Two new triangles of q-integers via q-Eulerian polynomials of type A and B

The classical Eulerian polynomials can be expanded in the basis t ^k?1(1+t) ^n+1?2k (1≤k≤?(n+1)/2?) with positive integral coefficients. This formula implies both the symmetry and the unimodality of the Eulerian polynomials. In this paper, we prove a q-analogue of this expansion for Carlitz’s q-Eulerian polynomials as well as a similar formula for Chow–Gessel’s q-Eulerian polynomials of type B. We shall give some applications of these two formulas, which involve two new sequences of polynomials in the variable q with positive integral coefficients. It is an open problem to give a combinatorial interpretation for these polynomials.     

Two-photon excited intramolecular energy transfer and light-harvesting effect in novel dendritic systems

Two-photon absorption excited intramolecular energy transfer and light-harvesting effects are demonstrated in three novel dendritic systems. These systems contain both an antenna structure that can effectively absorb two-photon energy at approximately 800 nm and emit fluorescence at approximately 515 nm and a core moiety that can absorb one-photon energy at approximately 520 nm and emit at approximately 590 nm. Covalently combining the core and antenna functionalities intrinsically changes the optical behavior of the component pieces. The two-photon energy absorbed by the antenna structure is resonantly transferred to the core, where the core's emission intensity is enhanced by 8, 20, and 34 times for the three dendritic systems.     

Linear theory of wave generation by a moving bottom

The computation of long wave propagation through the ocean obviously depends on the initial condition. When the waves are generated by a moving bottom, a traditional approach consists in translating the ‘frozen’ sea bed deformation to the free surface and propagating it. The present study shows the differences between the classical approach (passive generation) and the active generation where the bottom motion is included. The analytical solutions presented here exhibit some of the drawbacks of passive generation. The linearized solutions seem to be sufficient to consider the generation of water waves by a moving bottom. To cite this article: D. Dutykh et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Variations on Weyl's theorem

In this note we study the property (w), a variant of Weyl's theorem introduced by Rako?evi?, by means of the localized single-valued extension property (SVEP). We establish for a bounded linear operator defined on a Banach space several sufficient and necessary conditions for which property (w) holds. We also relate this property with Weyl's theorem and with another variant of it, a-Weyl's theorem. We show that Weyl's theorem, a-Weyl's theorem and property (w) for T (respectively T^*) coincide whenever T^* (respectively T) satisfies SVEP. As a consequence of these results, we obtain that several classes of commonly considered operators have property (w).     

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.     

Graphs with No Induced Five‐Vertex Path or Antipath

We prove that a graph G contains no induced ‐vertex path and no induced complement of a ‐vertex path if and only if G is obtained from 5‐cycles and split graphs by repeatedly applying the following operations: substitution, split unification, and split unification in the complement, where split unification is a new class‐preserving operation introduced here.     

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.