Optimal observers for ARMA models

A polynomial-based ARMA model, when posed in a state-space framework can be regarded in many different ways. In this paper two particular state-space forms of the ARMA model are considered, and although both are canonical in structure they differ in respect of the mode in which disturbances are fed into the state and output equations. For both forms a solution is found to the optimal discrete-time observer problem and algebraic connections between the two optimal observers are shown. The purpose of the paper is to highlight the fact that the optimal observer obtained from the first state-space form, commonly known as the innovations form, is not that employed in an optimal controller, in the minimum-output variance sense, whereas the optimal observer obtained from the second form is. Hence the second form is a much more appropriate state-space description to use for controller design, particularly when employed in self-tuning control schemes.

Canonical description of the perspective projections

A unique parameterization of the perspective projections in all whole-numbered dimensions is reported. The algorithm for generating a perspective transformation from parameters and for recovering parameters from a transformation is a modification of the Givens orthogonalization algorithm. The algorithm for recovering a perspective transformation from a perspective projection is a modification of Roberts' classical algorithm. Both algorithms have been implemented in Pop-11 with call-out to the NAG Fortran libraries. Preliminary monte-carlo tests show that the transformation algorithm is highly accurate, but that the projection algorithm cannot recover magnitude and shear parameters accurately. However, there is reason to believe that the projection algorithm might improve significantly with the use of many corresponding points, or with multiple perspective views of an object. Previous parameterizations of the perspective transformations in the computer graphics and computer vision literature are discussed.

Closed form approximations for spread options

This article expresses the price of a spread option as the sum of the prices of two compound options. One compound option is to exchange vanilla call options on the two underlying assets and the other is to exchange the corresponding put options. This way we derive a new closed form approximation for the price of a European spread option and a corresponding approximation for each of its price, volatility and correlation hedge ratios. Our approach has many advantages over existing analytical approximations, which have limited validity and an indeterminacy that renders them of little practical use. The compound exchange option approximation for European spread options is then extended to American spread options on assets that pay dividends or incur costs. Simulations quantify the accuracy of our approach; we also present an empirical application to the American crack spread options that are traded on NYMEX. For illustration, we compare our results with those obtained using the approximation attributed to Kirk (1996, Correlation in energy markets. In: V. Kaminski (Ed.), Managing Energy Price Risk, pp. 71–78 (London: Risk Publications)), which is commonly used by traders.

Mapping therapy for sentence production impairments in nonfluent aphasia

This study investigated a new treatment in which sentence production abilities were trained in a small group of individuals and nonfluent aphasia. It was based upon a mapping therapy approach which holds that sentence production and comprehension impairments are due to difficulties in mapping between the meaning form (thematic roles) and the syntactic form of sentences. We trained production of both canonical and noncanonical reversible sentences.Three patients received treatment and two served as control participants. Patients who received treatment demonstrated acquisition of all trained sentence structures. They also demonstrated across-task generalisation of treated and some untreated sentence structures on two tasks of constrained sentence production, and showed some improvements on a narrative task. One control participant improved on some of these measures and the other did not. There was no noted improvement in sentence comprehension abilities following treatment. Results are discussed with reference to the heterogeneity of underlying impairments in sentence production impairments in nonfluent patients, and the possible mechanisms by which improvement in sentence production might have been achieved in treatment.

Canonical Wnt signalling induces satellite-cell proliferation during adult skeletal muscle regeneration

Satellite cells represent the stem cell population of adult skeletal muscle. The molecular mechanisms that control the proliferation of satellite cells are not well understood. In this study, we show that in response to injury, myofibres activate Wnt ligand transcription and activate a reporter cell line that is sensitive to the canonical Wnt-signalling pathway. Activated satellite cells on isolated cultured myofibres show robust expression of activated-β-catenin (Act-β-Cat), a key downstream transcriptional coactivator of canonical Wnt signalling. We provide evidence that the Wnt family of secreted glycoproteins act on satellite cells in a ligand-specific manner. Overexpression of Wnt1, Wnt3a or Wnt5a protein causes a dramatic increase in satellite-cell proliferation. By contrast, exposure of satellite cells to Wnt4 or Wnt6 diminishes this process. Moreover, we show that the prolonged satellite-cell quiescence induced by inhibitory Wnt is reversible and exposing inhibited satellite cells to stimulatory Wnt signalling restores their proliferation rate. Stimulatory Wnt proteins induce premature satellite cell BrdU incorporation as well as nuclear translocation of Act-β-Cat. Finally, we provide evidence that the Act-β-Cat translocation observed in single fibres during in vitro culture also occurs in cases of acute and chronic skeletal muscle regeneration in rodents and humans. We propose that Wnt proteins may be key factors that regulate the rate of satellite-cell proliferation on adult muscle fibres during the wound-healing response.

Structural characterization of a new crystal form of the four-way Holliday junction formed by the DNA sequence d(CCGGTACCGG)2: sequence versus lattice?

DNA-strand exchange is a vital step in the recombination process, of which a key intermediate is the four-way DNA Holliday junction formed transiently in most living organisms. Here, the single-crystal structure at a resolution of 2.35 Å of such a DNA junction formed by d(CCGGTACCGG)2, which has crystallized in a more highly symmetrical packing mode to that previously observed for the same sequence, is presented. In this case, the structure is isomorphous to the mismatch sequence d(CCGGGACCGG)2, which reveals the roles of both lattice and DNA sequence in determining the junction geometry. The helices cross at the larger angle of 43.0° (the previously observed angle for this sequence was 41.4°) as a right-handed X. No metal cations were observed; the crystals were grown in the presence of only group I counter-cations.