Data-driven classification of ligand unbinding pathways.

Studying the pathways of ligand-receptor binding is essential to understand the mechanism of target recognition by small molecules. The binding free energy and kinetics of protein-ligand complexes can be computed using molecular dynamics (MD) simulations, often in quantitative agreement with experiments. However, only a qualitative picture of the ligand binding/unbinding paths can be obtained through a conventional analysis of the MD trajectories. Besides, the higher degree of manual effort involved in analyzing pathways limits its applicability in large-scale drug discovery. Here, we address this limitation by introducing an automated approach for analyzing molecular transition paths with a particular focus on protein-ligand dissociation. Our method is based on the dynamic time-warping algorithm, originally designed for speech recognition. We accurately classified molecular trajectories using a very generic descriptor set of contacts or distances. Our approach outperforms manual classification by distinguishing between parallel dissociation channels, within the pathways identified by visual inspection. Most notably, we could compute exit-path-specific ligand-dissociation kinetics. The unbinding timescale along the fastest path agrees with the experimental residence time, providing a physical interpretation to our entirely data-driven protocol. In combination with appropriate enhanced sampling algorithms, this technique can be used for the initial exploration of ligand-dissociation pathways as well as for calculating path-specific thermodynamic and kinetic properties.

Virtual blebbistatin: A robust and rapid software approach to motion artifact removal in optical mapping of cardiomyocytes.

Fluorescent reporters of cardiac electrophysiology provide valuable information on heart cell and tissue function. However, motion artifacts caused by cardiac muscle contraction interfere with accurate measurement of fluorescence signals. Although drugs such as blebbistatin can be applied to stop cardiac tissue from contracting by uncoupling calcium-contraction, their usage prevents the study of excitation-contraction coupling and, as we show, impacts cellular structure. We therefore developed a robust method to remove motion computationally from images of contracting cardiac muscle and to map fluorescent reporters of cardiac electrophysiological activity onto images of undeformed tissue. When validated on cardiomyocytes derived from human induced pluripotent stem cells (iPSCs), in both monolayers and engineered tissues, the method enabled efficient and robust reduction of motion artifact. As with pharmacologic approaches using blebbistatin for motion removal, our algorithm improved the accuracy of optical mapping, as demonstrated by spatial maps of calcium transient decay. However, unlike pharmacologic motion removal, our computational approach allowed direct analysis of calcium-contraction coupling. Results revealed calcium-contraction coupling to be more uniform across cells within engineered tissues than across cells in monolayer culture. The algorithm shows promise as a robust and accurate tool for optical mapping studies of excitation-contraction coupling in heart tissue.

Mapping individual structural covariance network in development brain with dynamic time warping.

A conspicuous property of brain development or maturity is coupled with coordinated or synchronized brain structural co-variation. However, there is still a lack of effective approach to map individual structural covariance network. Here, we developed a novel individual structural covariance network method using dynamic time warping algorithm and applied it to delineate developmental trajectories of topological organizations of structural covariance network from childhood to early adulthood with a large sample of 655 individuals from Human Connectome Project-Development dataset. We found that the individual structural covariance network exhibited small-worldness property and the network global topological characteristics including small-worldness, global efficiency, local efficiency, and modularity linearly increase with age while the shortest path length linearly decreases with age. The nodal topological properties including betweenness and degree increased with age in language and emotion regulation related brain areas, while it decreased with age mainly in visual cortex, sensorimotor area, and hippocampus. Moreover, the topological attributes of structural covariance network as features could predict the age of each individual. Taken together, our results demonstrate that dynamic time warping can effectively map individual structural covariance network to uncover the developmental trajectories of network topology, which may facilitate future investigations to establish the links of structural co-variations with respect to cognition and disease vulnerability.

Probing the Anisotropic Fermi Surface in Tetralayer Graphene via Transverse Magnetic Focusing.

Bernal-stacked tetralayer graphene (4LG) exhibits intriguing low-energy properties, featuring two massive sub-bands and showcasing diverse features of topologically distinct, anisotropic Fermi surfaces, including Lifshitz transitions and trigonal warping. Here, we study the influence of the band structure on electron dynamics within 4LG using transverse magnetic focusing. Our analysis reveals two distinct focusing peaks corresponding to the two sub-bands. Furthermore, we uncover a pronounced dependence of the focusing spectra on crystal orientations, indicative of an anisotropic Fermi surface. Utilizing the semiclassical model, we attribute this orientation-dependent behavior to the trigonal warping of the band structure. This phenomenon leads to variations in electron trajectories based on crystal orientation. Our findings not only enhance our understanding of the dynamics of electrons in 4LG but also offer a promising method for probing anisotropic Fermi surfaces in other materials.

