For G open bounded subset of R^2 with C^1 boundary, we study the regularity of the variational solution u in H^1_0(G) to the quasilinear elliptic equation of Leray-Lions type: -div A(x,Du)=f , when f belongs to the Zygmund space L(log L)^{\delta}, \delta>0. As an interpolation between known results for \delta=1/2 and \delta=1 of [Stampacchia] and [Alberico-Ferone], we prove that |Du| belongs to the Lorentz space L^{2, 1/\delta}(G) for \delta in [1/2, 1].

In this article an accurate and efficient technique for tissue typing is presented. The proposed technique is based on Canonical Correlation Analysis, a statistical method able to simultaneously exploit the spectral and spatial information characterizing the Magnetic Resonance Spectroscopic Imaging (MRSI) data. Recently, Canonical Correlation Analysis has been successfully applied to other types of biomedical data, such as functional MRI data.

Accurate quantitation of Magnetic Resonance Spectroscopy (MRS) signals is an essential step before converting the estimated signal parameters, such as frequencies, damping factors, and amplitudes, into biochemical quantities (concentration, pH). Several subspace-based parameter estimators have been developed for this task, which are efficient and accurate time-domain algorithms. However, they suffer from a serious drawback: they allow only a limited inclusion of prior knowledge which is important for accuracy and resolution.

Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding critical bases for all three-letter alphabets and we establish the fractal nature of these bases in function of the alphabets.

Two T helper (Th) cell subsets, namely Th1 and Th2 cells, play an important role in inflammatory diseases. The two subsets are thought to counter-regulate each other, and alterations in their balance result in different diseases. This paradigm has been challenged by recent clinical and experimental data. Because of the large number of genes involved in regulating Th1 and Th2 cells, assessment of this paradigm by modeling or experiments is difficult. Novel algorithms based on formal methods now permit the analysis of large gene regulatory networks.