Diffusion Maps Research Articles

A machine learning pipeline for efficient differentiation between bipolar and major depressive disorder based on multimodal structural neuroimaging

Due to the overlapping depressive symptomatology with major depressive disorder (MDD), 60% of patients with bipolar disorder (BD) are initially misdiagnosed, calling for the definition of reliable biomarkers that can support the diagnostic process. Here, we optimized a machine learning pipeline for the differentiation between depressed BD and MDD patients based on multimodal structural neuroimaging features. Diffusion tensor imaging (DTI) and T1-weighted magnetic resonance imaging (MRI) data were acquired for 282 depressed BD (n = 180) and MDD (n = 102) patients. Images were preprocessed to obtain axial (AD), radial (RD), mean (MD) diffusivity, fractional anisotropy (FA), and voxel-based morphometry (VBM) maps. Each feature was entered separately into a 5-fold nested cross-validated predictive pipeline differentiating between BD and MDD patients, comprising: confound regression for nuisance variables removal, feature standardization, principal component analysis for feature reduction, and an elastic-net penalized regression. The DTI-based models reached accuracies ranging from 75% to 78%, whereas the VBM model reached 61% of accuracy. All the models were significantly different from a null model distribution at a 5000-permutation test. A 5000 bootstrap procedure revealed that widespread differences drove the classification, with BD patients associated to overall higher values of AD and FA, and grey matter volumes. Our results suggest that structural neuroimaging, in particular white matter microstructure and grey matter volumes, may be able to differentiate between MDD and BD patients with good predictive accuracy, being significantly higher than chance-level.

Unsupervised pattern and outlier detection for pedestrian trajectories using diffusion maps

The movement of pedestrian crowds is studied both for real-world applications and to gain fundamental scientific insights into systems of self-driven particles. Trajectory data describes the dynamics of pedestrian crowds at the level of individual movement paths. Analysing such data is a central challenge in pedestrian dynamics research, coupled with increasing data availability this implies a need for efficient methods to identify key features of the captured crowd dynamics. In this paper, we show that diffusion maps, an unsupervised manifold learning method, can be used for this purpose. We show how to build an informative feature space by defining a set of observables from trajectories. We use our diffusion map approach to analyse pedestrian movement on a stadium-shaped track, and during egress from a room, considering hundreds of trajectories for each scenario. We first verify that our diffusion map analysis can recover known leading variables that determine the system dynamics. Then, we show how our analysis facilitates a qualitative comparison of the dynamics inherent in entire data sets, by contrasting experimental with numerically simulated data. Finally, we establish how our approach can be used to automatically detect outliers that show behaviour distinct to others. These results indicate that our work can contribute a computationally efficient and unsupervised approach to analyse pedestrian dynamics without needing much prior knowledge of the data. We suggest this could be useful for automatically monitoring live data, or as an initial step to inform a subsequent analysis.

Health communication strategy based on the factors that influence the prevention of chinkungunya, dengue and Zika in Latin America

Diseases chinkungunya, breakbone fever and zika cause big risks of infection in Latin America, due to low rate of existent communication regarding the forms to prevent these diseases. The objective of investigation is to propose a strategy of communication as from determining the factors that influence the chinkungunya's prevention, breakbone fever and zika in Latin America. The analysis of the conceptual diffuse map and the resulting womb highlight the sanitary communication like a central pillar that shows increased the power of by the effective implementation of them TIC and the well-designed formulation of strategies of communication. A significant link between these strategies and the governmental support are identified, that it is indispensable for the success of the programs of public health. The results of the conceptual map suggest than a sanitary robust communication and strategically designed improvement the regional step of health and key is for reducing the risk of sprouts of breakbone fever, chikungunya and zika. The importance of a communicative and interdisciplinary focus that incorporate multiple actors is stressed, once the governments were included, health-care professionals and the community in general, for the better the prevention of these diseases zoonóticas. The womb reaffirms the need of a design innovative comunicacional that you consider factors socioculturales and educational to guarantee that the information did not sole spread him out but also understand him and apply him. The findings derived of investigation back up the implementation of a telling strategy integrated and adapted that may respond to dynamically the evolution of the diseases and to the changes in perceptions and the population's behaviors

