The crystal structure of di-ortho-tolylmercury

The structure of di-ortho-tolylmercury has been determined by single crystal X-ray methods from counter data. The compound crystallizes in the monoclinic space group C2/c with unit cell dimensions a 10.970(2), b 10.448(3), c 11.409(3) Å; β 115.48(2)°, V 1180.5(5) ų, ?_calc 2.158 g/cm³ and Z = 4. The structure was solved with conventional heavy atom techniques. The crystal consists of individual molecular units with the mercury atom located on the crystallographic 2-fold axis of symmetry. The CHgC fragment is nearly linear with an angle of 178.0(4)°. The methyl groups lie on the same side of the molecule and the rings are twisted with respect to one another by 58.9°. The HgC bond distance is 2.09(1) Å.     

The structures of 5-methyl-5-phenyl-5H-dibenzo[b,f] silepin and its saturated analog

The structures of 5-methyl-5-phenyl-5H-dibenzo[b,f] silepin (I) and 5-methyl- 5-phenyl-1O,11-dihydro-5H-dibenzo [b,f] silepin (II) have been determined from three-dimensional X-ray data collected by counter methods. I crystallizes in the orthorhombic space group Pnam with a 7.596(3), b 18.102(5) and c 12.190(2) Å; observed and calculated densities (Z = 4) are 1.17 and 1.18 g cm^?3, respectively. II crystallizes in the monoclinic space group $\text{P}\text{2}{}_1\text{c}$ with a 11.115(3), b 7.920(3), c 20.765(5) Å and β 111.71(2)°; observed and calculated densities (Z = 4) are 1.17 g cm^?3. Anisotropic refinement of nonhydrogen atoms, with hydrogen atoms included at fixed ideal locations, gave conventional R-factors of 4.5% (I) and 5.0% (II). Compound I exhibits the boat conformation for the tricyclic framework and is located on a crystallographically required mirror plane. Com- pound II has the expected folded boat conformation. The torsion angle about the 10,11-bond is 0.0° for I, a crystallographic symmetry requirement, and 89.9° for II. Mean SiC bond distances are 1.863 Å(I) and 1.875 Å(II). The dihedral angles between the planar benzo groups are 129.7° (I) and 137.2° (II); introduc- tion of unsaturation at the 10,11-position decreases the dihedral angle in the tri- cyclic system, i.e., the tricyclic system is more bent.     

Pattern recognition and massively distributed computing

A feature of Peter Kollman's research was his exploitation of the latest computational techniques to devise novel applications of the free energy perturbation method. He would certainly have seized upon the opportunities offered by massively distributed computing. Here we describe the use of over a million personal computers to perform virtual screening of 3.5 billion druglike molecules against protein targets by pharmacophore pattern matching, together with other applications of pattern recognition such as docking ligands without any a priori knowledge about the binding site location.     

Three-dimensional blow-up solutions of the Navier-Stokes equations

In this paper we extend the plane blow-up results of Grundy& McLaughlin (1997) to the three-dimensional Navier-Stokes equations.Using a solution structure originally due to Lin we first providenumerical evidence for the existence of blow-up solutions on- < x, z < , 0 y 1 with boundary conditions on y = 0and y = 1 involving derivatives of the velocity components.The formulation enables us to consider plane and radial flowas special cases. Various features of the computations are isolatedand are used to construct a formal asymptotic solution closeto blow-up. We show that the numerical and asymptotic analysesprovide a mutually consistent global picture which supportsthe conclusion that, for the family of problems we considerhere, blow-up in fact can take place in three dimensions butat an inverse linear rate rather than the faster inverse squareof the plane case.     

Accurate Solution to Overdetermined Linear Equations with Errors Using L1 Norm Minimization

It has been known for many years that a robust solution to an overdetermined system of linear equations Ax b is obtained by minimizing the L1 norm of the residual error. A correct solution x to the linear system can often be obtained in this way, in spite of large errors (outliers) in some elements of the (m × n) matrix A and the data vector b. This is in contrast to a least squares solution, where even one large error will typically cause a large error in x. In this paper we give necessary and sufficient conditions that the correct solution is obtained when there are some errors in A and b. Based on the sufficient condition, it is shown that if k rows of [A b] contain large errors, the correct solution is guaranteed if (m – n)/n 2k/, where > 0, is a lower bound of singular values related to A. Since m typically represents the number of measurements, this inequality shows how many data points are needed to guarantee a correct solution in the presence of large errors in some of the data. This inequality is, in fact, an upper bound, and computational results are presented, which show that the correct solution will be obtained, with high probability, for much smaller values of m – n.     

Long-term retention of ice-nucleating active Pseudomonas fluorescens by overwintering colorado potato beetles

Ice nucleating-active Pseudomonas fluorescens F264C was fed to Colorado potato beetles to determine bacterial retentioin in the beetle gut and its effect on the cold hardiness of this insect pest. The bacrterium was present in beetles recovered after overwintering in the field, seven months after their exposure to P. fluorescens. Retention was evident not only in the detection of the P. fluorescens ice nucleating gene, inaW, in bacterial cultures from beetle guts but also in the elevated supercooling points of some treated beetles.     

Separation and probability of correct classification among two or more distributions

A function on theK-fold product of a set in normed vector space will be called a separation measurement if, for any collection ofK points, the function is bounded below and above, respectively, by maximum and total distance between pairs of points in the collection. Separation measurements are relavent toK-sample hypothesis testing and also to discrimination amongK classes, and several examples are given. In particular, ordinaryL ₁ distance between integrable functions can be generalized to a non-pairwise separation measurement for densitiesf ₁,f ₂,...,f _K inL ₁[μ]; and this separation is a linear transform of the optimal discriminant's probability of correct classification. This research was supported by grant A8044 from the National Research Council of Canada.