Unification of the probe and singular sources methods for the inverse boundary value problem by the no-response test

In this article, we use the no-response test idea, introduced in Luke and Potthast (2003) and Potthast (Preprint) and the inverse obstacle problem, to identify the interface of the discontinuity of the coefficient gamma of the equation del (.) gamma(x)del + c(x) with piecewise regular gamma and bounded function c(x). We use infinitely many Cauchy data as measurement and give a reconstructive method to localize the interface. We will base this multiwave version of the no-response test on two different proofs. The first one contains a pointwise estimate as used by the singular sources method. The second one is built on an energy (or an integral) estimate which is the basis of the probe method. As a conclusion of this, the probe and the singular sources methods are equivalent regarding their convergence and the no-response test can be seen as a unified framework for these methods. As a further contribution, we provide a formula to reconstruct the values of the jump of gamma(x), x is an element of partial derivative D at the boundary. A second consequence of this formula is that the blow-up rate of the indicator functions of the probe and singular sources methods at the interface is given by the order of the singularity of the fundamental solution.

Initial boundary value problems for the nonlinear Schrödinger equation

A new spectral method for solving initial boundary value problems for linear and integrable nonlinear partial differential equations in two independent variables is applied to the nonlinear Schrödinger equation and to its linearized version in the domain {x≥l(t), t≥0}. We show that there exist two cases: (a) if l″(t)<0, then the solution of the linear or nonlinear equations can be obtained by solving the respective scalar or matrix Riemann-Hilbert problem, which is defined on a time-dependent contour; (b) if l″(t)>0, then the Riemann-Hilbert problem is replaced by a respective scalar or matrix problem on a time-independent domain. In both cases, the solution is expressed in a spectrally decomposed form.

Differential effects of temperature on fruit development and bean quality of contrasting genotypes of cacao (Theobroma cacao)

The effects of temperature and light integral on fruit growth and development of five cacao genotypes (Amelonado, AMAZ 15/15, SCA 6, SPEC 54/1 and UF 676) were studied in semi-controlled environment glasshouses in which the thermal regimes of cacao-growing regions of Brazil, Ghana and Malaysia were simulated. Fruit losses because of physiological will (cherelle will) were greater at higher temperatures and also differed significantly between genotypes, reflecting genetic differences in competition for assimilates between vegetative and reproductive components. Short-term measurements of fruit growth indicated faster growth rates at higher temperatures. In addition, a significant negative linear relationship between temperature and development time was observed. There was an effect of genotype on this relationship, such that time to fruit maturation at a given temperature was greatest for the clone UF 676 and least for AMAZ 15/15. Analysis of base temperatures, derived from these relationships indicated genetic variability in sensitivity of cacao fruit growth to temperature (base temperatures ranged from 7.5 degrees C for Amelonado and AMAZ 15/15 to 12.9 for SPEC 54/1). Final fruit size was a positive function of beam number for all genotypes and a positive function of light integral for Amelonado in the Malaysia simulated environment (where the temperature was almost constant). In simulated environments where temperature was the main variable (Brazil and Ghana) increases in temperature resulted in a significant decrease in final pod size for one genotype (Amelonado) in Brazil and for two genotypes (SPEC 54/1 and UF 676) in Ghana. It was hypothesised that pod growth duration (mediated by temperature), assimilation and beam number are all determinants of final pod size but that under specific conditions one of these factors may override the others. There was variability between genotypes in the response of beam size and beam lipid content to temperature. Negative relationships between temperature and bean size were found for Amelonado and UF 676. Lipid concentration was a curvilinear function of temperature for Amelonado and UF 676, with optimal temperatures of 23 degrees C and 24 degrees C, respectively. The variability observed here of different cacao genotypes to temperature highlights the need and opportunities for appropriate matching of planting material with local environments.

Dietary vitamin E modulates differential gene expression in the rat hippocampus: potential implications for its neuroprotective properties

A wide range of cell culture, animal and human epidemiological studies are suggestive of a role of vitamin E (VE) in brain function and in the prevention of neurodegeneration. However, the underlying molecular mechanisms remain largely unknown. In the current investigation Affymetrix gene chip technology was utilised to establish the impact of chronic VE deficiency on hippocampal genes expression. Male albino rats were fed either a VE deficient or standard diet (60 mg/kg feed) for a period of 9 months. Rats were sacrificed, the hippocampus removed and genes expression established in individual animals. VE deficiency showed to have a strong impact on genes expression in the hippocampus. An important number of genes found to be regulated by VE was associated with hormones and hormone metabolism, nerve growth factor, apoptosis, dopaminergic neurotransmission, and clearance of amyloid-beta and advanced glycated endproducts. In particular, VE strongly affected the expression of an array of genes encoding for proteins directly or indirectly involved in the clearance of amyloid beta, changes which are consistent with a protective effect of VE on Alzheimer's disease progression.

PIGOK: linking protein identity to gene ontology and function

Here we introduce a computer database that allows for the rapid retrieval of physicochemical properties, Gene Ontology, and Kyoto Encyclopedia of Genes and Genomes information about a protein or a list of proteins. We applied PIGOK analyzing Schizosaccharomyces pombe proteins displaying differential expression under oxidative stress and identified their biological functions and pathways. The database is available on the Internet at http://pc4-133.ludwig.ucl.ac.uk/pigok.html.

