Lexicographic products with high reconstruction numbers

The reconstruction number of a graph is the smallest number of vertex-deleted subgraphs needed to uniquely determine the graph up to isomorphism. Bollobás showed that almost all graphs have reconstruction number equal to three. McMullen and Radziszowski published a catalogue of all graphs on at most ten vertices with reconstruction number greater than three. We introduce constructions that generalize the examples identified in their work. In particular, we use lexicographic products of vertex transitive graphs with certain starter graphs from the work of Myrvold and from the work of Harary and Plantholt to generate new infinite families of graphs with high reconstruction numbers. In the process, we settle a question of McMullen and Radziszowski.     

Selective MAO-B inhibitors: a lesson from natural products

Monoamine oxidases (MAOs) are mitochondrial bound enzymes, which catalyze the oxidative deamination of monoamine neurotransmitters. Inside the brain, MAOs are present in two isoforms: MAO-A and MAO-B. The activity of MAO-B is generally higher in patients affected by neurodegenerative diseases like Alzheimer’s and Parkinson’s. Therefore, the search for potent and selective MAO-B inhibitors is still a challenge for medicinal chemists. Nature has always been a source of inspiration for the discovery of new lead compounds. Moreover, natural medicine is a major component in all traditional medicine systems. In this review, we present the latest discoveries in the search for selective MAO-B inhibitors from natural sources. For clarity, compounds have been classified on the basis of structural analogy or source: flavonoids, xanthones, tannins, proanthocyanidins, iridoid glucosides, curcumin, alkaloids, cannabinoids, and natural sources extracts. MAO inhibition values reported in the text are not always consistent due to the high variability of MAO sources (bovine, pig, rat brain or liver, and human) and to the heterogeneity of the experimental protocols used.     

Computing the Longtime Behaviour of NMR Propagators in Porous Media Using a Pore Network Random Walk Model

We present a pore network model combined with a random walk algorithm allowing the simulation of molecular displacement distributions in porous media as measured by NMR. A particular feature of this technique is the ability to probe the time evolution of these distributions. The objective is to predict the displacement behaviour for time intervals larger than the experimental observation time and explore the asymptotic dispersion regime at long times. Starting from 3D micro-CT images, we computed the variance of displacement distributions of water molecules in a Fontainebleau sand and found very good agreement of the time evolution of the variance with experimental data, without fitting parameter. The model confirms a weak superdispersion in the asymptotic regime. In addition, we conclude that, since pore network models do not take into account small scale features of the porous medium (e.g., surface roughness and grain shape), the origin of the observed superdispersion is mainly due to the topology and geometry of the porous medium.     

T-duality for string in Hořava–Lifshitz gravity

We continue our study of the Lorentz-breaking string theories. These theories are defined as string theory with modified Hamiltonian constraint which breaks the Lorentz symmetry of target space-time. We analyze the properties of this theory in the target space-time that possesses isometry along one direction. We also derive the T-duality rules for Lorentz-breaking string theories and show that they are the same as that of Buscher’s T-duality for the relativistic strings.