Random multi-index matching problems

The multi-index matching problem (MIMP) generalizes the well known matching problem by going from pairs to d-uplets. We use the cavity method from statistical physics to analyze its properties when the costs of the d-uplets are random. At low temperatures we find for d>2 a frozen glassy phase with vanishing entropy. We also investigate some properties of small samples by enumerating the lowest cost matchings to compare with our theoretical predictions.Comment: 22 pages, 16 figure

Influence of sex, age, pubertal maturation and body mass index on circulating white blood cell counts in healthy European adolescents—the HELENA study

Percentiles 10th, 25th, 50th, 75th and 90th are presented for circulating white blood cells (WBC), neutrophils, lymphocytes, monocytes, eosinophils and basophils in healthy European adolescents (12.5–17.5 years, n = 405, 48.9 % boys), considering age, sex, puberty and body mass index (BMI). CD3+ (mature T cells), CD4+ (T helper), CD8+ (T cytotoxic), CD16+56+ (natural killer), CD19+ (B cells), CD3+CD45RA+, CD4+CD45RA+, CD8+CD45RA+ (naïve), CD3+CD45RO+, CD4+CD45RO+ and CD8+CD45RO+ (memory) lymphocytes were also analysed by immunophenotyping. Girls presented higher WBC, neutrophil, CD3+CD45RO+ and CD4+CD45RO+ cell counts and CD3+/CD19+ ratio, and lower CD3+CD45RA+ and CD4+CD45RA+ counts than boys. Age was associated with higher neutrophil counts and CD3+/CD19+, and lower CD19+ counts; in boys, with lower CD3+CD45RA+, CD4+CD45RA+ and CD8+CD45RA+ counts as well; in girls, with higher WBC, CD3+CD45RO+ and CD4+CD45RO+ counts. Pubertal maturation in boys was associated with lower WBC and lymphocyte counts; in girls, with higher basophil, CD3+CD45RO+ and CD4+CD45RO+ values. BMI was associated with higher WBC counts; in boys, also with higher lymphocyte counts; in girls, with higher neutrophil, CD4+, CD3+CD45RO+ and CD4+CD45RO+ counts. Conclusion: Our study provides normative values for circulating immune cells in adolescents, highlighting the importance of considering sex, age, pubertal maturation and BMI when establishing reference ranges for WBC in paediatric populations

Sorting a bridge hand www.elsevier.com/locate/disc

Sorting a permutation by block moves is a task that every bridge player has to solve every time she picks up a new hand of cards. It is also a problem for the computational biologist, for block moves are a fundamental type of mutation that can explain why genes common to two species do not occur in the same order in the chromosome. It is not known whether there exists an optimal sorting procedure running in polynomial time. Bafna and Pevzner gave a polynomial time algorithm that sorts any permutation of length n in at most 3n=4 moves. Our new algorithm improves this to ⌊(2n−2)=3 ⌋ for n ¿ 9. For the reverse permutation, we give an exact expression for the number of moves needed, namely ⌈(n +1)=2⌉. Computations of Bafna and Pevzner up to n = 10 seemed to suggest that this is the worst case; but as it turns out, a rst counterexample occurs for n = 13, i.e. the bridge player’s case. Professional card players never sort by rank, only by suit. For this case, we give a complet

A systematic review and cost-effectiveness analysis of the case for screening nulliparous women in late pregnancy using ultrasound

Background. Currently, pregnant women are screened using ultrasound at booking and around the middle of pregnancy. Ultrasound scans thereafter are performed for clinical indications only. Objectives. We sought to assess the case for offering universal late pregnancy ultrasound to all nulliparous women in the UK. The main questions addressed were to determine the diagnostic effectiveness of universal late pregnancy ultrasound to predict adverse outcome, and the cost effectiveness of either implementing universal ultrasound or conducting further research in this area. Design We performed diagnostic test accuracy reviews of five ultrasonic measurements in late pregnancy. We conducted cost effectiveness and value of information (VoI) analysis of screening for fetal presentation, screening for small for gestational age (SGA) fetuses and screening for large for gestational age (LGA) fetuses. We finally conducted a survey and a focus group to determine the willingness of women to participate in a future randomised trial. Data sources We searched Medline, EMBASE and the Cochrane library from inception. Review methods The protocol for the review was designed a priori and registered. Eligible studies were identified using key words with no restrictions for language or location. The risk of bias in studies was assessed using the Quality Assessment of Diagnostic Accuracy Studies 2 tool. Health economic modelling employed a decision tree analysed via Monte Carlo simulation. Health outcomes were from the fetal perspective and presented as quality-adjusted life years (QALYs). Costs were from the perspective of the public sector defined as the (English) NHS and costs of special educational needs. All costs and QALYs were discounted by 3.5% per annum and the reference case time horizon was 20 years. Results Umbilical artery Doppler, cerebro-placental ratio (CPR), severe oligohydramnios, and borderline oligohydramnios were all either non-predictive or weakly predictive of the risk of neonatal morbidity (summary positive likelihood ratios [LR+] between 1 and 2) and were all weakly predictive of the risk of delivering a SGA infant (summary LR+ between 2 and 4). Suspicion of fetal macrosomia is strongly predictive of the risk of delivering a large baby but it is only weakly – albeit statistically significantly – predictive of the risk of shoulder dystocia. Very few studies blinded the result of the ultrasound scan and most studies had high risk of bias through treatment paradox, ascertainment bias or iatrogenic harm. Health economic analysis indicated that universal ultrasound for fetal presentation only may be both clinically and economically justified on the basis of existing evidence. Universal ultrasound including fetal biometry was of borderline cost-effectiveness, and sensitive to assumptions. VoI analysis indicated that future research should be focused on the cost difference between IOL and expectant management. Limitations The primary literature on the diagnostic effectiveness of ultrasound in late pregnancy is weak. VoI analysis may have underestimated the uncertainty in the literature as it was focused on the internal validity of parameters, which is quantified, whereas the greatest uncertainty may be in the external validity to the research question, which is unquantified. Conclusions Universal screening for presentation at term may be justified on the basis of current knowledge. Universal screening for fetal growth disorders cannot currently be justified.The National Institute for Health Research Health Technology Assessment programm