Continued fractions for some transcendental numbers

We consider series of the form $p/q + \sum_{j=2}^\infty 1/x_j$, where $x_1=q$ and the integer sequence $x_n$ satisfies a certain non-autonomous recurrence of second order, which entails that $x_n|x_{n+1}$ for n?1. It is shown that the terms of the sequence, and multiples of the ratios of successive terms, appear interlaced in the continued fraction expansion of the sum of the series, which is a transcendental number

Use of molecular genetics and historical records to reconstruct the history of local communities

Recent advances in molecular genetics made the inference of past demographic events through the analysis of gene pools from modern populations possible. The technology uses genetic markers toprovide previously unavailable resolution into questions of human evolution, migration and the historical relationship of separated human populations. Some of the genetic markers used to measurevariation (polymorphism) within populations are found in the Y-chromosome and mitochondrial DNA. Variations in these two types of DNA can be grouped into continent-specific haplogroups or lineages.Geographic origin can be assigned to each lineage, and consequently trace back migration pattern of human populations. Y-chromosome and mitochondrial DNA are used to construct paternal and maternal lineages respectively. The use of these molecular techniques together with historical records in an integrated manner can greatly benefit the study of the social history of admixed communities, such as the Cape Muslim community living in the Western Cape of South Africa

Prevention is better than cure, but...: Preventive medication as a risk to ordinariness?

Preventive health remains at the forefront of public health concerns; recent initiatives, such as the NHS health check, may lead to recommendations for medication in response to the identification of 'at risk' individuals. Little is known about lay views of preventive medication. This paper uses the case of aspirin as a prophylactic against heart disease to explore views among people invited to screening for a trial investigating the efficacy of such an approach. Qualitative interviews (N=46) and focus groups (N=5, participants 31) revealed dilemmas about preventive medication in the form of clashes between norms: first, in general terms, assumptions about the benefit of prevention were complicated by dislike of medication; second, the individual duty to engage in prevention was complicated by the need not to be over involved with one's own health; third, the potential appeal of this alternative approach to health promotion was complicated by unease about the implications of encouraging irresponsible behaviour among others. Though respondents made different decisions about using the drug, they reported very similar ways of trying to resolve these conflicts, drawing upon concepts of necessity and legitimisation and the special ordinariness of the particular dru

Probability Models for Degree Distributions of Protein Interaction Networks

The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional form contains important clues as to underlying evolutionary processes that have shaped the network. Generally, the functional form for the degree distribution has been determined in an ad-hoc fashion, with clear power-law like behaviour often only extending over a limited range of connectivities. Here we apply formal model selection techniques to decide which probability distribution best describes the degree distributions of protein interaction networks. Contrary to previous studies this well defined approach suggests that the degree distribution of many molecular networks is often better described by distributions other than the popular power-law distribution. This, in turn, suggests that simple, if elegant, models may not necessarily help in the quantitative understanding of complex biological processes.

Towards More Accurate Molecular Dynamics Calculation of Thermal Conductivity. Case Study: GaN Bulk Crystals

Significant differences exist among literature for thermal conductivity of various systems computed using molecular dynamics simulation. In some cases, unphysical results, for example, negative thermal conductivity, have been found. Using GaN as an example case and the direct non-equilibrium method, extensive molecular dynamics simulations and Monte Carlo analysis of the results have been carried out to quantify the uncertainty level of the molecular dynamics methods and to identify the conditions that can yield sufficiently accurate calculations of thermal conductivity. We found that the errors of the calculations are mainly due to the statistical thermal fluctuations. Extrapolating results to the limit of an infinite-size system tend to magnify the errors and occasionally lead to unphysical results. The error in bulk estimates can be reduced by performing longer time averages using properly selected systems over a range of sample lengths. If the errors in the conductivity estimates associated with each of the sample lengths are kept below a certain threshold, the likelihood of obtaining unphysical bulk values becomes insignificant. Using a Monte-Carlo approach developed here, we have determined the probability distributions for the bulk thermal conductivities obtained using the direct method. We also have observed a nonlinear effect that can become a source of significant errors. For the extremely accurate results presented here, we predict a [0001] GaN thermal conductivity of 185 $\rm{W/K \cdot m}$ at 300 K, 102 $\rm{W/K \cdot m}$ at 500 K, and 74 $\rm{W/K \cdot m}$ at 800 K. Using the insights obtained in the work, we have achieved a corresponding error level (standard deviation) for the bulk (infinite sample length) GaN thermal conductivity of less than 10 $\rm{W/K \cdot m}$, 5 $\rm{W/K \cdot m}$, and 15 $\rm{W/K \cdot m}$ at 300 K, 500 K, and 800 K respectively

Statistical Mechanics of Two-dimensional Foams

The methods of statistical mechanics are applied to two-dimensional foams under macroscopic agitation. A new variable -- the total cell curvature -- is introduced, which plays the role of energy in conventional statistical thermodynamics. The probability distribution of the number of sides for a cell of given area is derived. This expression allows to correlate the distribution of sides ("topological disorder") to the distribution of sizes ("geometrical disorder") in a foam. The model predictions agree well with available experimental data

Dynamic Energy Management

We present a unified method, based on convex optimization, for managing the power produced and consumed by a network of devices over time. We start with the simple setting of optimizing power flows in a static network, and then proceed to the case of optimizing dynamic power flows, i.e., power flows that change with time over a horizon. We leverage this to develop a real-time control strategy, model predictive control, which at each time step solves a dynamic power flow optimization problem, using forecasts of future quantities such as demands, capacities, or prices, to choose the current power flow values. Finally, we consider a useful extension of model predictive control that explicitly accounts for uncertainty in the forecasts. We mirror our framework with an object-oriented software implementation, an open-source Python library for planning and controlling power flows at any scale. We demonstrate our method with various examples. Appendices give more detail about the package, and describe some basic but very effective methods for constructing forecasts from historical data.Comment: 63 pages, 15 figures, accompanying open source librar

Magnetic effects in a holographic Fermi-like liquid

We explore the magnetic properties of the Fermi-like liquid represented by the D3-D7' system. The system exhibits interesting magnetic properties such as ferromagnetism and an anomalous Hall effect, which are due to the Chern-Simons term in the effective gravitational action. We investigate the spectrum of quasi-normal modes in the presence of a magnetic field and show that the magnetic field mitigates the instability towards a striped phase. In addition, we find a critical magnetic field above which the zero sound mode becomes massive.Comment: 18 pages, 15 figure