The essential equivalence of pairwise and mutual conditional independence

For a large collection of random variables, pairwise conditional independence and mutual conditional independence are shown to be essentially equivalent — i.e., equivalent to up to null sets. Unlike in the finite setting, a large collection of random variables remains essentially conditionally independent under further conditioning. The essential equivalence of pairwise and multiple versions of exchangeability also follows as a corollary. Our result relies on an iterated extension of Bledsoe and Morse's completion of the product of two measure spaces. Part of this work was done while Peter Hammond was visiting the National University of Singapore in March–April 2004. The final version was completed while Yeneng Sun was on sabbatical leave at the University of Illinois at Urbana–Champaign and Stanford University in October 2004 – May 2005.     

Measurement of urinary cystine and cysteinyl-penicillamine in patients with cystinuria

A high-performance liquid chromatographic method with electrochemical detection (LC/EC) was developed to measure cystine and cysteinyl-penicillamine disulfide in the urine of patients screened or treated for cystinuria. Urine was acidified, centrifuged to remove urinary protein, diluted and injected. The disulfides were separated on a reversed-phase column, reduced at the upstream electrode of a dual electrochemical detector with gold-mercury amalgam (Au/Hg) electrodes and the resultant thiols measured at the downstream electrode. The sample preparation is simple, the analysis rapid, specimens can be easily batched and the specificity of the method is better than those of two other separative procedures with which it was compared. The coefficient of variation for cystine in cystinuric urine is 6.7%, 5.5% and 3.2% for levels of 0.09, 0.52 and 1.02 mmol/l respectively, and for cysteinyl-penicillamine disulfide 2.6% and 7.5% for levels of 0.45 and 0.98 mmol/l respectively. Urine for analysis of these disulfides should not be collected within 24 hours of administration of the radiopaque agent diatrizoate but no other interference to the assay has been noted. This method is suitable as a screen for cystinuria in patients with renal tract calculi, for ongoing monitoring of cystinuric patients and to check patient compliance with d-penicillamine therapy.     

Isomorphism of lattices of recursively enumerable sets

Let , and for , let be the lattice of subsets of which are recursively enumerable relative to the ``oracle' . Let be , where is the ideal of finite subsets of . It is established that for any , is effectively isomorphic to if and only if , where is the Turing jump of . A consequence is that if , then . A second consequence is that can be effectively embedded into preserving least and greatest elements if and only if .

     

Transfer of radionuclides to fruit

A study has been carried out to determine soil-plant transfer factors relevant to fruit crops. The current default values for¹³⁷Cs, Pu and Am used in the NRPB food-chain model FARMLAND were generally higher than the TFs observed. Lower values would be more appropriate for general assessments. For the United Kingdom, the current approach in which TF values for apples are applied to all domestically produced fruit is considered reasonable. This study also indicates that the assumption that TFs for fruit are the same as those for green vegetables is reasonable for¹³⁷Cs, Pu and Am, but, for⁹⁰Sr, data specific to apples would be preferable.     

Cationic copolymerization of tetrahydrofuran with epoxides. II. Characterization and gel-permeation chromatography of by-products formed during polymerization

The cyclic oligomers formed as by-products in the polymerization of propylene oxide. 1,2-butylene oxide, and n-propyl glycidyl ether, and in the copolymerization of these monomers with tetrahydrofuran have been studied by gel-permeation chromatography and otherwise and their structures have been determined. Some of the physical properties of the cyclic oligomers are described.     

Controlling mammalian cell interactions on patterned polyelectrolyte multilayer surfaces

