From a discrete to a continuum model of cell dynamics in one dimension

Multiscale modeling is emerging as one of the key challenges in mathematical biology. However, the recent rapid increase in the number of modeling methodologies being used to describe cell populations has raised a number of interesting questions. For example, at the cellular scale, how can the appropriate discrete cell-level model be identified in a given context? Additionally, how can the many phenomenological assumptions used in the derivation of models at the continuum scale be related to individual cell behavior? In order to begin to address such questions, we consider a discrete one-dimensional cell-based model in which cells are assumed to interact via linear springs. From the discrete equations of motion, the continuous Rouse [P. E. Rouse, J. Chem. Phys. 21, 1272 (1953)] model is obtained. This formalism readily allows the definition of a cell number density for which a nonlinear "fast" diffusion equation is derived. Excellent agreement is demonstrated between the continuum and discrete models. Subsequently, via the incorporation of cell division, we demonstrate that the derived nonlinear diffusion model is robust to the inclusion of more realistic biological detail. In the limit of stiff springs, where cells can be considered to be incompressible, we show that cell velocity can be directly related to cell production. This assumption is frequently made in the literature but our derivation places limits on its validity. Finally, the model is compared with a model of a similar form recently derived for a different discrete cell-based model and it is shown how the different diffusion coefficients can be understood in terms of the underlying assumptions about cell behavior in the respective discrete models.

Bayesian analysis of correlated evolution of discrete characters by reversible-jump Markov chain Monte Carlo

We describe a Bayesian method for investigating correlated evolution of discrete binary traits on phylogenetic trees. The method fits a continuous-time Markov model to a pair of traits, seeking the best fitting models that describe their joint evolution on a phylogeny. We employ the methodology of reversible-jump ( RJ) Markov chain Monte Carlo to search among the large number of possible models, some of which conform to independent evolution of the two traits, others to correlated evolution. The RJ Markov chain visits these models in proportion to their posterior probabilities, thereby directly estimating the support for the hypothesis of correlated evolution. In addition, the RJ Markov chain simultaneously estimates the posterior distributions of the rate parameters of the model of trait evolution. These posterior distributions can be used to test among alternative evolutionary scenarios to explain the observed data. All results are integrated over a sample of phylogenetic trees to account for phylogenetic uncertainty. We implement the method in a program called RJ Discrete and illustrate it by analyzing the question of whether mating system and advertisement of estrus by females have coevolved in the Old World monkeys and great apes.

Synthesis, crystal structure and hydrolysis of a dinuclear copper(II) complex constructed by N2O donor Schiff base and 4,4 '-bipyridine: discrete supra-molecular ensembles vs. oligomers

The tridentate Schiff base ligand, 7-amino-4-methyl-5-aza-3-hepten-2-one (HAMAH), prepared by the mono-condensation of 1,2diaminoethane and acetylacetone, reacts with Cu(BF4)(2) center dot 6H(2)O to produce initially a dinuclear Cu(II) complex, [{Cu(AMAH)}(2) (mu-4,4'-bipyJ](BF4)(2) (1) which undergoes hydrolysis in the reaction mixture and finally produces a linear polymeric chain compound, [Cu(acac)(2)(mu-4,4'-bipy)](n) (2). The geometry around the copper atom in compound 1 is distorted square planar while that in compound 2 is essentially an elongated octahedron. On the other hand, the ligand HAMAH reacts with Cu(ClO4)(2) center dot 6H(2)O to yield a polymeric zigzag chain, [{Cu(acac)(CH3OH)(mu-4,4'-bipy)}(ClO4)](n) (3). The geometry of the copper atom in 3 is square pyramidal with the two bipyridine molecules in the cis equatorial positions. All three complexes have been characterized by elemental analysis, IR and UV-Vis spectroscopy and single crystal X-ray diffraction studies. A probable explanation for the different size and shape of the reported polynuclear complexes formed by copper(II) and 4,4'-bipyridine has been put forward by taking into account the denticity and crystal field strength of the blocking ligand as well as the Jahn-Teller effect in copper(II). (c) 2007 Elsevier Ltd. All rights reserved.

Effect of citric acid and glycine addition on acrylamide and flavor in a potato model system

Acrylamide levels in cooked/processed food can be reduced by treatment with citric acid or glycine. In a potato model system cooked at 180 degrees C for 10-60 min, these treatments affected the volatile profiles. Strecker aldehydes and alkylpyrazines, key flavor compounds of cooked potato, were monitored. Citric acid limited the generation of volatiles, particularly the alkylpyrazines. Glycine increased the total volatile yield by promoting the formation of certain alkylpyrazines, namely, 2,3-dimethylpyrazine, trimethylpyrazine, 2-ethyl-3,5-dimethylpyrazine, tetramethylpyrazine, and 2,5-diethyl-3- methylpyrazine. However, the formation of other pyrazines and Strecker aldehydes was suppressed. It was proposed that the opposing effects of these treatments on total volatile yield may be used to best advantage by employing a combined treatment at lower concentrations, especially as both treatments were found to have an additive effect in reducing acrylamide. This would minimize the impact on flavor but still achieve the desired reduction in acrylamide levels.

