Analyticity of smooth eigenfunctions and spectral analysis of the Gauss map

We provide a sufficient condition of analyticity of infinitely differentiable eigenfunctions of operators of the form Uf(x) = integral a(x, y) f(b( x, y)) mu(dy) acting on functions f: [u, v] --> C ( evolution operators of one-dimensional dynamical systems and Markov processes have this form). We estimate from below the region of analyticity of the eigenfunctions and apply these results for studying the spectral properties of the Frobenius-Perron operator of the continuous fraction Gauss map. We prove that any infinitely differentiable eigenfunction f of this Frobenius-Perron operator, corresponding to a non-zero eigenvalue admits a (unique) analytic extension to the set C\(-infinity, 1]. Analyzing the spectrum of the Frobenius Perron operator in spaces of smooth functions, we extend significantly the domain of validity of the Mayer and Ropstorff asymptotic formula for the decay of correlations of the Gauss map.

The Effects of Anti-Hypertensive Drugs Evaluated Using Markov Modelling for Northern Ireland Chronic Kidney Disease Patients

The aim of this paper is to use Markov modelling to
investigate survival for particular types of kidney patients
in relation to their exposure to anti-hypertensive treatment
drugs. In order to monitor kidney function an intuitive three
point assessment is proposed through the collection of blood
samples in relation to Chronic Kidney Disease for Northern
Ireland patients. A five state Markov Model was devised
using specific transition probabilities for males and
females over all age groups. These transition probabilities
were then adjusted appropriately using relative risk scores
for the event death for different subgroups of patients. The
model was built using TreeAge software package in order to
explore the effects of anti-hypertensive drugs on patients.

Discretization of highly persistent correlated AR(1) shocks

The finite state Markov-chain approximation methods developed by Tauchen (1986) and Tauchen and Hussey (1991) are widely used in economics, finance and econometrics to solve functional equations in which state variables follow autoregressive processes. For highly persistent processes, the methods require a large number of discrete values for the state variables to produce close approximations which leads to an undesirable reduction in computational speed, especially in a multivariate case. This paper proposes an alternative method of discretizing multivariate autoregressive processes. This method can be treated as an extension of Rouwenhorst's (1995) method which, according to our finding, outperforms the existing methods in the scalar case for highly persistent processes. The new method works well as an approximation that is much more robust to the number of discrete values for a wide range of the parameter space.

In Situ Formation of Micron-Scale Li-Metal Anodes with High Cyclability

Scanning probe microscopy methods have been used to electrodeposit and cycle micron-scale Li anodes deposited electrochemically under nanofabricated Au current collectors. An average Li volume of 5 x 10(8) nm(3) was deposited and cycled with 100% coulombic efficiency for similar to 160 cycles. Integrated charge/discharge values agree with before/after topography, as well as in situ dilatometry, suggesting this is a reliable method to study solid-state electrochemical processes. In this work we illustrate the possibility to deposit highly cyclable nanometer thick Li electrodes by mature SPM and nanofab techniques which can pave the way for inexpensive nanoscale battery arrays. 

Complete framework for efficient characterisation of non-Markovian processes

A non-Markovian process is one that retains `memory' of its past. A systematic understanding of these processes is necessary to fully describe and harness a vast range of complex phenomena; however, no such general characterisation currently exists. This long-standing problem has hindered advances in understanding physical, chemical and biological processes, where often dubious theoretical assumptions are made to render a dynamical description tractable. Moreover, the methods currently available to treat non-Markovian quantum dynamics are plagued with unphysical results, like non-positive dynamics. Here we develop an operational framework to characterise arbitrary non-Markovian quantum processes. We demonstrate the universality of our framework and how the characterisation can be rendered efficient, before formulating a necessary and sufficient condition for quantum Markov processes. Finally, we stress how our framework enables the actual systematic analysis of non-Markovian processes, the understanding of their typicality, and the development of new master equations for the effective description of memory-bearing open-system evolution.

From a ‘borderless world’ to a ‘world of borders’: ‘bringing history back in’

The first part of the paper explores some of the reasons why contemporary border studies understate the full significance of state borders and their global primacy. It is argued that this failing is rooted in a much wider lack of historical reflexivity-a reluctance to acknowledge the historical positioning (the 'where and when') of contemporary border studies themselves. This reluctance encourages a form of pseudohistory, or 'epochal thinking', which disfigures perspective on the present. Among the consequences are (a) exaggerated claims of the novelty of contemporary border change, propped up by poorly substantiated benchmarks in the past; (b) an incapacity to recognise the 'past in the present' as in the various historical deposits of state formation processes; and (c) a failure to recognise the distinctiveness of contemporary state borders and how they differ from other borders in their complexity and globality. The second part of the paper argues for a recalibration of border studies aimed at balancing their spatial emphases with a much greater, and more critical, historical sensitivity. It insists that 'boundedness', and state boundedness in particular, is a variable that must be understood historically. This is illustrated by arguing that a better analysis of contemporary border change means rethinking the crude periodisation which distinguishes the age of empire from the age of nation-states and, in turn, from some putative contemporary era 'beyond nation-states' and their borders.

Discrete Conditional Phase-type models utilising classification trees: Application to modelling health service capacities

Discrete Conditional Phase-type (DC-Ph) models consist of a process component (survival distribution) preceded by a set of related conditional discrete variables. This paper introduces a DC-Ph model where the conditional component is a classification tree. The approach is utilised for modelling health service capacities by better predicting service times, as captured by Coxian Phase-type distributions, interfaced with results from a classification tree algorithm. To illustrate the approach, a case-study within the healthcare delivery domain is given, namely that of maternity services. The classification analysis is shown to give good predictors for complications during childbirth. Based on the classification tree predictions, the duration of childbirth on the labour ward is then modelled as either a two or three-phase Coxian distribution. The resulting DC-Ph model is used to calculate the number of patients and associated bed occupancies, patient turnover, and to model the consequences of changes to risk status.