A newly discovered class of cell resistant surfaces, specifically engineered polyelectrolyte multilayers, was patterned with varying densities of adhesion ligands to control attachment of mammalian cells and to study the effects of ligand density on cell activity. Cell adhesive patterns were created on cell resistant multilayer films composed of poly(acrylic acid) and polyacrylamide through polymer-on-polymer stamping of poly(allylamine hydrochloride) PAH and subsequent reaction of the amine functional groups with an adhesion ligand containing RGD (Arg-Gly-Asp). These cell patterns demonstrated great promise for long-term applications since they remained stable for over 1 month, unlike ethylene glycol functional surfaces. By changing the stamping conditions of PAH, it was possible to alter the number of available functional groups in the patterned regions, and as a result, control the ligand density. Cell spreading, morphology, and cytoskeletal organization were compared at four different RGD densities. The highest RGD density, approximately 152 000 molecules/microm2, was created by stamping PAH at a pH of 11.0. Lowering the stamping ink pH led to patterns with lower ligand surface densities (83 000 molecules/microm2 for pH 9.0, 53,000 molecules/ microm2 for pH 7.0, and 25 000 molecules/microm2 for pH 3.5). An increasing number of cells attached and spread as the RGD density of the patterns increased. In addition, more cells showed well-defined actin stress fibers and focal adhesions at higher levels of RGD density. Finally, we found that pattern geometry affected cytoskeletal protein organization. Well-formed focal adhesions and cell-spanning stress fibers were only found in cells on wider line patterns (at least 25 microm in width).     

Development of an enantioselective synthetic route to neocarzinostatin chromophore and its use for multiple radioisotopic incorporation

A convergent, enantioselective synthetic route to the natural product neocarzinostatin chromophore (1) is described. Synthesis of the chromophore aglycon (2) was targeted initially. Chemistry previously developed for the synthesis of a neocarzinostatin core model (4) failed in the requisite 1,3-transposition of an allylic silyl ether when applied toward the preparation of 2 with use of the more highly oxygenated substrates 27 and 54. An alternative synthetic plan was therefore developed, based upon a proposed reduction of the epoxy alcohol 58 to form the aglycon 2, a transformation that was achieved in a novel manner, using a combination of the reagents triphenylphosphine, iodine, and imidazole. The successful route to 1 and 2 began with the convergent coupling of the epoxydiyne 15, obtained in 9 steps (43% overall yield) from D-glyceraldehyde acetonide, and the cyclopentenone (+)-14, prepared in one step (75-85% yield) from the prostaglandin intermediate (+)-16, affording the alcohol 22 in 80% yield and with > or =20:1 diastereoselectivity. The alcohol 22 was then converted into the epoxy alcohol 58 in 17 steps with an average yield of 92% and an overall yield of 22%. Key features of this sequence include the diastereoselective Sharpless asymmetric epoxidation of allylic alcohol 81 (98% yield); intramolecular acetylide addition within the epoxy aldehyde 82, using Masamune's lithium diphenyltetramethyldisilazide base (85% yield); selective esterification of the diol 84 with the naphthoic acid 13 followed by selective cleavage of the chloroacetate protective group in situ to furnish the naphthoic acid ester 85 in 80% yield; and elimination of the tertiary hydroxyl group within intermediate 88 using the Martin sulfurane reagent (79% yield). Reductive transposition of the product epoxy alcohol (58) then formed neocarzinostatin chromophore aglycon (2, 71% yield). Studies directed toward the glycosylation of 2 focused initially on the preparation of the N-methylamino --> hydroxyl replacement analogue 3, an alpha-D-fucose derivative of neocarzinostatin chromophore, formed in 42% yield by a two-step Schmidt glycosylation-deprotection sequence. For the synthesis of 1, an extensive search for a suitable 2'-N-methylfucosamine glycosyl donor led to the discovery that the reaction of 2 with the trichloroacetimidate 108, containing a free N-methylamino group, formed the alpha-glycoside 114 selectively in the presence of boron trifluoride diethyl etherate. Subsequent deprotection of 114 under mildly acidic conditions then furnished the labile chromophore (1). The synthetic route was readily modified for the preparation of singly and doubly (3)H- and (14)C-labeled 1, compounds unavailable by other means, for studies of the mechanism of action of neocarzinostatin in vivo.     

