Simple deterministic dynamical systems with fractal diffusion coefficients

We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic scattering process of the map can be changed by a control parameter. This induces a parameter dependence for the macroscopic diffusion coefficient. We calculate the diffusion coefficent and the largest eigenmodes of the system by using Markov partitions and by solving the eigenvalue problems of respective topological transition matrices. For different boundary conditions we find that the largest eigenmodes of the map match to the ones of the simple phenomenological diffusion equation. Our main result is that the difffusion coefficient exhibits a fractal structure by varying the system parameter. To understand the origin of this fractal structure, we give qualitative and quantitative arguments. These arguments relate the sequence of oscillations in the strength of the parameter-dependent diffusion coefficient to the microscopic coupling of the single scatterers which changes by varying the control parameter.Comment: 28 pages (revtex), 12 figures (postscript), submitted to Phys. Rev.

The geology and geophysics of Kuiper Belt object (486958) Arrokoth

The Cold Classical Kuiper Belt, a class of small bodies in undisturbed orbits beyond Neptune, are primitive objects preserving information about Solar System formation. The New Horizons spacecraft flew past one of these objects, the 36 km long contact binary (486958) Arrokoth (2014 MU69), in January 2019. Images from the flyby show that Arrokoth has no detectable rings, and no satellites (larger than 180 meters diameter) within a radius of 8000 km, and has a lightly-cratered smooth surface with complex geological features, unlike those on previously visited Solar System bodies. The density of impact craters indicates the surface dates from the formation of the Solar System. The two lobes of the contact binary have closely aligned poles and equators, constraining their accretion mechanism

Fine-Scale Mapping of the 5q11.2 Breast Cancer Locus Reveals at Least Three Independent Risk Variants Regulating MAP3K1

Peer reviewe

The genetic architecture of the human cerebral cortex

INTRODUCTION The cerebral cortex underlies our complex cognitive capabilities. Variations in human cortical surface area and thickness are associated with neurological, psychological, and behavioral traits and can be measured in vivo by magnetic resonance imaging (MRI). Studies in model organisms have identified genes that influence cortical structure, but little is known about common genetic variants that affect human cortical structure. RATIONALE To identify genetic variants associated with human cortical structure at both global and regional levels, we conducted a genome-wide association meta-analysis of brain MRI data from 51,665 individuals across 60 cohorts. We analyzed the surface area and average thickness of the whole cortex and 34 cortical regions with known functional specializations. RESULTS We identified 306 nominally genome-wide significant loci (P < 5 × 10−8) associated with cortical structure in a discovery sample of 33,992 participants of European ancestry. Of the 299 loci for which replication data were available, 241 loci influencing surface area and 14 influencing thickness remained significant after replication, with 199 loci passing multiple testing correction (P < 8.3 × 10−10; 187 influencing surface area and 12 influencing thickness). Common genetic variants explained 34% (SE = 3%) of the variation in total surface area and 26% (SE = 2%) in average thickness; surface area and thickness showed a negative genetic correlation (rG = −0.32, SE = 0.05, P = 6.5 × 10−12), which suggests that genetic influences have opposing effects on surface area and thickness. Bioinformatic analyses showed that total surface area is influenced by genetic variants that alter gene regulatory activity in neural progenitor cells during fetal development. By contrast, average thickness is influenced by active regulatory elements in adult brain samples, which may reflect processes that occur after mid-fetal development, such as myelination, branching, or pruning. When considered together, these results support the radial unit hypothesis that different developmental mechanisms promote surface area expansion and increases in thickness. To identify specific genetic influences on individual cortical regions, we controlled for global measures (total surface area or average thickness) in the regional analyses. After multiple testing correction, we identified 175 loci that influence regional surface area and 10 that influence regional thickness. Loci that affect regional surface area cluster near genes involved in the Wnt signaling pathway, which is known to influence areal identity. We observed significant positive genetic correlations and evidence of bidirectional causation of total surface area with both general cognitive functioning and educational attainment. We found additional positive genetic correlations between total surface area and Parkinson’s disease but did not find evidence of causation. Negative genetic correlations were evident between total surface area and insomnia, attention deficit hyperactivity disorder, depressive symptoms, major depressive disorder, and neuroticism. CONCLUSION This large-scale collaborative work enhances our understanding of the genetic architecture of the human cerebral cortex and its regional patterning. The highly polygenic architecture of the cortex suggests that distinct genes are involved in the development of specific cortical areas. Moreover, we find evidence that brain structure is a key phenotype along the causal pathway that leads from genetic variation to differences in general cognitive function

Using structural MRI to identify bipolar disorders - 13 site machine learning study in 3020 individuals from the ENIGMA Bipolar Disorders Working Group.

Bipolar disorders (BDs) are among the leading causes of morbidity and disability. Objective biological markers, such as those based on brain imaging, could aid in clinical management of BD. Machine learning (ML) brings neuroimaging analyses to individual subject level and may potentially allow for their diagnostic use. However, fair and optimal application of ML requires large, multi-site datasets. We applied ML (support vector machines) to MRI data (regional cortical thickness, surface area, subcortical volumes) from 853 BD and 2167 control participants from 13 cohorts in the ENIGMA consortium. We attempted to differentiate BD from control participants, investigated different data handling strategies and studied the neuroimaging/clinical features most important for classification. Individual site accuracies ranged from 45.23% to 81.07%. Aggregate subject-level analyses yielded the highest accuracy (65.23%, 95% CI = 63.47-67.00, ROC-AUC = 71.49%, 95% CI = 69.39-73.59), followed by leave-one-site-out cross-validation (accuracy = 58.67%, 95% CI = 56.70-60.63). Meta-analysis of individual site accuracies did not provide above chance results. There was substantial agreement between the regions that contributed to identification of BD participants in the best performing site and in the aggregate dataset (Cohen's Kappa = 0.83, 95% CI = 0.829-0.831). Treatment with anticonvulsants and age were associated with greater odds of correct classification. Although short of the 80% clinically relevant accuracy threshold, the results are promising and provide a fair and realistic estimate of classification performance, which can be achieved in a large, ecologically valid, multi-site sample of BD participants based on regional neurostructural measures. Furthermore, the significant classification in different samples was based on plausible and similar neuroanatomical features. Future multi-site studies should move towards sharing of raw/voxelwise neuroimaging data