Cross Atlas Remapping via Optimal Transport (CAROT): Creating connectomes for different atlases when raw data is not available.

Open-source, publicly available neuroimaging datasets - whether from large-scale data collection efforts or pooled from multiple smaller studies - offer unprecedented sample sizes and promote generalization efforts. Releasing data can democratize science, increase the replicability of findings, and lead to discoveries. Partly due to patient privacy, computational, and data storage concerns, researchers typically release preprocessed data with the voxelwise time series parcellated into a map of predefined regions, known as an atlas. However, releasing preprocessed data also limits the choices available to the end-user. This is especially true for connectomics, as connectomes created from different atlases are not directly comparable. Since there exist several atlases with no gold standards, it is unrealistic to have processed, open-source data available from all atlases. Together, these limitations directly inhibit the potential benefits of open-source neuroimaging data. To address these limitations, we introduce Cross Atlas Remapping via Optimal Transport (CAROT) to find a mapping between two atlases. This approach allows data processed from one atlas to be directly transformed into a connectome based on another atlas without the need for raw data access. To validate CAROT, we compare reconstructed connectomes against their original counterparts (i.e., connectomes generated directly from an atlas), demonstrate the utility of transformed connectomes in downstream analyses, and show how a connectome-based predictive model can generalize to publicly available data that was processed with different atlases. Overall, CAROT can reconstruct connectomes from an extensive set of atlases - without needing the raw data - allowing already processed connectomes to be easily reused in a wide range of analyses while eliminating redundant processing efforts. We share this tool as both source code and as a stand-alone web application (http://carotproject.com/).

Stacking multiple optimal transport policies to map functional connectomes.

Connectomics is a popular approach for understanding the brain with neuroimaging data. However, a connectome generated from one atlas is different in size, topology, and scale compared to a connectome generated from another. Consequently, connectomes generated from different atlases cannot be used in the same analysis. This limitation hinders efforts toward increasing sample size and demonstrating generalizability across datasets. Recently, we proposed Cross Atlas Remapping via Optimal Transport (CAROT) to find a spatial mapping between a pair of atlases based on a set of training data. The mapping transforms timeseries fMRI data parcellated with an atlas to form a connectome based on a different one. Crucially, CAROT does not need raw fMRI data and thus does not require re-processing, which can otherwise be time-consuming and expensive. The current CAROT implementation leverages information from several source atlases to create robust mappings for a target atlas. In this work, we extend CAROT to combine existing mappings between a source and target atlas for an arbitrary number of mappings. This extension (labeled Stacking CAROT) allows mappings between a pair of atlases to be created once and re-used with other pre-trained mappings to create new mappings as needed. Reconstructed connectomes from Stacking CAROT perform as well as those from CAROT in downstream analyses. Importantly, Stacking CAROT significantly reduces training time and storage requirements compared to CAROT. Overall, Stacking CAROT improves previous versions of CAROT.

There is no single functional atlas even for a single individual: Functional parcel definitions change with task.

The goal of human brain mapping has long been to delineate the functional subunits in the brain and elucidate the functional role of each of these brain regions. Recent work has focused on whole-brain parcellation of functional Magnetic Resonance Imaging (fMRI) data to identify these subunits and create a functional atlas. Functional connectivity approaches to understand the brain at the network level require such an atlas to assess connections between parcels and extract network properties. While no single functional atlas has emerged as the dominant atlas to date, there remains an underlying assumption that such an atlas exists. Using fMRI data from a highly sampled subject as well as two independent replication data sets, we demonstrate that functional parcellations based on fMRI connectivity data reconfigure substantially and in a meaningful manner, according to brain state.

Individualized functional networks reconfigure with cognitive state.

There is extensive evidence that functional organization of the human brain varies dynamically as the brain switches between task demands, or cognitive states. This functional organization also varies across subjects, even when engaged in similar tasks. To date, the functional network organization of the brain has been considered static. In this work, we use fMRI data obtained across multiple cognitive states (task-evoked and rest conditions) and across multiple subjects, to measure state- and subject-specific functional network parcellation (the assignment of nodes to networks). Our parcellation approach provides a measure of how node-to-network assignment (NNA) changes across states and across subjects. We demonstrate that the brain's functional networks are not spatially fixed, but that many nodes change their network membership as a function of cognitive state. Such reconfigurations are highly robust and reliable to the extent that they can be used to predict cognitive state with up to 97% accuracy. Our findings suggest that if functional networks are to be defined via functional clustering of nodes, then it is essential to consider that such definitions may be fluid and cognitive-state dependent.

