties also depend on higher-order waveform modes.
  • 2.2. Exploratory Data Analysis and Baseline Comparison: The analysis uses one-dimensional summary statistics, Jensen-Shannon Divergence, 1-Wasserstein distance, and UMAP to establish baseline and high-dimensional disagreement before subspace decomposition.The pairwise divergence analysis yields 5x5 symmetric matrices for each key astrophysical parameter.
  • 2.4. Physics-Informed Discrepancy Decomposition: The physics-informed decomposition quantifies pairwise multi-dimensional JSD within four physical subspaces: mass and distance, effective spin, individual spin and orientation, and remnant properties.Each subspace produces a separate 5x5 discrepancy matrix, enabling targeted comparison of model disagreements.
  • 2.5. Robust Astrophysical Inference: Parameters classified as robust receive combined-model consensus medians and 90% credible intervals, while model-dependent parameters are reported using the range of model medians and physics-informed explanations.Robustness is assessed using pairwise divergence thresholds and overlap of medians and credible intervals.
  • 3.1. Baseline comparison: Significant divergence in key physical parameters: The secondary-mass median ranges from 110.04 M⊙–111.10 M⊙ for NRSur7dq4, SEOBNRv5PHM, and IMRPhenomTPHM to 55.08 M⊙ for IMRPhenomXO4a and 93.33 M⊙ for IMRPhenomXPHM.This disagreement indicates model-dependent mass-ratio inference and propagates to effective spin and redshift.
  • 3.1. Baseline comparison: Significant divergence in key physical parameters: The chi_eff median spans 0.04 for IMRPhenomXPHM to 0.44 for SEOBNRv5PHM and IMRPhenomTPHM, whereas chi_p varies only from 0.73 to 0.82.The results therefore show large model dependence in effective spin but consistently high inferred precession magnitude.
  • 3.1. Baseline comparison: Significant divergence in key physical parameters: JSD values frequently exceed 0.6 for mass and redshift, with IMRPhenomXPHM inferring redshift median 0.17 versus 0.58 for IMRPhenomXO4a.These one-dimensional posterior disagreements indicate near-complete non-overlap and substantial waveform-induced systematic uncertainty.
  • 3.2. High-dimensional degeneracy and model clustering: UMAP separates the models into a core cluster of NRSur7dq4, SEOBNRv5PHM, and IMRPhenomTPHM, while IMRPhenomXO4a and IMRPhenomXPHM form isolated clusters.The isolated models differ physically in their treatments of higher-order modes and spin precession, whereas the core models provide more consistent dynamics.
  • 3.3.3. Individual spin & orientation subspace: Individual spin and orientation show the strongest model dependence, with many JSD values approaching 0.693 because simplified twisting-up and full dynamical precession formalisms produce different posteriors.The decomposition attributes disagreements across physical subspaces to specific waveform approximations.
  • 3.3.1. Mass & distance subspace: The mass-and-distance subspace has many JSD values above 0.6, showing that masses and redshift are strongly degenerate with waveform modeling and are not robustly constrained.Effective-spin disagreements also range from JSD 0.636 between IMRPhenomXPHM and IMRPhenomTPHM to 0.043 between SEOBNRv5PHM and IMRPhenomTPHM.
  • 3.3.4. Remnant properties subspace: Remnant properties remain model-dependent, with IMRPhenomXPHM predicting final spin median 0.71 versus 0.81–0.89 for other models, while SEOBNRv5PHM and IMRPhenomTPHM have JSD 0.051.Differences are linked to merger-ringdown modeling and higher-order waveform modes.
  • 3.4. Robust astrophysical inference for GW231123: No key astrophysical parameter for GW231123 is robust across all five waveform models, with systematic differences precluding consensus measurements.Robustness required maximum pairwise JSD below 0.05 and median-value ranges below 10%.
  • 4.3. Implications for Astrophysical Inference: For GW231123, mass_2_source varies from 55.1 M⊙ to 111.1 M⊙ and chi_eff from 0.04 to 0.44, hindering firm conclusions about the binary’s formation history.The study attributes dominant biases primarily to spin-precession and merger-ringdown treatments and advocates explicit waveform-systematics modeling.
  • Simulation Analysis: A high-resolution 3D red-supergiant snapshot shows intermittent, clumpy mass transfer with no stable L1-crossing stream; broad plume-like outflows instead resemble a convection-driven wind.Radiation pressure is initially weak near the stellar surface but becomes the dominant accelerating force in lower-density regions away from the star.
  • 2.2. Comprehensive 3D statistical characterization of mass flux: The analysis quantified mass-flux intermittency and clumpiness through 3D vector fields, regional PDFs, and mean, variance, skewness, and kurtosis across the RSG surface, L1 vicinity, and accretion stream.Mass flux was defined as J = ρv, with radial component Jr = ρ · vel1 and magnitude |J| analyzed using logarithmic binning where needed.
  • 2.3. Identification and quantification of coherent structures: Velocity-gradient decomposition and the Q-criterion identified vortical regions where Q > 0, while correlation functions, structure functions, and spectra probed anisotropy, turbulent scales, and convective-cell sizes.The spectral analysis used density, kinetic energy, and mass-flux magnitude in the L1 vicinity and produced P(k) versus k distributions.
  • 2.3.4. Unsupervised flow regime classification: K-means clustering classified flow regimes from normalized log-density, log-pressure, Mach number, velocity divergence, and Q-criterion features, then mapped spatially distinct clusters to physical states.Cluster interpretation included high-velocity low-density outflow, turbulent convective plume, and quasi-static envelope regimes.
  • 2.4. Mapping and quantifying instantaneous mass transfer pathways: Streamline tracing from 10,000 uniformly distributed RSG-surface seeds mapped dominant pathways, tortuosity, and flux crossing a control surface near L1.The mass-flux streamlines were integrated with a 4th-order Runge-Kutta method and distributed across 128 CPUs.
  • 3.1. Global morphology and statistical properties of the flow: Dense, clumpy plumes are ejected from large convective cells rather than directed toward L1, while the L1 vicinity shows instantaneous inflow toward the donor.This morphology suggests a non-classical mass-transfer mechanism in the analyzed snapshot.
  • 3.1.1. Statistical moments of hydrodynamic quantities: 101.85 for density kurtosis on the RSG surface and 42.62 for radial mass-flux kurtosis in the accretion-stream region indicate highly intermittent, clumpy mass transfer.The heavy-tailed distributions imply dense, spatially localized clumps rather than smooth, quasi-steady flow.
  • 3.1.1. Statistical moments of hydrodynamic quantities: −3.17 for radial mass-flux skewness in the L1 vicinity indicates instantaneous flow back toward the donor, whereas 3.21 on the RSG surface shows dense outflows dominate net mass flux despite downdrafts.On the RSG surface, radial velocity skewness is −0.79, but radial mass flux is positively skewed because outflows occur in denser regions.
  • 3.1.2. Probability distribution functions (PDFs): Density and mass-flux PDFs are nearly linear on log-log plots, while velocity PDFs are non-Gaussian with asymmetry and heavy tails across the RSG surface, L1 vicinity, and accretion-stream region.These distributions support power-law or log-normal behavior and identify extreme dense-clump and outflow events dominating instantaneous transfer.
