Identifying EEG Biomarkers of Depression with Novel Explainable Deep Learning Architectures.

Deep learning methods are increasingly being applied to raw electroencephalogram (EEG) data. However, if these models are to be used in clinical or research contexts, methods to explain them must be developed, and if these models are to be used in research contexts, methods for combining explanations across large numbers of models must be developed to counteract the inherent randomness of existing training approaches. Model visualization-based explainability methods for EEG involve structuring a model architecture such that its extracted features can be characterized and have the potential to offer highly useful insights into the patterns that they uncover. Nevertheless, model visualization-based explainability methods have been underexplored within the context of multichannel EEG, and methods to combine their explanations across folds have not yet been developed. In this study, we present two novel convolutional neural network-based architectures and apply them for automated major depressive disorder diagnosis. Our models obtain slightly lower classification performance than a baseline architecture. However, across 50 training folds, they find that individuals with MDD exhibit higher ß power, potentially higher δ power, and higher brain-wide correlation that is most strongly represented within the right hemisphere. This study provides multiple key insights into MDD and represents a significant step forward for the domain of explainable deep learning applied to raw EEG. We hope that it will inspire future efforts that will eventually enable the development of explainable EEG deep learning models that can contribute both to clinical care and novel medical research discoveries.

Explainable fuzzy clustering framework reveals divergent default mode network connectivity dynamics in schizophrenia.

Introduction: Dynamic functional network connectivity (dFNC) analysis of resting state functional magnetic resonance imaging data has yielded insights into many neurological and neuropsychiatric disorders. A common dFNC analysis approach uses hard clustering methods like k-means clustering to assign samples to states that summarize network dynamics. However, hard clustering methods obscure network dynamics by assuming (1) that all samples within a cluster are equally like their assigned centroids and (2) that samples closer to one another in the data space than to their centroids are well-represented by their centroids. In addition, it can be hard to compare subjects, as in some cases an individual may not manifest a state strongly enough to enter a hard cluster. Approaches that allow a dimensional approach to connectivity patterns (e.g., fuzzy clustering) can mitigate these issues. In this study, we present an explainable fuzzy clustering framework by combining fuzzy c-means clustering with several explainability metrics and novel summary features. Methods: We apply our framework for schizophrenia (SZ) default mode network analysis. Namely, we extract dFNC from individuals with SZ and controls, identify 5 dFNC states, and characterize the dFNC features most crucial to those states with a new perturbation-based clustering explainability approach. We then extract several features typically used in hard clustering and further present a variety of unique features specially designed for use with fuzzy clustering to quantify state dynamics. We examine differences in those features between individuals with SZ and controls and further search for relationships between those features and SZ symptom severity. Results: Importantly, we find that individuals with SZ spend more time in states of moderate anticorrelation between the anterior and posterior cingulate cortices and strong anticorrelation between the precuneus and anterior cingulate cortex. We further find that individuals with SZ tend to transition more rapidly than controls between low-magnitude and high-magnitude dFNC states. Conclusion: We present a novel dFNC analysis framework and use it to identify effects of SZ upon network dynamics. Given the ease of implementing our framework and its enhanced insight into network dynamics, it has great potential for use in future dFNC studies.

Structural basis for the oligomerization-facilitated NLRP3 activation.

The NACHT-, leucine-rich-repeat-, and pyrin domain-containing protein 3 (NLRP3) is a critical intracellular inflammasome sensor and an important clinical target against inflammation-driven human diseases. Recent studies have elucidated its transition from a closed cage to an activated disk-like inflammasome, but the intermediate activation mechanism remains elusive. Here we report the cryo-electron microscopy structure of NLRP3, which forms an open octamer and undergoes a ~ 90° hinge rotation at the NACHT domain. Mutations on open octamer's interfaces reduce IL-1ß signaling, highlighting its essential role in NLRP3 activation/inflammasome assembly. The centrosomal NIMA-related kinase 7 (NEK7) disrupts large NLRP3 oligomers and forms NEK7/NLRP3 monomers/dimers which is a critical step preceding the assembly of the disk-like inflammasome. These data demonstrate an oligomeric cooperative activation of NLRP3 and provide insight into its inflammasome assembly mechanism.

Identifying Reproducibly Important EEG Markers of Schizophrenia with an Explainable Multi-Model Deep Learning Approach.

