A time‐accurate pseudo‐compressibility approach based on an unstructured hybrid finite volume technique applied to unsteady turbulent premixed flame propagation

A preconditioning approach based on the artificial compressibility formulation is extended to solve the governing equations for unsteady turbulent reactive flows with heat release, at low Mach numbers, on an unstructured hybrid grid context. Premixed reactants are considered and a flamelet approach for combustion modelling is adopted using a continuous quenched mean reaction rate. An overlapped cell‐vertex finite volume method is adopted as a discretisation scheme. Artificial dissipation terms for hybrid grids are explicitly added to ensure a stable, discretised set of equations. A second‐order, explicit, hybrid Runge–Kutta scheme is applied for the time marching in pseudo‐time. A time derivative of the dependent variable is added to recover the time accuracy of the preconditioned set of equations. This derivative is discretised by an implicit, second‐order scheme. The resulting scheme is applied to the calculation of an infinite planar (one‐dimensional) turbulent premixed flame propagating freely in reactants whose turbulence is supposed to be frozen, homogeneous and isotropic. The accuracy of the results obtained with the proposed method proves to be excellent when compared to the data available in the literature. Copyright © 2004 John Wiley & Sons, Ltd.     

Characterization and recognition of generalized clique-Helly graphs

Let p?1 and q?0 be integers. A family of sets F is (p,q)-intersecting when every subfamily F^′⊆F formed by p or less members has total intersection of cardinality at least q. A family of sets F is (p,q)-Helly when every (p,q)-intersecting subfamily F^′⊆F has total intersection of cardinality at least q. A graph G is a (p,q)-clique-Helly graph when its family of (maximal) cliques is (p,q)-Helly. According to this terminology, the usual Helly property and the clique-Helly graphs correspond to the case p=2,q=1. In this work we present a characterization for (p,q)-clique-Helly graphs. For fixed p,q, this characterization leads to a polynomial-time recognition algorithm. When p or q is not fixed, it is shown that the recognition of (p,q)-clique-Helly graphs is NP-hard.     

On the computation of the hull number of a graph

Let G be a graph. If u,v∈V(G), a u-vshortest path of G is a path linking u and v with minimum number of edges. The closed interval I[u,v] consists of all vertices lying in some u-v shortest path of G. For S⊆V(G), the set I[S] is the union of all sets I[u,v] for u,v∈S. We say that S is a convex set if I[S]=S. The convex hull of S, denoted I_h[S], is the smallest convex set containing S. A set S is a hull set of G if I_h[S]=V(G). The cardinality of a minimum hull set of G is the hull number of G, denoted by hn(G). In this work we prove that deciding whether hn(G)≤k is NP-complete.We also present polynomial-time algorithms for computing hn(G) when G is a unit interval graph, a cograph or a split graph.     

Algorithmic aspects of Steiner convexity and enumeration of Steiner trees

For a set \(W\) of vertices of a connected graph \(G=(V(G),E(G))\) , a Steiner W-tree is a connected subgraph \(T\) of \(G\) such that \(W\subseteq V(T)\) and \(|E(T)|\) is minimum. Vertices in \(W\) are called terminals. In this work, we design an algorithm for the enumeration of all Steiner \(W\) -trees for a constant number of terminals, which is the usual scenario in many applications. We discuss algorithmic issues involving space requirements to compactly represent the optimal solutions and the time delay to generate them. After generating the first Steiner \(W\) -tree in polynomial time, our algorithm enumerates the remaining trees with \(O(n)\) delay (where \(n=|V(G)|\) ). An algorithm to enumerate all Steiner trees was already known (Khachiyan et al., SIAM J Discret Math 19:966–984, 2005), but this is the first one achieving polynomial delay. A by-product of our algorithm is a representation of all (possibly exponentially many) optimal solutions using polynomially bounded space. We also deal with the following problem: given \(W\) and a vertex \(x\in V(G)\setminus W\) , is \(x\) in a Steiner \(W'\) -tree for some \(\emptyset \ne W' \subseteq W\) ? This problem is investigated from the complexity point of view. We prove that it is NP-hard when \(W\) has arbitrary size. In addition, we prove that deciding whether \(x\) is in some Steiner \(W\) -tree is NP-hard as well. We discuss how these problems can be used to define a notion of Steiner convexity in graphs.     