Crystal Symmetry-Dependent In-Plane Hall Effect.

The Hall effect has played a vital role in unraveling the intricate properties of electron transport in solid materials. Here, we report on a crystal symmetry-dependent in-plane Hall effect (CIHE) observed in a CuPt/CoPt ferromagnetic heterostructure. Unlike the planar Hall effect (PHE), the CIHE in CuPt/CoPt strongly depends on the current flowing direction (ϕI) with respect to the crystal structure. It reaches its maximum when the current is applied along the low crystal-symmetry axes and vanishes when applied along the high crystal-symmetry axes, exhibiting an unconventional angular dependence of cos(3ϕI). Utilizing a symmetry analysis based on the Invariant Theory, we demonstrate that the CIHE can exist in magnetic crystals possessing C3v symmetry. Using a tight-binding model and realistic first-principles calculations on the metallic heterostructure, we find that the CIHE originates from the trigonal warping of the Fermi surface. Our observations highlight the critical role of crystal symmetry in generating new types of Hall effects.

Physicochemical Evaluation of Remote Homology in the Twilight Zone.

A fundamental problem in the field of protein evolutionary biology is determining the degree and nature of evolutionary relatedness among homologous proteins that have diverged to a point where they share less than 30% amino acid identity yet retain similar structures and/or functions. Such proteins are said to lie within the "Twilight Zone" of amino acid identity. Many researchers have leveraged experimentally determined structures in the quest to classify proteins in the Twilight Zone. Such endeavors can be highly time consuming and prohibitively expensive for large-scale analyses. Motivated by this problem, here we use molecular weight-hydrophobicity physicochemical dynamic time warping (MWHP DTW) to quantify similarity of simulated and real-world homologous protein domains. MWHP DTW is a physicochemical method requiring only the amino acid sequence to quantify similarity of related proteins and is particularly useful in determining similarity within the Twilight Zone due to its resilience to primary sequence substitution saturation. This is a step forward in determination of the relatedness among Twilight Zone proteins and most notably allows for the discrimination of random similarity and true homology in the 0%-20% identity range. This method was previously presented expeditiously just after the outbreak of COVID-19 because it was able to functionally cluster ACE2-binding betacoronavirus receptor binding domains (RBDs), a task that has been elusive using standard techniques. Here we show that one reason that MWHP DTW is an effective technique for comparisons within the Twilight Zone is because it can uncover hidden homology by exploiting physicochemical conservation, a problem that protein sequence alignment algorithms are inherently incapable of addressing within the Twilight Zone. Further, we present an extended definition of the Twilight Zone that incorporates the dynamic relationship between structural, physicochemical, and sequence-based metrics.

Harmonizing three-dimensional MRI using pseudo-warping field guided GAN.

In pursuit of cultivating automated models for magnetic resonance imaging (MRI) to aid in diagnostics, an escalating demand for extensive, multisite, and heterogeneous brain imaging datasets has emerged. This potentially introduces biased outcomes when directly applied for subsequent analysis. Researchers have endeavored to address this issue by pursuing the harmonization of MRIs. However, most existing image-based harmonization methods for MRI are tailored for 2D slices, which may introduce inter-slice variations when they are combined into a 3D volume. In this study, we aim to resolve inconsistencies between slices by introducing a pseudo-warping field. This field is created randomly and utilized to transform a slice into an artificially warped subsequent slice. The objective of this pseudo-warping field is to ensure that generators can consistently harmonize adjacent slices to another domain, without being affected by the varying content present in different slices. Furthermore, we construct unsupervised spatial and recycle loss to enhance the spatial accuracy and slice-wise consistency across the 3D images. The results demonstrate that our model effectively mitigates inter-slice variations and successfully preserves the anatomical details of the images during the harmonization process. Compared to generative harmonization models that employ 3D operators, our model exhibits greater computational efficiency and flexibility.

Global patterns of rebound to normal RSV dynamics following COVID-19 suppression.

