Salem numbers and Pisot numbers via interlacing

We present a general construction of Salem numbers via rational functions whose zeros and poles mostly lie on the unit circle and satisfy an interlacing condition. This extends and unifies earlier work. We then consider the "obvious" limit points of the set of Salem numbers produced by our theorems, and show that these are all Pisot numbers, in support of a conjecture of Boyd. We then show that all Pisot numbers arise in this way. Combining this with a theorem of Boyd, we show that all Salem numbers are produced via an interlacing construction.Comment: 21 pages, 5 figures, updated in response to reviewer comment

Installing the "magic methyl" - C-H methylation in synthesis

The selective and efficient C-H methylation of sp2 and sp3 carbon centres has become a powerful transformation in the synthetic toolbox. Due to the potential for profound changes to physicochemical properties attributed to the installation of a "Magic Methyl" group at a strategic site in a lead compound, such techniques have become highly desirable in modern drug discovery and synthesis programmes. This review will cover the diverse techniques that have been employed to enable the selective installation of the C-Me bond in a wide range of chemical structures, from simple building blocks to complex drug-like architectures

Validation of Dunbar's number in Twitter conversations

Modern society's increasing dependency on online tools for both work and recreation opens up unique opportunities for the study of social interactions. A large survey of online exchanges or conversations on Twitter, collected across six months involving 1.7 million individuals is presented here. We test the theoretical cognitive limit on the number of stable social relationships known as Dunbar's number. We find that users can entertain a maximum of 100-200 stable relationships in support for Dunbar's prediction. The "economy of attention" is limited in the online world by cognitive and biological constraints as predicted by Dunbar's theory. Inspired by this empirical evidence we propose a simple dynamical mechanism, based on finite priority queuing and time resources, that reproduces the observed social behavior.Comment: 8 pages, 6 figure

Theoretical and Phenomenological Constraints on Form Factors for Radiative and Semi-Leptonic B-Meson Decays

We study transition form factors for radiative and rare semi-leptonic B-meson decays into light pseudoscalar or vector mesons, combining theoretical constraints and phenomenological information from Lattice QCD, light-cone sum rules, and dispersive bounds. We pay particular attention to form factor parameterisations which are based on the so-called series expansion, and study the related systematic uncertainties on a quantitative level. In this context, we also provide the NLO corrections to the correlation function between two flavour-changing tensor currents, which enters the unitarity constraints for the coefficients in the series expansion.Comment: 52 pages; v2: normalization error in (29ff.) corrected, conclusion about relevance of unitarity bounds modified; form factor fits unaffected; references added; v3: discussion on truncation of series expansion added, matches version to be published in JHEP; v4: corrected typos in Tables 5 and

Mammographic density, lobular involution, and risk of breast cancer

In this review, we propose that age-related changes in mammographic density and breast tissue involution are closely related phenomena, and consider their potential relevance to the aetiology of breast cancer. We propose that the reduction in mammographic density that occurs with increasing age, parity and menopause reflects the involution of breast tissue. We further propose that age-related changes in both mammographic density and breast tissue composition are observable and measurable phenomena that resemble Pike's theoretical construct of ‘breast tissue ageing'. Extensive mammographic density and delayed breast involution are both associated with an increased risk of breast cancer and are consistent with the hypothesis of the Pike model that cumulative exposure of breast tissue to hormones and growth factors that stimulate cell division, as well as the accumulation of genetic damage in breast cells, are major determinants of breast cancer incidence

The prenatal ultrasonographic detection of myelomeningocele in patients referred to Children's Hospital Medical Center: a cross sectional study

