All scale-free networks are sparse

We study the realizability of scale free-networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this finding by analytical reasoning and by a numerical method, proposed here, based on extreme value arguments, which can be applied to any given degree distribution. Our results reveal a fundamental reason why large scale-free networks without constraints on minimum and maximum degree must be sparse.Comment: 4 pages, 2 figure

Engineering of janus-like dendrimers with peptides derived from glycoproteins of herpes simplex virus type 1: Toward a versatile and novel antiviral platform

Novel antiviral nanotherapeutics, which may inactivate the virus and block it from entering host cells, represent an important challenge to face viral global health emergencies around the world. Using a combination of bioorthogonal copper-catalyzed 1,3-dipolar alkyne/azide cycloaddition (CuAAC) and photoinitiated thiol–ene coupling, monofunctional and bifunctional peptidodendrimer conjugates were obtained. The conjugates are biocompatible and demonstrate no toxicity to cells at biologically relevant concentrations. Furthermore, the orthogonal addition of multiple copies of two different antiviral peptides on the surface of a single dendrimer allowed the resulting biocon-jugates to inhibit Herpes simplex virus type 1 at both the early and the late stages of the infection process. The presented work builds on further improving this attractive design to obtain a new class of therapeutics

Effects of Extracorporeal Magnetic Stimulation in Fecal Incontinence.

Background: Fecal incontinence (FI) is a common condition that has devastating consequences for patients' QOL. In some patients, the conventional functional pelvic floor electrical stimulation has been effective but is an invasive and embarrassing treatment. The object of the study was to evaluate the feasibility of functional extracorporeal magnetic stimulation (FMS) in strengthening the pelvic floor muscles without an anal plug and the embarrassment of undressing. Materials and Methods: Thirty patients (26 female and 4 males) with FI were enrolled. All patients were assessed during a specialized coloproctology evaluation followed by endoanal ultrasonography and anorectal manometry. All patients underwent an FMS treatment once weekly for 8 weeks. Patients' outcome was assessed by the Cleveland Clinic Fecal Incontinence Score (CCFIS) and by the fecal incontinence QOL questionnaire (FIQL). Results: After 8 weeks, the number of solid and liquid stool leakage per week was significantly reduced (p<0.05) with a significant improvement of the CCFIS and of the FIQL (p<0.05). Moreover, the authors recorded a missed recruitment of the agonist and antagonists' defecation muscles. Conclusion: FMS is a safe, non-invasive and painless treatment for FI. It could be recommended for selected patients with non-surgical FI to ensure a rapid clinical improvement

Degree correlations in directed scale-free networks

Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which is a measure of the correlation between the degrees of the nodes at the end of the links. Degree correlations are known to affect both the structure of a network and the dynamics of the processes supported thereon, including the resilience to damage, the spread of information and epidemics, and the efficiency of defence mechanisms. Nonetheless, while many studies focus on undirected scale-free networks, the interactions in real-world systems often have a directionality. Here, we investigate the dependence of the degree correlations on the power-law exponents in directed scale-free networks. To perform our study, we consider the problem of building directed networks with a prescribed degree distribution, providing a method for proper generation of power-law-distributed directed degree sequences. Applying this new method, we perform extensive numerical simulations, generating ensembles of directed scale-free networks with exponents between~2 and~3, and measuring ensemble averages of the Pearson correlation coefficients. Our results show that scale-free networks are on average uncorrelated across directed links for three of the four possible degree-degree correlations, namely in-degree to in-degree, in-degree to out-degree, and out-degree to out-degree. However, they exhibit anticorrelation between the number of outgoing connections and the number of incoming ones. The findings are consistent with an entropic origin for the observed disassortativity in biological and technological networks.Comment: 10 pages, 5 figure

Depth-dependent ordering, two-length-scale phenomena and crossover behavior in a crystal featuring a skin-layer with defects

Structural defects in a crystal are responsible for the "two length-scale" behavior, in which a sharp central peak is superimposed over a broad peak in critical diffuse X-ray scattering. We have previously measured the scaling behavior of the central peak by scattering from a near-surface region of a V2H crystal, which has a first-order transition in the bulk. As the temperature is lowered toward the critical temperature, a crossover in critical behavior is seen, with the temperature range nearest to the critical point being characterized by mean field exponents. Near the transition, a small two-phase coexistence region is observed. The values of transition and crossover temperatures decay with depth. An explanation of these experimental results is here proposed by means of a theory in which edge dislocations in the near-surface region occur in walls oriented in the two directions normal to the surface. The strain caused by the dislocation lines causes the ordering in the crystal to occur as growth of roughly cylindrically shaped regions. After the regions have reached a certain size, the crossover in the critical behavior occurs, and mean field behavior prevails. At a still lower temperature, the rest of the material between the cylindrical regions orders via a weak first-order transition.Comment: 12 pages, 8 figure

Efficient and exact sampling of simple graphs with given arbitrary degree sequence

Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet modeling. Existing graph sampling methods are either link-swap based (Markov-Chain Monte Carlo algorithms) or stub-matching based (the Configuration Model). Both types are ill-controlled, with typically unknown mixing times for link-swap methods and uncontrolled rejections for the Configuration Model. Here we propose an efficient, polynomial time algorithm that generates statistically independent graph samples with a given, arbitrary, degree sequence. The algorithm provides a weight associated with each sample, allowing the observable to be measured either uniformly over the graph ensemble, or, alternatively, with a desired distribution. Unlike other algorithms, this method always produces a sample, without back-tracking or rejections. Using a central limit theorem-based reasoning, we argue, that for large N, and for degree sequences admitting many realizations, the sample weights are expected to have a lognormal distribution. As examples, we apply our algorithm to generate networks with degree sequences drawn from power-law distributions and from binomial distributions.Comment: 8 pages, 3 figure

Radiative forcing in the 21st century due to ozone changes in the troposphere and the lower stratosphere

Radiative forcing due to changes in ozone is expected for the 21st century. An assessment on changes in the tropospheric oxidative state through a model intercomparison ("OxComp'') was conducted for the IPCC Third Assessment Report (IPCC-TAR). OxComp estimated tropospheric changes in ozone and other oxidants during the 21st century based on the "SRES'' A2p emission scenario. In this study we analyze the results of 11 chemical transport models (CTMs) that participated in OxComp and use them as input for detailed radiative forcing calculations. We also address future ozone recovery in the lower stratosphere and its impact on radiative forcing by applying two models that calculate both tropospheric and stratospheric changes. The results of OxComp suggest an increase in global-mean tropospheric ozone between 11.4 and 20.5 DU for the 21st century, representing the model uncertainty range for the A2p scenario. As the A2p scenario constitutes the worst case proposed in IPCC-TAR we consider these results as an upper estimate. The radiative transfer model yields a positive radiative forcing ranging from 0.40 to 0.78 W m(-2) on a global and annual average. The lower stratosphere contributes an additional 7.5-9.3 DU to the calculated increase in the ozone column, increasing radiative forcing by 0.15-0.17 W m(-2). The modeled radiative forcing depends on the height distribution and geographical pattern of predicted ozone changes and shows a distinct seasonal variation. Despite the large variations between the 11 participating models, the calculated range for normalized radiative forcing is within 25%, indicating the ability to scale radiative forcing to global-mean ozone column change