Initial Data for General Relativity with Toroidal Conformal Symmetry

A new class of time-symmetric solutions to the initial value constraints of vacuum General Relativity is introduced. These data are globally regular, asymptotically flat (with possibly several asymptotic ends) and in general have no isometries, but a $U(1)\times U(1)$ group of conformal isometries. After decomposing the Lichnerowicz conformal factor in a double Fourier series on the group orbits, the solutions are given in terms of a countable family of uncoupled ODEs on the orbit space.Comment: REVTEX, 9 pages, ESI Preprint 12

The Momentum Constraints of General Relativity and Spatial Conformal Isometries

Transverse-tracefree (TT-) tensors on $({\bf R}^3,g_{ab})$, with $g_{ab}$ an asymptotically flat metric of fast decay at infinity, are studied. When the source tensor from which these TT tensors are constructed has fast fall-off at infinity, TT tensors allow a multipole-type expansion. When $g_{ab}$ has no conformal Killing vectors (CKV's) it is proven that any finite but otherwise arbitrary set of moments can be realized by a suitable TT tensor. When CKV's exist there are obstructions -- certain (combinations of) moments have to vanish -- which we study.Comment: 16 page

NTRC Plays a Crucial Role in Starch Metabolism, Redox Balance, and Tomato Fruit Growth

NADPH-thioredoxin reductase C (NTRC) forms a separate thiol-reduction cascade in plastids, combining both NADPHthioredoxin reductase and thioredoxin activities on a single polypeptide. While NTRC is an important regulator of photosynthetic processes in leaves, its function in heterotrophic tissues remains unclear. Here, we focus on the role of NTRC in developing tomato (Solanum lycopersicum) fruits representing heterotrophic storage organs important for agriculture and human diet. We used a fruit-specific promoter to decrease NTRC expression by RNA interference in developing tomato fruits by 60% to 80% compared to the wild type. This led to a decrease in fruit growth, resulting in smaller and lighter fully ripe fruits containing less dry matter and more water. In immature fruits, NTRC downregulation decreased transient starch accumulation, which led to a subsequent decrease in soluble sugars in ripe fruits. The inhibition of starch synthesis was associated with a decrease in the redox-activation state of ADP-Glc pyrophosphorylase and soluble starch synthase, which catalyze the first committed and final polymerizing steps, respectively, of starch biosynthesis. This was accompanied by a decrease in the level of ADP-Glc. NTRC downregulation also led to a strong increase in the reductive states of NAD(H) and NADP(H) redox systems. Metabolite profiling of NTRC-RNA interference lines revealed increased organic and amino acid levels, but reduced sugar levels, implying that NTRC regulates the osmotic balance of developing fruits. These results indicate that NTRC acts as a central hub in regulating carbon metabolism and redox balance in heterotrophic tomato fruits, affecting fruit development as well as final fruit size and qualit

Dynamics of a Brownian circle swimmer

Self-propelled particles move along circles rather than along a straight line when their driving force does not coincide with their propagation direction. Examples include confined bacteria and spermatozoa, catalytically driven nanorods, active, anisotropic colloidal particles and vibrated granulates. Using a non-Hamiltonian rate theory and computer simulations, we study the motion of a Brownian "circle swimmer" in a confining channel. A sliding mode close to the wall leads to a huge acceleration as compared to the bulk motion, which can further be enhanced by an optimal effective torque-to-force ratio.Comment: v2: changed title from "The fate of a Brownian circle swimmer"; mainly changes of introduction and conclusion

Antisense Suppression of the Small Chloroplast Protein CP12 in Tobacco Alters Carbon Partitioning and Severely Restricts Growth

Abstract The thioredoxin-regulated chloroplast protein CP12 forms a multienzyme complex with the Calvin-Benson cycle enzymes phosphoribulokinase (PRK) and glyceraldehyde-3-phosphate dehydrogenase (GAPDH). PRK and GAPDH are inactivated when present in this complex, a process shown in vitro to be dependent upon oxidized CP12. The importance of CP12 in vivo in higher plants, however, has not been investigated. Here, antisense suppression of CP12 in tobacco (Nicotiana tabacum) was observed to impact on NAD-induced PRK and GAPDH complex formation but had little effect on enzyme activity. Additionally, only minor changes in photosynthetic carbon fixation were observed. Despite this, antisense plants displayed changes in growth rates and morphology, including dwarfism and reduced apical dominance. The hypothesis that CP12 is essential to separate oxidative pentose phosphate pathway activity from Calvin-Benson cycle activity, as proposed in cyanobacteria, was tested. No evidence was found to support this role in tobacco. Evidence was seen, however, for a restriction to malate valve capacity, with decreases in NADP-malate dehydrogenase activity (but not protein levels) and pyridine nucleotide content. Antisense repression of CP12 also led to significant changes in carbon partitioning, with increased carbon allocation to the cell wall and the organic acids malate and fumarate and decreased allocation to starch and soluble carbohydrates. Severe decreases were also seen in 2-oxoglutarate content, a key indicator of cellular carbon sufficiency. The data presented here indicate that in tobacco, CP12 has a role in redox-mediated regulation of carbon partitioning from the chloroplast and provides strong in vivo evidence that CP12 is required for normal growth and development in plants.</jats:p

Conformally Einstein Products and Nearly K\"ahler Manifolds

In the first part of this note we study compact Riemannian manifolds (M,g) whose Riemannian product with R is conformally Einstein. We then consider compact 6--dimensional almost Hermitian manifolds of type W_1+W_4 in the Gray--Hervella classification admitting a parallel vector field and show that (under some regularity assumption) they are obtained as mapping tori of isometries of compact Sasaki-Einstein 5-dimensional manifolds. In particular, we obtain examples of inhomogeneous locally (non-globally) conformal nearly K\"ahler compact manifolds

