Modeling Cascading Failures in the North American Power Grid

The North American power grid is one of the most complex technological networks, and its interconnectivity allows both for long-distance power transmission and for the propagation of disturbances. We model the power grid using its actual topology and plausible assumptions about the load and overload of transmission substations. Our results indicate that the loss of a single substation can lead to a 25% loss of transmission efficiency by triggering an overload cascade in the network. We systematically study the damage inflicted by the loss of single nodes, and find three universal behaviors, suggesting that 40% of the transmission substations lead to cascading failures when disrupted. While the loss of a single node can inflict substantial damage, subsequent removals have only incremental effects, in agreement with the topological resilience to less than 1% node loss.Comment: 6 pages, 6 figure

A model for cascading failures in complex networks

Large but rare cascades triggered by small initial shocks are present in most of the infrastructure networks. Here we present a simple model for cascading failures based on the dynamical redistribution of the flow on the network. We show that the breakdown of a single node is sufficient to collapse the efficiency of the entire system if the node is among the ones with largest load. This is particularly important for real-world networks with an highly hetereogeneous distribution of loads as the Internet and electrical power grids.Comment: 4 pages, 4 figure

How big is too big? Critical Shocks for Systemic Failure Cascades

External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighoring agents. Several critical constellations determine whether this cascade remains finite or reaches the size of the system, i.e. leads to systemic risk. We investigate the critical parameters for such cascades in a simple model, where agents are characterized by an individual threshold \theta_i determining their capacity to handle a load \alpha\theta_i with 1-\alpha being their safety margin. If agents fail, they redistribute their load equally to K neighboring agents in a regular network. For three different threshold distributions P(\theta), we derive analytical results for the size of the cascade, X(t), which is regarded as a measure of systemic risk, and the time when it stops. We focus on two different regimes, (i) EEE, an external extreme event where the size of the shock is of the order of the total capacity of the network, and (ii) RIE, a random internal event where the size of the shock is of the order of the capacity of an agent. We find that even for large extreme events that exceed the capacity of the network finite cascades are still possible, if a power-law threshold distribution is assumed. On the other hand, even small random fluctuations may lead to full cascades if critical conditions are met. Most importantly, we demonstrate that the size of the "big" shock is not the problem, as the systemic risk only varies slightly for changes of 10 to 50 percent of the external shock. Systemic risk depends much more on ingredients such as the network topology, the safety margin and the threshold distribution, which gives hints on how to reduce systemic risk.Comment: 23 pages, 7 Figure

Cathepsin D and epidermal growth factor in human breast cyst fluid.

Cathespin D (Cath D) is a proteolytic enzyme secreted by human breast cancer cells with a growth promoting activity in vitro. In the present study, we measured Cath D and Epidermal Growth Factor/alpha Transforming Growth Factor (EGF/alpha-TGF) concentrations in the breast cyst fluid (BCF) of 43 patients with gross cystic disease of the breast. Both Cath D (median 2.45 pmoles mg-1 protein; range 0-4.84 vs 0.98 pmoles mg-1 protein; range 0-3.11) and EGF/alpha-TGF (28.71 ng mg-1 protein; range 7.05-50.63 vs 10.83 ng mg-1 protein; range 0.06-30.55) levels were higher in BCF of apocrine than flattened cysts (P less than 0.0005 and P less than 0.01, respectively). Premenopausal patients showed higher concentrations of Cath D (P less than 0.05) and EGF/alpha-TGF (P less than 0.05) than postmenopausal patients. A positive correlation was obtained between intracystic concentrations of Cath D and EGF/alpha-TGF (P less than 0.00001). The higher levels of Cath-D and EGF/alpha-TGF found in apocrine cysts could provide an explanation for the increased risk of subsequent breast cancer in women with this type of cyst

