The analysis of approximate quickselect and related problems

Approximate Quickselect, a simple modification of the well known Quickselect algorithm for selection, can be used to efficiently find an element with rank k in a given range [i..j], out of n given elements. We study basic cost measures of Approximate Quickselect by computing exact and asymptotic results for the expected number of passes, comparisons and data moves during the execution of this algorithm. The key element appearing in the analysis of Approximate Quickselect is a trivariate recurrence that we solve in full generality. The general solution of the recurrence proves to be very useful, as it allows us to tackle several related problems, besides the analysis that originally motivated us. In particular, we have been able to carry out a precise analysis of the expected number of moves of the ith element when selecting the jth smallest element with standard Quickselect, where we are able to give both exact and asymptotic results. Moreover, we can apply our general results to obtain exact and asymptotic results for several parameters in binary search trees, namely the expected number of common ancestors of the nodes with rank i and j, the expected size of the subtree rooted at the least common ancestor of the nodes with rank i and j, and the expected distance between the nodes of ranks i and j.

The efficacy of melatonin for sleep problems in children with autism, fragile X syndrome, or autism and fragile X syndrome.

STUDY OBJECTIVE: To determine the efficacy of melatonin on sleep problems in children with autistic spectrum disorder (ASD) and fragile X syndrome (FXS). METHODS: A 4-week, randomized, double blind, placebo-controlled, crossover design was conducted following a 1-week baseline period. Either melatonin, 3 mg, or placebo was given to participants for 2 weeks and then alternated for another 2 weeks. Sleep variables, including sleep duration, sleep-onset time, sleep-onset latency time, and the number of night awakenings, were recorded using an Actiwatch and from sleep diaries completed by parents. All participants had been thoroughly assessed for ASD and also had DNA testing for the diagnosis of FXS. RESULTS: Data were successfully obtained from the 12 of 18 subjects who completed the study (11 males, age range 2 to 15.25 years, mean 5.47, SD 3.6). Five participants met diagnostic criteria for ASD, 3 for FXS alone, 3 for FXS and ASD, and 1 for fragile X premutation. Eight out of 12 had melatonin first. The conclusions from a nonparametric repeated-measures technique indicate that mean night sleep duration was longer on melatonin than placebo by 21 minutes (p = .02), mean sleep-onset latency was shorter by 28 minutes (p = .0001), and mean sleep-onset time was earlier by 42 minutes (p = .02). CONCLUSION: The results of this study support the efficacy and tolerability of melatonin treatment for sleep problems in children with ASD and FXS.

Choledocholithiasis: repetitive thick-slab single-shot projection magnetic resonance cholangiopancreaticography versus endoscopic ultrasonography.

This prospective study compares repetitive thick-slab single-shot projection magnetic resonance cholangiopancreatography (MRCP) with endoscopic ultrasonography (EUS) for the detection of choledocholithiasis. Fifty-seven consecutive patients (36 women, mean age 61) referred for suspected choledocholithiasis underwent MRCP, followed by EUS. Each procedure was performed by different operators blinded to the results of the other investigation. MR technique included a turbo spin-echo T2-weighted axial sequence with selective fat saturation (SPIR/TSE, TE=70 ms, TR=1,600 ms), followed by coronal dynamic MRCP. The same thick-slab slice was sequentially acquired 12 times as breath-hold single-shot projection imaging (SSh, TE=900 ms, TE=8,000 ms) centred on the common bile duct (CBD). Two experienced radiologists independently and blindly evaluated MR images for the detection of CBD stones. Their inter-observer agreement kappa was determined. Secondly, the two observers read MR images in consensus again. CBD stones were demonstrated in 18 out of 57 patients (31.6 %) and confirmed by endoscopic retrograde cholangiography (ERCP, n=17) or intraoperative cholangiography (n=1). Clinical follow-up served as the "gold standard" in patients with negative results without following invasive procedure (n=28). Sensitivity, specificity, accuracy, positive and negative predictive value for MRCP resulting from consensus reading were 94.9%, 94.4%, 94.7%, 97.4% and 89.5%, respectively. Corresponding values of EUS were 97.4%, 94.4%, 96.5%, 97.4% and 94.4%. Inter-observer agreement kappa was 0.81. Repetitive thick-slab single-shot projection MRCP is an accurate non-invasive imaging modality for suspected choledocholithiasis and should be increasingly used to select those patients who require a subsequent therapeutic procedure, namely ERCP.

