The correlation structure of spatial autoregressions

This paper investigates how the correlations implied by a first-order simultaneous autoregressive (SAR(1)) process are affected by the weights matrix and the autocorrelation parameter. A graph theoretic representation of the covariances in terms of walks connecting the spatial units helps to clarify a number of correlation properties of the processes. In particular, we study some implications of row-standardizing the weights matrix, the dependence of the correlations on graph distance, and the behavior of the correlations at the extremes of the parameter space. Throughout the analysis differences between directed and undirected networks are emphasized. The graph theoretic representation also clarifies why it is difficult to relate properties ofW to correlation properties of SAR(1) models defined on irregular lattices.

Modeling data with structural and temporal correlation using lower level and higher level multilevel models

Novel imaging techniques are playing an increasingly important role in drug development, providing insight into the mechanism of action of new chemical entities. The data sets obtained by these methods can be large with complex inter-relationships, but the most appropriate statistical analysis for handling this data is often uncertain - precisely because of the exploratory nature of the way the data are collected. We present an example from a clinical trial using magnetic resonance imaging to assess changes in atherosclerotic plaques following treatment with a tool compound with established clinical benefit. We compared two specific approaches to handle the correlations due to physical location and repeated measurements: two-level and four-level multilevel models. The two methods identified similar structural variables, but higher level multilevel models had the advantage of explaining a greater proportion of variation, and the modeling assumptions appeared to be better satisfied.

Boundary integral methods for singularly perturbed boundary value problems

In this paper we consider boundary integral methods applied to boundary value problems for the positive definite Helmholtz-type problem -DeltaU + alpha U-2 = 0 in a bounded or unbounded domain, with the parameter alpha real and possibly large. Applications arise in the implementation of space-time boundary integral methods for the heat equation, where alpha is proportional to 1/root deltat, and deltat is the time step. The corresponding layer potentials arising from this problem depend nonlinearly on the parameter alpha and have kernels which become highly peaked as alpha --> infinity, causing standard discretization schemes to fail. We propose a new collocation method with a robust convergence rate as alpha --> infinity. Numerical experiments on a model problem verify the theoretical results.

Local gratings due to angular hole burning in a photorefractive polymer

We investigate the processes involved in writing real-time holographic gratings in a photorefractive polymer (PRP) that incorporates an azo-dye. In such systems there may be gratings due to mechanisms associated with trans–cis isomerization (angular hole burning (AHB) and/or angular redistribution), which appear in addition to those arising from the photorefractive (PR) effect. The work presented here helps to understand the interactions which may occur between these different gratings. The formation of local gratings due to mechanisms associated with photoisomerization is studied, in a new PRP based on the photoconductor poly(N-vinylcarbazole):2, 4, 7-trinitro-9-fluorenone, plasticized with N-ethylcarbazole. The polymer includes the azo-dye 4-nitro-4'-pentyloxy-azobenzene and we observe both PR and photoisomerization gratings. The gratings are shown to be both polarization-sensitive and reversible. The presence of the photoisomerization gratings (which diffract almost as strongly as the PR gratings) significantly affects the field-dependent diffractive behaviour of the composite. A measurement of the lifetime of the cis state is made (τcis = 38 s) using photoinduced dichroism. This is close to the decay time constant of the local gratings (τdecay = 42 s), and it is suggested that the local grating mechanism is AHB of the azo-dye. This is the first time (to the knowledge of the authors) that a local grating due to AHB has been demonstrated in a PRP.

Correlation shifts and real estate portfolio management

The success of any diversification strategy depends upon the quality of the estimated correlation between assets. It is well known, however, that there is a tendency for the average correlation among assets to increase when the market falls and vice-versa. Thus, assuming that the correlation between assets is a constant over time seems unrealistic. Nonetheless, these changes in the correlation structure as a consequence of changes in the market’s return suggests that correlation shifts can be modelled as a function of the market return. This is the idea behind the model of Spurgin et al (2000), which models the beta or systematic risk, of the asset as a function of the returns in the market. This is an approach that offers particular attractions to fund managers as it suggest ways by which they can adjust their portfolios to benefit from changes in overall market conditions. In this paper the Spurgin et al (2000) model is applied to 31 real estate market segments in the UK using monthly data over the period 1987:1 to 2000:12. The results show that a number of market segments display significant negative correlation shifts, while others show significantly positive correlation shifts. Using this information fund managers can make strategic and tactical portfolio allocation decisions based on expectations of market volatility alone and so help them achieve greater portfolio performance overall and especially during different phases of the real estate cycle.

Asset allocation, cross-class correlation and the structure of property returns

Practical applications of portfolio optimisation tend to proceed on a “top down” basis where funds are allocated first at asset class level (between, say, bonds, cash, equities and real estate) and then, progressively, at sub-class level (within property to sectors, office, retail, industrial for example). While there are organisational benefits from such an approach, it can potentially lead to sub-optimal allocations when compared to a “global” or “side-by-side” optimisation. This will occur where there are correlations between sub-classes across the asset divide that are masked in aggregation – between, for instance, City offices and the performance of financial services stocks. This paper explores such sub-class linkages using UK monthly stock and property data. Exploratory analysis using clustering procedures and factor analysis suggests that property performance and equity performance are distinctive: there is little persuasive evidence of contemporaneous or lagged sub-class linkages. Formal tests of the equivalence of optimised portfolios using top-down and global approaches failed to demonstrate significant differences, whether or not allocations were constrained. While the results may be a function of measurement of market returns, it is those returns that are used to assess fund performance. Accordingly, the treatment of real estate as a distinct asset class with diversification potential seems justified.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Exact design manifold control of a class of nonlinear singularly perturbed systems

