Lupeol

The title compound [systematic name: 3 beta-lup-20(29)-en-3-ol], C(30)H(50)O, was isolated from the leaves of Garcinia brasiliensis (common name: bacupari; a member of the Guttiferae family) and has been shown to have many useful medicinal and biological properties. The lupeol molecule consists of four six-membered rings (adopting chair conformations) and one five-membered ring (with an envelope conformation), all fused in trans fashion. Lupeol is isomorphic with the pentacyclic triterpene 3 beta,30-dihydroxylup-20(29)-ene, which differs from lupeol due to the presence of an additional hydroxy group. The crystal packing is stabilized by van der Waals interactions and intermolecular O-H center dot center dot center dot O hydrogen bonds, giving rise to an infinite helical chain along the c axis.

cis-Bis[1,1-dibenzyl-3-(furan-2-ylcarbonyl)thioureato-kappa(2)O,S]copper(II)

In the title compound, [Cu(C(20)H(17)N(2)O(2)S)(2)], the Cu(II) atom is coordinated by the S and O atoms of two 1,1-dibenzyl-3-(furan-2-ylcarbonyl)thioureate ligands in a distorted square-planar geometry. The two O and two S atoms are mutually cis to each other. The Cu-S and Cu-O bond lengths lie within the ranges of those found in related structures. The dihedral angle between the planes of the two chelating rings is 26.15 (6)degrees.

N-(4-chlorophenyl)maleimide

In the title compound, C10H6ClNO2, the dihedral angle between the benzene and maleimide rings is 47.54 (9)degrees. Molecules form centrosymmetric dimers through C-H center dot center dot center dot O hydrogen bonds, resulting in rings of graph- set motif R2 2(8) and chains in the [100] direction. Molecules are also linked by C-H center dot center dot center dot Cl hydrogen bonds along [001]. In this same direction, molecules are connected to other neighbouring molecules by C-H center dot center dot center dot O hydrogen bonds, forming edge- fused R-4(4)(24) rings.

An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

TESTING STATISTICAL HYPOTHESIS ON RANDOM TREES AND APPLICATIONS TO THE PROTEIN CLASSIFICATION PROBLEM

Efficient automatic protein classification is of central importance in genomic annotation. As an independent way to check the reliability of the classification, we propose a statistical approach to test if two sets of protein domain sequences coming from two families of the Pfam database are significantly different. We model protein sequences as realizations of Variable Length Markov Chains (VLMC) and we use the context trees as a signature of each protein family. Our approach is based on a Kolmogorov-Smirnov-type goodness-of-fit test proposed by Balding et at. [Limit theorems for sequences of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is a supremum over the space of trees of a function of the two samples; its computation grows, in principle, exponentially fast with the maximal number of nodes of the potential trees. We show how to transform this problem into a max-flow over a related graph which can be solved using a Ford-Fulkerson algorithm in polynomial time on that number. We apply the test to 10 randomly chosen protein domain families from the seed of Pfam-A database (high quality, manually curated families). The test shows that the distributions of context trees coming from different families are significantly different. We emphasize that this is a novel mathematical approach to validate the automatic clustering of sequences in any context. We also study the performance of the test via simulations on Galton-Watson related processes.

3,3-Bis[(4-chlorophenyl)sulfanyl]-1-methylpiperidin-2-one

The piperidone ring in the title compound, C(18)H(17)Cl(2)NOS(2), has a distorted half-chair conformation. The S-bound benzene rings are approximately perpendicular to and splayed out of the mean plane through the piperidone ring [dihedral angles = 71.86 (13) and 46.94 (11)degrees]. In the crystal, C-H center dot center dot center dot O interactions link the molecules into [010] supramolecular chains with a helical topology. C-H center dot center dot center dot Cl and C-H center dot center dot center dot pi interactions are also present.

5-Methyl-2,4-bis(methylsulfanyl)tricyclo[6.2.1.0(2,7)]undeca-4,9-diene-3,6-dione

The structure analysis of the title compound, C(14)H(16)O(2)S(2), shows the SMe and H atoms of the bond linking the six-membered rings to be syn and also to be syn to the bridgehead -CH(2)- group. Each of the five-membered rings adopts an envelope conformation at the bridgehead -CH(2)- group. The dione-substituted ring adopts a folded conformation about the 1,4-C center dot center dot center dot C vector, with the ketone groups lying to one side. The cyclohexene ring adopts a boat conformation.

4-Methyl-3-(2-phenoxyacetyl)-5-phenyl-1,3,4-oxadiazinan-2-one

The 1,3,4-oxadiazinane ring in the title compound, C(18)H(18)N(2)O(4), is in a twisted boat conformation. The two carbonyl groups are orientated towards the same side of the molecule. The dihedral angle between the planes of the benzene rings is 76.6 (3)degrees. Molecules are sustained in the three-dimensional structure by a combination of C-H center dot center dot center dot O, C-H center dot center dot center dot pi and pi-pi [shortest centroid-centroid distance = 3.672 (6) angstrom] interactions.