BACKGROUND: Annual epidemics of respiratory syncytial virus (RSV) had consistent timing and intensity between seasons prior to the SARS-CoV-2 pandemic (COVID-19). However, starting in April 2020, RSV seasonal activity declined due to COVID-19 non-pharmaceutical interventions (NPIs) before re-emerging after relaxation of NPIs. We described the unusual patterns of RSV epidemics that occurred in multiple subsequent waves following COVID-19 in different countries and explored factors associated with these patterns. METHODS: Weekly cases of RSV from twenty-eight countries were obtained from the World Health Organisation and combined with data on country-level characteristics and the stringency of the COVID-19 response. Dynamic time warping and regression were used to cluster time series patterns and describe epidemic characteristics before and after COVID-19 pandemic, and identify related factors. RESULTS: While the first wave of RSV epidemics following pandemic suppression exhibited unusual patterns, the second and third waves more closely resembled typical RSV patterns in many countries. Post-pandemic RSV patterns differed in their intensity and/or timing, with several broad patterns across the countries. The onset and peak timings of the first and second waves of RSV epidemics following COVID-19 suppression were earlier in the Southern than Northern Hemisphere. The second wave of RSV epidemics was also earlier with higher population density, and delayed if the intensity of the first wave was higher. More stringent NPIs were associated with lower RSV growth rate and intensity and a shorter gap between the first and second waves. CONCLUSION: Patterns of RSV activity have largely returned to normal following successive waves in the post-pandemic era. Onset and peak timings of future epidemics following disruption of normal RSV dynamics need close monitoring to inform the delivery of preventive and control measures.

Neural coding of space by time.

The intertwining of space and time poses a significant scientific challenge, transcending disciplines from philosophy and physics to neuroscience. Deciphering neural coding, marked by its inherent spatial and temporal dimensions, has proven to be a complex task. In this paper, we present insights into temporal and spatial modes of neural coding and their intricate interplay, drawn from neuroscientific findings. We illustrate the conversion of a purely spatial input into the temporal form of a singular spike train, demonstrating storage, transmission to remote locations, and recall through spike bursts corresponding to Sharp Wave Ripples. Moreover, the converted temporal representation can be transformed back into a spatiotemporal pattern. The principles of the transformation process are illustrated using a simple feed-forward spiking neural network. The frequencies and phases of Subthreshold Membrane potential Oscillations play a pivotal role in this framework. The model offers insights into information multiplexing and phenomena such as stretching or compressing time of spike patterns.

Seasonality of common respiratory viruses: Analysis of nationwide time-series data.

BACKGROUND AND OBJECTIVE: Understanding the seasonal behaviours of respiratory viruses is crucial for preventing infections. We evaluated the seasonality of respiratory viruses using time-series analyses. METHODS: This study analysed prospectively collected nationwide surveillance data on eight respiratory viruses, gathered from the Korean Influenza and Respiratory Surveillance System. The data were collected on a weekly basis by 52 nationwide primary healthcare institutions between 2015 and 2019. We performed Spearman correlation analyses, similarity analyses via dynamic time warping (DTW) and seasonality analyses using seasonal autoregressive integrated moving average (SARIMA). RESULTS: The prevalence of rhinovirus (RV, 23.6%-31.4%), adenovirus (AdV, 9.2%-16.6%), human coronavirus (HCoV, 3.0%-6.6%), respiratory syncytial virus (RSV, 11.7%-20.1%), influenza virus (IFV, 11.7%-21.5%), parainfluenza virus (PIV, 9.2%-12.6%), human metapneumovirus (HMPV, 5.6%-6.9%) and human bocavirus (HBoV, 5.0%-6.4%) were derived. Most of them exhibited a high positive correlation in Spearman analyses. In DTW analyses, all virus data from 2015 to 2019, except AdV, exhibited good alignments. In SARIMA, AdV and RV did not show seasonality. Other viruses showed 12-month seasonality. We describe the viruses as winter viruses (HCoV, RSV and IFV), spring/summer viruses (PIV, HBoV), a spring virus (HMPV) and all-year viruses with peak incidences during school periods (RV and AdV). CONCLUSION: This is the first study to comprehensively analyse the seasonal behaviours of the eight most common respiratory viruses using nationwide, prospectively collected, sentinel surveillance data.

Early Burst Suppression Similarity Association with Structural Brain Injury Severity on MRI After Cardiac Arrest.