  • 3.2.2. Unsupervised flow regime classification: K-means clustering objectively separates the flow into four regimes: a quasi-hydrostatic envelope, supersonic low-density outflow, turbulent convective surface, and subsonic circum-binary medium.The segmentation delineates the stellar interior, turbulent surface, and escaping outflow, validating the conceptual regions used for statistical analysis.
  • 3.4.1. Force balance analysis: Radiation pressure is negligible near the dense stellar surface but dominates acceleration in lower-density outflowing regions, reaching a mean force ratio of 5×106 over gas pressure in the accretion-stream region.Radiation force correlates positively with mass flux, while radiative heating and cooling patterns influence the gas thermal and dynamical state.
  • 4.1. Datasets and methods: The study combines regional mass-flux statistics, Q-criterion and power-spectrum analysis, K-means classification, 10,000-surface-seed streamline tracing, and local force-balance and radiative-hydrodynamic correlation analyses on one 3D snapshot.The snapshot contains density, velocity, pressure, and radiation-field information and is analyzed to characterize instantaneous mass transfer.
  • 3.2.1. Vortex identification and turbulence: Mass transfer is highly intermittent, clumpy, and turbulent, with non-Gaussian statistics, strong skewness, high kurtosis, vortical structures, and power spectra consistent with a turbulent cascade.Vortex cores occupy 2.50% of the simulation volume, indicating pervasive turbulence in the stellar envelope.
  • 3.3.1. The absence of a stable L1 accretion stream: Zero of 10,000 traced streamlines crossed L1, instead forming broad, relatively straight plumes consistent with a convection-driven wind rather than stable Roche Lobe Overflow.The mean streamline tortuosity was 1.000009, indicating nearly ballistic initial ejection paths.
  • 4.3. What we have learned: The results indicate that convection and gas pressure lift material from the star, after which radiation pressure drives acceleration and shapes wind-like mass loss, motivating detailed 3D time-dependent radiation-hydrodynamic models.These conclusions apply to the specific simulation snapshot and emphasize the limitations of smooth, time-averaged or one-dimensional descriptions.
  • 2. METHODS: The workflow integrated quality control, log1p normalization, highly variable gene selection, PCA, UMAP, stage-marker validation, and multiple-comparison-controlled differential expression.Genes with minimal detection were removed, while cell-level expression metrics and sparsity were assessed before downstream analysis.
  • 2.7. Developmental Trajectory Inference and Pseudotime Assignment: Developmental trajectories were reconstructed separately for laboratory and field parasites to compare topology, pseudotemporal expression dynamics, and stage-transition programs.The analysis considered asexual and, when sufficiently represented, sexual trajectories, anchoring the asexual root at the Ring stage.
  • 2.9. Identification and Characterization of Gene Modules: The broader analytical design clustered co-expressed genes along pseudotime and prioritized low-expression genes with transient peaks before stage transitions as candidate regulators.Putative downstream targets were inferred from expression changes immediately following regulator peaks, enabling comparisons of conserved and condition-specific regulatory networks.
  • 3.1. Dataset overview and quality control: The study analyzed 45,691 single cells and retained 5,274 genes after filtering genes detected in fewer than three cells.Laboratory cells comprised 82.3% of the dataset, field cells 17.7%, and the normalized matrix had 80.25% sparsity.
  • 3.1. Dataset overview and quality control: Field isolates were dominated by sexual stages and uniquely contained very late gametocytes, whereas laboratory cultures broadly represented asexual development but lacked these mature stages.The dataset included 45,691 cells: 37,624 laboratory and 8,067 field cells, with field samples from four asymptomatic patients in Mali.
  • 3.2. The transcriptional landscape of lab and field parasites: UMAP embeddings recapitulated the parasite life cycle, with asexual progression forming a semi-circular structure and sexual stages branching into distinct gametocyte clusters.Stage-specific marker expression broadly confirmed the supplied cell-stage annotations and the biological relevance of the embedding.
  • 3.2. The transcriptional landscape of lab and field parasites: Laboratory and field cells shared some developmental clusters but occupied distinct regions, with early asexual stages lab-specific and late-stage gametocytes field-specific.Even in shared stages, partially separated distributions indicated transcriptional differences beyond unequal stage representation.
  • 3.3. Stage-specific differential gene expression between lab and field isolates: Within shared stages, field parasites showed widespread transcriptional divergence, including strong field-isolate upregulation at late-ring and early-trophozoite stages.At late rings, PF3D7_1372200 and PF3D7_0831800 had LFCs of 4.87 and 2.33; at early trophozoites, PF3D7_1372200 and PF3D7_1001500 had LFCs of 10.44 and 5.39.
  • 3.3. Stage-specific differential gene expression between lab and field isolates: Field and laboratory gametocytes exhibited extensive differential expression, with field sexual development showing distinct male–female transcriptional states and late-stage maturation populations absent from laboratory trajectories.Field female gametocytes included upregulation of the male-associated Pfs25 gene, while field trajectories extended from male and female populations to late-stage cells.
  • 3.4. Developmental trajectories reveal altered progression dynamics: Laboratory asexual trajectories reconstructed the complete cyclical intraerythrocytic developmental cycle, whereas field data covered only late rings and early trophozoites and could not support full-cycle comparison.Laboratory PAGA showed strong connectivity between consecutive stages; the field trajectory was limited by missing early-ring and schizont stages.
  • 3.5. Identification of candidate master regulators and inferred regulatory networks: The Sexual Field trajectory contained 18 gene modules and 1,917 putative regulatory links, nearly five times more than the sexual-lab trajectory, with regulators acting later before late-stage gametocytes.
  • 4. CONCLUSIONS: Field isolates showed distinct transcriptional programs, expanded sexual development, and rewired regulatory networks compared with laboratory strains, including late-stage gametocytes unique to field samples.These conclusions were based on single-cell analysis of over 45,000 cells and differential expression, trajectory inference, and regulatory-network analyses.
  • Highlighting Data Imbalance Challenges: Deep-learning step counters failed across all tested conditions, predicting zero steps with near-zero F1-scores and 100% Mean Absolute Percentage Error, whereas peak detection achieved approximately 10-11% Mean Absolute Percentage Error for hip-worn data.The neural models reduced training loss but converged to a trivial solution under extreme class imbalance, which Focal Loss did not adequately mitigate.
