Generalized twisted modules associated to general automorphisms of a vertex operator algebra

We introduce a notion of strongly C^{\times}-graded, or equivalently, C/Z-graded generalized g-twisted V-module associated to an automorphism g, not necessarily of finite order, of a vertex operator algebra. We also introduce a notion of strongly C-graded generalized g-twisted V-module if V admits an additional C-grading compatible with g. Let V=\coprod_{n\in \Z}V_{(n)} be a vertex operator algebra such that V_{(0)}=\C\one and V_{(n)}=0 for n<0 and let u be an element of V of weight 1 such that L(1)u=0. Then the exponential of 2\pi \sqrt{-1} Res_{x} Y(u, x) is an automorphism g_{u} of V. In this case, a strongly C-graded generalized g_{u}-twisted V-module is constructed from a strongly C-graded generalized V-module with a compatible action of g_{u} by modifying the vertex operator map for the generalized V-module using the exponential of the negative-power part of the vertex operator Y(u, x). In particular, we give examples of such generalized twisted modules associated to the exponentials of some screening operators on certain vertex operator algebras related to the triplet W-algebras. An important feature is that we have to work with generalized (twisted) V-modules which are doubly graded by the group C/Z or C and by generalized eigenspaces (not just eigenspaces) for L(0), and the twisted vertex operators in general involve the logarithm of the formal variable.Comment: Final version to appear in Comm. Math. Phys. 38 pages. References on triplet W-algebras added, misprints corrected, and expositions revise

The role of strigolactones in P deficiency induced transcriptional changes in tomato roots

BACKGROUND: Phosphorus (P) is an essential macronutrient for plant growth and development. Upon P shortage, plant responds with massive reprogramming of transcription, the Phosphate Starvation Response (PSR). In parallel, the production of strigolactones (SLs)—a class of plant hormones that regulates plant development and rhizosphere signaling molecules—increases. It is unclear, however, what the functional link is between these two processes. In this study, using tomato as a model, RNAseq was used to evaluate the time-resolved changes in gene expression in the roots upon P starvation and, using a tomato CAROTENOID CLEAVAGE DIOXYGENASES 8 (CCD8) RNAi line, what the role of SLs is in this. RESULTS: Gene ontology (GO)-term enrichment and KEGG analysis of the genes regulated by P starvation and P replenishment revealed that metabolism is an important component of the P starvation response that is aimed at P homeostasis, with large changes occurring in glyco-and galactolipid and carbohydrate metabolism, biosynthesis of secondary metabolites, including terpenoids and polyketides, glycan biosynthesis and metabolism, and amino acid metabolism. In the CCD8 RNAi line about 96% of the PSR genes was less affected than in wild-type (WT) tomato. For example, phospholipid biosynthesis was suppressed by P starvation, while the degradation of phospholipids and biosynthesis of substitute lipids such as sulfolipids and galactolipids were induced by P starvation. Around two thirds of the corresponding transcriptional changes depend on the presence of SLs. Other biosynthesis pathways are also reprogrammed under P starvation, such as phenylpropanoid and carotenoid biosynthesis, pantothenate and CoA, lysine and alkaloids, and this also partially depends on SLs. Additionally, some plant hormone biosynthetic pathways were affected by P starvation and also here, SLs are required for many of the changes (more than two thirds for Gibberellins and around one third for Abscisic acid) in the gene expression. CONCLUSIONS: Our analysis shows that SLs are not just the end product of the PSR in plants (the signals secreted by plants into the rhizosphere), but also play a major role in the regulation of the PSR (as plant hormone). SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12870-021-03124-0

First long-term study of particle number size distributions and new particle formation events of regional aerosol in the North China Plain

Atmospheric particle number size distributions (size range 0.003–10 μm) were measured between March 2008 and August 2009 at Shangdianzi (SDZ), a rural research station in the North China Plain. These measurements were made in an attempt to better characterize the tropospheric background aerosol in Northern China. The mean particle number concentrations of the total particle, as well as the nucleation, Aitken, accumulation and coarse mode were determined to be 1.2 ± 0.9 × 104, 3.6 ± 7.9 × 103, 4.4 ± 3.4 × 103, 3.5 ± 2.8 × 103 and 2 ± 3 cm−3, respectively. A general finding was that the particle number concentration was higher during spring compared to the other seasons. The air mass origin had an important effect on the particle number concentration and new particle formation events. Air masses from northwest (i.e. inner Asia) favored the new particle formation events, while air masses from southeast showed the highest particle mass concentration. Significant diurnal variations in particle number were observed, which could be linked to new particle formation events, i.e. gas-to-particle conversion. During particle formation events, the number concentration of the nucleation mode rose up to maximum value of 104 cm−3. New particle formation events were observed on 36% of the effective measurement days. The formation rate ranged from 0.7 to 72.7 cm−3 s−1, with a mean value of 8.0 cm−3 s−1. The value of the nucleation mode growth rate was in the range of 0.3–14.5 nm h−1, with a mean value of 4.3 nm h−1. It was an essential observation that on many occasions the nucleation mode was able to grow into the size of cloud condensation nuclei (CCN) within a matter of several hours. Furthermore, the new particle formation was regularly followed by a measurable increase in particle mass concentration and extinction coefficient, indicative of a high abundance of condensable vapors in the atmosphere under study

The tomato cytochrome P450 CYP712G1 catalyzes the double oxidation of orobanchol <i>en route</i> to the rhizosphere signaling strigolactone, solanacol

