Assessment of clinical data of nonlinear stochastic deconvolution versus block-circulant singular value decomposition for quantitative dynamic susceptibility contrast magnetic resonance imaging

Dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI) allows the noninvasive assessment of brain hemodynamics alterations by quantifying, via deconvolution, the cerebral blood flow (CBF) and mean transit time (MTT). Singular value decomposition (SVD) and block-circulant SVD (cSVD) are the most widely adopted deconvolution method, although they bear some limitations, including unphysiological oscillations in the residue function and bias in the presence of delay and dispersion between the tissue and the arterial input function. A nonlinear stochastic regularization (NSR) has been proposed, which performs better than SVD and cSVD on simulated data both in the presence and absence of dispersion. Moreover, NSR allows to quantify the dispersion level. Here, cSVD and NSR are compared for the first time on a group of nine patients with severe atherosclerotic unilateral stenosis of internal carotid artery before and after carotid stenting to investigate the effect of arterial dispersion. According to region of interest-based analysis, NSR characterizes the pathologic tissue more accurately than cSVD, thus improving the quality of the information provided to physicians for diagnosis. In fact, in 7 (78%) of the 9 subjects, CBF and MTT maps provided by NSR allow to correctly identify the pathologic hemisphere to the physician. Moreover, by emphasizing the difference between pathologic and healthy tissues, NSR may be successfully used to monitor the subject's recovery after the treatment and/or surgery. NSR also generates dispersion level and non-dispersed CBF and MTT maps. The dispersion level provides information on CBF and MTT estimates reliability and may also be used as a clinical indicator of pathological tissue state complementary to CBF and MTT, thus increasing the clinical information provided by DSC-MRI analysis.     

On large deviations for some sequences of weighted means of Gaussian processes

In this paper we study some sequences of weighted means of continuous real valued Gaussian processes. More precisely we consider suitable generalizations of both arithmetic and logarithmic means of a Gaussian process with covariance function which satisfies either an exponential decay condition or a power decay condition. Our aim is to provide limits of variances of functionals of such weighted means which allow the application of some large deviation results in the literature.     

Birth of limit cycles bifurcating from a nonsmooth center

This paper is concerned with a codimension analysis of a two-fold singularity of piecewise smooth planar vector fields, when it behaves itself like a center of smooth vector fields (also called nondegenerate Σ-center). We prove that any nondegenerate Σ-center is Σ  -equivalent to a particular normal form _Z0$Z_0$. Given a positive integer number k   we explicitly construct families of piecewise smooth vector fields emerging from _Z0$Z_0$ that have k hyperbolic limit cycles bifurcating from the nondegenerate Σ  -center of _Z0$Z_0$ (the same holds for k=∞$k=\infty$). Moreover, we also exhibit families of piecewise smooth vector fields of codimension k   emerging from _Z0$Z_0$. As a consequence we prove that _Z0$Z_0$ has infinite codimension.     

Brønsted Acid Assisted Regio‐ and Enantioselective Direct O‐Nitroso Aldol Reaction Catalysed by α,α‐Diphenylprolinol Trimethylsilyl Ether

In the presence of p‐nitrobenzoic acid, the O‐nitroso aldol reaction of nitrosobenzene with enolisable aldehydes may be promoted by commercially available α,α‐diphenylprolinol trimethylsilyl ether. The reaction proceeds with good yields and essentially complete enantioselectivity, with catalyst loadings in the 5–10 mol % range. The resulting α‐oxyaldehyde adducts may be transformed in situ into α‐oxyimines, which provide 1,2‐amino alcohols upon treatment with Grignard reagents, in good overall yield (45–59 %) and with typical diastereomeric ratios ≥95:5.     

Optimal error estimates for an approximation of degenerate parabolic problems

A fully discrete scheme for a class of multidimensional degenerate parabolic equations is proposed. The discretization is given by $supoesup piecewise linear finite elements in space and backward differences in time (the smoothing procedure is avoided). Numerical integration is used; hence the proposed method is easy to implement. Optimal error estimates in energy norms are proved for the solutions.     

Reduction of Ozonides by Means of Polymeric Triphenylphosphine: Simplified Synthesis of Carbonyl Compounds from Alkenes

A classical system for the preparation of carbonyl compounds from alkenes relies upon ozonolysis of the double bond, followed by reductive cleavage of the ozonide so formed. Among the reagents of choice for such a reduction, triphenylphosphine certainly has enjoyed a widespread use.¹ However, in spite of the simplicity of the method, often one can face problems in the purification of the carbonyl compound from unreacted triphenylphosphine, especially if the polarities of both products are very similar. We have encountered such a problem during the preparation of the (20 S)-6β -ethoxy-3 α, 5-cyclo-5α -pregnane-20-carbaldehyde 4 from the suitably protected stigmasterol3². In this case, when triphenylphosphine was used for reduction of ozonide we never could isolate the aldehyde 2 uncontaninated by tripherylphosphine.     

Sensitizing effect of bio-based chemicals from urban wastes on the photodegradation of azo-dyes

To promote bio-based products for the industry, six bio-organic substances (cHALi) isolated from yard trimmings (green) and food (humid) urban residues aged under aerobic digestion for 0–60 days were investigated for their potential to perform as sensitizers for azo-dyes photodegradation. Ethylorange (EO) was used as probe molecule at 5 mg L^?1 starting concentration and irradiated in a closed Pyrex^® cell with a Xenon (1500 W) lamp and a cut-off filter for wavelengths below 340 nm or in a cylindrical photochemical reactor equipped with a 125 W medium pressure Hg lamp. The cHALi/EO ratio in the starting EO solution varied in the 0–200 (w/w) range. The % dye abatement was found a function of the irradiation time, of the type of cHALi substance and of the cHALi/EO ratio. The best results were achieved with cHALi isolated after 7 days biomass aerobic digestion. Total dye abatement was achieved within relatively short few hours. A progressive dye mineralization was observed under the same experimental conditions. On the contrary no significant degradation was evident for the cHALi substances within the same irradiation time. Several hydroxylated azo compounds were identified as likely responsible of residual color after total EO abatement. The results, coupled to the previously reported good performance of the same cHALi substances as auxiliaries for textile dyeing, augur well for the development of both efficient and environmentally friendly textile dyeing processes.