Asymptotic scaling symmetries for nonlinear PDEs

In some cases, solutions to nonlinear PDEs happen to be asymptotically (for large $x$ and/or $t$) invariant under a group $G$ which is not a symmetry of the equation. After recalling the geometrical meaning of symmetries of differential equations -- and solution-preserving maps -- we provide a precise definition of asymptotic symmetries of PDEs; we deal in particular, for ease of discussion and physical relevance, with scaling and translation symmetries of scalar equations. We apply the general discussion to a class of ``Richardson-like'' anomalous diffusion and reaction-diffusion equations, whose solution are known by numerical experiments to be asymptotically scale invariant; we obtain an analytical explanation of the numerically observed asymptotic scaling properties. We also apply our method to a different class of anomalous diffusion equations, relevant in optical lattices. The methods developed here can be applied to more general equations, as clear by their geometrical construction

Asymptotic scaling in a model class of anomalous reaction-diffusion equations

We analyze asymptotic scaling properties of a model class of anomalous reaction-diffusion (ARD) equations. Numerical experiments show that solutions to these have, for large $t$, well defined scaling properties. We suggest a general framework to analyze asymptotic symmetry properties; this provides an analytical explanation of the observed asymptotic scaling properties for the considered ARD equations.Comment: To appear in J. Nonlin. Math. Phy

Asymptotic symmetries of difference equations on a lattice

It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In this note we extend the approach to asymptotic symmetries for the analysis of PDEs, to the case of difference equations

Penguin Mediated B Decays at BABAR

We report on preliminary results of searches for penguin mediated B decays based on 20.7 fb^{-1} of data collected at the Y(4S) peak with the BABAR detector at PEP-II. The following branching fractions have been measured: BR(B+ --> phi K+) = (7.7^{+1.6}_{-1.4} +- 0.8)*10^{-6}, BR(B0 --> phi K0) = (8.1^{+3.1}_{-2.5} +- 0.8)*10^{-6}, BR(B+ --> phi K*+) = (9.7^{+4.2}_{-3.4} +- 1.7)*10^{-6}, BR(B0 --> phi K*0) = (8.7^{+2.5}_{-2.1} +- 1.1)*10^{-6}, BR(B+--> omega pi+) = (6.6^{+2.1}_{-1.8} +- 0.7)*10^{-6}, BR(B --> eta K^*0) = (19.8^{+6.5}_{-5.6} +-1.7)*10^{-6}, where the first error is statistical and the second systematic. For several other modes we report upper limits on their branching fractions; for example for the following flavor-changing neutral current decays, BR(B--> K l+ l-) K* l+ l-) < 2.5*10^{-6}, at 90% Confidence Level (C.L.)

Cell-free prediction of protein expression costs for growing cells

Translating heterologous proteins places significant burden on host cells, consuming expression resources leading to slower cell growth and productivity. Yet predicting the cost of protein production for any given gene is a major challenge, as multiple processes and factors combine to determine translation efficiency. To enable prediction of the cost of gene expression in bacteria, we describe here a standard cell-free lysate assay that provides a relative measure of resource consumption when a protein coding sequence is expressed. These lysate measurements can then be used with a computational model of translation to predict the in vivo burden placed on growing E. coli cells for a variety of proteins of different functions and lengths. Using this approach, we can predict the burden of expressing multigene operons of different designs and differentiate between the fraction of burden related to gene expression compared to action of a metabolic pathway

High frequency electro-optic measurement of strained silicon racetrack resonators

The observation of the electro-optic effect in strained silicon waveguides has been considered as a direct manifestation of an induced $\chi^{(2)}$ non-linearity in the material. In this work, we perform high frequency measurements on strained silicon racetrack resonators. Strain is controlled by a mechanical deformation of the waveguide. It is shown that any optical modulation vanishes independently of the applied strain when the applied voltage varies much faster than the carrier effective lifetime, and that the DC modulation is also largely independent of the applied strain. This demonstrates that plasma carrier dispersion is responsible for the observed electro-optic effect. After normalizing out free carrier effects, our results set an upper limit of $8\,pm/V$ to the induced high-speed $\chi^{(2)}_{eff,zzz}$ tensor element at an applied stress of $-0.5\,GPa$. This upper limit is about one order of magnitude lower than the previously reported values for static electro-optic measurements

