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.

Temporal relationship between the auditory brainstem response and focal responses of auditory nerve root and cochlear nucleus during development in the tammar wallaby (Macropus eugenii)

Thirty-two pouch-young tammar wallabies were used to discover the generators of the auditory brainstem response (ABR) during development by the use of simultaneous ABR and focal brainstem recordings. A click response from the auditory nerve root (ANR) in the wallaby was recorded from postnatal day (PND) 101, when no central auditory station was functional, and coincided with the ABR, a simple positive wave. The response of the cochlear nucleus (CN) was detected from PND 110, when the ABR had developed 1 positive and 1 negative peak. The dominant component of the focal ANR response, the N-1 wave, coincided with the first half of the ABR P wave, and that of the focal CN response, the N-1 wave, coincided with the later two thirds. In older animals, the ANR response coincided with the ABR's N-1, wave, while the CN response coincided with the ABR's P-2, N-2 and P-3 waves, with its contribution to the ABR P-2 dominant. The protracted development of the marsupial auditory system which facilitated these correlations makes the tammar wallaby a particularly suitable model. Copyright (C) 2001 S. Karger AG, Basel.

Medullary neurones regulate hypothalamic corticotropin-releasing factor cell responses to an emotional stressor

Hypothalamic-pituitary-adrenal axis activation is a hallmark of the stress response. In the case of physical stressors, there is considerable evidence that medullary catecholamine neurones are critical to the activation of the paraventricular nucleus corticotropin-releasing factor cells that constitute the apex of the hypothalamic-pituitary-adrenal axis. In contrast, it has been thought that hypothalamic-pituitary-adrenal axis responses to emotional stressors do not involve brainstem neurones. To investigate this issue we have mapped patterns of restraint-induced neuronal c fos expression in intact animals and in animals prepared with either paraventricular nucleus-directed injections of a retrograde tracer, lesions of paraventricular nucleus catecholamine terminals, or lesions of the medulla corresponding to the A1 or A2 noradrenergic cell groups. Restraint-induced patterns of neuronal activation within the medulla of intact animals were very similar to those previously reported in response to physical stressors, including the fact that most stressor-responsive, paraventricular nucleus-projecting cells were certainly catecholaminergic and probably noradrenergic. Despite this, the destruction of paraventricular nucleus catecholamine terminals with 6-hydroxydopamine did not alter corticotropin-releasing factor cell responses to restraint. However, animals with ibotenic acid lesions encompassing either the A1 or A2 noradrenergic cell groups displayed significantly suppressed corticotropin-releasing factor cell responses to restraint. Notably, these medullary lesions also suppressed neuronal responses in the medial amygdala, an area that is now considered critical to hypothalamic-pituitary-adrenal axis responses to emotional stressors and that is also known to display a significant increase in noradrenaline turnover during restraint. We conclude that medullary neurones influence corticotropin-releasing factor cell responses to emotional stressors via a multisynaptic pathway that may involve a noradrenergic input to the medial amygdala. These results overturn the idea that hypothalamic-pituitary-adrenal axis response to emotional stressors can occur independently of the brainstem. (C) 2001 IBRO. Published by Elsevier Science Ltd. All rights reserved.

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.

Blink startle modulation during anticipation of pleasant and unpleasant stimuli

The present research investigated blink startle modulation during the anticipation of pleasant, unpleasant, or neutral pictures. In Experiment 1 (N = 18), participants were presented with three different tone-picture pairings. Tones differed in pitch and were followed by pleasant, neutral or unpleasant pictures. Acoustic blink reflexes were elicited during some tones and during stimulus free intervals. Blink facilitation during tones that preceded pleasant and unpleasant pictures was larger than during the tone that preceded neutral pictures. Experiment 2 (N = 10) assessed whether this difference was due to a difference in the presentation frequency of the three conditions. No difference in blink facilitation between the conditions was found when pictures of flowers and mushrooms replaced the pleasant and unpleasant pictures, indicating that picture content was instrumental in causing the differential blink facilitation in Experiment 1. The results from Experiment 1 seem to indicate that startle modulation during the anticipation of pictorial material reflects the interest in or the arousal associated with the pictures rather than picture valence.

Contrasting Epstein-Barr virus-specific cytotoxic T cell responses to HLA A2-restricted epitopes in humans and HLA transgenic mice: implications for vaccine design

This study investigates the hierarchy of cytotoxic T cell (CTL) responses to twelve HLA A2-restricted epitopes from the latent, lytic and structural proteins of Epstein–Barr virus (EBV) in acute infectious mononucleosis and in healthy seropositive donors and the relative immunogenecity of these epitopes in transgenic mice. Responses to the lytic epitope were uniformly strong in all healthy seropositive individuals and acute infectious mononucleosis donors while moderate or low responses were observed to the latent and structural epitopes, respectively in both groups studied. In contrast, when HLA A2/Kb transgenic mice were immunised with these peptide epitopes, CTL responses were observed to all epitopes with a maximal response to the epitopes within the structural proteins and low to moderate responses to the latent epitopes. This hierarchy of CTL responses in mice was also reflected in an MHC stabilisation analysis. These contrasting CTL responses in humans following natural infection compared to the immunogenicity of these epitopes and their ability to stabilise MHC may need to be considered when designing an EBV vaccine.

Conversational influences on young children's responses to misleading questions

The present study investigated the degree to which young children's suggestible responses were related to their pragmatic language ability. In Experiment 1, forty-seven 5- and 6-year-olds were read a short picture story followed the next day by a postevent synopsis that included both consistent and misleading details about the original story. Six days later, a suggestibility effect was evident with responses to questions about the details that had been misled being less accurate than to those about details not misled. Although age significantly correlated with this effect, the relationship was not significant after controlling for the children's pragmatic language ability. The procedure in Experiment 2 was identical with the exception that the thirty-nine 5- and 6-year-olds were questioned in a format that made explicit the intended reference point of the interrogation. A suggestibility effect was now not evident nor was accuracy related to age. Taken together, these results support the position that young children's suggestibility requires a consideration not only in terms of suggestible memories but also in terms of suggestible responses that can result from incorrectly interpreting the intended message of an experimenter's questions. (C) 2001 Elsevier Science Inc. All rights reserved.

Association of clinical, radiological and synovial immunopathological responses to anti-rheumatic treatment in rheumatoid arthritis

Objectives. To compare immunohistochemical scoring with clinical scoring and radiology for the assessment of rheumatoid arthritis (RA) disease activity, synovial tissue (ST) biopsied arthroscopically was assessed from 18 patients before and after commencement of disease-modifying anti-rheumatic drug (DMARD) therapy. Methods. Lymphocytes, macrophages, differentiated dendritic cells (DC), vascularity, tumour necrosis factor (TNF)alpha and interleukin-1 beta levels were scored. Clinical status was scored using the American College of Rheumatology (ACR) core set and serial radiographs were scored using the Larsen and Sharp methods. Histopathological evidence of activity included infiltration by lymphocytes, DC, macrophages. tissue vascularity, and expression of lining and sublining TNF alpha. These indices co-varied across the set of ST biopsies and were combined as a synovial activity score for each biopsy. Results. The change in synovial activity with treatment correlated with the ACR clinical response and with decreased radiological progression by the Larsen score, The ACR response to DMARD therapy. the change in synovial activity score and the slowing of radiological progression were each greatest in patients with high initial synovial vascularity. Conclusions. The data demonstrate an association between clinical, radiological and synovial immunopathological responses to anti-rheumatic treatment in RA. High ST vascularity may predict favourable clinical and radiological responses to treatment.

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.