Hierarchical characterization of complex networks

While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be obtained by considering further neighborhoods. The current work discusses on how the concepts of hierarchical node degree and hierarchical clustering coefficient (introduced in cond-mat/0408076), complemented by new hierarchical measurements, can be used in order to obtain a powerful set of topological features of complex networks. The interpretation of such measurements is discussed, including an analytical study of the hierarchical node degree for random networks, and the potential of the suggested measurements for the characterization of complex networks is illustrated with respect to simulations of random, scale-free and regular network models as well as real data (airports, proteins and word associations). The enhanced characterization of the connectivity provided by the set of hierarchical measurements also allows the use of agglomerative clustering methods in order to obtain taxonomies of relationships between nodes in a network, a possibility which is also illustrated in the current article.Comment: 19 pages, 23 figure

Mathematical morphology on tensor data using the Loewner ordering

The notions of maximum and minimum are the key to the powerful tools of greyscale morphology. Unfortunately these notions do not carry over directly to tensor-valued data. Based upon the Loewner ordering for symmetric matrices this paper extends the maximum and minimum operation to the tensor-valued setting. This provides the ground to establish matrix-valued analogues of the basic morphological operations ranging from erosion/dilation to top hats. In contrast to former attempts to develop a morphological machinery for matrices, the novel definitions of maximal/minimal matrices depend continuously on the input data, a property crucial for the construction of morphological derivatives such as the Beucher gradient or a morphological Laplacian. These definitions are rotationally invariant and preserve positive semidefiniteness of matrix fields as they are encountered in DT-MRI data. The morphological operations resulting from a component-wise maximum/minimum of the matrix channels disregarding their strong correlation fail to be rotational invariant. Experiments on DT-MRI images as well as on indefinite matrix data illustrate the properties and performance of our morphological operators

Amoeba Techniques for Shape and Texture Analysis

Morphological amoebas are image-adaptive structuring elements for morphological and other local image filters introduced by Lerallut et al. Their construction is based on combining spatial distance with contrast information into an image-dependent metric. Amoeba filters show interesting parallels to image filtering methods based on partial differential equations (PDEs), which can be confirmed by asymptotic equivalence results. In computing amoebas, graph structures are generated that hold information about local image texture. This paper reviews and summarises the work of the author and his coauthors on morphological amoebas, particularly their relations to PDE filters and texture analysis. It presents some extensions and points out directions for future investigation on the subject.Comment: 38 pages, 19 figures v2: minor corrections and rephrasing, Section 5 (pre-smoothing) extende

Minkowski Tensors of Anisotropic Spatial Structure

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalisations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations, and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The article further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic method more readily accessible for future application in the physical sciences

Prenatal Famine and Genetic Variation Are Independently and Additively Associated with DNA Methylation at Regulatory Loci within IGF2/H19

Both the early environment and genetic variation may affect DNA methylation, which is one of the major molecular marks of the epigenome. The combined effect of these factors on a well-defined locus has not been studied to date. We evaluated the association of periconceptional exposure to the Dutch Famine of 1944–45, as an example of an early environmental exposure, and single nucleotide polymorphisms covering the genetic variation (tagging SNPs) with DNA methylation at the imprinted IGF2/H19 region, a model for an epigenetically regulated genomic region. DNA methylation was measured at five differentially methylated regions (DMRs) that regulate the imprinted status of the IGF2/H19 region. Small but consistent differences in DNA methylation were observed comparing 60 individuals with periconceptional famine exposure with unexposed same-sex siblings at all IGF2 DMRs (PBH<0.05 after adjustment for multiple testing), but not at the H19 DMR. IGF2 DMR0 methylation was associated with IGF2 SNP rs2239681 (PBH = 0.027) and INS promoter methylation with INS SNPs, including rs689, which tags the INS VNTR, suggesting a mechanism for the reported effect of the VNTR on INS expression (PBH = 3.4×10−3). Prenatal famine and genetic variation showed similar associations with IGF2/H19 methylation and their contributions were additive. They were small in absolute terms (<3%), but on average 0.5 standard deviations relative to the variation in the population. Our analyses suggest that environmental and genetic factors could have independent and additive similarly sized effects on DNA methylation at the same regulatory site

