Complex Data Research Articles

Nonseparable panel models with index structure and correlated random effects

. To facilitate semiparametric estimation of general discrete-choice, censored, sample selection, and other complex panel data models, we study identification and estimation of nonseparable multiple-index models in panel data with correlated random effects and a fixed number of time periods. The parameter vectors of interest are shown to be identified up to multiplicative constants and the average marginal effects are identified under the assumption that the distribution of individual effects depends on the explanatory variables only through their averages across time. Under this assumption, we propose to estimate the unknown parameters by the generalized method of moments based on the average and outer product of the difference of derivatives of the regression function. The rate of convergence and asymptotic distribution is established both for the proposed parameter estimates and the average marginal effects. We conduct Monte Carlo simulation studies to assess finite-sample performance of the proposed estimator. We also use it to model dynamic earnings of women, and using our general identification results, we find a negative effect of the number of children not only on the selection into employment as usual, but also on the average earnings.

Amputated life-testing based on extended Dagum percentiles for type of group inspection plans: optimal sample sizes, termination time ratios analysis

This paper introduces a novel approach to life-testing using Extended Dagum (EXD) percentiles within the framework of group inspection plans. The methodology focuses on optimizing sample sizes and analyzing termination time ratios to enhance the reliability of quality control procedures. By leveraging the flexibility of the EXD distribution, the proposed approach accurately models complex survival data, accommodating heavy-tailed characteristics often encountered in practice. The study presents a detailed analysis of optimal sample sizes and the critical termination time ratios that balance producer and consumer risks. Through comprehensive simulations and real applications, the paper demonstrates the effectiveness of the proposed methodology in ensuring robust and efficient life-testing strategies, offering valuable insights for practitioners in industries such as manufacturing, engineering, and reliability analysis.

Integration of Neuro-Fuzzy Systems in Medical Diagnostics and Data Security - A Review

Adaptive Neuro-Fuzzy Systems (ANFS) have become increasingly prevalent in a variety of fields due to their ability to process complex and uncertain data with high accuracy. This research article reviews three major contributions of ANFS: their application in deep neuro-fuzzy systems (DNFS) for healthcare and industrial systems, neuro-fuzzy logic controllers for paralysis estimation, and ANFIS-based solutions for secure cloud storage in medical IoT (MIoT). The findings emphasize the importance of ANFS in improving decision-making, diagnosis, and data security. This paper concludes with a discussion on challenges, future research directions, and the need for optimization in real-time applications.

Identifying and supporting vaccine champions in pediatric primary care: a qualitative interview study.

Implementation science research identifies clinical champions as instrumental in aligning healthcare professionals' (HCPs) behavior with practice guidelines for delivering health services, including vaccinations. However, we know relatively little about identifying or supporting champions. To characterize who vaccine champions are, what they do, and how to support their work in pediatric primary care. In 2022, we interviewed a purposive sample of peer-nominated or self-identified vaccine champions (n=20) and HCPs who worked with vaccine champions (n=4). We thematically analyzed qualitative data. Vaccine champions' defining characteristics were firsthand primary care experience, whether as providers or nursing staff, and a strong belief in vaccinations as uniquely effective tools for primary prevention. Participants noted these beliefs were "part of the DNA" of specialties like pediatrics and infectious disease, where they perceived champions as especially common. Being "insatiable in their quest for knowledge," champions primarily conceptualized their role as understanding and sharing complex information and performance metric data related to vaccine administration. Champions' role in leading other implementation strategies, such as communication training, was more peripheral. Champions reported that dedicated time and staff support helped them "go above and beyond" to improve vaccination rates. Our findings suggest that vaccine champions can be found among providers and nursing staff with deep clinical experience and commitment to primary prevention through vaccination, including through providing vaccine education to colleagues. Healthcare systems can allocate resources to support champions as educators, while exploring opportunities to extend their role in other implementation strategies to improve vaccination rates.