Aggregation of monitoring datasets for functional diversity estimation

Long-term monitoring data is central for the analysis of biodiversity change and its drivers. Time series allow a more accurate evaluation of diversity indices, trait identification and community turnover. However, evaluating data collected across different monitoring programs remains complicated because of data discrepancies and inconsistencies. Here we propose a method for aggregating datasets using diffusion maps. The method is illustrated by aggregating long-term phytoplankton abundance data from the Wadden Sea and Southern North Sea gathered by two institutions located in Germany and The Netherlands. The aggregated data allowed us to infer species traits, to reconstruct the main trait axis which drives community functionality, ultimately quantifying functional diversity of the individual samples, having used only the co-occurrence of species in samples. Although functional diversity varies greatly among sampling stations, we detect a slight positive trend in German stations, which contrasts with the clear decreasing trend observed in most of the Dutch Wadden Sea stations. At the Terschelling transect, in Southern North Sea, the stations also showed contrasting estimations of functional diversity between off-shore and in-shore stations. Our research provides further evidence that traits and functional diversity can be robustly reconstructed from monitoring data alone, showing that data aggregation can increase the accuracy of this reconstruction, being able to aggregate heterogeneous datasets.

Amide proton transfer weighted combined with diffusion kurtosis imaging for predicting lymph node metastasis in cervical cancer

ObjectiveTo investigate the value of amide proton transfer weighted (APTw) combined with diffusion kurtosis imaging (DKI) in quantitative prediction of lymph node metastasis (LNM) in cervical carcinoma (CC). MethodsData of 19 LNM(+) and 50 LNM(−) patients with CC were retrospectively analyzed. 3.0 T MRI scan was performed before the operation, including APTw and DKI. After post-processing, quantitative magnetization transfer ratio asymmetric at 3.5 ppm [MTRasym (3.5 ppm)], mean kurtosis (MK), and mean diffusivity (MD) maps were obtained. The MTRasym(3.5 ppm), MK, and MD values were respectively measured by two observers, and intra-class correlation coefficients (ICC) were used to test the consistency of the results. The independent samples t-test or Mann-Whitney U test was used to compare the differences in the values of each parameter. The ROC curve was used to analyze the predictive performance of parameters with significant differences and their combination parameter. ResultsThe two observers had good agreement in the measurement of each data (ICC > 0.75). The MTRasym(3.5 ppm) and MK values of the LNM(+) group(3.260 ± 0.538% and 0.531 ± 0.202) were higher than those of the LNM(−) group(2.698 ± 0.597% and 0.401 ± 0.148) (P < 0.05), while there was no significant difference in MD values between the two groups(P > 0.05). The area under the curves (AUCs) of MTRasym(3.5 ppm), MK value, and MTRasym(3.5 ppm) + MK value were 0.763, 0.716, and 0.813, respectively, when predicting LNM status of CC. ConclusionAPTw and DKI can quantitatively predict LNM status of CC, which is of importance in clinical diagnosis and treatment.

Spatiotemporal analysis of Rabies outbreaks in herbivores in Tocantins as a subsidy for the detection of epizootics