BACKGROUND: Identical bursts on electroencephalography (EEG) are considered a specific predictor of poor outcomes in cardiac arrest, but its relationship with structural brain injury severity on magnetic resonance imaging (MRI) is not known. METHODS: This was a retrospective analysis of clinical, EEG, and MRI data from adult comatose patients after cardiac arrest. Burst similarity in first 72 h from the time of return of spontaneous circulation were calculated using dynamic time-warping (DTW) for bursts of equal (i.e., 500 ms) and varying (i.e., 100-500 ms) lengths and cross-correlation for bursts of equal lengths. Structural brain injury severity was measured using whole brain mean apparent diffusion coefficient (ADC) on MRI. Pearson's correlation coefficients were calculated between mean burst similarity across consecutive 12-24-h time blocks and mean whole brain ADC values. Good outcome was defined as Cerebral Performance Category of 1-2 (i.e., independence for activities of daily living) at the time of hospital discharge. RESULTS: Of 113 patients with cardiac arrest, 45 patients had burst suppression (mean cardiac arrest to MRI time 4.3 days). Three study participants with burst suppression had a good outcome. Burst similarity calculated using DTW with bursts of varying lengths was correlated with mean ADC value in the first 36 h after cardiac arrest: Pearson's r: 0-12 h: - 0.69 (p = 0.039), 12-24 h: - 0.54 (p = 0.002), 24-36 h: - 0.41 (p = 0.049). Burst similarity measured with bursts of equal lengths was not associated with mean ADC value with cross-correlation or DTW, except for DTW at 60-72 h (- 0.96, p = 0.04). CONCLUSIONS: Burst similarity on EEG after cardiac arrest may be associated with acute brain injury severity on MRI. This association was time dependent when measured using DTW.

Automatic gait events detection with inertial measurement units: healthy subjects and moderate to severe impaired patients.

BACKGROUND: Recently, the use of inertial measurement units (IMUs) in quantitative gait analysis has been widely developed in clinical practice. Numerous methods have been developed for the automatic detection of gait events (GEs). While many of them have achieved high levels of efficiency in healthy subjects, detecting GEs in highly degraded gait from moderate to severely impaired patients remains a challenge. In this paper, we aim to present a method for improving GE detection from IMU recordings in such cases. METHODS: We recorded 10-meter gait IMU signals from 13 healthy subjects, 29 patients with multiple sclerosis, and 21 patients with post-stroke equino varus foot. An instrumented mat was used as the gold standard. Our method detects GEs from filtered acceleration free from gravity and gyration signals. Firstly, we use autocorrelation and pattern detection techniques to identify a reference stride pattern. Next, we apply multiparametric Dynamic Time Warping to annotate this pattern from a model stride, in order to detect all GEs in the signal. RESULTS: We analyzed 16,819 GEs recorded from healthy subjects and achieved an F1-score of 100%, with a median absolute error of 8 ms (IQR [3-13] ms). In multiple sclerosis and equino varus foot cohorts, we analyzed 6067 and 8951 GEs, respectively, with F1-scores of 99.4% and 96.3%, and median absolute errors of 18 ms (IQR [8-39] ms) and 26 ms (IQR [12-50] ms). CONCLUSIONS: Our results are consistent with the state of the art for healthy subjects and demonstrate a good accuracy in GEs detection for pathological patients. Therefore, our proposed method provides an efficient way to detect GEs from IMU signals, even in degraded gaits. However, it should be evaluated in each cohort before being used to ensure its reliability.

KARATECH: A Practice Support System Using an Accelerometer to Reduce the Preliminary Actions of Karate.

Kumite is a karate sparring competition in which two players face off and perform offensive and defensive techniques. Depending on the players, there may be preliminary actions (hereinafter referred to as "pre-actions"), such as pulling the arms or legs, lowering the shoulders, etc., just before a technique is performed. Since the presence of a pre-action allows the opponent to know the timing of the technique, it is important to reduce pre-actions in order to improve the kumite. However, it is difficult for beginners and intermediate players to accurately identify their pre-actions and to improve them through practice. Therefore, this study aims to construct a practice support system that enables beginners and intermediate players to understand their pre-actions. In this paper, we focus on the forefist punch, one of kumite's punching techniques. We propose a method to estimate the presence or absence of a pre-action based on the similarity between the acceleration data of an arbitrary forefist punch and a previously prepared dataset consisting of acceleration data of the forefist punch without a pre-action. We found that the proposed method can estimate the presence or absence of a pre-action in an arbitrary forefist punch with an accuracy of 86%. We also developed KARATECH as a system to support the practice of reducing pre-actions using the proposed method. KARATECH shows the presence or absence of pre-actions through videos and graphs. The evaluation results confirmed that the group using KARATECH had a lower pre-action rate.

The Influence of Fatigue, Recovery, and Environmental Factors on the Body Stability of Construction Workers.