Traffic data imputation via knowledge graph-enhanced generative adversarial network

Traffic data imputation is crucial for the reliability and efficiency of intelligent transportation systems (ITSs), forming the foundation for downstream tasks like traffic prediction and management. However, existing deep learning-based imputation methods struggle with two significant challenges: poor performance under high missing data rates and the limited incorporation of external traffic-related factors. To address these challenges, we propose a novel knowledge graph-enhanced generative adversarial network (KG-GAN) for traffic data imputation. Our approach uniquely integrates external knowledge with traffic spatiotemporal dependencies to improve data imputation quality. Specifically, we construct a fine-grained knowledge graph (KG) that differentiates attributes and relationships of external factors such as points of interest (POI) and weather conditions, facilitating more robust knowledge representation learning. We then introduce a knowledge-aware embedding cell (EM-cell) that merges traffic data with these learned external representations, providing richer inputs for the spatiotemporal GAN. Extensive experiments on a large-scale real-world traffic dataset demonstrate that KG-GAN significantly outperforms state-of-the-art methods under various missing data scenarios. Additionally, ablation studies confirm the superior performance gained from incorporating external knowledge, underscoring the importance of this approach in addressing complex missing data patterns.

The Use of Diagnostic Transcranial Magnetic Stimulation as a Predictor of the Functional Outcome in Ischemic Stroke

ABSTRACT. Determination of rehabilitation potential (RP) is necessary for optimal rehabilitation strategy and the best rehabilitation measures. Navigational transcranial magnetic stimulation (nTMS) has been proposed as a method for PR determination in after-stroke patients.THE AIM. was to study the importance of navigational diagnostic transcranial magnetic stimulation as a neurofunctional predictor of motor function recovery after ischemic stroke.MATERIAL AND METHODS. The study included 28 after-stroke patients, 19 men and 9 women, the mean age was 60.07±5.67 years, who underwent a course of inpatient medical rehabilitation at the Moscow Research and Practice Center for Medical Rehabilitation, Restorative and Sports Medicine named after S.I. Spasokukotsky in 2022–2023. Clinical examination and assessment were conducted before and after the rehabilitation course using validated scales and questionnaires — the Medical Research Committee (MRCs) scale, the Box and Block Test (BBT), the modified Rankin scale (mRS); the rehabilitation routing scale (RRS). The patients were also examined using nTMS at the N.V. Sklifosovsky Research Institute for Emergency Medicine with the determination of motor evoked potential (MEP) parameters from the muscles of the upper and lower extremities.RESULTS. In patients with preserved MEP, there was a significant increase in the strength of the paretic limb on the MRCs scale from 4.00 (2.94–4.06) to 4.22 (3.83–4.89) points (p <0.001) for the upper limb and from 4.00 (3.67–4.00) to 4.44 (3.83–4.61) (p<0.001) for the lower limb. Improvements were revealed according to the mRS scale — the number of patients with an mRS score of 2 points in the group of patients with defined MEP increased by 26.1%, reached values of 1 point — 13.0% of patients, and the number of patients with an assessment of disability and self-care ability of 4 points decreased by 8.7%.CONCLUSION. Navigational transcranial magnetic stimulation is one of the methods for assessing the rehabilitation potential in patients with ischemic stroke. But TMS should not be used as the only method of evaluating rehabilitation potential. The assessment of RP should be comprehensive and based on the complex data obtained.

Unraveling the Bivalent and Rapid Interactions Between a Multivalent RNA Recognition Motif and RNA: A Kinetic Approach.

The kinetics of the interaction between Musashi-1 (MSI1) and RNA have been characterized using surface plasmon resonance biosensor analysis. Truncated variants of human MSI1 encompassing the two homologous RNA recognition motifs (RRM1 and RRM2) in tandem (aa 1-200), and the two RRMs in isolation (aa 1-103 and aa 104-200, respectively) were produced. The proteins were injected over sensor surfaces with immobilized RNA, varying in sequence and length, and with one or two RRM binding motifs. The interactions of the individual RRMs with all RNA variants were well described by a 1:1 interaction model. The interaction between the MSI1 variant encompassing both RRM motifs was bivalent and rapid for all RNA variants. Due to difficulties in fitting this complex data using standard procedures, we devised a new method to quantify the interactions. It revealed that two RRMs in tandem resulted in a significantly longer residence time than a single RRM. It also showed that RNA with double UAG binding motifs and potential hairpin structures forms less stable bivalent complexes with MSI1 than the single UAG motif containing linear RNA. Substituting the UAG binding motif with a CAG sequence resulted in a reduction of the affinity of the individual RRMs, but for MSI1, this reduction was strongly enhanced, demonstrating the importance of bivalency for specificity. This study has provided new insights into the interaction between MSI1 and RNA and an understanding of how individual domains contribute to the overall interaction. It provides an explanation for why many RNA-binding proteins contain dual RRMs.

