Estimation of pharmacokinetic parameters from non-compartmental variables using Microsoft Excel((R))

This study was conducted to develop a method, termed 'back analysis (BA)', for converting non-compartmental variables to compartment model dependent pharmacokinetic parameters for both one- and two-compartment models. A Microsoft Excel((R)) spreadsheet was implemented with the use of Solver((R)) and visual basic functions. The performance of the BA method in estimating pharmacokinetic parameter values was evaluated by comparing the parameter values obtained to a standard modelling software program, NONMEM, using simulated data. The results show that the BA method was reasonably precise and provided low bias in estimating fixed and random effect parameters for both one- and two-compartment models. The pharmacokinetic parameters estimated from the BA method were similar to those of NONMEM estimation.

Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.

Why people underestimate y when extrapolating in linear functions

E. L. DeLosh, J. R. Busemeyer, and M. A. McDaniel (1997) found that when learning a positive, linear relationship between a continuous predictor (x) and a continuous criterion (y), trainees tend to underestimate y on items that ask the trainee to extrapolate. In 3 experiments, the authors examined the phenomenon and found that the tendency to underestimate y is reliable only in the so-called lower extrapolation region-that is, new values of x that lie between zero and the edge of the training region. Existing models of function learning, such as the extrapolation-association model (DeLosh et al., 1997) and the population of linear experts model (M. L. Kalish, S. Lewandowsky, & J. Kruschke, 2004), cannot account for these results. The authors show that with minor changes, both models can predict the correct pattern of results.

The PhD Finger Protein VRN5 Functions in the Epigenetic Silencing of Arabidopsis FLC

Vernalization, the acceleration of flowering by the prolonged cold of winter, ensures that plants flower in favorable spring conditions. During vernalization in Arabidopsis, cold temperatures repress FLOWERING LOCUS C (FLC) expression [1,2] in a mechanism involving VERNALIZATION INSENSITIVE 3 (VIN3) [3], and this repression is epigenetically maintained by a Polycomb-like chromatin regulation involving VERNALIZATION 2 (VRN2), a Su(z)12 homolog, VERNALIZATION 1 (VRN1), and LIKE-HETEROCHROMATIN PROTEIN 1 [4,5,6,7,8]. In order to further elaborate how cold repression triggers epigenetic silencing, we have targeted mutations that result in FLC misexpression both at the end of the prolonged cold and after subsequent development. This identified VERNALIZATION 5 (VRN5), a PHD finger protein and homolog of VIN3. Our results suggest that during the prolonged cold, VRN5 and VIN3 forma heterodimer necessary for establishing the vernalization-induced chromatin modifications, histone deacetylation, and H3 lysine 27 trimethylation required for the epigenetic silencing of FLC. Double mutant and FLC misexpression analyses reveal additional VRN5 functions, both FLC-dependent and -independent, and indicate a spatial complexity to FLC epigenetic silencing with VRN5 acting as a common component in multiple pathways.

Distinct contrast response functions in striate and extra-striate regions of visual cortex revealed with magnetoencephalography (MEG)

Objective: To spatially and temporally characterise the cortical contrast response function to pattern onset stimuli in humans. Methods: Magnetoencephalography (MEG) was used to investigate the human cortical contrast response function to pattern onset stimuli with high temporal and spatial resolution. A beamformer source reconstruction approach was used to spatially localise and identify the time courses of activity at various visual cortical loci. Results: Consistent with the findings of previous studies, MEG beamformer analysis revealed two simultaneous generators of the pattern onset evoked response. These generators arose from anatomically discrete locations in striate and extra-striate visual cortex. Furthermore, these loci demonstrated notably distinct contrast response functions, with striate cortex increasing approximately linearly with contrast, whilst extra-striate visual cortex followed a saturating function. Conclusions: The generators that underlie the pattern onset visual evoked response arise from two distinct regions in striate and extra-striate visual cortex. Significance: The spatially, temporally and functionally distinct mechanisms of contrast processing within the visual cortex may account for the disparate results observed across earlier studies and assist in elucidating causal mechanisms of aberrant contrast processing in neurological disorders. © 2005 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Fast algorithms for automatic mapping with space-limited covariance functions