An effective epidemiological surveillance system is essential to help control rabies, as it allows the early detection of unexpected increases in the disease as well as the identification of geographic areas with populations that need greater attention from the Official Veterinary Services (OVS). The present study aimed to comprehend the behavior of rabies outbreaks in herbivores, through a temporal analysis using a control diagram based on moving averages, and a spatial diffusion mapping. A spatial clustering analysis in rabies outbreaks was performed using both nearest neighbor analysis and ST-DBSCAN (Density-Based Spatial Clustering of Applications with Noise). Additionally, associated risk factors and the effectiveness of rabies vaccination was assessed using a chi-square (χ²) test and odds ratios as the association measure. The study detected rabies outbreaks in state of Tocantins in certain years, especially in 2015. Spatial analysis revealed clustering (nearest neighbor index = 0.555; p &lt; 0.05) in intermediate regions of Araguaína e Palmas. Risk factors identified included shelter linked to relief, vegetation, and anthropic factors. The findings of this study have significant implications for the control of rabies in herbivores, providing valuable information to guide vaccination efforts and the control of hematophagous bats, thus aiding in disease prevention and control actions not only Tocantins state but also in other geographic regions grappling with paralytic rabies.

Exponential Local Fisher Discriminant Analysis with Sparse Variables Selection: A Novel Fault Diagnosis Scheme for Industry Application

Local Fisher discriminant analysis (LFDA) has been widely applied to dimensionality reduction and fault classification fields. However, it often suffers from small sample size (SSS) problem and incorporates all process variables without emphasizing the key faulty ones, thus leading to degraded fault diagnosis performance and poor model interpretability. To this end, this paper develops the sparse variables selection based exponential local Fisher discriminant analysis (SELFDA) model, which can overcome the two limitations of basic LFDA concurrently. First, the responsible faulty variables are identified automatically through the least absolute shrinkage and selection operator, and the current optimization problem are subsequently recast as an iterative convex optimization problem and solved by the minimization-maximization method. After that, the matrix exponential strategy is implemented on LFDA, it can essentially overcome the SSS problem by ensuring that the within-class scatter matrix is always full-rank, thus more practical in real industrial practices, and the margin between different categories is enlarged due to the distance diffusion mapping, which is benefit for the enhancement of classification accuracy. Finally, the Tennessee Eastman process and a real-world diesel working process are employed to validate the proposed SELFDA method, experimental results prove that the SELFDA framework is more excellent than the other approaches.

Diffusion-Ordered Spectroscopy (DOSY) as a Powerful NMRMethod to Investigate Molecular Mobitiesand IntermolecularInteractions in Complex Oil Mixtures.

Studying the characteristics and molecular mechanisms of liquid self-diffusion coefficient and viscosity changes is of great significance for, e.g., chemical and petroleum processing. As an example of a highly complex liquid, asphaltene-free high-acid and high-viscosity crude oil and its extracted fractions were studied by comparing their 1H DOSY diffusion maps. The crude oil exhibited a polydisperse diffusion distribution, including multiple diffusion portions with diffusion coefficients much smaller than that of any single fraction in independent diffusion. The main mechanism that leads to the decreases in the diffusion coefficients of crude oil is attributed to diffusion resistance enhanced by Dynamical Molecular-Interaction Networks (DMINs), rather than by enlargement of the diffusion species caused by molecular aggregation. Constructed through the synergistic interactions of various polar molecules in crude oil, DMINs dynamically bind polar molecules, trap polarizable molecules, and spatially hinder the free motion of non-polar molecules. Overall, this reduces the diffusion coefficients of all molecular. This study demonstrates that DOSY is a powerful NMR method to investigate molecular motion abilities in complex mixtures. In addition, the insights in the influence of the interaction matrix on the molecular mobility also help to understand the contribution of "structural viscosity" to the viscosity of heavy oil.

