Cantor type functions in non-integer bases

Cantor's ternary function is generalized to arbitrary base-change functions in non-integer bases. Some of them share the curious properties of Cantor's function, while others behave quite differently

CSF metabolites associate with CSF tau and improve prediction of Alzheimer's disease status

Introduction: Cerebrospinal fluid (CSF) total tau (t-tau) and phosphorylated tau (p-tau) are biomarkers of Alzheimer's disease (AD), yet much is unknown about AD-associated changes in tau metabolism and tau tangle etiology. Methods: We assessed the variation of t-tau and p-tau explained by 38 previously identified CSF metabolites using linear regression models in middle-age controls from the Wisconsin Alzheimer's Disease Research Center, and predicted AD/mild cognitive impairment (MCI) versus an independent set of older controls using metabolites selected by the least absolute shrinkage and selection operator (LASSO). Results: The 38 CSF metabolites explained 70.3% and 75.7% of the variance in t-tau and p-tau, respectively. Of these, seven LASSO-selected metabolites improved the prediction ability of AD/MCI versus older controls (area under the curve score increased from 0.92 to 0.97 and 0.78 to 0.93) compared to the base model. Discussion: These tau-correlated CSF metabolites increase AD/MCI prediction accuracy and may provide insight into tau tangle etiology

Local multiresolution order in community detection

Community detection algorithms attempt to find the best clusters of nodes in an arbitrary complex network. Multi-scale ("multiresolution") community detection extends the problem to identify the best network scale(s) for these clusters. The latter task is generally accomplished by analyzing community stability simultaneously for all clusters in the network. In the current work, we extend this general approach to define local multiresolution methods, which enable the extraction of well-defined local communities even if the global community structure is vaguely defined in an average sense. Toward this end, we propose measures analogous to variation of information and normalized mutual information that are used to quantitatively identify the best resolution(s) at the community level based on correlations between clusters in independently-solved systems. We demonstrate our method on two constructed networks as well as a real network and draw inferences about local community strength. Our approach is independent of the applied community detection algorithm save for the inherent requirement that the method be able to identify communities across different network scales, with appropriate changes to account for how different resolutions are evaluated or defined in a particular community detection method. It should, in principle, easily adapt to alternative community comparison measures.Comment: 19 pages, 11 figure

Router-level community structure of the Internet Autonomous Systems

The Internet is composed of routing devices connected between them and organized into independent administrative entities: the Autonomous Systems. The existence of different types of Autonomous Systems (like large connectivity providers, Internet Service Providers or universities) together with geographical and economical constraints, turns the Internet into a complex modular and hierarchical network. This organization is reflected in many properties of the Internet topology, like its high degree of clustering and its robustness. In this work, we study the modular structure of the Internet router-level graph in order to assess to what extent the Autonomous Systems satisfy some of the known notions of community structure. We show that the modular structure of the Internet is much richer than what can be captured by the current community detection methods, which are severely affected by resolution limits and by the heterogeneity of the Autonomous Systems. Here we overcome this issue by using a multiresolution detection algorithm combined with a small sample of nodes. We also discuss recent work on community structure in the light of our results

Evidence for the role of EPHX2 gene variants in anorexia nervosa.

Anorexia nervosa (AN) and related eating disorders are complex, multifactorial neuropsychiatric conditions with likely rare and common genetic and environmental determinants. To identify genetic variants associated with AN, we pursued a series of sequencing and genotyping studies focusing on the coding regions and upstream sequence of 152 candidate genes in a total of 1205 AN cases and 1948 controls. We identified individual variant associations in the Estrogen Receptor-ß (ESR2) gene, as well as a set of rare and common variants in the Epoxide Hydrolase 2 (EPHX2) gene, in an initial sequencing study of 261 early-onset severe AN cases and 73 controls (P=0.0004). The association of EPHX2 variants was further delineated in: (1) a pooling-based replication study involving an additional 500 AN patients and 500 controls (replication set P=0.00000016); (2) single-locus studies in a cohort of 386 previously genotyped broadly defined AN cases and 295 female population controls from the Bogalusa Heart Study (BHS) and a cohort of 58 individuals with self-reported eating disturbances and 851 controls (combined smallest single locus P<0.01). As EPHX2 is known to influence cholesterol metabolism, and AN is often associated with elevated cholesterol levels, we also investigated the association of EPHX2 variants and longitudinal body mass index (BMI) and cholesterol in BHS female and male subjects (N=229) and found evidence for a modifying effect of a subset of variants on the relationship between cholesterol and BMI (P<0.01). These findings suggest a novel association of gene variants within EPHX2 to susceptibility to AN and provide a foundation for future study of this important yet poorly understood condition

Inference of hidden structures in complex physical systems by multi-scale clustering

We survey the application of a relatively new branch of statistical physics--"community detection"-- to data mining. In particular, we focus on the diagnosis of materials and automated image segmentation. Community detection describes the quest of partitioning a complex system involving many elements into optimally decoupled subsets or communities of such elements. We review a multiresolution variant which is used to ascertain structures at different spatial and temporal scales. Significant patterns are obtained by examining the correlations between different independent solvers. Similar to other combinatorial optimization problems in the NP complexity class, community detection exhibits several phases. Typically, illuminating orders are revealed by choosing parameters that lead to extremal information theory correlations.Comment: 25 pages, 16 Figures; a review of earlier work

The microstructure of coaching practice:Behaviours and activities of an elite rugby union head coach during preparation and competition

The activities and behaviours of a female head coach of a national rugby union team were recorded in both training and competition, across a whole rugby season, using the newly developed Rugby Coach Activities and Behaviours Instrument (RCABI). The instrument incorporates 24 categories of behaviour, embedded within three forms of activity (training form, playing form and competitive match) and seven sub-activity types. In contrast to traditional drill-based coaching, 58.5% of training time was found to have been spent in playing form activities. Moreover, the proportion of playing form activities increased to a peak average of 83.8% in proximity to the team’s annual international championship. Uniquely, one of the coach’s most prolific behaviours was conferring with associates (23.3%), highlighting the importance of interactions with assistant coaches, medical staff and others in shaping the coaching process. Additionally, the frequencies of key behaviours such as questioning and praise were found to vary between the different activity forms and types, raising questions about previous conceptions of effective coaching practice. The findings are discussed in the light of the Game Sense philosophy and the role of the head coach