The pulsar spectral index distribution

The flux density spectra of radio pulsars are known to be steep and, to first order, described by a power-law relationship of the form S_{\nu} \propto \nu^{\alpha}, where S_{\nu} is the flux density at some frequency \nu and \alpha is the spectral index. Although measurements of \alpha have been made over the years for several hundred pulsars, a study of the intrinsic distribution of pulsar spectra has not been carried out. From the result of pulsar surveys carried out at three different radio frequencies, we use population synthesis techniques and a likelihood analysis to deduce what underlying spectral index distribution is required to replicate the results of these surveys. We find that in general the results of the surveys can be modelled by a Gaussian distribution of spectral indices with a mean of -1.4 and unit standard deviation. We also consider the impact of the so-called "Gigahertz-peaked spectrum" pulsars. The fraction of peaked spectrum sources in the population with significant turn-over at low frequencies appears to be at most 10%. We demonstrate that high-frequency (>2 GHz) surveys preferentially select flatter-spectrum pulsars and the converse is true for lower-frequency (<1 GHz) surveys. This implies that any correlations between \alpha and other pulsar parameters (for example age or magnetic field) need to carefully account for selection biases in pulsar surveys. We also expect that many known pulsars which have been detected at high frequencies will have shallow, or positive, spectral indices. The majority of pulsars do not have recorded flux density measurements over a wide frequency range, making it impossible to constrain their spectral shapes. We also suggest that such measurements would allow an improved description of any populations of pulsars with 'non-standard' spectra.Comment: 8 pages, 5 figures. Accepted by MNRA

Emergence of steady and oscillatory localized structures in a phytoplankton-nutrient model

Co-limitation of marine phytoplankton growth by light and nutrient, both of which are essential for phytoplankton, leads to complex dynamic behavior and a wide array of coherent patterns. The building blocks of this array can be considered to be deep chlorophyll maxima, or DCMs, which are structures localized in a finite depth interior to the water column. From an ecological point of view, DCMs are evocative of a balance between the inflow of light from the water surface and of nutrients from the sediment. From a (linear) bifurcational point of view, they appear through a transcritical bifurcation in which the trivial, no-plankton steady state is destabilized. This article is devoted to the analytic investigation of the weakly nonlinear dynamics of these DCM patterns, and it has two overarching themes. The first of these concerns the fate of the destabilizing stationary DCM mode beyond the center manifold regime. Exploiting the natural singularly perturbed nature of the model, we derive an explicit reduced model of asymptotically high dimension which fully captures these dynamics. Our subsequent and fully detailed study of this model - which involves a subtle asymptotic analysis necessarily transgressing the boundaries of a local center manifold reduction - establishes that a stable DCM pattern indeed appears from a transcritical bifurcation. However, we also deduce that asymptotically close to the original destabilization, the DCM looses its stability in a secondary bifurcation of Hopf type. This is in agreement with indications from numerical simulations available in the literature. Employing the same methods, we also identify a much larger DCM pattern. The development of the method underpinning this work - which, we expect, shall prove useful for a larger class of models - forms the second theme of this article

Finite to infinite steady state solutions, bifurcations of an integro-differential equation

We consider a bistable integral equation which governs the stationary solutions of a convolution model of solid--solid phase transitions on a circle. We study the bifurcations of the set of the stationary solutions as the diffusion coefficient is varied to examine the transition from an infinite number of steady states to three for the continuum limit of the semi--discretised system. We show how the symmetry of the problem is responsible for the generation and stabilisation of equilibria and comment on the puzzling connection between continuity and stability that exists in this problem

Longtime behavior of nonlocal Cahn-Hilliard equations

Here we consider the nonlocal Cahn-Hilliard equation with constant mobility in a bounded domain. We prove that the associated dynamical system has an exponential attractor, provided that the potential is regular. In order to do that a crucial step is showing the eventual boundedness of the order parameter uniformly with respect to the initial datum. This is obtained through an Alikakos-Moser type argument. We establish a similar result for the viscous nonlocal Cahn-Hilliard equation with singular (e.g., logarithmic) potential. In this case the validity of the so-called separation property is crucial. We also discuss the convergence of a solution to a single stationary state. The separation property in the nonviscous case is known to hold when the mobility degenerates at the pure phases in a proper way and the potential is of logarithmic type. Thus, the existence of an exponential attractor can be proven in this case as well

On the spectral properties of L_{+-} in three dimensions

This paper is part of the radial asymptotic stability analysis of the ground state soliton for either the cubic nonlinear Schrodinger or Klein-Gordon equations in three dimensions. We demonstrate by a rigorous method that the linearized scalar operators which arise in this setting, traditionally denoted by L_{+-}, satisfy the gap property, at least over the radial functions. This means that the interval (0,1] does not contain any eigenvalues of L_{+-} and that the threshold 1 is neither an eigenvalue nor a resonance. The gap property is required in order to prove scattering to the ground states for solutions starting on the center-stable manifold associated with these states. This paper therefore provides the final installment in the proof of this scattering property for the cubic Klein-Gordon and Schrodinger equations in the radial case, see the recent theory of Nakanishi and the third author, as well as the earlier work of the third author and Beceanu on NLS. The method developed here is quite general, and applicable to other spectral problems which arise in the theory of nonlinear equations

Transforming Pharmacy and Pharmaceutical Sciences Education in the Context of Workforce Development

