The composite Euler method for stiff stochastic differential equations

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method. (C) 2001 Elsevier Science B.V. All rights reserved.

Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Differential inclusions and robust control theory

Uncontrolled systems (x) over dot is an element of Ax, where A is a non-empty compact set of matrices, and controlled systems (x) over dot is an element of Ax + Bu are considered. Higher-order systems 0 is an element of Px - Du, where and are sets of differential polynomials, are also studied. It is shown that, under natural conditions commonly occurring in robust control theory, with some mild additional restrictions, asymptotic stability of differential inclusions is guaranteed. The main results are variants of small-gain theorems and the principal technique used is the Krasnosel'skii-Pokrovskii principle of absence of bounded solutions.

Stability of linear difference and differential inclusions

Any given n X n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N x N matrix B of spectral radius p(B) arbitrarily close to p(A). A difference inclusion x(k+1) is an element of Ax(k), where A is a compact set of matrices, is asymptotically stable if and only if A can be extended to a set B of nonnegative matrices B with \ \B \ \ (1) < 1 or \ \B \ \ (infinity) < 1. Similar results are derived for differential inclusions.

Stiffly accurate Runge-Kutta methods for stiff stochastic differential equations

In this paper we discuss implicit methods based on stiffly accurate Runge-Kutta methods and splitting techniques for solving Stratonovich stochastic differential equations (SDEs). Two splitting techniques: the balanced splitting technique and the deterministic splitting technique, are used in this paper. We construct a two-stage implicit Runge-Kutta method with strong order 1.0 which is corrected twice and no update is needed. The stability properties and numerical results show that this approach is suitable for solving stiff SDEs. (C) 2001 Elsevier Science B.V. All rights reserved.

Mental evolution and development: Evidence for secondary representation in children, great apes, and other animals

Recent interest in the development and evolution of theory of mind has provided a wealth of information about representational skills in both children and animals, According to J, Perrier (1991), children begin to entertain secondary representations in the 2nd year of life. This advance manifests in their passing hidden displacement tasks, engaging in pretense and means-ends reasoning, interpreting external representations, displaying mirror self-recognition and empathic behavior, and showing an early understanding of mind and imitation. New data show a cluster of mental accomplishments in great apes that is very similar to that observed in 2-year-old humans. It is suggested that it is most parsimonious to assume that this cognitive profile is of homologous origin and that great apes possess secondary representational capacity. Evidence from animals other than apes is scant. This analysis leads to a number of predictions for future research.

An architectonic comparison of the ventrobasal complex of two Megachiropteran and one Microchiropteran bat: implications for the evolution of Chiroptera

The architectonic features of the thalamic ventrobasal complex (Vb) of two species of Megachiropteran (Grey-headed flying fox, Pteropus poliocephalus, and the Eastern tube-nosed bat, Nyctimene robinsoni) are compared with those of a Microchiropteran (Australian ghost bat, Macroderma gigas). The somatosensory system was chosen for comparison as it represents a sensory system that has undergone analogous modifications in both Chiropteran lineages (the evolution of the wing). The components of Vb were examined as there are taxon-specific features in this region of the brain. Within the Megachiropteran Vb, four subnuclei were recognized: the ventral posterior medial (VPM), the ventral posterior lateral (VPL), the ventral posterior inferior (VPI), and the basal ventral medial (VMb). In the ghost bat only VPM and VPL were identified with certainty. No VPI was evident in the ghost bat, however a putative VMb was observed. Vb of the ghost bat also lacked the arcuate lamina, which distinguishes VPM from VPL in the Megachiropterans and many other mammals. These taxon-specific differences lend support to the proposal that the order Chiroptera has a diphyletic origin.

Influence of deceleration profiles on occupant velocity differential and injury potential

This paper compares two hypothetical and identical vehicle deceleration profiles mirrored in time, one linearly descending with time and the other linearly ascending with time. The differences of such profiles on occupant velocity differential and by implication, injury levels at the point of occupant impact are presented. An indifference point is established to assist in comparing which occupant body part will benefit from the altered crash pulse. It is shown that for occupant proximity distances below the indifference point, an ascending profile results in lower injury risk. Above the indifference point, the result is reversed.

Phylogenetic relationships of Trypanosoma chelodina and Trypanosoma binneyi from Australian tortoises and platypuses inferred from small subunit rRNA analyses

Trypanosome infections are often difficult to detect by conventional microscopy and their pleomorphy often confounds differential diagnosis. Molecular techniques are now being used to diagnose infections and to determine phylogenetic relationships between species. Complete small subunit rRNA gene sequences were determined for isolates of Trypanosoma chelodina from the Brisbane River tortoise (Emydura signata), the saw-shelled tortoise (Elseya latisternum), and the eastern snake-necked tortoise (Chelodina longicollis) from southeast Queensland, Australia. Partial sequence data were also obtained for T. binneyi from a platypus (Ornithorhynchus anatinus) from Tasmania. Phylogenetic relationships between T. chelodina, T. binneyi and other species were examined by maximum parsimony and likelihood methods. The Australian tortoise and platypus trypanosomes did not exhibit any close phylogenetic relationships with those of mammals, reptiles or amphibians, but were closely related to each other, and to fish trypanosomes. This contra-indicates their co-evolution with their vertebrate hosts but does not exclude co-evolution with different groups of invertebrate vectors, notably insects and leeches.

