Recursive algorithms for the elimination of redundant paths in spatial lag operators

Recursive algorithms for the elimination of redundant paths in spatial lag operators are introduced. It is shown that these algorithms have superior computational properties in comparison with the cumbersome procedure proposed by Ross and Harary (1952). A rigorous definition of spatial lag operators is given, while a number of mathematical results and properties are derived. Theoretical and empirical results regarding the performance of the proposed algorithms are presented

Modelling and analysis of planar cell polarity

Planar cell polarity (PCP) occurs in the epithelia of many animals and can lead to the alignment of hairs, bristles and feathers; physiologically, it can organise ciliary beating. Here we present two approaches to modelling this phenomenon. The aim is to discover the basic mechanisms that drive PCP, while keeping the models mathematically tractable. We present a feedback and diffusion model, in which adjacent cell sides of neighbouring cells are coupled by a negative feedback loop and diffusion acts within the cell. This approach can give rise to polarity, but also to period two patterns. Polarisation arises via an instability provided a sufficiently strong feedback and sufficiently weak diffusion. Moreover, we discuss a conservative model in which proteins within a cell are redistributed depending on the amount of proteins in the neighbouring cells, coupled with intracellular diffusion. In this case polarity can arise from weakly polarised initial conditions or via a wave provided the diffusion is weak enough. Both models can overcome small anomalies in the initial conditions. Furthermore, the range of the effects of groups of cells with different properties than the surrounding cells depends on the strength of the initial global cue and the intracellular diffusion

Is a persistent global bias necessary for the establishment of planar cell polarity?

Planar cell polarity (PCP) — the coordinated polarisation of a whole field of cells within the plane of a tissue — relies on the interaction of three modules: a global module that couples individual cellular polarity to the tissue axis, a local module that aligns the axis of polarisation of neighbouring cells, and a readout module that directs the correct outgrowth of PCP-regulated structures such as hairs and bristles. While much is known about the molecular components that are required for PCP, the functional details of—and interactions between—the modules remain unclear. In this work, we perform a mathematical analysis of two previously proposed computational models of the local module (Amonlirdviman et al., Science, 307, 2005; Le Garrec et al., Dev. Dyn., 235, 2006). Both models can reproduce wild-type and mutant phenotypes of PCP observed in the Drosophila wing under the assumption that a tissue-wide polarity cue from the global module persists throughout the development of PCP. We demonstrate that both models can also generate tissue-level PCP when provided with only a transient initial polarity cue. However, such transient cues are not sufficient to ensure robustness of the resulting cellular polarisation

Shade as enrichment : testing preferences for shelter in two model fish species

N.A.R.J. was supported by an Fisheries Society of the British Isles studentship, F.M.J. by the St Andrews School of Biology and H.C.S.-J. by the John Templeton Foundation.We compared preferences shown by zebrafish Danio rerio and three‐spined stickleback Gasterosteus aculeatus for shelter provided by above‐tank shade and artificial plants. Zebrafish showed no preference for either shelter, whereas sticklebacks showed a preference for both shelter types over open areas and for shade over plants. Our results suggest shade may be used as enrichment for captive fish and re‐emphasise the importance of species‐specific welfare considerations.PostprintPeer reviewe

User acceptability of saliva and gargle samples for identifying COVID-19 positive high-risk workers and household contacts

Throughout the COVID-19 pandemic nasopharyngeal or nose and/or throat swabs (NTS) have been the primary approach for collecting patient samples for the subsequent detection of viral RNA. However, this procedure, if undertaken correctly, can be unpleasant and therefore deters individuals from providing high quality samples. To overcome these limitations other modes of sample collection have been explored. In a cohort of frontline health care workers we have compared saliva and gargle samples to gold-standard NTS. 93% of individuals preferred providing saliva or gargle samples, with little sex-dependent variation. Viral titers collected in samples were analyzed using standard methods and showed that gargle and saliva were similarly comparable for identifying COVID-19 positive individuals compared to NTS (92% sensitivity; 98% specificity). We suggest that gargle and saliva collection are viable alternatives to NTS swabs and may encourage testing to provide better disease diagnosis and population surveillance

Measuring brain atrophy with a generalized formulation of the boundary shift integral

AbstractBrain atrophy measured using structural magnetic resonance imaging (MRI) has been widely used as an imaging biomarker for disease diagnosis and tracking of pathologic progression in neurodegenerative diseases. In this work, we present a generalized and extended formulation of the boundary shift integral (gBSI) using probabilistic segmentations to estimate anatomic changes between 2 time points. This method adaptively estimates a non-binary exclusive OR region of interest from probabilistic brain segmentations of the baseline and repeat scans to better localize and capture the brain atrophy. We evaluate the proposed method by comparing the sample size requirements for a hypothetical clinical trial of Alzheimer's disease to that needed for the current implementation of BSI as well as a fuzzy implementation of BSI. The gBSI method results in a modest but reduced sample size, providing increased sensitivity to disease changes through the use of the probabilistic exclusive OR region

Growing old : Do women and men age differently?

Aging of the head and especially the face has been studied intensively, yet questions remain about the timing and rates of aging throughout adulthood and about the extent to which aging differs between men and women. Here we address these issues by developing statistical models of craniofacial aging to describe and compare aging through the life course in both sexes. We selected cranial surface meshes from 254 females and 252 males, aged from 20 to 90 years from the Headspace project, Liverpool, UK. Sixteen anatomical landmarks and 59 semilandmarks on curves and surfaces were used to parameterize these. Modes and degrees of aging throughout adulthood were assessed and compared among sexes using Procrustes-based geometric morphometric methods. Regression analyses of form through the whole age range indicate that age accounts for a small proportion of total variance in both sexes, but form is significantly related to age and males and females age in significantly different ways. Further analyses indicate that aging differs in character, timing, and rates in both sexes between early and later phases of adulthood. Sexual differences in aging are evident in the early and later phases of adulthood. The study adds to knowledge of the aging of adult craniofacial form and sexual dimorphism. It is based on a local population and so the findings are directly applicable to that population. Further studies are needed to assess generalizability and provide better data on population differences to facilitate clinical assessment and treatment planning

Modelling and analysis of planar cell polarity

Planar cell polarity (PCP) occurs in the epithelia of many animals and can lead to the alignment of hairs, bristles and feathers; physiologically, it can organise ciliary beating. Here we present two approaches to modelling this phenomenon. The aim is to discover the basic mechanisms that drive PCP, while keeping the models mathematically tractable. We present a feedback and diffusion model, in which adjacent cell sides of neighbouring cells are coupled by a negative feedback loop and diffusion acts within the cell. This approach can give rise to polarity, but also to period two patterns. Polarisation arises via an instability provided a sufficiently strong feedback and sufficiently weak diffusion. Moreover, we discuss a conservative model in which proteins within a cell are redistributed depending on the amount of proteins in the neighbouring cells, coupled with intracellular diffusion. In this case polarity can arise from weakly polarised initial conditions or via a wave provided the diffusion is weak enough. Both models can overcome small anomalies in the initial conditions. Furthermore, the range of the effects of groups of cells with different properties than the surrounding cells depends on the strength of the initial global cue and the intracellular diffusion