Electron paramagnetic resonance studies of the neutral nitrogen vacancy in diamond

Despite the numerous experimental and theoretical studies on the negatively charged nitrogen vacancy center (NV-) in diamond and the predictions that the neutral nitrogen vacancy center (NV0) should have an S=1/2 ground state, NV0 has not previously been detected by electron paramagnetic resonance (EPR). We report new EPR data on a trigonal nitrogen-containing defect in diamond with an S=3/2 excited state populated via optical excitation. Analysis of the spin Hamiltonian parameters and the wavelength dependence of the optical excitation leads to assignment of this S=3/2 state to the (4)A(2) excited state of NV0. This identification, together with an examination of the electronic structure of the NV centers in diamond, provides a plausible explanation for the lack of observation (to date) of an EPR signal from the NV0 ground state.

Late-time supernova light curves:The effect of internal conversion and auger electrons

Energy release from radioactive decays contributes significantly to supernova light curves. Previous works, which considered the energy deposited by ?-rays and positrons produced by Ni, Co, Ni, Co, Ti and Sc, have been quite successful in explaining the light curves of both core collapse and thermonuclear supernovae. We point out that Auger and internal conversion electrons, together with the associated X-ray cascade, constitute an additional heat source. When a supernova is transparent to ?-rays, these electrons can contribute significantly to light curves for reasonable nucleosynthetic yields. In particular, the electrons emitted in the decay of Co, which are largely due to internal conversion from a fortuitously low-lying 3/2 state in the daughter Fe, constitute an additional significant energy-deposition channel. We show that when the heating by these electrons is accounted for, a slow-down in the light curve of SN 1998bw is naturally obtained for typical hypernova nucleosynthetic yields. Additionally, we show that for generic Type Ia supernova yields, the Auger electrons emitted in the ground-state to ground-state electron capture decay of Fe exceed the energy released by the Ti decay chain for many years after the explosion. © 2009 RAS.

COMPUTATION OF SYNTHETIC SPECTRA FROM SIMULATIONS OF RELATIVISTIC SHOCKS

Particle-in-cell (PIC) simulations of relativistic shocks are in principle capable of predicting the spectra of photons that are radiated incoherently by the accelerated particles. The most direct method evaluates the spectrum using the fields given by the Lienard-Wiechart potentials. However, for relativistic particles this procedure is computationally expensive. Here we present an alternative method that uses the concept of the photon formation length. The algorithm is suitable for evaluating spectra both from particles moving in a specific realization of a turbulent electromagnetic field or from trajectories given as a finite, discrete time series by a PIC simulation. The main advantage of the method is that it identifies the intrinsic spectral features and filters out those that are artifacts of the limited time resolution and finite duration of input trajectories.

A Cross-Layer Optimized Scheme and Its Application in Mobile Multimedia Networks with QoS Provision

To cope with the rapid growth of multimedia applications that requires dynamic levels of quality of service (QoS), cross-layer (CL) design, where multiple protocol layers are jointly combined, has been considered to provide diverse QoS provisions for mobile multimedia networks. However, there is a lack of a general mathematical framework to model such CL scheme in wireless networks with different types of multimedia classes. In this paper, to overcome this shortcoming, we therefore propose a novel CL design for integrated real-time/non-real-time traffic with strict preemptive priority via a finite-state Markov chain. The main strategy of the CL scheme is to design a Markov model by explicitly including adaptive modulation and coding at the physical layer, queuing at the data link layer, and the bursty nature of multimedia traffic classes at the application layer. Utilizing this Markov model, several important performance metrics in terms of packet loss rate, delay, and throughput are examined. In addition, our proposed framework is exploited in various multimedia applications, for example, the end-to-end real-time video streaming and CL optimization, which require the priority-based QoS adaptation for different applications. More importantly, the CL framework reveals important guidelines as to optimize the network performance

Effect of major lifestyle risk factors, independent and jointly, on life expectancy with and without cardiovascular disease: results from the Consortium on Health and Ageing Network of Cohorts in Europe and the United States (CHANCES)

Seldom have studies taken account of changes in lifestyle habits in the elderly, or investigated their impact on disease-free life expectancy (LE) and LE with cardiovascular disease (CVD). Using data on subjects aged 50+ years from three European cohorts (RCPH, ESTHER and Tromsø), we used multi-state Markov models to calculate the independent and joint effects of smoking, physical activity, obesity and alcohol consumption on LE with and without CVD. Men and women aged 50 years who have a favourable lifestyle (overweight but not obese, light/moderate drinker, non-smoker and participates in vigorous physical activity) lived between 7.4 (in Tromsø men) and 15.7 (in ESTHER women) years longer than those with an unfavourable lifestyle (overweight but not obese, light/moderate drinker, smoker and does not participate in physical activity). The greater part of the extra life years was in terms of "disease-free" years, though a healthy lifestyle was also associated with extra years lived after a CVD event. There are sizeable benefits to LE without CVD and also for survival after CVD onset when people favour a lifestyle characterized by salutary behaviours. Remaining a non-smoker yielded the greatest extra years in overall LE, when compared to the effects of routinely taking physical activity, being overweight but not obese, and drinking in moderation. The majority of the overall LE benefit is in disease free years. Therefore, it is important for policy makers and the public to know that prevention through maintaining a favourable lifestyle is "never too late".