RADT-26. IMPROVING RADIATION TARGET VOLUME DEFINITION FOR GLIOBLASTOMA USING PREDICTIONS OF TUMOR RECURRENCE FROM MACHINE LEARNING AND PRE-RADIOTHERAPY ADVANCED MRI

Abstract INTRODUCTION Standard-of-care (SOC) radiation therapy (RT) planning only utilizes a fairly 1.5-2cm uniform expansion of T2-weighted-FLAIR MRI lesion to generate a clinical target volume (2cm-CTV), without considering the spatial heterogeneity and infiltrative nature of glioblastomas. This study aimed to use multi-parametric MRI with 2 artificial intelligence (AI)-based approaches to predict regions of subsequent tumor progression and compare the resulting predictions to the 2cm-CTV, with the hypothesis that applying deep learning will lead to improved detection of subclinical disease that is under-treated, and more accurately delineate areas at higher risk for progression, than the uniform 2cm-CTV. METHODS We used normalized maps of anatomical, diffusion, and metabolic MRI post-surgical resection and before RT and chemotherapy from 72 patients newly-diagnosed with glioblastoma to train Random-Forest and deep-learning UNet models to identify voxels that later exhibit progression by either the contrast-enhancing-lesion (CEL) or T2-lesion (T2L). All models were trained/validated on 54 and tested on 18 patients after careful inter-exam alignment and normalization. Model performance was compared to the 2cm-CTV using a Progression-Coverage-Coefficient (PCC), a weighted Dice coefficient that accounts for tumor-size. RESULTS Random-Forest models were able to predict subsequent contrast-enhancing (CE) and T2 non-enhancing (NE) progression with an average respective test AUC of 0.88 and 0.82, with 15.6%/9.6% higher performance on patients who progressed early. The 2cm-CTV treatment plan achieved the highest sensitivity (0.833 vs 0.795) but also the lowest specificity (0.879 vs 0.935), over-treating normal-appearing-brain. Our deep learning model outperformed the 2cm-CTV in covering the progressed lesion, with the highest specificity (0.935 vs 0.879), PCC (0.741 vs 0.734), and had comparable sensitivity (0.795) to the 2cm-CTV, while sparing more normal brain compared to the 2cm-CTV. CONCLUSION This study demonstrates the potential benefit of using multi-parametric MRI with deep learning to assist in RT treatment planning to reduce excessive treatment of normal brain parenchyma.

Abstract 12147: Flow-Induced Cellular Reprogramming in Mouse Atherosclerosis Model

Introduction: Atherosclerosis, a leading cause of death worldwide, is a chronic inflammatory disease that occurs preferentially in the arterial regions exposed to disturbed flow (d-flow), while those exposed to stable flow (s-flow) are protected. Recently, we reported d- F low I nduced R eprogramming of E ndothelial cells (ECs) ( FIRE ), including endothelial inflammation, endothelial-to-mesenchymal transition (EndMT) and endothelial-to-immune-cell transition (EndIT). Hypothesis: D-flow plus hypercholesterolemia (HighChol) exacerbates reprogramming of arterial cells leading to atherosclerosis development compared to d-flow alone and HighChol alone. Methods: To test this hypothesis, we induced atherosclerosis in C57BL/6 mice by an AAV-PCSK9 injection and high-fat diet to induce HighChol and/or partial carotid ligation (PCL) surgery to expose left carotid artery (LCA) to d-flow compared to the right CA (RCA) exposed to s-flow. Single cells prepared from collagenase digestion of the LCAs and RCAs at 2 and 4 weeks post-PCL were analyzed by scRNA-seq and integrated with our prior scRNA-seq data obtained at 2 days and 2 weeks post-PCL under normal blood cholesterol levels. Results: Overall, our data showed that d-flow was the most predominant regulator of arterial cell characteristics while HighChol alone had relatively minor effects. In the RCA, homeostatic EC, smooth muscle cell (SMC), and macrophage (MΦ) clusters were dominant regardless of cholesterol levels. Additionally, for these cell types, we found clusters that increased in response to d-flow in the LCA, which further increased with HighChol and time. Surprisingly, diffusion map trajectory analysis revealed a clear convergence of transcriptomic profiles of EndIT ECs, SMC-derived foam cell SMCs, and foamy MΦs. Conclusions: These results suggest FIRE initiated by d-flow is exacerbated by HighChol. We also found that SMCs and MΦs transition toward proatherogenic phenotypes under d-flow, which is further exacerbated by HighChol. Furthermore, differential gene expression analysis showed that proatherogenic ECs, SMCs, and MΦs show common transcriptomic profiles, suggesting common set of genes and pathways that could be targeted as effective atherosclerotic therapeutics.

