A heuristic clustering algorithm using union of overlapping pattern-cells

Relative geometric arrangements of the sample points, with reference to the structure of the imbedding space, produce clusters. Hence, if each sample point is imagined to acquire a volume of a small M-cube (called pattern-cell), depending on the ranges of its (M) features and number (N) of samples; then overlapping pattern-cells would indicate naturally closer sample-points. A chain or blob of such overlapping cells would mean a cluster and separate clusters would not share a common pattern-cell between them. The conditions and an analytic method to find such an overlap are developed. A simple, intuitive, nonparametric clustering procedure, based on such overlapping pattern-cells is presented. It may be classified as an agglomerative, hierarchical, linkage-type clustering procedure. The algorithm is fast, requires low storage and can identify irregular clusters. Two extensions of the algorithm, to separate overlapping clusters and to estimate the nature of pattern distributions in the sample space, are also indicated.

Local polynomial convexity of the union of two totally-real surfaces at their intersection

We consider the following question: Let S (1) and S (2) be two smooth, totally-real surfaces in C-2 that contain the origin. If the union of their tangent planes is locally polynomially convex at the origin, then is S-1 boolean OR S-2 locally polynomially convex at the origin? If T (0) S (1) a (c) T (0) S (2) = {0}, then it is a folk result that the answer is yes. We discuss an obstruction to the presumed proof, and provide a different approach. When dim(R)(T0S1 boolean AND T0S2) = 1, we present a geometric condition under which no consistent answer to the above question exists. We then discuss conditions under which we can expect local polynomial convexity.

Computing Reeb Graphs as a Union of Contour Trees

The Reeb graph of a scalar function tracks the evolution of the topology of its level sets. This paper describes a fast algorithm to compute the Reeb graph of a piecewise-linear (PL) function defined over manifolds and non-manifolds. The key idea in the proposed approach is to maximally leverage the efficient contour tree algorithm to compute the Reeb graph. The algorithm proceeds by dividing the input into a set of subvolumes that have loop-free Reeb graphs using the join tree of the scalar function and computes the Reeb graph by combining the contour trees of all the subvolumes. Since the key ingredient of this method is a series of union-find operations, the algorithm is fast in practice. Experimental results demonstrate that it outperforms current generic algorithms by a factor of up to two orders of magnitude, and has a performance on par with algorithms that are catered to restricted classes of input. The algorithm also extends to handle large data that do not fit in memory.

Homology between jacalin and artocarpin from jackfruit (Artocarpus integrifolia) seeds. Partial sequence and preliminary crystallographic studies of artocarpin

Jacalin and artocarpin, the two lectins from jackfruit (Artocarpus integrifolia) seeds, have different physicochemical properties and carbohydrate-binding specificities. However, comparison of the partial amino-acid sequence of artocarpin with the known sequence of jacalin indicates close to 50% sequence identity. Artocarpin crystallizes in two forms, both monoclinic P2(1), with one and two tetramic molecules, respectively, in the asymmetric units of form I (a = 69.9, b = 73.7, c = 60.6 Angstrom and beta = 95.1 degrees) and form II (a = 87.6, b = 72.2, c = 92.6 Angstrom and beta = 101.1 degrees). Both the crystal structures have been solved by the molecular replacement method using the known structure of jacalin as the search model and ope of them partially refined, confirming that the two lectins are indeed homologous.

X-ray studies on crystalline complexes involving amino acids and peptides. XXXIII. Crystal structures of L- and DL-arginine complexed with oxalic acid and a comparative study of amino acid oxalic acid complexes

The DL- and L-arginine complexes of oxalic acid are made up of zwitterionic positively charged amino acid molecules and semi-oxalate ions. The dissimilar molecules aggregate into separate alternating layers in the former. The basic unit in the arginine layer is a centrosymmetric dimer, while the semi-oxalate ions form hydrogen-bonded strings in their layer. In the L-arginine complex each semi-oxalate ion is surrounded by arginine molecules and the complex can be described as an inclusion compound. The oxalic acid complexes of basic amino acids exhibit a variety of ionization states and stoichiometry. They illustrate the effect of aggregation and chirality on ionization state and stoichiometry, and that of molecular properties on aggregation. The semi-oxalate/oxalate ions tend to be planar, but large departures from planarity are possible. The amino acid aggregation in the different oxalic acid complexes do not resemble one another significantly, but the aggregation of a particular amino acid in its oxalic acid complex tends to have similarities with its aggregation in other structures. Also, semi-oxalate ions aggregate into similar strings in four of the six oxalic acid complexes. Thus, the intrinsic aggregation propensities of individual molecules tend to be retained in the complexes.

