Measurable supports,reducible spaces and the structure of the optimal σ-field in unbiased estimation

This paper generalizes a result bySapozhnikov relating the structure of the optimal -field in unbiased estimation to the reducibility of certain linear subspaces of estimators. For this purpose, the concept of a measurable support of (uncountably infinite) sets consisting of random variables is introduced, which could be of general interest. It turns out, that for a wide class of measure spaces, measurable supports of any subsets of measurable functions exist.     

Undominated d.c. Decompositions of Quadratic Functions and Applications to Branch-and-Bound Approaches

In this paper we analyze difference-of-convex (d.c.) decompositions for indefinite quadratic functions. Given a quadratic function, there are many possible ways to decompose it as a difference of two convex quadratic functions. Some decompositions are dominated, in the sense that other decompositions exist with a lower curvature. Obviously, undominated decompositions are of particular interest. We provide three different characterizations of such decompositions, and show that there is an infinity of undominated decompositions for indefinite quadratic functions. Moreover, two different procedures will be suggested to find an undominated decomposition starting from a generic one. Finally, we address applications where undominated d.c.d.s may be helpful: in particular, we show how to improve bounds in branch-and-bound procedures for quadratic optimization problems.     

Aromatic 19F–13C TROSY—[19F, 13C]‐Pyrimidine Labeling for NMR Spectroscopy of RNA

We present the access to [5‐¹⁹F, 5‐¹³C]‐uridine and ‐cytidine phosphoramidites for the production of site‐specifically modified RNAs up to 65 nucleotides (nts). The amidites were used to introduce [5‐¹⁹F, 5‐¹³C]‐pyrimidine labels into five RNAs—the 30 nt human immunodeficiency virus trans activation response (HIV TAR) 2 RNA, the 61 nt human hepatitis B virus ? (hHBV ?) RNA, the 49 nt SAM VI riboswitch aptamer domain from B. angulatum, the 29 nt apical stem loop of the pre‐microRNA (miRNA) 21 and the 59 nt full length pre‐miRNA 21. The main stimulus to introduce the aromatic ¹⁹F–¹³C‐spin topology into RNA comes from a work of Boeszoermenyi et al., in which the dipole‐dipole interaction and the chemical shift anisotropy relaxation mechanisms cancel each other leading to advantageous TROSY properties shown for aromatic protein sidechains. This aromatic ¹³C–¹⁹F labeling scheme is now transferred to RNA. We provide a protocol for the resonance assignment by solid phase synthesis based on diluted [5‐¹⁹F, 5‐¹³C]/[5‐¹⁹F] pyrimidine labeling. For the 61 nt hHBV ? we find a beneficial ¹⁹F–¹³C TROSY enhancement, which should be even more pronounced in larger RNAs and will facilitate the NMR studies of larger RNAs. The [¹⁹F, ¹³C]‐labeling of the SAM VI aptamer domain and the pre‐miRNA 21 further opens the possibility to use the biorthogonal stable isotope reporter nuclei in in vivo NMR to observe ligand binding and microRNA processing in a biological relevant setting.     

Aromatic 19F–13C TROSY—[19F, 13C]-Pyrimidine Labeling for NMR Spectroscopy of RNA

We present the access to [5-¹⁹F, 5-¹³C]-uridine and -cytidine phosphoramidites for the production of site-specifically modified RNAs up to 65 nucleotides (nts). The amidites were used to introduce [5-¹⁹F, 5-¹³C]-pyrimidine labels into five RNAs—the 30 nt human immunodeficiency virus trans activation response (HIV TAR) 2 RNA, the 61 nt human hepatitis B virus ϵ (hHBV ϵ) RNA, the 49 nt SAM VI riboswitch aptamer domain from B. angulatum, the 29 nt apical stem loop of the pre-microRNA (miRNA) 21 and the 59 nt full length pre-miRNA 21. The main stimulus to introduce the aromatic ¹⁹F–¹³C-spin topology into RNA comes from a work of Boeszoermenyi et al., in which the dipole-dipole interaction and the chemical shift anisotropy relaxation mechanisms cancel each other leading to advantageous TROSY properties shown for aromatic protein sidechains. This aromatic ¹³C–¹⁹F labeling scheme is now transferred to RNA. We provide a protocol for the resonance assignment by solid phase synthesis based on diluted [5-¹⁹F, 5-¹³C]/[5-¹⁹F] pyrimidine labeling. For the 61 nt hHBV ϵ we find a beneficial ¹⁹F–¹³C TROSY enhancement, which should be even more pronounced in larger RNAs and will facilitate the NMR studies of larger RNAs. The [¹⁹F, ¹³C]-labeling of the SAM VI aptamer domain and the pre-miRNA 21 further opens the possibility to use the biorthogonal stable isotope reporter nuclei in in vivo NMR to observe ligand binding and microRNA processing in a biological relevant setting.     

