Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences.Comment: 25 page

Preterm labour - Is Mycoplasma hominis involved?

Objective. To assess whether Mycoplasma hominis is associated with preterm labour in primigravidae  and multigravidae with previous midtrimester abortion or preterm labour.Design. Cohort analytical study. Setting. Tygerberg Hospital, a tertiary academic hospital in the Western Cape.Methods. Gram's stains were done on smears taken from the posterior vaginal fornix, at the first  antenatal visit, between 16 and 26 weeks' gestation, in primigravidae and multigravidae at risk for preterm labour. Cultures for M. hominis and other commonly occurring organisms were done ·from endocervical swabs taken at the same visit. The outcome of pregnancy in mothers with positive cultures for M. hominis was then compared with outcome in women with negative cultures.Outcome measures. Prevalence of Chlamydia trachomatis, Ureaplasma urealyticum, bacterial vaginosis and preterm delivery, birth weight and perinatal deaths.Results. Cultures for M. hominis were positive in 83 patients  (21 %) and negative in 312 (79%).  Significantly more mothers in the positive group (40%) delivered before 37 weeks' gestation than in the negative group (28%, P = 0.0313). Their babies weighed significantly less (2 669 g v. 2 864 g, P = 0.0141). The positive group was also associated with more alcohol use in pregnancy and fewer of them  were married. C. trachomatis was found in 18% of mothers in the positive group but in 8% of the negative group (P = 0.0082). U. urealyticum was cultured in 96% of mothers in the positive group in contrast to 81 % in the negative group (P = 0.001). Bacterial vaginosis was observed on 75% of mothers  with positive cultures for M. hominis but in 22% with negative cultures (P = 0.00001, odds ratio 10.21, 95% confidence interval: 5.63 - 18.65). Conclusion. Positive culture for M. hominis was associated with more preterm deliveries and also with a higher frequency of C. trachomatis, U. urealyticum and bacterial vaginosis

The mission oriented terminal area simulation facility

The Mission Oriented Terminal Area Simulation (MOTAS) was developed to provide an ATC environment in which flight management and flight operations research studies can be conducted with a high degree of realism. This facility provides a flexible and comprehensive simulation of the airborne, ground-based and communication aspects of the airport terminal area environment. Major elements of the simulation are: an airport terminal area environment model, two air traffic controller stations, several aircraft models and simulator cockpits, four pseudo pilot stations, and a realistic air-ground communications network. MOTAS has been used for one study with the DC-9 simulator and a series of data link studies are planned in the near future

Preterm labour - is bacterial vaginosis involved?

Objective. To assess the efficacy of treatment of bacterial vaginosis (BV) using metronidazole to reduce  preterm labour in primiravidae and multigravidae with previous midtrimester abortion or preterm labour.Design. Randomised controlled trial.Setting. Tertiary academic hospital.Method. Two different groups of patients were screened for BV at the first antenatal visit, namely  primigravidae and high-risk multigravidae who had had a previous midtrimester abortion or preterm delivery. Patients where BV was diagnosed clinically or on Gram's stain of a smear taken from the posterior vaginal fornix, received either 400 mg metronidazole, or 100 mg vitamin C orally twice daily for 2 days. The Gram's stain was repeated after 4 weeks. If BV W?S found again, treatment with the same  drug was repeated.Outcome measures. Preterm delivery, birth weight and perinatal deaths.Results. One thousand and five patients entered the study, but 40 were excluded for various reasons and 10 were lost to follow-up. There were 464 primigravidae, of whom 150 (32%) had BV. Except for the 5-minute Apgar score, no significant differences were found between primigravidae negative for BV and those who received either metronidazole or vitamin C. There were 491 high-risk multigravidae, of whom 127 (26%) had BV. The mean gestational age in the BVnegative group was 37 weeks, in contrast to 37.4 weeks in the vitamin C group and 35.6 weeks in the metronidazole group. Birth weights in these three groups were 2 752 g, 2 759 g and 2 475 g respectively, significantly less (P == 0.0109) in the  metronidazole group in comparison with the BV-negative group. Delivery before 37 weeks occurred in 29% of high-risk multigravidae with no BV but in 24% of those who took  vitamin C and in 43% who took metronidazole. Differences were significant between the BV-negative and metronidazole groups (P = 0.0231) and also between the metrol'.idazole and vitamin C groups (P = 0.0274). Delivery before 28 weeks occurred in 4% of the high-risk multigravidae with no UV but in 10% of those with BV who took metronidazole. The difference was significant (P =0.0430). Analysis for maximum likelihood estimates for preterm labour identified only previous preterm labour or midtrimester abortion as risk factors.Conclusion. Metronidazole does not seem to reduce the prevalence of preterm labour when given for BV before 26 weeks' gestation

