Shortest path discovery of complex networks

In this paper we present an analytic study of sampled networks in the case of some important shortest-path sampling models. We present analytic formulas for the probability of edge discovery in the case of an evolving and a static network model. We also show that the number of discovered edges in a finite network scales much slower than predicted by earlier mean field models. Finally, we calculate the degree distribution of sampled networks, and we demonstrate that they are analogous to a destructed network obtained by randomly removing edges from the original network.Comment: 10 pages, 4 figure

Dromion solutions for an electron acoustic wave and its application to space observations

The nonlinear evolution of an electron acoustic wave is shown to obey the Davey-Stewartson I equation which admits so called dromion solutions. The importance of these two dimensional localized solutions for recent satellite observations of wave structures in the day side polar cap regions is discussed and the parameter regimes for their existence is delineated

Necessary conditions for the generation of acoustic solitons in magnetospheric and space plasmas with hot ions

International audienceNecessary conditions are discussed for the possible generation of large solitary acoustic modes in plasmas with one or more ion species which are hotter than some or all of the electron species. The analysis is based on a fluid dynamic approach. It is found that in most of these configurations the existence ranges for the solitary wave velocities are very narrow and close to one of the thermal velocities. In the latter situation, linear Landau damping may prevent the generation of nonlinear structures. The analysis indicates that both inertial and thermal effects for the ions need to be kept in the description, thus rendering an analytical investigation much more intricate

Dromion solutions for nonlinear electron acoustic waves in space plasmas

International audienceRecent high resolution measurements of POLAR and FAST satellites have revealed two-dimensional coherent structures in the polar cap boundary layer (PCBL) region. Since the ion temperature is often observed to be greater than the electron temperature in this region, electron acoustic waves can exist as a normal mode of the plasma system. It is shown that the nonlinear evolution of such waves can be modelled by the coupled Davey-Stewartson I equations. These equations, which are a generalization of the nonlinear Schrödinger equation to two dimensions, admit exponentially localized solutions called dromions. A detailed parametric characterization of the regions of existence of such solutions is presented in the context of the PCBL region

Dynamic Properties of Charmonium

Nonrelativistic quark models of charmonia are tested by comparison of theoretical charmonium decay constants, form factors, and $\gamma\gamma$ widths with experiment and lattice gauge computations. The importance of relativistic effects, a running coupling, and the correct implementation of bound state effects are demonstrated. We describe how an improved model and computational techniques resolve several outstanding issues in previous nonrelativistic quark models such as the use of `correction' factors in quark model form factors, artificial energy prescriptions in decay constant calculations, and ad hoc phase space modifications. We comment on the small experimental value of $f_{\psi''}$ and the D-wave component of the $J/\psi$. Decay constants and $\gamma\gamma$ widths for bottomonium are also presented.Comment: 22 pages, 22 ps figures (table entries corrected, text modified

Seizure evoked regulation of LIM-HD genes and co-factors in the postnatal and adult hippocampus

The LIM-homeodomain (LIM-HD) family of transcription factors is well known for its functions during several developmental processes including cell fate specification, cell migration and axon guidance, and its members play fundamental roles in hippocampal development. The hippocampus is a structure that displays striking activity dependent plasticity. We examined whether LIM-HD genes and their co-factors are regulated during kainic acid induced seizure in the adult rat hippocampus as well as in early postnatal rats, when the hippocampal circuitry is not fully developed. We report a distinct and field-specific regulation of LIM-HD genes Lhx1, Lhx2, and Lhx9, LIM-only gene Lmo4, and cofactor Clim1a in the adult hippocampus after seizure induction. In contrast none of these genes displayed altered levels upon induction of seizure in postnatal animals. Our results provide evidence of temporal and spatial seizure mediated regulation of LIM-HD family members and suggest that LIM-HD gene function may be involved in activity dependent plasticity in the adult hippocampus

Study of nonlinear ion- and electron-acoustic waves in multi-component space plasmas

Large amplitude ion-acoustic and electron-acoustic waves in an unmagnetized multi-component plasma system consisting of cold background electrons and ions, a hot electron beam and a hot ion beam are studied using Sagdeev pseudo-potential technique. Three types of solitary waves, namely, slow ion-acoustic, ion-acoustic and electron-acoustic solitons are found provided the Mach numbers exceed the critical values. The slow ion-acoustic solitons have the smallest critical Mach numbers, whereas the electron-acoustic solitons have the largest critical Mach numbers. For the plasma parameters considered here, both type of ion-acoustic solitons have positive potential whereas the electron-acoustic solitons can have either positive or negative potential depending on the fractional number density of the cold electrons relative to that of the ions (or total electrons) number density. For a fixed Mach number, increases in the beam speeds of either hot electrons or hot ions can lead to reduction in the amplitudes of the ion-and electron-acoustic solitons. However, the presence of hot electron and hot ion beams have no effect on the amplitudes of slow ion-acoustic modes. Possible application of this model to the electrostatic solitary waves (ESWs) observed in the plasma sheet boundary layer is discussed

Graph Annotations in Modeling Complex Network Topologies

The coarsest approximation of the structure of a complex network, such as the Internet, is a simple undirected unweighted graph. This approximation, however, loses too much detail. In reality, objects represented by vertices and edges in such a graph possess some non-trivial internal structure that varies across and differentiates among distinct types of links or nodes. In this work, we abstract such additional information as network annotations. We introduce a network topology modeling framework that treats annotations as an extended correlation profile of a network. Assuming we have this profile measured for a given network, we present an algorithm to rescale it in order to construct networks of varying size that still reproduce the original measured annotation profile. Using this methodology, we accurately capture the network properties essential for realistic simulations of network applications and protocols, or any other simulations involving complex network topologies, including modeling and simulation of network evolution. We apply our approach to the Autonomous System (AS) topology of the Internet annotated with business relationships between ASs. This topology captures the large-scale structure of the Internet. In depth understanding of this structure and tools to model it are cornerstones of research on future Internet architectures and designs. We find that our techniques are able to accurately capture the structure of annotation correlations within this topology, thus reproducing a number of its important properties in synthetically-generated random graphs

Bias reduction in traceroute sampling: towards a more accurate map of the Internet

Traceroute sampling is an important technique in exploring the internet router graph and the autonomous system graph. Although it is one of the primary techniques used in calculating statistics about the internet, it can introduce bias that corrupts these estimates. This paper reports on a theoretical and experimental investigation of a new technique to reduce the bias of traceroute sampling when estimating the degree distribution. We develop a new estimator for the degree of a node in a traceroute-sampled graph; validate the estimator theoretically in Erdos-Renyi graphs and, through computer experiments, for a wider range of graphs; and apply it to produce a new picture of the degree distribution of the autonomous system graph.Comment: 12 pages, 3 figure