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.     

Novel supramolecular polymer networks based on melamine‐ and imide‐containing oligomers

Reversible, supramolecular polymer networks based on commercially available bulk chemicals, and prepared using an industrially attractive route are described. The difunctional, low molecular weight polytetramethyleneoxide is functionalized with trimellitic imide, and reversibly crosslinked with the trifunctional melamine using the well known imide‐diaminopyridine triple hydrogen bonding pattern. Molecular modelling calculations as well as experimental studies on model compounds indicate that the aimed 1:3 melamine ‐ imide stoichiometry is obtained. The resulting reversible, supramolecular polymer structures show a rheological behaviour, that is typical for polymer networks. The results presented here describe an industrially accessible route to use supramolecular interactions in order to obtain materials with novel properties.     

Effects of Refractive Index and Viscosity on Fluorescence and Anisotropy Decays of Enhanced Cyan and Yellow Fluorescent Proteins

The fluorescence lifetime strongly depends on the immediate environment of the fluorophore. Time-resolved fluorescence measurements of the enhanced forms of ECFP and EYFP in water–glycerol mixtures were performed to quantify the effects of the refractive index and viscosity on the fluorescence lifetimes of these proteins. The experimental data show for ECFP and EYFP two fluorescence lifetime components: one short lifetime of about 1 ns and a longer lifetime of about 3.7 ns of ECFP and for EYFP 3.4. The fluorescence of ECFP is very heterogeneous, which can be explained by the presence of two populations: a conformation (67% present) where the fluorophore is less quenched than in the other conformation (33% present). The fluorescence decay of EYFP is much more homogeneous and the amplitude of the short fluorescence lifetime is about 5%. The fluorescence anisotropy decays show that the rotational correlation time of both proteins scales with increasing viscosity of the solvent similarly as shown earlier for GFP. The rotational correlation times are identical for ECFP and EYFP, which can be expected since both proteins have the same shape and size. The only difference observed is the slightly lower initial anisotropy for ECFP as compared to the one of EYFP.     

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.     

Low Pressure Carbonylation of Benzyl Carbonates and Carbamates for Applications in 13C Isotope Labeling and Catalytic CO2 Reduction

Herein, we report a methodology to access isotopically labeled esters and amides from carbonates and carbamates employing an oxygen deletion strategy. This methodology utilizes a decarboxylative carbonylation approach for isotope labeling with near stoichiometric, ex situ generated ¹²C, or ¹³C carbon monoxide. This reaction is characterized by its broad scope, functional group tolerance, and high yields, which is showcased with the synthesis of structurally complex molecules. A complementary method that operates by the catalytic in situ generation of CO via the reduction of CO₂ liberated during decarboxylation has also been developed as a proof-of-concept approach that CO₂-derived compounds can be converted to CO-containing frameworks. Mechanistic studies provide insight into the catalytic steps which highlight the impact of ligand choice to overcome challenges associated with low-pressure carbonylation methodologies, along with rational for the development of future methodologies.     

Elucidating the relationship between the spreading coefficient, surface-mediated partial coalescence and the whipping time of artificial cream

We studied the whipping of artificial creams composed of a blend of sunflower oil and hydrogenated palm fat stabilized by protein or a mixture or protein and low molecular weight (lmw) surfactant. It was found that an increased whipping speed, decreased protein concentration, and the addition of lmw surfactant leads to shorter whipping times. Further, shorter whipping times were observed for WPI-stabilized cream compared to cream stabilized by sodium caseinate. In all cases, the decrease in whipping time was due to a decrease in the length of the second stage of whipping, the stage characterized by the adhesion of fat droplets to the air bubble surface. The decrease in whipping time could be accounted for by considering the influence of the experimental variables on the fraction of bubble surface area at which fat droplet spreading is possible. The same changes in parameters that promote droplet spreading at the air/water interface cause a decrease in the whipping time of our model creams. Correlating the whipping time of cream with the spreading behavior of fat droplets at the air/water interface represents a new insight into the mechanisms involved in the whipping of cream.     

On the behavior of the solution of the Burgers equation as the viscosity goes to zero

The solution of the initial boundary-value problem u_?′ ? ?D²u_? + u_?Du_? = f on (a, b) x(0, T), u_?(a, t) = u_?(b, t) = 0 and u_?(x, 0) = 0 on (a, b), is shown to converge to the solution of the limiting equation as the viscosity tends to zero. Estimates on the rate of convergence are given.