BACKGROUND: To find out about the prenatal diagnosis rate of myelomeningocele (MMC) by ultrasound scan in patients referred to the Children's Hospital Medical Center in Tehran, Iran from July 2004 to July 2005. METHODS: We included 140 children born with MMC and who were referred for management, surgery and treatment of complications associated with it. The ultrasound reports were examined. Data on sex, age, location of MMC, time of prenatal ultrasound and the trimester in which the diagnosis was made along with the results of the diagnosis (MMC, hydrocephalus, or both), were collected. RESULTS: Among the studied patients, 136 (97.1%) cases had prenatal ultrasound, amongst those, 58 (42.6%) sonographic evaluations were diagnostic for hydrocephalus and/or MMC. The prenatal ultrasound was positive for MMC in 16 (11.8%), hydrocephalus in 25 (18.4%) and both MMC and hydrocephalus in 17 (12.5%) cases. Among all cases with prenatal diagnosis of MMC, 3.4% were detected in the first, 31% in the second and 65.5% in the third trimester. Thoracic/thoracolumbar lesions were found prenatally in 40% of cases, which is significantly higher than the detection rate of other locations including cervical/cervicothoracic and lumbar/lumbosacral/sacral regions diagnosed only in 0% and 21% of cases respectively. CONCLUSION: There is a large difference between the detection rate of our population (24.3%) compared to others (68%). Pregnant women should have an ultrasound at 20–22 week for detection of congenital anomalies including MMC

Background risk of breast cancer and the association between physical activity and mammographic density

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The role of TcdB and TccC subunits in secretion of the photorhabdus Tcd toxin complex

The Toxin Complex (TC) is a large multi-subunit toxin encoded by a range of bacterial pathogens. The best-characterized examples are from the insect pathogens Photorhabdus, Xenorhabdus and Yersinia. They consist of three large protein subunits, designated A, B and C that assemble in a 5:1:1 stoichiometry. Oral toxicity to a range of insects means that some have the potential to be developed as pest control technology. The three subunit proteins do not encode any recognisable export sequences and as such little progress has been made in understanding their secretion. We have developed heterologous TC production and secretion models in E. coli and used them to ascribe functions to different domains of the crucial B+C sub-complex. We have determined that the B and C subunits use a secretion mechanism that is either encoded by the proteins themselves or employ an as yet undefined system common to laboratory strains of E. coli. We demonstrate that both the N-terminal domains of the B and C subunits are required for secretion of the whole complex. We propose a model whereby the N-terminus of the C-subunit toxin exports the B+C sub-complex across the inner membrane while that of the B-subunit allows passage across the outer membrane. We also demonstrate that even in the absence of the B-subunit, that the C-subunit can also facilitate secretion of the larger A-subunit. The recognition of this novel export system is likely to be of importance to future protein secretion studies. Finally, the identification of homologues of B and C subunits in diverse bacterial pathogens, including Burkholderia and Pseudomonas, suggests that these toxins are likely to be important in a range of different hosts, including man

Electromagnetically Induced Transparency and Slow Light with Optomechanics

Controlling the interaction between localized optical and mechanical excitations has recently become possible following advances in micro- and nano-fabrication techniques. To date, most experimental studies of optomechanics have focused on measurement and control of the mechanical subsystem through its interaction with optics, and have led to the experimental demonstration of dynamical back-action cooling and optical rigidity of the mechanical system. Conversely, the optical response of these systems is also modified in the presence of mechanical interactions, leading to strong nonlinear effects such as Electromagnetically Induced Transparency (EIT) and parametric normal-mode splitting. In atomic systems, seminal experiments and proposals to slow and stop the propagation of light, and their applicability to modern optical networks, and future quantum networks, have thrust EIT to the forefront of experimental study during the last two decades. In a similar fashion, here we use the optomechanical nonlinearity to control the velocity of light via engineered photon-phonon interactions. Our results demonstrate EIT and tunable optical delays in a nanoscale optomechanical crystal device, fabricated by simply etching holes into a thin film of silicon (Si). At low temperature (8.7 K), we show an optically-tunable delay of 50 ns with near-unity optical transparency, and superluminal light with a 1.4 microseconds signal advance. These results, while indicating significant progress towards an integrated quantum optomechanical memory, are also relevant to classical signal processing applications. Measurements at room temperature and in the analogous regime of Electromagnetically Induced Absorption (EIA) show the utility of these chip-scale optomechanical systems for optical buffering, amplification, and filtering of microwave-over-optical signals.Comment: 15 pages, 9 figure