In the construction industry, falls, slips, and trips (FST) account for 42.3% of all accidents. The primary cause of FST incidents is directly related to the deterioration of workers' body stability. To prevent FST-related accidents, it is crucial to understand the interaction between physical fatigue and body stability in construction workers. Therefore, this study investigates the impact of fatigue on body stability in various construction site environments using Dynamic Time Warping (DTW) analysis. We conducted experiments reflecting six different fatigue levels and four environmental conditions. The analysis process involves comparing changes in DTW values derived from acceleration data obtained through wearable sensors across varying fatigue levels and construction environments. The results reveal the following changes in DTW values across different environments and fatigue levels: for non-obstacle, obstacle, water, and oil conditions, DTW values tend to increase as fatigue levels rise. In our experiments, we observed a significant decrease in body stability against external environments starting from fatigue Levels 3 or 4 (30% and 40% of the maximum failure point). In the non-obstacle condition, the DTW values were 9.4 at Level 0, 12.8 at Level 3, and 23.1 at Level 5. In contrast, for the oil condition, which exhibited the highest DTW values, the values were 10.5 at Level 0, 19.1 at Level 3, and 34.5 at Level 5. These experimental results confirm that the body stability of construction workers is influenced by both fatigue levels and external environmental conditions. Further analysis of recovery time, defined as the time it takes for body stability to return to its original level, revealed an increasing trend in recovery time as fatigue levels increased. This study quantitatively demonstrates through wearable sensor data that, as fatigue levels increase, workers experience decreased body stability and longer recovery times. The findings of this study can inform individual worker fatigue management in the future.

Specular Electron Focusing between Gate-Defined Quantum Point Contacts in Bilayer Graphene.

We report multiterminal measurements in a ballistic bilayer graphene (BLG) channel, where multiple spin- and valley-degenerate quantum point contacts (QPCs) are defined by electrostatic gating. By patterning QPCs of different shapes along different crystallographic directions, we study the effect of size quantization and trigonal warping on transverse electron focusing (TEF). Our TEF spectra show eight clear peaks with comparable amplitudes and weak signatures of quantum interference at the lowest temperature, indicating that reflections at the gate-defined edges are specular, and transport is phase coherent. The temperature dependence of the focusing signal shows that, despite the small gate-induced bandgaps in our sample (≲45 meV), several peaks are visible up to 100 K. The achievement of specular reflection, which is expected to preserve the pseudospin information of the electron jets, is promising for the realization of ballistic interconnects for new valleytronic devices.

Intra-annual vegetation changes and spatial variation in China over the past two decades based on remote sensing and time-series clustering.

Vegetation is an important link between land, atmosphere, and water, making its changes of great significance. However, existing research has predominantly focused on long-term vegetation changes, neglecting the intra-annual variations of vegetation. Hence, this study is based on the Enhanced Vegetation Index (EVI) data from 2000 to 2022, with a time step of 16 days, to analyze the intra-annual patterns of vegetation changes in China. The average intra-annual EVI values for each municipal-level administrative region were calculated, and the time-series k-means clustering algorithm was employed to divide these regions, exploring the spatial variations in China's intra-annual vegetation changes. Finally, the ridge regression and random forest methods were utilized to assess the drivers of intra-annual vegetation changes. The results showed that: (1) China's vegetation status exhibits a notable intra-annual variation pattern of "high in summer and low in winter," and the changes are more pronounced in the northern regions than in the southern regions; (2) the intra-annual vegetation changes exhibit remarkable regional disparities, and China can be optimally clustered into four distinct clusters, which align well with China's temperature and precipitation zones; and (3) the intra-annual vegetation changes demonstrate significant correlations with meteorological factors such as dew point temperature, precipitation, maximum temperature, and sea-level pressure. In conclusion, our study reveals the characteristics, spatial patterns and driving forces of intra-annual vegetation changes in China, which contribute to explaining ecosystem response mechanisms, providing valuable insights for ecological research and the formulation of ecological conservation and management strategies.

Inferring circadian gene regulatory relationships from gene expression data with a hybrid framework.

