Lucas' Theorem for Prime Powers

Lucas' theorem on binomial coefficients states that (AB)≡(arbr)⋯(a1b1)(a0b0)(mod p) where p is a prime and A = arpr + ⋯ + a0p + a0, B = brpr + ⋯ + b1p + b0 + are the p-adic expansions of A and B. If s ⩾ 2, it is shown that a similar formula holds modulo ps where the product involves a slightly modified binomial coefficient evaluated on blocks of s digits.

Structural Classification of Metal Complexes with Three-Coordinate Centres

Attempts to describe the geometry about three-coordinate silver(I) complexes have proven difficult because interatomic angles generally vary wildly and there is no adequate or readily available classification system found in the literature. A search of the Cambridge Structural Database shows that complexes formed between any metal centre and three non-metal donors (18001 examples) usually adopt geometries that are quite different than ideal ‘textbook’ extremes of either trigonal planar (∼4% with α = β = γ = 120 ± 2°), T-shaped (∼0.05% with α = 180 ± 2°, β = γ = 90 ± 2°), or trigonal pyramidal (∼0.3% with α = β = γ = 110 ± 2°). Moreover, there are multiple variations of “Y-type” and “other” shapes that require elaboration. Thus, to assist in future structural descriptions, we developed a classification system that spans all known and yet-to-be-discovered three-coordinate geometries. A spreadsheet has also been constructed that utilizes the “shape-space” approach to extract the structural description from a user input of three angles about a tri-coordinate centre and the number of atoms in a plane. The structures of two silver(I) complexes of new N-donor ligands p-NH2C6H4C6H4CH(pz = pyrazol-1-yl)2, L1, and 2-ferrocenyl-4,5-di(2-pyridyl)imidazole, L2, illustrate the utility of this classification system

A simple double-focusing electrostatic ion beam deflector

We have developed an electrostatic, double-focusing 90° deflector for fast ion beams consisting of concentric cylindrical plates of differing heights. In contrast to standard cylindrical deflectors, our design allows for focusing of an incoming parallel beam not only in the plane of deflection but also in the orthogonal direction. The optical properties of our design resemble those of a spherical capacitor deflector while it is much easier and more cost effective to manufacture

Prospectus, April 28, 1987

https://spark.parkland.edu/prospectus_1987/1014/thumbnail.jp

Horizontal transfer of expressed genes in a parasitic flowering plant

Background: Recent studies have shown that plant genomes have potentially undergone rampant horizontal gene transfer (HGT). In plant parasitic systems HGT appears to be facilitated by the intimate physical association between the parasite and its host. HGT in these systems has been invoked when a DNA sequence obtained from a parasite is placed phylogenetically very near to its host rather than with its closest relatives. Studies of HGT in parasitic plants have relied largely on the fortuitous discovery of gene phylogenies that indicate HGT, and no broad systematic search for HGT has been undertaken in parasitic systems where it is most expected to occur. Results: We analyzed the transcriptomes of the holoparasite Rafflesia cantleyi Solms-Laubach and its obligate host Tetrastigma rafflesiae Miq. using phylogenomic approaches. Our analyses show that several dozen actively transcribed genes, most of which appear to be encoded in the nuclear genome, are likely of host origin. We also find that hundreds of vertically inherited genes (VGT) in this parasitic plant exhibit codon usage properties that are more similar to its host than to its closest relatives. Conclusions: Our results establish for the first time a substantive number of HGTs in a plant host-parasite system. The elevated rate of unidirectional host-to- parasite gene transfer raises the possibility that HGTs may provide a fitness benefit to Rafflesia for maintaining these genes. Finally, a similar convergence in codon usage of VGTs has been shown in microbes with high HGT rates, which may help to explain the increase of HGTs in these parasitic plants.Organismic and Evolutionary Biolog

Dynamic Dual-Tracer MRI-Guided Fluorescence Tomography to Quantify Receptor Density In Vivo

The up-regulation of cell surface receptors has become a central focus in personalized cancer treatment; however, because of the complex nature of contrast agent pharmacokinetics in tumor tissue, methods to quantify receptor binding in vivo remain elusive. Here, we present a dual-tracer optical technique for noninvasive estimation of specific receptor binding in cancer. A multispectral MRI-coupled fluorescence molecular tomography system was used to image the uptake kinetics of two fluorescent tracers injected simultaneously, one tracer targeted to the receptor of interest and the other tracer a nontargeted reference. These dynamic tracer data were then fit to a dual-tracer compartmental model to estimate the density of receptors available for binding in the tissue. Applying this approach to mice with deep-seated gliomas that overexpress the EGF receptor produced an estimate of available receptor density of 2.3 ± 0.5 nM (n = 5), consistent with values estimated in comparative invasive imaging and ex vivo studies

Prospectus, February 18, 1987

https://spark.parkland.edu/prospectus_1987/1005/thumbnail.jp

Dual-Tracer Background Subtraction Approach for Fluorescent Molecular Tomography

Diffuse fluorescence tomography requires high contrast-to-background ratios to accurately reconstruct inclusions of interest. This is a problem when imaging the uptake of fluorescently labeled molecularly targeted tracers in tissue, which can result in high levels of heterogeneously distributed background uptake. We present a dual-tracer background subtraction approach, wherein signal from the uptake of an untargeted tracer is subtracted from targeted tracer signal prior to image reconstruction, resulting in maps of targeted tracer binding. The approach is demonstrated in simulations, a phantom study, and in a mouse glioma imaging study, demonstrating substantial improvement over conventional and homogenous background subtraction image reconstruction approaches