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.

Noise-free scattering of the quantized electromagnetic field from a dispersive linear dielectric

We study the scattering of the quantized electromagnetic field from a linear, dispersive dielectric using the scattering formalism for quantum fields. The medium is modeled as a collection of harmonic oscillators with a number of distinct resonance frequencies. This model corresponds to the Sellmeir expansion, which is widely used to describe experimental data for real dispersive media. The integral equation for the interpolating field in terms of the in field is solved and the solution used to find the out field. The relation between the ill and out creation and annihilation operators is found that allows one to calculate the S matrix for this system. In this model, we find that there are absorption bands, but the input-output relations are completely unitary. No additional quantum-noise terms are required.

Linear models of simple cells: Correspondence to real cell responses and space spanning properties

Despite their limitations, linear filter models continue to be used to simulate the receptive field properties of cortical simple cells. For theoreticians interested in large scale models of visual cortex, a family of self-similar filters represents a convenient way in which to characterise simple cells in one basic model. This paper reviews research on the suitability of such models, and goes on to advance biologically motivated reasons for adopting a particular group of models in preference to all others. In particular, the paper describes why the Gabor model, so often used in network simulations, should be dropped in favour of a Cauchy model, both on the grounds of frequency response and mutual filter orthogonality.

ENCORE: The effect of nutrient enrichment on coral reefs. Synthesis of results and conclusions

Coral reef degradation resulting from nutrient enrichment of coastal waters is of increasing global concern. Although effects of nutrients on coral reef organisms have been demonstrated in the laboratory, there is little direct evidence of nutrient effects on coral reef biota in situ. The ENCORE experiment investigated responses of coral reef organisms and processes to controlled additions of dissolved inorganic nitrogen (N) and/or phosphorus (P) on an offshore reef(One Tree Island) at the southern end of the Great Barrier Reef, Australia. A multi-disciplinary team assessed a variety of factors focusing on nutrient dynamics and biotic responses. A controlled and replicated experiment was conducted over two years using twelve small patch reefs ponded at low tide by a coral rim. Treatments included three control reefs (no nutrient addition) and three + N reefs (NH4Cl added), three + P reefs (KH2PO4 added), and three + N + P reefs. Nutrients were added as pulses at each low tide (ca twice per day) by remotely operated units. There were two phases of nutrient additions. During the initial, low-loading phase of the experiment nutrient pulses (mean dose = 11.5 muM NH4+; 2.3 muM PO4-3) rapidly declined, reaching near-background levels (mean = 0.9 muM NH4+; 0.5 muM PO4-3) within 2-3 h. A variety of biotic processes, assessed over a year during this initial nutrient loading phase, were not significantly affected, with the exception of coral reproduction, which was affected in all nutrient treatments. In Acropora longicyathus and A. aspera, fewer successfully developed embryos were formed, and in A. longicyathus fertilization rates and lipid levels decreased. In the second, high-loading, phase of ENCORE an increased nutrient dosage (mean dose = 36.2 muM NH4+; 5.1 muM PO4-3 declining to means of 11.3 muM NH4+ and 2.4 muM PO4-3 at the end of low tide) was used for a further year, and a variety of significant biotic responses occurred. Encrusting algae incorporated virtually none of the added nutrients. Organisms containing endosymbiotic zooxanthellae (corals and giant clams) assimilated dissolved nutrients rapidly and were responsive to added nutrients. Coral mortality, not detected during the initial low-loading phase, became evident with increased nutrient dosage, particularly in Pocillopora damicornis. Nitrogen additions stunted coral growth, and phosphorus additions had a variable effect. Coral calcification rate and linear extension increased in the presence of added phosphorus but skeletal density was reduced, making corals more susceptible to breakage. Settlement of all coral larvae was reduced in nitrogen treatments, yet settlement of larvae from brooded species was enhanced in phosphorus treatments. Recruitment of stomatopods, benthic crustaceans living in coral rubble, was reduced in nitrogen and nitrogen plus phosphorus treatments. Grazing rates and reproductive effort of various fish species were not affected by the nutrient treatments. Microbial nitrogen transformations in sediments,were responsive to nutrient loading with nitrogen fixation significantly increased in phosphorus treatments and denitrification increased in all treatments to which nitrogen had been added. Rates of bioerosion and grazing showed no significant effects of added nutrients, ENCORE has shown that reef organisms and processes investigated ill situ were impacted by elevated nutrients. Impacts mere dependent on dose level, whether nitrogen and/or phosphorus mere elevated and were often species-specific. The impacts were generally sub-lethal and subtle and the treated reefs at the end of the experiment mere visually similar to control reefs. Rapid nutrient uptake indicates that nutrient concentrations alone are not adequate to assess nutrient condition of reefs. Sensitive and quantifiable biological indicators need to be developed for coral reef ecosystems. The potential bioindicators identified in ENCORE should be tested in future research on coral reef/nutrient interactions. Synergistic and cumulative effects of elevated nutrients and other environmental parameters, comparative studies of intact vs. disturbed reefs, offshore vs, inshore reefs, or the ability of a nutrient-stressed reef to respond to natural disturbances require elucidation. An expanded understanding of coral reef responses to anthropogenic impacts is necessary, particularly regarding the subtle, sub-lethal effects detected in the ENCORE studies. (C) 2001 Published by Elsevier Science Ltd.

