A note on Neuberger's double pass algorithm

We analyze Neuberger's double pass algorithm for the matrix-vector multiplication R(H).Y (where R(H) is (n-1,n)-th degree rational polynomial of positive definite operator H), and show that the number of floating point operations is independent of the degree n, provided that the number of sites is much larger than the number of iterations in the conjugate gradient. This implies that the matrix-vector product $(H)^{-1/2} Y \simeq R^{(n-1,n)}(H) \cdot Y$ can be approximated to very high precision with sufficiently large n, without noticeably extra costs. Further, we show that there exists a threshold $n_T$ such that the double pass is faster than the single pass for $n > n_T$, where $n_T \simeq 12 - 25$ for most platforms.Comment: 18 pages, v3: CPU time formulas are obtained, to appear in Physical Review

Designs for generalized linear models with random block effects via information matrix approximations

The selection of optimal designs for generalized linear mixed models is complicated by the fact that the Fisher information matrix, on which most optimality criteria depend, is computationally expensive to evaluate. Our focus is on the design of experiments for likelihood estimation of parameters in the conditional model. We provide two novel approximations that substantially reduce the computational cost of evaluating the information matrix by complete enumeration of response outcomes, or Monte Carlo approximations thereof: (i) an asymptotic approximation which is accurate when there is strong dependence between observations in the same block; (ii) an approximation via Kriging interpolators. For logistic random intercept models, we show how interpolation can be especially effective for finding pseudo-Bayesian designs that incorporate uncertainty in the values of the model parameters. The new results are used to provide the first evaluation of the efficiency, for estimating conditional models, of optimal designs from closed-form approximations to the information matrix derived from marginal models. It is found that correcting for the marginal attenuation of parameters in binary-response models yields much improved designs, typically with very high efficiencies. However, in some experiments exhibiting strong dependence, designs for marginal models may still be inefficient for conditional modelling. Our asymptotic results provide some theoretical insights into why such inefficiencies occur

First-passage and extreme-value statistics of a particle subject to a constant force plus a random force

We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point $x_1$ of a particle which starts at $x_0$ with velocity $v_0$. The probability that the particle has not yet arrived at $x_1$ after a time $t$, the mean time of first arrival, and the velocity distribution at first arrival are all considered. We also study the statistics of the first return of the particle to its starting point. Finally, we point out that the extreme-value statistics of the particle and the first-passage statistics are closely related, and we derive the distribution of the maximum displacement $m={\rm max}_t[x(t)]$.Comment: Contains an analysis of the extreme-value statistics not included in first versio

Predicting the distributions of under-recorded Odonata using species distribution models

1. Absences in distributional data may result either from the true absence of a species or from a false absence due to lack of recording effort. I use general linear models (GLMs) and species distribution models (SDMs) to investigate this problem in North American Odonata and present a potential solution. 2. I use multi-model selection methods based on Akaike's information criterion to evaluate the ability of water-energy variables, human population density, and recording effort to explain patterns of odonate diversity in the USA and Canada using GLMs. Water-energy variables explain a large proportion of the variance in odonate diversity, but the residuals of these models are significantly related to recorder effort. 3. I then create SDMs for 176species that are found solely in the USA and Canada using model averaging of eight different methods. These give predictions of hypothetical true distributions of each of the 176species based on climate variables, which I compare with observed distributions to identify areas where potential under-recording may occur. 4. Under-recording appears to be highest in northern Canada, Alaska, and Quebec, as well as the interior of the USA. The proportion of predicted species that have been observed is related to recorder effort and population density. Maps for individual species have been made available online () to facilitate recording in the future. 5. This analysis has illustrated a problem with current odonate recording in the form of unbalanced recorder effort. However, the SDM approach also provides the solution, targeting recorder effort in such a way as to maximise returns from limited resources

Modelling of gas permeation through ceramic coatings produced by thermal spraying