Entanglement interferometry for precision measurement of atomic scattering properties

We report on a matter wave interferometer realized with entangled pairs of trapped 87Rb atoms. Each pair of atoms is confined at a single site of an optical lattice potential. The interferometer is realized by first creating a coherent spin superposition of the two atoms and then tuning the interstate scattering length via a Feshbach resonance. The selective change of the interstate scattering length leads to an entanglement dynamics of the two-particle state that can be detected in a Ramsey interference experiment. This entanglement dynamics is employed for a precision measurement of atomic interaction parameters. Furthermore, the interferometer allows us to separate lattice sites with one or two atoms in a nondestructive way.     

Coherent transport of neutral atoms in spin-dependent optical lattice potentials

We demonstrate the controlled coherent transport and splitting of atomic wave packets in spin-dependent optical lattice potentials. Such experiments open intriguing possibilities for quantum state engineering of many body states. After first preparing localized atomic wave functions in an optical lattice through a Mott insulating phase, we place each atom in a superposition of two internal spin states. Then state selective optical potentials are used to split the wave function of a single atom and transport the corresponding wave packets in two opposite directions. Coherence between the wave packets of an atom delocalized over up to seven lattice sites is demonstrated.     

Media Preparation Using Tuna-Processing Wastes for Improved Lipase Production by Shrimp Gut Isolate Staphylococcus epidermidis CMST Pi 2

Extracellular lipase production by Staphylococcus epidermidis CMST Pi 2 isolated from the intestine of shrimp Penaeus indicus has been investigated in shake-flask experiment using different preparations of tuna-processing waste such as raw fish meat, defatted fish meat, alkali hydrolysate, and acid hydrolysate as nitrogen source. Among the tested tuna preparations, defatted fish meat supported the maximum lipase production, and 2.5% concentration of the same was found to be optimum for maximizing the lipase production. The effect of carbon sources on lipase production revealed that glucose aided the higher lipase production than any other tested carbon source and a concentration of 2% glucose registered as optimum to enhance the lipase production. The halotolerancy of S. epidermidis CMST Pi 2 for lipase production indicated that 4% of sodium chloride was optimum to yield maximum lipase. Among the surfactants tested, lipase production was high in Tween 20 added medium when compared to other surfactants, and its optimum concentration recorded was 0.8%. Partial characterization of crude enzyme revealed that pH 7 and 55 °C temperature were optimum for maximum lipase activity.     

Multi-Standard Quadratic Optimization: interior point methods and cone programming reformulation

A Standard Quadratic Optimization Problem (StQP) consists of maximizing a (possibly indefinite) quadratic form over the standard simplex. Likewise, in a multi-StQP we have to maximize a (possibly indefinite) quadratic form over the Cartesian product of several standard simplices (of possibly different dimensions). Among many other applications, multi-StQPs occur in Machine Learning Problems. Several converging monotone interior point methods are established, which differ from the usual ones used in cone programming. Further, we prove an exact cone programming reformulation for establishing rigorous yet affordable bounds and finding improving directions.     

Duality respecting representations and compatible complexity measures for gammoids

We show that every gammoid has special digraph representations, such that a representation of the dual of the gammoid may be easily obtained by reversing all arcs. In an informal sense, the duality notion of a poset applied to the digraph of a special representation of a gammoid commutes with the operation of forming the dual of that gammoid. We use these special representations in order to define a complexity measure for gammoids, such that the classes of gammoids with bounded complexity are closed under duality, minors, and direct sums.     

Evolution towards the Maximum Clique

As is well known, the problem of finding a maximum clique in a graph isNP-hard. Nevertheless, NP-hard problems may have easy instances. This paperproposes a new, global optimization algorithm which tries to exploit favourabledata constellations, focussing on the continuous problem formulation: maximizea quadratic form over the standard simplex. Some general connections of thelatter problem with dynamic principles of evolutionary game theory areestablished. As an immediate consequence, one obtains a procedure whichconsists (a) of an iterative part similar to interior-path methods based on theso-called replicator dynamics; and (b) a routine to escape from inefficient,locally optimal solutions. For the special case of finding a maximum clique ina graph where the quadratic form arises from a regularization of the adjacencematrix, part (b), i.e. escaping from maximal cliques not of maximal size, isaccomplished with block pivoting methods based on (large) independent sets,i.e. cliques of the complementary graph. A simulation study is included whichindicates that the resulting procedure indeed has some merits.