Compressibility and shear compliance of spheroidal pores: Exact derivation via the Eshelby tensor, and asymptotic expressions in limiting cases

AbstractWe explicitly calculate the elastic compliance of a spheroidal pore in an isotropic solid, starting from Eshelby’s tensor. The exact expressions found for the pore compressibility, P, and the shear compliance, Q, are valid for any value of the aspect ratio α, from zero (cracks) to infinity (needles). This derivation clarifies previous work on this problem, in which different methods were used in different ranges of α, or typographical errors were present. The exact expressions obtained for P and Q are quite complex and unwieldy. Simple expressions for both P and Q have previously been available for the limiting cases of infinitely thin-cracks (α=0), infinitely long-needles (α=∞), and spherical pores (α=1). We have now calculated additional terms in the asymptotic expansions, yielding relatively simple approximations for P and Q that are valid for crack-like pores having aspect ratios as high as 0.3, needle-like pores having aspect ratios as low as 3, and nearly spherical pores. Their relatively simple forms will be useful for incorporation into various schemes to estimate the effective elastic moduli

The effect of chirality phenotype and genotype on the fecundity and viability of Partula suturalis and Lymnaea stagnalis: Implications for the evolution of sinistral snails

Why are sinistral snails so rare? Two main hypotheses are that selection acts against the establishment of new coiling morphs, because dextral and sinistral snails have trouble mating, or else a developmental constraint prevents the establishment of sinistrals. We therefore used an isolate of the snail Lymnaea stagnalis, in which sinistrals are rare, and populations of Partula suturalis, in which sinistrals are common, as well as a mathematical model, to understand the circumstances by which new morphs evolve. The main finding is that the sinistral genotype is associated with reduced egg viability in L. stagnalis, but in P. suturalis individuals of sinistral and dextral genotype appear equally fecund, implying a lack of a constraint. As positive frequency-dependent selection against the rare chiral morph in P. suturalis also operates over a narrow range (< 3%), the results suggest a model for chiral evolution in snails in which weak positive frequency-dependent selection may be overcome by a negative frequency-dependent selection, such as reproductive character displacement. In snails, there is not always a developmental constraint. As the direction of cleavage, and thus the directional asymmetry of the entire body, does not generally vary in other Spiralia (annelids, echiurans, vestimentiferans, sipunculids and nemerteans), it remains an open question as to whether this is because of a constraint and/or because most taxa do not have a conspicuous external asymmetry (like a shell) upon which selection can act

A new method for the estimation of variance matrix with prescribed zeros in nonlinear mixed effects models

We propose a new method for the Maximum Likelihood Estimator (MLE) of nonlinear mixed effects models when the variance matrix of Gaussian random effects has a prescribed pattern of zeros (PPZ). The method consists in coupling the recently developed Iterative Conditional Fitting (ICF) algorithm with the Expectation Maximization (EM) algorithm. It provides positive definite estimates for any sample size, and does not rely on any structural assumption on the PPZ. It can be easily adapted to many versions of EM.Comment: Accepted for publication in Statistics and Computin

The association between reasons for first using cannabis, later pattern of use, and risk of first-episode psychosis: the EU-GEI case-control study.

While cannabis use is a well-established risk factor for psychosis, little is known about any association between reasons for first using cannabis (RFUC) and later patterns of use and risk of psychosis. We used data from 11 sites of the multicentre European Gene-Environment Interaction (EU-GEI) case-control study. 558 first-episode psychosis patients (FEPp) and 567 population controls who had used cannabis and reported their RFUC.We ran logistic regressions to examine whether RFUC were associated with first-episode psychosis (FEP) case-control status. Path analysis then examined the relationship between RFUC, subsequent patterns of cannabis use, and case-control status. Controls (86.1%) and FEPp (75.63%) were most likely to report 'because of friends' as their most common RFUC. However, 20.1% of FEPp compared to 5.8% of controls reported: 'to feel better' as their RFUC (χ <sup>2</sup> = 50.97; p < 0.001). RFUC 'to feel better' was associated with being a FEPp (OR 1.74; 95% CI 1.03-2.95) while RFUC 'with friends' was associated with being a control (OR 0.56; 95% CI 0.37-0.83). The path model indicated an association between RFUC 'to feel better' with heavy cannabis use and with FEPp-control status. Both FEPp and controls usually started using cannabis with their friends, but more patients than controls had begun to use 'to feel better'. People who reported their reason for first using cannabis to 'feel better' were more likely to progress to heavy use and develop a psychotic disorder than those reporting 'because of friends'