Kleinberg Navigation in Fractal Small World Networks

We study the Kleinberg problem of navigation in Small World networks when the underlying lattice is a fractal consisting of N>>1 nodes. Our extensive numerical simulations confirm the prediction that most efficient navigation is attained when the length r of long-range links is taken from the distribution P(r)~r^{-alpha}, where alpha=d_f, the fractal dimension of the underlying lattice. We find finite-size corrections to the exponent alpha, proportional to 1/(ln N)^2

Designer Nets from Local Strategies

We propose a local strategy for constructing scale-free networks of arbitrary degree distributions, based on the redirection method of Krapivsky and Redner [Phys. Rev. E 63, 066123 (2001)]. Our method includes a set of external parameters that can be tuned at will to match detailed behavior at small degree k, in addition to the scale-free power-law tail signature at large k. The choice of parameters determines other network characteristics, such as the degree of clustering. The method is local in that addition of a new node requires knowledge of only the immediate environs of the (randomly selected) node to which it is attached. (Global strategies require information on finite fractions of the growing net.

Percolation in Hierarchical Scale-Free Nets

We study the percolation phase transition in hierarchical scale-free nets. Depending on the method of construction, the nets can be fractal or small-world (the diameter grows either algebraically or logarithmically with the net size), assortative or disassortative (a measure of the tendency of like-degree nodes to be connected to one another), or possess various degrees of clustering. The percolation phase transition can be analyzed exactly in all these cases, due to the self-similar structure of the hierarchical nets. We find different types of criticality, illustrating the crucial effect of other structural properties besides the scale-free degree distribution of the nets.Comment: 9 Pages, 11 figures. References added and minor corrections to manuscript. In pres

Efficient Immunization Strategies for Computer Networks and Populations

We present an effective immunization strategy for computer networks and populations with broad and, in particular, scale-free degree distributions. The proposed strategy, acquaintance immunization, calls for the immunization of random acquaintances of random nodes (individuals). The strategy requires no knowledge of the node degrees or any other global knowledge, as do targeted immunization strategies. We study analytically the critical threshold for complete immunization. We also study the strategy with respect to the susceptible-infected-removed epidemiological model. We show that the immunization threshold is dramatically reduced with the suggested strategy, for all studied cases.Comment: Revtex, 5 pages, 4 ps fig

Interactome comparison of human embryonic stem cell lines with the inner cell mass and trophectoderm

Networks of interacting co-regulated genes distinguish the inner cell mass (ICM) from the differentiated trophectoderm (TE) in the preimplantation blastocyst, in a species specific manner. In mouse the ground state pluripotency of the ICM appears to be maintained in murine embryonic stem cells (ESCs) derived from the ICM. This is not the case for human ESCs. In order to gain insight into this phenomenon, we have used quantitative network analysis to identify how similar human (h)ESCs are to the human ICM. Using the hESC lines MAN1, HUES3 and HUES7 we have shown that all have only a limited overlap with ICM specific gene expression, but that this overlap is enriched for network properties that correspond to key aspects of function including transcription factor activity and the hierarchy of network modules. These analyses provide an important framework which highlights the developmental origins of hESCs

Percolation Critical Exponents in Scale-Free Networks

We study the behavior of scale-free networks, having connectivity distribution P(k) k^-a, close to the percolation threshold. We show that for networks with 3<a<4, known to undergo a transition at a finite threshold of dilution, the critical exponents are different than the expected mean-field values of regular percolation in infinite dimensions. Networks with 2<a<3 possess only a percolative phase. Nevertheless, we show that in this case percolation critical exponents are well defined, near the limit of extreme dilution (where all sites are removed), and that also then the exponents bear a strong a-dependence. The regular mean-field values are recovered only for a>4.Comment: Latex, 4 page

Fractal and Transfractal Recursive Scale-Free Nets

We explore the concepts of self-similarity, dimensionality, and (multi)scaling in a new family of recursive scale-free nets that yield themselves to exact analysis through renormalization techniques. All nets in this family are self-similar and some are fractals - possessing a finite fractal dimension - while others are small world (their diameter grows logarithmically with their size) and are infinite-dimensional. We show how a useful measure of "transfinite" dimension may be defined and applied to the small world nets. Concerning multiscaling, we show how first-passage time for diffusion and resistance between hub (the most connected nodes) scale differently than for other nodes. Despite the different scalings, the Einstein relation between diffusion and conductivity holds separately for hubs and nodes. The transfinite exponents of small world nets obey Einstein relations analogous to those in fractal nets.Comment: Includes small revisions and references added as result of readers' feedbac

Androgen receptor as a mediator and biomarker of radioresistance in triple-negative breast cancer.

Increased rates of locoregional recurrence have been observed in triple-negative breast cancer despite chemotherapy and radiation therapy. Thus, approaches that combine therapies for radiosensitization in triple-negative breast cancer are critically needed. We characterized the radiation therapy response of 21 breast cancer cell lines and paired this radiation response data with high-throughput drug screen data to identify androgen receptor as a top target for radiosensitization. Our radiosensitizer screen nominated bicalutamide as the drug most effective in treating radiation therapy-resistant breast cancer cell lines. We subsequently evaluated the expression of androgen receptor in &gt;2100 human breast tumor samples and 51 breast cancer cell lines and found significant heterogeneity in androgen receptor expression with enrichment at the protein and RNA level in triple-negative breast cancer. There was a strong correlation between androgen receptor RNA and protein expression across all breast cancer subtypes (R2 = 0.72, p &lt; 0.01). In patients with triple-negative breast cancer, expression of androgen receptor above the median was associated with increased risk of locoregional recurrence after radiation therapy (hazard ratio for locoregional recurrence 2.9-3.2)) in two independent data sets, but there was no difference in locoregional recurrence in triple-negative breast cancer patients not treated with radiation therapy when stratified by androgen receptor expression. In multivariable analysis, androgen receptor expression was most significantly associated with worse local recurrence-free survival after radiation therapy (hazard ratio of 3.58) suggesting that androgen receptor expression may be a biomarker of radiation response in triple-negative breast cancer. Inhibition of androgen receptor with MDV3100 (enzalutamide) induced radiation sensitivity (enhancement ratios of 1.22-1.60) in androgen receptor-positive triple-negative breast cancer lines, but did not affect androgen receptor-negative triple-negative breast cancer or estrogen-receptor-positive, androgen receptor-negative breast cancer cell lines. androgen receptor inhibition with MDV3100 significantly radiosensitized triple-negative breast cancer xenografts in mouse models and markedly delayed tumor doubling/tripling time and tumor weight. Radiosensitization was at least partially dependent on impaired dsDNA break repair mediated by DNA protein kinase catalytic subunit. Our results implicate androgen receptor as a mediator of radioresistance in breast cancer and identify androgen receptor inhibition as a potentially effective strategy for the treatment of androgen receptor-positive radioresistant tumors