Strigolactones (SLs) are rhizosphere signalling molecules and phytohormones. The biosynthetic pathway of SLs in tomato has been partially elucidated, but the structural diversity in tomato SLs predicts that additional biosynthetic steps are required. Here, root RNA-seq data and co-expression analysis were used for SL biosynthetic gene discovery. This strategy resulted in a candidate gene list containing several cytochrome P450s. Heterologous expression in Nicotiana benthamiana and yeast showed that one of these, CYP712G1, can catalyse the double oxidation of orobanchol, resulting in the formation of three didehydro-orobanchol (DDH) isomers. Virus-induced gene silencing and heterologous expression in yeast showed that one of these DDH isomers is converted to solanacol, one of the most abundant SLs in tomato root exudate. Protein modelling and substrate docking analysis suggest that hydroxy-orbanchol is the likely intermediate in the conversion from orobanchol to the DDH isomers. Phylogenetic analysis demonstrated the occurrence of CYP712G1 homologues in the Eudicots only, which fits with the reports on DDH isomers in that clade. Protein modelling and orobanchol docking of the putative tobacco CYP712G1 homologue suggest that it can convert orobanchol to similar DDH isomers as tomato

Dynamic Ordering and Transverse Depinning of a Driven Elastic String in a Disordered Media

We examine the dynamics of an elastic string interacting with quenched disorder driven perpendicular and parallel to the string. We show that the string is the most disordered at the depinning transition but with increasing drive partial ordering is regained. For low drives the noise power is high and we observe a 1/f^2 noise signature crossing over to a white noise character with low power at higher drives. For the parallel driven moving string there is a finite transverse critical depinning force with the depinning transition occuring by the formation of running kinks.Comment: 4 pages, 4 postscript figure

Azimuthal anisotropy and correlations in p+p, d+Au and Au+Au collisions at 200 GeV

We present the first measurement of directed flow ($v_1$) at RHIC. $v_1$ is found to be consistent with zero at pseudorapidities $\eta$ from -1.2 to 1.2, then rises to the level of a couple of percent over the range $2.4 < |\eta| < 4$. The latter observation is similar to data from NA49 if the SPS rapidities are shifted by the difference in beam rapidity between RHIC and SPS. Back-to-back jets emitted out-of-plane are found to be suppressed more if compared to those emitted in-plane, which is consistent with {\it jet quenching}. Using the scalar product method, we systematically compared azimuthal correlations from p+p, d+Au and Au+Au collisions. Flow and non-flow from these three different collision systems are discussed.Comment: Quark Matter 2004 proceeding, 4 pages, 3 figure

Azimuthal anisotropy: the higher harmonics

We report the first observations of the fourth harmonic (v_4) in the azimuthal distribution of particles at RHIC. The measurement was done taking advantage of the large elliptic flow generated at RHIC. The integrated v_4 is about a factor of 10 smaller than v_2. For the sixth (v_6) and eighth (v_8) harmonics upper limits on the magnitudes are reported.Comment: 4 pages, 6 figures, contribution to the Quark Matter 2004 proceeding

Plasma Wakefield Acceleration with a Modulated Proton Bunch

The plasma wakefield amplitudes which could be achieved via the modulation of a long proton bunch are investigated. We find that in the limit of long bunches compared to the plasma wavelength, the strength of the accelerating fields is directly proportional to the number of particles in the drive bunch and inversely proportional to the square of the transverse bunch size. The scaling laws were tested and verified in detailed simulations using parameters of existing proton accelerators, and large electric fields were achieved, reaching 1 GV/m for LHC bunches. Energy gains for test electrons beyond 6 TeV were found in this case.Comment: 9 pages, 7 figure

The energy dependence of ptp_t angular correlations inferred from mean-ptp_{t} fluctuation scale dependence in heavy ion collisions at the SPS and RHIC

We present the first study of the energy dependence of $p_t$ angular correlations inferred from event-wise mean transverse momentum fluctuations in heavy ion collisions. We compare our large-acceptance measurements at CM energies $\sqrt{s_{NN}} =$ 19.6, 62.4, 130 and 200 GeV to SPS measurements at 12.3 and 17.3 GeV. $p_t$ angular correlation structure suggests that the principal source of $p_t$ correlations and fluctuations is minijets (minimum-bias parton fragments). We observe a dramatic increase in correlations and fluctuations from SPS to RHIC energies, increasing linearly with $\ln \sqrt{s_{NN}}$ from the onset of observable jet-related fluctuations near 10 GeV.Comment: 10 pages, 4 figure

All-optical switching and strong coupling using tunable whispering-gallery-mode microresonators

We review our recent work on tunable, ultrahigh quality factor whispering-gallery-mode bottle microresonators and highlight their applications in nonlinear optics and in quantum optics experiments. Our resonators combine ultra-high quality factors of up to Q = 3.6 \times 10^8, a small mode volume, and near-lossless fiber coupling, with a simple and customizable mode structure enabling full tunability. We study, theoretically and experimentally, nonlinear all-optical switching via the Kerr effect when the resonator is operated in an add-drop configuration. This allows us to optically route a single-wavelength cw optical signal between two fiber ports with high efficiency. Finally, we report on progress towards strong coupling of single rubidium atoms to an ultra-high Q mode of an actively stabilized bottle microresonator.Comment: 20 pages, 24 figures. Accepted for publication in Applied Physics B. Changes according to referee suggestions: minor corrections to some figures and captions, clarification of some points in the text, added references, added new paragraph with results on atom-resonator interactio