A bijection between unicellular and bicellular maps

In this paper we present a combinatorial proof of a relation between the generating functions of unicellular and bicellular maps. This relation is a consequence of the Schwinger-Dyson equation of matrix theory. Alternatively it can be proved using representation theory of the symmetric group. Here we give a bijective proof by rewiring unicellular maps of topological genus $(g+1)$ into bicellular maps of genus $g$ and pairs of unicellular maps of lower topological genera. Our result has immediate consequences for the folding of RNA interaction structures, since the time complexity of folding the transformed structure is $O((n+m)^5)$, where $n,m$ are the lengths of the respective backbones, while the folding of the original structure has $O(n^6)$ time complexity, where $n$ is the length of the longer sequence.Comment: 18 pages, 13 figure

A phase transition in energy-filtered RNA secondary structures

In this paper we study the effect of energy parameters on minimum free energy (mfe) RNA secondary structures. Employing a simplified combinatorial energy model, that is only dependent on the diagram representation and that is not sequence specific, we prove the following dichotomy result. Mfe structures derived via the Turner energy parameters contain only finitely many complex irreducible substructures and just minor parameter changes produce a class of mfe-structures that contain a large number of small irreducibles. We localize the exact point where the distribution of irreducibles experiences this phase transition from a discrete limit to a central limit distribution and subsequently put our result into the context of quantifying the effect of sparsification of the folding of these respective mfe-structures. We show that the sparsification of realistic mfe-structures leads to a constant time and space reduction and that the sparsifcation of the folding of structures with modified parameters leads to a linear time and space reduction. We furthermore identify the limit distribution at the phase transition as a Rayleigh distribution.Comment: 34 pages, 6 figure

ENIGMA and global neuroscience: A decade of large-scale studies of the brain in health and disease across more than 40 countries

This review summarizes the last decade of work by the ENIGMA (Enhancing NeuroImaging Genetics through Meta Analysis) Consortium, a global alliance of over 1400 scientists across 43 countries, studying the human brain in health and disease. Building on large-scale genetic studies that discovered the first robustly replicated genetic loci associated with brain metrics, ENIGMA has diversified into over 50 working groups (WGs), pooling worldwide data and expertise to answer fundamental questions in neuroscience, psychiatry, neurology, and genetics. Most ENIGMA WGs focus on specific psychiatric and neurological conditions, other WGs study normal variation due to sex and gender differences, or development and aging; still other WGs develop methodological pipelines and tools to facilitate harmonized analyses of "big data" (i.e., genetic and epigenetic data, multimodal MRI, and electroencephalography data). These international efforts have yielded the largest neuroimaging studies to date in schizophrenia, bipolar disorder, major depressive disorder, post-traumatic stress disorder, substance use disorders, obsessive-compulsive disorder, attention-deficit/hyperactivity disorder, autism spectrum disorders, epilepsy, and 22q11.2 deletion syndrome. More recent ENIGMA WGs have formed to study anxiety disorders, suicidal thoughts and behavior, sleep and insomnia, eating disorders, irritability, brain injury, antisocial personality and conduct disorder, and dissociative identity disorder. Here, we summarize the first decade of ENIGMA's activities and ongoing projects, and describe the successes and challenges encountered along the way. We highlight the advantages of collaborative large-scale coordinated data analyses for testing reproducibility and robustness of findings, offering the opportunity to identify brain systems involved in clinical syndromes across diverse samples and associated genetic, environmental, demographic, cognitive, and psychosocial factors

Analysis of Rare, Exonic Variation amongst Subjects with Autism Spectrum Disorders and Population Controls

We report on results from whole-exome sequencing (WES) of 1,039 subjects diagnosed with autism spectrum disorders (ASD) and 870 controls selected from the NIMH repository to be of similar ancestry to cases. The WES data came from two centers using different methods to produce sequence and to call variants from it. Therefore, an initial goal was to ensure the distribution of rare variation was similar for data from different centers. This proved straightforward by filtering called variants by fraction of missing data, read depth, and balance of alternative to reference reads. Results were evaluated using seven samples sequenced at both centers and by results from the association study. Next we addressed how the data and/or results from the centers should be combined. Gene-based analyses of association was an obvious choice, but should statistics for association be combined across centers (meta-analysis) or should data be combined and then analyzed (mega-analysis)? Because of the nature of many gene-based tests, we showed by theory and simulations that mega-analysis has better power than meta-analysis. Finally, before analyzing the data for association, we explored the impact of population structure on rare variant analysis in these data. Like other recent studies, we found evidence that population structure can confound case-control studies by the clustering of rare variants in ancestry space; yet, unlike some recent studies, for these data we found that principal component-based analyses were sufficient to control for ancestry and produce test statistics with appropriate distributions. After using a variety of gene-based tests and both meta- and mega-analysis, we found no new risk genes for ASD in this sample. Our results suggest that standard gene-based tests will require much larger samples of cases and controls before being effective for gene discovery, even for a disorder like ASD. © 2013 Liu et al

ENIGMA and global neuroscience: A decade of large-scale studies of the brain in health and disease across more than 40 countries

This review summarizes the last decade of work by the ENIGMA (Enhancing NeuroImaging Genetics through Meta Analysis) Consortium, a global alliance of over 1400 scientists across 43 countries, studying the human brain in health and disease. Building on large-scale genetic studies that discovered the first robustly replicated genetic loci associated with brain metrics, ENIGMA has diversified into over 50 working groups (WGs), pooling worldwide data and expertise to answer fundamental questions in neuroscience, psychiatry, neurology, and genetics. Most ENIGMA WGs focus on specific psychiatric and neurological conditions, other WGs study normal variation due to sex and gender differences, or development and aging; still other WGs develop methodological pipelines and tools to facilitate harmonized analyses of "big data" (i.e., genetic and epigenetic data, multimodal MRI, and electroencephalography data). These international efforts have yielded the largest neuroimaging studies to date in schizophrenia, bipolar disorder, major depressive disorder, post-traumatic stress disorder, substance use disorders, obsessive-compulsive disorder, attention-deficit/hyperactivity disorder, autism spectrum disorders, epilepsy, and 22q11.2 deletion syndrome. More recent ENIGMA WGs have formed to study anxiety disorders, suicidal thoughts and behavior, sleep and insomnia, eating disorders, irritability, brain injury, antisocial personality and conduct disorder, and dissociative identity disorder. Here, we summarize the first decade of ENIGMA's activities and ongoing projects, and describe the successes and challenges encountered along the way. We highlight the advantages of collaborative large-scale coordinated data analyses for testing reproducibility and robustness of findings, offering the opportunity to identify brain systems involved in clinical syndromes across diverse samples and associated genetic, environmental, demographic, cognitive, and psychosocial factors