Stability study of a model for the Klein-Gordon equation in Kerr spacetime

The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein-Gordon equation, describing the propagation of a scalar field of mass $\mu$ in the background of a rotating black hole. Rigorous results proof the stability of the reduced, by separation in the azimuth angle in Boyer-Lindquist coordinates, field for sufficiently large masses. Some, but not all, numerical investigations find instability of the reduced field for rotational parameters $a$ extremely close to 1. Among others, the paper derives a model problem for the equation which supports the instability of the field down to $a/M \approx 0.97$.Comment: Updated version, after minor change

An Updated Algorithm for the Generation of Neutral Landscapes by Spectral Synthesis

Background: Patterns that arise from an ecological process can be driven as much from the landscape over which the process is run as it is by some intrinsic properties of the process itself. The disentanglement of these effects is aided if it possible to run models of the process over artificial landscapes with controllable spatial properties. A number of different methods for the generation of so-called ‘neutral landscapes’ have been developed to provide just such a tool. Of these methods, a particular class that simulate fractional Brownian motion have shown particular promise. The existing methods of simulating fractional Brownian motion suffer from a number of problems however: they are often not easily generalisable to an arbitrary number of dimensions and produce outputs that can exhibit some undesirable artefacts. Methodology: We describe here an updated algorithm for the generation of neutral landscapes by fractional Brownian motion that do not display such undesirable properties. Using Monte Carlo simulation we assess the anisotropic properties of landscapes generated using the new algorithm described in this paper and compare it against a popular benchmark algorithm. Conclusion/Significance: The results show that the existing algorithm creates landscapes with values strongly correlated in the diagonal direction and that the new algorithm presented here corrects this artefact. A number of extensions of the algorithm described here are also highlighted: we describe how the algorithm can be employed to generate landscapes that display different properties in different dimensions and how they can be combined with an environmental gradient to produce landscapes that combine environmental variation at the local and macro scales

Estimating uncertainty in ecosystem budget calculations

© The Authors, 2010. This article is distributed under the terms of the Creative Commons Attribution-Noncommercial License. The definitive version was published in Ecosystems 13 (2010): 239-248, doi:10.1007/s10021-010-9315-8.Ecosystem nutrient budgets often report values for pools and fluxes without any indication of uncertainty, which makes it difficult to evaluate the significance of findings or make comparisons across systems. We present an example, implemented in Excel, of a Monte Carlo approach to estimating error in calculating the N content of vegetation at the Hubbard Brook Experimental Forest in New Hampshire. The total N content of trees was estimated at 847 kg ha−1 with an uncertainty of 8%, expressed as the standard deviation divided by the mean (the coefficient of variation). The individual sources of uncertainty were as follows: uncertainty in allometric equations (5%), uncertainty in tissue N concentrations (3%), uncertainty due to plot variability (6%, based on a sample of 15 plots of 0.05 ha), and uncertainty due to tree diameter measurement error (0.02%). In addition to allowing estimation of uncertainty in budget estimates, this approach can be used to assess which measurements should be improved to reduce uncertainty in the calculated values. This exercise was possible because the uncertainty in the parameters and equations that we used was made available by previous researchers. It is important to provide the error statistics with regression results if they are to be used in later calculations; archiving the data makes resampling analyses possible for future researchers. When conducted using a Monte Carlo framework, the analysis of uncertainty in complex calculations does not have to be difficult and should be standard practice when constructing ecosystem budgets

Quasi-Normal Modes of Stars and Black Holes

Perturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades. They are of particular importance today, because of their relevance to gravitational wave astronomy. In this review we present the theory of quasi-normal modes of compact objects from both the mathematical and astrophysical points of view. The discussion includes perturbations of black holes (Schwarzschild, Reissner-Nordstr\"om, Kerr and Kerr-Newman) and relativistic stars (non-rotating and slowly-rotating). The properties of the various families of quasi-normal modes are described, and numerical techniques for calculating quasi-normal modes reviewed. The successes, as well as the limits, of perturbation theory are presented, and its role in the emerging era of numerical relativity and supercomputers is discussed.Comment: 74 pages, 7 figures, Review article for "Living Reviews in Relativity