BACKGROUND: The central biological clock governs numerous facets of mammalian physiology, including sleep, metabolism, and immune system regulation. Understanding gene regulatory relationships is crucial for unravelling the mechanisms that underlie various cellular biological processes. While it is possible to infer circadian gene regulatory relationships from time-series gene expression data, relying solely on correlation-based inference may not provide sufficient information about causation. Moreover, gene expression data often have high dimensions but a limited number of observations, posing challenges in their analysis. METHODS: In this paper, we introduce a new hybrid framework, referred to as Circadian Gene Regulatory Framework (CGRF), to infer circadian gene regulatory relationships from gene expression data of rats. The framework addresses the challenges of high-dimensional data by combining the fuzzy C-means clustering algorithm with dynamic time warping distance. Through this approach, we efficiently identify the clusters of genes related to the target gene. To determine the significance of genes within a specific cluster, we employ the Wilcoxon signed-rank test. Subsequently, we use a dynamic vector autoregressive method to analyze the selected significant gene expression profiles and reveal directed causal regulatory relationships based on partial correlation. CONCLUSION: The proposed CGRF framework offers a comprehensive and efficient solution for understanding circadian gene regulation. Circadian gene regulatory relationships are inferred from the gene expression data of rats based on the Aanat target gene. The results show that genes Pde10a, Atp7b, Prok2, Per1, Rhobtb3 and Dclk1 stand out, which have been known to be essential for the regulation of circadian activity. The potential relationships between genes Tspan15, Eprs, Eml5 and Fsbp with a circadian rhythm need further experimental research.

Honeycomb Electron Lattice Induced Dirac Fermion with Trigonal Warping in Bilayer Electrides.

Emergent fermions arising from the excess electrons of electrides provide a new perspective for exploring semimetal states with unique Fermi surface geometries. In this study, a class of unique two-dimensional (2D) highly anisotropic Dirac fermions is designed using a sandwich structure. Based on the structural design and first-principles calculations, 2D electride MB (M = Ca/Sr, B = Cl/Br/I) is an ideal candidate material. The excess electrons of the bilayer MB could be stably localized in the interstitial cavities, constructing a natural zigzag honeycomb electron sublattice that further forms a Dirac fermion. Compared with traditional Dirac semimetals, 2D Dirac electrides exhibited rich physical properties: i) The Fermi surface shows trigonal warping in low-energy regions. In particular, the geometry of the Fermi surface determines the high anisotropy of the Fermi velocity. ii) A pair of Dirac fermions are protected by three-fold rotational symmetry and exhibit strong robustness. iii) Electride MB possesses a lower work function that strongly correlates with the surface area of the emission channel. Based on these properties, an electron-emitting device with multifunctional applications is fabricated. Therefore, this study provides an ideal platform for studying potential entanglement between structures, electrides, and topological states.

Pattern-based clustering of daily weigh-in trajectories using dynamic time warping.

"Smart"-scales are a new tool for frequent monitoring of weight change as well as weigh-in behavior. These scales give researchers the opportunity to discover patterns in the frequency that individuals weigh themselves over time, and how these patterns are associated with overall weight loss. Our motivating data come from an 18-month behavioral weight loss study of 55 adults classified as overweight or obese who were instructed to weigh themselves daily. Adherence to daily weigh-in routines produces a binary times series for each subject, indicating whether a participant weighed in on a given day. To characterize weigh-in by time-invariant patterns rather than overall adherence, we propose using hierarchical clustering with dynamic time warping (DTW). We perform an extensive simulation study to evaluate the performance of DTW compared to Euclidean and Jaccard distances to recover underlying patterns in adherence time series. In addition, we compare cluster performance using cluster validation indices (CVIs) under the single, average, complete, and Ward linkages and evaluate how internal and external CVIs compare for clustering binary time series. We apply conclusions from the simulation to cluster our real data and summarize observed weigh-in patterns. Our analysis finds that the adherence trajectory pattern is significantly associated with weight loss.

Latent deformation models for multivariate functional data and time-warping separability.

Multivariate functional data present theoretical and practical complications that are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are subject to mutual time warping. That is, the component processes exhibit a common shape but are subject to systematic phase variation across their domains in addition to subject-specific time warping, where each subject has its own internal clock. This motivates a novel model for multivariate functional data that connect such mutual time warping to a latent-deformation-based framework by exploiting a novel time-warping separability assumption. This separability assumption allows for meaningful interpretation and dimension reduction. The resulting latent deformation model is shown to be well suited to represent commonly encountered functional vector data. The proposed approach combines a random amplitude factor for each component with population-based registration across the components of a multivariate functional data vector and includes a latent population function, which corresponds to a common underlying trajectory. We propose estimators for all components of the model, enabling implementation of the proposed data-based representation for multivariate functional data and downstream analyses such as Fréchet regression. Rates of convergence are established when curves are fully observed or observed with measurement error. The usefulness of the model, interpretations, and practical aspects are illustrated in simulations and with application to multivariate human growth curves and multivariate environmental pollution data.