The Application of Combined Gas Chromatography-Mass Spectrometry to Compounds of Biological Interest: Steroid Analysis by the Use of Glass Open Tubular Gas Chromatographic Columns

Steroidal compounds are virtually ubiquitous in nature and frequently occur in complex mixtures as constituents of closely similar structure. Packed column gas chromatography-mass spectrometry (GC-MS) is an analytical technique of unique facility for the simultaneous separation and characterisation of complex mixtures of organic compounds. This thesis examines the additional facility provided by glass open tubular gas chromatographic columns of higher efficiency in the analysis by GC and GC-MS of complex mixtures of steroidal compounds derived from a number of natural sources. A method for the preparation of stable, efficient and reproducible glass open tubular gas chromatographic columns is described. The construction of chromatographic systems adapted to their somewhat more critical requirements is outlined. Particular attention is paid to the requirements for the interface of these columns to an LKB 9000 combined gas chromatograph-mass spectrometer. The performance of this system with emphasis on the nature of the advantage obtained over conventional packed columns is demonstrated by several model separations of mixtures of closely related standard steroidal compounds. Mixtures of sterols derived from yeast and marine sources frequently consist in mixtures of components differing in the degree and position of alkylation and unsaturation in the basic cholestanol structure. Correlation of gas chromatographic retention, on glass open tubular columns of OV-1 stationary phase, with sterol structure is described. Complementary data available in the literature are integrated into a scheme for the rationalisation of increments of Kovats retention index associated with particular alterations in sterol structure. This system and mass spectral correlations obtained by glass open tubular GC-MS is applied to the analysis of sterol mixtures derived from five species of marine invertebrate and two mutant strains of the yeast Candida albicans. Two other applications to sterol analysis are also described. A significant advantage is demonstrated over GC and GC-MS methods heretofore employed. Mixtures of hydroxy and ketosteroids may be derivatised as the alkyloxime-trimethylsilyl ether derivatives for GC and GC-MS analysis. The occurrence of syn- and anti-isomers in the alkyloximes of various ketosteroid structures is a complicating factor in their GC analysis, in particular at higher column efficiencies. Several alkyloximes of increasing hulk of the O-alkyl substituent were examined in this respect. The methyloxime is shown to provide the least complications for open tubular GC, though the "group separations" of hydroxy and ketosteroids provided by the higher alkyloximes may provide useful correlations. The utility of this approach is demonstrated in the analysis of mixtures of standard hydroxy and ketosteroids. Preliminary results obtained on a mixture of urinary steroid hormone metabolites of the human newborn by open tubular GC-MS of the isopentyloxime-trimethylsilyl ether derivatives are reported

Hypergraphic LP Relaxations for Steiner Trees

We investigate hypergraphic LP relaxations for the Steiner tree problem, primarily the partition LP relaxation introduced by Koenemann et al. [Math. Programming, 2009]. Specifically, we are interested in proving upper bounds on the integrality gap of this LP, and studying its relation to other linear relaxations. Our results are the following. Structural results: We extend the technique of uncrossing, usually applied to families of sets, to families of partitions. As a consequence we show that any basic feasible solution to the partition LP formulation has sparse support. Although the number of variables could be exponential, the number of positive variables is at most the number of terminals. Relations with other relaxations: We show the equivalence of the partition LP relaxation with other known hypergraphic relaxations. We also show that these hypergraphic relaxations are equivalent to the well studied bidirected cut relaxation, if the instance is quasibipartite. Integrality gap upper bounds: We show an upper bound of sqrt(3) ~ 1.729 on the integrality gap of these hypergraph relaxations in general graphs. In the special case of uniformly quasibipartite instances, we show an improved upper bound of 73/60 ~ 1.216. By our equivalence theorem, the latter result implies an improved upper bound for the bidirected cut relaxation as well.Comment: Revised full version; a shorter version will appear at IPCO 2010

Spin evolution of spin-1 Bose-Einstein condensates

An analytical formula is obtained to describe the evolution of the average populations of spin components of spin-1 atomic gases. The formula is derived from the exact time-dependent solution of the Hamiltonian $H_{S}=c mathbf{S}^{2}$ without using approximation. Therefore it goes beyond the mean field theory and provides a general, accurate, and complete description for the whole process of non-dissipative evolution starting from various initial states. The numerical results directly given by the formula coincide qualitatively well with existing experimental data, and also with other theoretical results from solving dynamic differential equations. For some special cases of initial state, instead of undergoing strong oscillation as found previously, the evolution is found to go on very steadily in a very long duration.Comment: 7 pages, 3 figures

Repeating head-on collisions in an optical trap and the evaluation of spin-dependent interactions among neutral particles