H3 histamine receptor-mediated activation of protein kinase calpha inhibits the growth of cholangiocarcinoma in vitro and in vivo

Histamine regulates functions via four receptors (HRH1, HRH2, HRH3, and HRH4). The D-myo-inositol 1,4,5-trisphosphate (IP(3))/Ca(2+)/protein kinase C (PKC)/mitogen-activated protein kinase pathway regulates cholangiocarcinoma growth. We evaluated the role of HRH3 in the regulation of cholangiocarcinoma growth. Expression of HRH3 in intrahepatic and extrahepatic cell lines, normal cholangiocytes, and human tissue arrays was measured. In Mz-ChA-1 cells stimulated with (R)-(alpha)-(-)-methylhistamine dihydrobromide (RAMH), we measured (a) cell growth, (b) IP(3) and cyclic AMP levels, and (c) phosphorylation of PKC and mitogen-activated protein kinase isoforms. Localization of PKC alpha was visualized by immunofluorescence in cell smears and immunoblotting for PKC alpha in cytosol and membrane fractions. Following knockdown of PKC alpha, Mz-ChA-1 cells were stimulated with RAMH before evaluating cell growth and extracellular signal-regulated kinase (ERK)-1/2 phosphorylation. In vivo experiments were done in BALB/c nude mice. Mice were treated with saline or RAMH for 44 days and tumor volume was measured. Tumors were excised and evaluated for proliferation, apoptosis, and expression of PKC alpha, vascular endothelial growth factor (VEGF)-A, VEGF-C, VEGF receptor 2, and VEGF receptor 3. HRH3 expression was found in all cells. RAMH inhibited the growth of cholangiocarcinoma cells. RAMH increased IP(3) levels and PKC alpha phosphorylation and decreased ERK1/2 phosphorylation. RAMH induced a shift in the localization of PKC alpha expression from the cytosolic domain into the membrane region of Mz-ChA-1 cells. Silencing of PKC alpha prevented RAMH inhibition of Mz-ChA-1 cell growth and ablated RAMH effects on ERK1/2 phosphorylation. In vivo, RAMH decreased tumor growth and expression of VEGF and its receptors; PKC alpha expression was increased. RAMH inhibits cholangiocarcinoma growth by PKC alpha-dependent ERK1/2 dephosphorylation. Modulation of PKC alpha by histamine receptors may be important in regulating cholangiocarcinoma growth. (Mol Cancer Res 2009;7(10):1704-13

Recent advances on the mechanisms regulating cholangiocyte proliferation and the significance of the neuroendocrine regulation of cholangiocyte pathophysiology

Cholangiocytes are epithelial cells lining the biliary epithelium. Cholangiocytes play several key roles in the modification of ductal bile and are also the target cells in chronic cholestatic liver diseases (i.e., cholangiopathies) such as PSC, PBC, polycystic liver disease (PCLD) and cholangiocarcinoma (CCA). During these pathologies, cholangiocytes (which in normal condition are in a quiescent state) begin to proliferate acquiring phenotypes of neuroendocrine cells, and start secreting different cytokines, growth factors, neuropeptides, and hormones to modulate cholangiocytes proliferation and interaction with the surrounding environment, trying to reestablish the balance between proliferation/loss of cholangiocytes for the maintenance of biliary homeostasis. The purpose of this review is to summarize the recent findings on the mechanisms regulating cholangiocyte proliferation and the significance of the neuroendocrine regulation of cholangiocyte pathophysiology. To clarify the mechanisms of action of these factors we will provide new potential strategies for the management of chronic liver diseases

The Antarctic dry valley lakes: Relevance to Mars

The similarity of the early environments of Mars and Earth, and the biological evolution which occurred on early Earth, motivates exobiologists to seriously consider the possiblity of an early Martian biota. Environments are being identified which could contain Martian life and areas which may presently contain evidence of this former life. Sediments which were thought to be deposited in large ice-covered lakes are present on Mars. Such localities were identified within some of the canyons of the Valles Marineris and more recently in the ancient terrain in the Southern Hemisphere. Perennially ice-covered Antarctic lakes are being studied in order to develop quantitative models that relate environmental factors to the nature of the biological community and sediment forming processes. These models will be applied to the Martian paleolakes to establish the scientific rationale for the exobiological study of ancient Martian sediments