Optimization of Network Robustness to Waves of Targeted and Random Attack

We study the robustness of complex networks to multiple waves of simultaneous (i) targeted attacks in which the highest degree nodes are removed and (ii) random attacks (or failures) in which fractions $p_t$ and $p_r$ respectively of the nodes are removed until the network collapses. We find that the network design which optimizes network robustness has a bimodal degree distribution, with a fraction $r$ of the nodes having degree k_2= (\kav - 1 +r)/r and the remainder of the nodes having degree $k_1=1$, where \kav is the average degree of all the nodes. We find that the optimal value of $r$ is of the order of $p_t/p_r$ for $p_t/p_r\ll 1$

Resilience of Complex Networks to Random Breakdown

Using Monte Carlo simulations we calculate $f_c$, the fraction of nodes which are randomly removed before global connectivity is lost, for networks with scale-free and bimodal degree distributions. Our results differ with the results predicted by an equation for $f_c$ proposed by Cohen, et al. We discuss the reasons for this disagreement and clarify the domain for which the proposed equation is valid

Individual Insurance: Health Insurers Try to Tap Potential Market Growth

Examines the challenges the current individual health insurance market poses for insurers and consumers, the market's growth potential, market and regulatory conditions across states, and trends in marketing strategies. Considers policy implications

A refined estimate for the topological degree

We sharpen an estimate of Bourgain, Brezis, and Nguyen for the topological degree of continuous maps from a sphere $\mathbb{S}^d$ into itself in the case $d \ge 2$. This provides the answer for $d \ge 2$ to a question raised by Brezis. The problem is still open for $d=1$

Morbidity after surgical management of cervical cancer in low and middle income countries: A systematic review and meta-analysis

Objective: To investigate morbidity for patients after the primary surgical management of cervical cancer in low and middle-income countries (LMIC). Methods: The Pubmed, Cochrane, the Cochrane Central Register of Controlled Trials, Embase, LILACS and CINAHL were searched for published studies from 1st Jan 2000 to 30th June 2017 reporting outcomes of surgical management of cervical cancer in LMIC. Randomeffects meta-analytical models were used to calculate pooled estimates of surgical complications including blood transfusions, ureteric, bladder, bowel, vascular and nerve injury, fistulae and thromboembolic events. Secondary outcomes included five-year progression free (PFS) and overall survival (OS). Findings: Data were available for 46 studies, including 10,847 patients from 11 middle income countries. Pooled estimates were: blood transfusion 29% (95%CI 0.19–0.41, P = 0.00, I 2 = 97.81), nerve injury 1% (95%CI 0.00–0.03, I 2 77.80, P = 0.00), bowel injury, 0.5% (95%CI 0.01–0.01, I 2 = 0.00, P = 0.77), bladder injury 1% (95%CI 0.01–0.02, P = 0.10, I 2 = 32.2), ureteric injury 1% (95%CI 0.01–0.01, I 2 0.00, P = 0.64), vascular injury 2% (95% CI 0.01– 0.03, I 2 60.22, P = 0.00), fistula 2% (95%CI 0.01–0.03, I 2 = 77.32, P = 0.00,), pulmonary embolism 0.4% (95%CI 0.00–0.01, I 2 26.69, P = 0.25), and infection 8% (95%CI 0.04–0.12, 2 95.72, P = 0.00). 5-year PFS was 83% for laparotomy, 84% for laparoscopy and OS was 85% for laparotomy cases and 80% for laparoscopy. Conclusion: This is the first systematic review and meta-analysis of surgical morbidity in cervical cancer in LMIC, which highlights the limitations of the current data and provides a benchmark for future health services research and policy implementation

Losing Weight: A KECK Spectroscopic Survey of the Massive Cluster of Galaxies RX J1347-1145

