Directed triangles in directed graphs

We show that each directed graph (with no parallel arcs) on n vertices, each with indegree and outdegree at least n/twhere t=2.888997… contains a directed circuit of length at most 3.     

Novel scaling behavior of directed polymers: Disorder distribution with long tails

We study the problem of directed polymers (DP) on a square lattice. The distribution of disorder is assumed to be independent but non-Gaussian. We show that for distributions with a power-law tailP() 1/||¹⁺ , where>2, so that the mean and variance are well defined, the scaling exponentv of the DP model depends on in a continuous fashion.     

Directed polymers in Hartree-Fock approximation

A replica trick is used to map the problem of directed polymers into a quantum mechanics problem ofn-body bound states. This bound-state problem is then treated using a self-consistent method of Hartree-Fock. Ford=2, the exact result of the DP exponents is reproduced; and for complex DP, the ground-state energyE _n n² is found, confirming previous numerical results.     

Nonuniversality and analytical continuation in moments of directed polymers on hierarchical lattices

We prove the moments of the directed polymer partition function GZ, using an exact position space renormalization group scheme on a hierarchical lattice. After sufficient iteration the characteristic functionf(n)=lnGZⁿ of the probability (Z) converges to a stable limitf ^*(n). For smalln the limiting behavior is independent of the initial distribution, while for largen,f ^*(n) is completely determined by it and is thus nonuniversal. There is a smooth crossover between the two regimes for small effective dimensions, and the nonlinear behavior of the small moments can be used to extract information on the universal scaling properties of the distribution. For large effective dimensions there is a sharp transition between the two regimes, and analytical continuation from integer moments ton0 is not possible. Replica arguments can account for most features of the observed results.     

Application of directed metalation in synthesis. Part 7: Synthesis of suitably functionalised benzo[b]thiophenes as key intermediates in the synthesis of benzothienopyranones

One-pot syntheses of (3-hydroxybenzo[b]thiophen-2-yl) aryl methanones from ortho-methylsulfanylaryl N,N-diethyl amides and of 1-(3-hydroxybenzo[b]thiophen-2-yl)ethanone and 1-(3-hydroxybenzo[b]thiophen-2-yl)propan-1-one via an anionic ortho-Fries rearrangement are described. The hydroxy ketones were used as key intermediates in the synthesis of benzothienopyranones.     

Two improved formulations for the minimum latency problem

In network problems, latency is associated with the metric used to evaluate the length of the path from a root vertex to each vertex in the network. In this work we are dealing with two applications or variations of the minimum latency problem known as the repairman problem and the deliveryman problem. We have developed two integer formulations for the minimum latency problem and compared them with other two formulations from the literature for the time-dependent traveling salesman problem. The present work highlights the similarities and differences between the different formulations. In addition, we discuss the convenience of including a set of constraints in order to reduce the computation time needed to reach the optimal solution. We have carried out extensive computational experimentation on asymmetrical instances, since they provide the characteristics of the deliveryman and repairman problems in a better way.     

Mechanism of enhanced conversion of 1,2,3-trichloropropane by mutant haloalkane dehalogenase revealed by molecular modeling

1,2,3-Trichloropropane (TCP) is a highly toxic, recalcitrant byproduct of epichlorohydrin manufacture. Haloalkane dehalogenase (DhaA) from Rhodococcus sp. hydrolyses the carbon–halogen bond in various halogenated compounds including TCP, but with low efficiency (k _cat/K _m = 36 s^-1 M^-1). A Cys176Tyr-DhaA mutant with a threefold higher catalytic efficiency for TCP dehalogenation has been previously obtained by error-prone PCR. We have used molecular simulations and quantum mechanical calculations to elucidate the molecular mechanisms involved in the improved catalysis of the mutant, and enantioselectivity of DhaA toward TCP. The Cys176Tyr mutation modifies the protein access and export routes. Substitution of the Cys residue by the bulkier Tyr narrows the upper tunnel, making the second tunnel “slot” the preferred route. TCP can adopt two major orientations in the DhaA enzyme, in one of which the halide-stabilizing residue Asn41 forms a hydrogen bond with the terminal halogen atom of the TCP molecule, while in the other it bonds with the central halogen atom. The differences in these binding patterns explain the preferential formation of the (R)- over the (S)-enantiomer of 2,3-dichloropropane-1-ol in the reaction catalyzed by the enzyme.     

Partially dynamic maintenance of minimum weight hyperpaths

We address the problem of dynamically maintaining minimum weight hyperpaths in a directed hypergraph in a decremental setting. For such a problem, we provide a new efficient algorithm that works for a wide class of hyperpath weight measures. This algorithm explicitly updates minimum weight hyperpaths in

Full-size image

worst case time under a sequence of L hyperarc weight increments and hyperarc deletions, where C is the maximum weight of minimum hyperpaths in and is the size of the representation of the hypergraph. Hyperpath weight measures are only required to belong to the class of strict weakly superior functions.