The Irreducible Spine(s) of Undirected Networks

Using closure concepts, we show that within every undirected network, or graph, there is a unique irreducible subgraph which we call its "spine". The chordless cycles which comprise this irreducible core effectively characterize the connectivity structure of the network as a whole. In particular, it is shown that the center of the network, whether defined by distance or betweenness centrality, is effectively contained in this spine. By counting the number of cycles of length 3 <= k <= max_length, we can also create a kind of signature that can be used to identify the network. Performance is analyzed, and the concepts we develop are illurstrated by means of a relatively small running sample network of about 400 nodes.Comment: Submitted to WISE 201

Topology of Cell-Aggregated Planar Graphs

We present new algorithm for growth of non-clustered planar graphs by aggregation of cells with given distribution of size and constraint of connectivity k=3 per node. The emergent graph structures are controlled by two parameters--chemical potential of the cell aggregation and the width of the cell size distribution. We compute several statistical properties of these graphs--fractal dimension of the perimeter, distribution of shortest paths between pairs of nodes and topological betweenness of nodes and links. We show how these topological properties depend on the control parameters of the aggregation process and discuss their relevance for the conduction of current in self-assembled nanopatterns.Comment: 8 pages, 5 figure

No-horizon theorem for vacuum gravity with spacelike G1 isometry groups

We show that (3+1) vacuum spacetimes admitting a global, spacelike, one-parameter Lie group of isometries of translational type cannot contain apparent horizons. The only assumption made is that of the existence of a global spacelike Killing vector field with infinite open orbits; the four-dimensional vacuum spacetime metric is otherwise arbitrary. This result may thus be viewed as a hoop conjecture theorem for vacuum gravity with one spacelike translational Killing symmetry.Comment: 6 pages, revtex4; published in Phys. Rev. D Rapid Com

Soluble axoplasm enriched from injured CNS axons reveals the early modulation of the actin cytoskeleton

Axon injury and degeneration is a common consequence of diverse neurological conditions including multiple sclerosis, traumatic brain injury and spinal cord injury. The molecular events underlying axon degeneration are poorly understood. We have developed a novel method to enrich for axoplasm from rodent optic nerve and characterised the early events in Wallerian degeneration using an unbiased proteomics screen. Our detergent-free method draws axoplasm into a dehydrated hydrogel of the polymer poly(2-hydroxyethyl methacrylate), which is then recovered using centrifugation. This technique is able to recover axonal proteins and significantly deplete glial contamination as confirmed by immunoblotting. We have used iTRAQ to compare axoplasm-enriched samples from naïve vs injured optic nerves, which has revealed a pronounced modulation of proteins associated with the actin cytoskeleton. To confirm the modulation of the actin cytoskeleton in injured axons we focused on the RhoA pathway. Western blotting revealed an augmentation of RhoA and phosphorylated cofilin in axoplasm-enriched samples from injured optic nerve. To investigate the localisation of these components of the RhoA pathway in injured axons we transected axons of primary hippocampal neurons in vitro. We observed an early modulation of filamentous actin with a concomitant redistribution of phosphorylated cofilin in injured axons. At later time-points, RhoA is found to accumulate in axonal swellings and also colocalises with filamentous actin. The actin cytoskeleton is a known sensor of cell viability across multiple eukaryotes, and our results suggest a similar role for the actin cytoskeleton following axon injury. In agreement with other reports, our data also highlights the role of the RhoA pathway in axon degeneration. These findings highlight a previously unexplored area of axon biology, which may open novel avenues to prevent axon degeneration. Our method for isolating CNS axoplasm also represents a new tool to study axon biology

Percolation in the classical blockmodel

Classical blockmodel is known as the simplest among models of networks with community structure. The model can be also seen as an extremely simply example of interconnected networks. For this reason, it is surprising that the percolation transition in the classical blockmodel has not been examined so far, although the phenomenon has been studied in a variety of much more complicated models of interconnected and multiplex networks. In this paper we derive the self-consistent equation for the size the global percolation cluster in the classical blockmodel. We also find the condition for percolation threshold which characterizes the emergence of the giant component. We show that the discussed percolation phenomenon may cause unexpected problems in a simple optimization process of the multilevel network construction. Numerical simulations confirm the correctness of our theoretical derivations.Comment: 7 pages, 6 figure

Do on-farm natural, restored, managed and constructed wetlands mitigate agricultural pollution in Great Britain and Ireland?: a systematic review

