A generalized nonlinear Schr\"odinger equation as model for turbulence, collapse, and inverse cascade

A two-dimensional generalized cubic nonlinear Schr\"odinger equation with complex coefficients for the group dispersion and nonlinear terms is used to investigate the evolution of a finite-amplitude localized initial perturbation. It is found that modulation of the latter can lead to side-band formation, wave condensation, collapse, turbulence, and inverse cascade, although not all together nor in that order.Comment: 12 pages, 5 figure

A power-law distribution for tenure lengths of sports managers

We show that the tenure lengths for managers of sport teams follow a power law distribution with an exponent between 2 and 3. We develop a simple theoretical model which replicates this result. The model demonstrates that the empirical phenomenon can be understood as the macroscopic outcome of pairwise interactions among managers in a league, threshold effects in managerial performance evaluation, competitive market forces, and luck at the microscopic level

Headache and Acute Illness in Children

Thirty-seven children with headaches who were seen in a walk-in clinic were matched to 37 headache-free controls. Thirty percent of the headache group and 11% of the headache-free control group had a body temperature above 38°C (p < 0.05). Nonrhythmic pain was more commonly associated with fever than was rhythmic pain (p < 0.05). Of 34 headache subjects who completed questionnaires, those with more intense headaches reported a greater number of headache-exacerbating factors (p < 0.01).Bilateral headaches were more painful than unilateral headaches, and in two thirds of the subjects, the intensity of pain paralleled the course of the underlying illness. A family history of migraine was more common in the headache group as compared to the headache-free control group (p < 0.05). Headaches associated with acute illnesses may be a precursor to later migraine. (J Child Neurol 1987;2:22-27)Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68022/2/10.1177_088307388700200104.pd

Worldwide spreading of economic crisis

We model the spreading of a crisis by constructing a global economic network and applying the Susceptible-Infected-Recovered (SIR) epidemic model with a variable probability of infection. The probability of infection depends on the strength of economic relations between the pair of countries, and the strength of the target country. It is expected that a crisis which originates in a large country, such as the USA, has the potential to spread globally, like the recent crisis. Surprisingly we show that also countries with much lower GDP, such as Belgium, are able to initiate a global crisis. Using the {\it k}-shell decomposition method to quantify the spreading power (of a node), we obtain a measure of ``centrality'' as a spreader of each country in the economic network. We thus rank the different countries according to the shell they belong to, and find the 12 most central countries. These countries are the most likely to spread a crisis globally. Of these 12 only six are large economies, while the other six are medium/small ones, a result that could not have been otherwise anticipated. Furthermore, we use our model to predict the crisis spreading potential of countries belonging to different shells according to the crisis magnitude.Comment: 13 pages, 4 figures and Supplementary Materia