Ms2lda.org: web-based topic modelling for substructure discovery in mass spectrometry

Motivation: We recently published MS2LDA, a method for the decomposition of sets of molecular fragment data derived from large metabolomics experiments. To make the method more widely available to the community, here we present ms2lda.org, a web application that allows users to upload their data, run MS2LDA analyses and explore the results through interactive visualisations. Results: Ms2lda.org takes tandem mass spectrometry data in many standard formats and allows the user to infer the sets of fragment and neutral loss features that co-occur together (Mass2Motifs). As an alternative workflow, the user can also decompose a dataset onto predefined Mass2Motifs. This is accomplished through the web interface or programmatically from our web service

Conditional probabilities in Ponzano-Regge minisuperspace

We examine the Hartle-Hawking no-boundary initial state for the Ponzano-Regge formulation of gravity in three dimensions. We consider the behavior of conditional probabilities and expectation values for geometrical quantities in this initial state for a simple minisuperspace model consisting of a two-parameter set of anisotropic geometries on a 2-sphere boundary. We find dependence on the cutoff used in the construction of Ponzano-Regge amplitudes for expectation values of edge lengths. However, these expectation values are cutoff independent when computed in certain, but not all, conditional probability distributions. Conditions that yield cutoff independent expectation values are those that constrain the boundary geometry to a finite range of edge lengths. We argue that such conditions have a correspondence to fixing a range of local time, as classically associated with the area of a surface for spatially closed cosmologies. Thus these results may hint at how classical spacetime emerges from quantum amplitudes.Comment: 26 pages including 10 figures, some reorganization in the presentation of results, expanded discussion of results in the context of 2+1 gravity in the Witten variables, 3 new reference

Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, 3j3j Symbols, and Character Localization

In this paper we employ a novel technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain the asymptotic behavior (in the limit of large representation index $J$) of generic Wigner matrix elements $D^{J}_{MM'}(g)$. We use this result to derive asymptotic formulae for the character $\chi^J(g)$ of an SU(2) group element and for Wigner's $3j$ symbol. Surprisingly, given that we perform five successive layers of approximations, the asymptotic formula we obtain for $\chi^J(g)$ is in fact exact. This result provides a non trivial example of a Duistermaat-Heckman like localization property for discrete sums.Comment: 36 pages, 3 figure

Blue laser cooling transitions in Tm I

We have studied possible candidates for laser cooling transitions in $^{169}$Tm in the spectral region 410 -- 420 nm. By means of saturation absorption spectroscopy we have measured the hyperfine structure and rates of two nearly closed cycling transitions from the ground state $4\textrm{f}^{13}6\textrm{s}^2(^2\textrm{F}_0)(J_g=7/2)$ to upper states $4\textrm{f}^{12}(^3\textrm{H}_5)5\textrm{d}_{3/2}6\textrm{s}^2(J_e=9/2)$ at 410.6 nm and $4\textrm{f}^{12}(^3\textrm{F}_4)5\textrm{d}_{5/2}6\textrm{s}^2(J_e=9/2)$ at 420.4 nm and evaluated the life times of the excited levels as 15.9(8) ns and 48(6) ns respectively. Decay rates from these levels to neighboring opposite-parity levels are evaluated by means of Hartree-Fock calculations. We conclude, that the strong transition at 410.6 nm has an optical leak rate of less then $2\cdot10^{-5}$ and can be used for efficient laser cooling of $^{169}$Tm from a thermal atomic beam. The hyperfine structure of two other even-parity levels which can be excited from the ground state at 409.5 nm and 418.9 nm is also measured by the same technique. In addition we give a calculated value of $7(2)$ s$^{-1}$ for the rate of magnetic-dipole transition at 1.14 $\mu$m between the fine structure levels $(J_g=7/2)\leftrightarrow(J'_g=5/2)$ of the ground state which can be considered as a candidate for applications in atomic clocks.Comment: 8 pages, 5 figure

Fictitious Magnetic Resonance by Quasi-Electrostatic Field

We propose a new kind of spin manipulation method using a {\it fictitious} magnetic field generated by a quasi-electrostatic field. The method can be applicable to every atom with electron spins and has distinct advantages of small photon scattering rate and local addressability. By using a $\rm{CO_2}$ laser as a quasi-electrostatic field, we have experimentally demonstrated the proposed method by observing the Rabi-oscillation of the ground state hyperfine spin F=1 of the cold $\rm{^{87}Rb}$ atoms and the Bose-Einstein condensate.Comment: 5 pages, 5 figure

Non-Abelian (p,q) Strings in the Warped Deformed Conifold

We calculate the tension of $(p,q)$-strings in the warped deformed conifold using the non-Abelian DBI action. In the large flux limit, we find exact agreement with the recent expression obtained by Firouzjahi, Leblond and Henry-Tye up to and including order $1/M^2$ terms if $q$ is also taken to be large. Furthermore using the finite $q$ prescription for the symmetrised trace operation we anticipate the most general expression for the tension valid for any $(p,q)$. We find that even in this instance, corrections to the tension scale as $1/M^2$ which is not consistent with simple Casimir scaling.Comment: 18 pages, Latex, 1 figure; Added a discussion of the case when the warp factor parameter $b\neq 1$ and typos correcte

Subfactors of index less than 5, part 1: the principal graph odometer

In this series of papers we show that there are exactly ten subfactors, other than $A_\infty$ subfactors, of index between 4 and 5. Previously this classification was known up to index $3+\sqrt{3}$. In the first paper we give an analogue of Haagerup's initial classification of subfactors of index less than $3+\sqrt{3}$, showing that any subfactor of index less than 5 must appear in one of a large list of families. These families will be considered separately in the three subsequent papers in this series.Comment: 36 pages (updated to reflect that the classification is now complete