A construction of integer-valued polynomials with prescribed sets of lengths of factorizations

For an arbitrary finite set S of natural numbers greater 1, we construct an integer-valued polynomial f, whose set of lengths in Int(Z) is S. The set of lengths of f is the set of all natural numbers n, such that f has a factorization as a product of n irreducibles in Int(Z)={g in Q[x] | g(Z) contained in Z}.Comment: To appear in Monatshefte f\"ur Mathematik; 11 page

Effects of protected areas on survival of threatened gibbons in China

Establishing protected areas (PAs) is an essential strategy to reduce biodiversity loss. However, many PAs do not provide adequate protection due to poor funding, inadequate staffing and equipment, and ineffective management. As part of China's recent economic growth, the Chinese government has significantly increased investment in nature reserves over the past 20 years, providing a unique opportunity to evaluate whether PAs can protect threatened species effectively. We compiled data from published literature on populations of gibbons (Hylobatidae), a threatened taxon with cultural significance, that occurred in Chinese reserves after 1980. We evaluated the ability of these PAs to maintain gibbon habitat and populations by comparing forest cover and human disturbance between reserves and their surrounding areas and modeling the impact of reserve characteristics on gibbon population trends. We also assessed the perspective of reserve staff concerning PA management effectiveness through an online survey. Reserves effectively protected gibbon habitat by reducing forest loss and human disturbance; however, half the reserves lost their gibbon populations since being established. Gibbons were more likely to survive in reserves established more recently, at higher elevation, with less forest loss and lower human impact, and that have been relatively well studied. A larger initial population size in the 1980s was positively associated with gibbon persistence. Although staff of all reserves reported increased investment and improved management over the past 20–30 years, no relationship was found between management effectiveness and gibbon population trends. We suggest early and emphatic intervention is critical to stop population decline and prevent extinction

On the Lawrence–Doniach and Anisotropic Ginzburg–Landau Models for Layered Superconductors

The authors consider two models, the Lawrence-Doniach and the anisotropic Ginzburg-Landau models for layered superconductors such as the recently discovered high-temperature superconductors. A mathematical description of both models is given and existence results for their solution are derived. The authors then relate the two models in the sense that they show that as the layer spacing tends to zero, the Lawrence-Doniach model reduces to the anisotropic Ginzburg- Landau model. Finally, simplified versions of the models are derived that can be used to accurately simulate high-temperature superconductors

On the molecules of numerical semigroups, Puiseux monoids, and Puiseux algebras

A molecule is a nonzero non-unit element of an integral domain (resp., commutative cancellative monoid) having a unique factorization into irreducibles (resp., atoms). Here we study the molecules of Puiseux monoids as well as the molecules of their corresponding semigroup algebras, which we call Puiseux algebras. We begin by presenting, in the context of numerical semigroups, some results on the possible cardinalities of the sets of molecules and the sets of reducible molecules (i.e., molecules that are not irreducibles/atoms). Then we study the molecules in the more general context of Puiseux monoids. We construct infinitely many non-isomorphic atomic Puiseux monoids all whose molecules are atoms. In addition, we characterize the molecules of Puiseux monoids generated by rationals with prime denominators. Finally, we turn to investigate the molecules of Puiseux algebras. We provide a characterization of the molecules of the Puiseux algebras corresponding to root-closed Puiseux monoids. Then we use such a characterization to find an infinite class of Puiseux algebras with infinitely many non-associated reducible molecules.Comment: 21 pages, 2 figure

Beating the classical limits of information transmission using a quantum decoder

© 2018 American Physical Society. Encoding schemes and error-correcting codes are widely used in information technology to improve the reliability of data transmission over real-world communication channels. Quantum information protocols can further enhance the performance in data transmission by encoding a message in quantum states; however, most proposals to date have focused on the regime of a large number of uses of the noisy channel, which is unfeasible with current quantum technology. We experimentally demonstrate quantum enhanced communication over an amplitude damping noisy channel with only two uses of the channel per bit and a single entangling gate at the decoder. By simulating the channel using a photonic interferometric setup, we experimentally increase the reliability of transmitting a data bit by greater than 20% for a certain damping range over classically sending the message twice. We show how our methodology can be extended to larger systems by simulating the transmission of a single bit with up to eight uses of the channel and a two-bit message with three uses of the channel, predicting a quantum enhancement in all cases

Redshifted emission lines and radiative recombination continuum from the Wolf-Rayet binary theta Muscae: evidence for a triplet system?

