Live and Dead Nodes

In this paper, we explore the consequences of a distinction between `live' and `dead' network nodes; `live' nodes are able to acquire new links whereas `dead' nodes are static. We develop an analytically soluble growing network model incorporating this distinction and show that it can provide a quantitative description of the empirical network composed of citations and references (in- and out-links) between papers (nodes) in the SPIRES database of scientific papers in high energy physics. We also demonstrate that the death mechanism alone can result in power law degree distributions for the resulting network.Comment: 12 pages, 3 figures. To be published in Computational and Mathematical Organization Theor

Impact of the surface roughness on the electrical capacitance

A new hybrid approach consists to use the advantages of both systems namely the high geometric aspects of the electrodes of the ultracapacitor and the high dielectric strength of polymer materials used in dielectric capacitors. The surface roughness of the electrodes of the ultracapacitor is manufactured with nano-porous materials; activated carbon and carbon nanotubes (CNTs). Many compositions of both carbonaceous materials are tested with different insulating materials (liquid and solid) to constitute the hybrid capacitor. It appears that the capacitance increases with the carbonaceous composition: An increasing from 15 to 40% is observed as compared to a plane capacitor, it can be twice with a 100 wt% of CNTs content. But, the impregnation of the insulating material in the surface roughness remains the key point of the realization of the hybrid capacitor. The roughness accessibility is a major property to optimize in order to improve the impregnation of the insulating material to increase the electrical capacitance

World-Wide Web scaling exponent from Simon's 1955 model

Recently, statistical properties of the World-Wide Web have attracted considerable attention when self-similar regimes have been observed in the scaling of its link structure. Here we recall a classical model for general scaling phenomena and argue that it offers an explanation for the World-Wide Web's scaling exponent when combined with a recent measurement of internet growth.Comment: 1 page RevTeX, no figure

Finite-time fluctuations in the degree statistics of growing networks

This paper presents a comprehensive analysis of the degree statistics in models for growing networks where new nodes enter one at a time and attach to one earlier node according to a stochastic rule. The models with uniform attachment, linear attachment (the Barab\'asi-Albert model), and generalized preferential attachment with initial attractiveness are successively considered. The main emphasis is on finite-size (i.e., finite-time) effects, which are shown to exhibit different behaviors in three regimes of the size-degree plane: stationary, finite-size scaling, large deviations.Comment: 33 pages, 7 figures, 1 tabl

Statistical ensemble of scale-free random graphs

A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is characterized by two global parameters, the fractal and the spectral dimensions, which are explicitly calculated. It is discussed in detail how the geometry of the graphs varies when the weights of the nodes are modified. The stability of the scale-free regime is also considered: when it breaks down, either a scale is spontaneously generated or else, a "singular" node appears and the graphs become crumpled. A new computer algorithm to generate these random graphs is proposed. Possible generalizations are also discussed. In particular, more general ensembles are defined along the same lines and the computer algorithm is extended to arbitrary (degenerate) scale-free random graphs.Comment: 10 pages, 6 eps figures, 2-column revtex format, minor correction

Impact of Node Ablation on the Morphogenesis of the Body Axis and the Lateral Asymmetry of the Mouse Embryo during Early Organogenesis

AbstractThe node of the mouse gastrula is the major source of the progenitor cells of the notochord, the floor plate, and the gut endoderm. The node may also play a morphogenetic role since it can induce a partial body axis following heterotopic transplantation. The impact of losing these progenitor cells and the morphogenetic activity on the development of the body axes was studied by the ablation of the node at late gastrulation. In the ablated embryo, an apparently intact anterior–posterior body axis with morphologically normal head folds, neural tube, and primitive streak developed during early organogenesis. Cell fate analysis revealed that the loss of the node elicits de novo recruitment of neural ectoderm and somitic mesoderm from the surrounding germ-layer tissues. This leads to the restoration of the neural tube and the paraxial mesoderm. However, the body axis of the embryo was foreshortened and somite formation was retarded. Histological and gene expression studies reveal that in most of the node-ablated embryos, the notochord in the trunk was either absent or interrupted, and the floor plate was absent in the ventral region of the reconstituted neural tube. The loss of the node did not affect the differentiation of the gut endoderm or the formation of the mid- and hindgut. In the node-ablated embryo, expression of the Pitx2 gene in the lateral plate mesoderm was no longer restricted to the left side but was found on both sides of the body or was completely absent from the lateral plate mesoderm. Therefore, the loss of the node results in the failure to delineate the laterality of the body axis. The node and its derivatives therefore play a critical role in the patterning of the ventral neural tube and lateral body axis but not of the anterior–posterior axis during early organogenesis