Observation of polarization quantum noise of laser radiation in Rb vapor cell

We present experimental study of polarization quantum noise of laser radiation passed through optically think vapor of Rb87. We observe a step-like noise spectrum. We discuss various factor which may result in such noise spectrum and prevent observation of squeezing of quantum fluctuations predicted in Matsko et al. PRA 63, 043814 (2001).Comment: 4 pages, 5 figures. Translated from Russian by I. Novikov

From SICs and MUBs to Eddington

This is a survey of some very old knowledge about Mutually Unbiased Bases (MUB) and Symmetric Informationally Complete POVMs (SIC). In prime dimensions the former are closely tied to an elliptic normal curve symmetric under the Heisenberg group, while the latter are believed to be orbits under the Heisenberg group in all dimensions. In dimensions 3 and 4 the SICs are understandable in terms of elliptic curves, but a general statement escapes us. The geometry of the SICs in 3 and 4 dimensions is discussed in some detail.Comment: 12 pages; from the Festschrift for Tony Sudber

Thermodynamic basis of the concept of "recombination resistances"

The concept of "recombination resistance" introduced by Shockley and Read (Phys. Rev. 87, 835 (1952)) is discussed within the framework of the thermodynamics of irreversible processes ruled by the principle of the minimum rate of entropy production. It is shown that the affinities of recombination processes represent "voltages" in a thermodynamic Ohm-like law where the net rates of recombinations represent the "currents". The quantities thus found allow for the definition of the "dissipated power" which is to be related to the rate of entropy production of the recombination processes dealt with.Comment: Submitted to Phys. Rev.

Histidine switch controlling pH-dependent protein folding and DNA binding in a transcription factor at the core of synthetic network devices

© 2016 The Royal Society of Chemistry. Therapeutic strategies have been reported that depend on synthetic network devices in which a urate-sensing transcriptional regulator detects pathological levels of urate and triggers production or release of urate oxidase. The transcription factor involved, HucR, is a member of the multiple antibiotic resistance (MarR) protein family. We show that protonation of stacked histidine residues at the pivot point of long helices that form the scaffold of the dimer interface leads to reversible formation of a molten globule state and significantly attenuated DNA binding at physiological temperatures. We also show that binding of urate to symmetrical sites in each protein lobe is communicated via the dimer interface. This is the first demonstration of regulation of a MarR family transcription factor by pH-dependent interconversion between a molten globule and a compact folded state. Our data further suggest that HucR may be utilized in synthetic devices that depend on detection of pH changes

Cohomogeneity one manifolds and selfmaps of nontrivial degree

We construct natural selfmaps of compact cohomgeneity one manifolds with finite Weyl group and compute their degrees and Lefschetz numbers. On manifolds with simple cohomology rings this yields in certain cases relations between the order of the Weyl group and the Euler characteristic of a principal orbit. We apply our construction to the compact Lie group SU(3) where we extend identity and transposition to an infinite family of selfmaps of every odd degree. The compositions of these selfmaps with the power maps realize all possible degrees of selfmaps of SU(3).Comment: v2, v3: minor improvement