A THEORETICAL SOLUTION FOR THE ESTIMATION OF "RAINFLOW" RANGES FROM POWER SPECTRAL DENSITY DATA

Abstract— This report outlines a theoretical solution for the estimation of rainflow range density functions using statistics computed directly from power spectral density data. The rainflow range mechanism is broken down into a set of events which can be analyzed using Markov process theory. The dependence between extremes in this instance is modelled using an approximation of the joint distribution of peaks and troughs first proposed by Kowalewski.     

MIMO Channel Capacity and Configuration Selection for Switched Parasitic Antennas

Multiple-input multiple-output (MIMO) systems offer significant enhancements in terms of their data rate and channel capacity compared to traditional systems. However, correlation degrades the system performance and imposes practical limits on the number of antennas that can be incorporated into portable wireless devices. The use of switched parasitic antennas (SPAs) is a possible solution, especially where it is difficult to obtain sufficient signal decorrelation by conventional means. The covariance matrix represents the correlation present in the propagation channel, and has significant impact on the MIMO channel capacity. The results of this work demonstrate a significant improvement in the MIMO channel capacity by using SPA with the knowledge of the covariance matrix for all pattern configurations. By employing the “water-pouring algorithm” to modify the covariance matrix, the channel capacity is significantly improved compared to traditional systems, which spread transmit power uniformly across all the antennas. A condition number is also proposed as a selection metric to select the optimal pattern configuration for MIMO-SPAs.     

Cellular automata and integrodifferential equation models for cell renewal in mosaic tissues

Mosaic tissues are composed of two or more genetically distinct cell types. They occur naturally, and are also a useful experimental method for exploring tissue growth and maintenance. By marking the different cell types, one can study the patterns formed by proliferation, renewal and migration. Here, we present mathematical modelling suggesting that small changes in the type of interaction that cells have with their local cellular environment can lead to very different outcomes for the composition of mosaics. In cell renewal, proliferation of each cell type may depend linearly or nonlinearly on the local proportion of cells of that type, and these two possibilities produce very different patterns. We study two variations of a cellular automaton model based on simple rules for renewal. We then propose an integrodifferential equation model, and again consider two different forms of cellular interaction. The results of the continuous and cellular automata models are qualitatively the same, and we observe that changes in local environment interaction affect the dynamics for both. Furthermore, we demonstrate that the models reproduce some of the patterns seen in actual mosaic tissues. In particular, our results suggest that the differing patterns seen in organ parenchymas may be driven purely by the process of cell replacement under different interaction scenarios.     

Repressor titration: a novel system for selection and stable maintenance of recombinant plasmids

The propagation of recombinant plasmids in bacterial hosts, particularly in Escherichia coli, is essential for the amplification and manipulation of cloned DNA and the production of recombinant proteins. The isolation of bacterial transformants and subsequent stable plasmid maintenance have traditionally been accomplished using plasmid-borne selectable marker genes. Here we describe a novel system that employs plasmid-mediated repressor titration to activate a chromosomal selectable marker, removing the requirement for a plasmid-borne marker gene. A modified E.coli host strain containing a conditionally essential chromosomal gene (kan) under the control of the lac operator/promoter, lac O/P, has been constructed. In the absence of an inducer (allolactose or IPTG) this strain, DH1 lackan , cannot grow on kanamycin-containing media due to the repression of kan expression by LacI protein binding to lac O/P. Transformation with a high copy-number plasmid containing the lac operator, lac O, effectively induces kan expression by titrating LacI from the operator. This strain thus allows the selection of plasmids without antibiotic resistance genes (they need only contain lac O and an origin of replication) which have clear advantages for use as gene therapy vectors. Regulation in the same way of an essential, endogenous bacterial gene will allow the production of recombinant therapeutics devoid of residual antibiotic contamination.     

Scanning transmission electron microscopy mass analysis of fibrillin-containing microfibrils from foetal elastic tissues

We have applied scanning transmission electron microscopy to intact native fibrillin-containing microfibrils isolated from foetal bovine elastic tissues in order to derive new insights into microfibril organisation. This technique provides quantitative data on the mass per unit length and axial mass distribution of unstained, unshadowed macromolecules. Scanning transmission electron microscopy of microfibrils from aorta, skin and nuchal ligament revealed that the beads corresponded to peaks of mass and the interbead regions to troughs of mass. These major features of axial mass distribution were characteristic of all microfibrils examined. Tissue-specific and age-dependent variations in mass were identified in microfibrils that were structurally comparable by rotary shadowing electron microscopy. Increased microfibril mass correlated with increasing gestational age. The additional mass was associated predominantly at, or close to, the bead. Some microfibril populations exhibited pronounced assymetry in their axial mass distribution. These data indicate that intact native microfibrillar assemblies from developing elastic tissues are heterogeneous in composition. Loss of mass following chondroitinase ABC or AC lyase treatment confirmed the presence of chondroitin sulphate in nuchal ligament microfibrillar assemblies.     

Oscillatory and chaotic wakes behind moving boundaries in reaction-diffusion systems

Oscillatory wakes occur in a wide range of reaction-diffusion systems, consisting of either periodic travelling waves or irregular spatiotemporal oscillations, behind a moving transition front. In this paper, the use of a finite boundary moving with an imposed speed to mimic the transition front is considered. For both λ-ω systems and standard predator-prey models, the solutions behind these moving boundaries agree very closely with the behaviour behind transition fronts, provided suitable end conditions are used on the moving boundary. This confirms that the transition front can be regarded as determining the solution, by forcing a particular periodic wave at the boundary of the wake region. In the case of λ-ω systems, a detailed numerical study of solutions on a fixed-length finite domain with a periodic wave solution forced at the boundaries is performed. As the domain length is varied as a parameter, the long-term temporal behaviour undergoes bifurcation sequences that are well known as routes to chaos in ordinary differential equations. This suggests that irregular wakes actually have the form of a perpetual transient in a progression towards chaos. Finally, the way in which the moving boundary results can be used to design an experimental verification of the oscillatory wakes phenomenon in a chemical system is discussed.     

Periodic travelling waves in cyclic populations: field studies and reaction–diffusion models

Periodic travelling waves have been reported in a number of recent spatio-temporal field studies of populations undergoing multi-year cycles. Mathematical modelling has a major role to play in understanding these results and informing future empirical studies. We review the relevant field data and summarize the statistical methods used to detect periodic waves. We then discuss the mathematical theory of periodic travelling waves in oscillatory reaction-diffusion equations. We describe the notion of a wave family, and various ecologically relevant scenarios in which periodic travelling waves occur. We also discuss wave stability, including recent computational developments. Although we focus on oscillatory reaction-diffusion equations, a brief discussion of other types of model in which periodic travelling waves have been demonstrated is also included. We end by proposing 10 research challenges in this area, five mathematical and five empirical.