Is it really possible to grow isotropic on-lattice diffusion-limited aggregates?

In a recent paper (Bogoyavlenskiy V A 2002 \JPA \textbf{35} 2533), an algorithm aiming to generate isotropic clusters of the on-lattice diffusion-limited aggregation (DLA) model was proposed. The procedure consists of aggregation probabilities proportional to the squared number of occupied sites ($k^2$). In the present work, we analyzed this algorithm using the noise reduced version of the DLA model and large scale simulations. In the noiseless limit, instead of isotropic patterns, a $45^\circ$ ($30^\circ$) rotation in the anisotropy directions of the clusters grown on square (triangular) lattices was observed. A generalized algorithm, in which the aggregation probability is proportional to $k^\nu$, was proposed. The exponent $\nu$ has a nonuniversal critical value $\nu_c$, for which the patterns generated in the noiseless limit exhibit the original (axial) anisotropy for $\nu<\nu_c$ and the rotated one (diagonal) for $\nu>\nu_c$. The values $\nu_c = 1.395\pm0.005$ and $\nu_c = 0.82\pm 0.01$ were found for square and triangular lattices, respectively. Moreover, large scale simulations show that there are a nontrivial relation between noise reduction and anisotropy direction. The case $\nu=2$ (\bogo's rule) is an example where the patterns exhibit the axial anisotropy for small and the diagonal one for large noise reduction.Comment: 12 pages, 8 figure

Modeling the effect of variation in sagittal curvature on the force required to produce a follower load in the lumbar spine

Peer reviewedPreprin

Correlations between stochastic endemic infection in multiple interacting subpopulations.

Heterogeneity plays an important role in the emergence, persistence and control of infectious diseases. Metapopulation models are often used to describe spatial heterogeneity, and the transition from random- to heterogeneous-mixing is made by incorporating the interaction, or coupling, within and between subpopulations. However, such couplings are difficult to measure explicitly; instead, their action through the correlations between subpopulations is often all that can be observed. We use moment-closure methods to investigate how the coupling and resulting correlation are related, considering systems of multiple identical interacting populations on highly symmetric complex networks: the complete network, the k-regular tree network, and the star network. We show that the correlation between the prevalence of infection takes a relatively simple form and can be written in terms of the coupling, network parameters and epidemiological parameters only. These results provide insight into the effect of metapopulation network structure on endemic disease dynamics, and suggest that detailed case-reporting data alone may be sufficient to infer the strength of between population interaction and hence lead to more accurate mathematical descriptions of infectious disease behaviour

The lumbar spine has an intrinsic shape specific to each individual that remains a characteristic throughout flexion and extension

Peer reviewedPostprin

Diffusion-limited deposition of dipolar particles

Deposits of dipolar particles are investigated by means of extensive Monte Carlo simulations. We found that the effect of the interactions is described by an initial, non-universal, scaling regime characterized by orientationally ordered deposits. In the dipolar regime, the order and geometry of the clusters depend on the strength of the interactions and the magnetic properties are tunable by controlling the growth conditions. At later stages, the growth is dominated by thermal effects and the diffusion-limited universal regime obtains, at finite temperatures. At low temperatures the crossover size increases exponentially as T decreases and at T=0 only the dipolar regime is observed.Comment: 5 pages, 4 figure

The reliability of 31P-MRS and NIRS measurements of spinal muscle function

This is the accepted, peer reviewed version of the article, which has been published in final form at doi: 10.1055/s-0034-1372639Phosphorous magnetic resonance spectroscopy (31P-MRS) and near-infra red spectroscopy (NIRS) provide methods for measuring spinal muscle function non-invasively but their reliability is not established. The aim of this study was assess the reliability (ICC) and error magnitude (CV%) of measurements of muscle phosphocreatine (PCr), tissue oxygenation index (TOI), and muscle deoxyhaemoglobin (HHb) acquired during fatigue and in recovery after 24 s exercise in the lumbar muscles. Ten healthy participants (19-25 years, 5 male, 5 female) performed exercise that involved holding the upper body unsupported in slight extension until fatigue and then, after 30 minutes of rest, for repeated bursts of 24 seconds. ICCs indicated good to excellent reliability of baseline measures (TOI:0.75) and of amplitude changes during fatigue (PCr:0.73, TOI:0.69, HHb:0.80), and recovery (HHb:0.96) and poor to fair reliability for time constants describing rates of change during fatigue (PCr:0.11) and recovery (PCr:0.31, HHb:0.47). CV% indicated varying relative measurement error across baseline measures (TOI:5%), amplitude changes during fatigue (PCr:7%, TOI:38%, HHb:31%) and recovery (HHb:31%), and in time constants for fatigue (PCr:39%) and recovery (PCr:20%, HHb:37%). The results suggested that reliability would be sufficient for future studies on spinal muscle function but that measurement error may be too large to evaluate individuals.NIHREPSR

The relationship between sagittal curvature and extensor muscle volume in the lumbar spine.

