Comments, with reply, on "Computational algorithms for pole assignment" by N.K. Nichols

Some points of the paper by N.K. Nichols (see ibid., vol.AC-31, p.643-5, 1986), concerning the robust pole assignment of linear multiinput systems, are clarified. It is stressed that the minimization of the condition number of the closed-loop eigenvector matrix does not necessarily lead to robustness of the pole assignment. It is shown why the computational method, which Nichols claims is robust, is in fact numerically unstable with respect to the determination of the gain matrix. In replying, Nichols presents arguments to support the choice of the conditioning of the closed-loop poles as a measure of robustness and to show that the methods of J Kautsky, N. K. Nichols and P. VanDooren (1985) are stable in the sense that they produce accurate solutions to well-conditioned problems.

Robustness in partial pole placement

The robustness of state feedback solutions to the problem of partial pole placement obtained by a new projection procedure is examined. The projection procedure gives a reduced-order pole assignment problem. It is shown that the sensitivities of the assigned poles in the complete closed-loop system are bounded in terms of the sensitivities of the assigned reduced-order poles, and the sensitivities of the unaltered poles are bounded in terms of the sensitivities of the corresponding open-loop poles. If the assigned poles are well-separated from the unaltered poles, these bounds are expected to be tight. The projection procedure is described in [3], and techniques for finding robust (or insensitive) solutions to the reduced-order problem are given in [1], [2].

On computational algorithms for pole assignment

A number of computationally reliable direct methods for pole assignment by feedback have recently been developed. These direct procedures do not necessarily produce robust solutions to the problem, however, in the sense that the assigned poles are insensitive to perturbalions in the closed-loop system. This difficulty is illustrated here with results from a recent algorithm presented in this TRANSACTIONS and its causes are examined. A measure of robustness is described, and techniques for testing and improving robustness are indicated.

Algorithms for Robust Pole Assignment in Singular Systems

The solution of the pole assignment problem by feedback in singular systems is parameterized and conditions are given which guarantee the regularity and maximal degree of the closed loop pencil. A robustness measure is defined, and numerical procedures are described for selecting the free parameters in the feedback to give optimal robustness.

Analysis of growth physiology and phytochemical content of Eruca and Diplotaxis Cultivars under different light and temperature regimes

Rocket is a leafy brassicaceous salad crop that encompasses two major genera (Diplotaxis and Eruca) and many different cultivars. Rocket is a rich source of antioxidants and glucosinolates, many of which are produced as secondary products by the plant in response to stress. In this paper we examined the impact of temperature and light stress on several different cultivars of wild and salad rocket. Growth habit of the plants varied in response to stress and with different genotypes, reflecting the wide geographical distribution of the plant and the different environments to which the genera have naturally adapted. Preharvest environmental stress and genotype also had an impact on how well the cultivar was able to resist postharvest senescence, indicating that breeding or selection of senescence-resistant genotypes will be possible in the future. The abundance of key phytonutrients such as carotenoids and glucosinolates are also under genetic control. As genetic resources improve for rocket it will therefore be possible to develop a molecular breeding programme specifically targeted at improving stress resistance and nutritional levels of plant secondary products. Concomitantly, it has been shown in this paper that controlled levels of abiotic stress can potentially improve the levels of chlorophyll, carotenoids and antioxidant activity in this leafy vegetable.

Raytracing simulation for predicting light pipe transmittance

Daylighting systems can offer energy savings primarily by reducing electric lighting usage. Accurate predictive models of daylighting system performances are crucial for effective design and implementation of this renewable energy technology. A comparative study of predictive methods was performed and the use of a commercial raytracing software program was validated as a method of predicting light pipe performance. Raytracing simulation was shown to more accurately predict transmission effi ciency than existing analytical methods.

The boreal forest and the polar front

The analysis presented in this paper suggests that the larger heating over the boreal forest in the spring and summer, as contrasted with weaker heating over the adjacent tundra, results in a preferred position of the polar front along the northern edge of the boreal forest. This positioning is well documented in the literature (see, for example, Bryson, 1966; Barry and Hare, 1974; Kreps and Barry, 1970). This heating results from the lower albedo of the boreal forest which is not compensated by an increase in transpiration, even with the larger leaf area index of the forest. The warmer temperatures are mixed upward by the deep boundary layer over the forest and mesoscale circulations which result from the patchiness of heating associated with the heterogeneous landscapes of the forest. Thus in contrast to previous assumptions in which the arctic front position in the summer determines the northern limit of the boreal tree line, our study suggests the boreal forest itself significantly influences the preferred position of the front. This conclusion reinforces the findings of Bonan et al. (1992) and Foley et al. (1994) on the important role of boreal forest-tundra interactions with climate.

Paul the Silentiary’s description of Hagia Sophia in the light of new archaeological evidence

A discussion of the implications of of recent archaeological work at Hagia Sophia in Istanbul for understanding Paul the Silentiary's sixth-century Ekphrasis of the Byzantine church.

Physicality, difference, and the challenge of representation: Werner Herzog in the Light of the new waves

This chapter looks into the gap between presentational realism and the representation of physical experience in Werner Herzog's work so as to retrieve the indexical trace – or the absolute materiality of death. To that end, it draws links between Herzog and other directors akin to realism in its various forms, including surrealism. In particular, it focuses on François Truffaut and Glauber Rocha, representing respectively the Nouvelle Vague and the Cinema Novo, whose works had a decisive weight on Herzog’s aesthetic choices to the point of originating distinct phases of his outputs. The analyses, though restricted to a small number of films, intends to re-evaluate Herzog’s position within, and contribution to, film history.

The global distribution of phytoplankton size spectrum and size classes from their light-absorption spectra derived from satellite data

The absorption spectra of phytoplankton in the visible domain hold implicit information on the phytoplankton community structure. Here we use this information to retrieve quantitative information on phytoplankton size structure by developing a novel method to compute the exponent of an assumed power-law for their particle-size spectrum. This quantity, in combination with total chlorophyll-a concentration, can be used to estimate the fractional concentration of chlorophyll in any arbitrarily-defined size class of phytoplankton. We further define and derive expressions for two distinct measures of cell size of mixed populations, namely, the average spherical diameter of a bio-optically equivalent homogeneous population of cells of equal size, and the average equivalent spherical diameter of a population of cells that follow a power-law particle-size distribution. The method relies on measurements of two quantities of a phytoplankton sample: the concentration of chlorophyll-a, which is an operational index of phytoplankton biomass, and the total absorption coefficient of phytoplankton in the red peak of visible spectrum at 676 nm. A sensitivity analysis confirms that the relative errors in the estimates of the exponent of particle size spectra are reasonably low. The exponents of phytoplankton size spectra, estimated for a large set of in situ data from a variety of oceanic environments (~ 2400 samples), are within a reasonable range; and the estimated fractions of chlorophyll in pico-, nano- and micro-phytoplankton are generally consistent with those obtained by an independent, indirect method based on diagnostic pigments determined using high-performance liquid chromatography. The estimates of cell size for in situ samples dominated by different phytoplankton types (diatoms, prymnesiophytes, Prochlorococcus, other cyanobacteria and green algae) yield nominal sizes consistent with the taxonomic classification. To estimate the same quantities from satellite-derived ocean-colour data, we combine our method with algorithms for obtaining inherent optical properties from remote sensing. The spatial distribution of the size-spectrum exponent and the chlorophyll fractions of pico-, nano- and micro-phytoplankton estimated from satellite remote sensing are in agreement with the current understanding of the biogeography of phytoplankton functional types in the global oceans. This study contributes to our understanding of the distribution and time evolution of phytoplankton size structure in the global oceans.