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Associating stimuli with positive or negative reinforcement is essential for survival, but a complete wiring diagram of a higher-order circuit supporting associative memory has not been previously available. Here we reconstruct one such circuit at synaptic resolution, the Drosophila larval mushroom body. We find that most Kenyon cells integrate random combinations of inputs but that a subset receives stereotyped inputs from single projection neurons. This organization maximizes performance of a model output neuron on a stimulus discrimination task. We also report a novel canonical circuit in each mushroom body compartment with previously unidentified connections: reciprocal Kenyon cell to modulatory neuron connections, modulatory neuron to output neuron connections, and a surprisingly high number of recurrent connections between Kenyon cells. Stereotyped connections found between output neurons could enhance the selection of learned behaviours. The complete circuit map of the mushroom body should guide future functional studies of this learning and memory centre.
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Encéfalo/citología , Encéfalo/fisiología , Conectoma , Drosophila melanogaster/citología , Drosophila melanogaster/fisiología , Memoria/fisiología , Animales , Retroalimentación Fisiológica , Femenino , Larva/citología , Larva/fisiología , Cuerpos Pedunculados/citología , Cuerpos Pedunculados/fisiología , Vías Nerviosas , Sinapsis/metabolismoRESUMEN
Replicability, the ability to replicate scientific findings, is a prerequisite for scientific discovery and clinical utility. Troublingly, we are in the midst of a replicability crisis. A key to replicability is that multiple measurements of the same item (e.g., experimental sample or clinical participant) under fixed experimental constraints are relatively similar to one another. Thus, statistics that quantify the relative contributions of accidental deviations-such as measurement error-as compared to systematic deviations-such as individual differences-are critical. We demonstrate that existing replicability statistics, such as intra-class correlation coefficient and fingerprinting, fail to adequately differentiate between accidental and systematic deviations in very simple settings. We therefore propose a novel statistic, discriminability, which quantifies the degree to which an individual's samples are relatively similar to one another, without restricting the data to be univariate, Gaussian, or even Euclidean. Using this statistic, we introduce the possibility of optimizing experimental design via increasing discriminability and prove that optimizing discriminability improves performance bounds in subsequent inference tasks. In extensive simulated and real datasets (focusing on brain imaging and demonstrating on genomics), only optimizing data discriminability improves performance on all subsequent inference tasks for each dataset. We therefore suggest that designing experiments and analyses to optimize discriminability may be a crucial step in solving the replicability crisis, and more generally, mitigating accidental measurement error.
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Conectoma , Genoma , Artefactos , Mapeo Encefálico/métodos , Conjuntos de Datos como Asunto , Humanos , Reproducibilidad de los ResultadosRESUMEN
Clustering is concerned with coherently grouping observations without any explicit concept of true groupings. Spectral graph clustering-clustering the vertices of a graph based on their spectral embedding-is commonly approached via K-means (or, more generally, Gaussian mixture model) clustering composed with either Laplacian spectral embedding (LSE) or adjacency spectral embedding (ASE). Recent theoretical results provide deeper understanding of the problem and solutions and lead us to a "two-truths" LSE vs. ASE spectral graph clustering phenomenon convincingly illustrated here via a diffusion MRI connectome dataset: The different embedding methods yield different clustering results, with LSE capturing left hemisphere/right hemisphere affinity structure and ASE capturing gray matter/white matter core-periphery structure.
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Genome-wide association studies have demonstrated significant links between human brain structure and common DNA variants. Similar studies with rodents have been challenging because of smaller brain volumes. Using high field MRI (9.4 T) and compressed sensing, we have achieved microscopic resolution and sufficiently high throughput for rodent population studies. We generated whole brain structural MRI and diffusion connectomes for four diverse isogenic lines of mice (C57BL/6J, DBA/2J, CAST/EiJ, and BTBR) at spatial resolution 20,000 times higher than human connectomes. We measured narrow sense heritability (h2) I.e. the fraction of variance explained by strains in a simple ANOVA model for volumes and scalar diffusion metrics, and estimates of residual technical error for 166 regions in each hemisphere and connectivity between the regions. Volumes of discrete brain regions had the highest mean heritability (0.71 ± 0.23 SD, n = 332), followed by fractional anisotropy (0.54 ± 0.26), radial diffusivity (0.34 ± 0.022), and axial diffusivity (0.28 ± 0.19). Connection profiles were statistically different in 280 of 322 nodes across all four strains. Nearly 150 of the connection profiles were statistically different between the C57BL/6J, DBA/2J, and CAST/EiJ lines. Microscopic whole brain MRI/DTI has allowed us to identify significant heritable phenotypes in brain volume, scalar DTI metrics, and quantitative connectomes.
