1,820 research outputs found
Giant strongly connected component of directed networks
We describe how to calculate the sizes of all giant connected components of a
directed graph, including the {\em strongly} connected one. Just to the class
of directed networks, in particular, belongs the World Wide Web. The results
are obtained for graphs with statistically uncorrelated vertices and an
arbitrary joint in,out-degree distribution . We show that if
does not factorize, the relative size of the giant strongly
connected component deviates from the product of the relative sizes of the
giant in- and out-components. The calculations of the relative sizes of all the
giant components are demonstrated using the simplest examples. We explain that
the giant strongly connected component may be less resilient to random damage
than the giant weakly connected one.Comment: 4 pages revtex, 4 figure
A novel configuration model for random graphs with given degree sequence
Recently, random graphs in which vertices are characterized by hidden
variables controlling the establishment of edges between pairs of vertices have
attracted much attention. Here, we present a specific realization of a class of
random network models in which the connection probability between two vertices
(i,j) is a specific function of degrees ki and kj. In the framework of the
configuration model of random graphs, we find analytical expressions for the
degree correlation and clustering as a function of the variance of the desired
degree distribution. The expressions obtained are checked by means of numerical
simulations. Possible applications of our model are discussed.Comment: 7 pages, 3 figure
Laplacian spectra of complex networks and random walks on them: Are scale-free architectures really important?
We study the Laplacian operator of an uncorrelated random network and, as an
application, consider hopping processes (diffusion, random walks, signal
propagation, etc.) on networks. We develop a strict approach to these problems.
We derive an exact closed set of integral equations, which provide the averages
of the Laplacian operator's resolvent. This enables us to describe the
propagation of a signal and random walks on the network. We show that the
determining parameter in this problem is the minimum degree of vertices
in the network and that the high-degree part of the degree distribution is not
that essential. The position of the lower edge of the Laplacian spectrum
appears to be the same as in the regular Bethe lattice with the
coordination number . Namely, if , and
if . In both these cases the density of eigenvalues
as , but the limiting behaviors near
are very different. In terms of a distance from a starting vertex,
the hopping propagator is a steady moving Gaussian, broadening with time. This
picture qualitatively coincides with that for a regular Bethe lattice. Our
analytical results include the spectral density near
and the long-time asymptotics of the autocorrelator and the
propagator.Comment: 25 pages, 4 figure
Exact Solution for the Time Evolution of Network Rewiring Models
We consider the rewiring of a bipartite graph using a mixture of random and
preferential attachment. The full mean field equations for the degree
distribution and its generating function are given. The exact solution of these
equations for all finite parameter values at any time is found in terms of
standard functions. It is demonstrated that these solutions are an excellent
fit to numerical simulations of the model. We discuss the relationship between
our model and several others in the literature including examples of Urn,
Backgammon, and Balls-in-Boxes models, the Watts and Strogatz rewiring problem
and some models of zero range processes. Our model is also equivalent to those
used in various applications including cultural transmission, family name and
gene frequencies, glasses, and wealth distributions. Finally some Voter models
and an example of a Minority game also show features described by our model.Comment: This version contains a few footnotes not in published Phys.Rev.E
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A weighted configuration model and inhomogeneous epidemics
A random graph model with prescribed degree distribution and degree dependent
edge weights is introduced. Each vertex is independently equipped with a random
number of half-edges and each half-edge is assigned an integer valued weight
according to a distribution that is allowed to depend on the degree of its
vertex. Half-edges with the same weight are then paired randomly to create
edges. An expression for the threshold for the appearance of a giant component
in the resulting graph is derived using results on multi-type branching
processes. The same technique also gives an expression for the basic
reproduction number for an epidemic on the graph where the probability that a
certain edge is used for transmission is a function of the edge weight. It is
demonstrated that, if vertices with large degree tend to have large (small)
weights on their edges and if the transmission probability increases with the
edge weight, then it is easier (harder) for the epidemic to take off compared
to a randomized epidemic with the same degree and weight distribution. A recipe
for calculating the probability of a large outbreak in the epidemic and the
size of such an outbreak is also given. Finally, the model is fitted to three
empirical weighted networks of importance for the spread of contagious diseases
and it is shown that can be substantially over- or underestimated if the
correlation between degree and weight is not taken into account
Ising Model on Networks with an Arbitrary Distribution of Connections
We find the exact critical temperature of the nearest-neighbor
ferromagnetic Ising model on an `equilibrium' random graph with an arbitrary
degree distribution . We observe an anomalous behavior of the
magnetization, magnetic susceptibility and specific heat, when is
fat-tailed, or, loosely speaking, when the fourth moment of the distribution
diverges in infinite networks. When the second moment becomes divergent,
approaches infinity, the phase transition is of infinite order, and size effect
is anomalously strong.Comment: 5 page
Quantitative Proteomic Profiling of Small Molecule Treated Mesenchymal Stem Cells Using Chemical Probes.