  • 1. INTRODUCTION: The wearable step-counting problem was motivated by sensor-placement and sampling-rate trade-offs, demographic variability, and extreme sparsity of step events, which can drive models toward predicting no steps.The study targeted accuracy and computational-efficiency trade-offs for robust, resource-constrained deployment.
  • 1. INTRODUCTION: The step-counting study compared a compact 1D Convolutional Neural Network, a MobileNet-inspired model, and peak detection across hip and wrist sensors at 100Hz and 25Hz using subject-independent 5-fold cross-validation.Data came from 39 participants, and evaluation included F1-score, Mean Absolute Percentage Error, model size, and inference speed.
  • 2.1. Data preparation and exploratory data analysis: The step-counting methods began by loading, consolidating, and characterizing accelerometer data from 39 participants across hip and wrist locations and 100Hz and 25Hz sampling conditions.The four primary conditions were Hip 100Hz, Hip 25Hz, Wrist 100Hz, and Wrist 25Hz.
  • 2.1.3. Data segmentation and labeling: Two-second, highly overlapping windows segmented three-axis accelerometer streams for step-event detection, using 200 samples at 100Hz and 50 samples at 25Hz.A 90% overlap produced strides of 20 samples for 100Hz data and 5 samples for 25Hz data.
  • 2.1.4. Data splitting: A 5-fold subject-independent cross-validation scheme evaluated each model across Hip-100Hz, Hip-25Hz, Wrist-100Hz, and Wrist-25Hz conditions without participant leakage.Approximately 31 participants were used for training and 8 for testing in each fold, with every participant serving in the test set once.
  • 2.2. Model development and training: Three models were developed for step counting: a peak-detection baseline, a compact 1D-CNN, and a resource-efficient MobileNet-inspired 1D-CNN.The models address the trade-off between accuracy and computational efficiency, with the resource-efficient architecture using depthwise separable convolutions to reduce parameters and computational cost.
  • 2.2.4. Training protocol: The deep learning models used focal loss for severe step-event class imbalance and were trained separately for each sensor-location and sampling-frequency condition.Training used γ = 2, α = 0.25, Adam with a 0.001 learning rate, learning-rate reduction on plateau, and early stopping after five unimproved validation epochs.
  • 2.3.1. Post-processing and step identification: Model outputs were stitched across overlapping windows, averaged at shared time points, and converted into steps using probability peaks above 0.5 with physiological minimum-distance constraints.The minimum distance was 25 samples at 100Hz and 6 samples at 25Hz.
  • 2.3.2. Performance metrics: Evaluation compared F1-Score, MAPE, model size, and inference time across the three models and four conditions, with additional tests for sensor placement, sampling frequency, and demographic effects.Step events were matched within ±150ms; Wilcoxon tests assessed placement and frequency effects, while Mann-Whitney U and Kruskal-Wallis tests assessed sex and age-group differences in MAPE.
  • 3.2. Baseline peak-detection algorithm performance: The baseline achieved F1-scores of 0.420 and 0.436 with MAPE of approximately 10–11% for Hip_100Hz and Hip_25Hz, respectively.Its performance reflected clearer, less noisy gait signals from hip-worn sensors.
  • 3.5.1. Location comparison (Hip vs. wrist): Baseline MAPE increased to 57.62% for Wrist_100Hz and 54.69% for Wrist_25Hz, reflecting false positives and false negatives from complex wrist movements.Sensor location significantly affected baseline MAPE at both frequencies (p < 0.001).
  • 3.3. Deep learning models: CompactCNN and MobileNetCNN performance: Low validation loss, including approximately 0.0015, did not translate into task performance because the models minimized loss by predicting the majority “no step” class.Post-processing found no output peaks above the 0.5 threshold, producing zero predicted steps and 100% MAPE.
  • 3.4.1. Model size: MobileNetCNN used approximately 12,252 parameters versus over 52,705 for CompactCNN, making it more suitable for memory-constrained edge deployment.The difference was attributed to depthwise separable convolutions reducing trainable parameters and memory footprint.
  • 3.4.2. Inference time: Inference remained fast: CompactCNN required 37.57 seconds at 100Hz and 7.00 seconds at 25Hz, while MobileNetCNN required 11.55 and 10.13 seconds.Lower 25Hz cost for CompactCNN reflected its smaller 50-sample input window versus 200 samples at 100Hz.
  • 3.5.2. Frequency comparison (100Hz vs. 25Hz): Reducing baseline sampling from 100Hz to 25Hz significantly lowered wrist F1-score (p < 0.001) but not hip F1-score (p = 0.35), with no significant MAPE changes.The results suggest higher-frequency signal components were more important for complex wrist patterns than for hip gait signals.
  • 3.6. Demographic analysis: Demographic comparisons were not practically informative because CompactCNN produced 100% MAPE for every participant, with sex p = 0.605 and age p = 0.349.The tests compared identical error distributions rather than meaningful model variation.
  • 4.3. Results obtained: Both deep learning models predicted zero steps across all conditions, yielding F1-scores of effectively 0.000 and MAPE values of 100%.This failure occurred despite apparently successful training and was attributed to extreme class imbalance; Focal Loss was insufficient to recover minority step events.
  • I. INTRODUCTION: The pipeline addresses high-dimensional conformational analysis and limited transition sampling by combining structural metrics, dimensionality reduction, clustering, free-energy surfaces, and Markov State Models.It targets quantitative folding pathways, rates, and state transitions from molecular-dynamics data.
  • B. Collective Variable Selection and Dimensionality Reduction: Conventional structural metrics, PCA, TICA, and Diffusion Maps are integrated to identify collective variables capturing large-scale global structural changes and subtle, kinetically important motions that are slow to decorrelate.
  • Collective Variable Selection and Markov State Models: The integrated workflow constructs free-energy surfaces and validates Markov State Models through implied-timescale convergence and Chapman–Kolmogorov tests.It estimates folding and unfolding rates, mean first passage times, and dominant transition pathways while supporting larger datasets through subsampling and incremental methods.
  • A. Molecular Dynamics Trajectory and Data Preparation: A 10 µs NTL9 trajectory containing 5000 frames sampled every 2 ns is aligned to a folded reference using backbone heavy atoms before analysis.The full trajectory supports primary analysis, while optional frame subsampling tests scalability and kinetic fidelity for longer datasets.
  • C. State Partitioning and Clustering: Conformational space is partitioned into folded, unfolded, and intermediate states using k-means, Gaussian Mixture Models, and DBSCAN to assess robustness across state definitions.Cluster counts use silhouette scores and BIC, while DBSCAN parameters are selected from clustering and density visualizations.
  • C. State Partitioning and Clustering: Frames are structurally and kinetically characterized after clustering, with folded states typically showing low RMSD and high native-contact fraction Q.Robustness is assessed by comparing assignments across clustering algorithms and selected collective-variable combinations.