The evolution of controlled multitasked gene networks: The role of introns and other noncoding RNAs in the development of complex organisms

Eukaryotic phenotypic diversity arises from multitasking of a core proteome of limited size. Multitasking is routine in computers, as well as in other sophisticated information systems, and requires multiple inputs and outputs to control and integrate network activity. Higher eukaryotes have a mosaic gene structure with a dual output, mRNA (protein-coding) sequences and introns, which are released from the pre-mRNA by posttranscriptional processing. Introns have been enormously successful as a class of sequences and comprise up to 95% of the primary transcripts of protein-coding genes in mammals. In addition, many other transcripts (perhaps more than half) do not encode proteins at all, but appear both to be developmentally regulated and to have genetic function. We suggest that these RNAs (eRNAs) have evolved to function as endogenous network control molecules which enable direct gene-gene communication and multitasking of eukaryotic genomes. Analysis of a range of complex genetic phenomena in which RNA is involved or implicated, including co-suppression, transgene silencing, RNA interference, imprinting, methylation, and transvection, suggests that a higher-order regulatory system based on RNA signals operates in the higher eukaryotes and involves chromatin remodeling as well as other RNA-DNA, RNA-RNA, and RNA-protein interactions. The evolution of densely connected gene networks would be expected to result in a relatively stable core proteome due to the multiple reuse of components, implying,that cellular differentiation and phenotypic variation in the higher eukaryotes results primarily from variation in the control architecture. Thus, network integration and multitasking using trans-acting RNA molecules produced in parallel with protein-coding sequences may underpin both the evolution of developmentally sophisticated multicellular organisms and the rapid expansion of phenotypic complexity into uncontested environments such as those initiated in the Cambrian radiation and those seen after major extinction events.

Differential perturbation of neuronal and glial glutamate transport systems in retinal ischaemia

Glutamate is the major excitatory neurotransmitter in the retina and is removed from the extracellular space by an energy-dependent process involving neuronal and glial cell transporters. The radial glial Muller cells express the glutamate transporter, GLAST, and preferentially accumulate glutamate. However, during an ischaemic episode, extracellular glutamate concentrations may rise to excitotoxic levels. Is this catastrophic rise in extracellular glutamate due to a failure of GLAST? Using immunocytochemistry, we monitored the transport of the glutamate transporter substrate, D-aspartate, in the retina under normal and ischaemic conditions. Two models of compromised retinal perfusion were compared: (1) Anaesthetised rats had their carotid arteries occluded for 7 days to produce a chronic reduction in retinal blood flow. Retinal function was assessed by electroretinography. D-aspartate was injected into the eye for 45 min, Following euthanasia, the retina was processed for D-aspartate. GLAST and glutamate immunocytochemistry. Although reduced retinal perfusion suppresses the electroretinogram b-wave, neither retinal histology, GLAST expression, nor the ability of Muller cells to uptake D-aspartate is affected. As this insult does not appear to cause excitotoxic neuronal damage, these data suggest that GLAST function and glutamate clearance are maintained during periods of reduced retinal perfusion. (2) Occlusion of the central retinal artery for 60 min abolishes retinal perfusion, inducing histological damage and electroretinogram suppression. Although GLAST expression appears to be normal. its ability to transport D-aspartate into Muller cells is greatly reduced. Interestingly, D-aspartate is transported into neuronal cells, i.e. photoreceptors, bipolar and ganglion cells. This suggests that while GLAST is vitally important for the clearance of excess extracellular glutamate, its capability to sustain inward transport is particularly susceptible to an acute ischaemic attack. Manipulation of GLAST function could alleviate the degeneration and blindness that result from ischaemic retinal disease. (C) 2001 Elsevier Science Ltd, All rights reserved.

Differential inhibition of human CYP1A1 AND CYP1A2 by quinidine and quinine.

The inhibition of recombinant CYP1A1 and CYP1A2 activity by quinidine and quinine was evluated using ethoxyresorufin O -deethylation, phenacetin O -deethylation and propranolol desisopropylation as probe catalytic pathways. 2. With substrate concentrations near the K m of catalysis, both quinidine and quinine potently inhibited CYP1A1 activity with [ I ] 0.5 ~ 1-3 μM, whereas in contrast, there was little inhibition of CYP1A2 activity. The Lineweaver-Burk plots with varying inhibitor concentrations suggested that inhibition by quinidine and quinine was competitive. 3. There was only trace metabolism of quinidine by recombinant CYP1A1, whereas rat liver microsomes as a control showed extensive consumption of quinidine and metabolite production. 4. This work suggests that quinidine is a non-classical inhibitor of CYP1A1 and that it is not as highly specific at inhibiting CYP2D6 as previously thought.