The differentiation of human adipose derived stem cells toward a neural phenotype by small molecules has been a vogue topic in the last decade. The characterization of the produced cells has been explored on a broad scale, examining morphological and specific surface protein markers; however, the lack of insight into the expression of functional proteins and their interactive partners is required to further understand the extent of the process. The phenotypic characterization by proteomic profiling allows for a substantial in-depth analysis of the molecular machinery induced and directing the cellular changes through the process. Herein we describe the temporal analysis and quantitative profiling of neural differentiating human adipose-derived stem cells after sub-proteome enrichment using a bisindolylmaleimide chemical probe. The results show that proteins enriched by the Bis-probe were identified reproducibly with 133, 118, 126 and 89 proteins identified at timepoints 0, 1, 6 and 12, respectively. Each temporal timepoint presented several shared and unique proteins relative to neural differentiation and their interactivity. The major protein classes enriched and quantified were enzymes, structural and ribosomal proteins that are integral to differentiation pathways. There were 42 uniquely identified enzymes identified in the cells, many acting as hubs in the networks with several interactions across the network modulating key biological pathways. From the cohort, it was found by gene ontology analysis that 18 enzymes had direct involvement with neurogenic differentiation
Network robustness and fragility: Percolation on random graphs
Recent work on the internet, social networks, and the power grid has
addressed the resilience of these networks to either random or targeted
deletion of network nodes. Such deletions include, for example, the failure of
internet routers or power transmission lines. Percolation models on random
graphs provide a simple representation of this process, but have typically been
limited to graphs with Poisson degree distribution at their vertices. Such
graphs are quite unlike real world networks, which often possess power-law or
other highly skewed degree distributions. In this paper we study percolation on
graphs with completely general degree distribution, giving exact solutions for
a variety of cases, including site percolation, bond percolation, and models in
which occupation probabilities depend on vertex degree. We discuss the
application of our theory to the understanding of network resilience.Comment: 4 pages, 2 figure
Diluted antiferromagnet in a ferromagnetic enviroment
The question of robustness of a network under random ``attacks'' is treated
in the framework of critical phenomena. The persistence of spontaneous
magnetization of a ferromagnetic system to the random inclusion of
antiferromagnetic interactions is investigated. After examing the static
properties of the quenched version (in respect to the random antiferromagnetic
interactions) of the model, the persistence of the magnetization is analysed
also in the annealed approximation, and the difference in the results are
discussed
Evaluating the use of Apo-neocarzinostatin as a cell penetrating protein.
Protein-ligand complex neocarzinostatin (NCS) is a small, thermostable protein-ligand complex that is able to deliver its ligand cargo into live mammalian cells where it induces DNA damage. Apo-NCS is able to functionally display complementarity determining regions loops, and has been hypothesised to act as a cell-penetrating protein, which would make it an ideal scaffold for cell targeting, and subsequent intracellular delivery of small-molecule drugs. In order to evaluate apo-NCS as a cell penetrating protein, we have evaluated the efficiency of its internalisation into live HeLa cells using matrix-assisted laser-desorption ionization-time-of-flight mass spectrometry and fluorescence microscopy. Following incubation of cells with apo-NCS, we observed no evidence of internalisation
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