State estimation using model order reduction for unstable systems

The problem of state estimation occurs in many applications of fluid flow. For example, to produce a reliable weather forecast it is essential to find the best possible estimate of the true state of the atmosphere. To find this best estimate a nonlinear least squares problem has to be solved subject to dynamical system constraints. Usually this is solved iteratively by an approximate Gauss–Newton method where the underlying discrete linear system is in general unstable. In this paper we propose a new method for deriving low order approximations to the problem based on a recently developed model reduction method for unstable systems. To illustrate the theoretical results, numerical experiments are performed using a two-dimensional Eady model – a simple model of baroclinic instability, which is the dominant mechanism for the growth of storms at mid-latitudes. It is a suitable test model to show the benefit that may be obtained by using model reduction techniques to approximate unstable systems within the state estimation problem.

A comparative review of dimension reduction methods in approximate Bayesian computation

Approximate Bayesian computation (ABC) methods make use of comparisons between simulated and observed summary statistics to overcome the problem of computationally intractable likelihood functions. As the practical implementation of ABC requires computations based on vectors of summary statistics, rather than full data sets, a central question is how to derive low-dimensional summary statistics from the observed data with minimal loss of information. In this article we provide a comprehensive review and comparison of the performance of the principal methods of dimension reduction proposed in the ABC literature. The methods are split into three nonmutually exclusive classes consisting of best subset selection methods, projection techniques and regularization. In addition, we introduce two new methods of dimension reduction. The first is a best subset selection method based on Akaike and Bayesian information criteria, and the second uses ridge regression as a regularization procedure. We illustrate the performance of these dimension reduction techniques through the analysis of three challenging models and data sets.

Modeling of carrier transport in nanowires

We consider a physical model of ultrafast evolution of an initial electron distribution in a quantum wire. The electron evolution is described by a quantum-kinetic equation accounting for the interaction with phonons. A Monte Carlo approach has been developed for solving the equation. The corresponding Monte Carlo algorithm is NP-hard problem concerning the evolution time. To obtain solutions for long evolution times with small stochastic error we combine both variance reduction techniques and distributed computations. Grid technologies are implemented due to the large computational efforts imposed by the quantum character of the model.

Femtosecond evolution of spatially inhomogeneous carrier excitations: part 2: stochastic approach and GRID implementation

We present a stochastic approach for solving the quantum-kinetic equation introduced in Part I. A Monte Carlo method based on backward time evolution of the numerical trajectories is developed. The computational complexity and the stochastic error are investigated numerically. Variance reduction techniques are applied, which demonstrate a clear advantage with respect to the approaches based on symmetry transformation. Parallel implementation is realized on a GRID infrastructure.

Reduction of arsenic uptake by lettuce with ferrous sulfate applied to contaminated soil

Soil contamination by arsenic (As) presents a hazard in many countries and there is a need for techniques to minimize As uptake by plants. A proposed in situ remediation method was tested by growing lettuce (Lactuca sativa L. cv. Kermit) in a greenhouse pot experiment on soil that contained 577 mg As kg(-1), taken from a former As smelter site. All combinations of iron (Fe) oxides, at concentrations of 0.00, 0.22, 0.54, and 1.09% (w/w), and lime, at concentrations of 0.00, 0.27, 0.68, and 1.36% (w/w), were tested in a factorial design. To create the treatments, field-moist soil, commercial-grade FeSO4, and ground agricultural lime were mixed and stored for one week, allowing Fe oxides to precipitate. Iron oxides gave highly significant (P < 0.001) reductions in lettuce As concentrations, down to 11% of the lettuce As concentration for untreated soil. For the Fe oxides and lime treatment combinations where soil pH was maintained nearly constant, the lettuce As concentration declined in an exponential relationship with increasing FeSO4 application rate and lettuce yield was almost unchanged. Iron oxides applied at a concentration of 1.09% did not give significantly lower lettuce As concentrations than the 0.54% treatment. Simultaneous addition of lime with FeSO4 was essential. Ferrous sulfate with insufficient lime lowered soil pH and caused mobilization of Al, Ba, Co, Cr, Cu, Fe, K, Mg, Mn, Na, Ni, Pb, Sr, and Zn. At the highest Fe oxide to lime ratios, Mn toxicity caused severe yield loss.

