The puzzles in B→ππB\to \pi\pi and πK \pi K decays: possible implications for R-parity violating supersymmetry

Recent experiments suggest that certain data of $B \to \pi\pi,\pi K$ decays are inconsistent with the standard model expectations. We try to explain the discrepancies with R-parity violating suppersymmetry. By employing the QCD factorization approach, we study these decays in the minimal supersymmetric standard model with R-parity violation. We show that R-parity violation can resolve the discrepancies in both $B \to \pi\pi$ and $B \to \pi K$ decays, and find that in some regions of parameter spaces all these requirements, including the CP averaged branching ratios and the direct CP asymmetries, can be satisfied. Furthermore, we have derived stringent bounds on relevant R-parity violating couplings from the latest experimental data, and some of these constraints are stronger than the existing bounds.Comment: 24 pages, 6 figures and 5 tables. Text revised. Final version to appear in PR

An entropic uncertainty principle for positive operator valued measures

Extending a recent result by Frank and Lieb, we show an entropic uncertainty principle for mixed states in a Hilbert space relatively to pairs of positive operator valued measures that are independent in some sense. This yields spatial-spectral uncertainty principles and log-Sobolev inequalities for invariant operators on homogeneous spaces, which are sharp in the compact case.Comment: 14 pages. v2: a technical assumption removed in main resul

Polarizations in decays B_{u,d}\to VV and possible implications for R-parity violating SUSY

Recently BABAR and Belle have measured anomalous large transverse polarizations in some pure penguin $B \to VV$ decays, which might be inconsistent with the Standard Model expectations. We try to explore its implications for R-parity violating (RPV) supersymmetry. The QCD factorization approach is employed for the hadronic dynamics of B decays. We find that it is possible to have parameter spaces solving the anomaly. Furthermore, we have derived stringent bounds on relevant RPV couplings from the experimental data, which is useful for further studies of RPV phenomena.Comment: 26 pages, 12 eps figures. Typos corrected and references added. Final version to appear in PR

Curvature-dimension inequalities and Li-Yau inequalities in sub-Riemannian spaces

In this paper we present a survey of the joint program with Fabrice Baudoin originated with the paper \cite{BG1}, and continued with the works \cite{BG2}, \cite{BBG}, \cite{BG3} and \cite{BBGM}, joint with Baudoin, Michel Bonnefont and Isidro Munive.Comment: arXiv admin note: substantial text overlap with arXiv:1101.359

The subelliptic heat kernel on SU(2): Representations, Asymptotics and Gradient bounds

The Lie group SU(2) endowed with its canonical subriemannian structure appears as a three-dimensional model of a positively curved subelliptic space. The goal of this work is to study the subelliptic heat kernel on it and some related functional inequalities.Comment: Update: Added section + Correction of typo

First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-hermitian manifolds

We calculate the first and the second variation formula for the sub-Riemannian area in three dimensional pseudo-hermitian manifolds. We consider general variations that can move the singular set of a C^2 surface and non-singular variation for C_H^2 surfaces. These formulas enable us to construct a stability operator for non-singular C^2 surfaces and another one for C2 (eventually singular) surfaces. Then we can obtain a necessary condition for the stability of a non-singular surface in a pseudo-hermitian 3-manifold in term of the pseudo-hermitian torsion and the Webster scalar curvature. Finally we classify complete stable surfaces in the roto-traslation group RT .Comment: 36 pages. Misprints corrected. Statement of Proposition 9.8 slightly changed and Remark 9.9 adde

Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds

Measure contraction property is one of the possible generalizations of Ricci curvature bound to more general metric measure spaces. In this paper, we discover sufficient conditions for a three dimensional contact subriemannian manifold to satisfy this property.Comment: 49 page

Proteomic study uncovers molecular principles of single-cell-level phenotypic heterogeneity in lipid storage of Nannochloropsis oceanica

Abstract Background Nannochloropsis oceanica belongs to a large group of photoautotrophic eukaryotic organisms that play important roles in fixation and cycling of atmospheric CO2. Its capability of storing solar energy and carbon dioxide in the form of triacylglycerol (TAG) of up to 60% of total weight under nitrogen deprivation stress sparked interest in its use for biofuel production. Phenotypes varying in lipid accumulation among an N. oceanica population can be disclosed by single-cell analysis/sorting using fluorescence-activated cell sorting (FACS); yet the phenomenon of single cell heterogeneity in an algae population remains to be fully understood at the molecular level. In this study, combination of FACS and proteomics was used for identification, quantification and differentiation of these heterogeneities on the molecular level. Results For N. oceanica cultivated under nitrogen deplete (−N) and replete (+N) conditions, two groups differing in lipid content were distinguished. These differentiations could be recognized on the population as well as the single-cell levels; proteomics uncovered alterations in carbon fixation and flux, photosynthetic machinery, lipid storage and turnover in the populations. Although heterogeneity patterns have been affected by nitrogen supply and cultivation conditions of the N. oceanica populations, differentiation itself seems to be very robust against these factors: cultivation under +N, −N, in shaker bottles, and in a photo-bioreactor all split into two subpopulations. Intriguingly, population heterogeneity resumed after subpopulations were separately recultivated for a second round, refuting the possible development of genetic heterogeneity in the course of sorting and cultivation. Conclusions This work illustrates for the first time the feasibility of combining FACS and (prote)-omics for mechanistic understanding of phenotypic heterogeneity in lipid-producing microalgae. Such combinatorial method can facilitate molecular breeding and design of bioprocesses