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Mapeo Encefálico , Encéfalo/anatomía & histología , Encéfalo/fisiología , Imagen de Difusión Tensora , Animales , Conectoma/métodos , Imagen de Difusión por Resonancia Magnética/métodos , Imagen de Difusión Tensora/métodos , Estudio de Asociación del Genoma Completo , Imagen por Resonancia Magnética/métodos , RatonesRESUMEN
In this article we propose a lightning fast graph embedding method called one-hot graph encoder embedding. It has a linear computational complexity and the capacity to process billions of edges within minutes on standard PC - making it an ideal candidate for huge graph processing. It is applicable to either adjacency matrix or graph Laplacian, and can be viewed as a transformation of the spectral embedding. Under random graph models, the graph encoder embedding is approximately normally distributed per vertex, and asymptotically converges to its mean. We showcase three applications: vertex classification, vertex clustering, and graph bootstrap. In every case, the graph encoder embedding exhibits unrivalled computational advantages.
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Graph matching algorithms attempt to find the best correspondence between the nodes of two networks. These techniques have been used to match individual neurons in nanoscale connectomes-in particular, to find pairings of neurons across hemispheres. However, since graph matching techniques deal with two isolated networks, they have only utilized the ipsilateral (same hemisphere) subgraphs when performing the matching. Here, we present a modification to a state-of-the-art graph matching algorithm that allows it to solve what we call the bisected graph matching problem. This modification allows us to leverage the connections between the brain hemispheres when predicting neuron pairs. Via simulations and experiments on real connectome datasets, we show that this approach improves matching accuracy when sufficient edge correlation is present between the contralateral (between hemisphere) subgraphs. We also show how matching accuracy can be further improved by combining our approach with previously proposed extensions to graph matching, which utilize edge types and previously known neuron pairings. We expect that our proposed method will improve future endeavors to accurately match neurons across hemispheres in connectomes, and be useful in other applications where the bisected graph matching problem arises.
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Comparing connectomes can help explain how neural connectivity is related to genetics, disease, development, learning, and behavior. However, making statistical inferences about the significance and nature of differences between two networks is an open problem, and such analysis has not been extensively applied to nanoscale connectomes. Here, we investigate this problem via a case study on the bilateral symmetry of a larval Drosophila brain connectome. We translate notions of 'bilateral symmetry' to generative models of the network structure of the left and right hemispheres, allowing us to test and refine our understanding of symmetry. We find significant differences in connection probabilities both across the entire left and right networks and between specific cell types. By rescaling connection probabilities or removing certain edges based on weight, we also present adjusted definitions of bilateral symmetry exhibited by this connectome. This work shows how statistical inferences from networks can inform the study of connectomes, facilitating future comparisons of neural structures.
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Conectoma , Animales , Encéfalo/diagnóstico por imagen , Sistema Nervioso , Drosophila , LarvaRESUMEN
Brains contain networks of interconnected neurons and so knowing the network architecture is essential for understanding brain function. We therefore mapped the synaptic-resolution connectome of an entire insect brain (Drosophila larva) with rich behavior, including learning, value computation, and action selection, comprising 3016 neurons and 548,000 synapses. We characterized neuron types, hubs, feedforward and feedback pathways, as well as cross-hemisphere and brain-nerve cord interactions. We found pervasive multisensory and interhemispheric integration, highly recurrent architecture, abundant feedback from descending neurons, and multiple novel circuit motifs. The brain's most recurrent circuits comprised the input and output neurons of the learning center. Some structural features, including multilayer shortcuts and nested recurrent loops, resembled state-of-the-art deep learning architectures. The identified brain architecture provides a basis for future experimental and theoretical studies of neural circuits.
