Anisotropy-based performance analysis of linear discrete time invariant control systems

The anisotropic norm of a linear discrete-time-invariant system measures system output sensitivity to stationary Gaussian input disturbances of bounded mean anisotropy. Mean anisotropy characterizes the degree of predictability (or colouredness) and spatial non-roundness of the noise. The anisotropic norm falls between the H-2 and H-infinity norms and accommodates their loss of performance when the probability structure of input disturbances is not exactly known. This paper develops a method for numerical computation of the anisotropic norm which involves linked Riccati and Lyapunov equations and an associated special type equation.

A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case. (C) 2000 Elsevier Science Ltd. All rights reserved.

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.

Fossil trees in ancient fluvial channel deposits: evidence of seasonal and longer-term climatic variability

It has been established that large numbers of certain trees can survive in the beds of rivers of northeastern Australia where a strongly seasonal distribution of precipitation causes extreme variations in flow on both a yearly and longer-term basis. In these rivers, minimal flow occurs throughout much of any year and for periods of up to several years, allowing the trees to become established and to adapt their form in order to facilitate their survival in environments that experience periodic inundation by fast-flowing, debris-laden water. Such trees (notably paperbark trees of the angiosperm genus Melaleuca) adopt a reclined to prostrate, downstream-trailing habit, have a multiple-stemmed form, modified crown with weeping foliage, development of thick, spongy bark, anchoring of roots into firm to lithified substrates beneath the channel floor, root regeneration, and develop in flow-parallel, linear groves. Individuals from within flow-parallel, linear groves are preserved in situ within the alluvial deposit of the river following burial and death. Four examples of in situ tree fossils within alluvial channel deposits in the Permian of eastern Australia demonstrate that specialised riverbed plant communities also existed at times in the geological past. These examples, from the Lower Permian Carmila Beds, Upper Permian Moranbah Coal Measures and Baralaba Coal Measures of central Queensland and the Upper Permian Newcastle Coal Measures of central New South Wales, show several of the characteristics of trees described from modern rivers in northeastern Australia, including preservation in closely-spaced groups. These properties, together with independent sedimentological evidence, suggest that the Permian trees were adapted to an environment affected by highly variable runoff, albeit in a more temperate climatic situation than the modem Australian examples. It is proposed that occurrences of fossil trees preserved in situ within alluvial channel deposits may be diagnostic of environments controlled by seasonal and longer-term variability in fluvial runoff, and hence may have value in interpreting aspects of palaeoclimate from ancient alluvial successions. (C) 2001 Elsevier Science B.V. All rights reserved.

Dorsal and ventral medullary catecholamine cell groups contribute differentially to systemic interleukin-1 beta-induced hypothalamic pituitary adrenal axis responses

Medial parvocellular paraventricular corticotropin-releasing hormone (mPVN CRH) cells are critical in generating hypothalamic-pituitary-adrenal (HPA) axis responses to systemic interleukin-1 beta (IL-1 beta). However, although it is understood that catecholamine inputs are important in initiating mPVN CRH cell responses to IL-1 beta, the contributions of distinct brainstem catecholamine cell groups are not known. We examined the role of nucleus tractus solitarius (NTS) and ventrolateral medulla (VLM) catecholamine cells in the activation of mPVN CRH, hypothalamic oxytocin (OT) and central amygdala cells in response to IL-1 beta (1 mug/kg, i.a.). Immunolabelling for the expression of c-fos was used as a marker of neuronal activation in combination with appropriate cytoplasmic phenotypic markers. First we confirmed that PVN 6-hydroxydopamine lesions, which selectively depleted catecholaminergic terminals, significantly reduced IL-1 beta -induced mPVN CRH cell activation. The contribution of VLM (A1/C1 cells) versus NTS (A2 cells) catecholamine cells to mPVN CRH cell responses was then examined by placing ibotenic acid lesions in either the VLM or NTS. The precise positioning of these lesions was guided by prior retrograde tracing studies in which we mapped the location of IL-1 beta -activated VLM and NTS cells that project to the mPVN. Both VLM and NTS lesions reduced the mPVN CRH and OT cell responses to IL-1 beta. Unlike VLM lesions, NTS lesions also suppressed the recruitment of central amygdala neurons. These studies provide novel evidence that both the NTS and VLM catecholamine cells have important, but differential, contributions to the generation of IL-1 beta -induced HPA axis responses. Copyright (C) 2001 S. Karger AG, Basel.

Stressor categorization: acute physical and psychological stressors elicit distinctive recruitment patterns in the amygdala and in medullary noradrenergic cell groups

It has been hypothesized that the brain categorizes stressors and utilizes neural response pathways that vary in accordance with the assigned category. If this is true, stressors should elicit patterns of neuronal activation within the brain that are category-specific. Data from previous Immediate-early gene expression mapping studies have hinted that this is the case, but interstudy differences in methodology render conclusions tenuous. In the present study, immunolabelling for the expression of c-fos was used as a marker of neuronal activity elicited in the rat brain by haemorrhage, immune challenge, noise, restraint and forced swim. All stressors elicited c-fos expression in 25-30% of hypothalamic paraventricular nucleus corticotrophin-releasing-factor cells, suggesting that these stimuli were of comparable strength, at least with regard to their ability to activate the hypothalamic-pituitary-ad renal axis. In the amygdala, haemorrhage and immune challenge both elicited c-fos expression in a large number of neurons in the central nucleus of the amygdala, whereas noise, restraint and forced swim primarily elicited recruitment of cells within the medial nucleus of the amygdala. In the medulla, all stressors recruited similar numbers of noradrenergic (A1 and A2) and adrenergic (C1 and C2) cells. However, haemorrhage and immune challenge elicited c-fos expression In subpopulations of A1 and A2 noradrenergic cells that were significantly more rostral than those recruited by noise, restraint or forced swim. The present data support the suggestion that the brain recognizes at least two major categories of stressor, which we have referred to as 'physical' and 'psychological'. Moreover, the present data suggest that the neural activation footprint that is left in the brain by stressors can be used to determine the category to which they have been assigned by the brain.