A clustering ensemble algorithm for handling deep embeddings using cluster confidence

Abstract Clustering ensemble, which aims to learn a robust consensus clustering from multiple weak base clusterings, has achieved promising performance on various applications. With the development of big data, the scale and complexity of data is constantly increasing. However, most existing clustering ensemble methods typically employ shallow clustering algorithms to generate base clusterings. When confronted with high-dimensional complex data, these shallow algorithms fail to fully utilize the intricate features present in the latent data space. As a result, the quality and diversity of the generated base clusterings are insufficient, thus affecting the subsequent ensemble performance. To address this issue, we propose a novel clustering ensemble algorithm for handling deep embeddings using cluster confidence (CEDECC) to improve the robustness and performance. Instead of simply combining deep clustering with clustering ensembles, we take into consideration that the performance of existing deep clustering methods heavily relies on the quality of low-dimensional embeddings generated during the pre-training stage. The quality of embeddings is unstable due to the influence of different initialization parameters. In CEDECC, specifically, we first construct a cluster confidence measure to evaluate the quality of low-dimensional embeddings. Typically, high-quality low-dimensional embeddings yield accurate clustering results with the same model parameters. Then, we utilize multiple high-quality embeddings to generate the base partitions. In the ensemble strategy phase, we consider the cluster-wise diversity and propose a novel ensemble cluster estimation to improve the overall consensus performance of the model. Extensive experiments on three benchmark datasets and four real-world biological datasets have demonstrated that the proposed CEDECC consistently outperforms the state-of-the-art clustering ensemble methods.

Holomics and Artificial Intelligence-Driven Precision Oncology for Medullary Thyroid Carcinoma: Addressing Challenges of a Rare and Aggressive Disease.

Background/Objective: Medullary thyroid carcinoma (MTC) is a rare yet aggressive form of thyroid cancer comprising a disproportionate share of thyroid cancer-related mortalities, despite its low prevalence. MTC differs from other differentiated thyroid malignancies due to its heterogeneous nature, presenting complexities in both hereditary and sporadic cases. Traditional management guidelines, which are designed primarily for papillary thyroid carcinoma (PTC), fall short in providing the individualized care required for patients with MTC. In recent years, the sheer volume of data generated from clinical evaluations, radiological imaging, pathological assessments, genetic mutations, and immunological profiles has made it humanly impossible for clinicians to simultaneously analyze and integrate these diverse data streams effectively. This data deluge necessitates the adoption of advanced technologies to assist in decision-making processes. Holomics, which is an integrated approach that combines various omics technologies, along with artificial intelligence (AI), emerges as a powerful solution to address these challenges. Methods: This article reviews how AI-driven precision oncology can enhance the diagnostic workup, staging, risk stratification, management, and follow-up care of patients with MTC by processing vast amounts of complex data quickly and accurately. Articles published in English language and indexed in Pubmed were searched. Results: AI algorithms can identify patterns and correlations that may not be apparent to human clinicians, thereby improving the precision of personalized treatment plans. Moreover, the implementation of AI in the management of MTC enables the collation and synthesis of clinical experiences from across the globe, facilitating a more comprehensive understanding of the disease and its treatment outcomes. Conclusions: The integration of holomics and AI in the management of patients with MTC represents a significant advancement in precision oncology. This innovative approach not only addresses the complexities of a rare and aggressive disease but also paves the way for global collaboration and equitable healthcare solutions, ultimately transforming the landscape of treatment and care of patients with MTC. By leveraging AI and holomics, we can strive toward making personalized healthcare accessible to every individual, regardless of their economic status, thereby improving overall survival rates and quality of life for MTC patients worldwide. This global approach aligns with the United Nations Sustainable Development Goal 3, which aims to ensure healthy lives and promote well-being at all ages.

II-LA-KM: Improved Initialization of a Learning-Augmented Clustering Algorithm for Effective Rock Discontinuity Grouping

Rock mass discontinuities are an excellent information set for reflecting the geometric, spatial, and physical properties of the rock mass. Using clustering algorithms to analyze them is a significant way to select advantageous orientations of structural surfaces and provide a scientific theoretical basis for other rock mass engineering research. Traditional clustering algorithms often suffer from sensitivity to initialization and lack practical applicability, as discontinuity data are typically rough, low-precision, and unlabeled. Confronting these challenges, II-LA-KM, a learning-augmented clustering algorithm with improved initialization for rock discontinuity grouping, is proposed. Our method begins with heuristically selecting initial centers to ensure they are well-separated. Then, optimal transport is used to adjust these centers, minimizing the transport cost between them and other points. To enhance fault tolerance, a learning-augmented algorithm is integrated that iteratively reduces clustering costs, refining the initial results toward optimal clustering. Extensive experiments on a simulated artificial dataset and a real dataset from Woxi, Hunan, China, featuring both orientational and non-orientational attributes, demonstrate the effectiveness of II-LA-KM. The algorithm achieves a 97.5% accuracy on the artificial dataset and successfully differentiates between overlapping groups. Its performance is even more pronounced on the real dataset, underscoring its robustness for handling complex and noisy data. These strengths make our approach highly beneficial for practical rock discontinuity grouping applications.

