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.     

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.     

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.     

Helium emission spectra—I. intermediate pressure studies

The apparent cross sections of the n¹P(n = 3,4,5,6) and n^1,3D(n = 4,5,6,7) levels have been measured as a function of pressure between 5 and 200 mTorr at 1·5KeV electron impact excitation energy. The 4¹S apparent cross section was measured under the same conditions to observe secondary electron effects. A detailed analysis is made on the mechanisms of excitation transfer out of the n¹P levels in terms of radiative and collision processes. Collisional n¹P?nF transfer cross sections are calculated for the n = 4 and n = 5 levels and the results are in agreement with the principle of detailed balance. An analysis of the 6¹P apparent cross section indicates that collision processes other than n¹P?nF become important at n = 6 level in determining collisional transfer out of n¹P. Evaluation of n^1,3D apparent cross sections show that direct collisional gain and loss become more important as n increases.     

Protein type effects on steady-state crossflow membrane ultrafiltration fluxes and protein transmission

The permeate fluxes and percent protein transmission were evaluated for steady-state crossflow ultrafiltration of two proteins of different composition: bovine serum albumin (BSA), containing fatty acid, and “fatty-acid-poor” BSA, from which most of the fatty acids had been removed (BSA/FAP). The influences of protein concentration up to 6.5 percent w/v, transmembrane pressure, ionic environment and membrane type (i.e. nominal molecular weight cut-off) were investigated. For both BSA and BSA/FAP, the fluxes and the protein transmission were dependent on the amount of salt present. The higher fatty acid content in the BSA apparently enhanced protein-protein interaction, resulting in a more cohesive and resistant fouling layer; permeate fluxes were lower with BSA/FAP than with BSA at otherwise corresponding operating conditions. A hysteresis behaviour of the flux (J)-transmembrane pressure (TMP) relationship was observed whenever the ultrafiltration unit was operated at a TMP less than some higher value to which the membrane previously had been exposed.     

Approximating Data in \mathfrak{R}^{n} by a Quadratic Underestimator with Specified Hessian Minimum and Maximum Eigenvalues

The problem of approximating m data points (x _i , y _i ) in , with a quadratic function q(x, p) with s parameters, m ≥ s, is considered. The parameter vector is to be determined so as to satisfy three conditions: (1) q(x, p) must underestimate all m data points, i.e. q(x _i , p) ≤ y _i , i=1,...,m. (2) The error of the approximation is to be minimized in the L1 norm. (3) The eigenvalues of H are to satisfy specified lower and upper bounds, where H is the Hessian of q(x, p) with respect to x. This is called the Quadratic Underestimator with Bounds on Eigenvalues (QUBE) problem. An algorithm for its solution (QUBE algorithm) is given and justified, and computational results presented. The QUBE algorithm has application to finding the global minimum of a basin (or funnel) shaped function with a large number of local minima. Such problems arise in computational biology where it is desired to find the global minimum of an energy surface, in order to predict native protein-ligand docking geometry (drug design) or protein structure. Computational results for a simulated docking energy surface, with n=15, are presented. It is shown that specifying a small condition number for H improves the ability of the underestimator to correctly predict the global minimum point.