Pharmacokinetics and posterior segment biodistribution of ESBA105, an anti-TNF-alpha single-chain antibody, upon topical administration to the rabbit eye.

PURPOSE: The purpose of this study was to characterize local distribution and systemic absorption of the tumor necrosis factor (TNF)-alpha inhibitory single-chain antibody fragment (scFv) ESBA105 following topical administration to the eye in vivo. METHODS: Rabbits received ESBA105 as topical eye drops in two dosing regimens. First, pharmacokinetics after the topical route of administration was compared to the intravenous (i.v.) route by means of applying the identical cumulative daily dose of ESBA105. In a second study rabbits received five eye drops daily for six consecutive days in a lower frequency topical dosing regimen. Kinetics and biodistribution of ESBA105 in ocular tissues and fluids as well as in sera were determined in all animals. RESULTS: After topical administration to the eye, ESBA105 quickly reaches therapeutic concentrations in all ocular compartments. Systemic exposure after topical administration is 25,000-fold lower than exposure after i.v. injection of the identical cumulative daily dose. ESBA105 levels in vitreous humor and neuroretina are significantly higher on topical administration than after i.v. injection. Absolute and relative intraocular biodistribution of ESBA105 is different with topical and systemic delivery routes. Compared to its terminal half-life in circulation (7 hours), the vitreal half-life of ESBA105 is significantly enhanced (16-24 hours). CONCLUSIONS: On topical administration, ESBA105 is efficiently absorbed and distributed to all compartments of the eye, whereby systemic drug exposure is very low. Based on its unique intraocular biodistribution and pharmacokinetics and the absolute intraocular levels reached, topical ESBA105 appears highly attractive for treatment of various ophthalmological disorders.

RecA-mediated annealing of single-stranded DNA and its relation to the mechanism of homologous recombination.

We demonstrate that RecA protein can mediate annealing of complementary DNA strands in vitro by at least two different mechanisms. The first annealing mechanism predominates under conditions where RecA protein causes coaggregation of single-stranded DNA (ssDNA) molecules and where RecA-free ssDNA stretches are present on both reaction partners. Under these conditions annealing can take place between locally concentrated protein-free complementary sequences. Other DNA aggregating agents like histone H1 or ethanol stimulate annealing by the same mechanism. The second mechanism of RecA-mediated annealing of complementary DNA strands is best manifested when preformed saturated RecA-ssDNA complexes interact with protein-free ssDNA. In this case, annealing can occur between the ssDNA strand resident in the complex and the ssDNA strand that interacts with the preformed RecA-ssDNA complex. Here, the action of RecA protein reflects its specific recombination promoting mechanism. This mechanism enables DNA molecules resident in the presynaptic RecA-DNA complexes to be exposed for hydrogen bond formation with DNA molecules contacting the presynaptic RecA-DNA filament.

Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy.

On Strategy-proofness and symmetric single-peakedness

We characterize the class of strategy-proof social choice functions on the domain of symmetric single-peaked preferences. This class is strictly larger than the set of generalized median voter schemes (the class of strategy-proof and tops-only social choice functions on the domain of single-peaked preferences characterized by Moulin (1980)) since, under the domain of symmetric single-peaked preferences, generalized median voter schemes can be disturbed by discontinuity points and remain strategy-proof on the smaller domain. Our result identifies the specific nature of these discontinuities which allow to design non-onto social choice functions to deal with feasibility constraints.

Discharge properties of single neurons in the dorsal nucleus of the lateral lemniscus of the rat.

The aim of the present study was to characterize the discharge properties of single neurons in the dorsal nucleus of the lateral lemniscus (DNLL) of the rat. In the absence of acoustic stimulation, two types of spontaneous discharge patterns were observed: units tended to fire in a bursting or in a nonbursting mode. The distribution of units in the DNLL based on spontaneous firing rate followed a rostrocaudal gradient: units with high spontaneous rates were most commonly located in the rostral part of the DNLL, whereas in the caudal part units had lower spontaneous discharge rates. The most common response pattern of DNLL units to 200 ms binaural noise bursts contained a prominent onset response followed by a lower but steady-state response and an inhibitory response in the early-off period. Thresholds of response to noise bursts were on average higher for DNLL units than for units recorded in the inferior colliculus under the same experimental conditions. The DNLL units were arranged according to a mediolateral sensitivity gradient with the lowest threshold units in the most lateral part of the nucleus. In the rat, as in other mammals, the most common DNLL binaural input type was an excitatory response to contralateral ear stimulation and inhibitory response to ipsilateral ear stimulation (EI type). Pure tone bursts were in general a more effective stimulus compared to noise bursts. Best frequency (BF) was established for 97 DNLL units and plotted according to their spatial location. The DNLL exhibits a loose tonotopic organization, where there is a concentric pattern with high BF units located in the most dorsal and ventral parts of the DNLL and lower BF units in the middle part of the nucleus.