A dynamic process of repeating collisions of a pair of trapped neutral particles with weak spin-dependent interaction is designed and studied. Related theoretical derivation and numerical calculation have been performed to study the inherent coordinate-spin and momentum-spin correlation. Due to the repeating collisions the effect of the weak interaction can be accumulated and enlarged, and therefore can be eventually detected. Numerical results suggest that the Cr-Cr interaction, which has not yet been completely clear, could be thereby determined. The design can be in general used to determine various interactions among neutral atoms and molecules, in particular for the determination of very weak forces.Comment: 15 pages, 7 figure

Quantum computing with nearest neighbor interactions and error rates over 1%

Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure that requires only a 2-D square lattice of qubits that can interact with their nearest neighbors, yet can tolerate quantum gate error rates over 1%. The precise maximum tolerable error rate depends on the error model, and we calculate values in the range 1.1--1.4% for various physically reasonable models. Even the lowest value represents the highest threshold error rate calculated to date in a geometrically constrained setting, and a 50% improvement over the previous record.Comment: 4 pages, 8 figure

Momentum distributions and spectroscopic factors of doubly-closed shell nuclei in correlated basis function theory

The momentum distributions, natural orbits, spectroscopic factors and quasi-hole wave functions of the C12, O16, Ca40, Ca48, and Pb208 doubly closed shell nuclei, have been calculated in the framework of the Correlated Basis Function theory, by using the Fermi hypernetted chain resummation techniques. The calculations have been done by using the realistic Argonne v8' nucleon-nucleon potential, together with the Urbana IX three-body interaction. Operator dependent correlations, which consider channels up to the tensor ones, have been used. We found noticeable effects produced by the correlations. For high momentum values, the momentum distributions show large enhancements with respect to the independent particle model results. Natural orbits occupation numbers are depleted by about the 10\% with respect to the independent particle model values. The effects of the correlations on the spectroscopic factors are larger on the more deeply bound states.Comment: Modified version of the previous paper (there are new figures). The paper has been accepted for publication in Physical Review

Towards practical classical processing for the surface code: timing analysis

Topological quantum error correction codes have high thresholds and are well suited to physical implementation. The minimum weight perfect matching algorithm can be used to efficiently handle errors in such codes. We perform a timing analysis of our current implementation of the minimum weight perfect matching algorithm. Our implementation performs the classical processing associated with an nxn lattice of qubits realizing a square surface code storing a single logical qubit of information in a fault-tolerant manner. We empirically demonstrate that our implementation requires only O(n^2) average time per round of error correction for code distances ranging from 4 to 512 and a range of depolarizing error rates. We also describe tests we have performed to verify that it always obtains a true minimum weight perfect matching.Comment: 13 pages, 13 figures, version accepted for publicatio

Towards practical classical processing for the surface code

The surface code is unarguably the leading quantum error correction code for 2-D nearest neighbor architectures, featuring a high threshold error rate of approximately 1%, low overhead implementations of the entire Clifford group, and flexible, arbitrarily long-range logical gates. These highly desirable features come at the cost of significant classical processing complexity. We show how to perform the processing associated with an nxn lattice of qubits, each being manipulated in a realistic, fault-tolerant manner, in O(n^2) average time per round of error correction. We also describe how to parallelize the algorithm to achieve O(1) average processing per round, using only constant computing resources per unit area and local communication. Both of these complexities are optimal.Comment: 5 pages, 6 figures, published version with some additional tex

Final project report, staff exchange with Finnigan Corporation

The objective of the exchange between Pacific Northwest Laboratory (PNL) and Finnigan Corporation is a transfer of expertise and technology for the design and operation of efficient and sensitive atmospheric pressure/vacuum electrospray ionization (ESI) sources. The development of such ion sources will permit wider application of mass spectrometry instrumentation in applied studies in a variety of disciplines including clinical, forensic, biochemical, biotechnical, and environmental studies where sensitivity is a paramount concern. Two meetings were held between representatives of Finnigan Corporation (led by Dr. Ian Jardine, Director for Marketing, Finnigan Corporation) and PNL staff members. During these meetings, Finnigan and PNL staff surveyed the existing technology for atmosphere/vacuum interface of mass spectrometry to ESI. The representatives from Finnigan viewed demonstrations of recent developments that increased efficiency and sensitivity for ESI mass spectrometry. During these meetings, knowledge and expertise were shared in the development of instrumentation, methods, and applications of ESI mass spectrometry with particular emphasis on current and planned Finnigan instrumentation. With the objective of more effective and competitive products for Finnigan Corporation, concepts for a Cooperative Research and Development Agreement (CRADA) were directed toward the development and commercialization of advanced high efficiency and sensitivity ESI technology. A detailed proposal and work plan for the cooperative project was developed and is included in this report