Brevianes Revisited

Breviones are a new family of secondary metabolites that were originally isolated from the New Zealand endemic fungus Penicillium brevicompactum var. Dierckx. These compounds are generally characterized by a new carbon skeleton, known as breviane, which that has three possible structural variations, such as breviane, abeo-breviane, and abeo-norbreviane. Brevianes present a basic diterpenic tricyclic core that is mevalonic in origin and is similar to that of perhydrophenanthrene. The core bears four methyl groups at positions C4, C8, C10, and C13 and has defined stereochemistry at positions C5, C8, C9, C10, and C14. The C1'-C7' side chain has been proposed to have a polyketide biosynthetic origin and is joined to the diterpenic moiety through carbons C2'-C15'. The cyclization and lactonization of this part of the molecule leads to the characteristic breviane spiranic ring fused to the α-pyrone

Investigation of continuous-time quantum walk by using Krylov subspace-Lanczos algorithm

In papers\cite{js,jsa}, the amplitudes of continuous-time quantum walk on graphs possessing quantum decomposition (QD graphs) have been calculated by a new method based on spectral distribution associated to their adjacency matrix. Here in this paper, it is shown that the continuous-time quantum walk on any arbitrary graph can be investigated by spectral distribution method, simply by using Krylov subspace-Lanczos algorithm to generate orthonormal bases of Hilbert space of quantum walk isomorphic to orthogonal polynomials. Also new type of graphs possessing generalized quantum decomposition have been introduced, where this is achieved simply by relaxing some of the constrains imposed on QD graphs and it is shown that both in QD and GQD graphs, the unit vectors of strata are identical with the orthonormal basis produced by Lanczos algorithm. Moreover, it is shown that probability amplitude of observing walk at a given vertex is proportional to its coefficient in the corresponding unit vector of its stratum, and it can be written in terms of the amplitude of its stratum. Finally the capability of Lanczos-based algorithm for evaluation of walk on arbitrary graphs (GQD or non-QD types), has been tested by calculating the probability amplitudes of quantum walk on some interesting finite (infinite) graph of GQD type and finite (infinite) path graph of non-GQD type, where the asymptotic behavior of the probability amplitudes at infinite limit of number of vertices, are in agreement with those of central limit theorem of Ref.\cite{nko}.Comment: 29 pages, 4 figure

Wigner formula of rotation matrices and quantum walks

Quantization of a random-walk model is performed by giving a qudit (a multi-component wave function) to a walker at site and by introducing a quantum coin, which is a matrix representation of a unitary transformation. In quantum walks, the qudit of walker is mixed according to the quantum coin at each time step, when the walker hops to other sites. As special cases of the quantum walks driven by high-dimensional quantum coins generally studied by Brun, Carteret, and Ambainis, we study the models obtained by choosing rotation as the unitary transformation, whose matrix representations determine quantum coins. We show that Wigner's $(2j+1)$-dimensional unitary representations of rotations with half-integers $j$'s are useful to analyze the probability laws of quantum walks. For any value of half-integer $j$, convergence of all moments of walker's pseudovelocity in the long-time limit is proved. It is generally shown for the present models that, if $(2j+1)$ is even, the probability measure of limit distribution is given by a superposition of $(2j+1)/2$ terms of scaled Konno's density functions, and if $(2j+1)$ is odd, it is a superposition of $j$ terms of scaled Konno's density functions and a Dirac's delta function at the origin. For the two-, three-, and four-component models, the probability densities of limit distributions are explicitly calculated and their dependence on the parameters of quantum coins and on the initial qudit of walker is completely determined. Comparison with computer simulation results is also shown.Comment: v2: REVTeX4, 15 pages, 4 figure

Starch Granule Re-Structuring by Starch Branching Enzyme and Glucan Water Dikinase Modulation Affects Caryopsis Physiology and Metabolism

Starch is of fundamental importance for plant development and reproduction and its optimized molecular assembly is potentially necessary for correct starch metabolism. Re-structuring of starch granules in-planta can therefore potentially affect plant metabolism. Modulation of granule micro-structure was achieved by decreasing starch branching and increasing starch-bound phosphate content in the barley caryopsis starch by RNAi suppression of all three Starch Branching Enzyme (SBE) isoforms or overexpression of potato Glucan Water Dikinase (GWD). The resulting lines displayed Amylose-Only (AO) and Hyper-Phosphorylated (HP) starch chemotypes, respectively. We studied the influence of these alterations on primary metabolism, grain composition, starch structural features and starch granule morphology over caryopsis development at 10, 20 and 30 days after pollination (DAP) and at grain maturity. While HP showed relatively little effect, AO showed significant reduction in starch accumulation with re-direction to protein and β-glucan (BG) accumulation. Metabolite profiling indicated significantly higher sugar accumulation in AO, with re-partitioning of carbon to accumulate amino acids, and interestingly it also had high levels of some important stress-related metabolites and potentially protective metabolites, possibly to elude deleterious effects. Investigations on starch molecular structure revealed significant increase in starch phosphate and amylose content in HP and AO respectively with obvious differences in starch granule morphology at maturity. The results demonstrate that decreasing the storage starch branching resulted in metabolic adjustments and re-directions, tuning to evade deleterious effects on caryopsis physiology and plant performance while only little effect was evident by increasing starch-bound phosphate as a result of overexpressing GWD