High-resolution refinement of orthorhombic bovine pancreatic phospholipase A2

The X-ray structure of recombinant bovine pancreatic phospholipase A(2) (PLA2), which specifically catalyzes the cleavage of the sn-2 acylester bond of phospholipids, has been refined at 1.5 Angstrom resolution. The crystal belongs to the space group P2(1)2(1)2(1) with unit-cell parameters a = 47.12, b = 64.59 and c = 38.14 Angstrom similar to the native enzyme reported previously by Dijkstra et nl. [J. Mel. Biol. (1981), 147, 97-123]. The refinement converged to an R value of 18.4% (R-free = 22.8%) for 16 374 reflections between 10.0 and 1.5 Angstrom resolution. The surface-loop residues (60-70) art: ordered in the present orthorhombic recombinant enzyme, but disordered in the trigonal recombinant enzyme. The active-site residues, His48, Asp99, and the catalytic water superimpose well with the trigonal form. Besides the catalytic water which is hydrogen bonded to His48, it is often seen that there is a second water attached to the same N atom of His48 and simultaneously hydrogen bonded to the O atom of Asp49. It is thought that the second water facilitates the tautomerism of His48 for enzyme catalysis, The catalytic water is also hydrogen bonded to the equatorial water coordinated to the calcium ion, In addition to the equatorial water, there is also an axial calcium water and the additional structural water. These five common water molecules are hydrogen bonded to the additional 16 water molecules in the present orthorhombic structure which may further enhance the structural integrity of the active site. Besides the protein and one calcium ion, a total of 134 water molecules were located in the present high-resolution refinement.

Solution of singular integral equations with logarithmic and Cauchy kernels

A direct method of solution is presented for singular integral equations of the first kind, involving the combination of a logarithmic and a Cauchy type singularity. Two typical cages are considered, in one of which the range of integration is a Single finite interval and, in the other, the range of integration is a union of disjoint finite intervals. More such general equations associated with a finite number (greater than two) of finite, disjoint, intervals can also be handled by the technique employed here.

Mycobacterium tuberculosis pantothenate kinase: possible changes in location of ligands during enzyme action

The crystal structures of complexes of Mycobacterium tuberculosis pantothenate kinase with the following ligands have been determined: (i) citrate; (ii) the nonhydrolysable ATP analogue AMPPCP and pantothenate (the initiation complex); (iii) ADP and phosphopantothenate resulting from phosphorylation of pantothenate by ATP in the crystal (the end complex); (iv) ATP and ADP, each with half occupancy, resulting from a quick soak of crystals in ATP (the intermediate complex); (v) CoA; (vi) ADP prepared by soaking and cocrystallization, which turned out to have identical structures, and (vii) ADP and pantothenate. Solution studies on CoA binding and catalytic activity have also been carried out. Unlike in the case of the homologous Escherichia coli enzyme, AMPPCP and ADP occupy different, though overlapping, locations in the respective complexes; the same is true of pantothenate in the initiation complex and phosphopantothenate in the end complex. The binding site of MtPanK is substantially preformed, while that of EcPanK exhibits considerabl plasticity. The difference in the behaviour of the E. coli and M. tuberculosis enzymes could be explained in terms of changes in local structure resulting from substitutions. It is unusual for two homologous enzymes to exhibit such striking differences in action. Therefore, the results have to be treated with caution. However, the changes in the locations of ligands exhibited by M. tuberculosis pantothenate kinase are remarkable and novel.

Structure of nonactin-calcium perchlorate, C40H64O12.Ca(ClO4)2, and a comparative study of metal-nonactin complexes

M r= 975.9, orthorhombic, Pnna, a = 20.262 (3), b= 15.717 (2), c= 15.038 (1)A, V= 4788.97 A 3, z = 4, D x = 1.35 Mg m -3, Cu Kct radiation, 2 = 1.5418 A, /t = 2.79 mm -1, F(000) -= 2072, T = 293 K, R = 0.08, 3335 observed reflections. The molecular structure and the crystal packing are similar to those observed in the nonactin complexes of sodium thiocyanate and potassium thiocyanate. The eight metal-O distances are nearly the same in the potassium complex whereas the four distances involving carbonyl O atoms are shorter than the remaining four involving the tetrahydrofuran-ring O atoms in the Na and the Ca complexes. This observation can be explained in terms of the small ionic radii of Na + and Ca 2+, and leads to a plausible structural rationale for the stronger affinity of nonactin for K + than for the other two metal ions.

