Some Useful Integral Representations for Information-Theoretic Analyses

This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas for quantities that involve expectations of the logarithm of a positive random variable. Here, in the same spirit, we derive an exact integral representation (in one or two dimensions) of the moment of a nonnegative random variable, or the sum of such independent random variables, where the moment order is a general positive non-integer real (also known as fractional moments). The proposed formula is applied to a variety of examples with an information-theoretic motivation, and it is shown how it facilitates their numerical evaluations. In particular, when applied to the calculation of a moment of the sum of a large number, n, of nonnegative random variables, it is clear that integration over one or two dimensions, as suggested by our proposed integral representation, is significantly easier than the alternative of integrating over n dimensions, as needed in the direct calculation of the desired moment.     

New Results on Rational Approximation

Results in Mathematics - First asymptotic relations of Voronovskaya-type for rational operators of Shepard-type are shown. A positive answer in some senses to a problem on the pointwise...     

Hereditary nonpolyposis colorectal cancer: an approach to the selection of candidates to genetic testing based on clinical and molecular characteristics

OBJECTIVE: Identification of clinical and molecular characteristics associated with constitutional MLH1 and MSH2 mutations and definition of a stepwise strategy for the selection of colorectal cancer (CRC) patients amenable to MLH1 and MSH2 genetic testing. METHODS: 90 unrelated CRC patients were initially selected on the basis of either familial or early onset occurrence of CRC. They were screened for the presence of constitutional MLH1 and MSH2 mutations and for microsatellite instability (MSI). RESULTS: 16 pathogenetic mutations (9 MLH1 and 7 MSH2) were identified in 41% of Amsterdam hereditary nonpolyposis colorectal cancer (HNPCC) families, 5% of suspected HNPCC families, and 14% of sporadic early-onset CRC patients. The presence of the mutations correlated with MSI, with early age of onset and proximal location of the tumor, and with the presence of some extracolonic tumors of the HNPCC spectrum and/or multiple tumors in the family. CONCLUSIONS: Evaluation of clinical and molecular characteristics is useful for the identification of candidates to MLH1 and MSH2 mutational analysis and allows the application of a rational approach to genetic testing.     

Nitric oxide release mediated by calix[4]hydroquinones

Calix[4]monohydroquinone has been used as a supramolecular system for the generation of NO gas. In a one-electron reduction scheme involving NO+ subsetcalix[4]monohydroquinone complex, NO is released without the presence of an external reducing agent. Free calix[4]monoquinone, thus obtained, can be reused for a new NO-releasing cycle after NaBH4-reduction to calix[4]monohydroquinone.     

Catalytic behavior of supported Pd catalysts in the selective hydrogenation of campholenic aldehyde to naturanol

Selective catalytic reduction of campholenic aldehyde to naturanol was investigated over Sn-and Fe-doped SiO₂, and Fe₂O₃-supported Pd catalysts. On Pd/SiO₂ and Pd-Sn/SiO₂ only saturated campholenic aldehyde is formed. Addition of Fe increases the C=O hydrogenation rate producing the corresponding unsaturated alcohol with a good selectivity. Also Fe₂O₃-supported catalysts were found to be more selective towards carbonyl hydrogenation. Addition of tin to Pd/Fe₂O₃ contributes to a further selectivity enhancement towards naturanol.     

Synthesis and conformational studies of peptidomimetics containing a new bifunctional diketopiperazine scaffold acting as a beta-hairpin inducer

A practical synthesis of a new bifunctional diketopiperazine (DKP) scaffold 1, formally derived from the cyclization of L-aspartic acid and (S)-2,3-diaminopropionic acid, is reported. DKP-1 bears a carboxylic acid and an amino functionalities in a cis relationship, which have been used to grow peptide sequences. Tetra-, penta-, and hexapeptidomimetic sequences were prepared by solution-phase peptide synthesis (Boc strategy). Conformational analysis of these derivatives was carried out by a combination of 1H NMR spectroscopy, IR spectroscopy, CD spectroscopy, and computer modeling, and reveals the formation of beta-hairpin mimics involving 10-membered and 18-membered H-bonded rings and a reverse turn of the growing peptide chain.     

Magnetic nanoparticles coated with polyaniline to stabilize immobilized trypsin

It is reported the synthesis of magnetic nanoparticles via the chemical co-precipitation of Fe ³⁺ ions and their preparation by coating them with polyaniline. The electronic micrograph analysis showed that the mean diameter for the nanoparticles is ～15 nm. FTIR, powder X-ray diffraction and Mössbauer spectroscopy were used to understand the chemical, crystallographic and ⁵⁷Fe hyperfine structures for the two samples. The nanoparticles, which exhibited magnetic behavior with relatively high spontaneous magnetization at room temperature, were identified as being mainly formed by maghemite (γFe₂O₃). The coated magnetic nanoparticles (sample labeled “mPANI”) presented a real ability to bind biological molecules such as trypsin, forming the magnetic enzyme derivative (sample “mPANIG-Trypsin”). The amount of protein and specific activity of the immobilized trypsin were found to be 13±5 μg of protein/mg of mPANI (49.3 % of immobilized protein) and 24.1±0.7 U/mg of immobilized protein, respectively. After 48 days of storage at 4 ^°C, the activity of the immobilized trypsin was found to be 89 % of its initial activity. This simple, fast and low-cost procedure was revealed to be a promising way to prepare mPANI nanoparticles if technological applications addressed to covalently link biomolecules are envisaged. This route yields chemically stable derivatives, which can be easily recovered from the reaction mixture with a magnetic field and recyclable reused.