Functional diffusion maps

Nowadays many real-world datasets can be considered as functional, in the sense that the processes which generate them are continuous. A fundamental property of this type of data is that in theory they belong to an infinite-dimensional space. Although in practice we usually receive finite observations, they are still high-dimensional and hence dimensionality reduction methods are crucial. In this vein, the main state-of-the-art method for functional data analysis is Functional PCA. Nevertheless, this classic technique assumes that the data lie in a linear manifold, and hence it could have problems when this hypothesis is not fulfilled. In this research, attention has been placed on a non-linear manifold learning method: Diffusion Maps. The article explains how to extend this multivariate method to functional data and compares its behavior against Functional PCA over different simulated and real examples.

Using reflectometry to minimize the dependence of fluorescence intensity on optical absorption and scattering.

The total diffuse reflectance RT and the effective attenuation coefficient µeff of an optically diffuse medium map uniquely onto its absorption and reduced scattering coefficients. Using this premise, we developed a methodology where RT and the slope of the logarithmic spatially resolved reflectance, a quantity related to µeff, are the inputs of a look-up table to correct the dependence of fluorescent signals on the media's optical properties. This methodology does not require an estimation of the medium's optical property, avoiding elaborate simulations and their errors to offer accurate and fast corrections. The experimental demonstration of our method yielded a mean relative error in fluorophore concentrations of less than 4% over a wide range of optical property variations. We discuss how the method developed can be employed to improve image fidelity and fluorochrome quantification in fluorescence molecular imaging clinical applications.

Simultaneous perfusion, diffusion, T2 *, and T1 mapping with MR fingerprinting.

Quantitative mapping of brain perfusion, diffusion, T2 *, and T1 has important applications in cerebrovascular diseases. At present, these sequences are performed separately. This study aims to develop a novel MRI technique to simultaneously estimate these parameters. This sequence to measure perfusion, diffusion, T2 *, and T1 mapping with magnetic resonance fingerprinting (MRF) was based on a previously reported MRF-arterial spin labeling (ASL) sequence, but the acquisition module was modified to include different TEs and presence/absence of bipolar diffusion-weighting gradients. We compared parameters derived from the proposed method to those derived from reference methods (i.e., separate sequences of MRF-ASL, conventional spin-echo DWI, and T2 * mapping). Test-retest repeatability and initial clinical application in two patients with stroke were evaluated. The scan time of our proposed method was 24% shorter than the sum of the reference methods. Parametric maps obtained from the proposed method revealed excellent image quality. Their quantitative values were strongly correlated with those from reference methods and were generally in agreement with values reported in the literature. Repeatability assessment revealed that ADC, T2 *, T1 , and B1 + estimation was highly reliable, with voxelwise coefficient of variation (CoV) <5%. The CoV for arterial transit time and cerebral blood flow was 16% ± 3% and 25% ± 9%, respectively. The results from the two patients with stroke demonstrated that parametric maps derived from the proposed method can detect both ischemic and hemorrhagic stroke. The proposed method is a promising technique for multi-parametric mapping and has potential use in patients with stroke.

Dissimilarity analysis based on diffusion maps

Compositional measurements from species assemblages define a high dimensional dataspace in which the data can form complex structures, termed manifolds. Comparing assemblages in this dataspace is difficult because the data is often sparse relative to its dimensionality and the complex structure of the manifold introduces bias and error in measurements of distance. Here, we apply diffusion maps, a manifold learning method, to find and characterize manifolds in high‐dimensional compositional data. We show that diffusion maps embed the data in reduced dimensions in which the Euclidean distance between data points approximates the distance between them along the manifold. This is especially useful when species turnover is high, as it provides a way to measure meaningful distances between assemblages even when they harbor disjoint sets of species. We anticipate diffusion maps will therefore be particularly useful for characterizing community change over large spatial and temporal scales.