The diagnosis of schizophrenia (SZ) can be challenging due to its diverse symptom presentation. As such, many studies have sought to identify diagnostic biomarkers of SZ using explainable machine learning methods. However, the generalizability of identified biomarkers in many machine learning-based studies is highly questionable given that most studies only analyze explanations from a small number of models. In this study, we present (1) a novel feature interaction-based explainability approach and (2) several new approaches for summarizing multi-model explanations. We implement our approach within the context of electroencephalogram (EEG) spectral power data. We further analyze both training and test set explanations with the goal of extracting generalizable insights from the models. Importantly, our analyses identify effects of SZ upon the α, ß, and θ frequency bands, the left hemisphere of the brain, and interhemispheric interactions across a majority of folds. We hope that our analysis will provide helpful insights into SZ and inspire the development of robust approaches for identifying neuropsychiatric disorder biomarkers from explainable machine learning models.

Human coronavirus OC43-elicited CD4+ T cells protect against SARS-CoV-2 in HLA transgenic mice.

SARS-CoV-2-reactive T cells are detected in some healthy unexposed individuals. Human studies indicate these T cells could be elicited by the common cold coronavirus OC43. To directly test this assumption and define the role of OC43-elicited T cells that are cross-reactive with SARS-CoV-2, we develop a model of sequential infections with OC43 followed by SARS-CoV-2 in HLA-B*0702 and HLA-DRB1*0101 Ifnar1-/- transgenic mice. We find that OC43 infection can elicit polyfunctional CD8+ and CD4+ effector T cells that cross-react with SARS-CoV-2 peptides. Furthermore, pre-exposure to OC43 reduces subsequent SARS-CoV-2 infection and disease in the lung for a short-term in HLA-DRB1*0101 Ifnar1-/- transgenic mice, and a longer-term in HLA-B*0702 Ifnar1-/- transgenic mice. Depletion of CD4+ T cells in HLA-DRB1*0101 Ifnar1-/- transgenic mice with prior OC43 exposure results in increased viral burden in the lung but no change in virus-induced lung damage following infection with SARS-CoV-2 (versus CD4+ T cell-sufficient mice), demonstrating that the OC43-elicited SARS-CoV-2 cross-reactive T cell-mediated cross-protection against SARS-CoV-2 is partially dependent on CD4+ T cells. These findings contribute to our understanding of the origin of pre-existing SARS-CoV-2-reactive T cells and their effects on SARS-CoV-2 clinical outcomes, and also carry implications for development of broadly protective betacoronavirus vaccines.

Structural basis of the human NAIP/NLRC4 inflammasome assembly and pathogen sensing.

The NLR family caspase activation and recruitment domain-containing 4 (NLRC4) inflammasome is a critical cytosolic innate immune machine formed upon the direct sensing of bacterial infection and in response to cell stress during sterile chronic inflammation. Despite its major role in instigating the subsequent host immune response, a more complete understanding of the molecular events in the formation of the NLRC4 inflammasome in humans is lacking. Here we identify Bacillus thailandensis type III secretion system needle protein (Needle) as a potent trigger of the human NLR family apoptosis inhibitory protein (NAIP)/NLRC4 inflammasome complex formation and determine its structural features by cryogenic electron microscopy. We also provide a detailed understanding of how type III secretion system pathogen components are sensed by human NAIP to form a cascade of NLRC4 protomer through a critical lasso-like motif, a 'lock-key' activation model and large structural rearrangement, ultimately forming the full human NLRC4 inflammasome. These results shed light on key regulatory mechanisms specific to the NLRC4 inflammasome assembly, and the innate immune modalities of pathogen sensing in humans.

Molecular determinants of ASIC1 modulation by divalent cations.

Acid-sensing ion channels (ASICs) are proton-gated cation channels widely expressed in the nervous system. ASIC gating is modulated by divalent cations as well as small molecules; however, the molecular determinants of gating modulation by divalent cations are not well understood. Previously, we identified two small molecules that bind to ASIC1a at a novel site in the acidic pocket and modulate ASIC1 gating in a manner broadly resembling divalent cations, raising the possibility that these small molecules may help to illuminate the molecular determinants of gating modulation by divalent cations. Here, we examined how these two groups of modulators might interact as well as mutational effects on ASIC1a gating and its modulation by divalent cations. Our results indicate that binding of divalent cations to an acidic pocket site plays a key role in gating modulation of the channel.

