Noniterative compensation for the distance-dependent detector response and photon attenuation in SPECT imaging

A filtering approach is described, which accurately compensates for the 2D distance-dependent detector response, as well as for photon attenuation in a uniform attenuating medium. The filtering method is based on the frequency distance principle (FDP) which states that points in the object at a specific source-to-detector distance provide the most significant contribution to specified frequency regions in the discrete Fourier transform (DFT) of the sinogram. By modeling the detector point spread function as a 2D Gaussian function whose width is dependent on the source-to-detector distance, a spatially variant inverse filter can be computed and applied to the 3D DFT of the set of all sinogram slices. To minimize noise amplification the inverse filter is rolled off at high frequencies by using a previously published Wiener filter strategy. Attenuation compensation is performed with Bellini's method. It was observed that the tomographic point response, after distance-dependent filtering with the FDP, was approximately isotropic and varied substantially less with position than that obtained with other correction methods. Furthermore, it was shown that processing with this filtering technique provides reconstructions with minimal degradation in image fidelity.     

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.     

STUDIES OF ADHESION OF METAL PARTICLES TO SILICA PARTICLES BASED ON ZETA POTENTIAL MEASUREMENTS

The zeta-potentials of silica, copper, platinum and gold particles have been measured as a function of pH. The isoelectric points were found to be at pH 3.0, 5.8, 3.0 and 3.5, respectively. In the pH range 3.0 to 5.8 copper and silica particles are oppositely charged and accordingly the coating of silica with copper particles could be demonstrated. In the case of gold and platinum the sign of the charge is such that direct adhesion to silica particles cannot be expected and this was also demonstrated in the case of platinum.     

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.