On the Local Convergence Analysis of the Gradient Sampling Method for Finite Max-Functions

The gradient sampling method is a recently developed tool for solving unconstrained nonsmooth optimization problems. Using just first-order information about the objective function, it generalizes the steepest descent method, one of the most classical methods for minimizing a smooth function. This study aims at determining under which circumstances one can expect the same local convergence result of the Cauchy method for the gradient sampling algorithm under the assumption that the problem is stated by a finite max-function around the optimal point. Additionally, at the end, we show how to practically accomplish the required hypotheses during the execution of the algorithm.     

MOVIPAC: Vibrational spectroscopy with a robust meta‐program for massively parallel standard and inverse calculations

We present the software package MO VI PAC for calculations of vibrational spectra, namely infrared, Raman, and Raman Optical Activity (ROA) spectra, in a massively parallelized fashion. MO VI PAC unites the latest versions of the programs SNF and AKIRA alongside with a range of helpful add‐ons to analyze and interpret the data obtained in the calculations. With its efficient parallelization and meta‐program design, MO VI PAC focuses in particular on the calculation of vibrational spectra of very large molecules containing on the order of a hundred atoms. For this purpose, it also offers different subsystem approaches such as Mode‐ and Intensity‐Tracking to selectively calculate specific features of the full spectrum. Furthermore, an approximation to the entire spectrum can be obtained using the Cartesian Tensor Transfer Method. We illustrate these capabilities using the example of a large π‐helix consisting of 20 (S)‐alanine residues. In particular, we investigate the ROA spectrum of this structure and compare it to the spectra of α‐ and 3₁₀‐helical analogs. © 2012 Wiley Periodicals, Inc.     

An fMRI study of magnitude comparison and exact addition in children

By contrast to the adult literature, in which a consistent parietofrontal network for number processing has been identified, the data from studies of number processing in children have been less consistent, probably due to differences in study design and control conditions. Number processing was examined using functional magnetic resonance imaging in 18 right-handed children (8–12 years) from the Cape Coloured community in Cape Town, South Africa, using Proximity Judgment and Exact Addition (EA) tasks. The findings were consistent with the hypothesis that, as in adults, the anterior horizontal intraparietal sulcus (HIPS) plays a major role in the representation and manipulation of quantity in children. The posterior medial frontal cortex, believed to be involved in performance monitoring in more complex arithmetic manipulations in adults, was extensively activated even for relatively simple symbolic number processing in the children. Other areas activated to a greater degree in the children included the left precentral sulcus, which may mediate number knowledge and, for EA, the head of the caudate nucleus, which is part of a fronto-subcortical circuit involved in the behavioral execution of sequences. Two regions that have been linked to number processing in adults — the angular gyrus and posterior superior parietal lobule — were not activated in the children. The data are consistent with the inference that although the functional specialization of the anterior HIPS may increase as symbolic number processing becomes increasingly automatic, this region and other elements of the parietofrontal network identified in adults are already reliably and robustly activated by middle childhood.     

Spiro[1,3-benzoxathiepin-4(5H),1′-cyclohexa[2,4]dien]-2,2′-dione,a Novel Heterocyclic Ring System

Abstract

Besides the common cyclisation reactions between divalent electrophiles such as Soc1₂, SC1₂, etc. and 2,2′-alkylidene-bisphenols 1 with selective attack by the two oxygens yielding dibenzo[d,g][1,3,2]dioxathiocines [1] we observed previously an unusual cyclisation of 1 with S₂CI₂ with a nucleophilic attack by the ortho- and para-carbon atoms (C(2) and C(4)) of bisphenol 1 [2]. We now report a new type of cyclocondensation reaction of 4,4′,6,6′-tetrasubstituted 2,2′-alkylidene-bisphenols 1 with ClSCOCl affording spiro[1,3-benzoxathiepin-4(5H),1′-cyclohexa[2,4]dien]-2,2′-diones 2 together with the cyclic carbonates 3. The structures of the products were elucidated mainly by ^l3C-NMR- and ¹H-NMR-spectroscopy. The mode of formation of the novel spiro thiocarbonates 2 resp. the known carbonates 3 [3] is discussed.     

Complexation and Transport of Alkali and Alkaline Earth Metal Cations by p-tert-Butyldihomooxacalix[4]arene Tetraketone Derivatives

The binding properties of three p-tert-butyldihomooxacalix[4]arene tetraketone derivatives (tert-butyl 2b, adamantyl 2c and phenyl 2d) in the cone conformation and one derivative (methyl 2a) in a partial cone conformation, towards alkali and alkaline earth metal cations have been established by extraction studies of metal picrates from water into dichloromethane, stability constant measurements in methanol and acetonitrile, and by ¹H NMR spectrometry. Transport experiments of metal picrates through a dichloromethane membrane were also performed. The results are compared to those obtained with closely-related calix[n]arene derivatives (n = 4 and 5) and discussed in terms of the substituents, size and conformational effects. Methylketone 2a is a poor binder for all the cations studied, due to its partial cone conformation. Ketones 2b, 2c and 2d show high extraction and complexation levels for the alkali cations, with similar profiles and preference for K⁺ and Na⁺ (plateau selectivity). Towards alkaline earth cations, these ketones show a strong peak selectivity for Ba²⁺ in extraction, but a plateau selectivity for Ca²⁺, Sr²⁺ and Ba²⁺ in complexation. The nature of the substituent attached to the ketone function has some influence on their binding properties, with phenylketone 2d being a slightly weaker binder than ketones 2b and 2c. ¹H NMR titrations confirm the formation of 1:1 complexes between the ketones and the cations studied, also indicating that they should be located inside the cavity defined by the phenoxy and carbonyl oxygen atoms. Ketones 2b, 2c and 2d show transport rates that do not follow, in general, the same trends observed in extraction and complexation.