Stability of nonlinear difference inclusions

The stability of difference inclusions x(k+1) is an element of F(x(k)) is studied, where F(x) = {F(x, gimel) : is an element of Lambda} and the selections F(., gimel) : E -->E assume values in a Banach space E, partially ordered by a cone K. It is assumed that the operators F(.,gimel) are heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, and include the case of a single equilibrium point. The results are applied to a number of practical problems.

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.

Estimates of the real structured radius of stability of linear dynamic systems

A question is examined as to estimates of the norms of perturbations of a linear stable dynamic system, under which the perturbed system remains stable in a situation R:here a perturbation has a fixed structure.

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.

The human temporal cortex: Characterization of neurons expressing nitric oxide synthase, neuropeptides and calcium-binding proteins, and their glutamate receptor subunit profiles

Immunocytochemical techniques were used to examine the distribution of neurons immunoreactive (-ir) for nitric oxide synthase (nNOS), somatostatin (SOM), neuropeptide Y (NPY), parvalbumin (PV), calbindin (CB) and calretinin (CH), in the inferotemporal gyros (Brodmann's area 21) of the human neocortex. Neurons that colocalized either nNOS or SOM with PV, CB or CR were also identified by double-labeling techniques. Furthermore, glutamate receptor subunit profiles (GluR1, GluR2/3, GluR2/4, GluR5/6/7 and NMDAR1) were also determined for these cells. The number and distribution of cells containing nNOS, SOM, NPY, PV, CB or CR differed for each antigen. In addition, distinct subpopulations of neurons displayed different degrees of colocalization of these antigens depending on which antigens were compared. Moreover, cells that contained nNOS, SOM, NPY, PV, GB or CR expressed different receptor subunit profiles. These results show that specific subpopulations of neurochemically identified nonpyramidal cells may be activated via different receptor subtypes. As these different subpopulations of cells project to specific regions of pyramidal calls, facilitation of subsets of these cells via different receptor subunits may activate different inhibitory circuits. Thus, various distinct, but overlapping, inhibitory circuits may act in concert in the modulation of normal cortical function, plasticity and disease.

Interlaminar differences in the pyramidal cell phenotype in cortical areas 7m and STP (the superior temporal polysensory area) of the macaque monkey

Pyramidal neurones were injected with Lucifer Yellow in slices cut tangential to the surface of area 7m and the superior temporal polysensory area (STP) of the macaque monkey. Comparison of the basal dendritic arbors of supra- and infragranular pyramidal neurones (n=139) that were injected in the same putative modules in the different cortical areas revealed variation in their structure. Moreover, there were relative differences in dendritic morphology of supra- and infragranular pyramidal neurones in the two cortical areas. Shell analyses revealed that layer III pyramidal neurones in area STP had considerably higher peak complexity (maximum number of dendritic intersections per Shell circle) than those in layer V, whereas peak complexities were similar for supra- and infragranular pyramidal neurones in area 7m. In both cortical areas, the basal dendritic trees of layer m pyramidal neurones were characterized by a higher spine density than those in layer V. Calculations of the total number of dendritic spines in the average basal dendritic arbor revealed that layer V pyramidal neurones in area 7m had twice as many spines as cells in layer III. (4535 and 2294, respectively). A similar calculation for neurones in area STP revealed that layer III pyramidal neurones had approximately the same number of spines as cells in layer V (3585 and 3850 spines, respectively). Relative differences in the branching patterns of, and the number of spines in, the basal dendritic arbors of supra- and infragranular pyramidal neurones in the different cortical areas may allow for integration of different numbers of inputs, and different degrees of dendritic processing. These results support the thesis that intra-areal circuitry differs in different cortical areas.

Valproic acid has temporal variability in urinary clearance of metabolites

The reasons for the intra- and interindividual variability in the clearance of valproic acid (VPA) have not been completely characterized. The aim of this study was to examine day-night changes in the clearance of 3-oxo-valproate (3-oxo-VPA), 4-hydroxy-valproate (4-OH-VPA), and valproic acid glucuronides under steady state. Six diurnally active healthy male volunteers ingested 200 mg sodium valproate 12 hourly, at 0800 and 2000, for 28 days. On the last study day, two sequential 12-h urine samples were collected commencing at 2000 the evening before. Plasma samples were obtained at the end of each collection. Following alkaline hydrolysis, urine was analyzed for concentrations of VPA, 3-oxo-VPA, and 4-OH-VPA. A separate aliquot was assayed for creatinine (CR). The plasma concentrations of VPA, 3-oxo-VPA, 2-en-VPA, and CR were determined. The analysis of VPA and its metabolites was performed by CC-MS. There was an increase in plasma 3-oxo-VPA concentration at 0800, sampling as compared to 2000 sampling (p < .05). The urinary excretion of 3-oxo-VPA and VPA glucuronides were decreased between 2000 and 0800, compared to between 0800, and 2000, by 30% and 50% respectively (p < .05). These results indicate a nocturnal decrease in renal clearance of 3-oxo-VPA rather than a decrease in the beta -oxidation of VPA at night. These differences were not explained by differences between the sampling periods in CR excretion. These results indicate the importance of collecting samples of 24-h duration when studying metabolic profiles of VPA.