This is the peer reviewed version of the article, which has been published in final form at doi: 10.1111/joa.12047. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.A previous modelling study predicted that the forces applied by the extensor muscles to stabilise the lumbar spine would be greater in spines that have a larger sagittal curvature (lordosis). Because the force-generating capacity of a muscle is related to its size, it was hypothesised that the size of the extensor muscles in a subject would be related to the size of their lumbar lordosis. Magnetic resonance imaging (MRI) data were obtained, together with age, height, body mass and back pain status, from 42 female subjects. The volume of the extensor muscles (multifidus and erector spinae) caudal to the mid-lumbar level was estimated from cross-sectional area measurements in axial T1-weighted MRIs spanning the lumbar spine. Lower lumbar curvature was determined from sagittal T1-weighted images. A stepwise linear regression model was used to determine the best predictors of muscle volume. The mean lower lumbar extensor muscle volume was 281 cm(3) (SD = 49 cm(3)). The mean lower lumbar curvature was 30 ° (SD = 7 °). Five subjects reported current back pain and were excluded from the regression analysis. Nearly half the variation in muscle volume was accounted for by the variables age (standardised coefficient, B = -3.2, P = 0.03) and lower lumbar curvature (B = 0.47, P = 0.002). The results support the hypothesis that extensor muscle volume in the lower lumbar spine is related to the magnitude of the sagittal curvature; this has implications for assessing muscle size as an indicator of muscle strength

The effect of axial load on the sagittal plane curvature of the upright human spine in vivo

Copyright © 2008 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Pattern Recognition . Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Biomechanics, Vol. 41 Issue 13 (2008), DOI: 10.1016/j.jbiomech.2008.06.035Determining the effect of load carriage on the human spine in vivo is important for determining spinal forces and establishing potential mechanisms of back injury. Previous studies have suggested that the natural curvature of the spine straightens under load, but are based on modelling and external measurements from the surface of the back. In the current study, an upright positional MRI scanner was used to acquire sagittal images of the lumbar and lower thoracic spine of 24 subjects. The subjects were imaged in standing whilst supporting 0, 8 and 16 kg of load which was applied axially across the shoulders using an apron. An active shape model of the vertebral bodies from T10 to S1 was created and used to characterise the effect of load. The results from the shape model showed that the behaviour of the average-shaped spine was to straighten slightly. However, the shape model also showed that the effect of load exhibited systematic variation between individuals. Those who had a smaller than average curvature before loading straightened under load, whereas those who had a greater than average curvature before loading showed an increase in curvature under load. The variation in behaviour of differently shaped spines may have further implications for the effects of load in lifting manoeuvres and in understanding the aetiology of back pain

No self-similar aggregates with sedimentation

Two-dimensional cluster-cluster aggregation is studied when clusters move both diffusively and sediment with a size dependent velocity. Sedimentation breaks the rotational symmetry and the ensuing clusters are not self-similar fractals: the mean cluster width perpendicular to the field direction grows faster than the height. The mean width exhibits power-law scaling with respect to the cluster size, ~ s^{l_x}, l_x = 0.61 +- 0.01, but the mean height does not. The clusters tend to become elongated in the sedimentation direction and the ratio of the single particle sedimentation velocity to single particle diffusivity controls the degree of orientation. These results are obtained using a simulation method, which becomes the more efficient the larger the moving clusters are.Comment: 10 pages, 10 figure

Inverse monoids and immersions of 2-complexes

It is well known that under mild conditions on a connected topological space $\mathcal X$, connected covers of $\mathcal X$ may be classified via conjugacy classes of subgroups of the fundamental group of $\mathcal X$. In this paper, we extend these results to the study of immersions into 2-dimensional CW-complexes. An immersion $f : {\mathcal D} \rightarrow \mathcal C$ between CW-complexes is a cellular map such that each point $y \in {\mathcal D}$ has a neighborhood $U$ that is mapped homeomorphically onto $f(U)$ by $f$. In order to classify immersions into a 2-dimensional CW-complex $\mathcal C$, we need to replace the fundamental group of $\mathcal C$ by an appropriate inverse monoid. We show how conjugacy classes of the closed inverse submonoids of this inverse monoid may be used to classify connected immersions into the complex