Almost sure asymptotics for the random binary search tree

We consider a (random permutation model) binary search tree with n nodes and give asymptotics on the loglog scale for the height H_n and saturation level h_n of the tree as n\to\infty, both almost surely and in probability. We then consider the number F_n of particles at level H_n at time n, and show that F_n is unbounded almost surely.Comment: 12 pages, 2 figure

Fine asymptotics for the consistent maximal displacement of branching Brownian motion

It is well-known that the maximal particle in a branching Brownian motion sits near $\sqrt2 t - \frac{3}{2\sqrt2}\log t$ at time $t$. One may then ask about the paths of particles near the frontier: how close can they stay to this critical curve? Two different approaches to this question have been developed. We improve upon the best-known bounds in each case, revealing new qualitative features including marked differences between the two approaches.Comment: 25 pages; corrected several mistake

Timing and volume of fluid administration for patients with bleeding

Original article can be found at: http://www3.interscience.wiley.com Copyright John Wiley & Sons. ‘This review is published as a Cochrane Review in the Cochrane Database of Systematic Reviews 2003, Issue 3. Cochrane Reviews are regularly updated as new evidence emerges and in response to comments and criticisms, and the Cochrane Database of Systematic Reviews should be consulted for the most recent version of the Review.’ Kwan, I. , Bunn, F. and Roberts, I. 'Timing and volume of fluid administration for patients with bleeding.' Cochrane Database Systematic Reviews 2003, (3) CD002245. DOI: 10.1002/14651858.CD002245 http://dx.doi.org/10.1002/14651858.CD002245Background: Treatment of haemorrhagic shock involves maintaining blood pressure and tissue perfusion until bleeding is controlled. Different resuscitation strategies have been used to maintain the blood pressure in trauma patients until bleeding is controlled. However, while maintaining blood pressure may prevent shock, it may worsen bleeding. Objectives: To assess the effects of early versus delayed, and larger versus smaller volume of fluid administration in trauma patients with bleeding. Search strategy: We searched the CENTRAL (The Cochrane Library 2008, Issue 4), the Cochrane Injuries Group's Specialised Register (searched October 2008), MEDLINE (to October 2008), EMBASE (to October 2008), the National Research Register (in Current controlled trials.gov; searched October 2008) and the Science Citation Index (to October 2008). We checked reference lists of identified articles and contacted authors and experts in the field. Selection criteria: Randomised trials of the timing and volume of intravenous fluid administration in trauma patients with bleeding. Trials in which different types of intravenous fluid were compared were excluded. Data collection and analysis: Two authors independently extracted data and assessed trial quality. Main results: We did not combine the results quantitatively because the interventions and patient populations were so diverse. Early versus delayed fluid administration Three trials reported mortality and two coagulation data. In the first trial (n=598) relative risk (RR) for death with early fluid administration was 1.26 (95% confidence interval of 1.00−1.58). The weighted mean differences (WMD) for prothrombin time and partial thromboplastin time were 2.7 (95% CI 0.9−4.5) and 4.3 (95% CI 1.74−6.9) seconds respectively. In the second trial (n=50) RR for death with early blood transfusion was 5.4 (95% CI 0.3−107.1). The WMD for partial thromboplastin time was 7.0 (95% CI 6.0−8.0) seconds. In the third trial (n=1309) RR for death with early fluid administration was 1.06 (95% CI 0.77−1.47). Larger versus smaller volume of fluid administration Three trials reported mortality and one coagulation data. In the first trial (n=36) RR for death with a larger volume of fluid resuscitation was 0.80 (95% CI 0.28−22.29). Prothrombin time and partial thromboplastin time were 14.8 and 47.3 seconds in those who received a larger volume of fluid, as compared to 13.9 and 35.1 seconds in the comparison group. In the second trial (n=110) RR for death with a high systolic blood pressure resuscitation target (100mmHg) maintained with a larger volume of fluid, as compared to low systolic blood pressure resuscitation target (70mmHg) maintained with a smaller volume of fluid was 1.00 (95% CI 0.26−3.81). In the third trial (n=25) there were no deaths. Authors' conclusions: We found no evidence from randomised controlled trials for or against early or larger volume of intravenous fluid administration in uncontrolled haemorrhage. There is continuing uncertainty about the best fluid administration strategy in bleeding trauma patients. Further randomised controlled trials are needed to establish the most effective fluid resuscitation strategy.Peer reviewe

Gangliosides for acute spinal cord injury.