D. Free Energy Surface and Local Structural Analysis · E. Markov State Model Construction and Validation · F. Scalability and Automation

The analysis combines free-energy surfaces and local contact monitoring to characterize NTL9 folding transitions, then uses validated Markov State Models to quantify their kinetics. The pipeline also incorporates scalable, automated analysis strategies for larger systems and longer trajectories.

  • D. Free Energy Surface and Local Structural Analysis: Free-energy surfaces projected onto two informative collective variables mapped stable and metastable basins and the barriers separating them.Surfaces were computed from binned trajectory probabilities using F = −kBT ln P, with the minimum free energy set to zero.
  • D. Free Energy Surface and Local Structural Analysis: Hydrogen bonds and native contacts were correlated with free-energy-surface positions and cluster assignments to identify structural changes underlying folded, unfolded, and intermediate-state transitions.Hydrogen bonds used donor–acceptor distance and angular criteria, while native contacts were monitored using a 0.45 nm heavy-atom distance cutoff.
  • E. Markov State Model Construction and Validation: MSMs represented transitions between clustered discrete states as memoryless dynamics and estimated lag-time transition probabilities by normalized state-to-state transition counts.The transition matrix element T_ij denotes the probability of moving from state i to state j over lag time τ.
  • E. Markov State Model Construction and Validation: The final MSM lag time was selected from the implied-timescale plateau, balancing memory loss within states against sufficient transition sampling.A plateau indicates that the slowest relaxation processes are well described as Markovian at that lag time.
  • E. Markov State Model Construction and Validation: Chapman–Kolmogorov tests assessed MSM self-consistency by comparing predicted and observed transition probabilities over multiple cumulative lag times.Agreement supports the Markovian assumption and the chosen state decomposition.
  • E. Markov State Model Construction and Validation: Validated MSMs yielded folding and unfolding rates, mean first passage times, and dominant transition pathways from state-to-state flux.Rates were calculated between folded and unfolded macrostates, while MFPTs described transitions between state sets such as unfolded-to-folded states.
  • F. Scalability and Automation: Scalability and reproducibility were supported through frame subsampling, chunked incremental PCA and TICA, extensibility to multi-domain proteins, and automated parameter selection.Automation covered embedding dimensionality and cluster-number choices using variance explained, eigengap, silhouette scores, gap statistics, or BIC.

G. Sensitivity and Robustness Analysis · III. RESULTS

The study applies a comprehensive computational pipeline to a 10 µs NTL9 molecular-dynamics trajectory, analyzing conformational landscapes and kinetics. Sensitivity analyses test whether state definitions, free-energy surfaces, and kinetic parameters remain stable across parameter choices.

  • G. Sensitivity and Robustness Analysis: Sensitivity analyses assess robustness to parameter choices in the computational pipeline.The analyses repeat key pipeline steps under alternative settings.
  • G. Sensitivity and Robustness Analysis: The study varies cluster numbers, DBSCAN’s ϵ parameter, and lag times used for Markov-state-model construction.These variations probe choices in k-means/GMM clustering, DBSCAN analysis, and MSM construction.
  • G. Sensitivity and Robustness Analysis: Stability is evaluated for state definitions, free-energy surfaces, rates, and mean first-passage times across parameter variations.The analysis checks whether the major findings are overly sensitive to specific analysis settings.
  • III. RESULTS: The analysis uses a comprehensive computational pipeline on a 10 µs molecular-dynamics trajectory of NTL9.The pipeline integrates collective-variable selection, state partitioning, free-energy analysis, and kinetic modeling.
  • III. RESULTS: The results systematically characterize NTL9’s conformational landscape and kinetics.The analysis combines conformational and kinetic perspectives within the computational workflow.
  • III. RESULTS: The workflow integrates collective-variable selection, state partitioning, free-energy analysis, and kinetic modeling.These components are applied together to analyze the simulation trajectory.

A. Data preparation, alignment, and quality assessment

The study prepared and aligned a complete 10 µs NTL9 molecular-dynamics trajectory, verified its integrity, and confirmed broad sampling from folded to unfolded conformations. Subsampled trajectories were also generated to assess how reduced data size affects later analyses.

  • Trajectory preparation and quality assessment: The 10 µs NTL9 trajectory contained 5000 frames sampled every 2 ns, aligned to a folded reference using backbone heavy atoms, with no missing frames or significant anomalies.This preparation focused the analysis on internal protein conformational changes.
  • Structural metrics and sampling: RMSD ranged from 0.1333 to 1.252 nm and Rg from 0.9138 to 1.4662 nm, indicating sampling of folded, intermediate, and unfolded conformations.Mean RMSD was approximately 0.965 nm, while mean Rg was 1.0388 nm; Figures 1–3 visualize these structural transitions.
  • Scalability preparation: Subsampling factors of 2, 5, and 10 were generated to evaluate how reduced trajectory size affects dimensionality reduction and kinetic modeling.These variants supported subsequent scalability analyses of performance and accuracy.

B. Collective variable selection and dimensionality reduction … Transport

This section presents integrated computational and analytical approaches spanning protein folding, cognitive aging, and interfacial water dynamics. Across these applications, the studies combine dimensionality reduction, state identification, kinetic or behavioral analysis, and machine-learning frameworks to characterize complex molecular and biological systems.