MRI radiomics for hamstring strain injury identification and return to sport classification: a pilot study.

To determine if MRI-based radiomics from hamstring muscles are related to injury and if the features could be used to perform a time to return to sport (RTS) classification. We hypothesize that radiomics from hamstring muscles, especially T2-weighted and diffusion tensor imaging-based features, are related to injury and can be used for RTS classification. MRI data from 32 athletes at the University of Wisconsin-Madison that sustained a hamstring strain injury were collected. Diffusion tensor imaging and T1- and T2-weighted images were processed, and diffusion maps were calculated. Radiomics features were extracted from the four hamstring muscles in each limb and for each MRI modality, individually. Feature selection was performed and multiple support vector classifiers were cross-validated to differentiate between involved and uninvolved limbs and perform binary (≤ or > 25days) and multiclass (< 14 vs. 14-42 vs. > 42days) classification of RTS. The combination of radiomics features from all diffusion tensor imaging and T2-weighted images provided the most accurate differentiation between involved and uninvolved limbs (AUC ≈ 0.84 ± 0.16). For the binary RTS classification, the combination of all extracted radiomics offered the most accurate classification (AUC ≈ 0.95 ± 0.15). While for the multiclass RTS classification, the combination of features from all the diffusion tensor imaging maps provided the most accurate classification (weighted one vs. rest AUC ≈ 0.81 ± 0.16). This pilot study demonstrated that radiomics features from hamstring muscles are related to injury and have the potential to predict RTS.

Diffusion maps for embedded manifolds with boundary with applications to PDEs

Given only a finite collection of points sampled from a Riemannian manifold embedded in a Euclidean space, in this paper we propose a new method to numerically solve elliptic and parabolic partial differential equations (PDEs) supplemented with boundary conditions. Since the construction of triangulations on unknown manifolds can be both difficult and expensive, both in terms of computational and data requirements, our goal is to solve these problems without a triangulation. Instead, we rely only on using the sample points to define quadrature formulas on the unknown manifold. Our main tool is the diffusion maps algorithm. We re-analyze this well-known method in a variational sense for manifolds with boundary. Our main result is that the variational diffusion maps graph Laplacian is a consistent estimator of the Dirichlet energy on the manifold. This improves upon previous results and provides a rigorous justification of the well-known relationship between diffusion maps and the Neumann eigenvalue problem. Moreover, using semigeodesic coordinates we derive the first uniform asymptotic expansion of the diffusion maps kernel integral operator for manifolds with boundary. This expansion relies on a novel lemma which relates the extrinsic Euclidean distance to the coordinate norm in a normal collar of the boundary. We then use a recently developed method of estimating the distance to boundary function (notice that the boundary location is assumed to be unknown) to construct a consistent estimator for boundary integrals. Finally, by combining these various estimators, we illustrate how to impose Dirichlet and Neumann conditions for some common PDEs based on the Laplacian. Several numerical examples illustrate our theoretical findings.

Disruptions of Hierarchical Cortical Organization in Early Psychosis and Schizophrenia

