Growing Scale-Free Networks with Small World Behavior

In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases logartihmically as in random networks, the clustering coefficient assumes a large value independent of system size. We derive expressions for the clustering coefficient in two limiting cases: random (C ~ (ln N)^2 / N) and highly clustered (C = 5/6) scale-free networks.Comment: 4 pages, 4 figure

Path finding strategies in scale-free networks

We numerically investigate the scale-free network model of Barab{\'a}si and Albert [A. L. Barab{\'a}si and R. Albert, Science {\bf 286}, 509 (1999)] through the use of various path finding strategies. In real networks, global network information is not accessible to each vertex, and the actual path connecting two vertices can sometimes be much longer than the shortest one. A generalized diameter depending on the actual path finding strategy is introduced, and a simple strategy, which utilizes only local information on the connectivity, is suggested and shown to yield small-world behavior: the diameter $D$ of the network increases logarithmically with the network size $N$, the same as is found with global strategy. If paths are sought at random, $D \sim N^{0.5}$ is found.Comment: 4 pages, final for

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

Clinical effect of IRT-5 probiotics on immune modulation of autoimmunity or alloimmunity in the eye

Background: Although the relation of the gut microbiota to a development of autoimmune and inflammatory diseases has been investigated in various animal models, there are limited studies that evaluate the effect of probiotics in the autoimmune eye disease. Therefore, we aimed to investigate the effect of IRT-5 probiotics consisting of Lactobacillus casei, Lactobacillus acidophilus, Lactobacillus reuteri, Bifidobacterium bifidum, and Streptococcus thermophilus on the autoimmunity of uveitis and dry eye and alloimmunity of corneal transplantation. Methods: Experimental autoimmune uveitis was induced by subcutaneous immunization with interphotoreceptor-binding protein and intraperitoneal injection of pertussis toxin in C57BL/6 (B6) mice. For an autoimmune dry eye model, 12-weeks-old NOD.B10.H2b mice were used. Donor cornea of B6 mice was transplanted into BALB/C mice. IRT-5 probiotics or phosphate buffered saline (PBS) were administered for three weeks immediately after induction of uveitis or transplantation. The inflammation score of the retinal tissues, dry eye manifestations (corneal staining and tear secretion), and graft survival were measured in each model. The changes of T cells were evaluated in drainage lymph nodes using fluorescence-activated cell sorting. Results: Retinal histology score in IRT-5 group of uveitis was lower than that in PBS group (p = 0.045). Ocular staining score was lower (p < 0.0001) and tear secretion was higher (p < 0.0001) in the IRT-5 group of NOD.B10.H2b mice than that in the PBS group. However, the graft survival in the IRT-5 group was not different from those of PBS group. The percentage of regulatory T cells was increased in the IRT-5-treated dry eye models (p = 0.032). The percentage of CD8+IL-17hi (p = 0.027) and CD8+ interferon gamma (IFN��)hi cells (p = 0.022) were significantly decreased in the IRT-5-treated uveitis models and the percentage of CD8+IFN��hi cells was markedly reduced (p = 0.036) in IRT-5-treated dry eye model. Conclusion: Our results suggest that administration of IRT-5 probiotics may modulate clinical manifestations of autoimmunity in the eye, but not on alloimmunity of corneal transplantation. ? 2017 by the authors.112Nsciescopu

Infinite-Order Percolation and Giant Fluctuations in a Protein Interaction Network

We investigate a model protein interaction network whose links represent interactions between individual proteins. This network evolves by the functional duplication of proteins, supplemented by random link addition to account for mutations. When link addition is dominant, an infinite-order percolation transition arises as a function of the addition rate. In the opposite limit of high duplication rate, the network exhibits giant structural fluctuations in different realizations. For biologically-relevant growth rates, the node degree distribution has an algebraic tail with a peculiar rate dependence for the associated exponent.Comment: 4 pages, 2 figures, 2 column revtex format, to be submitted to PRL 1; reference added and minor rewording of the first paragraph; Title change and major reorganization (but no result changes) in response to referee comments; to be published in PR

A Geometric Fractal Growth Model for Scale Free Networks

We introduce a deterministic model for scale-free networks, whose degree distribution follows a power-law with the exponent $\gamma$. At each time step, each vertex generates its offsprings, whose number is proportional to the degree of that vertex with proportionality constant m-1 (m>1). We consider the two cases: first, each offspring is connected to its parent vertex only, forming a tree structure, and secondly, it is connected to both its parent and grandparent vertices, forming a loop structure. We find that both models exhibit power-law behaviors in their degree distributions with the exponent $\gamma=1+\ln (2m-1)/\ln m$. Thus, by tuning m, the degree exponent can be adjusted in the range, $2 <\gamma < 3$. We also solve analytically a mean shortest-path distance d between two vertices for the tree structure, showing the small-world behavior, that is, $d\sim \ln N/\ln {\bar k}$, where N is system size, and $\bar k$ is the mean degree. Finally, we consider the case that the number of offsprings is the same for all vertices, and find that the degree distribution exhibits an exponential-decay behavior

Edge overload breakdown in evolving networks

We investigate growing networks based on Barabasi and Albert's algorithm for generating scale-free networks, but with edges sensitive to overload breakdown. the load is defined through edge betweenness centrality. We focus on the situation where the average number of connections per vertex is, as the number of vertices, linearly increasing in time. After an initial stage of growth, the network undergoes avalanching breakdowns to a fragmented state from which it never recovers. This breakdown is much less violent if the growth is by random rather than preferential attachment (as defines the Barabasi and Albert model). We briefly discuss the case where the average number of connections per vertex is constant. In this case no breakdown avalanches occur. Implications to the growth of real-world communication networks are discussed.Comment: To appear in Phys. Rev.

The spread of epidemic disease on networks

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are non-uniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.Comment: 12 pages, 3 figure