Elementary processes governing the evolution of road networks

Urbanisation is a fundamental phenomenon whose quantitative characterisation is still inadequate. We report here the empirical analysis of a unique data set regarding almost 200 years of evolution of the road network in a large area located north of Milan (Italy). We find that urbanisation is characterised by the homogenisation of cell shapes, and by the stability throughout time of high-centrality roads which constitute the backbone of the urban structure, confirming the importance of historical paths. We show quantitatively that the growth of the network is governed by two elementary processes: (i) `densification', corresponding to an increase in the local density of roads around existing urban centres and (ii) `exploration', whereby new roads trigger the spatial evolution of the urbanisation front. The empirical identification of such simple elementary mechanisms suggests the existence of general, simple properties of urbanisation and opens new directions for its modelling and quantitative description.Comment: 10 pages, 6 figure

HIV and STI Prevalence among Female Sex Workers in Côte d'Ivoire: Why Targeted Prevention Programs Should Be Continued and Strengthened

Objective: To assess condom use and prevalence of STIs and HIV among female sex workers (FSWs), as part of a comprehensive monitoring and evaluation plan of a nationwide sex worker prevention project in Côte d’Ivoire. Design and Methods: Cross sectional surveys were conducted among FSWs attending five project clinics in Abidjan and San Pedro (2007), and in Yamoussoukro and Gagnoa (2009). A standardized questionnaire was administered in a face-toface interview, which included questions on socio-demographic characteristics, sexual behaviour and condom use. After the interview, the participants were asked to provide samples for STI and HIV testing. Results: A total of 1110 FSWs participated in the surveys. There were large differences in socio-demographic and behavioural characteristics between FSW coming for the first time as compared to FSW coming on a routine visit. The prevalence of N. gonorrhoeae or C.trachomatis was 9.1%, 11.8 % among first vs. 6.9 % routine attendees (p = 0.004). The overall HIV prevalence was 26.6%, it was lower among first time attendees (17.5 % as compared to 33.9 % for routine attendees, p,0.001). The HIV prevalence among first attendees was also lower than the proportion of HIV positive tests from routine testing and counselling services in the same clinics. Conclusions: The results show a relatively high STI and HIV prevalence among FSWs in different cities in Côte d’Ivoire. In th

Comparative analysis of the vaginal microbiome of pregnant women with either Trichomonas vaginalis or Chlamydia trachomatis

BACKGROUND:Although the significance of the human vaginal microbiome for health and disease is increasingly acknowledged, there is paucity of data on the differences in the composition of the vaginal microbiome upon infection with different sexually transmitted pathogens. METHOD:The composition of the vaginal bacterial community of women with Trichomonas vaginalis (TV, N = 18) was compared to that of women with Chlamydia trachomatis (CT, N = 14), and to that of controls (N = 21) (women negative for TV, CT and bacterial vaginosis). The vaginal bacterial composition was determined using high throughput sequencing with the Ion 16S metagenomics kit of the variable regions 2, 4 and 8 of the bacterial 16S ribosomal RNA gene from the vaginal swab DNA extract of the women. QIIME and R package "Phyloseq" were used to assess the α- and β-diversity and absolute abundance of the 16S rRNA gene per sample in the three groups. Differences in taxa at various levels were determined using the independent T-test. RESULTS:A total of 545 operational taxonomic units (OTUs) were identified in all the three groups of which 488 occurred in all three groups (core OTUs). Bacterial α-diversity, by both Simpson's and Shannon's indices, was significantly higher, (p = 0.056) and (p = 0.001) respectively, among women with either TV or CT than among controls (mean α-diversity TV-infected > CT-infected > Controls). At the genus level, women infected with TV had a significantly (p < 0.01) higher abundance of Parvimonas and Prevotella species compared to both controls and CT-infected women, whereas women infected with CT had a significantly (p < 0.05) higher abundance of Anaerococcus, Collinsella, Corynebacterium and Dialister. CONCLUSION:The vaginal microbiomes of TV and CT-infected women were markedly different from each other and from women without TV and CT. Future studies should determine whether the altered microbiomes are merely markers of disease, or whether they actively contribute to the pathology of the two genital infections