The acquisition of movement skills: Practice enhances the dynamic stability of bimanual coordination

During bimanual movements, two relatively stable inherent patterns of coordination (in-phase and anti-phase) are displayed (e.g., Kelso, Am. J. Physiol. 246 (1984) R1000). Recent research has shown that new patterns of coordination can be learned. For example, following practice a 90 degrees out-of-phase pattern can emerge as an additional, relatively stable, state (e.g., Zanone & Kelso, J. Exp. Psychol.: Human Performance and Perception 18 (1992) 403). On this basis, it has been concluded that practice leads to the evolution and stabilisation of the newly learned pattern and that this process of learning changes the entire attractor layout of the dynamic system. A general feature of such research has been to observe the changes of the targeted pattern's stability characteristics during training at a single movement frequency. The present study was designed to examine how practice affects the maintenance of a coordinated pattern as the movement frequency is scaled. Eleven volunteers were asked to perform a bimanual forearm pronation-supination task. Time to transition onset was used as an index of the subjects' ability to maintain two symmetrically opposite coordinated patterns (target task - 90 degrees out-of-phase - transfer task - 270 degrees out-of-phase). Their ability to maintain the target task and the transfer task were examined again after five practice sessions each consisting of 15 trials of only the 90 degrees out-of-phase pattern. Concurrent performance feedback (a Lissajous figure) was available to the participants during each practice trial. A comparison of the time to transition onset showed that the target task was more stable after practice (p = 0.025). These changes were still observed one week (p = 0.05) and two months (p = 0.075) after the practice period. Changes in the stability of the transfer task were not observed until two months after practice (p = 0.025). Notably, following practice, transitions from the 90 degrees pattern were generally to the anti-phase (180 degrees) pattern, whereas, transitions from the 270 degrees pattern were to the 90 degrees pattern. These results suggest that practice does improve the stability of a 90 degrees pattern, and that such improvements are transferable to the performance of the unpractised 270 degrees pattern. In addition, the anti-phase pattern remained more stable than the practised 90 degrees pattern throughout. (C) 2001 Elsevier Science B.V. All rights reserved.

Let your feet do the walking: constraints on the stability of bipedal coordination

In this paper we consider whether the behaviour of the neural circuitry that controls lower limb movements in humans is shaped primarily by the spatiotemporal characteristics of bipedal gait patterns, or by selective pressures that are sensitive to considerations of balance and energetics. During the course of normal locomotion, the full dynamics of the neural circuitry are masked by the inertial properties of the limbs. In the present study, participants executed bipedal movements in conditions in which their feet were either unloaded or subject to additional inertial loads. Two patterns of rhythmic coordination were examined. In the in-phase mode, participants were required to flex their ankles and extend their ankles in synchrony. In the out-of-phase mode, the participants flexed one ankle while extending the other and vice versa. The frequency of movement was increased systematically throughout each experimental trial. All participants were able to maintain both the in-phase and the out-of-phase mode of coordination, to the point at which they could no longer increase their frequency of movement. Transitions between the two modes were not observed, and the stability of the out-of-phase and in-phase modes of coordination was equivalent at all movement frequencies. These findings indicate that, in humans, the behaviour of the neural circuitry underlying coordinated movements of the lower limbs is not constrained strongly by the spatiotemporal symmetries of bipedal gait patterns.

Effects of temporal association on recognition memory

The influence of temporal association on the representation and recognition of objects was investigated. Observers were shown sequences of novel faces in which the identity of the face changed as the head rotated. As a result, observers showed a tendency to treat the views as if they were of the same person. Additional experiments revealed that this was only true if the training sequences depicted head rotations rather than jumbled views: in other words, the sequence had to be spatially as well as temporally smooth. Results suggest that we are continuously associating views of objects to support later recognition, and that we do so not only on the basis of the physical similarity, but also the correlated appearance in time of the objects.

Techniques to determine ignition, flame stability and burnout of blended coals in p.f. power station boilers

The blending of coals has become popular to improve the performance of coals, to meet specifications of power plants and, to reduce the cost of coals, This article reviews the results and provides new information on ignition, flame stability, and carbon burnout studies of blended coals. The reviewed studies were conducted in laboratory-, pilot-, and full-scale facilities. The new information was taken in pilot-scale studies. The results generally show that blending a high-volatile coal with a low-volatile coal or anthracite can improve the ignition, flame stability and burnout of the blends. This paper discusses two general methods to predict the performance of blended coals: (1) experiment; and (2) indices. Laboratory- and pilot-scale tests, at least, provide a relative ranking of the combustion performance of coal/blends in power station boilers. Several indices, volatile matter content, heating value and a maceral index, can be used to predict the relative ranking of ignitability and flame stability of coals and blends. The maceral index, fuel ratio, and vitrinite reflectance can also be used to predict the absolute carbon burnout of coal and blends within limits. (C) 2000 Elsevier Science Ltd. All rights reserved.

Olfaction in the Queensland fruit fly, Bactrocera tryoni. II: Response spectra and temporal encoding characteristics of the carbon dioxide receptors

Single-unit electrophysiology was used to record the nerve impulses from the carbon dioxide receptors of female Queensland fruit flies, Bactrocera tryoni. The receptors responded to stimulation in a phasic-tonic manner and also had a period of inhibition of the nerve impulses after the end of stimulation, at high stimulus intensities. The cell responding to carbon dioxide was presented with a range of environmental odorants and found to respond to methyl butyrate and 2-butanone. The coding characteristics of the carbon dioxide cell and the ability to detect other odorants are discussed, with particular reference to the known behavior of the fly.