The relative order and inverses of recurrent networks

Differential geometry is used to investigate the structure of neural-network-based control systems. The key aspect is relative order—an invariant property of dynamic systems. Finite relative order allows the specification of a minimal architecture for a recurrent network. Any system with finite relative order has a left inverse. It is shown that a recurrent network with finite relative order has a local inverse that is also a recurrent network with the same weights. The results have implications for the use of recurrent networks in the inverse-model-based control of nonlinear systems.

The dependence of clear-sky outgoing longwave radiation on surface temperature and relative humidity

A simulation of the earth's clear-sky long-wave radiation budget is used to examine the dependence of clear-sky outgoing long-wave radiation (OLR) on surface temperature and relative humidity. the simulation uses the European Centre for Medium-Range Weather Forecasts global reanalysed fields to calculate clear-sky OLR over the period from January 1979 to December 1993, thus allowing the seasonal and interannual time-scales to be resolved. the clear-sky OLR is shown to be primarily dependent on temperature changes at high latitudes and on changes in relative humidity at lower latitudes. Regions exhibiting a ‘super-greenhouse’ effect are identified and are explained by considering the changes in the convective regime associated with the Hadley circulation over the seasonal cycle, and with the Walker circulation over the interannual time-scale. the sensitivity of clear-sky OLR to changes in relative humidity diminishes with increasing relative humidity. This is explained by the increasing saturation of the water-vapour absorption bands with increased moisture. By allowing the relative humidity to vary in specified vertical slabs of the troposphere over an interannual time-scale it is shown that changes in humidity in the mid troposphere (400 to 700 hPa) are of most importance in explaining clear-sky OLR variations. Relative humidity variations do not appear to affect the positive thermodynamic water-vapour feedback significantly in response to surface temperature changes.

The relative importance sector and regional factors in Italy

The benefits of sector and regional diversification have been well documented in the literature but have not previously been investigated in Italy. In addition, previous studies have used geographically defined regions, rather than economically functional areas, when performing the analysis even though most would argue that it is the economic structure of the area that will lead to differences in demand and hence property performance. This study therefore uses economically defined regions of Italy to test the relative benefits of regional diversification versus sector diversification within the Italian real estate portfolio. To examine this issue we use constrained cross-section regressions the on the sector and regional affiliation of 14 cities in Italy to extract the “pure” return effects of the different factors using annual data over the period 1989 to 2003. In contrast, to previous studies we find that regional factors effects in Italy have a much greater influence on property returns than sector-specific effects, which is probably a direct result of using the extremely diverse economic regions of Italy rather than arbitrary geographically locations. Be that as it may, the results strongly suggest that that diversification across the regions of Italy used here is likely to offer larger risk reduction benefits than a sector diversification strategy within a region. In other words, fund managers in Italy must monitor the regional composition of their portfolios more closely than its sector allocation. Additionally, the results supports that contemporary position that ‘regional areas’ based on economic function, provide greater diversification benefits rather than areas defined by geographical location.

Another look at the relative importance of sectors and regions in determining property returns

This paper re-examines the relative importance of sector and regional effects in determining property returns. Using the largest property database currently available in the world, we decompose the returns on individual properties into a national effect, common to all properties, and a number of sector and regional factors. However, unlike previous studies, we categorise the individual property data into an ever-increasing number of property-types and regions, from a simple 3-by-3 classification, up to a 10 by 63 sector/region classification. In this way we can test the impact that a finer classification has on the sector and regional effects. We confirm the earlier findings of previous studies that sector-specific effects have a greater influence on property returns than regional effects. We also find that the impact of the sector effect is robust across different classifications of sectors and regions. Nonetheless, the more refined sector and regional partitions uncover some interesting sector and regional differences, which were obscured in previous studies. All of which has important implications for property portfolio construction and analysis.

