Multiresolution community detection for megascale networks by information-based replica correlations

We use a Potts model community detection algorithm to accurately and quantitatively evaluate the hierarchical or multiresolution structure of a graph. Our multiresolution algorithm calculates correlations among multiple copies ("replicas") of the same graph over a range of resolutions. Significant multiresolution structures are identified by strongly correlated replicas. The average normalized mutual information, the variation of information, and other measures in principle give a quantitative estimate of the "best" resolutions and indicate the relative strength of the structures in the graph. Because the method is based on information comparisons, it can in principle be used with any community detection model that can examine multiple resolutions. Our approach may be extended to other optimization problems. As a local measure, our Potts model avoids the "resolution limit" that affects other popular models. With this model, our community detection algorithm has an accuracy that ranks among the best of currently available methods. Using it, we can examine graphs over 40 million nodes and more than one billion edges. We further report that the multiresolution variant of our algorithm can solve systems of at least 200000 nodes and 10 million edges on a single processor with exceptionally high accuracy. For typical cases, we find a super-linear scaling, O(L^{1.3}) for community detection and O(L^{1.3} log N) for the multiresolution algorithm where L is the number of edges and N is the number of nodes in the system.Comment: 19 pages, 14 figures, published version with minor change

A receptor-based analysis of local ecosystems in the human brain.

BackgroundAs a complex system, the brain is a self-organizing entity that depends on local interactions among cells. Its regions (anatomically defined nuclei and areas) can be conceptualized as cellular ecosystems, but the similarity of their functional profiles is poorly understood. The study used the Allen Human Brain Atlas to classify 169 brain regions into hierarchically-organized environments based on their expression of 100 G protein-coupled neurotransmitter receptors, with no a priori reference to the regions' positions in the brain's anatomy or function. The analysis was based on hierarchical clustering, and multiscale bootstrap resampling was used to estimate the reliability of detected clusters.ResultsThe study presents the first unbiased, hierarchical tree of functional environments in the human brain. The similarity of brain regions was strongly influenced by their anatomical proximity, even when they belonged to different functional systems. Generally, spatial vicinity trumped long-range projections or network connectivity. The main cluster of brain regions excluded the dentate gyrus of the hippocampus. The nuclei of the amygdala formed a cluster irrespective of their striatal or pallial origin. In its receptor profile, the hypothalamus was more closely associated with the midbrain than with the thalamus. The cerebellar cortical areas formed a tight and exclusive cluster. Most of the neocortical areas (with the exception of some occipital areas) clustered in a large, statistically well supported group that included no other brain regions.ConclusionsThis study adds a new dimension to the established classifications of brain divisions. In a single framework, they are reconsidered at multiple scales-from individual nuclei and areas to their groups to the entire brain. The analysis provides support for predictive models of brain self-organization and adaptation

Multiscale Markov Decision Problems: Compression, Solution, and Transfer Learning

Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure, particularly beyond a single level of abstraction, has remained a longstanding challenge. We describe a fast multiscale procedure for repeatedly compressing, or homogenizing, Markov decision processes (MDPs), wherein a hierarchy of sub-problems at different scales is automatically determined. Coarsened MDPs are themselves independent, deterministic MDPs, and may be solved using existing algorithms. The multiscale representation delivered by this procedure decouples sub-tasks from each other and can lead to substantial improvements in convergence rates both locally within sub-problems and globally across sub-problems, yielding significant computational savings. A second fundamental aspect of this work is that these multiscale decompositions yield new transfer opportunities across different problems, where solutions of sub-tasks at different levels of the hierarchy may be amenable to transfer to new problems. Localized transfer of policies and potential operators at arbitrary scales is emphasized. Finally, we demonstrate compression and transfer in a collection of illustrative domains, including examples involving discrete and continuous statespaces.Comment: 86 pages, 15 figure

Mapping road network communities for guiding disease surveillance and control strategies

Human mobility is increasing in its volume, speed and reach, leading to the movement and introduction of pathogens through infected travelers. An understanding of how areas are connected, the strength of these connections and how this translates into disease spread is valuable for planning surveillance and designing control and elimination strategies. While analyses have been undertaken to identify and map connectivity in global air, shipping and migration networks, such analyses have yet to be undertaken on the road networks that carry the vast majority of travellers in low and middle income settings. Here we present methods for identifying road connectivity communities, as well as mapping bridge areas between communities and key linkage routes. We apply these to Africa, and show how many highly-connected communities straddle national borders and when integrating malaria prevalence and population data as an example, the communities change, highlighting regions most strongly connected to areas of high burden. The approaches and results presented provide a flexible tool for supporting the design of disease surveillance and control strategies through mapping areas of high connectivity that form coherent units of intervention and key link routes between communities for targeting surveillance.Comment: 11 pages, 5 figures, research pape

Mining SOM expression portraits: Feature selection and integrating concepts of molecular function

Background: 
Self organizing maps (SOM) enable the straightforward portraying of high-dimensional data of large sample collections in terms of sample-specific images. The analysis of their texture provides so-called spot-clusters of co-expressed genes which require subsequent significance filtering and functional interpretation. We address feature selection in terms of the gene ranking problem and the interpretation of the obtained spot-related lists using concepts of molecular function.

Results: 
Different expression scores based either on simple fold change-measures or on regularized Students t-statistics are applied to spot-related gene lists and compared with special emphasis on the error characteristics of microarray expression data. The spot-clusters are analyzed using different methods of gene set enrichment analysis with the focus on overexpression and/or overrepresentation of predefined sets of genes. Metagene-related overrepresentation of selected gene sets was mapped into the SOM images to assign gene function to different regions. Alternatively we estimated set-related overexpression profiles over all samples studied using a gene set enrichment score. It was also applied to the spot-clusters to generate lists of enriched gene sets. We used the tissue body index data set, a collection of expression data of human tissues, as an illustrative example. We found that tissue related spots typically contain enriched populations of gene sets well corresponding to molecular processes in the respective tissues. In addition, we display special sets of housekeeping and of consistently weak and highly expressed genes using SOM data filtering. 

Conclusions:
The presented methods allow the comprehensive downstream analysis of SOM-transformed expression data in terms of cluster-related gene lists and enriched gene sets for functional interpretation. SOM clustering implies the ability to define either new gene sets using selected SOM spots or to verify and/or to amend existing ones

Decoding the neural substrates of reward-related decision making with functional MRI

Although previous studies have implicated a diverse set of brain regions in reward-related decision making, it is not yet known which of these regions contain information that directly reflects a decision. Here, we measured brain activity using functional MRI in a group of subjects while they performed a simple reward-based decision-making task: probabilistic reversal-learning. We recorded brain activity from nine distinct regions of interest previously implicated in decision making and separated out local spatially distributed signals in each region from global differences in signal. Using a multivariate analysis approach, we determined the extent to which global and local signals could be used to decode subjects' subsequent behavioral choice, based on their brain activity on the preceding trial. We found that subjects' decisions could be decoded to a high level of accuracy on the basis of both local and global signals even before they were required to make a choice, and even before they knew which physical action would be required. Furthermore, the combined signals from three specific brain areas (anterior cingulate cortex, medial prefrontal cortex, and ventral striatum) were found to provide all of the information sufficient to decode subjects' decisions out of all of the regions we studied. These findings implicate a specific network of regions in encoding information relevant to subsequent behavioral choice