Non-Sexual Transmission of Trichomonas vaginalis in Adolescent Girls Attending School in Ndola, Zambia

OBJECTIVES: To identify risk factors for trichomoniasis among young women in Ndola, Zambia. METHOD: The study was a cross-sectional study among adolescent girls aged 13-16 years in Ndola, Zambia. Study participants were recruited from schools in selected administrative areas that represented the different socio-economic strata in town. Consenting participants were interviewed about their socio-demographic characteristics; sexual behaviour; and hygiene practices. Self-administered vaginal swabs were tested for Trichomonas vaginalis. HSV-2 antibodies were determined on serum to validate the self-reported sexual activity. RESULTS: A total of 460 girls participated in the study. The overall prevalence of trichomoniasis was 27.1%, 33.9% among girls who reported that they had ever had sex and 24.7% among virgins. In multivariate analysis the only statistically significant risk factor for trichomoniasis was inconsistent use of soap. For the virgins, none of the risk factors was significantly associated with trichomoniasis, but the association with use of soap (not always versus always) and type of toilet used (pit latrine/bush versus flush toilet) was of borderline significance. CONCLUSION: We found a high prevalence of trichomoniasis in girls in Ndola who reported that they had never had sex. We postulate that the high prevalence of trichomoniasis in virgins in Ndola is due to non-sexual transmission of trichomoniasis via shared bathing water and inconsistent use of soap

Role of Network Topology in the Synchronization of Power Systems

We study synchronization dynamics in networks of coupled oscillators with bimodal distribution of natural frequencies. This setup can be interpreted as a simple model of frequency synchronization dynamics among generators and loads working in a power network. We derive the minimum coupling strength required to ensure global frequency synchronization. This threshold value can be efficiently found by solving a binary optimization problem, even for large networks. In order to validate our procedure, we compare its results with numerical simulations on a realistic network describing the European interconnected high-voltage electricity system, finding a very good agreement. Our synchronization threshold can be used to test the stability of frequency synchronization to link removals. As the threshold value changes only in very few cases when aplied to the European realistic network, we conclude that network is resilient in this regard. Since the threshold calculation depends on the local connectivity, it can also be used to identify critical network partitions acting as synchronization bottlenecks. In our stability experiments we observe that when a link removal triggers a change in the critical partition, its limits tend to converge to national borders. This phenomenon, which can have important consequences to synchronization dynamics in case of cascading failure, signals the influence of the uncomplete topological integration of national power grids at the European scale.Comment: The final publication is available at http://www.epj.org (see http://www.springerlink.com/content/l22k574x25u6q61m/

Systemic Risk in a Unifying Framework for Cascading Processes on Networks

We introduce a general framework for models of cascade and contagion processes on networks, to identify their commonalities and differences. In particular, models of social and financial cascades, as well as the fiber bundle model, the voter model, and models of epidemic spreading are recovered as special cases. To unify their description, we define the net fragility of a node, which is the difference between its fragility and the threshold that determines its failure. Nodes fail if their net fragility grows above zero and their failure increases the fragility of neighbouring nodes, thus possibly triggering a cascade. In this framework, we identify three classes depending on the way the fragility of a node is increased by the failure of a neighbour. At the microscopic level, we illustrate with specific examples how the failure spreading pattern varies with the node triggering the cascade, depending on its position in the network and its degree. At the macroscopic level, systemic risk is measured as the final fraction of failed nodes, $X^\ast$, and for each of the three classes we derive a recursive equation to compute its value. The phase diagram of $X^\ast$ as a function of the initial conditions, thus allows for a prediction of the systemic risk as well as a comparison of the three different model classes. We could identify which model class lead to a first-order phase transition in systemic risk, i.e. situations where small changes in the initial conditions may lead to a global failure. Eventually, we generalize our framework to encompass stochastic contagion models. This indicates the potential for further generalizations.Comment: 43 pages, 16 multipart figure