KEY MESSAGES: 1.1 The continued development of pharmacy services and the pharmaceutical sciences relies on a well educated, competent, sufficient and well distributed pharmaceutical workforce. 1.2 There is no workforce without education. It is fundamental for the international community to agree on how pharmaceutical workforce competency is developed and assured through initial and subsequent professional education. 1.3 The concept of a continuously competent workforce is of fundamental interest for professional leadership bodies and stakeholders. 1.4 As FIP member organisations drive the development of the profession at the national level, they should always consider encompassing an education component [initial education and Continuing Professional Development (CPD)/Continuing Education (CE)] into their strategies. 1.5 FIP brought together global health and pharmacy leaders from across the world to set the future milestones for pharmaceutical education in the context of workforce development during an exceptional event, which took place in Nanjing, China, on 7 and 8 November 2016: the Global Conference on Pharmacy and Pharmaceutical Sciences Education — "Creating a global vision for a global workforce". 1.6 The conference set the future milestones for education and workforce development of pharmacists and pharmaceutical scientists, and created a global vision for transformative pharmacy and pharmaceutical sciences education. 2. PRINCIPAL OUTCOMES: Following extensive consultation, three milestone documents were presented and adopted at the global conference. Participants at the conference were able to influence and contribute to them. These are: 2.1 A Global Vision for Education and Workforce that provides a description of the future directions of our profession and how education can support the evolution of science and practice. 2.2 A set of 13 Pharmaceutical Workforce Development Goals (PWDGs) which aim to facilitate the implementation of the global vision through a series of measurable, feasible and tangible goals. 2.3 A set of 67 statements on Pharmacy and Pharmaceutical Sciences Education ("the Nanjing Statements") that describe an envisioned future for education, to enable the enhancement of professional education standards worldwide

Genotype imputation accuracy in a F2 pig population using high density and low density SNP panels

Background: F2 resource populations have been used extensively to map QTL segregating between pig breeds. A limitation associated with the use of these resource populations for fine mapping of QTL is the reduced number of founding individuals and recombinations of founding haplotypes occurring in the population. These limitations, however, become advantageous when attempting to impute unobserved genotypes using within family segregation information. A trade-off would be to re-type F2 populations using high density SNP panels for founding individuals and low density panels (tagSNP) in F2 individuals followed by imputation. Subsequently a combined meta-analysis of several populations would provide adequate power and resolution for QTL mapping, and could be achieved at relatively low cost. Such a strategy allows the wealth of phenotypic information that has previously been obtained on experimental resource populations to be further mined for QTL identification. In this study we used experimental and simulated high density genotypes (HD-60K) from an F2 cross to estimate imputation accuracy under several genotyping scenarios. Results: Selection of tagSNP using physical distance or linkage disequilibrium information produced similar imputation accuracies. In particular, tagSNP sets averaging 1 SNP every 2.1 Mb (1,200 SNP genome-wide) yielded imputation accuracies (IA) close to 0.97. If instead of using custom panels, the commercially available 9K chip is used in the F2, IA reaches 0.99. In order to attain such high imputation accuracy the F0 and F1 generations should be genotyped at high density. Alternatively, when only the F0 is genotyped at HD, while F1 and F2 are genotyped with a 9K panel, IA drops to 0.90. Conclusions: Combining 60K and 9K panels with imputation in F2 populations is an appealing strategy to re-genotype existing populations at a fraction of the cost.Fil: Gualdron Duarte, Jose Luis. Michigan State University; Estados Unidos. Universidad de Buenos Aires. Facultad de Agronomia. Departamento de Producción Animal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Bates, Ronald O.. Michigan State University; Estados UnidosFil: Ernst, Catherine W.. Michigan State University; Estados UnidosFil: Raney, Nancy E.. Michigan State University; Estados UnidosFil: Cantet, Rodolfo Juan Carlos. Universidad de Buenos Aires. Facultad de Agronomia. Departamento de Producción Animal; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Steibel, Juan P.. Michigan State University; Estados Unido

Bulk phase behaviour of binary hard platelet mixtures from density functional theory

We investigate isotropic-isotropic, isotropic-nematic and nematic-nematic phase coexistence in binary mixtures of circular platelets with vanishing thickness, continuous rotational degrees of freedom and radial size ratios $\lambda$ up to 5. A fundamental measure density functional theory, previously used for the one-component model, is proposed and results are compared against those from Onsager theory as a benchmark. For $\lambda \leq 1.7$ the system displays isotropic-nematic phase coexistence with a widening of the biphasic region for increasing values of $\lambda$. For size ratios $\lambda \geq 2$, we find demixing into two nematic states becomes stable and an isotropic-nematic-nematic triple point can occur. Fundamental measure theory gives a smaller isotropic-nematic biphasic region than Onsager theory and locates the transition at lower densities. Furthermore, nematic-nematic demixing occurs over a larger range of compositions at a given value of $\lambda$ than found in Onsager theory. Both theories predict the same topologies of the phase diagrams. The partial nematic order parameters vary strongly with composition and indicate that the larger particles are more strongly ordered than the smaller particles

Machines on Genes: Enzymes that Make, Break and Move DNA and RNA

As the vital information repositories of the cell, the nucleic acids DNA and RNA pose many challenges as enzyme substrates. To produce, maintain and repair DNA and RNA, and to extract the genetic information that they encode, a battery of remarkable enzymes has evolved, which includes translocases, polymerases/replicases, helicases, nucleases, topoisomerases, transposases, recombinases, repair enzymes and ribosomes. An understanding of how these enzymes function is essential if we are to have a clear view of the molecular biology of the cell and aspire to manipulate genomes and gene expression to our advantage. To bring together scientists working in this fast-developing field, the Biochemical Society held a Focused Meeting, ‘Machines on Genes: Enzymes that Make, Break and Move DNA and RNA’, at Robinson College, University of Cambridge, U.K., in August 2009. The present article summarizes the research presented at this meeting and the reviews associated with the talks which are published in this issue of Biochemical Society Transactions