On the strong p-Helly property

The notion of strong p-Helly hypergraphs was introduced by Golumbic and Jamison in 1985 [M.C. Golumbic, R.E. Jamison, The edge intersection graphs of paths in a tree, J. Combin. Theory Ser. B 38 (1985) 8-22]. Independently, other authors [A. Bretto, S. Ubéda, J. ?erovnik, A polynomial algorithm for the strong Helly property. Inform. Process. Lett. 81 (2002) 55-57, E. Prisner, Hereditary clique-Helly graphs, J. Combin. Math. Combin. Comput. 14 (1993) 216-220, W.D. Wallis, Guo-Hui Zhang, On maximal clique irreducible graphs. J. Combin. Math. Combin. Comput. 8 (1990) 187-193.] have also considered the strong Helly property in other contexts. In this paper, we characterize strong p-Helly hypergraphs. This characterization leads to an algorithm for recognizing such hypergraphs, which terminates within polynomial time whenever p is fixed. In contrast, we show that the recognition problem is co-NP-complete, for arbitrary p. Further, we apply the concept of strong p-Helly hypergraphs to the cliques of a graph, leading to the class of strong p-clique-Helly graphs. For p=2, this class is equivalent to that of hereditary clique-Helly graphs [E. Prisner, Hereditary clique-Helly graphs, J. Combin. Math. Combin. Comput. 14 (1993) 216-220]. We describe a characterization for this class and obtain an algorithm for recognizing such graphs. Again, the algorithm has polynomial-time complexity for p fixed, and we show the corresponding recognition problem to be NP-hard, for arbitrary p.     

Mammalian cytosolic glutathione transferases

Glutathione Transferases (GSTs) are crucial enzymes in the cell detoxification process catalyzing the nucleophilic attack of glutathione (GSH) on toxic electrophilic substrates and producing a less dangerous compound. GSTs studies are of great importance since they have been implicated in the development of drug resistance in tumoral cells and are related to human diseases such as Parkinson's, Alzheimer's, atherosclerois, liver cirrhosis, aging and cataract formation. In this review we start by providing an evolutionary perspective of the mammalian cytosolic GSTs known to date. Later on we focus on the more abundant classes alpha, mu and pi and their structure, catalysis, metabolic associated functions, drug resistance relation and inhibition methods. Finally, we introduce the recent insights on the GST class zeta from a metabolic perspective.     

Glutathione transferase: new model for glutathione activation

Glutathione transferases are enzymes of the cellular detoxification system that metabolize a vast spectrum of xenobiotic and endobiotic toxic compounds. They are homodimers or heterodimers and each monomer has an active center composed of a G-site in which glutathione (GSH) binds and an H-site for the electrophilic substrate. When GSH binds to the G-site, the pKa value of its thiol group drops by 2.5 units; this promotes its deprotonation and, therefore, produces a strong nucleophilic thiolate that is able to react with the electrophilic substrate. The mechanism behind the deprotonation of the thiol group is still unknown. Some studies point to the fact that the GSH glutamyl alpha-carboxylate group is essential for GSH activation, whereas others indicate the importance of the active-center water molecules. On the basis of QM/MM calculations, we propose a mechanism of GSH activation in which a water molecule, acting as a bridge, is able to assist in the transfer of the proton from the GSH thiol group to the GSH glutamyl alpha-carboxylate group, after an initial GSH conformational rearrangement. We calculated the potential of mean force of this GSH structural rearrangement that would be necessary for the approach of both groups and we then performed a QM/MM ONIOM scan of water-assisted proton transfer. The overall free-energy barrier for the process is consistent with experimental studies of the enzyme kinetics.