We present a sample of 47 spectroscopically confirmed members of RX J1347-1145, the most luminous X-ray cluster of galaxies discovered to date. With two exceptions, all the galaxies in this sample have red B-R colors and red spectral indices, with spectra similar to old local ellipticals. Using all 47 cluster members, we derive a mean redshift of 0.4509\pm 0.003, and a velocity dispersion of 910\pm130 km/sec, which corresponds to a virial mass of 4.4 x 10^{14} h^{-1} Solar masses with an harmonic radius of 380 h^{-1} kpc. The derived total dynamical mass is marginally consistent with that deduced from the cluster's X-ray emission based on the analysis of ROSAT/ASCA images (Schindler et al. 1997), but not consistent with the more recent X-ray analyses of Allen (2000), Ettori, Allen & Fabian (2001) and Allen, Schmidt & Fabian (2002). Furthermore, the dynamical mass is significantly smaller than that derived from weak lensing (Fischer & Tyson 1997) and from strong lensing (Sahu et al. 1998). We propose that these various discrepant mass estimates may be understood if RX J1347-1145 is the product of two clusters caught in the act of merging in a direction perpendicular to the line of sight, although there is no evidence from the galaxy redshift distribution supporting this hypothesis. Even with this hypothesis, a significant part of the extremely high X-ray luminosity must still arise from non-virialized, presumably shocked, gas. Finally, we report the serendipitous discovery of a lensed background galaxy at z=4.083 which will put strong constraints on the lensing mass determination once its counter-image is securely identified.Comment: Minor changes to conform to version accepted by Ap

Graph Partitioning Induced Phase Transitions

We study the percolation properties of graph partitioning on random regular graphs with N vertices of degree $k$. Optimal graph partitioning is directly related to optimal attack and immunization of complex networks. We find that for any partitioning process (even if non-optimal) that partitions the graph into equal sized connected components (clusters), the system undergoes a percolation phase transition at $f=f_c=1-2/k$ where $f$ is the fraction of edges removed to partition the graph. For optimal partitioning, at the percolation threshold, we find $S \sim N^{0.4}$ where $S$ is the size of the clusters and $\ell\sim N^{0.25}$ where $\ell$ is their diameter. Additionally, we find that $S$ undergoes multiple non-percolation transitions for $f<f_c$

Percolation theory applied to measures of fragmentation in social networks

We apply percolation theory to a recently proposed measure of fragmentation $F$ for social networks. The measure $F$ is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after removing a fraction $q$ of nodes and the total number of pairs in the original fully connected network. We compare $F$ with the traditional measure used in percolation theory, $P_{\infty}$, the fraction of nodes in the largest cluster relative to the total number of nodes. Using both analytical and numerical methods from percolation, we study Erd\H{o}s-R\'{e}nyi (ER) and scale-free (SF) networks under various types of node removal strategies. The removal strategies are: random removal, high degree removal and high betweenness centrality removal. We find that for a network obtained after removal (all strategies) of a fraction $q$ of nodes above percolation threshold, $P_{\infty}\approx (1-F)^{1/2}$. For fixed $P_{\infty}$ and close to percolation threshold ($q=q_c$), we show that $1-F$ better reflects the actual fragmentation. Close to $q_c$, for a given $P_{\infty}$, $1-F$ has a broad distribution and it is thus possible to improve the fragmentation of the network. We also study and compare the fragmentation measure $F$ and the percolation measure $P_{\infty}$ for a real social network of workplaces linked by the households of the employees and find similar results.Comment: submitted to PR

RX J0911+05: A Massive Cluster Lens at z=0.769

We report the detection of a massive high-redshift cluster of galaxies near the quadruple quasar RX J0911+05, using the LRIS instrument on the Keck-II telescope. The cluster is found to have a mean redshift of =0.7689+/-0.002 and a velocity dispersion of sigma=836{+180-200} km/s, based on redshift measurements for 24 member galaxies. This massive high-redshift cluster is the origin of the unusually large external shear required by lensing models of the quadruple quasar system. We predict the expected time delay depending on the exact contribution of the cluster. A measurement of the time delay and further deep lensing and X-ray observations will unravel useful properties of this serendipitously discovered high-redshift cluster, and may put interesting cosmological constraints on H0.Comment: Submitted to ApJL, 7 pages, 5 figure