Structure of the Monosodium Salt of D-Glucose 6-Hydrogenphosphate

Na+.C6HI209 P-, Mr=282.1, monoclinic, e2~, a=5-762(1), b=7.163(2), c=12.313(1)A, fl= 99.97 (1) °, U= 500.5 A 3, Z= 2, D m = 1.86, D x = 1.87 Mg m -s, Cu Ka, 2 = 1.5418 A, /a = 3-3 mm -1, F(000) = 292, T= 300 K, final R for 922 observed reflections is 0-042. The phosphate ester bond, P-O(6), is 1.575 (5)A, slightly shorter than the P~O bond in monopotassium phosphoenolpyruvate [1.612 (6) A] [Hosur & Viswamitra (1981). Acta Cryst. B37, 839-843]. The pyranose sugar ring takes a 4C 1 chair conformation. The conformation about the exocyclic C(5)-C(6) bond is gauche-trans. The endocyclic C-O bonds in the glucose ring are nearly equal with C(5)-O(5) = 1.435 (8) and C(1)-O(5) = 1.436 (9) A. The sodium ion has seven near neighbours within a distance of 2.9 A. The crystal structure is stabilized by hydrogen bonds between the O atoms of symmetryrelated molecules.

Conformational flexibility in androgenic steroids - the structure of a new form of (+)-17-beta-hydroxy-19-nor-4-androsten-3-one (19-nortestosterone), c18h26o2

The structure and conformation of a second crystalline modification of 19-nortestosterone has been determined by X-ray methods. M r = 274, monoclinic P2 l, a=9.755(2), b= 11.467(3), c= 14.196(3)/L fl=101.07(2) ° , V=1558.4 (8) A 3, Z=4, Ox= I. 168 g cm -3, Mo Ka, 2 = 0.7107 ,/k, ~ = 0.80 cm -l, F(000) = 600, T= 300 K. R = 0.060 for 2158 observed reflections. The two molecules in the asymmetric unit show significant differences in the A-ring conformation from that of the previously reported form of the title compound [Precigoux, Busetta, Courseille & Hospital (1975). Acta Cryst. B31, 1527-1532]. The l a,2fl-half-chair conformation of the A ring increases its conformational freedom compared with testosterone.

Structure of tri-1-naphthylborane-benzene (1/1) complex, c30h21b.c6h6

M r= 470.46, rhombohedral, R3, a =8.710(4)A, a=91.10(3) o, V= 660.4 (9) A 3, Z= 1,D m= 1.170 (flotation in KI solution), D x=1.183 Mg m -a, Mo Kct, 2 = 0.7107/~,, /t =0.033 mm -1, F(000) - 248.0, T= 293 K, R -- 4.6%(481 unique reflections). The molecule has C a symmetry and is propeller shaped, the angle of twist about the B-C bond being 41.5 (7) °. The space group being chiral, this is yet another example of spontaneous resolution. The results of a thermal-motion analysis are discussed.

Structure of 5'-O-acetyl-2',3'-O-isopropylideneuridine, C14H18N2O7

M r = 326.3, monoclinic, P21, a --= 6.510 (2), b=8.432 (2), c= 15.114 (2),a, /~= 101.42 (3) ° , Z = 2, V= 813.15 A 3, D x = 1-33 Mg m -3, F(000) = 172, 2(Cu Ka) = 1.5418/~,, g(Cu Ka) = 0.906 mm -~, final R = 6.4% for 1924 observed counter reflections. The conformation about the glycosidic bond is syn [torsion angle C(6)-N(1)-C(1')-O(4')=-103.9(3)°]. The sugar pucker is C(2')-exo,C(3')-endo (3Tz). The conformation about the C(4')-C(5') bond is gauche-trans. An uncommon intermolecular hydrogen bond involving the ribose-ring oxygen O(1') and the base-nitrogen N(3) stabilizes the crystal structure.