On the characterization of local aromatic properties in benzenoid hydrocarbons

A generalization of the Kekulé index for composite valence structures provides a quantitative value corresponding to Clar's assessment of benzenoid character of aromatic ring systems. The idea involved is further specialized for the individual local rings in the molecules. Comparison with limited experimental data supports the validity of this approach.     

On the evaluation of the characteristic polynomial via symmetric function theory

The use of power sum symmetric functions leads to Newton's identities, which relate the traces of various powers ofA, the adjacency matrix of a graph, and the coefficients of the characteristic polynomials. While it is possible to solve Newton's identities and generate the coefficients by recursion or, alternatively, to derive them by sequential manipulations (yielding the explicit formulas), we show how the results can be expressed using a combinatorial approach and relate the evaluation of the coefficients to selected Young diagrams.     

Partitioning of <Emphasis Type="Italic">π</Emphasis> -electrons in rings of polycyclic conjugated hydrocarbons: Part 6. Comparison with other methods for estimating the local aromaticity of rings in polycyclic benzenoids

By adopting the convention that shared double bonds in polycyclic conjugated hydrocarbons contribute with one -electron and unshared ones with two -electrons, a partition of -electrons in each ring (-electron content, EC) can be obtained by averaging over all Kekulé structures, which are assumed to have equal weights. This affords a simple measure of local aromaticity that is comparable with other such local aromaticity indices in polycyclic benzenoids.     

(Z)-3-p-tolylsulfinylacrylonitrile as a chiral dienophile: diels-alder reactions with furan and acyclic dienes

The behavior of (Z)-3-p-tolylsulfinylacrylonitrile (1) as a chiral dienophile has been evaluated from its reactions with furan and acyclic dienes. Electrostatic interactions of the cyano group with the sulfinyl one restrict the conformational mobility around the C-S bond, thus controlling the pi-facial selectivity, which is almost complete in all cases, the approach of the diene from the less-hindered face of the dienophile (that bearing the lone electron pair) in the predominant rotamer being the favored one. The regioselectivity is also completely controlled by the cyano group. Additionally, the reactivity of compound 1 as well as its endo-selectivity are both higher than those observed for the corresponding (Z)-3-sulfinylacrylates, thus proving the potential of sulfinylnitriles as chiral dienophiles.     

Novel characterization of proteomics maps by sequential neighborhoods of protein spots

We consider a characterization of proteomics maps based on an alternative kind of neighborhood graphs for the protein spots on 2-D gel. The novel approach considers for every protein spot only the nearest neighborhood consisting of protein spots of higher abundance. The approach has the simplicity and advantages of the recently introduced characterization of proteome maps based on considering the nearest neighborhoods of protein spots, but it also has important additional desirable computational features. The characterization of the nearest neighborhood graphs of 2-D gel proteomics maps is sensitive to the number of spots considered and may lead to changes in the degree of similarity of different maps when the number of points has been changed, thus imposing restrictions on the protocol used for comparison of maps. The novel approach presented in this work is less sensitive to the number of points used in the analysis because graphs are constructed in a stepwise process in which the role of more distant neighbors has been diminished by linking a new spot to the nearest spot that has been already part of the neighborhood graph. In this way a graph with N + 1 spots is obtained from the graph on N spots by adding a single new link, while in the case of the nearest neighborhood graphs adding a new spot introduces novel neighborhoods and generally results in a graph that may differ significantly from the neighborhood graph on N points.     

On 3-D graphical representation of proteomics maps and their numerical characterization

We consider numerical characterization of proteomics maps by representing a map as a three-dimensional graphical object based on x, y coordinates of the spots and using their relative abundance as the z coordinate. In our representation the protein spots are first ordered based on their relative abundance and labeled accordingly. In the next step a 3-D path is constructed connecting spots having adjacent labels. Finally a matrix is constructed by assigning to each pairs of labels (i, j) matrix element, the numerical value of which is based on the quotients of the Euclidean distance and the distance along the 3-D zigzag between the two points. The approach has been illustrated on a fragment of a proteomics map and compared with 2-D graphical representation of proteomics maps.     

Narrow band quantitative and multivariate electroencephalogram analysis of peri-adolescent period

ABSTRACT: BACKGROUND: The peri-adolescent period is a crucial developmental moment of transition from childhood to emergent adulthood. The present report analyses the differences in Power Spectrum (PS) of the Electroencephalogram (EEG) between late childhood (24 children between 8 and 13 years old) and young adulthood (24 young adults between 18 and 23 years old). RESULTS: The narrow band analysis of the Electroencephalogram was computed in the frequency range of 0--20 Hz. The analysis of mean and variance suggested that six frequency ranges presented a different rate of maturation at these ages, namely: low delta, delta-theta, low alpha, high alpha, low beta and high beta. For most of these bands the maturation seems to occur later in anterior sites than posterior sites. Correlational analysis showed a lower pattern of correlation between different frequencies in children than in young adults, suggesting a certain asynchrony in the maturation of different rhythms. The topographical analysis revealed similar topographies of the different rhythms in children and young adults. Principal Component Analysis (PCA) demonstrated the same internal structure for the Electroencephalogram of both age groups. Principal Component Analysis allowed to separate four subcomponents in the alpha range. All these subcomponents peaked at a lower frequency in children than in young adults. CONCLUSIONS: The present approaches complement and solve some of the incertitudes when the classical brain broad rhythm analysis is applied. Children have a higher absolute power than young adults for frequency ranges between 0-20 Hz, the correlation of Power Spectrum (PS) with age and the variance age comparison showed that there are six ranges of frequencies that can distinguish the level of EEG maturation in children and adults. The establishment of maturational order of different frequencies and its possible maturational interdependence would require a complete series including all the different ages.     

Spectral representation of reduced protein models

We consider a spectrum-like two-dimensional graphical representation of proteins based on a reduced protein model in which 20 amino acids are grouped into five classes. This particular grouping of amino acids was suggested by Riddle and co-workers in 1997. The graphical representation is based on depicting sequentially the amino acids on five horizontal lines at equal separations. One-letter codes, B, O, U, X and Y, to which numerical values 1 to 5 have been assigned, are suggested as labels for the fictional amino acids that represent all the amino acids within each group. The approach is illustrated on ND6 proteins of eight species having from 168 to 175 amino acids. While visual inspection of the novel spectral graphical representations of proteins may reveal local similarities and dissimilarities of protein sequences, arithmetic manipulations of spectra offer an elegant route to graphic visualization of the degree of similarity for selected pairs of proteins.     

Novel matrix invariants for characterization of changes of proteomics maps

Previous studies on mathematical characterization of proteomics maps by sets of map invariants were based on the construction of a set of distance-related matrices obtained by matrix multiplication of a single matrix by itself. Here we consider an alternative characterization of proteomics maps based on a set of matrices characterizing local features of an embedded zigzag curve over the map. It is shown that novel invariants can well characterize proteomics maps. Advantages of the novel approach are discussed.