Resolving structural variability in network models and the brain

Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little is known about mechanistic drivers of structured networks. Here we contrast network properties derived from diffusion spectrum imaging data of the human brain with 13 synthetic network models chosen to probe the roles of physical network embedding and temporal network growth. We characterize both the empirical and synthetic networks using familiar diagnostics presented in statistical form, as scatter plots and distributions, to reveal the full range of variability of each measure across scales in the network. We focus on the degree distribution, degree assortativity, hierarchy, topological Rentian scaling, and topological fractal scaling---in addition to several summary statistics, including the mean clustering coefficient, shortest path length, and network diameter. The models are investigated in a progressive, branching sequence, aimed at capturing different elements thought to be important in the brain, and range from simple random and regular networks, to models that incorporate specific growth rules and constraints. We find that synthetic models that constrain the network nodes to be embedded in anatomical brain regions tend to produce distributions that are similar to those extracted from the brain. We also find that network models hardcoded to display one network property do not in general also display a second, suggesting that multiple neurobiological mechanisms might be at play in the development of human brain network architecture. Together, the network models that we develop and employ provide a potentially useful starting point for the statistical inference of brain network structure from neuroimaging data.Comment: 24 pages, 11 figures, 1 table, supplementary material

Phase diagram analysis and crystal growth of solid solutions Ca_{1-x}Sr_xF_2

The binary phase diagram CaF$_2$--SrF$_2$ was investigated by differential thermal analysis (DTA). Both substances exhibit unlimited mutual solubility with an azeotropic point showing a minimum melting temperature of T_\mathrm{min}=1373^{\circ}$C for the composition Ca$_{0.582}$Sr$_{0.418}$F$_2$. Close to this composition, homogeneous single crystals up to 30 mm diameter without remarkable segregation could be grown by the Czochralski method.Comment: accepted for publication in J. Crystal Growt

New magnetic phase in metallic V_{2-y}O_3 close to the metal insulator transition

We have observed two spin density wave (SDW) phases in hole doped metallic V_{2-y}O_3, one evolves from the other as a function of doping, pressure or temperature. They differ in their response to an external magnetic field, which can also induce a transition between them. The phase boundary between these two states in the temperature-, doping-, and pressure-dependent phase diagram has been determined by magnetization and magnetotransport measurements. One phase exists at high doping level and has already been described in the literature. The second phase is found in a small parameter range close to the boundary to the antiferromagnetic insulating phase (AFI). The quantum phase transitions between these states as a function of pressure and doping and the respective metamagnetic behavior observed in these phases are discussed in the light of structurally induced changes of the band structure.Comment: REVTeX, 8 pages, 12 EPS figures, submitted to PR

Wirkung des Kaliumkanalblockers Glipizid auf den Noradrenalinbedarf und das Überleben in einem chronisch-instrumentierten, endotoxinämischen Schafmodell

Adenosin-sensitive Kaliumkanäle (KATP) spielen eine bedeutende Rolle in Sepsis und septischem Schock. Diese Studie untersucht den Einfluss des Kaliumkanalblockers Glipizid auf den Noradrenalinbedarf und das Überleben an einem chronisch-instrumentierten endotoxinämischen Schafmodell. Ziel ist das Finden neuer Therapiemöglichkeiten durch Blockade von (KATP)-Kanälen, um die katecholamininduzierte refraktäre Vasodilatation und Hypotonie in Sepsis aufzuheben. Hierzu wurden zwanzig Schafe in zwei äquivalente Gruppen (Glipizid vs. Kontrolle) randomisiert und für die hämodynamische Überwachung instrumentiert. Alle Tiere erhielten eine kontinuierliche Endotoxin-Infusion (Salmonella typhosa, 5ng/kg/min) mit steigender Dosierung. Die Behandlung mit Glipizid (8mg/kg/h) führte gegenüber der mit 0,9% NaCl-Lösung und Noradrenalin behandelten Kontrollgruppe jedoch weder zu einer signifikanten Verringerung des Noradrenalinbedarfs noch zu einem Überlebensvorteil

Improved Approximation Algorithms for the Expanding Search Problem

A searcher faces a graph with edge lengths and vertex weights, initially having explored only a given starting vertex. In each step, the searcher adds an edge to the solution that connects an unexplored vertex to an explored vertex. This requires an amount of time equal to the edge length. The goal is to minimize the weighted sum of the exploration times over all vertices. We show that this problem is hard to approximate and provide algorithms with improved approximation guarantees. For the general case, we give a (2e+?)-approximation for any ? > 0. For the case that all vertices have unit weight, we provide a 2e-approximation. Finally, we provide a PTAS for the case of a Euclidean graph. Previously, for all cases only an 8-approximation was known