Functionally Fractal Urban Networks: Geospatial Co-location and Homogeneity of Infrastructure

Just as natural river networks are known to be globally self-similar, recent research has shown that human-built urban networks, such as road networks, are also functionally self-similar, and have fractal topology with power-law node-degree distributions (p(k) = a k). Here we show, for the first time, that other urban infrastructure networks (sanitary and storm-water sewers), which sustain flows of critical services for urban citizens, also show scale-free functional topologies. For roads and drainage networks, we compared functional topological metrics, derived from high-resolution data (70,000 nodes) for a large US city providing services to about 900,000 citizens over an area of about 1,000 km2. For the whole city and for different sized subnets, we also examined these networks in terms of geospatial co-location (roads and sewers). Our analyses reveal functional topological homogeneity among all the subnets within the city, in spite of differences in several urban attributes. The functional topologies of all subnets of both infrastructure types resemble power-law distributions, with tails becoming increasingly power-law as the subnet area increases. Our findings hold implications for assessing the vulnerability of these critical infrastructure networks to cascading shocks based on spatial interdependency, and for improved design and maintenance of urban infrastructure networks

Increase of cell proliferation after bleaching.

<p>Cell proliferation (mean ± S.E.M.; EdU+ cell density in treated anemones divided by EdU+ cell density in controls) in the gastrodermis (<b>a</b>) and ectodermis (<b>b</b>) shows a rapid and transient increase following the bleaching procedure (N = 10–17/time point). Asterisk represents values significantly different than pre-stress values following ANOVA and Dunnett’s <i>post hoc</i> test (p<0.001).</p

Increase of mucocyte density after bleaching.

<p>Mucocyte density (mean ± S.E.M.) in the ectodermis shows a delayed and transient increase following the bleaching procedure (N = 10–17/time point). Asterisk represents values significantly different than pre-stress values following ANOVA and Dunnett’s <i>post hoc</i> test (p<0.0001).</p

EdU and WGA labeling.

<p>Transversal section of a tentacle showing histological labeling of EdU⁺ nuclei (<i>green</i>) and mucocytes (<i>arrow</i>) stained with WGA (<i>red</i>). DAPI staining (<i>blue</i>) was used to visualize nuclei. E, endodermis; G, gastrodermis.</p

Vladavina slučajnosti u repertoarnoj politici hrvatskih kazališta

(*, p < 0.05; **, p < 0.01).<p><b>Copyright information:</b></p><p>Taken from "Benfotiamine, a synthetic S-acyl thiamine derivative, has different mechanisms of action and a different pharmacological profile than lipid-soluble thiamine disulfide derivatives"</p><p>http://www.biomedcentral.com/1471-2210/8/10</p><p>BMC Pharmacology 2008;8():10-10.</p><p>Published online 12 Jun 2008</p><p>PMCID:PMC2435522.</p><p></p

Benfotiamine, a synthetic S-acyl thiamine derivative, has different mechanisms of action and a different pharmacological profile than lipid-soluble thiamine disulfide derivatives-2

(*, p < 0.05; **, p < 0.01).<p><b>Copyright information:</b></p><p>Taken from "Benfotiamine, a synthetic S-acyl thiamine derivative, has different mechanisms of action and a different pharmacological profile than lipid-soluble thiamine disulfide derivatives"</p><p>http://www.biomedcentral.com/1471-2210/8/10</p><p>BMC Pharmacology 2008;8():10-10.</p><p>Published online 12 Jun 2008</p><p>PMCID:PMC2435522.</p><p></p