Reduction of arsenic uptake by lettuce with ferrous sulfate applied to contaminated soil

Soil contamination by arsenic (As) presents a hazard in many countries and there is a need for techniques to minimize As uptake by plants. A proposed in situ remediation method was tested by growing lettuce (Lactuca sativa L. cv. Kermit) in a greenhouse pot experiment on soil that contained 577 mg As kg(-1), taken from a former As smelter site. All combinations of iron (Fe) oxides, at concentrations of 0.00, 0.22, 0.54, and 1.09% (w/w), and lime, at concentrations of 0.00, 0.27, 0.68, and 1.36% (w/w), were tested in a factorial design. To create the treatments, field-moist soil, commercial-grade FeSO4, and ground agricultural lime were mixed and stored for one week, allowing Fe oxides to precipitate. Iron oxides gave highly significant (P < 0.001) reductions in lettuce As concentrations, down to 11% of the lettuce As concentration for untreated soil. For the Fe oxides and lime treatment combinations where soil pH was maintained nearly constant, the lettuce As concentration declined in an exponential relationship with increasing FeSO4 application rate and lettuce yield was almost unchanged. Iron oxides applied at a concentration of 1.09% did not give significantly lower lettuce As concentrations than the 0.54% treatment. Simultaneous addition of lime with FeSO4 was essential. Ferrous sulfate with insufficient lime lowered soil pH and caused mobilization of Al, Ba, Co, Cr, Cu, Fe, K, Mg, Mn, Na, Ni, Pb, Sr, and Zn. At the highest Fe oxide to lime ratios, Mn toxicity caused severe yield loss.

Using aircraft measurements to determine the refractive index of Saharan dust during the DODO Experiments

Much uncertainty in the value of the imaginary part of the refractive index of mineral dust contributes to uncertainty in the radiative effect of mineral dust in the atmosphere. A synthesis of optical, chemical and physical in-situ aircraft measurements from the DODO experiments during February and August 2006 are used to calculate the refractive index mineral dust encountered over West Africa. Radiative transfer modeling and measurements of broadband shortwave irradiance at a range of altitudes are used to test and validate these calculations for a specific dust event on 23 August 2006 over Mauritania. Two techniques are used to determine the refractive index: firstly a method combining measurements of scattering, absorption, size distributions and Mie code simulations, and secondly a method using composition measured on filter samples to apportion the content of internally mixed quartz, calcite and iron oxide-clay aggregates, where the iron oxide is represented by either hematite or goethite and clay by either illite or kaolinite. The imaginary part of the refractive index at 550 nm (ni550) is found to range between 0.0001 i to 0.0046 i, and where filter samples are available, agreement between methods is found depending on mineral combination assumed. The refractive indices are also found to agree well with AERONET data where comparisons are possible. ni550 is found to vary with dust source, which is investigated with the NAME model for each case. The relationship between both size distribution and ni550 on the accumulation mode single scattering albedo at 550 nm (ω0550) are examined and size distribution is found to have no correlation to ω0550, while ni550 shows a strong linear relationship with ω0550. Radiative transfer modeling was performed with different models (Mie-derived refractive indices, but also filter sampling composition assuming both internal and external mixing). Our calculations indicate that Mie-derived values of ni550 and the externally mixed dust where the iron oxide-clay aggregate corresponds to the goethite-kaolinite combination result in the best agreement with irradiance measurements. The radiative effect of the dust is found to be very sensitive to the mineral combination (and hence refractive index) assumed, and to whether the dust is assumed to be internally or externally mixed.

Effectiveness of landmark analysis for establishing locality in p2p networks

Locality to other nodes on a peer-to-peer overlay network can be established by means of a set of landmarks shared among the participating nodes. Each node independently collects a set of latency measures to landmark nodes, which are used as a multi-dimensional feature vector. Each peer node uses the feature vector to generate a unique scalar index which is correlated to its topological locality. A popular dimensionality reduction technique is the space filling Hilbert’s curve, as it possesses good locality preserving properties. However, there exists little comparison between Hilbert’s curve and other techniques for dimensionality reduction. This work carries out a quantitative analysis of their properties. Linear and non-linear techniques for scaling the landmark vectors to a single dimension are investigated. Hilbert’s curve, Sammon’s mapping and Principal Component Analysis have been used to generate a 1d space with locality preserving properties. This work provides empirical evidence to support the use of Hilbert’s curve in the context of locality preservation when generating peer identifiers by means of landmark vector analysis. A comparative analysis is carried out with an artificial 2d network model and with a realistic network topology model with a typical power-law distribution of node connectivity in the Internet. Nearest neighbour analysis confirms Hilbert’s curve to be very effective in both artificial and realistic network topologies. Nevertheless, the results in the realistic network model show that there is scope for improvements and better techniques to preserve locality information are required.

Crops and cultures in the Pacific: new data and new techniques for the investigation of old questions

Fifty years ago Carl Sauer suggested, controversially and on the basis of theory rather than evidence, that Southeast Asia was the source area for agriculture throughout the Old World, including the Pacific. Since then, the archaeobotanical record (macroscopic and microscopic) from the Pacific islands has increased, leading to suggestions, also still controversial, that Melanesia was a center of origin of agriculture independent of South-east Asia, based on tree fruits and nuts and vegetatively propagated starchy staples. Such crops generally lack morphological markers of domestication, so exploitation, cultivation and domestication cannot easily be distinguished in the archaeological record. Molecular studies involving techniques such as chromosome painting, DNA fingerprinting and DNA sequencing, can potentially complement the archaeological record by suggesting where species which were spread through the Pacific by man originated and by what routes they attained their present distributions. A combination of archaeobotanical and molecular studies should therefore eventually enable the rival claims of Melanesia versus South-east Asia as independent centers of invention of agriculture to be assessed.