  • B. Collective variable selection and dimensionality reduction: TICA emphasized slow kinetic modes, whereas PCA captured global folded-to-unfolded variation; PCA explained 62.4% or 71.0% variance in the first three components for backbone or Cα distances, respectively.PCA separated global ensembles but represented subtle intermediate states less clearly than nonlinear methods.
  • B. Collective variable selection and dimensionality reduction: Diffusion Maps resolved heterogeneous intermediate microstates missed by linear projections, while conventional CVs, PCA, and TICA provided interpretable global or kinetically relevant descriptions.Diffusion Maps retained eight coordinates using an eigengap criterion but required more computation than PCA or TICA.
  • C. State partitioning and clustering: Clustering consistently supported 3–4 major ensembles, with TICA and Diffusion Maps distinguishing intermediate microstates more finely than conventional CVs or PCA.The identified ensembles corresponded to folded, unfolded, and one or more intermediate states, while some methods merged or dispersed intermediate conformations.
  • D. Free energy surface construction and kinetic analysis: Free-energy surfaces showed folded minima, unfolded regions, intermediate basins, and barriers of a few kJ/mol, consistent with NTL9’s rapid folding.The major energy basins closely matched the clusters identified from low-dimensional representations.
  • 2. Local structural analysis: Hydrogen bonds and native contacts: Breaking core hydrogen bonds and native contacts coincided with transition regions, indicating that local unfolding precedes larger-scale conformational expansion.Reformation of these contacts accompanied transitions back toward the folded state.
  • 3. Kinetic modeling and MSM construction: Intermediate-to-folded transitions were approximately twofold faster than transitions toward the fully unfolded state, while folding occurred on microsecond timescales.Implied-timescale convergence and Chapman–Kolmogorov tests supported the MSM’s Markovian validity at the selected lag time.
  • 1. Frame subsampling and incremental algorithms: Incremental PCA reduced memory and runtime for larger trajectories with only a 1–2% decrease in cumulative variance, while TICA preserved timescale separation across subsampling rates.These results support resource-efficient analysis of longer trajectories and larger datasets.
  • 2. Automated parameter selection: Automated variance, eigengap, silhouette, and BIC criteria reduced subjective choices, consistently recommending 3–4 clusters; modular descriptors and domain-wise strategies extend the workflow to complex proteins.The pipeline’s scalability through subsampling and incremental methods is important for larger datasets and multi-domain systems.
  • IV. CONCLUSIONS: Combining structural metrics with PCA, TICA, and Diffusion Maps captured global structure, slow kinetic modes, and fine intermediate-state heterogeneity.The complementary methods were essential for representing the full complexity of the folding conformational space.
  • IV. CONCLUSIONS: Clustering consistently identified three to four major NTL9 conformational ensembles: folded, unfolded, and one or two intermediate states.These discrete states supported subsequent thermodynamic and kinetic analyses.
  • IV. CONCLUSIONS: Low free-energy barriers matched NTL9’s fast-folding kinetics, while hydrogen-bond and native-contact disruption in the protein core often initiated unfolding.Two-dimensional free-energy surfaces mapped stable basins and the barriers separating them.
  • IV. CONCLUSIONS: The validated Markov State Model produced folding and unfolding kinetics consistent with experiments and showed that intermediate-to-folded transitions were favored over intermediate-to-unfolded transitions.Implied-timescale convergence and Chapman-Kolmogorov tests supported model accuracy at the selected lag time.
  • IV. CONCLUSIONS: The folding workflow scaled to larger datasets and longer trajectories through frame subsampling, incremental dimensionality reduction, and automated parameter selection.These strategies improved the pipeline’s robustness, efficiency, and reproducibility for future protein studies.
  • Integrated Study of Epigenetic Age and Spatial Memory: In 33 Egyptian fruit bats, epigenetic age was unrelated to total brain volume, older bats learned initially more slowly but made fewer perseverative errors, and brain volume did not predict cognitive resilience.Regression models controlled for sex and origin colony, indicating that maintained cognition may depend on mechanisms beyond overall brain size.
  • 4.2. Methods & datasets: The study’s methods combined a 33-bat multimodal cohort, DNA-methylation age, DTI-derived global brain volume, a multi-phase foraging task, and regression models controlling for sex and origin colony.Cognitive resilience was defined as better-than-expected performance for a given epigenetic age.
  • 3.1. Brain volume quantification and its association with epigenetic age: No significant association was found between epigenetic age and total brain volume, indicating no evidence of global brain atrophy in the bat cohort.The regression estimated β = 0.457, p = 0.968; the overall model was also nonsignificant (R2 = 0.109).
  • 3.2. Age-related changes in spatial cognitive performance: The remaining cognitive measures showed no significant age association: errors before the first reward, STM perseverative error, and LTM perseveration count.Their reported p-values were 0.427, 0.130, and 0.630, respectively.
  • 3.3. Exploratory correlation analysis: Spearman correlations confirmed age-related increases in Time to First Reward and decreases in STM Perseveration Count and LTM Perseverative Error.The correlations were ρ = 0.29, ρ = −0.43, and ρ = −0.42, respectively; Time to First Reward also correlated negatively with STM Perseveration Count (ρ = −0.70) and STM Perseverative Error (ρ = −0.68).
  • 3.3. Exploratory correlation analysis: Larger brain volume was positively correlated with first-entry STM perseverative error (ρ = 0.51, p < 0.01), despite its lack of association with age.This finding suggests that global size did not uniformly correspond to better inhibitory control in this task.
  • 3.4. Analysis of cognitive resilience: Global brain volume did not predict age-adjusted cognitive resilience for Time to First Reward, STM Perseveration Count, or LTM Perseverative Error.The corresponding brain-volume coefficients had p-values of 0.805, 0.204, and 0.874.
  • 4.3. Key findings: Older bats took longer to find the first reward but made fewer perseverative errors in short-term and long-term memory tasks.Time to First Reward increased with age (β = 837.8, p = 0.049), whereas STM Perseveration Count (β = −1.071, p = 0.009) and LTM Perseverative Error (β = −0.156, p = 0.007) decreased.
  • Transport: For functionalized graphene, K-Means identified 10 interfacial water states from 91 simulations, while interpretable gradient boosting showed that salt concentration and functionalization—especially carboxyl groups—enabled five-fold mobility tuning.High salt with high-coverage carboxyl groups produced ordered, minimally diffusive layers; low-salt unfunctionalized surfaces produced disordered, maximally diffusive layers.

I. INTRODUCTION … 2. Pairwise interaction effects revealed by heatmaps

This section analyzes how functionalization, salt concentration, and surface coverage affect water mobility on functionalized graphene using molecular-dynamics simulations, structural clustering, interpretable regression, and parametric analysis. It examines both independent and pairwise effects, highlighting surface chemistry and interaction patterns in water diffusion.