We present XMM-Newton observations of the WC binary Theta Muscae (WR 48), the second brightest Wolf-Rayet binary in optical wavelengths. The system consists of a short-period (19.1375 days) WC5/WC6 + O6/O7V binary and possibly has an additional O supergiant companion (O9.5/B0Iab) which is optically identified at a separation of ~46 mas. Strong emission lines from highly ionized ions of C, O, Ne, Mg, Si, S, Ar, Ca and Fe are detected. The spectra are fitted by a multi-temperature thin-thermal plasma model with an interstellar absorption N_H = 2--3*10**21 cm**-2. Lack of nitrogen line indicates that the abundance of carbon is at least an order of magnitude larger than that of nitrogen. A Doppler shift of ~630 km/s is detected for the OVIII line, while similar shifts are obtained from the other lines. The reddening strongly suggests that the emission lines originated from the wind-wind shock zone, where the average velocity is ~600 km/s. The red-shift motion is inconsistent with a scenario in which the X-rays originate from the wind-wind collision zone in the short-period binary, and would be evidence supporting the widely separated O supergiant as a companion. This may make up the collision zone be lying behind the short-period binary. In addition to the emission lines, we also detected the RRC (radiative recombination continuum) structure from carbon around 0.49 keV. This implies the existence of additional cooler plasma.Comment: 6 pages, 4 figures, accepted to A&

Ensuring an Essential Supply of Allied Health Professions (AHP) Placements: Using Crowdsourcing to Develop a National Call to Action

Sustainable growth in the Allied Health Professions (AHP) workforce is an ambition of the United Kingdom’s NHS Long Term Plan. However historically, access to good quality placements has been a barrier to increasing pre-registration training numbers. This article focuses on work carried out by Health Education England (HEE) to gain insights on the impact of the COVID-19 pandemic on capacity. Using a pragmatic, embedded mixed-methods approach, insights were gathered using an online workshop, crowdsourcing, open for two weeks in the summer of 2020. AHP placement stakeholders could vote, share ideas or comment. Descriptive data were extracted, and comments made were analysed using inductive thematic analysis. Participants (N = 1,800) made over 8,500 comments. The themes identified included: diversity of placement opportunity, improved placement coordination, a more joined-up system, supervision models and educator capacity. Alongside considering the challenges to placement capacity, several areas of innovative practice owing to the pandemic were highlighted. Generated insights have shaped the aims and objectives of the Health Education (HEE) pre-registration AHP student practice learning programme for 2020/2021 and beyond. The COVID-19 pandemic has disrupted the delivery of AHP placements. In the absence of face-to-face activities, crowdsourcing provided an online data collection tool offering stakeholders an opportunity to engage with the placement capacity agenda and share learning. Findings have shaped the HEE approach to short-term placement recovery and long-term growth

The Uncertainty in Newton's Constant and Precision Predictions of the Primordial Helium Abundance

The current uncertainty in Newton's constant, G_N, is of the order of 0.15%. For values of the baryon to photon ratio consistent with both cosmic microwave background observations and the primordial deuterium abundance, this uncertainty in G_N corresponds to an uncertainty in the primordial 4He mass fraction, Y_P, of +-1.3 x 10^{-4}. This uncertainty in Y_P is comparable to the effect from the current uncertainty in the neutron lifetime, which is often treated as the dominant uncertainty in calculations of Y_P. Recent measurements of G_N seem to be converging within a smaller range; a reduction in the estimated error on G_N by a factor of 10 would essentially eliminate it as a source of uncertainty in the calculation of the primordial 4He abundance.Comment: 3 pages, no figures, fixed typos, to appear in Phys. Rev.

The MrCYP52 Cytochrome P450 Monoxygenase Gene of Metarhizium robertsii Is Important for Utilizing Insect Epicuticular Hydrocarbons

Fungal pathogens of plants and insects infect their hosts by direct penetration of the cuticle. Plant and insect cuticles are covered by a hydrocarbon-rich waxy outer layer that represents the first barrier against infection. However, the fungal genes that underlie insect waxy layer degradation have received little attention. Here we characterize the single cytochrome P450 monoxygenase family 52 (MrCYP52) gene of the insect pathogen Metarhizium robertsii, and demonstrate that it encodes an enzyme required for efficient utilization of host hydrocarbons. Expressing a green florescent protein gene under control of the MrCYP52 promoter confirmed that MrCYP52 is up regulated on insect cuticle as well as by artificial media containing decane (C10), extracted cuticle hydrocarbons, and to a lesser extent long chain alkanes. Disrupting MrCYP52 resulted in reduced growth on epicuticular hydrocarbons and delayed developmental processes on insect cuticle, including germination and production of appressoria (infection structures). Extraction of alkanes from cuticle prevented induction of MrCYP52 and reduced growth. Insect bioassays against caterpillars (Galleria mellonella) confirmed that disruption of MrCYP52 significantly reduces virulence. However, MrCYP52 was dispensable for normal germination and appressorial formation in vitro when the fungus was supplied with nitrogenous nutrients. We conclude therefore that MrCYP52 mediates degradation of epicuticular hydrocarbons and these are an important nutrient source, but not a source of chemical signals that trigger infection processes