QCLUE: a quantum clustering algorithm for multi-dimensional datasets

Clustering algorithms are at the basis of several technological applications, and are fueling the development of rapidly evolving fields such as machine learning. In the recent past, however, it has become apparent that they face challenges stemming from datasets that span more spatial dimensions. In fact, the best-performing clustering algorithms scale linearly in the number of points, but quadratically with respect to the local density of points. In this work, we introduce qCLUE, a quantum clustering algorithm that scales linearly in both the number of points and their density. qCLUE is inspired by CLUE, an algorithm developed to address the challenging time and memory budgets of Event Reconstruction (ER) in future High-Energy Physics experiments. As such, qCLUE marries decades of development with the quadratic speedup provided by quantum computers. We numerically test qCLUE in several scenarios, demonstrating its effectiveness and proving it to be a promising route to handle complex data analysis tasks – especially in high-dimensional datasets with high densities of points.

Predictive modeling for coiled tubing fatigue using advanced machine learning techniques

Coiled tubing CT plays Pivotal role in oil and gas well intervention operations due to its advantages such as flexibility, fast mobilization, safe, low cost and wide range of applications, including: well intervention, cleaning, stimulation, fluid displacement, cementing, and drilling. However, CT is subject of fatigue and mechanical damage caused by repeated bending cycles, internal pressure and environmental factors which can lead to a premature failure, high operational cost and production downtime. With the development of CT proprieties and application traditional fatigue life prediction methods based on analytical models integrated in tracking process showed in some cases an underestimate or overestimate of the actual fatigue life of CT particularly when complex factor like welding type, corrosive environment, and high-pressure variation are involved. This study addresses this limitation by introducing a comprehensive machine learning-based approach to improve the accuracy of CT fatigue life prediction, using a data set derived from over 350 tests both lab scale and full-scale fatigue test. The study has incorporated the impact of different parameters such as CT, grades, wall, thickness, CT diameter, internal pressure and welding types. By using advanced machine learning techniques such as artificial network (ANN), Gradient boosting regressor we got a more precise estimation of the number of cycles to failure than traditional models. The results of this study shown the importance of integration of machine learning for CT fatigue life analysis and demonstrating its capacity to enhance the prediction accuracy and reduce the uncertainty. A detailed machine Learning models is presented, emphasizing their capability to handle complex data and improve prediction under diverse operational conditions. This study contributes to more reliable, CT management and safer more cost-efficient well intervention operations.

Greylag goose optimization and multilayer perceptron for enhancing lung cancer classification

Lung cancer is an important global health problem, and it is defined by abnormal growth of the cells in the tissues of the lung, mostly leading to significant morbidity and mortality. Its timely identification and correct staging are very important for proper therapy and prognosis. Different computational methods have been used to enhance the precision of lung cancer classification, among which optimization algorithms such as Greylag Goose Optimization (GGO) are employed. These algorithms have the purpose of improving the performance of machine learning models that are presented with a large amount of complex data, selecting the most important features. As per lung cancer classification, data preparation is one of the most important steps, which contains the operations of scaling, normalization, and handling gap factor to ensure reasonable and reliable input data. In this domain, the use of GGO includes refining feature selection, which mainly focuses on enhancing the classification accuracy compared to other binary format optimization algorithms, like bSC, bMVO, bPSO, bWOA, bGWO, and bFOA. The efficiency of the bGGO algorithm in choosing the optimal features for improved classification accuracy is an indicator of the possible application of this method in the field of lung cancer diagnosis. The GGO achieved the highest accuracy with MLP model performance at 98.4%. The feature selection and classification results were assessed using statistical analysis, which utilized the Wilcoxon signed-rank test and ANOVA. The results were also accompanied by a set of graphical illustrations that ensured the adequacy and efficiency of the adopted hybrid method (GGO + MLP).