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Encéfalo , Conectoma , Drosophila melanogaster , Red Nerviosa , Animales , Encéfalo/ultraestructura , Neuronas/ultraestructura , Sinapsis/ultraestructura , Drosophila melanogaster/ultraestructura , Red Nerviosa/ultraestructuraRESUMEN
Neural networks have achieved remarkable successes in machine learning tasks. This has recently been extended to graph learning using neural networks. However, there is limited theoretical work in understanding how and when they perform well, especially relative to established statistical learning techniques such as spectral embedding. In this short paper, we present a simple generative model where unsupervised graph convolutional network fails, while the adjacency spectral embedding succeeds. Specifically, unsupervised graph convolutional network is unable to look beyond the first eigenvector in certain approximately regular graphs, thus missing inference signals in non-leading eigenvectors. The phenomenon is demonstrated by visual illustrations and comprehensive simulations.
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We consider the problem of extracting features from passive, multi-channel electroencephalogram (EEG) devices for downstream inference tasks related to high-level mental states such as stress and cognitive load. Our proposed feature extraction method uses recently developed spectral-based multi-graph tools and applies them to the time series of graphs implied by the statistical dependence structure (e.g., correlation) amongst the multiple sensors. We study the features in the context of two datasets each consisting of at least 30 participants and recorded using multi-channel EEG systems. We compare the classification performance of a classifier trained on the proposed features to a classifier trained on the traditional band power-based features in three settings and find that the two feature sets offer complementary predictive information. We conclude by showing that the importance of particular channels and pairs of channels for classification when using the proposed features is neuroscientifically valid.
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Graph matching consists of aligning the vertices of two unlabeled graphs in order to maximize the shared structure across networks; when the graphs are unipartite, this is commonly formulated as minimizing their edge disagreements. In this paper we address the common setting in which one of the graphs to match is a bipartite network and one is unipartite. Commonly, the bipartite networks are collapsed or projected into a unipartite graph, and graph matching proceeds as in the classical setting. This potentially leads to noisy edge estimates and loss of information. We formulate the graph matching problem between a bipartite and a unipartite graph using an undirected graphical model, and introduce methods to find the alignment with this model without collapsing. We theoretically demonstrate that our methodology is consistent, and provide non-asymptotic conditions that ensure exact recovery of the matching solution. In simulations and real data examples, we show how our methods can result in a more accurate matching than the naive approach of transforming the bipartite networks into unipartite, and we demonstrate the performance gains achieved by our method in simulated and real data networks, including a co-authorship-citation network pair, and brain structural and functional data.
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Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a method to jointly embed multiple undirected graphs. Given a set of graphs, the joint embedding method identifies a linear subspace spanned by rank one symmetric matrices and projects adjacency matrices of graphs into this subspace. The projection coefficients can be treated as features of the graphs, while the embedding components can represent vertex features. We also propose a random graph model for multiple graphs that generalizes other classical models for graphs. We show through theory and numerical experiments that under the model, the joint embedding method produces estimates of parameters with small errors. Via simulation experiments, we demonstrate that the joint embedding method produces features which lead to state of the art performance in classifying graphs. Applying the joint embedding method to human brain graphs, we find it extracts interpretable features with good prediction accuracy in different tasks.
