The oscillatory distribution of distances in random tries

We investigate \Delta_n, the distance between randomly selected pairs of nodes among n keys in a random trie, which is a kind of digital tree. Analytical techniques, such as the Mellin transform and an excursion between poissonization and depoissonization, capture small fluctuations in the mean and variance of these random distances. The mean increases logarithmically in the number of keys, but curiously enough the variance remains O(1), as n\to\infty. It is demonstrated that the centered random variable \Delta_n^*=\Delta_n-\lfloor2\log_2n\rfloor does not have a limit distribution, but rather oscillates between two distributions.Comment: Published at http://dx.doi.org/10.1214/105051605000000106 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Is Helicobacter Pylori Associated with a Migraine?

Objective: To determine whether Helicobacter pylori (H. pylori) is associated with migraine headache. Design: Case-control study. Settings: Local tertiary Hospitals in Cairo, Egypt and in HaferAlbaten, Saudi Arabia. Participants: A total of 70 patients with migraine who were 7 to 17 years old and who fulfilled the International Headache Society criteria for migraine and a total of 50 controls without migraine who were matched by the country of origin, age, sex, ethnicity, and socioeconomic status to the 70 migraine cases. Main Outcome Measures: Antibody levels to H. pylori (IgG) and H. pylori stool antigens were compared between the two groups. Results: Significant association was found between H. pylori and migraine and of the total of 70 migraineur cases, 55.7% were positive for H. pylori stool antigen testing compared to 20% in control group (P value=0.0002). Joint pain was reported in 44.3% and 18.0% of cases and controls respectively (P value=0.0034). Conclusion: H. pylori is associated with migraine without aura and may be a causative factor. Moreover, H. pylori may induce joint pain in the migraineur patients

Coxsackie B2 Virus Infection Causing Multiorgan Failure and Cardiogenic Shock in a 42-Year-Old Man

Infections from coxsackie B2 viruses often cause viral myocarditis and, only rarely, multisystem organ impairment. We present the unusual case of a 42-year-old man in whom coxsackie B2 virus infection caused multiorgan infection, necessitating distal pancreatectomy, splenectomy, renal dialysis, and venoarterial extracorporeal membrane oxygenation with mechanical ventilation. In addition, the patient had a rapid-eye-movement sleep-related conduction abnormality that caused frequent sinus pauses of longer than 10 s, presumably due to myocarditis from the coxsackievirus infection. He recovered after permanent pacemaker placement and was discharged from the hospital. We discuss our aggressive supportive care and the few other reports of multiorgan impairment from coxsackieviruses

Recurrence Relations for Moments of Dual Generalized Order Statistics from Weibull Gamma Distribution and Its Characterizations

In this paper, we establish explicit forms and new recurrence relations satisfied by the single and product moments of dual generalized order statistics from Weibull gamma distribution (WGD). The results include as particular cases the relations for moments of reversed order statistics and lower records.We present characterizations ofWGD based on (i) recurrence relation for single moments, (ii) truncated moments of certain function of the variable and (iii) hazrad function