Landscape as a Model: The Importance of Geometry

In all models, but especially in those used to predict uncertain processes (e.g., climate change and nonnative species establishment), it is important to identify and remove any sources of bias that may confound results. This is critical in models designed to help support decisionmaking. The geometry used to represent virtual landscapes in spatially explicit models is a potential source of bias. The majority of spatial models use regular square geometry, although regular hexagonal landscapes have also been used. However, there are other ways in which space can be represented in spatially explicit models. For the first time, we explicitly compare the range of alternative geometries available to the modeller, and present a mechanism by which uncertainty in the representation of landscapes can be incorporated. We test how geometry can affect cell-to-cell movement across homogeneous virtual landscapes and compare regular geometries with a suite of irregular mosaics. We show that regular geometries have the potential to systematically bias the direction and distance of movement, whereas even individual instances of landscapes with irregular geometry do not. We also examine how geometry can affect the gross representation of real-world landscapes, and again show that individual instances of regular geometries will always create qualitative and quantitative errors. These can be reduced by the use of multiple randomized instances, though this still creates scale-dependent biases. In contrast, virtual landscapes formed using irregular geometries can represent complex real-world landscapes without error. We found that the potential for bias caused by regular geometries can be effectively eliminated by subdividing virtual landscapes using irregular geometry. The use of irregular geometry appears to offer spatial modellers other potential advantages, which are as yet underdeveloped. We recommend their use in all spatially explicit models, but especially for predictive models that are used in decisionmaking

Avalanche dynamics, surface roughening and self-organized criticality - experiments on a 3 dimensional pile of rice

We present a two-dimensional system which exhibits features of self-organized criticality. The avalanches which occur on the surface of a pile of rice are found to exhibit finite size scaling in their probability distribution. The critical exponents are $\tau$ = 1.21(2) for the avalanche size distribution and $D$ = 1.99(2) for the cut-off size. Furthermore the geometry of the avalanches is studied leading to a fractal dimension of the active sites of $d_B$ = 1.58(2). Using a set of scaling relations, we can calculate the roughness exponent $\alpha = D - d_B$ = 0.41(3) and the dynamic exponent $z = D(2 - \tau)$ = 1.56(8). This result is compared with that obtained from a power spectrum analysis of the surface roughness, which yields $\alpha$ = 0.42(3) and $z$ = 1.5(1) in excellent agreement with those obtained from the scaling relations.Comment: 7 pages, 8 figures, accepted for publication in PR

Comparison of different methods for analyzing μ\muSR line shapes in the vortex state of type-II superconductors

A detailed analysis of muon-spin rotation ($\mu$SR) spectra in the vortex state of type-II superconductors using different theoretical models is presented. Analytical approximations of the London and Ginzburg-Landau (GL) models, as well as an exact solution of the GL model were used. The limits of the validity of these models and the reliability to extract parameters such as the magnetic penetration depth $\lambda$ and the coherence length $\xi$ from the experimental $\mu$SR spectra were investigated. The analysis of the simulated $\mu$SR spectra showed that at high magnetic fields there is a strong correlation between obtained $\lambda$ and $\xi$ for any value of the Ginzburg-Landau parameter $\kappa = \lambda/\xi$. The smaller the applied magnetic field is, the smaller is the possibility to find the correct value of $\xi$. A simultaneous determination of $\lambda$ and $\xi$ without any restrictions is very problematic, independent of the model used to describe the vortex state. It was found that for extreme type-II superconductors and low magnetic fields, the fitted value of $\lambda$ is practically independent of $\xi$. The second-moment method frequently used to analyze $\mu$SR spectra by means of a multi-component Gaussian fit, generally yields reliable values of $\lambda$ in the whole range of applied fields $H_{c1} \ll H \lesssim H_{c2}$ ($H_{c1}$ and $H_{c2}$ are the first and second critical fields, respectively). These results are also relevant for the interpretation of small-angle neutron scattering (SANS) experiments of the vortex state in type-II superconductors.Comment: 17 pages, 19 figure

Incorporating chemical signalling factors into cell-based models of growing epithelial tissues

In this paper we present a comprehensive computational framework within which the effects of chemical signalling factors on growing epithelial tissues can be studied. The method incorporates a vertex-based cell model, in conjunction with a solver for the governing chemical equations. The vertex model provides a natural mesh for the finite element method (FEM), with node movements determined by force laws. The arbitrary Lagrangian–Eulerian formulation is adopted to account for domain movement between iterations. The effects of cell proliferation and junctional rearrangements on the mesh are also examined. By implementing refinements of the mesh we show that the finite element (FE) approximation converges towards an accurate numerical solution. The potential utility of the system is demonstrated in the context of Decapentaplegic (Dpp), a morphogen which plays a crucial role in development of the Drosophila imaginal wing disc. Despite the presence of a Dpp gradient, growth is uniform across the wing disc. We make the growth rate of cells dependent on Dpp concentration and show that the number of proliferation events increases in regions of high concentration. This allows hypotheses regarding mechanisms of growth control to be rigorously tested. The method we describe may be adapted to a range of potential application areas, and to other cell-based models with designated node movements, to accurately probe the role of morphogens in epithelial tissues

