Optimal control of a class of discrete–continuous non-linear systems — decomposition and hierarchical structure

A technique is derived for solving a non-linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form. The technique is designed to achieve the correct solution of the original non-linear optimal control problem in spite of these simplifications. A mixed approach with a discrete performance index and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local sub-system problems and a co-ordinator within a hierarchical framework. An analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non-separable performance index.

An optimization problem concerning multiplicative functions

In this paper we study the problem of maximizing a quadratic form 〈Ax,x〉 subject to ‖x‖q=1, where A has matrix entries View the MathML source with i,j|k and q≥1. We investigate when the optimum is achieved at a ‘multiplicative’ point; i.e. where x1xmn=xmxn. This turns out to depend on both f and q, with a marked difference appearing as q varies between 1 and 2. We prove some partial results and conjecture that for f multiplicative such that 0

Retrievals of sea surface temperature from infrared imagery: origin and form of systematic errors

We show that retrievals of sea surface temperature from satellite infrared imagery are prone to two forms of systematic error: prior error (familiar from the theory of atmospheric sounding) and error arising from nonlinearity. These errors have different complex geographical variations, related to the differing geographical distributions of the main geophysical variables that determine clear-sky brightness-temperatures over the oceans. We show that such errors arise as an intrinsic consequence of the form of the retrieval (rather than as a consequence of sub-optimally specified retrieval coefficients, as is often assumed) and that the pattern of observed errors can be simulated in detail using radiative-transfer modelling. The prior error has the linear form familiar from atmospheric sounding. A quadratic equation for nonlinearity error is derived, and it is verified that the nonlinearity error exhibits predominantly quadratic behaviour in this case.

Sensitivity of feature-based analysis methods of storm tracks to the form of background field removal

For the tracking of extrema associated with weather systems to be applied to a broad range of fields it is necessary to remove a background field that represents the slowly varying, large spatial scales. The sensitivity of the tracking analysis to the form of background field removed is explored for the Northern Hemisphere winter storm tracks for three contrasting fields from an integration of the U. K. Met Office's (UKMO) Hadley Centre Climate Model (HadAM3). Several methods are explored for the removal of a background field from the simple subtraction of the climatology, to the more sophisticated removal of the planetary scales. Two temporal filters are also considered in the form of a 2-6-day Lanczos filter and a 20-day high-pass Fourier filter. The analysis indicates that the simple subtraction of the climatology tends to change the nature of the systems to the extent that there is a redistribution of the systems relative to the climatological background resulting in very similar statistical distributions for both positive and negative anomalies. The optimal planetary wave filter removes total wavenumbers less than or equal to a number in the range 5-7, resulting in distributions more easily related to particular types of weather system. For the temporal filters the 2-6-day bandpass filter is found to have a detrimental impact on the individual weather systems, resulting in the storm tracks having a weak waveguide type of behavior. The 20-day high-pass temporal filter is less aggressive than the 2-6-day filter and produces results falling between those of the climatological and 2-6-day filters.

A geometric algorithm for an artificial life form based on anachronistic methods

Modern methods of spawning new technological motifs are not appropriate when it is desired to realize artificial life as an actual real world entity unto itself (Pattee 1995; Brooks 2006; Chalmers 1995). Many fundamental aspects of such a machine are absent in common methods, which generally lack methodologies of construction. In this paper we mix classical and modern studies in order to attempt to realize an artificial life form from first principles. A model of an algorithm is introduced, its methodology of construction is presented, and the fundamental source from which it sprang is discussed.

The four major N- and C-terminal splice variants of the excitatory amino acid transporter GLT-1 form cell surface homomeric and heteromeric assemblies

The L-glutamate transporter GLT-1 is an abundant CNS membrane protein of the excitatory amino acid transporter (EAAT) family which controls extracellular L-glutamate levels and is important in limiting excitotoxic neuronal death. Using RT-PCR, we have determined that four mRNAs encoding GLT-1 exist in mouse brain, with the potential to encode four GLT-1 isoforms that differ in their N- and C-termini. We expressed all four isoforms (termed MAST-KREK, MPK-KREK, MAST-DIETCI and MPK-DIETCI according to amino acid sequence) in a range of cell lines and primary astrocytes and show that each isoform can reach the cell surface. In transfected HEK-293 or COS-7 cells, all four isoforms support high-affinity sodium-dependent L-glutamate uptake with identical pharmacological and kinetic properties. Inserting a viral epitope (V5, HA or FLAG) into the second extracellular domain of each isoform allowed co-immunoprecipitation and tr-FRET studies using transfected HEK-293 cells. Here we show for the first time that each of the four isoforms are able to combine to form homomeric and heteromeric assemblies, each of which are expressed at the cell surface of primary astrocytes. After activation of protein kinase C by phorbol ester, V5-tagged GLT-1 is rapidly removed from the cell surface of HEK-293 cells and degraded. This study provides direct biochemical evidence for oligomeric assembly of GLT-1 and reports the development of novel tools to provide insight into the trafficking of GLT-1.

