Edges in graphs with large girth

Several upper bounds are given for the maximum number of edgese possible in a graph depending upon its orderp, girthg and, in certain cases, minimum degree. In particular, one upper bound has an asymptotic order ofp ^1+2/(g–1) wheng is odd. A corollary of our final result is that whenk = e/p 2. Asymptotic and numerical comparisons are also presented.     

Heritability of Stroop and flanker performance in 12-year old children

Background  

There is great interest in appropriate phenotypes that serve as indicator of genetically transmitted frontal (dys)function, such as ADHD. Here we investigate the ability to deal with response conflict, and we ask to what extent performance variation on response interference tasks is caused by genetic variation. We tested a large sample of 12-year old monozygotic and dizygotic twins on two well-known and closely related response interference tasks; the color Stroop task and the Eriksen flanker task. Using structural equation modelling we assessed the heritability of several performance indices derived from those tasks.     

The contribution of high frequencies to human brain activity underlying horizontal localization of natural spatial sounds

Background  

In the field of auditory neuroscience, much research has focused on the neural processes underlying human sound localization. A recent magnetoencephalography (MEG) study investigated localization-related brain activity by measuring the N1m event-related response originating in the auditory cortex. It was found that the dynamic range of the right-hemispheric N1m response, defined as the mean difference in response magnitude between contralateral and ipsilateral stimulation, reflects cortical activity related to the discrimination of horizontal sound direction. Interestingly, the results also suggested that the presence of realistic spectral information within horizontally located spatial sounds resulted in a larger right-hemispheric N1m dynamic range. Spectral cues being predominant at high frequencies, the present study further investigated the issue by removing frequencies from the spatial stimuli with low-pass filtering. This resulted in a stepwise elimination of direction-specific spectral information. Interaural time and level differences were kept constant. The original, unfiltered stimuli were broadband noise signals presented from five frontal horizontal directions and binaurally recorded for eight human subjects with miniature microphones placed in each subject's ear canals. Stimuli were presented to the subjects during MEG registration and in a behavioral listening experiment.     

Modeling mechanical properties of polyhydroxyalkanoate during degradation in animal tissue

Polyhydroxyalkanoates (PHAs) are a family of biodegradable and biocompatible polymers produced by several species microorganisms that possess favorable mechanical properties (e.g. strength and elongation properties). Different types of PHA polymers have been used in medical applications. However, in order to better understand the use of this polymer in the different applications, a thorough understanding of the kinetics of in vivo degradation is one of the major requirements. In this study, poly(3‐hydroxybutyrate) (PHB) was subcutaneously implanted in mice and incubated for 2, 4, 8, or 16 weeks. After removal from the animal, the strength, elongation, mass loss, and enthalpy of the PHB were tested for each time point. From these data, a mathematical model was generated by Rayleigh's method of dimensional analysis, where polymer strength over tissue contact time could be predicted. To prove the model, previous data obtained by our group were used: poly(3‐hydroxybutyrate‐co‐3‐hydroxyhexanoate) [P(HB‐co‐HHx)] incubation in the presence of human embryonic kidney cells (HEK). It was found that the developed model was aligned with experimental results, could predict the strength of the polymer when in contact with cells, and the predicted strength follows the trend of the experimental data. Also, the dimensionless constant (K) value associated with the model is different for both experiments, where this constant, produced via experimental data, is used for construction of a homogeneous equation. Copyright © 2017 John Wiley & Sons, Ltd.     

In situ vinylindole synthesis. Diels-alder reactions with maleimides to give tetrahydrocarbazoles

Tetrahydrocarbazoles have been prepared in one-flask syntheses from indoles, ketones or aldehydes, and maleimides, with acid catalysis. The reactions involve a condensation of the indole with the ketone or aldehyde, followed by an in situ trapping of the vinylindole in a Diels-Alder addition with a maleimide. Isomerization of the double bond into the indole nucleus gave the tetrahydrocarbazoles which were isolated ( 6, 9 , and 10 ). Variation of the indole, carbonyl compound, and maleimide has been explored. The predominant stereochemistry of the tetrahydro ring in the products is all-cis, although a second stereoisomer has been isolated. Two regioisomers were generated from all unsymmetrical 2-alkanones, except 2-butanone, which gave the single isomer 9a . Aromatization of tetrahydrocarbazoles 6 to carbazoles 7 was accomplished with 2,3-dichloro-5,6-dicyano-1,4-benzoquinone.     

Generalized k-tuple colorings of cycles and other graphs

Stahl's concept of k-tuple coloring the nodes of a graph is extended to specify that adjacent nodes must have i colors in common. Complete results for a minimum such coloring are obtained for bipartite graphs and odd cycles. Partial results are shown for complete graphs.