Learning neural connectivity from firing activity: efficient algorithms with provable guarantees on topology.

The connectivity of a neuronal network has a major effect on its functionality and role. It is generally believed that the complex network structure of the brain provides a physiological basis for information processing. Therefore, identifying the network's topology has received a lot of attentions in neuroscience and has been the center of many research initiatives such as Human Connectome Project. Nevertheless, direct and invasive approaches that slice and observe the neural tissue have proven to be time consuming, complex and costly. As a result, the inverse methods that utilize firing activity of neurons in order to identify the (functional) connections have gained momentum recently, especially in light of rapid advances in recording technologies; It will soon be possible to simultaneously monitor the activities of tens of thousands of neurons in real time. While there are a number of excellent approaches that aim to identify the functional connections from firing activities, the scalability of the proposed techniques plays a major challenge in applying them on large-scale datasets of recorded firing activities. In exceptional cases where scalability has not been an issue, the theoretical performance guarantees are usually limited to a specific family of neurons or the type of firing activities. In this paper, we formulate the neural network reconstruction as an instance of a graph learning problem, where we observe the behavior of nodes/neurons (i.e., firing activities) and aim to find the links/connections. We develop a scalable learning mechanism and derive the conditions under which the estimated graph for a network of Leaky Integrate and Fire (LIf) neurons matches the true underlying synaptic connections. We then validate the performance of the algorithm using artificially generated data (for benchmarking) and real data recorded from multiple hippocampal areas in rats.

An exemplar-based approach to individualized parcellation reveals the need for sex specific functional networks.

Recent work with functional connectivity data has led to significant progress in understanding the functional organization of the brain. While the majority of the literature has focused on group-level parcellation approaches, there is ample evidence that the brain varies in both structure and function across individuals. In this work, we introduce a parcellation technique that incorporates delineation of functional networks both at the individual- and group-level. The proposed technique deploys the notion of "submodularity" to jointly parcellate the cerebral cortex while establishing an inclusive correspondence between the individualized functional networks. Using this parcellation technique, we successfully established a cross-validated predictive model that predicts individuals' sex, solely based on the parcellation schemes (i.e. the node-to-network assignment vectors). The sex prediction finding illustrates that individualized parcellation of functional networks can reveal subgroups in a population and suggests that the use of a global network parcellation may overlook fundamental differences in network organization. This is a particularly important point to consider in studies comparing patients versus controls or even patient subgroups. Network organization may differ between individuals and global configurations should not be assumed. This approach to the individualized study of functional organization in the brain has many implications for both neuroscience and clinical applications.

Estimating the Size of a Large Network and its Communities from a Random Sample.

Most real-world networks are too large to be measured or studied directly and there is substantial interest in estimating global network properties from smaller sub-samples. One of the most important global properties is the number of vertices/nodes in the network. Estimating the number of vertices in a large network is a major challenge in computer science, epidemiology, demography, and intelligence analysis. In this paper we consider a population random graph G = (V, E) from the stochastic block model (SBM) with K communities/blocks. A sample is obtained by randomly choosing a subset W ⊆ V and letting G(W) be the induced subgraph in G of the vertices in W. In addition to G(W), we observe the total degree of each sampled vertex and its block membership. Given this partial information, we propose an efficient PopULation Size Estimation algorithm, called PULSE, that accurately estimates the size of the whole population as well as the size of each community. To support our theoretical analysis, we perform an exhaustive set of experiments to study the effects of sample size, K, and SBM model parameters on the accuracy of the estimates. The experimental results also demonstrate that PULSE significantly outperforms a widely-used method called the network scale-up estimator in a wide variety of scenarios.

Noise facilitation in associative memories of exponential capacity.

Recent advances in associative memory design through structured pattern sets and graph-based inference algorithms have allowed reliable learning and recall of an exponential number of patterns that satisfy certain subspace constraints. Although these designs correct external errors in recall, they assume neurons that compute noiselessly, in contrast to the highly variable neurons in brain regions thought to operate associatively, such as hippocampus and olfactory cortex. Here we consider associative memories with boundedly noisy internal computations and analytically characterize performance. As long as the internal noise level is below a specified threshold, the error probability in the recall phase can be made exceedingly small. More surprising, we show that internal noise improves the performance of the recall phase while the pattern retrieval capacity remains intact: the number of stored patterns does not reduce with noise (up to a threshold). Computational experiments lend additional support to our theoretical analysis. This work suggests a functional benefit to noisy neurons in biological neuronal networks.