Regularized iterative and noniterative procedures for object restoration in the presence of noise :an error analysis

An analysis is carried out, using the prolate spheroidal wave functions, of certain regularized iterative and noniterative methods previously proposed for the achievement of object restoration (or, equivalently, spectral extrapolation) from noisy image data. The ill-posedness inherent in the problem is treated by means of a regularization parameter, and the analysis shows explicitly how the deleterious effects of the noise are then contained. The error in the object estimate is also assessed, and it is shown that the optimal choice for the regularization parameter depends on the signal-to-noise ratio. Numerical examples are used to demonstrate the performance of both unregularized and regularized procedures and also to show how, in the unregularized case, artefacts can be generated from pure noise. Finally, the relative error in the estimate is calculated as a function of the degree of superresolution demanded for reconstruction problems characterized by low space–bandwidth products.

Localization in systems of non-identical oscillators

A singular perturbation method is applied to a non-conservative system of two weakly coupled strongly nonlinear non-identical oscillators. For certain parameters, localized solutions exist for which the amplitude of one oscillator is an order of magnitude smaller than the other. It is shown that these solutions are described by coupled equations for the phase difference and scaled amplitudes. Three types of localized solutions are obtained as solutions to these equations which correspond to phase locking, phase drift, and phase entrainment. Quantitative results for the phases and amplitudes of the oscillators and the stability of these phenomena are expressed in terms of the parameters of the model.

Ets-1 p27: A novel Ets-1 isoform with dominant-negative effects on the transcriptional properties and the subcellular localization of Ets-1 p51

The transcription factor Ets-1 is implicated in various physiological processes and invasive pathologies. We identified a novel variant of ets-1, ets-1Delta(III-VI), resulting from the alternative splicing of exons III to VI. This variant encodes a 27 kDa isoform, named Ets-1 p27. Ets-1 p27 lacks the threonine-38 residue, the Pointed domain and the transactivation domain, all of which are required for the transactivation of Ets-1 target genes. Both inhibitory domains surrounding the DNA-binding domain are conserved, suggesting that Ets-1 p27, like the full-length Ets-1 p51 isoform, is autoinhibited for DNA binding. We showed that Ets-1 p27 binds DNA in the same way as Ets-1 p51 does and that it acts both at a transcriptional and a subcellular localization level, thereby constituting a dual-acting dominant negative of Ets-1 p51. Ets-1 p27 blocks Ets-1 p51-mediated transactivation of target genes and induces the translocation of Ets-1 p51 from the nucleus to the cytoplasm. Furthermore, Ets-1 p27 overexpression represses the tumor properties of MDA-MB-231 mammary carcinoma cells in correlation with the known implication of Ets-1 in various cellular mechanisms. Thus the dual-acting dominant-negative function of Ets-1 p27 gives to the Ets-1 p27/Ets-1 p51 ratio a determining effect on cell fate.