Molecular epidemiology of Streptococcus uberis clinical mastitis in dairy herds: strain heterogeneity and transmission

Multi Locus Sequence Typing was successfully completed on 494 isolates of S. uberis from clinical mastitis cases in a study of 52 commercial dairy herds over a 12 month period. In total, 195 sequence types (STs) were identified. S. uberis mastitis cases occurring in different cows within the same herd and attributed to a common ST were classified as 'potential transmission events' (PTE). Clinical cases attributed to 35 of the 195 STs identified in this study were classified PTE. PTE were identified in 63% of herds. PTE associated cases, which include the first recorded occurrence of that ST in that herd (Index case) and all persistent infections with that PTE ST represented 40% of all the clinical mastitis cases and occurred in 63% of herds. PTE associated cases accounted for over 50% of all S. uberis clinical mastitis cases in 33% of herds. Nine sequence types (ST 5, 6, 20, 22, 24, 35, 233, 361, and 512), eight of which grouped within a clonal complex (sharing at least four alleles), were statistically overrepresented (OVR STs). The findings indicate that 38% of all clinical mastitis cases and 63% of the potential transmission events attributed to S. uberis in dairy herds may be caused by the nine most prevalent strains. The findings suggest that to a small subset of sequence types are disproportionally important in the epidemiology of S. uberis mastitis in the UK with cow to cow transmission of S. uberis potentially occurring in the majority of UK herds and may be the most important route of infection in many herds

The structure of flame filaments in chaotic flows

The structure of flame filaments resulting from chaotic mixing within a combustion reaction is considered. The transverse profile of the filaments is investigated numerically and analytically based on a one-dimensional model that represents the effect of stirring as a convergent flow. The dependence of the steady solutions on the Damkohler number and Lewis number is treated in detail. It is found that, below a critical Damkohler number Da(crit), the flame is quenched by the flow. The quenching transition appears as a result of a saddle-node bifurcation where the stable steady filament solution collides with an unstable one. The shape of the steady solutions for the concentration and temperature profiles changes with the Lewis number and the value of Da(crit) increases monotonically with the Lewis number. Properties of the solutions are studied analytically in the limit of large Damkohler number and for small and large Lewis number.Comment: 17 pages, 13 figures, to be published in Physica

Generic scale of the "scale-free" growing networks

We show that the connectivity distributions $P(k,t)$ of scale-free growing networks ($t$ is the network size) have the generic scale -- the cut-off at $k_{cut} \sim t^\beta$. The scaling exponent $\beta$ is related to the exponent $\gamma$ of the connectivity distribution, $\beta=1/(\gamma-1)$. We propose the simplest model of scale-free growing networks and obtain the exact form of its connectivity distribution for any size of the network. We demonstrate that the trace of the initial conditions -- a hump at $k_h \sim k_{cut} \sim t^\beta$ -- may be found for any network size. We also show that there exists a natural boundary for the observation of the scale-free networks and explain why so few scale-free networks are observed in Nature.Comment: 4 pages revtex, 3 figure

Growing dynamics of Internet providers

In this paper we present a model for the growth and evolution of Internet providers. The model reproduces the data observed for the Internet connection as probed by tracing routes from different computers. This problem represents a paramount case of study for growth processes in general, but can also help in the understanding the properties of the Internet. Our main result is that this network can be reproduced by a self-organized interaction between users and providers that can rearrange in time. This model can then be considered as a prototype model for the class of phenomena of aggregation processes in social networks