  • D. Machine learning framework for state identification and design principle extraction: The framework uses 91 simulations spanning functionalization, coverage, and salt concentration to map interfacial water states and derive quantitative transport design principles.It combines diffusion coefficients, density profiles, and radial distribution functions with K-Means clustering and interpretable Gradient Boosting with SHAP.
  • A. Data acquisition and feature extraction: The curated dataset records diffusion targets alongside functionalization, coverage, salt concentration, hydration-layer density features, and O-O radial-distribution features for subsequent analyses.Feature extraction includes density peak height and position, bulk density, and RDF peak height and position.
  • A. Global trends in water mobility: Water diffusion spans 0.40×10−5 to 1.98×10−5 cm2/s across 91 systems, with mean 1.17 × 10−5 cm2/s and standard deviation 0.41 × 10−5 cm2/s.The distribution is unimodal but skewed, indicating nonlinear sensitivity to the multidimensional parameter space.
  • 1. Main effects of individual parameters: Functionalization ranks average mobility as UNFUNC > CH3 > CO > OH > COOH, with Dmean = 1.51 × 10−5 cm2/s for UNFUNC and Dmean = 0.84 × 10−5 cm2/s for COOH.Hydrogen-bonding polar groups impede diffusion, while pristine graphene supports less structured and more mobile interfacial water.
  • 1. Main effects of individual parameters: Average diffusion decreases from 1.79×10−5 cm2/s at 0 NaCl to 0.79 × 10−5 cm2/s at 45 NaCl because ion hydration and increased viscosity reduce mobility.Na+ and Cl− hydration shells immobilize nearby water and contribute to lower mobility of the water-ion system.
  • 1. Main effects of individual parameters: Functional-group coverage has a nonlinear effect: functionalized surfaces average Dmean = 1.21×10−5 cm2/s at 8 groups versus approximately 1.10 × 10−5 cm2/s at 16 and 24 groups.Increasing coverage causes overlapping pinning effects that form a more continuous barrier to diffusion.
  • 2. Pairwise interaction effects revealed by heatmaps: The analysis identifies non-additive pairwise interactions, including salt sensitivity that depends strongly on functionalization and is amplified for polar groups.Heatmaps compare functionalization–salt, coverage–salt, and functionalization–coverage effects under fixed complementary conditions.
  • 2. Pairwise interaction effects revealed by heatmaps: High-coverage COOH surfaces drop from 1.11×10−5 cm2/s at 0 NaCl to 0.40×10−5 cm2/s at 45 NaCl, revealing synergistic immobilization.The combined ion-water and water-COOH interactions produce highly ordered, quasi-frozen interfacial water.
  • 2. Pairwise interaction effects revealed by heatmaps: Water diffusion decreases systematically with both increasing salt concentration and increasing surface coverage, indicating largely additive effects for weakly interacting functional groups.The heatmap for CH3-functionalized graphene shows that both parameters independently contribute to reduced water transport.
  • 2. Pairwise interaction effects revealed by heatmaps: At 18 NaCl pairs, functional-group chemistry dominates water mobility across coverage levels, following COOH < OH < CO < CH3 < UNFUNC.Polar groups, especially COOH, impede diffusion most strongly, while unfunctionalized and CH3 surfaces retain higher mobility; greater coverage further reduces diffusion on functionalized surfaces.

C. Structural basis for extreme water dynamics … 2. Interpretable regression for extracting design principles

The study links interfacial water mobility to structural ordering and uses unsupervised clustering plus interpretable regression to identify physically meaningful states and design principles. High salt, COOH functionalization, and coverage suppress diffusion, whereas unfunctionalized or low-coverage CH3 surfaces promote mobile, liquid-like water.

  • C. Structural basis for extreme water dynamics: Figure 7 shows that COOH functionalization most strongly sharpens the first hydration peak, with salt concentration and functional-group coverage further increasing interfacial ordering and reducing diffusion.The resulting high-amplitude density peaks indicate highly structured interfacial water.
  • C. Structural basis for extreme water dynamics: High-coverage COOH surfaces at high salt form sharp, near-surface hydration peaks and immobile, ice-like water, whereas low-salt unfunctionalized or CH3 surfaces show broader peaks and high mobility.COOH groups, ionic hydration shells, and hydrogen-bonding networks anchor water, while weaker surface interactions facilitate exchange with the bulk-like region.
  • D. Machine learning framework for state identification and design: The machine-learning framework combines structural-state identification with predictive regression to connect molecular organization and input parameters to interfacial water transport.The methodology was designed to support quantitative interpretation and engineering of water mobility.
  • 1. Unsupervised clustering of interfacial water states: K-Means clustering of density-peak height and position identified 10 distinct interfacial water states among 91 systems, using silhouette analysis to select the cluster number.The clusters classify systems from emergent structural properties without using input parameters or diffusion coefficients.
  • 1. Unsupervised clustering of interfacial water states: Cluster 9 had the lowest average diffusion, 0.55 × 10−6 cm2/s, and combined 24 functional groups with 45 NaCl pairs, while Cluster 3 reached 1.44 × 10−5 cm2/s under lower-salt, disordered conditions.These states represent trapped-immobile and disordered-mobile interfacial organizations, respectively.
  • 2. Interpretable regression for extracting design principles: Salt concentration was the dominant SHAP feature, with Mean |SHAP value| = 3.07 × 10−6 and increasingly negative effects as salt increased.The regression diagnostics showed strong predicted-versus-actual agreement and residuals distributed around zero, supporting interpretation within the studied parameter space.
  • 2. Interpretable regression for extracting design principles: COOH functionalization ranked second at Mean |SHAP value| = 1.42 × 10−6, coverage ranked third at 0.74 × 10−6, and both generally reduced diffusion.OH had a moderate negative effect; UNF and CO had smaller importance, while unfunctionalized surfaces typically enhanced diffusion.
  • 2. Interpretable regression for extracting design principles: To maximize diffusion, use unfunctionalized or low-coverage CH3 surfaces with salt-free or very low salt; to minimize it, combine high-coverage COOH with high salt.These conditions respectively produce disordered liquid-like water or strongly pinned, ice-like layers hindered by ionic hydration shells.

E. Analysis of non-additive interaction effects

Interaction matrices show that water diffusion departs from additive predictions through antagonistic effects on unfunctionalized graphene at high salt and saturation-like synergistic effects for highly covered carboxylated surfaces under extreme conditions.

