Dye laser frequency tripling at 106 nm

The laser emission from a new substituted-terphenyl dye has been frequency tripled in pure xenon gas to generate tunable vacuum-ultraviolet radiation around 106 nm, close to the LiF transmission limit.     

Pegasos: primal estimated sub-gradient solver for SVM

We describe and analyze a simple and effective stochastic sub-gradient descent algorithm for solving the optimization problem cast by Support Vector Machines (SVM). We prove that the number of iterations required to obtain a solution of accuracy e{\epsilon} is [(O)\tilde](1 / e){\tilde{O}(1 / \epsilon)}, where each iteration operates on a single training example. In contrast, previous analyses of stochastic gradient descent methods for SVMs require W(1 / e²){\Omega(1 / \epsilon^2)} iterations. As in previously devised SVM solvers, the number of iterations also scales linearly with 1/λ, where λ is the regularization parameter of SVM. For a linear kernel, the total run-time of our method is [(O)\tilde](d/(le)){\tilde{O}(d/(\lambda \epsilon))}, where d is a bound on the number of non-zero features in each example. Since the run-time does not depend directly on the size of the training set, the resulting algorithm is especially suited for learning from large datasets. Our approach also extends to non-linear kernels while working solely on the primal objective function, though in this case the runtime does depend linearly on the training set size. Our algorithm is particularly well suited for large text classification problems, where we demonstrate an order-of-magnitude speedup over previous SVM learning methods.     

Mass-correlated pulsed extraction: Theoretical analysis and implementation with a linear matrix-assisted laser desorption/ionization time of flight mass spectrometer

The pulsed extraction (PE) of ions produced by matrix-assisted laser desorption/ionization in time-of-flight mass spectrometers greatly improves mass resolution but, unfortunately, this method is mass dependent. Here we report an approach to expand the capabilities of the PE method so as to provide uniform focusing conditions over a wide mass range. Along with an extraction pulse, an additional pulse is applied to correct the mass dependency of the standard PE method. We describe the algorithm for derivation of this correction pulse waveform, where the first-order focusing conditions are valid all along the mass region of interest. Experimental verification of this method for correction of ion velocities demonstrated better mass resolution than standard PE over a wide mass range.     

On Noether’s Theorem for the Euler–Poincaré Equation on the Diffeomorphism Group with Advected Quantities

We show how Noether conservation laws can be obtained from the particle relabelling symmetries in the Euler–Poincaré theory of ideal fluids with advected quantities. All calculations can be performed without Lagrangian variables, by using the Eulerian vector fields that generate the symmetries, and we identify the time-evolution equation that these vector fields satisfy. When advected quantities (such as advected scalars or densities) are present, there is an additional constraint that the vector fields must leave the advected quantities invariant. We show that if this constraint is satisfied initially then it will be satisfied for all times. We then show how to solve these constraint equations in various examples to obtain evolution equations from the conservation laws. We also discuss some fluid conservation laws in the Euler–Poincaré theory that do not arise from Noether symmetries, and explain the relationship between the conservation laws obtained here, and the Kelvin–Noether theorem given in Sect. 4 of Holm et al. (Adv. Math. 137:1–81, 1998).     

Development and application of a direct vinyl lithiation of cis-stilbene and a directed vinyl lithiation of an unsymmetrical cis-stilbene

[reaction: see text] The vinyl deprotonation of cis-stilbene can be readily achieved using s-BuLi in THF at -25 degrees C. The generated 1-lithio-1,2-diphenylethene undergoes an in situ Z-to-E isomerization, and subsequent reaction with electrophiles results in an efficient stereoselective synthesis of trisubstituted alkenes. A directed vinyl lithiation of the unsymmetrical cis-stilbene 2-styryl-phenyl-carbamic acid tert-butyl ester can be achieved regioselectively, thereby expanding this methodology for further synthetic applications in indole chemistry.     

High-performance liquid chromatography-time-of-flight mass spectrometry and its application to peptide analyses

High-performance liquid chromatography (HPLC) has been successfully interfaced on-line with liquid secondary-ion time-of-flight mass spectrometry, utilizing a continuous-flow interface. Time-of-flight mass spectrometry (TOF-MS) is a low-resolution, high-mass-range technique, compatible with extremely rapid data acquisition rates. Thus a TOF-MS system is extremely well suited for coupling with HPLC. This paper describes the interface used to couple the HPLC and TOF-MS as well as the basic operating principles of such a system. Using both standard and packed-capillary reversed-phase HPLC columns, the HPLC-TOF-MS system has been successfully used to separate and detect peptides, providing molecular weight information for the peptide analytes. Experimental data, including chromatograms (UV, reconstructed ion and selected ion) and mass spectra, are presented to demonstrate the ability of the HPLC-liquid secondary-ion TOF-MS system to resolve chromatographically analytes as well as to resolve mass spectrometrically analytes which are unresolved on the chromatographic column.     

High Energy Collisions on Tandem Time-of-Flight Mass Spectrometers

Long before the introduction of matrix-assisted laser desorption/ionization (MALDI), electrospray ionization (ESI), Orbitraps, and any of the other tools that are now used ubiquitously for proteomics and metabolomics, the highest performance mass spectrometers were sector instruments, providing high resolution mass measurements by combining an electrostatic energy analyzer (E) with a high field magnet (B). In its heyday, the four sector mass spectrometer (or EBEB) was the crown jewel, providing the highest performance tandem mass spectrometry using single, high energy collisions to induce fragmentation. During a time in which quadrupole and tandem triple quadrupole instruments were also enjoying increased usage and popularity, there were, nonetheless, some clear advantages for sectors over their low collision energy counterparts. Time-of-flight (TOF) mass spectrometers are high voltage, high vacuum instruments that have much in common with sectors and have inspired the development of tandem instruments exploiting single high energy collisions. In this retrospective, we recount our own journey to produce high performance TOFs and tandem TOFs, describing the basic theory, problems, and the advantages for such instruments. An experiment testing impulse collision theory (ICT) underscores the similarities with sector mass spectrometers where this concept was first developed. Applications provide examples of more extensive fragmentation, side chain cleavages, and charge-remote fragmentation, also characteristic of high energy sector mass spectrometers. Moreover, the so-called curved-field reflectron has enabled the design of instruments that are simpler, collect and focus all of the ions, and may provide the future technology for the clinic, for tissue imaging, and the characterization of microorganisms.