Fast approximation schemes for Boolean programming and scheduling problems related to positive convex Half-Product

We address a version of the Half-Product Problem and its restricted variant with a linear knapsack constraint. For these minimization problems of Boolean programming, we focus on the development of fully polynomial-time approximation schemes with running times that depend quadratically on the number of variables. Applications to various single machine scheduling problems are reported: minimizing the total weighted flow time with controllable processing times, minimizing the makespan with controllable release dates, minimizing the total weighted flow time for two models of scheduling with rejection.     

Integration of enzyme kinetic models and isotopomer distribution analysis for studies of <Emphasis Type="Italic">in situ</Emphasis>cell operation

A current trend in neuroscience research is the use of stable isotope tracers in order to address metabolic processes in vivo. The tracers produce a huge number of metabolite forms that differ according to the number and position of labeled isotopes in the carbon skeleton (isotopomers) and such a large variety makes the analysis of isotopomer data highly complex. On the other hand, this multiplicity of forms does provide sufficient information to address cell operation in vivo. By the end of last millennium, a number of tools have been developed for estimation of metabolic flux profile from any possible isotopomer distribution data. However, although well elaborated, these tools were limited to steady state analysis, and the obtained set of fluxes remained disconnected from their biochemical context. In this review we focus on a new numerical analytical approach that integrates kinetic and metabolic flux analysis. The related computational algorithm estimates the dynamic flux based on the time-dependent distribution of all possible isotopomers of metabolic pathway intermediates that are generated from a labeled substrate. The new algorithm connects specific tracer data with enzyme kinetic characteristics, thereby extending the amount of data available for analysis: it uses enzyme kinetic data to estimate the flux profile, and vice versa, for the kinetic analysis it uses in vivo tracer data to reveal the biochemical basis of the estimated metabolic fluxes.     

Photochemically controlled electrochemical deposition and dissolution of Ag0 nanoclusters on au electrode surfaces

A photoisomerizable thiolated nitrospiropyran SP, (1a), monolayer is assembled on a Au electrode by the primary deposition of thiolated nitromerocyanine isomer 1b as a monolayer on the electrode, followed by the irradiation of the surface with visible light, lambda > 475 nm. The surface coverage of nitrospiropyran units (1a) on the electrode is 2 x 10-10 mole cm-2. Irradiation of the electrode with UV light, 320 nm < lambda < 360 nm, results in the nitromerocyanine, MR, monolayer on the electrode that binds Ag+ ions to the phenolate units. The Ag+ ions associated with the MR monolayer undergo cyclic reduction to surface-confined Ag0 nanoclusters, and reoxidation and dissolution of the Ag0 nanoclusters to Ag+ ions associated with the monolayer are demonstrated. The electron-transfer rate constants for the reduction of Ag+ to Ag0 and for the dissolution of Ag0 were determined by chronoamperometry and correspond to ketred = 12.7 s-1 and ketox = 10.5 s-1, respectively. The nanoclustering rate was characterized by surface plasmon resonance measurements, and it proceeds on a time scale of 10 min. The size of the Ag0 nanoclusters is in the range of 2 to 20 nm. The electrochemically induced reduction of the MR-Ag+ monolayer to the MR-Ag0 surface and the reoxidation of the MR-Ag0 surface control the hydrophilic-hydrophobic properties of the surface. The advancing contact angle of the MR-Ag0-functionalized surface is 59 degrees , and the contact angle of the MR-Ag+-monolayer-functionalized surface is 74 degrees . Photoisomerization of the Ag0-MR surface to the Ag0-SP state, followed by the oxidation of the Ag0 nanoclusters, results in the dissolution of the Ag+ ions into the electrolyte solution.     