Neuropsychiatric Disorder Subtyping Via Clustered Deep Learning Classifier Explanations.

Identifying subtypes of neuropsychiatric disorders based on characteristics of their brain activity has tremendous potential to contribute to a better understanding of those disorders and to the development of new diagnostic and personalized treatment approaches. Many studies focused on neuropsychiatric disorders examine the interaction of brain networks over time using dynamic functional network connectivity (dFNC) extracted from resting-state functional magnetic resonance imaging data. Some of these studies involve the use of either deep learning classifiers or traditional clustering approaches, but usually not both. In this study, we present a novel approach for subtyping individuals with neuropsychiatric disorders within the context of schizophrenia (SZ). We trained an explainable deep learning classifier to differentiate between dFNC data from individuals with SZ and controls, obtaining a test accuracy of 79%. We next used cross-validation to obtain robust average explanations for SZ training participants across folds, identifying 5 SZ subtypes that each differed from controls in a distinct manner and that had different degrees of symptom severity. These subtypes specifically differed from one another in their interactions between the visual network and the subcortical, sensorimotor, and auditory networks and between the cerebellar network and the cognitive control and subcortical networks. Additionally, we uncovered statistically significant differences in negative symptom scores between the subtypes. It is our hope that the proposed novel subtyping approach will contribute to the improved understanding and characterization of SZ and other neuropsychiatric disorders.

Network Differential in Gaussian Graphical Models from Multimodal Neuroimaging Data.

Multimodal brain network analysis has the potential to provide insights into the mechanisms of brain disorders. Most previous studies have analyzed either unimodal brain graphs or focused on local/global graphic metrics with little consideration of details of disrupted paths in the patient group. As we show, the combination of multimodal brain graphs and disrupted path-based analysis can be highly illuminating to recognize path-based disease biomarkers. In this study, we first propose a way to estimate multimodal brain graphs using static functional network connectivity (sFNC) and gray matter features using a Gaussian graphical model of schizophrenia versus controls. Next, applying the graph theory approach we identify disconnectors or connectors in the patient group graph that create additional paths or cause absent paths compared to the control graph. Results showed several edges in the schizophrenia group graph that trigger missing or additional paths. Identified edges associated with these disrupted paths were identified both within and between dFNC and gray matter which highlights the importance of considering multimodal studies and moving beyond pairwise edges to provide a more comprehensive understanding of brain disorders.Clinical Relevance- We identified a path-based biomarker in schizophrenia, by imitating the structure of paths in a multimodal (sMIR+fMRI) brain graph of the control group. Identified cross-modal edges associated with disrupted paths were related to the middle temporal gyrus and cerebellar regions.

Hyperlocal Spatial Flows in BOLD fMRI Expose Novel Brain-Based Correlates of Schizophrenia.

While analysis of temporal signal fluctuations has long been a fixture of blood oxygenation-level dependent (BOLD) functional magnetic resonance imaging (fMRI) research, the role of spatially localized directional diffusion in both signal propagation and emergent large-scale functional integration remains almost entirely neglected. We are proposing an extensible framework to capture and analyze spatially localized fMRI directional signal flow dynamics. The approach is validated in a large resting-state fMRI schizophrenia study where it uncovers significant and novel relationships between hyperlocal spatial dynamics and subject diagnostic status.

A Novel Explainable Fuzzy Clustering Approach for fMRI Dynamic Functional Network Connectivity Analysis.

Resting state functional magnetic resonance imaging (rs-fMRI) dynamic functional network connectivity (dFNC) analysis has illuminated brain network interactions across many neuropsychiatric disorders. A common analysis approach involves using hard clustering methods to identify transitory states of brain activity, and in response to this, other methods have been developed to quantify the importance of specific dFNC interactions to identified states. Some of these methods involve perturbing individual features and examining the number of samples that switch states. However, only a minority of samples switch states. As such, these methods actually identify the importance of dFNC features to the clustering of a subset of samples rather than the overall clustering. In this study, we present a novel approach that more capably identifies the importance of each feature to the overall clustering. Our approach uses fuzzy clustering to output probabilities of each sample belonging to states and then measures their Kullback-Leibler divergence after perturbation. We show the viability of our approach in the context of schizophrenia (SZ) default mode network analysis, identifying significant differences in state dynamics between individuals with SZ and healthy controls. We further compare our approach with an existing approach, showing that it captures the effects of perturbation upon most samples. We also find that interactions between the posterior cingulate cortex (PCC) and the anterior cingulate cortex and the PCC and precuneus are important across methods. We expect that our novel explainable clustering approach will enable further progress in rs-fMRI analysis and to other clustering applications.

