Power laws, Pareto distributions and Zipf's law

When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distributions of the sizes of cities, earthquakes, solar flares, moon craters, wars and people's personal fortunes all appear to follow power laws. The origin of power-law behaviour has been a topic of debate in the scientific community for more than a century. Here we review some of the empirical evidence for the existence of power-law forms and the theories proposed to explain them.Comment: 28 pages, 16 figures, minor corrections and additions in this versio

Jamming in complex networks with degree correlation

We study the effects of the degree-degree correlations on the pressure congestion J when we apply a dynamical process on scale free complex networks using the gradient network approach. We find that the pressure congestion for disassortative (assortative) networks is lower (bigger) than the one for uncorrelated networks which allow us to affirm that disassortative networks enhance transport through them. This result agree with the fact that many real world transportation networks naturally evolve to this kind of correlation. We explain our results showing that for the disassortative case the clusters in the gradient network turn out to be as much elongated as possible, reducing the pressure congestion J and observing the opposite behavior for the assortative case. Finally we apply our model to real world networks, and the results agree with our theoretical model

Network 'small-world-ness': a quantitative method for determining canonical network equivalence

Background: Many technological, biological, social, and information networks fall into the broad class of 'small-world' networks: they have tightly interconnected clusters of nodes, and a shortest mean path length that is similar to a matched random graph (same number of nodes and edges). This semi-quantitative definition leads to a categorical distinction ('small/not-small') rather than a quantitative, continuous grading of networks, and can lead to uncertainty about a network's small-world status. Moreover, systems described by small-world networks are often studied using an equivalent canonical network model-the Watts-Strogatz (WS) model. However, the process of establishing an equivalent WS model is imprecise and there is a pressing need to discover ways in which this equivalence may be quantified. Methodology/Principal Findings: We defined a precise measure of 'small-world-ness' S based on the trade off between high local clustering and short path length. A network is now deemed a 'small-world' if S. 1-an assertion which may be tested statistically. We then examined the behavior of S on a large data-set of real-world systems. We found that all these systems were linked by a linear relationship between their S values and the network size n. Moreover, we show a method for assigning a unique Watts-Strogatz (WS) model to any real-world network, and show analytically that the WS models associated with our sample of networks also show linearity between S and n. Linearity between S and n is not, however, inevitable, and neither is S maximal for an arbitrary network of given size. Linearity may, however, be explained by a common limiting growth process. Conclusions/Significance: We have shown how the notion of a small-world network may be quantified. Several key properties of the metric are described and the use of WS canonical models is placed on a more secure footing

Obesity-induced changes in lipid mediators persist after weight loss.

BackgroundObesity induces significant changes in lipid mediators, however, the extent to which these changes persist after weight loss has not been investigated.Subjects/methodsWe fed C57BL6 mice a high-fat diet to generate obesity and then switched the diet to a lower-fat diet to induce weight loss. We performed a comprehensive metabolic profiling of lipid mediators including oxylipins, endocannabinoids, sphingosines and ceramides in key metabolic tissues (including adipose, liver, muscle and hypothalamus) and plasma.ResultsWe found that changes induced by obesity were largely reversible in most metabolic tissues but the adipose tissue retained a persistent obese metabolic signature. Prostaglandin signaling was perturbed in the obese state and lasting increases in PGD2, and downstream metabolites 15-deoxy PGJ2 and delta-12-PGJ2 were observed after weight loss. Furthermore expression of the enzyme responsible for PGD2 synthesis (hematopoietic prostaglandin D synthase, HPGDS) was increased in obese adipose tissues and remained high after weight loss. We found that inhibition of HPGDS over the course of 5 days resulted in decreased food intake in mice. Increased HPGDS expression was also observed in human adipose tissues obtained from obese compared with lean individuals. We then measured circulating levels of PGD2 in obese patients before and after weight loss and found that while elevated relative to lean subjects, levels of this metabolite did not decrease after significant weight loss.ConclusionsThese results suggest that lasting changes in lipid mediators induced by obesity, still present after weight loss, may play a role in the biological drive to regain weight

Women\u2019s human rights when experiencing humanitarian crises and conflicts: the impact of United Nations Security Council Resolutions on women, peace, security, and the CEDAW General Recommendation no. 30.