Determination of cadmium, lead, and nickel by simultaneous multielement flame atomic absorption spectrometry in burned and unburned Venezuelan crude oil

This work describes the use of simultaneous multielement flame atomic absorption spectrometry for the determination of cadmium, lead, and nickel in burned and unburned Venezuelan crude oil (5 ml volumes) in controlled laboratory experiments. The simultaneous detection limits were 0.010 mug ml(-1) (Cd), 0.04 mug ml(-1) (Pb), and 0.40 mug ml(-1) (Ni) with precision's of these elements at concentrations of 10x above these detections limits, and in the crude oil, of 1-2%. Loss of elemental concentrations in the crude oil in a 3-5 ml volume when burned were 4% (Cd), 50% (Pb), and 22% (Ni). These results suggest that the form of the elements and the temperature attained in the burning crude oil effect the removal of the elements. The type of surface affected the volume of oil removed. Soil gave a 15% and a smooth surface almost 50% volume reduction.     

Structural properties of a series of photochromic fluorinated indolylfulgides

Fluorinated indolyl­fulgides are a class of photochromic organic compounds that meet many of the requirements for use as optical memory media and optical switches. The X‐ray crystal structures of a series of five photochromic fluorinated indolyl­fulgides have been determined, namely (3Z)‐3‐[1‐(1,2‐di­methyl‐1H‐indol‐3‐yl)‐2,2,2‐tri­fluoro­ethyl­idene]‐4‐(1‐methyl­ethyl­idene)­dihydrofuran‐2,5‐dione (tri­fluoro­methyl­iso­propyl­idene­indolyl­fulgide), C₁₉H₁₆F₃NO₃, (I), (3Z)‐3‐[1‐(1,2‐dimethyl‐1H‐indol‐3‐yl)‐2,2,3,3,3‐penta­fluoro­propyl­idene]‐4‐(1‐methyl­ethyl­idene)­dihydrofuran‐2,5‐dione (penta­fluoro­ethyl­iso­propyl­idene­indolyl­fulgide), C₂₀H₁₆F₅NO₃, (II), (3Z)‐3‐[1‐(1,2‐di­methyl‐1H‐indol‐3‐yl)‐2,2,3,3,4,4,4‐hepta­fluoro­butyl­idene]‐4‐(1‐methyl­ethyl­idene)­dihydrofuran‐2,5‐dione (hepta­fluoro­propyl­iso­propyl­idene­indolyl­fulgide), C₂₁H₁₆F₇NO₃, (III), (3Z)‐3‐[1‐(1,2‐di­methyl‐1H‐indol‐3‐yl)‐2,2,2‐tri­fluoro­ethyl­idene]‐4‐(tri­cyclo­[3.3.1.1^3,7]­decyl­idene­)dihydrofuran‐2,5‐dione (tri­fluoro­methyl­adamantyl­idene­indolyl­fulgide), C₂₆H₂₄F₃NO₃, (IV), and (3Z)‐3‐[1‐(1,2‐di­methyl‐1H‐indol‐3‐yl)‐2,2,3,3,4,4,4‐hepta­fluoro­butyl­idene]‐4‐(tri­cyclo­[3.3.1.1^3,7]­decyl­idene­)dihydrofuran‐2,5‐dione (hepta­fluoro­propyl­adamantylidenein­dolyl­fulgide), C₂₈H₂₄F₇NO₃, (V). The photochromic property of fulgides is based on the photochemically allowed electrocyclic ring closure of a hexatriene system to form a cyclo­hexa­diene. For each fulgide examined, the bond lengths within the hexatriene system alternate between short and long, as expected. Comparing the structures of the five fulgides with each other demonstrates no significant difference in bond lengths, bond angles or dihedral angles within the hexatriene systems. The distance between the bond‐forming C atoms at each end of the hexatriene system does vary. Correlations of structural properties with optical properties are addressed.     

The influence of lysis buffer composition on the expression and activity of protein tyrosine phosphatase

Lysis conditions are crucial in the extraction and solubilization of phosphotyrosine-containing proteins in a form that is immunoreactive, undegraded and enzymatically active. To establish optimal experimental conditions, we evaluated protein tyrosine phosphatase enzyme activity and the detection of PTP-1 B protein in human acute promyelocytic leukaemic cells, both before and after retinoic acid treatment. We found that the composition of the lysing buffer greatly influenced the efficiency of solubilization, resulting in major alterations in the activity of protein tyrosine phosphatases and on the mobility of PTP-1 B protein.