Techniques for quantifying effects of dietary antioxidants on transcription factor translocation and nitric oxide production in cultured cells

Dietary antioxidants can affect cellular processes relevant to chronic inflammatory diseases such as atherosclerosis. We have used non- standard techniques to quantify effects of the antioxidant soy isoflavones genistein and daidzein on translocation of Nuclear Factor-KB (NF-KB) and nitric oxide (NO) production, which are important in these diseases. Translocation was quantified using confocal immunofluoresecence microscopy and ratiometric image analysis. NO was quantified by an electrochemical method after reduction of its oxidation products in cell culture supernatants. Activation of the RAW 264.7 murine monocyte/macrophage cell line increased the ratio of nuclear to cytoplasmic immunostaining for NF-kB. The increase was exacerbated by pre-treatment with genistein or daidzein. To show that decreases could also be detected, pre-treatment with the pine bark extract Pycnogenol (R) r was examined, and found to reduce translocation. NO production was also increased by activation, but was reduced by pre-treatment with genistein or daidzein. In the EA. hy926 human endothelial cell line, constitutive production was detectable and was increased by thrombin. The confocal and electrochemical methods gave data that agreed with results obtained using the established electromobility shift and Griess assays, but were more sensitive, more convenient, gave more detailed information and avoided the use of radioisotopes.

Using modelling tools to optimise the calculation and subsequent reduction of cable distortion parameters with application to oil well logging systems

This paper discusses how the use of computer-based modelling tools has aided the design of a telemetry unit for use with oil well logging. With the aid of modern computer-based simulation techniques, the new design is capable of operating at data rates of 2.5 times faster than previous designs.

Real estate portfolio size and risk reduction

The reduction of portfolio risk is important to all investors but is particularly important to real estate investors as most property portfolios are generally small. As a consequence, portfolios are vulnerable to a significant risk of under-performing the market, or a target rate of return and so investors may be exposing themselves to greater risk than necessary. Given the potentially higher risk of underperformance from owning only a few properties, we follow the approach of Vassal (2001) and examine the benefits of holding more properties in a real estate portfolio. Using Monte Carlo simulation and the returns from 1,728 properties in the IPD database, held over the 10-year period from 1995 to 2004, the results show that increases in portfolio size offers the possibility of a more stable and less volatile return pattern over time, i.e. down-side risk is diminished with increasing portfolio size. Nonetheless, increasing portfolio size has the disadvantage of restricting the probability of out-performing the benchmark index by a significant amount. In other words, although increasing portfolio size reduces the down-side risk in a portfolio, it also decreases its up-side potential. Be that as it may, the results provide further evidence that portfolios with large numbers of properties are always preferable to portfolios of a smaller size.

On merging gradient estimation with mean-tracking techniques for cluster identification

This paper discusses how numerical gradient estimation methods may be used in order to reduce the computational demands on a class of multidimensional clustering algorithms. The study is motivated by the recognition that several current point-density based cluster identification algorithms could benefit from a reduction of computational demand if approximate a-priori estimates of the cluster centres present in a given data set could be supplied as starting conditions for these algorithms. In this particular presentation, the algorithm shown to benefit from the technique is the Mean-Tracking (M-T) cluster algorithm, but the results obtained from the gradient estimation approach may also be applied to other clustering algorithms and their related disciplines.

Stomatal conductance and not stomatal density determines the long-term reduction in leaf transpiration of poplar in elevated CO2

Using a free-air CO2 enrichment (FACE) experiment, poplar trees (Populus · euramericana clone I214) were exposed to either ambient or elevated [CO2] from planting, for a 5-year period during canopy development, closure, coppice and re-growth. In each year, measurements were taken of stomatal density (SD, number mm2) and stomatal index (SI, the proportion of epidermal cells forming stomata). In year 5, measurements were also taken of leaf stomatal conductance (gs, lmol m2 s1), photosynthetic CO2 fixation (A, mmol m2 s1), instantaneous water-use efficiency (A/E) and the ratio of intercellular to atmospheric CO2 (Ci:Ca). Elevated [CO2] caused reductions in SI in the first year, and in SD in the first 2 years, when the canopy was largely open. In following years, when the canopy had closed, elevated [CO2] had no detectable effects on stomatal numbers or index. In contrast, even after 5 years of exposure to elevated [CO2], gs was reduced, A/E was stimulated, and Ci:Ca was reduced relative to ambient [CO2]. These outcomes from the long-term realistic field conditions of this forest FACE experiment suggest that stomatal numbers (SD and SI) had no role in determining the improved instantaneous leaf-level efficiency of water use under elevated [CO2]. We propose that altered cuticular development during canopy closure may partially explain the changing response of stomata to elevated [CO2], although the mechanism for this remains obscure.