Two native pools of phytochrome A in monocots: Evidence from fluorescence investigations of phytochrome mutants of rice

Fluorescence investigations of phytochrome (phy) in rice (Oryza sativa L. cv. Nipponbare) mutants deficient in phyA, phyB and phyA plus phyB were performed. Total content of the pigment (P(tot)) and its spectroscopic and photochemical characteristics were determined in different parts of the dark-grown and far-red light (FR)-grown coleoptiles. Spectroscopically, phyA in the phyB mutant was identical to phyA in the wild-type (WT) and the extent of the conversion from Pr to lumi-R at 85 K was the same for phyA in both lines and varied similarly, depending on the part of the coleoptile used. The latter finding proved that phyA in rice is heterogeneous and comprises two phyA populations, phyA' and phyA". Functional properties of phyA were also determined. In the dark the phyB mutant had a higher content of phyA, inactive protochlorophyllide (Pchlide633) and active protochlorophyllide (Pchlide655) than WT and its coleoptile was longer, indicating that phyB may affect the development of WT seedlings in the dark. Constant FR drastically reduced the content of phyA, Pchlide633 and Pchlide655 and brought about coleoptile shortening and appearance of the first leaf, whereas pulsed FR of equal fluence was less effective. This suggested that the reactions were primarily of the high irradiance responses type, which are likely to be mediated by phyA'. The effects on protochlorophyllide biosynthesis and growth responses type were more pronounced in the phyB mutant than in the WT seedlings, which can be connected with the higher phyA' content in the phyB mutant and/or phyB interference with its action in WT seedlings. In the phyA mutant induction of Pchlide633 and Pchlide655 biosynthesis was observed under constant FR, indicating that phyC may be responsible for this effect.     

Bispectral and (\mathfrak{gl}_{N},\mathfrak{gl}_{M}) dualities

Let be a space of quasipolynomials of dimension N=N ₁+⋅⋅⋅+N _n . We define the regularized fundamental operator of V as the polynomial differential operator D=∑ _i=0 ^N A _N−i (x)∂ _x ⁱ annihilating V and such that its leading coefficient A ₀ is a polynomial of the minimal possible degree. We apply a suitable integral transformation to V to construct a space of quasipolynomials whose regularized fundamental operator is the differential operator ∑ _i=0 ^N u ⁱ A _N−i (∂ _u ). Our integral transformation corresponds to the bispectral involution on the space of rational solutions (vanishing at infinity) of the KP hierarchy. As a corollary of the properties of the integral transformation, we obtain a correspondence between critical points of the two master functions associated with the -dual Gaudin models and also between the corresponding Bethe vectors. The research of E. M. was supported in part by the NSF (Grant No. DMS-0140460). The research of A. V. was supported in part by the NSF (Grant No. DMS-0244579).     

Electric dipole moments of water clusters from a beam deflection measurement

The response of (H2O)(n=3-18) clusters to an electric field is studied by beam deflection. All clusters deflect uniformly, behaving as polarizable particles. The effective polarizabilities exceed the electronic component and increase as the clusters are cooled, revealing a large permanent dipole contribution. The results resolve a discrepancy concerning the polarity of water clusters and show that all species access conformations with moments exceeding 1 D. The data show no evidence for a freezing transition down to approximately 120 K, but suggest a shift in the conformer arrangement at n=8-9.     

Convenient one-step synthesis of 4-unsubstituted 2-amino-4H-chromene-2-carbonitriles and 5-unsubstituted 5H-chromeno[2,3-b]pyridine-3-carbonitriles from quaternary ammonium salts

We have reported DBU catalyzed synthesis of 4-unsubstituted 2-amino-4H-chromene-2-carbonitriles in water under reflux. The attractive features of this process are mild reaction conditions, short reaction times, easy isolation of products and good yields. 5H-chromeno[2,3-b]pyridine-3-carbonitriles were obtained by refluxing excess of malononitrile and quaternary ammonium salts in ethanol in the presence of NaOH as catalyst. The mechanisms of these reactions are believed to involve the formation of the o-quinone methide intermediate.     

Homogeneous monomial groups and centralizers

The construction of homogeneous monomial groups are given and their basic properties are studied. The structure of a centralizer of an element is completely described and the problem of conjugacy of two elements is resolved. Moreover, the classification of homogeneous monomial groups are determined by using the lattice of Steinitz numbers, namely, we prove the following: Let λ and μ be two Steinitz numbers. The homogeneous monomial groups Σ_λ(H) and Σ_μ(G) are isomorphic if and only if λ = μ and H?G provided that the splittings of Σ_λ(H) and Σ_μ(G) are regular.