Differential cognitive effects of Ginkgo biloba after acute and chronic treatment in healthy young volunteers

Acute doses of Ginkgo biloba have been shown to improve attention and memory in young, healthy participants, but there has been a lack of investigation into possible effects on executive function. In addition, only one study has investigated the effects of chronic treatment in young volunteers. This study was conducted to compare the effects of ginkgo after acute and chronic treatment on tests of attention, memory and executive function in healthy university students. Using a placebo-controlled double-blind design, in experiment 1, 52 students were randomly allocated to receive a single dose of ginkgo (120 mg, n=26) or placebo (n=26), and were tested 4h later. In experiment 2, 40 students were randomly allocated to receive ginkgo (120 mg/day; n=20) or placebo (n=20) for a 6-week period and were tested at baseline and after 6 weeks of treatment. In both experiments, participants underwent tests of sustained attention, episodic and working memory, mental flexibility and planning, and completed mood rating scales. The acute dose of ginkgo significantly improved performance on the sustained-attention task and pattern-recognition memory task; however, there were no effects on working memory, planning, mental flexibility or mood. After 6 weeks of treatment, there were no significant effects of ginkgo on mood or any of the cognitive tests. In line with the literature, after acute administration ginkgo improved performance in tests of attention and memory. However, there were no effects after 6 weeks, suggesting that tolerance develops to the effects in young, healthy participants.

Estimation of Hidden Markov Models parameters using differential evolution

Hidden Markov Models (HMMs) have been successfully applied to different modelling and classification problems from different areas over the recent years. An important step in using HMMs is the initialisation of the parameters of the model as the subsequent learning of HMM’s parameters will be dependent on these values. This initialisation should take into account the knowledge about the addressed problem and also optimisation techniques to estimate the best initial parameters given a cost function, and consequently, to estimate the best log-likelihood. This paper proposes the initialisation of Hidden Markov Models parameters using the optimisation algorithm Differential Evolution with the aim to obtain the best log-likelihood.

Neurofuzzy network model construction using Bézier-Bernstein polynomial functions

Neurofuzzy modelling systems combine fuzzy logic with quantitative artificial neural networks via a concept of fuzzification by using a fuzzy membership function usually based on B-splines and algebraic operators for inference, etc. The paper introduces a neurofuzzy model construction algorithm using Bezier-Bernstein polynomial functions as basis functions. The new network maintains most of the properties of the B-spline expansion based neurofuzzy system, such as the non-negativity of the basis functions, and unity of support but with the additional advantages of structural parsimony and Delaunay input space partitioning, avoiding the inherent computational problems of lattice networks. This new modelling network is based on the idea that an input vector can be mapped into barycentric co-ordinates with respect to a set of predetermined knots as vertices of a polygon (a set of tiled Delaunay triangles) over the input space. The network is expressed as the Bezier-Bernstein polynomial function of barycentric co-ordinates of the input vector. An inverse de Casteljau procedure using backpropagation is developed to obtain the input vector's barycentric co-ordinates that form the basis functions. Extension of the Bezier-Bernstein neurofuzzy algorithm to n-dimensional inputs is discussed followed by numerical examples to demonstrate the effectiveness of this new data based modelling approach.

Generalized neurofuzzy network modeling algorithms using Bezier-Bernstein polynomial functions and additive decomposition

This paper introduces a new neurofuzzy model construction algorithm for nonlinear dynamic systems based upon basis functions that are Bezier-Bernstein polynomial functions. This paper is generalized in that it copes with n-dimensional inputs by utilising an additive decomposition construction to overcome the curse of dimensionality associated with high n. This new construction algorithm also introduces univariate Bezier-Bernstein polynomial functions for the completeness of the generalized procedure. Like the B-spline expansion based neurofuzzy systems, Bezier-Bernstein polynomial function based neurofuzzy networks hold desirable properties such as nonnegativity of the basis functions, unity of support, and interpretability of basis function as fuzzy membership functions, moreover with the additional advantages of structural parsimony and Delaunay input space partition, essentially overcoming the curse of dimensionality associated with conventional fuzzy and RBF networks. This new modeling network is based on additive decomposition approach together with two separate basis function formation approaches for both univariate and bivariate Bezier-Bernstein polynomial functions used in model construction. The overall network weights are then learnt using conventional least squares methods. Numerical examples are included to demonstrate the effectiveness of this new data based modeling approach.

Applying the extended Kalman filter to systems described by nonlinear differential-algebraic equations

This paper describes a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation models using the extended Kalman filter. The method involves the use of a time-varying linearisation of a semi-explicit index one differential-algebraic equation. The estimation technique consists of a simplified extended Kalman filter that is integrated with the differential-algebraic equation model. The paper describes a simulation study using a model of a batch chemical reactor. It also reports a study based on experimental data obtained from a mixing process, where the model of the system is solved using the sequential modular method and the estimation involves a bank of extended Kalman filters.