Machine learning applications in studying mental health among immigrants and racial and ethnic minorities: an exploratory scoping review

BackgroundThe use of machine learning (ML) in mental health (MH) research is increasing, especially as new, more complex data types become available to analyze. By examining the published literature, this review aims to explore the current applications of ML in MH research, with a particular focus on its use in studying diverse and vulnerable populations, including immigrants, refugees, migrants, and racial and ethnic minorities.MethodsFrom October 2022 to March 2024, Google Scholar, EMBASE, and PubMed were queried. ML-related, MH-related, and population-of-focus search terms were strung together with Boolean operators. Backward reference searching was also conducted. Included peer-reviewed studies reported using a method or application of ML in an MH context and focused on the populations of interest. We did not have date cutoffs. Publications were excluded if they were narrative or did not exclusively focus on a minority population from the respective country. Data including study context, the focus of mental healthcare, sample, data type, type of ML algorithm used, and algorithm performance were extracted from each.ResultsUltimately, 13 peer-reviewed publications were included. All the articles were published within the last 6 years, and over half of them studied populations within the US. Most reviewed studies used supervised learning to explain or predict MH outcomes. Some publications used up to 16 models to determine the best predictive power. Almost half of the included publications did not discuss their cross-validation method.ConclusionsThe included studies provide proof-of-concept for the potential use of ML algorithms to address MH concerns in these special populations, few as they may be. Our review finds that the clinical application of these models for classifying and predicting MH disorders is still under development.

Motor Insurance Claim Frequency Prediction Using XGBoost

Insurance claim frequency modelling is an important task for non-life insurers, this together with other variables forms an important part of product pricing and risk management. The traditional frequency models such as Poisson, Negative Binomial and Zero Inflated models have several weakness such as scalibility issues, overdispersion and independence assumptions for large datasets and therefore not ideal to use when dealing with complex and unstructured data. Extreme gradient Boosting Algorithm (XGBoost) is an ensemble learning which has the capacity to effectively handle big complex and unstructured insurance data. XGBoost creates tree-based models by iteratively fitting decision trees to the residuals of the previous predictions, effectively reducing the error in each iteration. This research utilized and explored the XGBoost algorithm to process motor insurance claims large dataset in-order to predict the frequencies of insurance claims, that is 0,1,2,and 3. Using this algorithm we aim to enhance the accuracy of predictions that will yield better estimates for improved risk assessment and pricing of insurance products. Cross validation was performed to assess the true performance of our model. Cross validation results showed that XGBoost models for the claim frequency had a RMSE estimate of 0.949, MAE of 0.7741 and RSQ 0.781. This demonstrated a strong predictive performance, with an RMSE of 0.949 and an MAE of 0.7741, indicating a low average error in the predictions.The RSQ of 0.781 suggests further that the model explained a significant proportion of variability of the insurance data. Our model was evaluated with a confusion matrix. The results of the confusion matrix showed that for the frequency 0 99.59% of cases were correctly predicted, frequency 1 94.01% were correctly predicted and frequency 2 84.80% and finally frequency 3 only 40.96% of the observations were correctly predicted.These results highlights the potential of XGBoost as a robust modeling technique for handling big data and accurately predicting insurance claim frequency. The results corroborate with other studies that XGBoost is an invaluable tool for insurance companies.

Genomics and Bioinformatics in One Health: Transdisciplinary Approaches for Health Promotion and Disease Prevention.

The One Health concept underscores the interconnectedness of human, animal, and environmental health, necessitating an integrated, transdisciplinary approach to tackle contemporary health challenges. This perspective paper explores the pivotal role of genomics and bioinformatics in advancing One Health initiatives. By leveraging genomic technologies and bioinformatics tools, researchers can decode complex biological data, enabling comprehensive insights into pathogen evolution, transmission dynamics, and host-pathogen interactions across species and environments (or ecosystems). These insights are crucial for predicting and mitigating zoonotic disease outbreaks, understanding antimicrobial resistance patterns, and developing targeted interventions for health promotion and disease prevention. Furthermore, integrating genomic data with environmental and epidemiological information enhances the precision of public health responses. Here we discuss case studies demonstrating successful applications of genomics and bioinformatics in One Health contexts, such as including data integration, standardization, and ethical considerations in genomic research. By fostering collaboration among geneticists, bioinformaticians, epidemiologists, zoologists, and data scientists, the One Health approach can harness the full potential of genomics and bioinformatics to safeguard global health. This perspective underscores the necessity of continued investment in interdisciplinary education, research infrastructure, and policy frameworks to effectively employ these technologies in the service of a healthier planet.

