Coorbits for projective representations with an application to Bergman spaces

Recently representation theory has been used to provide atomic decompositions for a large collection of classical Banach spaces. In this paper we extend the techniques to also include projective representations. As our main application we obtain atomic decompositions of Bergman spaces on the unit ball through the holomorphic discrete series for the group of isometries of the ball

The physics and kinematics of the evolved, interacting planetary nebula PN G342.0-01.7

Here we aim to study the physical and kinematical characteristics of the unstudied old planetary nebula (PN) PN G342.0-01.7, which shows evidence of interaction with its surrounding interstellar medium. We used Integral Field Spectra from the Wide Field Spectrograph on the ANU 2.3 m telescope to provide spectroscopy across the whole object covering the spectral range 3400-7000 {\AA}. We formed narrow-band images to investigate the excitation structure. The spectral analysis shows that the object is a distant Peimbert Type I PN of low excitation, formally of excitation class of 0.5. The low electron density, high dynamical age, and low surface brightness of the object confirm that it is observed fairly late in its evolution. It shows clear evidence for dredge-up of CN-processed material characteristic of its class. In addition, the low peculiar velocity of 7 km s$^{-1}$ shows it to be a member of the young disk component of our Galaxy. We built a self-consistent photoionisation model for the PNe matching the observed spectrum, the H$\beta$ luminosity, and the diameter. On the basis of this we derive an effective temperature $\log T_{\rm eff} \sim 5.05$ and luminosity $1.85 < \log L < 2.25$. The temperature is much higher than might have been expected using the excitation class, proving that this can be misleading in classifying evolved PNe. PN G342.0-01.7 is in interaction with its surrounding interstellar medium through which the object is moving in the south-west direction. This interaction drives a slow shock into the outer PN ejecta. A shock model suggests that it only accounts for about 10\% of the total luminosity, but has an important effect on the global spectrum of the PN.Comment: 15 pages, 6 figures, A&A accepted 201

A dynamic model for the evolution of protein structure

Protein domains are three-dimensional arrangements of atomic structure that are recurrent in the proteomes of organisms. Since the three-dimensional structure of a protein determines its function, it is the fold, much more than the underlying protein sequence and underlying chemistry, that is evolutionarily conserved. We are interested in probing the history of life with these domain structures and glimpsing qualitative changes over time by studying a dynamic model of protein evolution. Using standard phylogenetic methods and a census of protein domain structure in hundreds of genomes, we have reconstructed phylogenetic trees of protein domains, defined using the Structural Classification of Proteins (SCOP), where the nodes are folds or fold superfamilies (FSFs), the character vector for each node is a list of abundances of said fold or FSF across a range of species that spans all three superkingdoms of life, and the character states are linearly polarized by abundance; higher abundance within and among species equates to older structures and determines tree structure. Here we explore at what rate fold or FSF variants and new folds or FSFs appear in evolution. We also explore what collective model of proteome evolution explains such rates. Briefly, what are the dynamics of change? A set of birth-death differential equations was selected to capture the change of interest, with one set for folds and another for FSFs. The models assume that at any given moment there are a certain number of different folds or FSFs, with various abundances, and as each fold or FSF diversifies there are slight changes in the folds or FSFs, producing fold or FSF variants. Eventually as the variants continue to diversify and change as well, a new fold or FSF is born. Thus, there are two rate parameters in each model: the growth rate of fold or FSF variants and the rate of appearance of new folds or FSFs. The model governs the rate change of the average total abundance of a fold or FSF with time. It is fit to the tree so only those fold or FSF transitions actually present in the tree are assumed possible in the equations. It assumes a global perspective: the total abundance of a fold or FSF is that of the fold or FSF across all species, not within one organism. This perspective is used to properly discount terms of horizontal transfer in a birth-death model since such a transfer contributes no new folds or FSFs to the net abundance across all organisms. Our model determines 1) that there is a tight connection between the history of folds and FSFs, 2) that the corresponding transition probabilities to new variants of a fold experienced a sharp increase just as the transition probabilities to new folds experienced a steep decline and 3) that this simultaneous sharp increase and decline is explainable by and consistent with the combinatorial explosion of structural domains, referring to the period of high combination and rearrangement of domains and distribution of these new combinations in novel lineages, and the rise of organismal diversification. Our simulations suggest a picture of the past in which exploration of protein structure space proceeds much like that of a budding field of knowledge: first, coarse grain discoveries are made, followed by fine-grain elaboration of each once the coarse-grain discoveries have been exhausted

The Interacting Branching Process as a Simple Model of Innovation

We describe innovation in terms of a generalized branching process. Each new invention pairs with any existing one to produce a number of offspring, which is Poisson distributed with mean p. Existing inventions die with probability p/\tau at each generation. In contrast to mean field results, no phase transition occurs; the chance for survival is finite for all p > 0. For \tau = \infty, surviving processes exhibit a bottleneck before exploding super-exponentially - a growth consistent with a law of accelerating returns. This behavior persists for finite \tau. We analyze, in detail, the asymptotic behavior as p \to 0.Comment: 4 pages, 4 figure

Some genetic aspects in two strains of chicken and their crosses

International audienc

Canopy Resistance as Affected by Soil and Meteorological Factors in Potato

Precision irrigation requires a method of quantifying the crop water status or root zone depletion of water to determine when and how much water to apply to the soil. Changes in canopy resistance (rc) and canopy temperatures have the potential of being used as a crop water status indicator for irrigation management. A study was conducted on potato (Solanum tuberosum L.) grown in northern Egypt at Shibin El-Kom on an alluvial loamy soil for winter (20 Sept. 2001 through 20 Jan. 2002) and spring (1 Feb. 2002 through 20 May 2002) seasons to determine if rc derived from energy balance and plant parameters could be used to determine the onset of water stress and the amount of water required to refill the soil profile. Diurnal rc was determined for well-watered conditions and achieved minimum values of 20 and 10 s m-1 at noontime during winter and spring periods, environmenrespectively. A power relationship of -0.86 for well-watered conditions was developed between rc and net radiation (Rn) at various plant growth stages. In deficit soil water conditions, rc increased linearly with decreasing available soil water (ASW), with a change in potato rc of 0.75 and 0.39 s m-1 per percentage ASW for 1 and 2 MJ m-2 h-1 of Rn at midgrowth, respectively. A ratio of actual/potential canopy resistance (rc/rcp) was derived to normalize the meteorological differences between growing seasons. This ratio was 2.5 when 50% of ASW was removed and can be used as a parameter to determine the need for irrigations using weather factors and canopy temperature. Canopy resistance increased linearly with increasing soil solution salinity, electrical conductivity, when the soil solution was above the threshold soil salinity value. A ratio of rc/rcp was found to normalize the effects of different environments across saline and water deficit conditions