Googling the brain: discovering hierarchical and asymmetric network structures, with applications in neuroscience

Hierarchical organisation is a common feature of many directed networks arising in nature and technology. For example, a well-defined message-passing framework based on managerial status typically exists in a business organisation. However, in many real-world networks such patterns of hierarchy are unlikely to be quite so transparent. Due to the nature in which empirical data is collated the nodes will often be ordered so as to obscure any underlying structure. In addition, the possibility of even a small number of links violating any overall “chain of command” makes the determination of such structures extremely challenging. Here we address the issue of how to reorder a directed network in order to reveal this type of hierarchy. In doing so we also look at the task of quantifying the level of hierarchy, given a particular node ordering. We look at a variety of approaches. Using ideas from the graph Laplacian literature, we show that a relevant discrete optimization problem leads to a natural hierarchical node ranking. We also show that this ranking arises via a maximum likelihood problem associated with a new range-dependent hierarchical random graph model. This random graph insight allows us to compute a likelihood ratio that quantifies the overall tendency for a given network to be hierarchical. We also develop a generalization of this node ordering algorithm based on the combinatorics of directed walks. In passing, we note that Google’s PageRank algorithm tackles a closely related problem, and may also be motivated from a combinatoric, walk-counting viewpoint. We illustrate the performance of the resulting algorithms on synthetic network data, and on a real-world network from neuroscience where results may be validated biologically

Parasites in Myodes glareolus and their association with diet assessed by stable isotope analysis

Vertebrates are hosts to numerous parasites, belonging to many different taxa. These parasites differ in transmission, being through either direct contact, a faecal-oral route, ingestion of particular food items, vertical or sexual transmission, or by a vector. Assessing the impact of diet on parasitism can be difficult because analysis of faecal and stomach content are uncertain and labourious; and as with molecular methods, do not provide diet information over a longer period of time. We here explored whether the analysis of stable isotopes in hair provides insight into the impact of diet and the presence of parasites in the rodent Myodes glareolus. Twenty-one animals were examined for parasites and their hair analysed for stable isotopes (C and N). A positive correlation between δ15N and one species of intestinal parasite was observed in females. Furthermore, several ectoparasites were negatively correlated with δ15N, indicating that infections are further associated with foraging habits (size and layout of the home range, length and timing of foraging, interaction with other rodents, etc.) that set the rodents in direct contact with infected hosts. Although a limited number of animals were included, it seemed that the isotope values allowed for identification of the association between diet and parasite occurrence in this rodent. We therefore propose that this method is useful in providing further insight into host biology, feeding preferences and potential exposure to parasites species, contributing to the understanding of the complex relationship between hosts and parasites. Keywords: δ13C, δ15N, Isotope, Diet, Bank vole, Hair, Parasitis

Finding 2-Edge and 2-Vertex Strongly Connected Components in Quadratic Time

We present faster algorithms for computing the 2-edge and 2-vertex strongly connected components of a directed graph, which are straightforward generalizations of strongly connected components. While in undirected graphs the 2-edge and 2-vertex connected components can be found in linear time, in directed graphs only rather simple $O(m n)$-time algorithms were known. We use a hierarchical sparsification technique to obtain algorithms that run in time $O(n^2)$. For 2-edge strongly connected components our algorithm gives the first running time improvement in 20 years. Additionally we present an $O(m^2 / \log{n})$-time algorithm for 2-edge strongly connected components, and thus improve over the $O(m n)$ running time also when $m = O(n)$. Our approach extends to k-edge and k-vertex strongly connected components for any constant k with a running time of $O(n^2 \log^2 n)$ for edges and $O(n^3)$ for vertices

The Pauli principle in a three-body cluster model and the momentum distributions after fragmentation of 6He and 11Li

We investigate two simple prescriptions to account for the Pauli principle in a three-body cluster model employing a new method based on an adiabatic hyperspherical expansion to solve the Faddeev equations in coordinate space. The resulting wave functions are computed and compared. They are furthermore tested on halo nuclei by calculations of momentum distributions and invariant mass spectra arising after fragmentation of fast $^6$He and $^{11}$Li in collisions with light targets. The prescriptions are very accurate and the available measured quantities are remarkably well reproduced when final state interactions are included.Comment: 18 pages, LaTex file, 15 postscript figures included using epsf.st

Cross sections for Coulomb and nuclear breakup of three-body halo nuclei

All possible dissociation cross sections for the loosely bound three-body halo nuclei $^6$He (n+n+$\alpha$) and $^{11}$Li (n+n+$^{9}$Li) are computed as functions of target and beam energy. Both Coulomb and nuclear interactions are included in the same theoretical framework. The measurements agree with the calculations for energies above 100 Mev/nucleon. The largest cross sections correspond to final states with zero or three particles for heavy and with two neutrons for light targets.Comment: 5 pages, 3 figures, revte