Pitfalls in Interpretive Applications of Artificial Intelligence in Radiology.

Interpretive artificial intelligence (AI) tools are poised to change the future of radiology. However, certain pitfalls may pose particular challenges for optimal AI interpretative performance. These include anatomic variants, age-related changes, postoperative changes, medical devices, image artifacts, lack of integration of prior and concurrent imaging examinations and clinical information, and the satisfaction-of-search effect. Model training and development should account for such pitfalls to minimize errors and optimize interpretation accuracy. More broadly, AI algorithms should be exposed to diverse and complex training datasets to yield a holistic interpretation that considers all relevant information beyond the individual examination. Successful clinical deployment of AI tools will require that radiologist end users recognize these pitfalls and other limitations of the available models. Furthermore, developers should incorporate explainable AI techniques (e.g., heat maps) into their tools, to improve radiologists' understanding of model outputs and to enable radiologists to provide feedback for guiding continuous learning and iterative refinement. In this article, we provide an overview of common pitfalls that radiologists may encounter when using interpretive AI products in daily practice. We present how such pitfalls lead to AI errors and offer potential strategies that AI developers may use for their mitigation.

SKYQUANT 3D: Quantifying Vascular Anatomy With an Open-Source Workflow for Comprehensive Analysis of Volumetric Optoacoustic Angiography Data.

Efficient visualization of the vascular system is of key importance in biomedical research into tumor angiogenesis, cerebrovascular alterations, and other angiopathies. Optoacoustic (OA) angiography offers a promising solution combining molecular optical contrast with high resolution and deep penetration of ultrasound. However, its hybrid nature implies complex data collection and processing workflows, with significant variability in methodologies across developers and users. To streamline interoperability, we introduce SKYQUANT 3D, a Python-based set of instructions for the Thermo Fisher Scientific Amira/Avizo 3D Visualization & Analysis Software. Our workflow simplifies the batch processing of volumetric optoacoustic angiography images, extracting meaningful quantitative information while also providing statistical analysis and graphical representation of the results. Quantification performance of SKYQUANT 3D is demonstrated using functional preclinical and clinical in vivo 3D OA angiographic tests involving ambient temperature variations and repositioning of the imaged limb.

Parameter optimization for stable clustering using FlowSOM: a case study from CyTOF.

High-dimensional cell phenotyping is a powerful tool to study molecular and cellular changes in health and diseases. CyTOF enables high-dimensional cell phenotyping using tens of surface and intra-cellular markers. To utilize the full potential of CyTOF, we need advanced clustering and machine learning methodologies to enable automated gating of the complex data. Here we show that critical modifications to a machine learning based FlowSOM package and precise parameter optimization can enable us to reliably analyze the complex CyTOF data. We show the impact of key parameters on clustering outcomes while addressing bugs within the publicly available package. We modified the FlowSOM pipeline to fix the bugs, enable scalability to handle large datasets and perform parameter optimization. We further validated this modified pipeline on a substantial external immunological dataset demonstrating the need of data-specific tailored parameter optimization to ensure reliable definition and interrogation of immune cell populations associated with immune disorders.

Deep learning as Ricci flow.

Deep neural networks (DNNs) are powerful tools for approximating the distribution of complex data. It is known that data passing through a trained DNN classifier undergoes a series of geometric and topological simplifications. While some progress has been made toward understanding these transformations in neural networks with smooth activation functions, an understanding in the more general setting of non-smooth activation functions, such as the rectified linear unit (ReLU), which tend to perform better, is required. Here we propose that the geometric transformations performed by DNNs during classification tasks have parallels to those expected under Hamilton's Ricci flow-a tool from differential geometry that evolves a manifold by smoothing its curvature, in order to identify its topology. To illustrate this idea, we present a computational framework to quantify the geometric changes that occur as data passes through successive layers of a DNN, and use this framework to motivate a notion of 'global Ricci network flow' that can be used to assess a DNN's ability to disentangle complex data geometries to solve classification problems. By training more than 1500 DNN classifiers of different widths and depths on synthetic and real-world data, we show that the strength of global Ricci network flow-like behaviour correlates with accuracy for well-trained DNNs, independently of depth, width and data set. Our findings motivate the use of tools from differential and discrete geometry to the problem of explainability in deep learning.