A Convolutional Autoencoder-based Explainable Clustering Approach for Resting-State EEG Analysis.

Machine learning methods have frequently been applied to electroencephalography (EEG) data. However, while supervised EEG classification is well-developed, relatively few studies have clustered EEG, which is problematic given the potential for clustering EEG to identify novel subtypes or patterns of dynamics that could improve our understanding of neuropsychiatric disorders. There are established methods for clustering EEG using manually extracted features that reduce the richness of the feature space for clustering, but only a couple studies have sought to use deep learning-based approaches with automated feature learning to cluster EEG. Those studies involve separately training an autoencoder and then performing clustering on the extracted features, and the separation of those steps can lead to poor quality clustering. In this study, we propose an explainable convolutional autoencoder-based approach that combines model training with clustering to yield high quality clusters. We apply the approach within the context of schizophrenia (SZ), identifying 8 EEG states characterized by varying levels of δ activity. We also find that individuals who spend more time outside of the dominant state tend to have increased negative symptom severity. Our approach represents a significant step forward for clustering resting-state EEG data and has the potential to lead to novel findings across a variety of neurological and neuropsychological disorders in future years.

CROSS-SAMPLING RATE TRANSFER LEARNING FOR ENHANCED RAW EEG DEEP LEARNING CLASSIFIER PERFORMANCE IN MAJOR DEPRESSIVE DISORDER DIAGNOSIS.

Transfer learning offers a route for developing robust deep learning models on small raw electroencephalography (EEG) datasets. Nevertheless, the utility of applying representations learned from large datasets with a lower sampling rate to smaller datasets with higher sampling rates remains relatively unexplored. In this study, we transfer representations learned by a convolutional neural network on a large, publicly available sleep dataset with a 100 Hertz sampling rate to a major depressive disorder (MDD) diagnosis task at a sampling rate of 200 Hertz. Importantly, we find that the early convolutional layers contain representations that are generalizable across tasks. Moreover, our approach significantly increases mean model accuracy from 82.33% to 86.99%, increases the model's use of lower frequencies, (θ-band), and increases its robustness to channel loss. We expect this analysis to provide useful guidance and enable more widespread use of transfer learning in EEG deep learning studies.

Improving Multichannel Raw Electroencephalography-based Diagnosis of Major Depressive Disorder via Transfer Learning with Single Channel Sleep Stage Data.

As the field of deep learning has grown in recent years, its application to the domain of raw resting-state electroencephalography (EEG) has also increased. Relative to traditional machine learning methods or deep learning methods applied to manually engineered features, there are fewer methods for developing deep learning models on small raw EEG datasets. One potential approach for enhancing deep learning performance, in this case, is the use of transfer learning. While a number of studies have presented transfer learning approaches for manually engineered EEG features, relatively few approaches have been developed for raw resting-state EEG. In this study, we propose a novel EEG transfer learning approach wherein we first train a model on a large publicly available single-channel sleep stage classification dataset. We then use the learned representations to develop a classifier for automated major depressive disorder diagnosis with raw multichannel EEG. Statistical testing reveals that our approach significantly improves the performance of our model (p < 0.05), and we also find that the performance of our approach exceeds that of many previous studies using both engineered features and raw EEG. We further examine how transfer learning affected the representations learned by the model through a pair of explainability analyses, identifying key frequency bands and channels utilized across models. Our proposed approach represents a significant step forward for the domain of raw resting-state EEG classification and has broader implications for use with other electrophysiology and time-series modalities. Importantly, it has the potential to expand the use of deep learning methods across a greater variety of raw EEG datasets and lead to the development of more reliable EEG classifiers.

Structural and mechanistic insights into the inhibition of respiratory syncytial virus polymerase by a non-nucleoside inhibitor.