Changes in the relative importance of sector and regional factors: 1987-2002

A stylised fact in the real estate portfolio diversification literature is that sector (property-type) effects are relatively more important than regional (geographical) factors in determining property returns. Thus, for those portfolio managers who follow a top-down approach to portfolio management, they should first choose in which sectors to invest and then select the best properties in each market. However, the question arises as to whether the dominance of the sector effects relative to regional effects is constant. If not property fund managers will need to take account of regional effects in developing their portfolio strategy. Using monthly data over the period 1987:1 to 2002:12 for a sample of over 1000 properties the results show that the sector-specific factors dominate the regional-specific factors for the vast majority of the time. Nonetheless, there are periods when the regional factors are of equal or greater importance than the sector effects. In particular, the sector effects tend to dominate during volatile periods of the real estate cycle; however, during calmer periods the sector and regional effects are of equal importance. These findings suggest that the sector effects are still the most important aspect in the development of an active portfolio strategy.

Relative order defines a topology for recurrent networks

This paper uses techniques from control theory in the analysis of trained recurrent neural networks. Differential geometry is used as a framework, which allows the concept of relative order to be applied to neural networks. Any system possessing finite relative order has a left-inverse. Any recurrent network with finite relative order also has an inverse, which is shown to be a recurrent network.

A comparison of the relative toxicity of bone meal and other P sources used as remedial treatments to the earthworm Eisenia fetida

It has been suggested that sources of P could be used to remediate metal-contaminated soil. The toxicity of four potential P sources, potassium hydrogen phosphate (PHP), triple superphosphate (TSP), rock phosphate (RP) and raw bone meal (RBM) to Eisenia fetida was determined. The concentration of P that is statistically likely to kill 50% of the population (LC50) for PHP, TSP and RBM was determined in OECD acute toxicity tests. 14 day LC50s expressed as bulk P concentration lay in the range 3319–4272 mg kg−1 for PHP, 3107–3590 mg kg−1 for TSP and 1782–2196 mg kg−1 for RBM (ranges present the 95% confidence intervals). For PHP and TSP mortality was significantly impacted by the electrical conductivity of the treated soils. No consistent relationship existed between mortality and electrical conductivity, soil pH and available (Olsen) P across the PHP, TSP and RBM amendment types. In RP toxicity tests mortality was low and it was not possible to determine a LC50 value. Incineration of bone meal at temperatures between 200 and 300 ◦C, pre-washing the bone meal, co-amendment with 5% green waste compost and delaying introduction of earthworms after bone meal amendments by 21 days or more led to significant reductions in the bone meal toxicity. These results are consistent with the toxicity being associated with the release and/or degradation of a soluble organic component present in raw bone meal. Bone meal can be used as an earthworm-friendly remedial amendment in metal-contaminated soils but initial additions may have a negative effect on any earthworms surviving in the contaminated soil before the organic component in the bone meal degrades in the soil.

Unsaturated σ-hydrocarbyl transition-metal complexes. Part 4. Crystal and molecular structure of trans-chlorobis(diethylphenylphosphine)-(phenylethynyl)platinum(II) and comments on the relative trans influence of various carbon ligands

The molecular structure of trans-[PtCl(CCPh)(PEt2Ph)2] has been determined by X-ray diffraction methods. The crystals are monoclinic, space group P21, with a= 12.359(3), b= 13.015(3), c= 9.031(2)Å, β= 101.65(2)°, and Z= 2. The structure has been solved by the heavy-atom method and refined by full-matrix least squares to R 0.046 for 1 877 diffractometric intensity data. The crystals contain discrete molecules in which the platinum coordination is square planar. The phenylethynyl group is non-linear, with a Pt–CC angle of 163(2)°. Selected bond lengths are Pt–Cl 2.407(5) and Pt–C 1.98(2)Å. The structural trans influences of CCPh, CHCH2, and CH2SiMe3 ligands in platinum(II) complexes are compared; there is only a small dependence on hybridization at the ligating carbon atom.