BACKGROUND: Spinal cord injury (SCI) results in loss of feeling and movement. The consequences can be devastating for the patient and his or her carers. Global estimates of the number of new cases annually range from 15 to 40 per million. Leading causes of acute SCI are road traffic injury, violence, and injuries sustained in sports and other recreational activities. Care for people with SCI has improved, leading to an increase in survival rates. Attempts to improve patients' feeling and movement have involved the use of a wide range of treatments. Gangliosides are compounds that occur naturally in cell membranes. Laboratory studies have suggested they may have protective effects on nerves and even help them to re-grow. Clinical trials have taken place using gangliosides (usually GM1 ganglioside) for a number of neurological conditions. OBJECTIVES: To quantify the evidence for the effectiveness and safety of gangliosides when used to treat acute SCI. SEARCH STRATEGY: We searched the following databases to identify trials for inclusion: CENTRAL, MEDLINE, EMBASE, and the National Research Register. We also searched web-based trials registers, such as Current Controlled Trials. We approached the manufacturers of the most widely used ganglioside and researchers in this field to try to locate any unpublished data. SELECTION CRITERIA: Randomised controlled trials of any ganglioside versus controls, in patients with SCI. Outcome measures specified were: mortality, recovery of motor function, improvement in sensory measures, measures of functional activity, infections and any other adverse events. DATA COLLECTION AND ANALYSIS: Data were extracted from published studies and authors were contacted for further information. All data found was dichotomous and odds ratios (with 95% CIs) were calculated. A fixed-effects model was assumed. MAIN RESULTS: Two studies met the inclusion criteria. There were no deaths in one (n=37). In the other (n=760), there were slightly more deaths in the treatment group than in the control group; odds ratio 1.07 (0.57, 2.00 95%CI) - a result that can be explained by the play of chance. Methodological weaknesses regarding the collection and presentation of data from the two studies made it impossible to reach any conclusions regarding the effect of gangliosides on the other specified outcomes. AUTHORS' CONCLUSIONS: The evidence available does not support the use of ganglioside treatment to reduce the death rate in SCI patients. No evidence has yet emerged that ganglioside treatment improves recovery or quality of life in survivors

Video Evidence That London Infants Can Resettle Themselves Back to Sleep After Waking in the Night, as well as Sleep for Long Periods, by 3 Months of Age

Objective: Most infants become settled at night by 3 months of age, whereas infants not settled by 5 months are likely to have long-term sleep-waking problems. We assessed whether normal infant development in the first 3 months involves increasing sleep-period length or the ability to resettle autonomously after waking in the night. Methods: One hundred one infants were assessed at 5 weeks and 3 months of age using nighttime infrared video recordings and parental questionnaires. Results: The clearest development was in sleep length; 45% of infants slept continuously for 5 hours or more at night at 3 months compared with 10% at 5 weeks. In addition, around a quarter of infants woke and resettled themselves back to sleep in the night at each age. Autonomous resettling at 5 weeks predicted prolonged sleeping at 3 months suggesting it may be a developmental precursor. Infants reported by parents to sleep for a period of 5 hours or more included infants who resettled themselves and those with long sleeps. Three-month olds fed solely breast milk were as likely to self-resettle or have long sleep bouts as infants fed formula or mixed breast and formula milk. Conclusions: Infants are capable of resettling themselves back to sleep in the first 3 months of age; both autonomous resettling and prolonged sleeping are involved in “sleeping through the night” at an early age. Findings indicate the need for physiological studies of how arousal, waking, and resettling develop into sustained sleeping and of how environmental factors support these endogenous and behavioral processes

Solubility behaviour, crystallisation kinetics and pour point : a comparison of linear alkane and triacyl glyceride solute/solvent mixtures

Mixtures of either a hydrocarbon wax in a hydrocarbon solvent or a long chain triacyl glyceride (TAG) in a TAG solvent show complex solubility boundary temperature hysteresis and precipitated crystal network formation leading to gelation. For these industrially-important systems, we show how the equilibrium solubility and its hysteresis, crystallisation kinetics and pour point temperature vary with solute concentration for representative examples of both hydrocarbon (n-tetracosane (C24) solute in n-heptane (C7) solvent) and TAG (tristearin (SSS) solute in tricaprylin (CCC) solvent) mixtures. The behaviour is modelled with good accuracy; thereby providing a useful aid to formulation and process optimisation