The Goldbeter-Koshland switch in the first-order region and its response to dynamic disorder

In their classical work (Proc. Natl. Acad. Sci. USA, 1981, 78:6840-6844), Goldbeter and Koshland mathematically analyzed a reversible covalent modification system which is highly sensitive to the concentration of effectors. Its signal-response curve appears sigmoidal, constituting a biochemical switch. However, the switch behavior only emerges in the "zero-order region", i.e. when the signal molecule concentration is much lower than that of the substrate it modifies. In this work we showed that the switching behavior can also occur under comparable concentrations of signals and substrates, provided that the signal molecules catalyze the modification reaction in cooperation. We also studied the effect of dynamic disorders on the proposed biochemical switch, in which the enzymatic reaction rates, instead of constant, appear as stochastic functions of time. We showed that the system is robust to dynamic disorder at bulk concentration. But if the dynamic disorder is quasi-static, large fluctuations of the switch response behavior may be observed at low concentrations. Such fluctuation is relevant to many biological functions. It can be reduced by either increasing the conformation interconversion rate of the protein, or correlating the enzymatic reaction rates in the network.Comment: 23 pages, 4 figures, accepted by PLOS ON

Arenavirus budding resulting from viral-protein-associated cell membrane curvature

Viral replication occurs within cells, with release (and onward infection) primarily achieved through two alternative mechanisms: lysis, in which virions emerge as the infected cell dies and bursts open; or budding, in which virions emerge gradually from a still living cell by appropriating a small part of the cell membrane. Virus budding is a poorly understood process that challenges current models of vesicle formation. Here, a plausible mechanism for arenavirus budding is presented, building on recent evidence that viral proteins embed in the inner lipid layer of the cell membrane. Experimental results confirm that viral protein is associated with increased membrane curvature, whereas a mathematical model is used to show that localized increases in curvature alone are sufficient to generate viral buds. The magnitude of the protein-induced curvature is calculated from the size of the amphipathic region hypothetically removed from the inner membrane as a result of translation, with a change in membrane stiffness estimated from observed differences in virion deformation as a result of protein depletion. Numerical results are based on experimental data and estimates for three arenaviruses, but the mechanisms described are more broadly applicable. The hypothesized mechanism is shown to be sufficient to generate spontaneous budding that matches well both qualitatively and quantitatively with experimental observations

PrP Expression, PrPSc Accumulation and Innervation of Splenic Compartments in Sheep Experimentally Infected with Scrapie

BACKGROUND: In prion disease, the peripheral expression of PrP(C) is necessary for the transfer of infectivity to the central nervous system. The spleen is involved in neuroinvasion and neural dissemination in prion diseases but the nature of this involvement is not known. The present study undertook the investigation of the spatial relationship between sites of PrP(Sc) accumulation, localisation of nerve fibres and PrP(C) expression in the tissue compartments of the spleen of scrapie-inoculated and control sheep. METHODOLOGY/PRINCIPAL FINDINGS: Laser microdissection and quantitative PCR were used to determine PrP mRNA levels and results were compared with immunohistochemical protocols to distinguish PrP(C) and PrP(Sc) in tissue compartments of the spleen. In sheep experimentally infected with scrapie, the major sites of accumulation of PrP(Sc) in the spleen, namely the lymphoid nodules and the marginal zone, expressed low levels of PrP mRNA. Double immunohistochemical labelling for PrP(Sc) and the pan-nerve fibre marker, PGP, was used to evaluate the density of innervation of splenic tissue compartments and the intimacy of association between PrP(Sc) and nerves. Some nerve fibres were observed to accompany blood vessels into the PrP(Sc)-laden germinal centres. However, the close association between nerves and PrP(Sc) was most apparent in the marginal zone. Other sites of close association were adjacent to the wall of the central artery of PALS and the outer rim of germinal centres. CONCLUSIONS/SIGNIFICANCE: The findings suggest that the degree of PrP(Sc) accumulation does not depend on the expression level of PrP(C). Though several splenic compartments may contribute to neuroinvasion, the marginal zone may play a central role in being the compartment with most apparent association between nerves and PrP(Sc)

