Algorithms for computing the time-corrected instantaneous frequency (reassigned) spectrogram, with applications

A modification of the spectrogram (log magnitude of the short-time Fourier transform) to more accurately show the instantaneous frequencies of signal components was first proposed in 1976 [Kodera et al., Phys. Earth Planet. Inter. 12, 142-150 (1976)], and has been considered or reinvented a few times since but never widely adopted. This paper presents a unified theoretical picture of this time-frequency analysis method, the time-corrected instantaneous frequency spectrogram, together with detailed implementable algorithms comparing three published techniques for its computation. The new representation is evaluated against the conventional spectrogram for its superior ability to track signal components. The lack of a uniform framework for either mathematics or implementation details which has characterized the disparate literature on the schemes has been remedied here. Fruitful application of the method is shown in the realms of speech phonation analysis, whale song pitch tracking, and additive sound modeling.     

A Revision of the Proof of the Kepler Conjecture

The Kepler conjecture asserts that no packing of congruent balls in three-dimensional Euclidean space has density greater than that of the face-centered cubic packing. The original proof, announced in 1998 and published in 2006, is long and complex. The process of revision and review did not end with the publication of the proof. This article summarizes the current status of a long-term initiative to reorganize the original proof into a more transparent form and to provide a greater level of certification of the correctness of the computer code and other details of the proof. A final part of this article lists errata in the original proof of the Kepler conjecture.     

Determination of the potassium content of explosive residues using miniaturised isotachophoresis

A new method has been developed to allow the determination of potassium in post-explosion residues to be made using miniaturised isotachophoresis. The method is based on the use of a caesium leading ion with 4.5 mM 18-crown-6 ether added to retard the potassium to allow reliable determinations to be made. With the conditions selected no interference was noted from other small inorganic cations, such as ammonium, barium, calcium, magnesium, sodium or strontium. The method was successfully applied to the analysis of seven samples containing explosive residues obtained from the unconfined burning of several flash powders. The procedure was found to offer good linearity for potassium determinations over the concentration range of 1.25-150 μg/mL with a coefficient of determination of 0.999 achieved.     

Microbial Fed-batch Production of 1,3-Propanediol Using Raw Glycerol with Suspended and Immobilized Klebsiella pneumoniae

The production of 1,3-propanediol (1,3-PD) was investigated with Klebsiella pneumoniae DSM 4799 using raw glycerol without purification obtained from a biodiesel production process. Fed-batch cultures with suspended cells revealed that 1,3-PD production was more effective when utilizing raw glycerol than pure glycerol (productivity after 47 h of fermentation, 0.84 g?L^?1?h^?1 versus 1.51 g?L^?1?h^?1 with pure and raw glycerol, respectively). In addition, more than 80 g/L of 1,3-PD was produced using raw glycerol; this is the highest 1,3-PD concentration reported thus far for K. pneumoniae using raw glycerol. Repeated fed-batch fermentation with cell immobilization in a fixed-bed reactor was performed to enhance 1,3-PD production. Production of 1,3-PD increased with the cycle number (1.06 g?L^?1?h^?1 versus 1.61 g?L^?1?h^?1 at the first and fourth cycle, respectively) due to successful cell immobilization. During 46 cycles of fed-batch fermentation taking place over 1,460 h, a stable and reproducible 1,3-PD production performance was observed with both pure and raw glycerol. Based on our results, repeated fed batch with immobilized cells is an efficient fermentor configuration, and raw glycerol can be utilized to produce 1,3-PD without inhibitory effects caused by accumulated impurities.     

Tailoring enzyme-rich environmental DNA clones: a source of enzymes for generating libraries of unnatural natural products

A detailed bioinformatics analysis of six glycopeptide biosynthetic gene clusters isolated from soil environmental DNA (eDNA) megalibraries indicates that a subset of these gene clusters contains collections of tailoring enzymes that are predicted to result in the production of new glycopeptide congeners. In particular, sulfotransferases appear in eDNA-derived gene clusters at a much higher frequency than would be predicted from the characterization of glycopeptides from cultured Actinomycetes . Enzymes found on tailoring-enzyme-rich eDNA clones associated with these six gene clusters were used to produce a series of new sulfated glycopeptide derivatives in both in vitro and in vivo derivatization studies. The derivatization of known natural products with eDNA-derived tailoring enzymes is likely to be a broadly applicable strategy for generating libraries of new natural product variants.     

