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 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 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.)

The influence of allochthonous leaf detritus on the occurrence of crustacean detritivores in the soft-bottom macrobenthos of the Po River delta area (northwestern Adriatic Sea)

Core samples were examined quarterly at two coastal sites (S1 and S2) and at an offshore station (S3) located in the Po River delta area (northwestern Adriatic Sea). Analyses focused on (i) occurrence of coarse detritus of allochthonous origin in the sedimentary matrix and (ii) the relative influence of macrodetritus enrichment and other environmental factors on the vagile macrofauna. Plant debris occurred in site S1 sediments only in summer and autumn, in contrast, fragments of the phanerogams Cymodocea nodosa and Zostera spp. were found in site S2 sediment throughout the sampling period. Sediments from the offshore site S3 were characterized by negligible plant material, even though in summer and autumn samples debris of continental origin was observed. Even though leaf detritus occurrence at site S2 was similar to5-fold higher compared to the other coastal site S1, it did not influence the total organic matter and its distribution among grain-size classes. Conversely, the specific organic content of dimensional fractions provided an effective assessment of detritus enrichment processes occurring at the two coastal sites. A group of brackish-originated crustaceans (i.e. the amphipods Gammarus insensibilis and G. aequicauda and the isopod Idotea baltica) was the main determinant of among-site multivariate differences in the vagile macrofauna; depositivorous ophiuroids accounted for the residual differences observed during the study period. The analysis of taxa abundance and individual body size indicated that in both site S1 and S3 macrodetritus advection to the benthic system corresponded with passive dispersal of brackish crustaceans, that provided a negligible contribution to the macrobenthic production. In contrast, in site S2 allochthonous inputs from marginal environments could have represented the key factor for the persistence of an authochthonous population of Gammarus insensibilis. The amphipod provided a considerable (19.4%) contribution to the total macrobenthic production of the site, dominated by filter-feeding bivalves and tubicolous deposit feeders. The potential effects of detritivorous crustaceans on soft-bottom macrobenthic assemblages of the northern Adriatic Sea are discussed. (C) 2002 Elsevier Science Ltd. All rights reserved

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

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

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

Carbon budget and national gross domestic product in the framework of the Paris Climate Agreement

In 2015 an unprecedented effort was made in Paris by the countries adhering to the United Nations Framework Convention on Climate Change to decrease the CO2 emissions due to the close relationships of greenhouse gases with global warming. Under the previous Kyoto Protocol, only advanced countries were committed to reduce greenhouse emissions while under the Paris Climate Agreement all countries were committed to fight against global warming. The urgency of real action has been prompted by extreme events like bushfires, heatwaves, and the ongoing pandemic. Given the strong commitments, it looks interesting, seen that all countries are involved, to verify if any sustainability pattern is evident. Our approach is encouraging, as the downward emission trend shows a high increase in sustainability between 2027 and 2037. Without exacerbating the climate discussion, we used the national gross domestic product (hereafter: GDP) as environmental indicator to propose for the first time an allometric ranking of countries that need to change drastically their energy policy to meet their climate commitments. Any sustainability downturn in one country, especially if advanced, might rationally bring concern about the actual prospects of other countries which are all committed to the Paris Climate Agreement. But the departure from the annual allometric model GDP−CO2 may be much greater than can be accounted for by statistical expectations, as for Ukraine, Uzbekistan and Turkmenistan that are entering a sustainable condition where their CO2 emissions will be lower than they would have been without the Paris Climate Agreement