Determination of breeding strategies for beef cattle bull breeders selling bulls into two competing markets on a non-linear price grid

Computer simulation was used to suggest potential selection strategies for beef cattle breeders with different mixes of clients between two potential markets. The traditional market paid on the basis of carcass weight (CWT), while a new market considered marbling grade in addition to CWT as a basis for payment. Both markets instituted discounts for CWT in excess of 340 kg and light carcasses below 300 kg. Herds were simulated for each price category on the carcass weight grid for the new market. This enabled the establishment of phenotypic relationships among the traits examined [CWT, percent intramuscular fat (IMF), carcass value in the traditional market, carcass value in the new market, and the expected proportion of progeny in elite price cells in the new market pricing grid]. The appropriateness of breeding goals was assessed on the basis of client satisfaction. Satisfaction was determined by the equitable distribution of available stock between markets combined with the assessment of the utility of the animal within the market to which it was assigned. The best goal for breeders with predominantly traditional clients was a CWT in excess of 330 kg, while that for breeders with predominantly new market clients was a CWT of between 310 and 329 kg and with a marbling grade of AAA in the Ontario carcass pricing system. For breeders who wished to satisfy both new and traditional clients, the optimal CWT was 310-329 kg and the optimal marbling grade was AA-AAA. This combination resulted in satisfaction levels of greater than 75% among clients, regardless of the distribution of the clients between the traditional and new marketplaces.

An aggregate sales model for consumer durables incorporating a time-varying mean replacement age

Forecasting category or industry sales is a vital component of a company's planning and control activities. Sales for most mature durable product categories are dominated by replacement purchases. Previous sales models which explicitly incorporate a component of sales due to replacement assume there is an age distribution for replacements of existing units which remains constant over time. However, there is evidence that changes in factors such as product reliability/durability, price, repair costs, scrapping values, styling and economic conditions will result in changes in the mean replacement age of units. This paper develops a model for such time-varying replacement behaviour and empirically tests it in the Australian automotive industry. Both longitudinal census data and the empirical analysis of the replacement sales model confirm that there has been a substantial increase in the average aggregate replacement age for motor vehicles over the past 20 years. Further, much of this variation could be explained by real price increases and a linear temporal trend. Consequently, the time-varying model significantly outperformed previous models both in terms of fitting and forecasting the sales data. Copyright (C) 2001 John Wiley & Sons, Ltd.

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.

Two-link approximation schemes for loss networks with linear structure and trunk reservation

Loss networks have long been used to model various types of telecommunication network, including circuit-switched networks. Such networks often use admission controls, such as trunk reservation, to optimize revenue or stabilize the behaviour of the network. Unfortunately, an exact analysis of such networks is not usually possible, and reduced-load approximations such as the Erlang Fixed Point (EFP) approximation have been widely used. The performance of these approximations is typically very good for networks without controls, under several regimes. There is evidence, however, that in networks with controls, these approximations will in general perform less well. We propose an extension to the EFP approximation that gives marked improvement for a simple ring-shaped network with trunk reservation. It is based on the idea of considering pairs of links together, thus making greater allowance for dependencies between neighbouring links than does the EFP approximation, which only considers links in isolation.

An investigation into the interference rejection capability of a linear array in a wireless communications system

The suitable use of an array antenna at the base station of a wireless communications system can result in improvement in the signal-to-interference ratio (SIR). In general, the SIR is a function of the direction of arrival of the desired signal and depends on the configuration of the array, the number of elements, and their spacing. In this paper, we consider a uniform linear array antenna and study the effect of varying the number of its elements and inter-element spacing on the SIR performance. (C) 2002 Wiley Periodicals, Inc.

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.