Central limit theorems for empirical product densities of stationary point processes

We prove the asymptotic normality of kernel estimators of second- and higher-order product densities (and of the pair correlation function) for spatially homogeneous (and isotropic) point processes observed on a sampling window \(W_n\) , which is assumed to expand unboundedly in all directions as \(n \rightarrow \infty \,\) . We first study the asymptotic behavior of the covariances of the empirical product densities under minimal moment and weak dependence assumptions. The proof of the main results is based on the Brillinger-mixing property of the underlying point process and certain smoothness conditions on the higher-order reduced cumulant measures. Finally, the obtained limit theorems enable us to construct \(\chi ^2\) -goodness-of-fit tests for hypothetical product densities.     

Employing different loss functions for the classification of images via supervised learning

Supervised learning methods are powerful techniques to learn a function from a given set of labeled data, the so-called training data. In this paper the support vector machines approach is applied to an image classification task. Starting with the corresponding Tikhonov regularization problem, reformulated as a convex optimization problem, we introduce a conjugate dual problem to it and prove that, whenever strong duality holds, the function to be learned can be expressed via the dual optimal solutions. Corresponding dual problems are then derived for different loss functions. The theoretical results are applied by numerically solving a classification task using high dimensional real-world data in order to obtain optimal classifiers. The results demonstrate the excellent performance of support vector classification for this particular problem.     

Antioxidant activity of methimazole-copper(II) bioactive species and spectroscopic investigations on the mechanism of its interaction with Bovine Serum Albumin

Free radical-mediated oxidative stress has been implicated in numerous autoimmune disorders including Graves’ disease. Hyperthyroidism results in a marked increase in intracellular antioxidant enzymes including superoxide dismutase. The later activity is significantly increased in untreated Graves’ patients while treatment with methimazole results in normalization of the free radical and antioxidant activity indices. In this context, and considering the findings mentioned above, the aim of the present study was to evaluate unknown biological activities of methimazole and its methimazole-copper(II) complex investigating their superoxide scavenger power. Under the applied experimental conditions, methimazole did not show superoxide dismutase (SOD) activity while the copper complexes exhibited a strong superoxide radical scavenging capacity. Bearing in mind that the capacity of drugs to bind and/or interact with albumin is essential for their pharmacokinetic and pharmacodynamic properties, a complete investigation of the binding ability of both compounds by using Fourier transform infrared (FT-IR), Raman and Fluorescence spectroscopies, and UV-Vis spectrophotometry was included. Besides, in order to probe the copper ligand environment the EPR spectra of such compounds were analyzed.     

Preparation of planar‐chiral multidonor phosphanylferrocene carboxamides and their application as ligands for palladium‐catalysed asymmetric allylic alkylation

Amide coupling of (S_p)‐2‐(diphenylphosphanyl)ferrocene‐1‐carboxylic acid with appropriate terminal amines mediated by 1‐hydroxybenzotriazole and a carbodiimide affords multi‐donor amides terminally functionalized with planar‐chiral (S_p)‐2‐(diphenylphosphanyl)ferrocen‐1‐yl moieties in good to excellent yields. Palladium catalysts based on these ligands efficiently promote asymmetric allylic alkylation of 1,3‐diphenylallyl acetate with in situ generated dimethyl malonate anion to give the C‐alkylated product with ees up to 93% at room temperature. Copyright © 2010 John Wiley & Sons, Ltd.     

Synthesis of NMP/RAFT inifers and preparation of block copolymers

Two different initiator/transfer agents (inifers) containing an alkoxyamine and a dithiobenzoate were synthetized and used to trigger out either reversible addition‐fragmentation chain transfer (RAFT) polymerization or nitroxide‐mediated polymerization (NMP). α‐Dithiobenzoate‐ω‐alkoxyamine‐difunctional polymers were produced in both cases which were subsequently used as precursors in the formation of block copolymers. This synthetic approach was applied to N‐isopropylacrylamide (NIPAM) or polyethylene oxide methacrylate (EOMA) to form α,ω‐heterodifunctional homopolymers via RAFT at 60°C which were chain extended with styrene by activating the alkoxyamine moiety at 120°C. Under such temperature conditions, it is proposed that a tandem NMP/RAFT polymerization is initiated producing a simultaneous growth of polystyrene blocks at both chain‐ends. Self‐assembled nanostructures of these amphiphilic block copolymers were evidenced by scanning electron microscopy. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012