1-(4-Bromophenyl)-2-ethylsulfinyl-2-(phenylselanyl)ethanone monohydrate

In the title hydrate, C(16)H(15)BrO(2)SSe center dot H(2)O, the sulfinyl O atom lies on the opposite side of the molecule to the Se and carbonyl O atoms. The benzene rings form a dihedral angle of 51.66 (17)degrees and are splayed with respect to each other. The observed conformation allows the water molecules to bridge sulfinyl O atoms via O-H center dot center dot center dot O hydrogen bonds, generating a linear supramolecular chain along the b axis; the chain is further stabilized by C-H center dot center dot center dot O contacts. The chains are held in place in the crystal structure by C center dot center dot center dot H center dot center dot center dot pi and C-Br center dot center dot center dot pi interactions.

Imidazolium 4-aminobenzoate

In the title salt, C(3)H(5)N(2)(+) center dot C(7)H(6)NO(2)(-), the carboxylate group of the 4-aminobenzoate anion forms a dihedral angle of 13.23 (17)degrees with respect to the benzene ring. There are N-H center dot center dot center dot O hydrogen-bonding interactions between the anion and cation, and weak intermolecular C-H center dot center dot center dot O contacts with carboxylate O-atom acceptors of the 4-aminobenzoate anion result in extended three-dimensional R(4)(4)(22) and R(5)(6)(30) edge-fused rings along the [100], [010] and [001] directions.

(4-Hydroxy-2,5-dimethylphenyl)phenylmethanone

The title compound, C(15)H(14)O(2), was obtained by Friedel-Crafts acylation between 2,5-dimethylphenol and benzoyl chloride in the presence of aluminium chloride as a catalyst. The dihedral angle between the benzene rings is 61.95 (4)degrees. In the crystal, O-H center dot center dot center dot O hydrogen bonding and C-H center dot center dot center dot O weak interactions lead to polymeric C(6), C(8) and C(11) chains along the a, b and c-axis directions, respectively.

Redetermination of 3-methylbenzoic acid

The asymmetric unit of the title compound, C(8)H(8)O(2), contains two crystallographically independent molecules, which form dimers linked by O center dot center dot center dot H-O hydrogen bonds. The benzene rings in the dimers are inclined at a dihedral angle of 7.30 (8)degrees and both methyl groups display rotational disorder. This redetermination results in a crystal structure with significantly higher precision than the original determination [Ellas & Garcia-Blanco (1963). Acta Cryst. 16, 434], in which the authors reported only the unit-cell parameters and space group, without any detailed information on the atomic arrangement. In the crystal, dimers are connected by weak C-H center dot center dot center dot O interactions, forming R(2)(2)(10) and R(4)(4)(18) rings along [110] and an infinite zigzag chain of dimers along the [001] direction also occurs.

Imidazole-imidazolium picrate monohydrate

The asymmetric unit of the title compound, C(3)H(5)N(2)(+)center dot C(6)H(2)N(3)O(7)(-)center dot C(3)H(4)N(2)center dot H(2)O or H(C(3)H(4)N(2))(2)(+)center dot C(6)H(2)N(3)O(7)(-)center dot H(2)O, contains a diimidazolium cationic unit, one picrate anion and one molecule of water. In the crystal, the components are connected by N-H center dot center dot center dot O, N-H center dot center dot center dot N and O-H center dot center dot center dot O hydrogen bonds, forming a two-dimensional network parallel to (001). In addition, weak intermolecular C-H center dot center dot center dot O hydrogen bonds lead to the formation of a three-dimensional network featuring R(5)(5)(19) rings.

2-(2-Nitroanilino)-5,6,7,8-tetrahydro-4H-cyclohepta[b]thiophene-3-carbonitrile

The title compound, C(16)H(15)N(3)O(2)S, was synthesized by the reaction of 2-amino-5,6,7,8-tetrahydro-4H-cyclohepta[b]thiophene-3-carbonitrile and o-fluoronitrobenzene. The thiophene and nitrophenyl rings and amino and carbonitrile groups are coplanar with a maximum deviation of 0.046 (2) angstrom and a dihedral angle of 0.92 (6)degrees between the rings. The cyclohepta ring adopts a chair conformation. Intramolecular N-H center dot center dot center dot O and C-H center dot center dot center dot S interactions occur. In the crystal, the molecules form layers that are linked by pi-pi stacking interactions between the thiophene and benzene rings [centroid-centroid distances = 3.7089 (12) and 3.6170 (12) angstrom].

2-(4-Methylphenyl)-1H-anthraceno-[1,2-d]imidazole-6,11-dione: a fluorescent chemosensor

In the title compound, C(22)H(14)N(2)O(2), the five rings of the molecule are not coplanar. There is a significant twist between the four fused rings, which have a slightly arched conformation, and the pendant aromatic ring, as seen in the dihedral angle of 13.16 (8)degrees between the anthraquinonic ring system and the pendant aromatic ring plane.