Direct observation of the flux-line vortex glass phase in a type II superconductor

The order of the vortex state in La_{1.9} Sr_{0.1} CuO_{4} is probed using muon spin rotation and small-angle neutron scattering. A transition from a Bragg glass to a vortex glass is observed, where the latter is composed of disordered vortex lines. In the vicinity of the transition the microscopic behavior reflects a delicate interplay of thermally-induced and pinning-induced disorder.Comment: 14 pages, 4 colour figures include

Self-organized criticality induced by quenched disorder: experiments on flux avalanches in NbHx_x films

We present an experimental study of the influence of quenched disorder on the distribution of flux avalanches in type-II superconductors. In the presence of much quenched disorder, the avalanche sizes are power-law distributed and show finite size scaling, as expected from self-organized criticality (SOC). Furthermore, the shape of the avalanches is observed to be fractal. In the absence of quenched disorder, a preferred size of avalanches is observed and avalanches are smooth. These observations indicate that a certain minimum amount of disorder is necessary for SOC behavior. We relate these findings to the appearance or non-appearance of SOC in other experimental systems, particularly piles of sand.Comment: 4 pages, 4 figure

Photo-elastic properties of the wing imaginal disc of Drosophila

In the study of developmental biology, the physical properties and constraints of the developing tissues are of great importance. In spite of this, not much is known about the elastic properties of biologically relevant tissues that are studied in biology labs. Here, we characterize properties of the wing imaginal disc of Drosophila, which is a precursor organ intensely studied in the framework of growth control and cell polarity. In order to determine the possibility of measuring mechanical stresses inside the tissue during development, we quantify the photo-elastic properties of the tissue by direct mechanical manipulation. We obtain a photo-elastic constant of [Formula: see text]

Predictors and indicators of disability and quality of life 4 years after a severe traumatic brain injury. A Structural Equation Modelling analysis from the PariS-TBI study

ObjectiveTo assess the predictors and indicators of disability and quality of life four years after a severe traumatic brain injury (TBI), using a Structural Equation Modelling (SEM). SEM is a multivariate approach permitting to take into account the complex inter-relationships between individual predictors, in order to disentangle factors which have a direct or indirect relationship with the dependant variable.MethodsThe Paris-TBI study is a longitudinal inception cohort study of 504 patients with severe TBI in the Parisian area [1]. Among 245 survivors, 147 patients were assessed four years post-injury. Two outcome measures were analysed separately using SEM: the Glasgow Outcome Scale-extended (GOS-E) [2], which is a global measure of disability after TBI, and the QOLIBRI, a disease-specific measure of quality of life after TBI [3]. Four groups of variable were entered in the model: demographics; injury severity; psychological and cognitive impairments; somatic impairments.ResultsThe GOS-E was directly significantly related to all four groups of variables (age, gender, severity of injury, psycho-cognitive and somatic impairments). Education duration had an indirect effect, mediated by psycho-cognitive impairments. In contrast, the QOLIBRI was only directly predicted by psycho-cognitive impairments. Age and somatic impairments had an indirect influence on the QOLIBRI, via psycho-cognitive impairments.Discussion/ConclusionDisability and quality of life were directly influenced by different factors. While disability appeared to result from an interaction of a wide range of factors, including demographics, injury severity, psycho-cognitive and somatic deficiencies, quality of life was solely directly related to psycho-cognitive factors. Other factors, such as age and somatic impairments only had an indirect effect

Solid state electrochromic display based on polymer electrode-polymer electrolyte interface

The electropolymerization of ortho-toluidine and ortho-anisidine gave uniform electroactive polymer films which were analysed by cyclic voltammetry, impedance and uv-vis absorption spectra. These films exhibit a reversible electrochemical response during cyclic voltammetry experiments in aqueous, non-aqueous and polymer electrolytes. Their electrochromic efficiency is high in aqueous and non-aqueous electrolytes but decreases in the polymer electrolyte. A solid state cell having the configuration ITO/TiO2-CeO2/LiN(SO2CF3)2-PEO complex/polymer/ITO, has been assembled. The transmittance variation of this system between the oxidized and reduced state is about 20% at 632.8 nm