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The development of models and methodology for the analysis of data from multiple heterogeneous networks is of importance both in statistical network theory and across a wide spectrum of application domains. Although single-graph analysis is well-studied, multiple graph inference is largely unexplored, in part because of the challenges inherent in appropriately modeling graph differences and yet retaining sufficient model simplicity to render estimation feasible. This paper addresses exactly this gap, by introducing a new model, the common subspace independent-edge multiple random graph model, which describes a heterogeneous collection of networks with a shared latent structure on the vertices but potentially different connectivity patterns for each graph. The model encompasses many popular network representations, including the stochastic blockmodel. The model is both flexible enough to meaningfully account for important graph differences, and tractable enough to allow for accurate inference in multiple networks. In particular, a joint spectral embedding of adjacency matrices-the multiple adjacency spectral embedding-leads to simultaneous consistent estimation of underlying parameters for each graph. Under mild additional assumptions, the estimates satisfy asymptotic normality and yield improvements for graph eigenvalue estimation. In both simulated and real data, the model and the embedding can be deployed for a number of subsequent network inference tasks, including dimensionality reduction, classification, hypothesis testing, and community detection. Specifically, when the embedding is applied to a data set of connectomes constructed through diffusion magnetic resonance imaging, the result is an accurate classification of brain scans by human subject and a meaningful determination of heterogeneity across scans of different individuals.
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This work presents a novel strategy for classifying neurons, represented by nodes of a directed graph, based on their circuitry (edge connectivity). We assume a stochastic block model (SBM) in which neurons belong together if they connect to neurons of other groups according to the same probability distributions. Following adjacency spectral embedding of the SBM graph, we derive the number of classes and assign each neuron to a class with a Gaussian mixture model-based expectation maximization (EM) clustering algorithm. To improve accuracy, we introduce a simple variation using random hierarchical agglomerative clustering to initialize the EM algorithm and picking the best solution over multiple EM restarts. We test this procedure on a large (≈212-215 neurons), sparse, biologically inspired connectome with eight neuron classes. The simulation results demonstrate that the proposed approach is broadly stable to the choice of embedding dimension, and scales extremely well as the number of neurons in the network increases. Clustering accuracy is robust to variations in model parameters and highly tolerant to simulated experimental noise, achieving perfect classifications with up to 40% of swapped edges. Thus, this approach may be useful to analyze and interpret large-scale brain connectomics data in terms of underlying cellular components.
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The problem of finding the vertex correspondence between two noisy graphs with different number of vertices where the smaller graph is still large has many applications in social networks, neuroscience, and computer vision. We propose a solution to this problem via a graph matching matched filter: centering and padding the smaller adjacency matrix and applying graph matching methods to align it to the larger network. The centering and padding schemes can be incorporated into any algorithm that matches using adjacency matrices. Under a statistical model for correlated pairs of graphs, which yields a noisy copy of the small graph within the larger graph, the resulting optimization problem can be guaranteed to recover the true vertex correspondence between the networks. However, there are currently no efficient algorithms for solving this problem. To illustrate the possibilities and challenges of such problems, we use an algorithm that can exploit a partially known correspondence and show via varied simulations and applications to Drosophila and human connectomes that this approach can achieve good performance.
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Algoritmos , Procesamiento de Imagen Asistido por Computador/métodos , Modelos Estadísticos , Animales , Encéfalo/diagnóstico por imagen , Conectoma , Imagen de Difusión Tensora , Drosophila , HumanosRESUMEN
This article describes a large multi-institutional analysis of the shape and structure of the human hippocampus in the aging brain as measured via MRI. The study was conducted on a population of 101 subjects including nondemented control subjects (n = 57) and subjects clinically diagnosed with Alzheimer's Disease (AD, n = 38) or semantic dementia (n = 6) with imaging data collected at Washington University in St. Louis, hippocampal structure annotated at the Massachusetts General Hospital, and anatomical shapes embedded into a metric shape space using large deformation diffeomorphic metric mapping (LDDMM) at the Johns Hopkins University. A global classifier was constructed for discriminating cohorts of nondemented and demented subjects based on linear discriminant analysis of dimensions derived from metric distances between anatomical shapes, demonstrating class conditional structure differences measured via LDDMM metric shape (P < 0.01). Localized analysis of the control and AD subjects only on the coordinates of the population template demonstrates shape changes in the subiculum and the CA1 subfield in AD (P < 0.05). Such large scale collaborative analysis of anatomical shapes has the potential to enhance the understanding of neurodevelopmental and neuropsychiatric disorders.
