Extreme value distribution for singular measures

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that, numerically, the Extreme Value distribution for these maps can be associated to the Generalised Extreme Value family where the parameters scale with the information dimension. The numerical analysis are performed on a few low dimensional maps. For the middle third Cantor set and the Sierpinskij triangle obtained using Iterated Function Systems, experimental parameters show a very good agreement with the theoretical values. For strange attractors like Lozi and H\`enon maps a slower convergence to the Generalised Extreme Value distribution is observed. Even in presence of large statistics the observed convergence is slower if compared with the maps which have an absolute continuous invariant measure. Nevertheless and within the uncertainty computed range, the results are in good agreement with the theoretical estimates.

Correlations between two sets of angular relation equations

It is shown here that the angular relation equations between direct and reciprocal vectors are very similar to the angular relation equations in Euler's theorem. These two sets of equations are usually treated separately as unrelated equations in different fields. In this careful study, the connection between the two sets of angular equations is revealed by considering the cosine rule for the spherical triangle. It is found that understanding of the correlation is hindered by the facts that the same variables are defined differently and different symbols are used to represent them in the two fields. Understanding the connection between different concepts is not only stimulating and beneficial, but also a fundamental tool in innovation and research, and has historical significance. The background of the work presented here contains elements of many scientific disciplines. This work illustrates the common ground of two theories usually considered separately and is therefore of benefit not only for its own sake but also to illustrate a general principle that a theory relevant to one discipline can often be used in another. The paper works with chemistry related concepts using mathematical methodologies unfamiliar to the usual audience of mainstream experimental and theoretical chemists.

Does the PMSP connectionist model of single word reading learn to read in the same way as a child?

The Plaut, McClelland, Seidenberg and Patterson (1996) connectionist model of reading was evaluated at two points early in its training against reading data collected from British children on two occasions during their first year of literacy instruction. First, the network’s non-word reading was poor relative to word reading when compared with the children. Second, the network made more non-lexical than lexical errors, the opposite pattern to the children. Three adaptations were made to the training of the network to bring it closer to the learning environment of a child: an incremental training regime was adopted; the network was trained on grapheme– phoneme correspondences; and a training corpus based on words found in children’s early reading materials was used. The modifications caused a sharp improvement in non-word reading, relative to word reading, resulting in a near perfect match to the children’s data on this measure. The modified network, however, continued to make predominantly non-lexical errors, although evidence from a small-scale implementation of the full triangle framework suggests that this limitation stems from the lack of a semantic pathway. Taken together, these results suggest that, when properly trained, connectionist models of word reading can offer insights into key aspects of reading development in children.

Asymmetric oxidation of vinyl- and ethynyl terthiophene ligands in triruthenium complexes

A series of ruthenium(II) complexes [{RuCl(CO)(PMe3)3(–CHvCH–)}nX], 1a–1c (1a: n = 3, X = 3,3’’- dimethyl-2,2’:3’,2’’-terthiophene; 1b: n = 2, X = 2,2’-bithiophene; 1c: n = 2, X = 2,3-bis(3-methylthiophen- 2-yl)benzothiophene) and [{Cp*(dppe)2Ru(–CuC–)}3X], 1d (X = 3,3’’-dimethyl-2,2’:3’,2’’- terthiophene), were prepared and characterized by 1H, 13C and 31P NMR. Their redox, spectroscopic and bonding properties were studied with a range of spectro-electrochemical methods in combination with density functional theory calculations. The first two anodic steps observed for 1a and 1d are largely localized on the lateral frameworks of the molecular triangle, the direct conjugation between them being precluded due to the photostable open form of the dithienyl ethene moiety. The third anodic step is then mainly localized on the centerpiece of the triangular structure, affecting both bithiophene laterals. The experimental IR and UV-vis-NIR spectroelectrochemical data and, largely, also DFT calculations account for this explanation, being further supported by direct comparison with the anodic behavior of reference diruthenium complexes 1b and 1c.