The what and where of adding channel noise to the Hodgkin-Huxley equations

One of the most celebrated successes in computational biology is the Hodgkin-Huxley framework for modeling electrically active cells. This framework, expressed through a set of differential equations, synthesizes the impact of ionic currents on a cell's voltage -- and the highly nonlinear impact of that voltage back on the currents themselves -- into the rapid push and pull of the action potential. Latter studies confirmed that these cellular dynamics are orchestrated by individual ion channels, whose conformational changes regulate the conductance of each ionic current. Thus, kinetic equations familiar from physical chemistry are the natural setting for describing conductances; for small-to-moderate numbers of channels, these will predict fluctuations in conductances and stochasticity in the resulting action potentials. At first glance, the kinetic equations provide a far more complex (and higher-dimensional) description than the original Hodgkin-Huxley equations. This has prompted more than a decade of efforts to capture channel fluctuations with noise terms added to the Hodgkin-Huxley equations. Many of these approaches, while intuitively appealing, produce quantitative errors when compared to kinetic equations; others, as only very recently demonstrated, are both accurate and relatively simple. We review what works, what doesn't, and why, seeking to build a bridge to well-established results for the deterministic Hodgkin-Huxley equations. As such, we hope that this review will speed emerging studies of how channel noise modulates electrophysiological dynamics and function. We supply user-friendly Matlab simulation code of these stochastic versions of the Hodgkin-Huxley equations on the ModelDB website (accession number 138950) and http://www.amath.washington.edu/~etsb/tutorials.html.Comment: 14 pages, 3 figures, review articl

Framework, principles and recommendations for utilising participatory methodologies in the co-creation and evaluation of public health interventions

Background: Due to the chronic disease burden on society, there is a need for preventive public health interventions to stimulate society towards a healthier lifestyle. To deal with the complex variability between individual lifestyles and settings, collaborating with end-users to develop interventions tailored to their unique circumstances has been suggested as a potential way to improve effectiveness and adherence. Co-creation of public health interventions using participatory methodologies has shown promise but lacks a framework to make this process systematic. The aim of this paper was to identify and set key principles and recommendations for systematically applying participatory methodologies to co-create and evaluate public health interventions. Methods: These principles and recommendations were derived using an iterative reflection process, combining key learning from published literature in addition to critical reflection on three case studies conducted by research groups in three European institutions, all of whom have expertise in co-creating public health interventions using different participatory methodologies. Results: Key principles and recommendations for using participatory methodologies in public health intervention co-creation are presented for the stages of: Planning (framing the aim of the study and identifying the appropriate sampling strategy); Conducting (defining the procedure, in addition to manifesting ownership); Evaluating (the process and the effectiveness) and Reporting (providing guidelines to report the findings). Three scaling models are proposed to demonstrate how to scale locally developed interventions to a population level. Conclusions: These recommendations aim to facilitate public health intervention co-creation and evaluation utilising participatory methodologies by ensuring the process is systematic and reproducible

A pilot survey of post-deployment health care needs in small community-based primary care clinics

<p>Abstract</p> <p>Background</p> <p>Relatively little is known regarding to what extent community-based primary care physicians are encountering post-deployment health care needs among veterans of the Afghanistan or Iraq conflicts and their family members.</p> <p>Methods</p> <p>This pilot study conducted a cross-sectional survey of 37 primary care physicians working at small urban and suburban clinics belonging to a practice-based research network in the south central region of Texas.</p> <p>Results</p> <p>Approximately 80% of the responding physicians reported caring for patients who have been deployed to the Afghanistan or Iraq war zones, or had a family member deployed. Although these physicians noted a variety of conditions related to physical trauma, mental illnesses and psychosocial disruptions such as marital, family, financial, and legal problems appeared to be even more prevalent among their previously deployed patients and were also noted among family members of deployed veterans.</p> <p>Conclusions</p> <p>Community-based primary care physicians should be aware of common post-deployment health conditions and the resources that are available to meet these needs.</p