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Envejecimiento , Enfermedad de Alzheimer/patología , Mapeo Encefálico/métodos , Hipocampo/anatomía & histología , Hipocampo/patología , Anciano , Anciano de 80 o más Años , Algoritmos , Encéfalo/patología , Estudios de Cohortes , Análisis Discriminante , Femenino , Humanos , Imagenología Tridimensional/métodos , Imagen por Resonancia Magnética , Masculino , Persona de Mediana EdadRESUMEN
Understanding the relationships between different properties of data, such as whether a genome or connectome has information about disease status, is increasingly important. While existing approaches can test whether two properties are related, they may require unfeasibly large sample sizes and often are not interpretable. Our approach, 'Multiscale Graph Correlation' (MGC), is a dependence test that juxtaposes disparate data science techniques, including k-nearest neighbors, kernel methods, and multiscale analysis. Other methods may require double or triple the number of samples to achieve the same statistical power as MGC in a benchmark suite including high-dimensional and nonlinear relationships, with dimensionality ranging from 1 to 1000. Moreover, MGC uniquely characterizes the latent geometry underlying the relationship, while maintaining computational efficiency. In real data, including brain imaging and cancer genetics, MGC detects the presence of a dependency and provides guidance for the next experiments to conduct.
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Algoritmos , Análisis de Datos , Biomarcadores de Tumor/metabolismo , Encéfalo/diagnóstico por imagen , Encéfalo/fisiología , Simulación por Computador , Humanos , Neoplasias/metabolismo , Tamaño de la MuestraRESUMEN
Cognitive phenotypes characterize our memories, beliefs, skills, and preferences, and arise from our ancestral, developmental, and experiential histories. These histories are written into our brain structure through the building and modification of various brain circuits. Connectal coding, by way of analogy with neural coding, is the art, study, and practice of identifying the network structures that link cognitive phenomena to individual histories. We propose a formal statistical framework for connectal coding and demonstrate its utility in several applications spanning experimental modalities and phylogeny.
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Encéfalo , Cognición , Memoria , Fenotipo , FilogeniaRESUMEN
In brain imaging and connectomics, the study of brain networks, estimating the mean of a population of graphs based on a sample is a core problem. Often, this problem is especially difficult because the sample or cohort size is relatively small, sometimes even a single subject, while the number of nodes can be very large with noisy estimates of connectivity. While the element-wise sample mean of the adjacency matrices is a common approach, this method does not exploit the underlying structural properties of the graphs. We propose using a low-rank method that incorporates dimension selection and diagonal augmentation to smooth the estimates and improve performance over the naïve methodology for small sample sizes. Theoretical results for the stochastic block model show that this method offers major improvements when there are many vertices. Similarly, we demonstrate that the low-rank methods outperform the standard sample mean for a variety of independent edge distributions as well as human connectome data derived from the magnetic resonance imaging, especially when the sample sizes are small. Moreover, the low-rank methods yield "eigen-connectomes," which correlate with the lobe-structure of the human brain and superstructures of the mouse brain. These results indicate that the low-rank methods are the important parts of the toolbox for researchers studying populations of graphs in general and statistical connectomics in particular.
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Encéfalo/diagnóstico por imagen , Conectoma/métodos , Procesamiento de Imagen Asistido por Computador/métodos , Algoritmos , Animales , Humanos , Imagen por Resonancia Magnética/métodos , Ratones , Procesos EstocásticosRESUMEN
This paper describes the application of the alternating Kernel mixture (AKM) segmentation algorithm to high resolution MRI subvolumes acquired from a 1.5T scanner (hippocampus, n = 10 and prefrontal cortex, n = 9) and a 3T scanner (hippocampus, n = 10 and occipital lobe, n = 10). Segmentation of the subvolumes into cerebrospinal fluid, gray matter, and white matter tissue is validated by comparison with manual segmentation. When compared with other segmentation methods that use traditional Bayesian segmentation, AKM yields smaller errors (P < .005, exact Wilcoxon signed rank test) demonstrating the robustness and wide applicability of AKM across different structures. By generating multiple mixtures for each tissue compartment, AKM mimics the increased variation of manual segmentation in partial volumes due to the highly folded tissues. AKM's superior performance makes it useful for tissue segmentation of subcortical and cortical structures in large-scale neuroimaging studies.