  • E. Analysis of non-additive interaction effects: Interaction matrices reveal antagonistic effects for unfunctionalized surfaces at high salt and synergistic, saturation-like effects for carboxyl-functionalized surfaces at high salt or coverage.Values measure actual minus additive-model-predicted diffusion, identifying pairwise deviations that help fine-tune water transport.
  • E. Analysis of non-additive interaction effects: 0.8 × 10−5 cm2/s actual diffusion versus 1.2 × 10−5 cm2/s predicted produced a −0.3 × 10−5 cm2/s interaction for 0UNFUNC_45nacl.The combination of hydrophobicity and ions may amplify ion adsorption, interfacial water structuring, salting out, or rigid hydration shells.
  • E. Analysis of non-additive interaction effects: 0.2 × 10−5 cm2/s positive interaction occurred for 24COOH_45nacl, indicating that high coverage and salt effects plateau rather than combine linearly.The system approaches an extremely low-diffusion threshold, so the combined effect is less restrictive than a purely additive prediction.

F. Limitations of the analysis … 4. CONCLUSIONS

These sections examine how physical conditions, feedback prescriptions, and learned feature representations shape modeled scientific relationships across diverse analyses. They also identify limitations in data, interpretability, feature design, training, and baseline comparisons, framing the results as useful for interpretation and hypothesis generation rather than broad generalization.