BackgroundThe cerebral cortex is organized hierarchically along an axis that spans unimodal sensorimotor to transmodal association areas. This hierarchy is often characterized using low-dimensional embeddings, termed gradients, of interregional functional coupling estimates measured with resting-state functional magnetic resonance imaging. Such analyses may offer insights into the pathophysiology of schizophrenia, which has been frequently linked to dysfunctional interactions between association and sensorimotor areas. MethodsTo examine disruptions of hierarchical cortical function across distinct stages of psychosis, we applied diffusion map embedding to 2 independent functional magnetic resonance imaging datasets: one comprising 114 patients with early psychosis and 48 control participants, and the other comprising 50 patients with established schizophrenia and 121 control participants. Then, we analyzed the primary sensorimotor-to-association and secondary visual-to-sensorimotor gradients of each participant in both datasets. ResultsThere were no significant differences in regional gradient scores between patients with early psychosis and control participants. Patients with established schizophrenia showed significant differences in the secondary, but not primary, gradient compared with control participants. Gradient differences in schizophrenia were characterized by lower within-network dispersion in the dorsal attention (false discovery rate [FDR]–corrected p [pFDR] < .001), visual (pFDR = .003), frontoparietal (pFDR = .018), and limbic (pFDR = .020) networks and lower between-network dispersion between the visual network and other networks (pFDR < .001). ConclusionsThese findings indicate that differences in cortical hierarchical function occur along the secondary visual-to-sensorimotor axis rather than the primary sensorimotor-to-association axis as previously thought. The absence of differences in early psychosis suggests that visual-sensorimotor abnormalities may emerge as the illness progresses.

Confidence-Aware Multiscale Learning for Online Modeling of Distributed Parameter Systems With Application to Curing Process

In industrial applications, the modeling of distributed parameter systems (DPSs) is of significance for process control and monitoring. Due to infinite dimension, spatiotemporal coupled dynamics, nonlinearity and model uncertainties, however, modeling and online applications of DPSs are very difficult. To address these issues, an online spatiotemporal modeling method is proposed based on confidence-aware multiscale learning. From the spacial-scale perspective, an evolutionary learning-based spatial basis function is designed by learning from two dimensionality reduction methods, including Karhunen-Lo <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\grave{e}$</tex-math></inline-formula> ve and diffusion maps. From the temporal-scale perspective, an efficient broad learning system is developed as reduced-order model to online address temporal dynamics of DPSs. As for the spatiotemporal-scale learning, Gaussian process regression is proposed as confidence-aware estimator to compensate for model generalization errors caused by spatiotemporal coupled dynamics. Through integration with the three-scale learning, the proposed method enables online confidence-aware prediction for DPSs. Experiments based on the curing process in snap curing oven demonstrate the effectiveness of proposed method.

Using Diffusion Maps to Analyze Reaction Dynamics for a Hydrogen Combustion Benchmark Dataset.

We use local diffusion maps to assess the quality of two types of collective variables (CVs) for a recently published hydrogen combustion benchmark dataset1 that contains ab initio molecular dynamics (MD) trajectories and normal modes along minimum energy paths. This approach was recently advocated in2 for assessing CVs and analyzing reactions modeled by classical MD simulations. We report the effectiveness of this approach to molecular systems modeled by quantum ab initio MD. In addition to assessing the quality of CVs, we also use global diffusion maps to perform committor analysis as proposed in.2 We show that the committor function obtained from the global diffusion map allows us to identify transition regions of interest in several hydrogen combustion reaction channels.

Unsupervised Learning of non‐Hermitian Photonic Bulk Topology

AbstractMachine‐learning has proven useful in distinguishing topological phases. However, there is still a lack of relevant research in the non‐Hermitian community, especially from the perspective of the momentum‐space. Here, an unsupervised machine‐learning method, diffusion maps, is used to study non‐Hermitian topologies in the momentum‐space. Choosing proper topological descriptors as input datasets, topological phases are successfully distinguished in several prototypical cases, including a line‐gapped tight‐binding model, a line‐gapped Floquet model, and a point‐gapped tight‐binding model. The datasets can be further reduced when certain symmetries exist. A mixed diffusion kernel method is proposed and developed, which could study several topologies at the same time and give hierarchical clustering results. As an application, a novel phase transition process is discovered in a non‐Hermitian honeycomb lattice without tedious numerical calculations. This study characterizes band properties without any prior knowledge, which provides a convenient and powerful way to study topology in non‐Hermitian systems.