Self-perceived health status and mental health outcomes in young adults born with less than 1000 g.

AIM: To assess self-perceived health status and mental health outcomes of former extremely low-birth-weight (ELBW) infants at young adulthood compared with community norms and to analyse predictors of poor outcome. METHODS: Fifty-five ELBW adults, 18 men (33%), with median (range) gestational age of 28.7 (25.0-34.0) weeks and birth weight of 930 (680-990) grams, born in Switzerland, were included. They self-rated their health status and mental health at a mean (range) age of 23.3 (21.8-25.9) years. Health status was measured by the Medical Outcomes Study Short Form-36 questionnaire and mental health by the Brief Symptom Inventory. RESULTS: The mean scores for both outcome measures were in the normal range. However, the study group self-rated significantly higher physical health status and lower mental health status compared with the community norms, and scores for self-perceived mental health tended to be worse in the former. ELBW adults reported more problems in socio-emotional role functioning compared with the community norms. Female sex was associated with poorer and bronchopulmonary dysplasia with better mental health status. CONCLUSION: Health status and mental health of former ELBW adults were overall satisfying. However, the comparison with the community norms revealed differences, which may be important for parental and patient counselling and developing support strategies.

Application of standard and refined heat balance integral methods to one-dimensional Stefan problems

The work in this paper concerns the study of conventional and refined heat balance integral methods for a number of phase change problems. These include standard test problems, both with one and two phase changes, which have exact solutions to enable us to test the accuracy of the approximate solutions. We also consider situations where no analytical solution is available and compare these to numerical solutions. It is popular to use a quadratic profile as an approximation of the temperature, but we show that a cubic profile, seldom considered in the literature, is far more accurate in most circumstances. In addition, the refined integral method can give greater improvement still and we develop a variation on this method which turns out to be optimal in some cases. We assess which integral method is better for various problems, showing that it is largely dependent on the specified boundary conditions.

MMP-9 as predictive factor for response and progression free survival in breast cancer patients treated with bevacizumab and pegylated liposomal doxorubicin. A multicenter, single-arm phase II trial (SAKK24/06). On behalf of the Swiss Group for Clinical Cancer Research (SAKK).

The benefit of bevacizumab (Bv) has been shown in different tumors including colorectal cancer, renal cancer, pulmonary non-small cell cancer and also breast cancer. However to date, there is no established test evaluating the angiogenic status of a patient and monitoring the effects of anti-angiogenic treatments. Tumor angiogenesis is the result of a balance between multiple pro- and anti¬angiogenic molecules. There is very little published clinical data exploring the impact of the anti-angiogenic therapy on the different angiogenesis-related molecules and the potential role of these molecules as prognostic or predictive factors.

GPs' role in the detection of psychological problems of young people: a population-based study.

BACKGROUND: Among young people, about one in three females and one in five males report experiencing emotional distress but 65-95% of them do not receive help from health professionals. AIM: To assess the differences among young people who seek help and those who do not seek help for their psychological problems, considering the frequency of consultations to their GP and their social resources. DESIGN OF STUDY: School survey. SETTING: Post-mandatory school. METHOD: Among a Swiss national representative sample of 7429 students and apprentices (45.6% females) aged 16-20 years, 1931 young people reported needing help for a problem of depression/sadness (26%) and were included in the study. They were divided into those who sought help (n = 256) and those who did not (n = 1675), and differences between them were assessed. RESULTS: Only 13% of young people needing help for psychological problems consulted for that reason and this rate was positively associated with the frequency of consultations to the GP. However, 80% of young people who did not consult for psychological problems visited their GP at least once during the previous year. Being older or a student, having a higher depression score, or a history of suicide attempt were linked with a higher rate of help seeking. Moreover, confiding in adults positively influenced the rate of help seeking. CONCLUSION: The large majority of young people reporting psychological problems do not seek help, although they regularly consult their GP. While young people have difficulties in tackling issues about mental health, GPs could improve the situation by systematically inquiring about this issue.