An analytical model has been developed for simulation of gas permeation through thermal spray coatings, and for prediction of the permeability. The model is based on a geometrical representation of the coating microstructure. This involves thin splats, with limited inter-splat bridging, and microcracks within the splats. Important variables include the thickness (smallest dimension) of the inter-splat pores and intra-splat microcracks. Uniform values of these parameters are used in the model. Predicted permeabilities are compared with experimental data obtained using plasma-sprayed zirconia coatings, both in the as-sprayed state and after heat treatments sufficient to generate significant microstructural changes via sintering effects. In general, good agreement is obtained and it is concluded that the model constitutes a useful tool for exploration of gas permeation characteristics in coatings or layers produced by thermal sprayin

Involvement of the proteasome and caspase activation in hippocampal long-term depression induced by the serine protease subtilisin

The serine protease subtilisin-A produces a long-term depression (LTD) of synaptic potentials in hippocampal slices which differs mechanistically from classical LTD. Since caspases have been implicated in hippocampal plasticity, this study examined a possible role for these enzymes in subtilisin-induced LTD. Subtilisin produced a concentration-dependent decrease in the size of field excitatory synaptic potentials (fEPSPs), which was not prevented or modified by the caspase inhibitors Z-VAD(OMe)-fmk and Z-DEVD-fmk. Similarly Z-VAD(OMe)-fmk did not modify the selective loss of protein expression produced by subtilisin. Subtilisin reduced the expression of procaspase-3 and caspase-9 but, while caspase-9 was converted to its conventionally activated form (39 kDa), caspase-3 was metabolised along a non-canonical pathway to a 29/30 kDa protein rather than the classical 17/19 kDa fragments. Both Z-VAD(OMe)-fmk and Z-DEVD-fmk were unable to prevent the reduced expression of Postsynaptic Density Protein-95, Vesicle-Associated Membrane Protein-1 and Unco-ordinated 5H3 proteins produced by subtilisin, although MG132 did produce partial recovery from subtilisin-induced depression of fEPSPs. When tested on long-term potentiation (LTP) induced by theta stimulation in the stratum radiatum, MG132 inhibited the immediate increase in fEPSP size but generated a higher plateau LTP. Twin LTP stimulation generated a further increase in LTP amplitude in control slices but not in slices exposed to MG132. The results indicate that subtilisin does produce caspase activation but that this does not contribute to its induction of LTD. However, activation of the proteasome does contribute to subtilisin-induced LTD and may also play a modulatory role in electrically induced LTP

Food and feed safety aspects of cisgenic crop plant varieties

This report presents the results of the discussions that identified food and feed safety aspects of cisgenic plant varieties in comparison to conventional varieties on the one hand and transgenic plant varieties on the other hand. It was concluded that on the basis of the general characteristics of cisgenic plant varieties, there is, from a food and feed safety perspective, no scientific basis for a general reduction of requirements for cisgenic crop plant varieties

Effects of ethylenediamine – a putative GABA-releasing agent – on rat hippocampal slices and neocortical activity in vivo

The simple diamine diaminoethane (ethylenediamine, EDA) has been shown to activate GABA receptors in the central and peripheral nervous systems, partly by a direct action and partly by releasing endogenous GABA. These effects have been shown to be produced by the complexation of EDA with bicarbonate to form a carbamate. The present work has compared EDA, GABA and [beta]-alanine responses in rat CA1 neurons using extracellular and intracellular recordings, as well as neocortical evoked potentials in vivo. Superfusion of GABA onto hippocampal slices produced depolarisation and a decrease of field epsps, both effects fading rapidly, but showing sensitivity to blockade by bicuculline. EDA produced an initial hyperpolarisation and increase of extracellular field epsp size with no fade and only partial sensitivity to bicuculline, with subsequent depolarisation, while [beta]-alanine produces a much larger underlying hyperpolarisation and increase in fepsps, followed by depolarisation and inhibition of fepsps. The responses to [beta]-alanine, but not GABA or EDA, were blocked by strychnine. In vivo experiments, recording somatosensory evoked potentials, confirmed that EDA produced an initial increase followed by depression, and that this effect was not fully blocked by bicuculline. Overall the results indicate that EDA has actions in addition to the activation of GABA receptors. These actions are not attributable to activation of [beta]-alanine-sensitive glycine receptors, but may involve the activation of sites sensitive to adipic acid, which is structurally equivalent to the dicarbamate of EDA. The results emphasise the complex pharmacology of simple amines in bicarbonate-containing solution