  • F. Limitations of the analysis: Parsing failures excluded RDF structural features and rendered bulk_density consistently zero, so clustering relied only on first-hydration-layer density peaks.Including reliable RDF and bulk-density data could refine the water states, while the 91-system dataset supports interpretation and hypothesis generation within the studied parameter space rather than robust generalization to unseen systems.
  • IV. CONCLUSIONS: The framework combines structural clustering with interpretable regression to provide a quantitative atlas for engineering water transport in nanofluidics, membranes, and electrochemical materials.The identified states and design principles are intended to guide surfaces with tailored interfacial water behavior.
  • IV. CONCLUSIONS: Water mobility was tuned over a five-fold range, from 0.40 × 10−5 cm2/s to 1.98 × 10−5 cm2/s, with salt concentration, functionalization, and surface coverage forming the dominant influence hierarchy.Unfunctionalized and methyl-functionalized surfaces generally promoted mobility, whereas polar groups—especially carboxyl—impeded diffusion; increasing salt consistently reduced transport.
  • IV. CONCLUSIONS: Structural analysis linked high mobility to disordered, liquid-like interfacial layers and low mobility to ordered, ice-like layers formed by strong hydrogen bonding and ionic hydration.High-coverage COOH surfaces at high salt predominantly exhibited sharp, high-amplitude density peaks and trapped water molecules.
  • IV. CONCLUSIONS: The analysis identified 10 interfacial water states and translated SHAP results into design rules: low-salt, unfunctionalized or low-coverage CH3 surfaces maximize diffusion, whereas high-coverage COOH at high salt minimizes it.The analysis also found an antagonistic high-salt effect on unfunctionalized graphene and a synergistic saturation plateau for high-coverage COOH at high salt.
  • 3.2. Diversity in the MBH–Mstar scaling relation: Across 1,000 catalogs, MBH–Mstar relation properties and black hole occupation fractions show substantial catalog-to-catalog diversity that depends strongly on stellar mass range and input parameters.The analysis considered 1,000 simulated catalogs and found distinct behavior across low, intermediate, and high stellar-mass regimes.
  • 3.2.1. Distributions by stellar mass bin: The relation steepens and occupation fraction approaches unity with increasing stellar mass, while parameter spreads are greatest in the low-mass bin.Low, intermediate, and high bins are defined as Mstar < 10^9 M⊙, 10^9 ≤ Mstar < 10^10 M⊙, and Mstar ≥ 10^10 M⊙, respectively.
  • 3.2.1. Distributions by stellar mass bin: Low-mass fits are highly variable, with median β ≈ 0.76, median scatter ≈ 0.27 dex, occupation fraction ≈ 0.84, and 129 α plus 131 β outliers.The low-mass α distribution extends approximately from −15.25 to +6.20, whereas intermediate-mass fits show almost no significant outliers and high-mass fits have median β near 1.22, scatter ≈ 0.40 dex, and occupation fraction ≈ 0.96.
  • 3.2.2. Catalog-to-catalog diversity and fit reliability: The pipeline attempted 2,991 of 3,000 catalog–mass-bin fits, requiring at least 10 galaxies with MBH > 0 per bin, and found greatest outlier diversity at low and high masses.Intermediate-mass relations showed almost no outliers, while varying ASN1 substantially altered the fitted relation, especially at low masses.
  • 3.3. Dependence on feedback and cosmological parameters: Across mass bins, feedback parameters primarily drive MBH–Mstar diversity, shifting from SN feedback at low masses to AGN feedback at intermediate and high masses.Cosmological parameters remain secondary, modulating the relation and occupation fraction rather than dominating them.
  • 3.3.1. Feature importance in low-mass galaxies: In low-mass galaxies, models reach R2 up to 0.97, with ASN1 dominating β and scatter, AAGN1 also strongly affecting α and β, and Ωm influencing occupation fraction.Increasing ASN1 lowers α, makes β shallower, increases scatter, and suppresses occupation fraction; these effects are attributed to stronger feedback in shallow potential wells.
  • 3.3.2. Dependencies in intermediate-mass galaxies: In intermediate-mass galaxies, AAGN1 dominates with R2 values of 0.97–0.99, importance approaching 1.70, and regression coefficients near −3.57 for α and +0.39 for β.Stronger AAGN1 lowers normalization and steepens the slope, while intrinsic scatter and occupation fraction are comparatively insensitive to parameter choices.
  • 3.3.3. Dependencies in high-mass galaxies: In high-mass galaxies, AAGN1 remains dominant at importance ≈ 1.65 but can flatten β, while occupation fraction stays near 0.96 and cosmological parameters exert modest modulation.The AAGN1 effect reverses sign relative to intermediate masses, consistent with strong AGN feedback suppressing further black hole growth; scatter has median ≈ 0.40 dex.
  • 3.4. Catalog-to-catalog variations, uncertainties, and outlier analysis: The MBH–Mstar relation is not universal across simulations but forms a family of relations determined by underlying physical parameters.Overall, the study maps relation properties and occupation fractions to six cosmological and feedback parameters across 1,000 simulated catalogs.
  • 3.6. Comparison with previous methodologies and new insights: Robust regression, bootstrap uncertainty estimates, broad exploration of 1,000 catalogs, and interpretable ensemble models enabled quantitative identification of nonlinear, mass-dependent feedback effects.The analysis revealed a transition in feedback dominance near Mstar ∼10^9−10^10 M⊙ and a possible high-mass sign reversal in AAGN1’s influence on slope.
  • 4. CONCLUSIONS: Supernova feedback dominates below 10^9 M⊙, producing shallower slopes, lower normalizations, greater scatter, suppressed occupation, and the largest catalog-to-catalog variation.The low-mass regime is especially sensitive to feedback physics and potentially stochastic growth processes.
  • 4. CONCLUSIONS: AGN feedback dominates at 10^9 ≤ Mstar < 10^10 M⊙, generally steepening the relation and yielding a remarkably uniform scaling relation across 1,000 catalogs.This behavior is attributed to AGN regulation of gas flows that fuel star formation and black hole accretion.
  • 4. CONCLUSIONS: At Mstar ≥ 10^10 M⊙, AGN feedback remains dominant but may flatten or reverse its slope influence through self-regulation and quenching, while cosmology modulates normalization and scatter.The high-mass bin has the highest intrinsic scatter and near-unity black hole occupation fraction, with minimal occupation dependence on inputs.
  • 4. CONCLUSIONS: The simulations broadly match observed massive-galaxy slopes and scatter but predict greater relation diversity and lower black hole occupation at low masses, consistent with dwarf-galaxy observations.Large low-mass catalog variation suggests sensitivity to specific feedback physics.
  • 3.1. Data Processing, Substructure Characterization, and Feature Engineering Summary: The pipeline represented each substructure with 10 physical features and a 64-dimensional GraphSAGE embedding, concatenated into 74-dimensional vectors and padded or truncated to 60 substructures.Each tree therefore produced a tensor of shape (60, 74), using a canonical null-substructure representation for padding.
  • 3.2. QITT Decomposition and Feature Generation: QITT reshaped each tree tensor to (60, 2, 37), selected ranks (1, 2, 2, 1) by validation, and produced a 202-dimensional feature vector.The selected ranks achieved a validation sum RMSE of 0.0925.
  • 3.3.2. Performance of QITT-based Models: QITT_LinearRegression performed best among QITT models for Ωm, while QITT_XGBoost and QITT_RandomForest performed slightly worse on this feature set.QITT_XGBoost achieved Ωm RMSE 0.0303 and R² 0.8834, and σ8 RMSE 0.0711 and R² 0.5577; QITT_RandomForest achieved Ωm RMSE 0.0320 and R² 0.8696, and σ8 RMSE 0.0763 and R² 0.4896.
  • 3.3.3. Comparison with Baselines: B1_Aggregate_LinearRegression achieved the best overall performance for Ωm (RMSE 0.0155, R² 0.9696), while QITT_LinearRegression remained competitive for both parameters.For QITT_LinearRegression, Ωm performance was RMSE 0.0246 and R² 0.9231, while σ8 performance was RMSE 0.0658 and R² 0.6206.
  • 3.3.3. Comparison with Baselines: Raw physical substructure features performed poorly, with B2_RawSubPhys_XGBoost reaching only Ωm R²=0.6109 and σ8 R²=0.3042.The results support using topological embedding or QITT processing rather than directly modeling high-dimensional raw physical features.
  • 3.3.4. Statistical Significance: QITT_XGBoost significantly outperformed B4_FlatCombined_XGBoost, whereas its improvement over B1_Aggregate_XGBoost was not statistically significant.The results indicate that QITT compresses and structures high-dimensional features effectively, but aggregate features are already highly informative.
  • 3.3.5. Predicted vs. True Values: QITT_XGBoost predictions aligned closely with the identity line for Ωm (R² 0.8834), while σ8 showed greater variance and lower accuracy (R² 0.5577).No strong systematic biases were apparent, but σ8 was more difficult to constrain with the current feature set and models.
  • 3.4.1. Topological Embeddings: The topological embeddings showed diffuse clustering rather than clearly separated groups, with some coherence between embedding regions and substructure branch sizes.The embedding visualization used a t-SNE projection of 10,000 sampled 64-dimensional embeddings colored by halo count.
  • 3.4.2. QITT Core Analysis: QITT cores yield 202 compressed features, with Core 2 carrying the largest magnitude range and high-leverage interactions, although individual features lack direct physical interpretation.Core 2 spans approximately -66.6 to 302.3, while the compressed features represent complex interaction terms that are difficult to map back to original substructure properties.
  • 3.4.3. Qualitative View of Substructures: Example substructures vary substantially in size and temporal extent, including 200-node structures spanning scale factors 0.13–0.71 and 12-node structures spanning 0.34–0.45.These structures are processed by the GNN and contribute to the QITT features.
  • 3.5.2. Role of Topological Information and Substructure Analysis: Topological embeddings encode substructure size, and combining them with QITT improves over raw physical features and simple flattening.The embeddings distinguish substructures spanning 1 to 1178 halos, with median 10, while QITT-XGBoost outperformed the corresponding raw-physical and flattened-feature baselines.
  • 3.5.3. Interpretation of Model Performance Differences: Global merger-tree properties strongly constrain Ωm, whereas σ8 is harder to estimate because it likely depends on subtler substructure and merger-history effects.The aggregate Linear Regression baseline achieved R²=0.9696 for Ωm and R²=0.6257 for σ8.
  • 3.5.4. Limitations: The analysis is limited by weak QITT-feature interpretability, only five GNN training epochs, non-exhaustive substructure features, and a dataset of 1000 trees.Baseline B3 was skipped, and some high-dimensional baselines are computationally intensive.
  • 3.6. Summary of Results: The study presents QITT-enhanced multi-scale substructure analysis with learned GNN embeddings as a promising approach for cosmological parameter estimation, especially for subtler σ8-related effects.Future work targets interpretable QITT features, advanced GNNs, larger datasets, and broader cosmological and astrophysical applications.
  • 4. CONCLUSIONS: Using 1000 simulated halo merger trees, the workflow extracts substructure features, generates GNN embeddings, applies QITT, and evaluates Linear Regression, Random Forest, XGBoost, and multiple baselines.The compared baselines use aggregate graph-level, raw substructure, and flattened combined features.
  • 3.5.1. Efficacy of the QITT-Enhanced Approach: QITT-XGBoost significantly outperformed flattened combined features and raw physical-substructure features, while aggregate-feature Linear Regression achieved the best Ωm performance.QITT compressed 4440 features into 202 while maintaining or improving nonlinear-model performance, but did not surpass the aggregate baseline on test accuracy.
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