Wetlands in agricultural landscapes offer a number of benefits to the landscape function in which they are set, reducing nutrient runoff, providing additional habitat mosaics and offering various ecosystem services. They require careful planning and maintenance in order to perform their optimum design function over a prolonged period of time. They should be treated as functional units of farm infrastructure rather than fit-and-forget systems. A high priority topic within the Department for Environment, Food and Rural Affairs (DEFRA) water quality programme is the mitigation of pollution from agriculture. This programme was set up to meet the requirements of the European Water Framework Directive (WFD) EU (2000). Nutrient loss from agricultural land has been suggested as a major cause of elevated nutrient concentrations in surface waters in the UK. Nitrogen (N) and phosphorus (P) are of particular concern as an excess of either nutrient can lead to eutrophication of freshwater systems and coastal waters. Agriculture has also been identified as a significant source of suspended sediment (SS) concentrations in UK rivers and agriculturally derived sediment has been identified as a source of increased bed-sediment P concentrations in rivers. High bed sediments loads have other negative impacts, such as clogging river gravels reducing fish spawning. There is considerable evidence in the published and grey literature that wetlands have the ability to remove nutrients and sediment and thus reduce the load on receiving waters. Wetlands have also been reported to perform other ecosystem services, such as reducing floods, supporting biodiversity and sequestering carbon. A policy to promote the conservation, management, restoration or construction of wetlands could help to mitigate the impacts of N, P and SS from agriculture delivering requirements of WFD through Catchment Sensitive Farming following an Ecosystem Approach and Catchment Based Approach promoted by Defra. It could also meet other commitments such as implementing the Ramsar and Biodiversity Conventions to which the UK is a signatory. However, the term wetlands covers a wide range of habitat types and it is important that policy makers are provided with accurate, robust and independently reviewed information on the degree to which different types of wetland perform these services under different circumstances, so that policy can most best targeted. This systematic review assesses the available evidence on the performance of various wetland types on farms to reduce nutrient input and suspended sediments to receiving waters. It provides a defensible evidence base on which to base policy. The studies reviewed cover different input loads and the analysis compares performance of these wetland systems in respect of % reduction efficiency. In England and Wales, Defra, working closely with the Environment Agency and Natural England, has commissioned this systematic review on how effective, and what influences the effectiveness of wetlands at mitigating N, P and SS inputs from agriculture to receiving freshwater in the United Kingdom and Ireland

Network Landscape from a Brownian Particle's Perspective

Given a complex biological or social network, how many clusters should it be decomposed into? We define the distance $d_{i,j}$ from node $i$ to node $j$ as the average number of steps a Brownian particle takes to reach $j$ from $i$. Node $j$ is a global attractor of $i$ if $d_{i,j}\leq d_{i,k}$ for any $k$ of the graph; it is a local attractor of $i$, if $j\in E_i$ (the set of nearest-neighbors of $i$) and $d_{i,j}\leq d_{i,l}$ for any $l\in E_i$. Based on the intuition that each node should have a high probability to be in the same community as its global (local) attractor on the global (local) scale, we present a simple method to uncover a network's community structure. This method is applied to several real networks and some discussion on its possible extensions is made.Comment: 5 pages, 4 color-figures. REVTeX 4 format. To appear in PR

Role of Initial Data in Higher Dimensional Quasi-Spherical Gravitational Collapse

We study the gravitational collapse in ($n+2$)-D quasi-spherical Szekeres space-time (which possess no killing vectors) with dust as the matter distribution. Instead of choosing the radial coordinate `$r$' as the initial value for the scale factor $R$, we consider a power function of $r$ as the initial scale for the radius $R$. We examine the influence of initial data on the formation of singularity in gravitational collapse.Comment: 7 Latex Pages, RevTex Style, No figure

Convergence of the critical attractor of dissipative maps: Log-periodic oscillations, fractality and nonextensivity

For a family of logistic-like maps, we investigate the rate of convergence to the critical attractor when an ensemble of initial conditions is uniformly spread over the entire phase space. We found that the phase space volume occupied by the ensemble W(t) depicts a power-law decay with log-periodic oscillations reflecting the multifractal character of the critical attractor. We explore the parametric dependence of the power-law exponent and the amplitude of the log-periodic oscillations with the attractor's fractal dimension governed by the inflexion of the map near its extremal point. Further, we investigate the temporal evolution of W(t) for the circle map whose critical attractor is dense. In this case, we found W(t) to exhibit a rich pattern with a slow logarithmic decay of the lower bounds. These results are discussed in the context of nonextensive Tsallis entropies.Comment: 8 pages and 8 fig