Colliding Solitons for the Nonlinear Schrödinger Equation

We study the collision of two fast solitons for the nonlinear Schrödinger equation in the presence of a slowly varying external potential. For a high initial relative speed ||v|| of the solitons, we show that, up to times of order ||v|| after the collision, the solitons preserve their shape (in L ²-norm), and the dynamics of the centers of mass of the solitons is approximately determined by the external potential, plus error terms due to radiation damping and the extended nature of the solitons. We remark on how to obtain longer time scales under stronger assumptions on the initial condition and the external potential.     

Hartogs-Bochner type theorem in projective space

We prove the following Hartogs-Bochner type theorem: Let M be a connected C² hypersurface of P_n(C) (n≥2) which divides P_n(C) in two connected open sets Ω₁ and Ω₂. Suppose that M has at most one open CR orbit. Then there exists i∈{1,2} such that C¹ CR functions defined on M extends holomorphically to Ω _i . Supported by the TMR network.     

Persistence stability for geometric complexes

In this paper we study the properties of the homology of different geometric filtered complexes (such as Vietoris–Rips, ?ech and witness complexes) built on top of totally bounded metric spaces. Using recent developments in the theory of topological persistence, we provide simple and natural proofs of the stability of the persistent homology of such complexes with respect to the Gromov–Hausdorff distance. We also exhibit a few noteworthy properties of the homology of the Rips and ?ech complexes built on top of compact spaces.     

Comparison of alignment free string distances for complete genome phylogeny

In this paper, we compare the accuracy of four string distances on complete genomes to reconstruct phylogenies using simulated and real biological data. These distances are based on common words shared by raw genomic sequences and do not require preliminary processing steps such as gene identification or sequence alignment. Moreover, they are computable in linear time. The first distance is based on Maximum Significant Matches (MSM). The second is computed from the frequencies of all the words of length k (KW). The third distance is based on the Average length of maximum Common Substrings at any position (ACS). The last one is based on the Ziv–Lempel compression algorithm (ZL). We describe a simulation process of evolution to generate a set of sequences having evolved according to a random tree topology T. This process allows both base substitution and fragment insertion/deletion, including horizontal transfers. The distances between the generated sequences are computed using the four formulas and the corresponding trees T′ are reconstructed using Neighbor-Joining. T and T′ are compared according to topological criteria. These comparisons show that the MSM distance outperforms the others whatever the parameters used to generate sequences. Finally, we test the MSM and KW distances on real biological data (i.e. prokaryotic complete genomes) and we compare the NJ trees to a Maximum Likelihood 16S + 23S RNA tree. We show that the MSM distance provides accurate results to study intra-phylum relationships, much better than those given by KW.     

Heuristics and lower bounds for minimizing fuel consumption in hybrid-electrical vehicles

In hybrid electric vehicles, the electrical powertrain system has multiple energy sources that it can gather power from to satisfy the propulsion power requested by the vehicle at each instant. This paper focusses on the minimization of the fuel consumption of such a vehicle, taking advantage of the different energy sources. Based on global optimization approaches, the proposed heuristics find solutions that best split the power requested between the multi-electrical sources available. A lower bounding procedure is introduced to validate the quality of the solutions. Computational results show a significant improvement over previous results from the literature in both the computing time and the quality of the solutions.     

Changes in dynamics of SRE-RNA on binding to the VTS1p-SAM domain studied by 13C NMR relaxation

RNA recognition by proteins is often accompanied by significant changes in RNA dynamics in addition to conformational changes. However, there are very few studies which characterize the changes in molecular motions in RNA on protein binding. We present a quantitative (13)C NMR relaxation study of the changes in RNA dynamics in the pico-nanosecond time scale and micro-millisecond time scale resulting from interaction of the stem-loop SRE-RNA with the VTS1p-SAM domain. (13)C relaxation rates of the protonated carbons of the nucleotide base and anomeric carbons have been analyzed by employing the model-free formalism, for a fully (13)C/(15)N-labeled sample of the SRE-RNA in the free and protein-bound forms. In the free RNA, the nature of molecular motions are found to be distinctly different in the stem and the loop region. On binding to the protein, the nature of motions becomes more homogeneous throughout the RNA, with many residues showing increased flexibility at the aromatic carbon sites, while the anomeric carbon sites become more rigid. Surprisingly, we also observe indications of a slow collective motion of the RNA in the binding pocket of the protein. The observation of increased motions on binding is interesting in the context of growing evidence that binding does not always lead to motional restrictions and the resulting entropy gain could favor the free energy of association.     