Periconceptional Maternal Folic Acid Use of 400 µg per Day Is Related to Increased Methylation of the IGF2 Gene in the Very Young Child

Background: Countries worldwide recommend women planning pregnancy to use daily 400 mg of synthetic folic acid in the periconceptional period to prevent birth defects in children. The underlying mechanisms of this preventive effect are not clear, however, epigenetic modulation of growth processes by folic acid is hypothesized. Here, we investigated whether periconceptional maternal folic acid use and markers of global DNA methylation potential (S-adenosylmethionine and S-adenosylhomocysteine blood levels) in mothers and children affect methylation of the insulin-like growth factor 2 gene differentially methylation region (IGF2 DMR) in the child. Moreover, we tested whether the methylation of the IGF2 DMR was independently associated with birth weight. Methodology/Principal Findings: IGF2 DMR methylation in 120 children aged 17 months (SD 0.3) of whom 86 mothers had used and 34 had not used folic acid periconceptionally were studied. Methylation was measured of 5 CpG dinucleotides covering the DMR using a mass spectrometry-based method. Children of mother who used folic acid had a 4.5% higher methylation of the IGF2 DMR than children who were not exposed to folic acid (49.5% vs. 47.4%; p = 0.014). IGF2 DMR methylation of the children also was associated with the S-adenosylmethionine blood level of the mother but not of the child (+1.7% methylation per SD S-adenosylmethionine; p = 0.037). Finally, we observed an inverse independent association between IGF2 DMR methylation and birth weight (-1.7% methylation per SD birthweight; p = 0.034). Conclusions: Periconceptional folic acid use is associated with epigenetic changes in IGF2 in the child that may affect intrauterine programming of growth and development with consequences for health and disease throughout life. These results indicate plasticity of IGF2 methylation by periconceptional folic acid use

Genome-wide Linkage Scan to Identify Loci for Age at First Cigarette in Dutch Sibling Pairs

Most smokers begin smoking during adolescence and early age of smoking initiation is related to more frequent current smoking, daily smoking and more dependent smoking (Everret et al., 1999; Lando et al.

Association of cord blood methylation fractions at imprinted insulin-like growth factor 2 (IGF2), plasma IGF2, and birth weight

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The effect of temperature on growth and competition between Sphagnum species

Peat bogs play a large role in the global sequestration of C, and are often dominated by different Sphagnum species. Therefore, it is crucial to understand how Sphagnum vegetation in peat bogs will respond to global warming. We performed a greenhouse experiment to study the effect of four temperature treatments (11.2, 14.7, 18.0 and 21.4°C) on the growth of four Sphagnum species: S. fuscum and S. balticum from a site in northern Sweden and S. magellanicum and S. cuspidatum from a site in southern Sweden. In addition, three combinations of these species were made to study the effect of temperature on competition. We found that all species increased their height increment and biomass production with an increase in temperature, while bulk densities were lower at higher temperatures. The hollow species S. cuspidatum was the least responsive species, whereas the hummock species S. fuscum increased biomass production 13-fold from the lowest to the highest temperature treatment in monocultures. Nutrient concentrations were higher at higher temperatures, especially N concentrations of S. fuscum and S. balticum increased compared to field values. Competition between S. cuspidatum and S. magellanicum was not influenced by temperature. The mixtures of S. balticum with S. fuscum and S. balticum with S. magellanicum showed that S. balticum was the stronger competitor, but it lost competitive advantage in the highest temperature treatment. These findings suggest that species abundances will shift in response to global warming, particularly at northern sites where hollow species will lose competitive strength relative to hummock species and southern species