The symmetric traveling salesman problem and edge exchanges in minimal 1-trees

In this article the effect of exchanging edges inside a minimal 1-tree with edges outside is analysed. In combination with an upper bound this analysis enables the elimination of variables in the symmetric traveling salesman problem. After discussion on a number of improvements for this analysis, the implementation is described in a traveling salesman algorithm based on the 1-tree relaxation. Computational results show the advantages of the edges exchanges for Euclidean problems (up to 120 cities) as well as for random table problems (up to 200 cities).     

A branch and bound algorithm for the symmetric traveling salesman problem based on the 1-tree relaxation

In 1970 Held and Karp introduced the Lagrangean approach to the symmetric traveling salesman problem. We use this 1-tree relaxation in a new branch and bound algorithm. It differs from other algorithms not only in the branching scheme, but also in the ascent method to calculate the 1-tree bounds. urthermore we determine heuristic solutions throughout the computations to provide upperbounds. We present computational results for both a depth-first and a breadth-first version of our algorithm. On the average our results on a number of Euclidean problems from the literature are obtained in about 60% less 1-trees than the best known algorithm based on the 1-tree relaxation. For random table problems (up to 100 cities) the average results are also satisfactory.     

White matter abnormalities in children and adolescents with temporal lobe epilepsy

Background and Purpose

The widespread propagation of synchronized neuronal firing in seizure disorders may affect cortical and subcortical brain regions. Diffusion tensor imaging (DTI) can noninvasively quantify white matter integrity. The purpose of this study was to investigate the abnormal changes of white matter in children and adolescents with focal temporal lobe epilepsy (TLE) using DTI.

Materials and Methods

Eight patients with clinically diagnosed TLE and eight age- and sex-matched healthy controls were studied. DTI images were obtained with a 3-T magnetic resonance imaging scanner. The epileptic foci were localized with magnetoencephalography. Fractional anisotropy (FA), mean diffusivity (MD), parallel (λ_||) and perpendicular (λ_⊥) diffusivities in the genu of the corpus callosum, splenium of the corpus callosum (SCC), external capsule (EC), anterior limbs of the internal capsule (AIC), and the posterior limbs of the internal capsule (PIC) were calculated. The DTI parameters between patients and controls were statistically compared. Correlations of these DTI parameters of each selected structure with age of seizure onset and duration of epilepsy were analysed.

Results

In comparison to controls, both patients' seizure ipsilateral and contralateral had significantly lower FA in the AIC; PIC and SCC and higher MD, λ_|| and λ_⊥ in the EC, AIC, PIC and SCC. The MD, λ_|| and λ_⊥ were significantly correlated with age of seizure onset in the EC and PIC. λ_|| was significantly correlated with the duration of epilepsy in the EC and PIC.

Conclusion

The results of the present study indicate that children and adolescents with TLE had significant abnormalities in the white matter in the hemisphere with seizure foci. Furthermore, these abnormalities may extend to the other brain hemisphere. The age of seizure onset and duration of epilepsy may be important factors in determining the extent of influence of children and adolescents TLE on white matter.     

Lysine‐based functional blocked isocyanates for the preparation of polyurethanes provided with pendant side groups

This article describes a methodology to prepare polyurethanes (PUs), decorated with pendant (bio)functional side groups, by polymerizing (bio)functionalized blocked diisocyanates with polyols. Caprolactam blocked lysine diisocyanate methyl ester (BLDI‐OMe) was prepared in high yields, by reacting the methyl ester of lysine with carbonyl biscaprolactam. In the absence of a catalyst, the polymerization of BLDI‐OMe with polycaprolactone and polytetrahydrofuran resulted in strictly linear PUs due to the high selective reactivity of the blocked isocyanates (BIs). Although the ester appeared to be less reactive, we found hydrolyzing conditions for the ester, without affecting the BIs. The free acid groups were converted into a N‐hydroxysuccinimide (NHS) activated ester, which was a versatile intermediate for further functionalization. After having demonstrated that model amines were able to substitute NHS without effecting the BIs groups, the same chemistry was used to couple biotin, giving a biotin functional caprolactam blocked lysine diisocyanate. The polymerization with polyols afforded the corresponding biotin‐functional PUs. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2036–2049