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.

Evaluation of the BEASY program using linear and piecewise linear approaches for the boundary conditions

The boundary element method (BEM) was used to study galvanic corrosion using linear and logarithmic boundary conditions. The linear boundary condition was implemented by using the linear approach and the piecewise linear approach. The logarithmic boundary condition was implemented by the piecewise linear approach. The calculated potential and current density distribution were compared with the prior analytical results. For the linear boundary condition, the BEASY program using the linear approach and the piecewise linear approach gave accurate predictions of the potential and the galvanic current density distributions for varied electrolyte conditions, various film thicknesses, various electrolyte conductivities and various area ratio of anode/cathode. The 50-point piecewise linear method could be used with both linear and logarithmic polarization curves.

Optimal unravellings for feedback control in linear quantum systems

For quantum systems with linear dynamics in phase space much of classical feedback control theory applies. However, there are some questions that are sensible only for the quantum case: Given a fixed interaction between the system and the environment what is the optimal measurement on the environment for a particular control problem? We show that for a broad class of optimal (state- based) control problems ( the stationary linear-quadratic-Gaussian class), this question is a semidefinite program. Moreover, the answer also applies to Markovian (current-based) feedback.

A Nonstationary Model of Newborn EEG

The detection of seizure in the newborn is a critical aspect of neurological research. Current automatic detection techniques are difficult to assess due to the problems associated with acquiring and labelling newborn electroencephalogram (EEG) data. A realistic model for newborn EEG would allow confident development, assessment and comparison of these detection techniques. This paper presents a model for newborn EEG that accounts for its self-similar and non-stationary nature. The model consists of background and seizure sub-models. The newborn EEG background model is based on the short-time power spectrum with a time-varying power law. The relationship between the fractal dimension and the power law of a power spectrum is utilized for accurate estimation of the short-time power law exponent. The newborn EEG seizure model is based on a well-known time-frequency signal model. This model addresses all significant time-frequency characteristics of newborn EEG seizure which include; multiple components or harmonics, piecewise linear instantaneous frequency laws and harmonic amplitude modulation. Estimates of the parameters of both models are shown to be random and are modelled using the data from a total of 500 background epochs and 204 seizure epochs. The newborn EEG background and seizure models are validated against real newborn EEG data using the correlation coefficient. The results show that the output of the proposed models has a higher correlation with real newborn EEG than currently accepted models (a 10% and 38% improvement for background and seizure models, respectively).

Biaxial failure model for fiber reinforced concrete

Steel fiber reinforced concrete (SFRC) is widely applied in the construction industry. Numerical elastoplastic analysis of the macroscopic behavior is complex. This typically involves a piecewise linear failure curve including corner singularities. This paper presents a single smooth biaxial failure curve for SFRC based on a semianalytical approximation. Convexity of the proposed model is guaranteed so that numerical problems are avoided. The model has sufficient flexibility to closely match experimental results. The failure curve is also suitable for modeling plain concrete under biaxial loading. Since this model is capable of simulating the failure states in all stress regimes with a single envelope, the elastoplastic formulation is very concise and simple. The finite element implementation is developed to demonstrate the conciseness and the effectiveness of the model. The computed results display good agreement with published experimental data.

Modeling hybridoma cell metabolism using a generic genome-scale metabolic model of Mus musculus

The reconstructed cellular metabolic network of Mus musculus, based on annotated genomic data, pathway databases, and currently available biochemical and physiological information, is presented. Although incomplete, it represents the first attempt to collect and characterize the metabolic network of a mammalian cell on the basis of genomic data. The reaction network is generic in nature and attempts to capture the carbon, energy, and nitrogen metabolism of the cell. The metabolic reactions were compartmentalized between the cytosol and the mitochondria, including transport reactions between the compartments and the extracellular medium. The reaction list consists of 872 internal metabolites involved in a total of 1220 reactions, whereof 473 relate to known open reading frames. Initial in silico analysis of the reconstructed model is presented.

Suppressing chaos via Lyapunov-Krasovskii's method

An algorithm for suppressing the chaotic oscillations in non-linear dynamical systems with singular Jacobian matrices is developed using a linear feedback control law based upon the Lyapunov-Krasovskii (LK) method. It appears that the LK method can serve effectively as a generalised method for the suppression of chaotic oscillations for a wide range of systems. Based on this method, the resulting conditions for undisturbed motions to be locally or globally stable are sufficient and conservative. The generalized Lorenz system and disturbed gyrostat equations are exemplified for the validation of the proposed feedback control rule. (c) 2005 Elsevier 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.

Periodic or Bounded Solutions of Carathéodory Systems of Ordinary Differential Equations

In this paper we extend the guiding function approach to show that there are periodic or bounded solutions for first order systems of ordinary differential equations of the form x1 =f(t,x), a.e. epsilon[a,b], where f satisfies the Caratheodory conditions. Our results generalize recent ones of Mawhin and Ward.

Applying linear time-varying constraints to econometric models: With an application to demand systems

When linear equality constraints are invariant through time they can be incorporated into estimation by restricted least squares. If, however, the constraints are time-varying, this standard methodology cannot be applied. In this paper we show how to incorporate linear time-varying constraints into the estimation of econometric models. The method involves the augmentation of the observation equation of a state-space model prior to estimation by the Kalman filter. Numerical optimisation routines are used for the estimation. A simple example drawn from demand analysis is used to illustrate the method and its application.

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.

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.

Brief note on the variation of constants formula for fuzzy differential equations

This note gives a theory of state transition matrices for linear systems of fuzzy differential equations. This is used to give a fuzzy version of the classical variation of constants formula. A simple example of a time-independent control system is used to illustrate the methods. While similar problems to the crisp case arise for time-dependent systems, in time-independent cases the calculations are elementary solutions of eigenvalue-eigenvector problems. In particular, for nonnegative or nonpositive matrices, the problems at each level set, can easily be solved in MATLAB to give the level sets of the fuzzy solution. (C) 2002 Elsevier Science B.V. All rights reserved.

Detection and description of non-linear interdependence in normal multichannel human EEG data

Objectives: This study examines human scalp electroencephalographic (EEG) data for evidence of non-linear interdependence between posterior channels. The spectral and phase properties of those epochs of EEG exhibiting non-linear interdependence are studied. Methods: Scalp EEG data was collected from 40 healthy subjects. A technique for the detection of non-linear interdependence was applied to 2.048 s segments of posterior bipolar electrode data. Amplitude-adjusted phase-randomized surrogate data was used to statistically determine which EEG epochs exhibited non-linear interdependence. Results: Statistically significant evidence of non-linear interactions were evident in 2.9% (eyes open) to 4.8% (eyes closed) of the epochs. In the eyes-open recordings, these epochs exhibited a peak in the spectral and cross-spectral density functions at about 10 Hz. Two types of EEG epochs are evident in the eyes-closed recordings; one type exhibits a peak in the spectral density and cross-spectrum at 8 Hz. The other type has increased spectral and cross-spectral power across faster frequencies. Epochs identified as exhibiting non-linear interdependence display a tendency towards phase interdependencies across and between a broad range of frequencies. Conclusions: Non-linear interdependence is detectable in a small number of multichannel EEG epochs, and makes a contribution to the alpha rhythm. Non-linear interdependence produces spatially distributed activity that exhibits phase synchronization between oscillations present at different frequencies. The possible physiological significance of these findings are discussed with reference to the dynamical properties of neural systems and the role of synchronous activity in the neocortex. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.