Evaluation of binding of perylene diimide and benzannulated perylene diimide ligands to dna by electrospray ionization mass spectrometry

Electrospray ionization mass spectrometry (ESI-MS) and spectroscopic studies in solution were used to evaluate the self-association, G-quadruplex DNA binding, and selectivity of a series of perylene diimides (PDIs) (PIPER, Tel01, Tel11, Tel12, and Tel18) or benzannulated perylene diimide ligands (Tel34 and Tel32). Fluorescence and resonance light scattering spectra of Tel01, Tel12, Tel32, and Tel34 reveal that these analogs undergo self-association in solution. UV-Vis and fluorescence titrations with G-quadruplex, duplex, or single-stranded DNA demonstrate that all the analogs, with the exception of Tel32, bind to G-quadruplex DNA, with those PDIs that are self-associated in solution showing the highest degree of selectivity for binding G-quadruplex DNA. Parallel ESI-MS analysis of the stoichiometries demonstrates the ability of the ligands, with the exception of Tel32, to bind to G-quadruplex DNA. While most ligands show major 1:1 and 2:1 binding stoichiometries as expected in the case of end-stacking, interestingly, three of the most quadruplex-selective ligands show a different behavior. Tel01 forms 3:1 complexes, while Tel12 and Tel32 only form 1:1 complexes. Collisional activation dissociation patterns are compatible with ligand binding to G-quadruplex DNA via stacking on the ends of the terminal G-tetrads. Experiments with duplex and single strand DNA were performed to assess the binding selectivities of the ligands. PIPER, Tel11, and Tel18 demonstrated extensive complexation with duplex DNA, while Tel11 and Tel18 bound to single strand DNA, confirming the lack of selectivity of these two ligands. Our results indicate that Tel01, Tel12, and Tel34 are the most selective for G-quadruplex DNA.     

Rotational spectrum and inversion motions in the neon-dimethyl sulfide complex

The rotational spectra of the (20)Ne and (22)Ne isotopomers of the Ne-dimethyl sulfide (DMS) rare gas dimer have been measured by Fourier transform microwave spectroscopy. MP2/6-311++G(2d,2p) calculations, and the experimental spectroscopic data, suggest a structure of C(s) symmetry in which the Ne atom lies above the heavy atom plane of the DMS (in the sigma(v) plane which bisects the CSC angle). Experimental rotational constants are consistent with a S...Ne distance of 3.943(6) Angstroms and a (cm...S...Ne) angle of 63.2(6) degrees (where cm is the center of mass of DMS). A motion of the Ne atom from one side of the DMS to the other gives rise to inversion splittings of around 3 MHz in the c-type transitions. An ab initio potential energy surface calculation has allowed examination of several possible tunneling pathways, and suggests a barrier of between 20 and 40 cm(-1) for the inversion motion, depending on the tunneling pathway taken by the Ne. Dipole moment measurements are consistent with both the experimental and ab initio structures.     

Reactivity of molecularly chemisorbed oxygen on a Au/TiO2 model catalyst

We present results of an investigation into the reactivity of molecularly chemisorbed oxygen with CO on a Au/TiO2 model catalyst at 77 K. We previously discovered that exposing the model catalyst sample to a radio-frequency-generated plasma jet of oxygen results in co-population of both atomically and molecularly chemisorbed oxygen species on the sample. We tested the reactivity of the molecularly chemisorbed oxygen by comparing the CO2 produced from a sample populated with both species to the CO2 produced from a sample that has been cleared of molecularly chemisorbed oxygen employing collision-induced desorption. Samples that are populated with both species consistently result in greater CO2 produced than samples with only atomic oxygen. We interpret this result to indicate that molecularly chemisorbed oxygen on the sample can directly participate in the CO oxidation reaction. The reactivity of molecularly chemisorbed oxygen has been investigated for five different gold coverages (0.5, 0.75, 1, 1.25, and 2 ML), and we observe that there is a greater fractional difference in the CO2 produced (difference between sample populated with both molecularly and atomically adsorbed oxygen and sample populated solely with atomically adsorbed oxygen) for the 1 ML Au coverage than for the other coverages for equivalent oxygen plasma-jet exposures. However, it is not possible to unambiguously conclude that this observation is directly related to a particle size effect on the chemistry since the absolute O(2,a) and O(a) content on the various surfaces is different for all the coverages studied because of the plasma-jet technique that we employed for populating the surfaces with oxygen. Unfortunately, this precludes a direct comparison of the reactivity of molecular oxygen in the carbon monoxide oxidation reaction as a function of gold coverage and hence particle size.     

A finitely presented group with unbounded dead-end depth

The dead-end depth of an element of a group , with respect to a generating set , is the distance from to the complement of the radius closed ball, in the word metric defined with respect to . We exhibit a finitely presented group with a finite generating set with respect to which there is no upper bound on the dead-end depth of elements.

     

Simulation of photoelectron spectra with anharmonicity fully included: Application to the X 2A2<--X 1A1 band of furan

Using a new unconventional procedure for calculating Franck-Condon factors with anharmonicity fully included the X 2A2<--X 1A1 band in the photoelectron spectrum of furan (and deuterated furan) was simulated at the second-order perturbation theory level. All 21 vibrational modes were considered but, in the end, only 4 are required to accurately reproduce the spectrum. Except for our own recent work on ethylene such calculations have been previously limited to tri- or tetraatomic molecules. Most of the effect of anharmonicity is accounted for in first order, although second-order corrections to the vibrational frequencies are important. Based on these simulations we were able to improve upon and extend previous assignments as well as suggest further measurements.