Relaxation methods in control theory

Two different relaxed problems associated with a problem of optimal control theory, governed by an ODE, are considered: the first is obtained by Young's methods and the second by semicontinuity arguments. A formula which relates the two relaxed functionals to each other is given.     

Using multidimensional projection techniques for reaching a high distinguishing ability in biosensing

Recent advances in the control of molecular engineering architectures have allowed unprecedented ability of molecular recognition in biosensing, with a promising impact for clinical diagnosis and environment control. The availability of large amounts of data from electrical, optical, or electrochemical measurements requires, however, sophisticated data treatment in order to optimize sensing performance. In this study, we show how an information visualization system based on projections, referred to as Projection Explorer (PEx), can be used to achieve high performance for biosensors made with nanostructured films containing immobilized antigens. As a proof of concept, various visualizations were obtained with impedance spectroscopy data from an array of sensors whose electrical response could be specific toward a given antibody (analyte) owing to molecular recognition processes. In addition to discussing the distinct methods for projection and normalization of the data, we demonstrate that an excellent distinction can be made between real samples tested positive for Chagas disease and Leishmaniasis, which could not be achieved with conventional statistical methods. Such high performance probably arose from the possibility of treating the data in the whole frequency range. Through a systematic analysis, it was inferred that Sammon's mapping with standardization to normalize the data gives the best results, where distinction could be made of blood serum samples containing 10(-7) mg/mL of the antibody. The method inherent in PEx and the procedures for analyzing the impedance data are entirely generic and can be extended to optimize any type of sensor or biosensor.     

An integral form of the isoperimetric inequality

We study stability for an integral isoperimetric inequality.     

The influence of an initial twisting on tapered beams undergoing large displacements

Meccanica - The behaviour of pre-twisted and tapered beams (such as turbine or helicopter blades) is characterized by stress distributions that may be quite different from those of the usual beam...     

Alkyl- and arylthiodediazoniations of dry arenediazonium o-benzenedisulfonimides. Efficient and safe modifications of the stadler and ziegler reactions to prepare alkyl aryl and diaryl sulfides

The reaction between dry arenediazonium o-benzenedisulfonimides 1 and sodium thiolates in anhydrous methanol represents an efficient and safe procedure, of general validity, for the preparation of unfunctionalized or variously functionalized alkyl aryl and diaryl sulfides. As a rule, the reaction temperature was maintained at 0-5 degrees C for the alkylthiodediazoniations and at room temperature (20-25 degrees C) for the arylthiodediazoniations. The sulfide yields are generally high; of the 63 considered examples, 43 gave yields greater than 80% and 13 were between 70% and 80%. Lower yields were obtained only when sterically hindered diazonium salts or thiols were used. A good amount of the o-benzenedisulfonimide (8) was always recovered from the reactions and could be reused to prepare salts 1. The copious experimental data collected in homogeneous conditions have offered several starting points for the study of the mechanism of these reactions.     

LSD1: more than demethylation of histone lysine residues

Lysine-specific histone demethylase 1 (LSD1) represents the first example of an identified nuclear protein with histone demethylase activity. In particular, it plays a special role in the epigenetic regulation of gene expression, as it removes methyl groups from mono- and dimethylated lysine 4 and/or lysine 9 on histone H3 (H3K4me1/2 and H3K9me1/2), behaving as a repressor or activator of gene expression, respectively. Moreover, it has been recently found to demethylate monomethylated and dimethylated lysine 20 in histone H4 and to contribute to the balance of several other methylated lysine residues in histone H3 (i.e., H3K27, H3K36, and H3K79). Furthermore, in recent years, a plethora of nonhistone proteins have been detected as targets of LSD1 activity, suggesting that this demethylase is a fundamental player in the regulation of multiple pathways triggered in several cellular processes, including cancer progression. In this review, we analyze the molecular mechanism by which LSD1 displays its dual effect on gene expression (related to the specific lysine target), placing final emphasis on the use of pharmacological inhibitors of its activity in future clinical studies to fight cancer.Subject terms: Epigenetics, Histone post-translational modifications