Violence and insecurity are strictly linked to unequal political, social, and economic power. However, the continuity of violence is obscured by masculinist and patriarchal rules of security within gendered structures, especially inside the division of public/private dimensions and spaces, of production-reproduction activities, and of conflicts of war/peace. Nowadays, there is a general perception of the gendered dimensions of humanitarian emergencies in public policy outcomes and more in general in institutional contexts where the central role of women in security and maintaining peace, at all levels of decision making, both prior to, during, and after the conflict stage, hostilities, and peace-keeping and peace-building stages, as well as in trying to pursue a condition of reconciliation and reconstruction, has been formally recognized at international level. Nevertheless, it is necessary to focus on some problems related to the conceptualization of and legal provision for \u2018gender based security\u2019 and its subsequent effects upon accountability, with particular reference to transitional justice and post-conflict societies. It is important to assess a range of contemporary issues implicated for women and security, such as violence and other forms of harassment in times of post-conflict

Evolving Clustered Random Networks

We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as generic models for studying the impacts of degree distributions and clustering on dynamical processes as well as null models for detecting other structural properties in empirical networks

System size resonance in an attractor neural network

We study the response of an attractor neural network, in the ferromagnetic phase, to an external, time-dependent stimulus, which drives the system periodically two different attractors. We demonstrate a non-trivial dependance of the system via a system size resonance, by showing a signal amplification maximum at a certain finite size.Comment: 7 pages, 9 figures, submitted to Europhys. Let

A New Approach to Analyzing Patterns of Collaboration in Co-authorship Networks - Mesoscopic Analysis and Interpretation

This paper focuses on methods to study patterns of collaboration in co-authorship networks at the mesoscopic level. We combine qualitative methods (participant interviews) with quantitative methods (network analysis) and demonstrate the application and value of our approach in a case study comparing three research fields in chemistry. A mesoscopic level of analysis means that in addition to the basic analytic unit of the individual researcher as node in a co-author network, we base our analysis on the observed modular structure of co-author networks. We interpret the clustering of authors into groups as bibliometric footprints of the basic collective units of knowledge production in a research specialty. We find two types of coauthor-linking patterns between author clusters that we interpret as representing two different forms of cooperative behavior, transfer-type connections due to career migrations or one-off services rendered, and stronger, dedicated inter-group collaboration. Hence the generic coauthor network of a research specialty can be understood as the overlay of two distinct types of cooperative networks between groups of authors publishing in a research specialty. We show how our analytic approach exposes field specific differences in the social organization of research.Comment: An earlier version of the paper was presented at ISSI 2009, 14-17 July, Rio de Janeiro, Brazil. Revised version accepted on 2 April 2010 for publication in Scientometrics. Removed part on node-role connectivity profile analysis after finding error in calculation and deciding to postpone analysis

Dose-related liver injury of Geniposide associated with the alteration in bile acid synthesis and transportation.

Fructus Gardenia (FG), containing the major active constituent Geniposide, is widely used in China for medicinal purposes. Currently, clinical reports of FG toxicity have not been published, however, animal studies have shown FG or Geniposide can cause hepatotoxicity in rats. We investigated Geniposide-induced hepatic injury in male Sprague-Dawley rats after 3-day intragastric administration of 100 mg/kg or 300 mg/kg Geniposide. Changes in hepatic histomorphology, serum liver enzyme, serum and hepatic bile acid profiles, and hepatic bile acid synthesis and transportation gene expression were measured. The 300 mg/kg Geniposide caused liver injury evidenced by pathological changes and increases in serum alanine aminotransferase (ALT), aspartate aminotransferase (AST), alkaline phosphatase (ALP) and γ-glutamytransferase (γ-GT). While liver, but not sera, total bile acids (TBAs) were increased 75% by this dose, dominated by increases in taurine-conjugated bile acids (t-CBAs). The 300 mg/kg Geniposide also down-regulated expression of Farnesoid X receptor (FXR), small heterodimer partner (SHP) and bile salt export pump (BSEP). In conclusion, 300 mg/kg Geniposide can induce liver injury with associated changes in bile acid regulating genes, leading to an accumulation of taurine conjugates in the rat liver. Taurocholic acid (TCA), taurochenodeoxycholic acid (TCDCA) as well as tauro-α-muricholic acid (T-α-MCA) are potential markers for Geniposide-induced hepatic damage