Electrochemical insights into the mechanisms of proton reduction by [Fe2(CO)6{micro-SCH2N(R)CH2S}] complexes related to the [2Fe](H) subsite of [FeFe]hydrogenase

Electrochemical investigations on a structural analogue of the [2Fe](H) subsite of [FeFe]H(2)ases, namely, [Fe(2)(CO)(6){micro-SCH(2)N(CH(2)CH(2)- OCH(3))CH(2)S}] (1), were conducted in MeCN/NBu(4)PF(6) in the presence of HBF(4)/Et(2)O or HOTs. Two different catalytic proton reduction processes operate, depending on the strength and the concentration of the acid used. The first process, which takes place around -1.2 V for both HBF(4)/Et(2)O and HOTs, is limited by the slow release of H(2) from the product of the {2 H(+)/2 e} pathway, 1-2H. The second catalytic process, which occurs at higher acid concentrations, takes place at different potentials depending on the acid present. We propose that this second mechanism is initiated by protonation of 1-2H when HBF(4)/Et(2)O is used, whereas the reduction of 1-2H is the initial step in the presence of the weaker acid HOTs. The potential of the second process, which occurs around -1.4 V (reduction potential of 1-3H(+)) or around -1.6 V (the reduction potential of 1-2H) is thus dependent on the strength of the available proton source.     

Comprehensive two-dimensional gas chromatography for enhanced analysis of naphthas: new column combination involving permethylated cyclodextrin in the second dimension

A new column association using comprehensive two-dimensional gas chromatography for the detailed molecular analysis of hydrocarbon mixtures is reported in this paper. In order to compare the impact of two different secondary columns, a novel column combination relying on a GC x 2GC system was used. This system is based on a non-polar first column (PONA) combined with both a permethylated beta-cyclodextrin (beta-Dex 120) stationary phase and a polysilphenylensiloxane (BPX 50) in the second dimension. Compared to BPX 50 stationary phase, the implementation of beta-cyclodextrin columns as the second dimension was found to improve the resolution between paraffins and naphthenes in the naphtha range but not in the middle distillate range. Attempts to improve the results and to understand the interaction mechanism remained unsuccessful. Therefore, the benefits of the beta-Dex 120-column are only demonstrated on heavy naphtha cut for the quantitation of hydrocarbons.     

Use of 1,10-phenanthroline in diiron dithiolate derivatives related to the [Fe-Fe] hydrogenase active site

Treatment of [Fe(2)(micro-pdt)(CO)(6)] (pdt = S(CH(2))(3)S) with 1,10-phenanthroline (phen) in refluxing toluene affords the asymmetric complex [Fe(2)(micro-pdt)(CO)(4)(phen)] (1); the protonation of with HBF(4).OEt(2) in CD(2)Cl(2) at 203 K has been monitored by (1)H NMR.     

Redox Multifunctionality in a Series of PtII Dithiolene Complexes of a Tetrathiafulvalene‐Based Diphosphine Ligand

The redox‐active and chelating diphosphine, 3,4‐dimethyl‐3′,4′‐bis(diphenylphosphino)‐tetrathiafulvalene, denoted as P2 , is engaged in a series of platinum complexes, [(P2)Pt(dithiolene)], with different dithiolate ligands, such as 1,2‐benzenedithiolate (bdt), 1,3‐dithiole‐2‐thione‐4,5‐dithiolate (dmit), and 5,6‐dihydro‐1,4‐dithiin‐2,3‐dithiolate (dddt). The complexes are structurally characterized by X‐ray diffraction, together with a model compound derived from bis(diphenylphosphino)ethane, namely, [(dppe)Pt(dddt)] . Four successive reversible electron‐transfer processes are found for the [(P2)Pt(dddt)] complex, associated with the two covalently linked but electronically uncoupled electrophores, that is, the TTF core and the platinum dithiolene moiety. The assignments of the different redox processes to either one or the other electrophore is made thanks to the electrochemical properties of the model compound [(dppe)Pt(dddt)] lacking the TTF redox core, and with the help of theoretical calculations (DFT) to understand the nature and energy of the frontier orbitals of the [(P2)Pt(dithiolene)] complexes in their different oxidation states. The first oxidation of the highly electron‐rich [(P2)Pt(dddt)] complex can be unambiguously assigned to the redox process affecting the Pt(dddt) moiety rather than the TTF core, a rare example in the coordination chemistry of tetrathiafulvalenes acting as ligands.