The respiratory syncytial virus polymerase complex, consisting of the polymerase (L) and phosphoprotein (P), catalyzes nucleotide polymerization, cap addition, and cap methylation via the RNA dependent RNA polymerase, capping, and Methyltransferase domains on L. Several nucleoside and non-nucleoside inhibitors have been reported to inhibit this polymerase complex, but the structural details of the exact inhibitor-polymerase interactions have been lacking. Here, we report a non-nucleoside inhibitor JNJ-8003 with sub-nanomolar inhibition potency in both antiviral and polymerase assays. Our 2.9 Å resolution cryo-EM structure revealed that JNJ-8003 binds to an induced-fit pocket on the capping domain, with multiple interactions consistent with its tight binding and resistance mutation profile. The minigenome and gel-based de novo RNA synthesis and primer extension assays demonstrated that JNJ-8003 inhibited nucleotide polymerization at the early stages of RNA transcription and replication. Our results support that JNJ-8003 binding modulates a functional interplay between the capping and RdRp domains, and this molecular insight could accelerate the design of broad-spectrum antiviral drugs.

4D DYNAMIC SPATIAL BRAIN NETWORKS AT REST LINKED TO COGNITION SHOW ATYPICAL VARIABILITY AND COUPLING IN SCHIZOPHRENIA.

Despite increasing interest in the dynamics of functional brain networks, most studies focus on the changing relationships over time between spatially static networks or regions. Here we propose an approach to study dynamic spatial brain net-works in human resting state functional magnetic resonance imaging (rsfMRI) data and evaluate the temporal changes in the volumes of these 4D networks. Our results show significant volumetric coupling (i.e., synchronized shrinkage and growth) between networks during the scan. We find that several features of such dynamic spatial brain networks are associated with cognition, with higher dynamic variability in these networks and higher volumetric coupling between network pairs positively associated with cognitive performance. We show that these networks are modulated differently in individuals with schizophrenia versus typical controls, resulting in network growth or shrinkage, as well as altered focus of activity within a network. Schizophrenia also shows lower spatial dynamical variability in several networks, and lower volumetric coupling between pairs of networks, thus upholding the role of dynamic spatial brain networks in cognitive impairment seen in schizophrenia. Our data show evidence for the importance of studying the typically overlooked voxelwise changes within and between brain networks.

Improving Multichannel Raw Electroencephalography-based Diagnosis of Major Depressive Disorder by Pretraining Deep Learning Models with Single Channel Sleep Stage Data.

As the field of deep learning has grown in recent years, its application to the domain of raw resting-state electroencephalography (EEG) has also increased. Relative to traditional machine learning methods or deep learning methods applied to extracted features, there are fewer methods for developing deep learning models on small raw EEG datasets. One potential approach for enhancing deep learning performance in this case is the use of transfer learning. In this study, we propose a novel EEG transfer learning approach wherein we first train a model on a large publicly available sleep stage classification dataset. We then use the learned representations to develop a classifier for automated major depressive disorder diagnosis with raw multichannel EEG. We find that our approach improves model performance, and we further examine how transfer learning affected the representations learned by the model through a pair of explainability analyses. Our proposed approach represents a significant step forward for the domain raw resting-state EEG classification. Furthermore, it has the potential to expand the use of deep learning methods across more raw EEG datasets and lead to the development of more reliable EEG classifiers.

An Explainable and Robust Deep Learning Approach for Automated Electroencephalography-based Schizophrenia Diagnosis.

Schizophrenia (SZ) is a neuropsychiatric disorder that affects millions globally. Current diagnosis of SZ is symptom-based, which poses difficulty due to the variability of symptoms across patients. To this end, many recent studies have developed deep learning methods for automated diagnosis of SZ, especially using raw EEG, which provides high temporal precision. For such methods to be productionized, they must be both explainable and robust. Explainable models are essential to identify biomarkers of SZ, and robust models are critical to learn generalizable patterns, especially amidst changes in the implementation environment. One common example is channel loss during EEG recording, which could be detrimental to classifier performance. In this study, we developed a novel channel dropout (CD) approach to increase the robustness of explainable deep learning models trained on EEG data for SZ diagnosis to channel loss. We developed a baseline convolutional neural network (CNN) architecture and implement our approach as a CD layer added to the baseline (CNN-CD). We then applied two explainability approaches to both models for insight into learned spatial and spectral features and show that the application of CD decreases model sensitivity to channel loss. The CNN and CNN-CD achieved accuracies of 81.9% and 80.9% on testing data, respectively. Furthermore, our models heavily prioritized the parietal electrodes and the α-band, which is supported by existing literature. It is our hope that this study motivates the further development of explainable and robust models and bridges the transition from research to application in a clinical decision support role.