The integral manifold approach captures from a geometric point of view the intrinsic two-time-scale behavior of singularly perturbed systems. An important class of nonlinear singularly perturbed systems considered in this note are fast actuator-type systems. For a class of fast actuator-type systems, which includes many physical systems, an explicit corrected composite control, the sum of a slow control and a fast control, is derived. This corrected control will steer the system exactly to a required design manifold.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Exact design manifold control of a class of nonlinear singularly perturbed systems

The integral manifold approach captures from a geometric point of view the intrinsic two-time-scale behavior of singularly perturbed systems. An important class of nonlinear singularly perturbed systems considered in this note are fast actuator-type systems. For a class of fast actuator-type systems, which includes many physical systems, an explicit corrected composite control, the sum of a slow control and a fast control, is derived. This corrected control will steer the system exactly to a required design manifold.

Aerosol-induced correlation between visibility and atmospheric electricity.

Atmospheric aerosol acts to both reduce the background concentration of natural cluster ions, and to attenuate optical propagation. Hence, the presence of aerosol has two consequences, the reduction of the air’s electrical conductivity and the visual range. Ion-aerosol theory and Koschmieder’s visibility theory are combined here to derive the related non-linear variation of the atmospheric electric potential gradient with visual range. A substantial sensitivity is found under poor visual range conditions, but, for good visual range conditions the sensitivity diminishes and little influence of local aerosol on the fair weather potential gradient occurs. This allows visual range measurements, made simply and routinely at many meteorological sites, to provide inference about the local air’s electrical properties.

Comparative genomics of Brachyspira pilosicoli strains: genome rearrangements, reductions and correlation of genetic compliment with phenotypic diversity.

Background. The anaerobic spirochaete Brachyspira pilosicoli causes enteric disease in avian, porcine and human hosts, amongst others. To date, the only available genome sequence of B. pilosicoli is that of strain 95/1000, a porcine isolate. In the first intra-species genome comparison within the Brachyspira genus, we report the whole genome sequence of B. pilosicoli B2904, an avian isolate, the incomplete genome sequence of B. pilosicoli WesB, a human isolate, and the comparisons with B. pilosicoli 95/1000. We also draw on incomplete genome sequences from three other Brachyspira species. Finally we report the first application of the high-throughput Biolog phenotype screening tool on the B. pilosicoli strains for detailed comparisons between genotype and phenotype. Results. Feature and sequence genome comparisons revealed a high degree of similarity between the three B. pilosicoli strains, although the genomes of B2904 and WesB were larger than that of 95/1000 (~2,765, 2.890 and 2.596 Mb, respectively). Genome rearrangements were observed which correlated largely with the positions of mobile genetic elements. Through comparison of the B2904 and WesB genomes with the 95/1000 genome, features that we propose are non-essential due to their absence from 95/1000 include a peptidase, glycine reductase complex components and transposases. Novel bacteriophages were detected in the newly-sequenced genomes, which appeared to have involvement in intra- and inter-species horizontal gene transfer. Phenotypic differences predicted from genome analysis, such as the lack of genes for glucuronate catabolism in 95/1000, were confirmed by phenotyping. Conclusions. The availability of multiple B. pilosicoli genome sequences has allowed us to demonstrate the substantial genomic variation that exists between these strains, and provides an insight into genetic events that are shaping the species. In addition, phenotype screening allowed determination of how genotypic differences translated to phenotype. Further application of such comparisons will improve understanding of the metabolic capabilities of Brachyspira species.

Correlation between Fourier series expansion and Hückel orbital theory

The Fourier series can be used to describe periodic phenomena such as the one-dimensional crystal wave function. By the trigonometric treatements in Hückel theory it is shown that Hückel theory is a special case of Fourier series theory. Thus, the conjugated π system is in fact a periodic system. Therefore, it can be explained why such a simple theorem as Hückel theory can be so powerful in organic chemistry. Although it only considers the immediate neighboring interactions, it implicitly takes account of the periodicity in the complete picture where all the interactions are considered. Furthermore, the success of the trigonometric methods in Hückel theory is not accidental, as it based on the fact that Hückel theory is a specific example of the more general method of Fourier series expansion. It is also important for education purposes to expand a specific approach such as Hückel theory into a more general method such as Fourier series expansion.

Angular momentum conservation and gravity wave drag parameterization: implications for climate models

The robustness of the parameterized gravity wave response to an imposed radiative perturbation in the middle atmosphere is examined. When momentum is conserved and for reasonable gravity wave drag parameters, the response to a polar cooling induces polar downwelling above the region of the imposed cooling, with consequent adiabatic warming. This response is robust to changes in the gravity wave source spectrum, background flow, gravity wave breaking criterion, and model lid height. When momentum is not conserved, either in the formulation or in the implementation of the gravity wave drag parameterization, the response becomes sensitive to the above-mentioned factors—in particular to the model lid height. The spurious response resulting from nonconservation is found to be nonnegligible in terms of the total gravity wave drag–induced downwelling.