Light-induced off-flavor development in cloudy apple juice

Cloudy apple juice has been found to develop off-flavors during storage in daylight. The development of off-flavors and volatile compounds was monitored in reconstituted juice prepared from 'Golden Delicious' and 'Fuji' apple concentrates stored in glass bottles under fluorescent light (3000 Ix, 8 degrees C). A strong metallic off-flavor was formed by photooxidation. A major contributor to the off-flavor was identified as 1-octen-3-one by gas chromatography-olfactometry. In addition, six volatile compounds, pentanal, 2-methyl-1-penten-3-one, hexanal, (E)-2-heptenal, 6-methyl-5-hepten-2-one, and (E)-2octenal, increased significantly after light exposure and could contribute to the off-flavor. Except for pentanal and hexanal, these volatiles were found only after light exposure. Higher levels of volatiles were observed in juice from 'Golden Delicious' apples than in juice from 'Fuji' apples, and this difference was consistent with higher levels of suspended solids. When the suspended solids were removed by centrifugation, the development of volatiles on exposure to light was reduced significantly.

Flavor characterization of sugar-added pennywort (Centella asiatica L.) juices treated with ultra-high pressure and thermal processes

The flavor characteristics of pennywort juices with added sugar treated by ultra-high pressure, pasteurization, and sterilization were investigated using solid phase microextraction combined with gas chromatography-mass spectrometry. It was found that sesquiterpene hydrocarbons comprised the major class of volatile components present and the juices had a characteristic aroma due to the presence of volatiles including beta-caryophyllene and humulene and alpha-copaene. In comparison with heated juices, HPP-treated samples could retain more volatile compounds such as linalool and geraniol similar to those present in fresh juice, whereas some volatiles such as alpha-terpinene and ketone class were apparently formed by thermal treatment. All processing operations produced juice that was not significantly different in the concentration of total volatiles. Practical Application: Pennywort juice is considered a nutraceutical drink for health benefits. Therefore, to preserve all aroma and active components in this juice, a nonthermal process such as ultra-high pressure should be a more appropriate technique for retention of its nutritive values than pasteurization and sterilization.

Investigation into low power of a 2D Inverse Discrete CosineTransform (IDCT) in FPGAs

Design for low power in FPGA is rather limited since technology factors affecting power are either fixed or limited for FPGA families. This paper investigates opportunities for power savings of a pipelined 2D IDCT design at the architecture and logic level. We report power consumption savings of over 25% achieved in FPGA circuits obtained from clock gating implementation of optimizations made at the algorithmic level(1).

Comparison of extrasystolic ECG signal classifiers using discrete wavelet transforms

This work compares and contrasts results of classifying time-domain ECG signals with pathological conditions taken from the MITBIH arrhythmia database. Linear discriminant analysis and a multi-layer perceptron were used as classifiers. The neural network was trained by two different methods, namely back-propagation and a genetic algorithm. Converting the time-domain signal into the wavelet domain reduced the dimensionality of the problem at least 10-fold. This was achieved using wavelets from the db6 family as well as using adaptive wavelets generated using two different strategies. The wavelet transforms used in this study were limited to two decomposition levels. A neural network with evolved weights proved to be the best classifier with a maximum of 99.6% accuracy when optimised wavelet-transform ECG data wits presented to its input and 95.9% accuracy when the signals presented to its input were decomposed using db6 wavelets. The linear discriminant analysis achieved a maximum classification accuracy of 95.7% when presented with optimised and 95.5% with db6 wavelet coefficients. It is shown that the much simpler signal representation of a few wavelet coefficients obtained through an optimised discrete wavelet transform facilitates the classification of non-stationary time-variant signals task considerably. In addition, the results indicate that wavelet optimisation may improve the classification ability of a neural network. (c) 2005 Elsevier B.V. All rights reserved.

A novel radix-3/9 algorithm for type-III generalized discrete Hartley transform

A novel radix-3/9 algorithm for type-III generalized discrete Hartley transform (GDHT) is proposed, which applies to length-3(P) sequences. This algorithm is especially efficient in the case that multiplication is much more time-consuming than addition. A comparison analysis shows that the proposed algorithm outperforms a known algorithm when one multiplication is more time-consuming than five additions. When combined with any known radix-2 type-III GDHT algorithm, the new algorithm also applies to length-2(q)3(P) sequences.

Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations

We analyze a fully discrete spectral method for the numerical solution of the initial- and periodic boundary-value problem for two nonlinear, nonlocal, dispersive wave equations, the Benjamin–Ono and the Intermediate Long Wave equations. The equations are discretized in space by the standard Fourier–Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L2-error bound of spectral accuracy in space and of second-order accuracy in time.

On a class of nonselfadjoint periodic boundary value problems with discrete real spectrum

In a previous paper (J. of Differential Equations, Vol. 249 (2010), 3081-3098) we examined a family of periodic Sturm-Liouville problems with boundary and interior singularities which are highly non-self-adjoint but have only real eigenvalues. We now establish Schatten class properties of the associated resolvent operator.