A method for capturing dynamic spectral coupling in resting fMRI reveals domain-specific patterns in schizophrenia.

Introduction: Resting-state functional magnetic resonance imaging (rs-fMRI) is a powerful tool for assessing functional brain connectivity. Recent studies have focused on shorter-term connectivity and dynamics in the resting state. However, most of the prior work evaluates changes in time-series correlations. In this study, we propose a framework that focuses on time-resolved spectral coupling (assessed via the correlation between power spectra of the windowed time courses) among different brain circuits determined via independent component analysis (ICA). Methods: Motivated by earlier work suggesting significant spectral differences in people with schizophrenia, we developed an approach to evaluate time-resolved spectral coupling (trSC). To do this, we first calculated the correlation between the power spectra of windowed time-courses pairs of brain components. Then, we subgrouped each correlation map into four subgroups based on the connectivity strength utilizing quartiles and clustering techniques. Lastly, we examined clinical group differences by regression analysis for each averaged count and average cluster size matrices in each quartile. We evaluated the method by applying it to resting-state data collected from 151 (114 males, 37 females) people with schizophrenia (SZ) and 163 (117 males, 46 females) healthy controls (HC). Results: Our proposed approach enables us to observe the change of connectivity strength within each quartile for different subgroups. People with schizophrenia showed highly modularized and significant differences in multiple network domains, whereas males and females showed less modular differences. Both cell count and average cluster size analysis for subgroups indicate a higher connectivity rate in the fourth quartile for the visual network in the control group. This indicates increased trSC in visual networks in the controls. In other words, this shows that the visual networks in people with schizophrenia have less mutually consistent spectra. It is also the case that the visual networks are less spectrally correlated on short timescales with networks of all other functional domains. Conclusions: The results of this study reveal significant differences in the degree to which spectral power profiles are coupled over time. Importantly, there are significant but distinct differences both between males and females and between people with schizophrenia and controls. We observed a more significant coupling rate in the visual network for the healthy controls and males in the upper quartile. Fluctuations over time are complex, and focusing on only time-resolved coupling among time-courses is likely to miss important information. Also, people with schizophrenia are known to have impairments in visual processing but the underlying reasons for the impairment are still unknown. Therefore, the trSC approach can be a useful tool to explore the reasons for the impairments.

Interpretable LSTM model reveals transiently-realized patterns of dynamic brain connectivity that predict patient deterioration or recovery from very mild cognitive impairment.

Alzheimer's Disease (AZD) is a neurodegenerative disease for which there is now no known effective treatment. Mild cognitive impairment (MCI) is considered a precursor to AZD and affects cognitive abilities. Patients with MCI have the potential to recover cognitive health, can remain mildly cognitively impaired indefinitely or eventually progress to AZD. Identifying imaging-based predictive biomarkers for disease progression in patients presenting with evidence of very mild/questionable MCI (qMCI) can play an important role in triggering early dementia intervention. Dynamic functional network connectivity (dFNC) estimated from resting-state functional magnetic resonance imaging (rs-fMRI) has been increasingly studied in brain disorder diseases. In this work, employing a recent developed a time-attention long short-term memory (TA-LSTM) network to classify multivariate time series data. A gradient-based interpretation framework, transiently-realized event classifier activation map (TEAM) is introduced to localize the group-defining "activated" time intervals over the full time series and generate the class difference map. To test the trustworthiness of TEAM, we did a simulation study to validate the model interpretative power of TEAM. We then applied this simulation-validated framework to a well-trained TA-LSTM model which predicts the progression or recovery from questionable/mild cognitive impairment (qMCI) subjects after three years from windowless wavelet-based dFNC (WWdFNC). The FNC class difference map points to potentially important predictive dynamic biomarkers. Moreover, the more highly time-solved dFNC (WWdFNC) achieves better performance in both TA-LSTM and a multivariate CNN model than dFNC based on windowed correlations between timeseries, suggesting that better temporally resolved measures can enhance the model's performance.