In this paper we discuss a fast Bayesian extension to kriging algorithms which has been used successfully for fast, automatic mapping in emergency conditions in the Spatial Interpolation Comparison 2004 (SIC2004) exercise. The application of kriging to automatic mapping raises several issues such as robustness, scalability, speed and parameter estimation. Various ad-hoc solutions have been proposed and used extensively but they lack a sound theoretical basis. In this paper we show how observations can be projected onto a representative subset of the data, without losing significant information. This allows the complexity of the algorithm to grow as O(n m 2), where n is the total number of observations and m is the size of the subset of the observations retained for prediction. The main contribution of this paper is to further extend this projective method through the application of space-limited covariance functions, which can be used as an alternative to the commonly used covariance models. In many real world applications the correlation between observations essentially vanishes beyond a certain separation distance. Thus it makes sense to use a covariance model that encompasses this belief since this leads to sparse covariance matrices for which optimised sparse matrix techniques can be used. In the presence of extreme values we show that space-limited covariance functions offer an additional benefit, they maintain the smoothness locally but at the same time lead to a more robust, and compact, global model. We show the performance of this technique coupled with the sparse extension to the kriging algorithm on synthetic data and outline a number of computational benefits such an approach brings. To test the relevance to automatic mapping we apply the method to the data used in a recent comparison of interpolation techniques (SIC2004) to map the levels of background ambient gamma radiation. © Springer-Verlag 2007.

R.A. Armstrong

Richard Armstrong was educated at King’s College London (1968-1971) and subsequently at St. Catherine’s College Oxford (1972-1976). His early research involved the application of statistical methods to problems in botany and ecology. For the last 34 years, he has been a lecturer in Botany, Microbiology, Ecology, Neuroscience, and Optometry at the University of Aston. His current research interests include the application of quantitative methods to the study of neuropathology of neurodegenerative diseases with special reference to vision and the visual system.

A survey of methods of numerical approximation to functions

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A multigene family encoding R-SNAREs in the ciliate Paramecium tetraurelia

SNARE proteins (soluble N-ethylmaleimide-sensitive factor attachment protein receptors) mediate membrane interactions and are conventionally divided into Q-SNAREs and R-SNAREs according to the possession of a glutamine or arginine residue at the core of their SNARE domain. Here, we describe a set of R-SNAREs from the ciliate Paramecium tetraurelia consisting of seven families encoded by 12 genes that are expressed simultaneously. The complexity of the endomembrane system in Paramecium can explain this high number of genes. All P. tetraurelia synaptobrevins (PtSybs) possess a SNARE domain and show homology to the Longin family of R-SNAREs such as Ykt6, Sec22 and tetanus toxin-insensitive VAMP (TI-VAMP). We localized four exemplary PtSyb subfamilies with GFP constructs and antibodies on the light and electron microscopic level. PtSyb1-1, PtSyb1-2 and PtSyb3-1 were found in the endoplasmic reticulum, whereas PtSyb2 is localized exclusively in the contractile vacuole complex. PtSyb6 was found cytosolic but also resides in regularly arranged structures at the cell cortex (parasomal sacs), the cytoproct and oral apparatus, probably representing endocytotic compartments. With gene silencing, we showed that the R-SNARE of the contractile vacuole complex, PtSyb2, functions to maintain structural integrity as well as functionality of the osmoregulatory system but also affects cell division.

Complete Systems of Hermite Associated Functions

It is proved that if the increasing sequence {kn} n=0..∞ n=0 of nonnegative integers has density greater than 1/2 and D is an arbitrary simply connected subregion of C\R then the system of Hermite associated functions Gkn(z) n=0..∞ is complete in the space H(D) of complex functions holomorphic in D.

Generalized Problem of Sratlikeness for Products of P-Valent Starlike Functions

∗ Partially supported by grant No. 433/94 NSF of the Ministry of Education and Science of the Republic of Bulgaria 1991 Mathematics Subject Classification:30C45

Involutivity and Symple Waves in R^2

A strictly hyperbolic quasi-linear 2×2 system in two independent variables with C2 coefficients is considered. The existence of a simple wave solution in the sense that the solution is a 2-dimensional vector-valued function of the so called Riemann invariant is discussed. It is shown, through a purely geometrical approach, that there always exists simple wave solution for the general system when the coefficients are arbitrary C^2 functions depending on both, dependent and independent variables.

Functionally Countable Spaces and Baire Functions

The concept of the distinguished sets is applied to the investigation of the functionally countable spaces. It is proved that every Baire function on a functionally countable space has a countable image. This is a positive answer to a question of R. Levy and W. D. Rice.

A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory

The first motivation for this note is to obtain a general version of the following result: let E be a Banach space and f : E → R be a differentiable function, bounded below and satisfying the Palais-Smale condition; then, f is coercive, i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references therein. A general result of this type was given in [3, Theorem 5.1] for a lower semicontinuous function defined on a Banach space, through an approach based on an abstract notion of subdifferential operator, and taking into account the “smoothness” of the Banach space. Here, we give (Theorem 1) an extension in a metric setting, based on the notion of slope from [11] and coercivity is considered in a generalized sense, inspired by [9]; our result allows to recover, for example, the coercivity result of [19], where a weakened version of the Palais-Smale condition is used. Our main tool (Proposition 1) is a consequence of Ekeland’s variational principle extending [12, Corollary 3.4], and deals with a function f which is, in some sense, the “uniform” Γ-limit of a sequence of functions.