Wavelets and the generalization of the variogram

The experimental variogram computed in the usual way by the method of moments and the Haar wavelet transform are similar in that they filter data and yield informative summaries that may be interpreted. The variogram filters out constant values; wavelets can filter variation at several spatial scales and thereby provide a richer repertoire for analysis and demand no assumptions other than that of finite variance. This paper compares the two functions, identifying that part of the Haar wavelet transform that gives it its advantages. It goes on to show that the generalized variogram of order k=1, 2, and 3 filters linear, quadratic, and cubic polynomials from the data, respectively, which correspond with more complex wavelets in Daubechies's family. The additional filter coefficients of the latter can reveal features of the data that are not evident in its usual form. Three examples in which data recorded at regular intervals on transects are analyzed illustrate the extended form of the variogram. The apparent periodicity of gilgais in Australia seems to be accentuated as filter coefficients are added, but otherwise the analysis provides no new insight. Analysis of hyerpsectral data with a strong linear trend showed that the wavelet-based variograms filtered it out. Adding filter coefficients in the analysis of the topsoil across the Jurassic scarplands of England changed the upper bound of the variogram; it then resembled the within-class variogram computed by the method of moments. To elucidate these results, we simulated several series of data to represent a random process with values fluctuating about a mean, data with long-range linear trend, data with local trend, and data with stepped transitions. The results suggest that the wavelet variogram can filter out the effects of long-range trend, but not local trend, and of transitions from one class to another, as across boundaries.

Is the OECD acute worm toxicity test environmentally relevant? The effect of mineral form on calculated lead toxicity

In a series of experiments the toxicity of lead to worms in soil was determined following the draft OECD earthworm reproduction toxicity protocol except that lead was added as solid lead nitrate, carbonate and sulphide rather than as lead nitrate solution as would normally be the case. The compounds were added to the test soil to give lead concentrations of 625-12500 pg Pb g-1 of soil. Calculated toxicities of the lead decreased in the order nitrate > carbonate > sulphide, the same order as the decrease in the solubility of the metal compounds used. The 7-day LC50 (lethal concentration when 50% of the population is killed) for the nitrate was 5321 +/- 275 mug Pb g(-1) of soil and this did not change with time. The LC50 values for carbonate and sulphide could not be determined at the concentration ranges used. The only parameter sensitive enough to distinguish the toxicities of the three compounds was cocoon (egg) production. The EC50S for cocoon production (the concentration to produce a 50% reduction in cocoon production) were 993, 8604 and 10 246 mug Pb g(-1) of soil for lead nitrate, carbonate and sulphide, respectively. Standard toxicity tests need to take into account the form in which the contaminant is present in the soil to be of environmental relevance. (C) 2002 Elsevier Science Ltd. All rights reserved.

A bow-form burrow and its sedimentological and palaeoecological significance

A deep-tier, bow-form burrow with a long apertural neck, and several different types of infill is described from Upper Jurassic shelfal carbonates of Saudi Arabia, Miocene pelagic packstones and wackestones of Malta, and Lower Cretaceous shoreface sands and mudrocks of southern England. The two most commonly observed types of infill are a coarse-grained infill, referred to as Glyphichnus-mode (formed by sediment entering the burrow following breakage of the apertural neck), and a laminated, muddy infill, referred to as Cylindrichnus-mode, which is considered to represent passive, drought filling through a complete burrow. The type of infill and aspects of preservation show that these burrows can be used to assess the style of sedimentation, particularly steady aggradation versus periodic erosion. At present the bow-form burrow is not assigned to a specific ichnotaxon.

Transfer across form and modality in implicit and explicit memory

Three experiments examined transfer across form (words/pictures) and modality (visual/ auditory) in written word, auditory word, and pictorial implicit memory tests, as well as on a free recall task. Experiment 1 showed no significant transfer across form on any of the three implicit memory tests,and an asymmetric pattern of transfer across modality. In contrast, the free recall results revealed a very different picture. Experiment 2 further investigated the asymmetric modality effects obtained for the implicit memory measures by employing articulatory suppression and picture naming to control the generation of phonological codes. Finally, Experiment 3 examined the effects of overt word naming and covert picture labelling on transfer between study and test form. The results of the experiments are discussed in relation to Tulving and Schacter's (1990) Perceptual Representation Systems framework and Roediger's (1990) Transfer Appropriate Processing theory.