Fitting theories of nuclear binding energies

In developing theories of nuclear binding energy such as density-functional theory, the effort required to make a fit can be daunting due to the large number of parameters that may be in the theory and the large number of nuclei in the mass table. For theories based on the Skyrme interaction, the effort can be reduced considerably by using the singular value decomposition to reduce the size of the parameter space. We find that the sensitive parameters define a space of dimension four or so, and within this space a linear refit is adequate for a number of Skyrme parameters sets from the literature. We do not find marked differences in the quality of the fit between the SLy4, the Bky4 and SkP parameter sets. The r.m.s. residual error in even-even nuclei is about 1.5 MeV, half the value of the liquid drop model. We also discuss an alternative norm for evaluating mass fits, the Chebyshev norm. It focuses attention on the cases with the largest discrepancies between theory and experiment. We show how it works with the liquid drop model and make some applications to models based on Skyrme energy functionals. The Chebyshev norm seems to be more sensitive to new experimental data than the root-mean-square norm. The method also has the advantage that candidate improvements to the theories can be assessed with computations on smaller sets of nuclei.Comment: 17 pages and 4 figures--version encorporates referee's comment

Compact Nuclei in Galaxies at Moderate Redshift:II. Their Nature and Implications for the AGN Luminosity Function

This study explores the space density and properties of active galaxies to z=0.8. We have investigated the frequency and nature of unresolved nuclei in galaxies at moderate redshift as indicators of nuclear activity such as Active Galactic Nuclei (AGN) or starbursts. Candidates are selected by fitting imaged galaxies with multi-component models using maximum likelihood estimate techniques to determine the best model fit. We select those galaxies requiring an unresolved point-source component in the galaxy nucleus, in addition to a disk and/or bulge component, to adequately model the galaxy light. We have searched 70 WFPC2 images primarily from the Medium Deep Survey for galaxies containing compact nuclei. In our survey of 1033 galaxies, the fraction containing an unresolved nuclear component greater than 5% of the total galaxy light is 9+/-1% corrected for incompleteness. In this second of two papers in this series, we discuss the nature of the compact nuclei and their hosts. We present the upper limit luminosity function (LF) for low-luminosity AGN (LLAGN) in two redshift bins to z=0.8. Mild number density evolution is detected for nuclei at -18 -16 and this flatness, combined with the increase in number density, is inconsistent with pure luminosity evolution. Based on the amount of density evolution observed for these objects, we find that almost all present-day spiral galaxies could have hosted a LLAGN at some point in their lives. We also comment on the likely contribution of these compact nuclei to the soft X-ray background.Comment: 50 pages, 14 figures, to appear in ApJ, April 199

Improving the condition number of estimated covariance matrices

High dimensional error covariance matrices and their inverses are used to weight the contribution of observation and background information in data assimilation procedures. As observation error covariance matrices are often obtained by sampling methods, estimates are often degenerate or ill-conditioned, making it impossible to invert an observation error covariance matrix without the use of techniques to reduce its condition number. In this paper we present new theory for two existing methods that can be used to ‘recondition’ any covariance matrix: ridge regression, and the minimum eigenvalue method. We compare these methods with multiplicative variance inflation, which cannot alter the condition number of a matrix, but is often used to account for neglected correlation information. We investigate the impact of reconditioning on variances and correlations of a general covariance matrix in both a theoretical and practical setting. Improved theoretical understanding provides guidance to users regarding method selection, and choice of target condition number. The new theory shows that, for the same target condition number, both methods increase variances compared to the original matrix, with larger increases for ridge regression than the minimum eigenvalue method. We prove that the ridge regression method strictly decreases the absolute value of off-diagonal correlations. Theoretical comparison of the impact of reconditioning and multiplicative variance inflation on the data assimilation objective function shows that variance inflation alters information across all scales uniformly, whereas reconditioning has a larger effect on scales corresponding to smaller eigenvalues. We then consider two examples: a general correlation function, and an observation error covariance matrix arising from interchannel correlations. The minimum eigenvalue method results in smaller overall changes to the correlation matrix than ridge regression, but can increase off-diagonal correlations. Data assimilation experiments reveal that reconditioning corrects spurious noise in the analysis but underestimates the true signal compared to multiplicative variance inflation

Myosin-X is a molecular motor that functions in filopodia formation

Despite recent progress in understanding lamellipodia extension, the molecular mechanisms regulating filopodia formation remain largely unknown. Myo10 is a MyTH4-FERM myosin that localizes to the tips of filopodia and is hypothesized to function in filopodia formation. To determine whether endogenous Myo10 is required for filopodia formation, we have used scanning EM to assay the numerous filopodia normally present on the dorsal surfaces of HeLa cells. We show here that siRNA-mediated knockdown of Myo10 in HeLa cells leads to a dramatic loss of dorsal filopodia. Overexpressing the coiled coil region from Myo10 as a dominant- negative also leads to a loss of dorsal filopodia, thus providing independent evidence that Myo10 functions in filopodia formation. We also show that expressing Myo10 in COS-7 cells, a cell line that normally lacks dorsal filopodia, leads to a massive induction of dorsal filopodia. Because the dorsal filopodia induced by Myo10 are not attached to the substrate, Myo10 can promote filopodia by a mechanism that is independent of substrate attachment. Consistent with this observation, a Myo10 construct that lacks the FERM domain, the region that binds to integrin, retains the ability to induce dorsal filopodia. Deletion of the MyTH4-FERM region, however, completely abolishes Myo10's filopodia-promoting activity, as does deletion of the motor domain. Additional experiments on the mechanism of Myo10 action indicate that it acts downstream of Cdc42 and can promote filopodia in the absence of VASP proteins. Together, these data demonstrate that Myo10 is a molecular motor that functions in filopodia formation

Simulation of Yield and Environmental Impacts of Wheat after Rice in Bangladesh and Australia

CERES-wheat and SWAGMAN Destiny models, respectively, were used to estimate the optimum time of sowing, and trade-off between yield and net recharge of the watertable, for wheat grown after rice in northern Bangladesh and southern NSW, Australia. Simulated wheat yields in Bangladesh, for sowings from Sept to Jan, with two supplemental irrigations, ranged from 0.4 to 4.6 t/ha. November-sown crops yielded more than the earlier- or later-sown crops due to reduced water and heat stress during grain filling. In Australia, simulated yields of non-irrigated wheat were always greater for April than June sowings due to less water deficit at the end of the season. With an initial shallow (0.5 m), fresh (1 dS/m) watertable, simulated yields usually exceeded 3 t/ha, and declined as watertable salinity increased. Nonirrigated wheat almost always lowered the watertable. Frequent irrigation increased simulated yields to 5-6 t/ha, regardless of initial conditions and sowing date, but this was at the cost of decreased discharge or increased recharge leading to rising watertables

Spectral structure and decompositions of optical states, and their applications

We discuss the spectral structure and decomposition of multi-photon states. Ordinarily `multi-photon states' and `Fock states' are regarded as synonymous. However, when the spectral degrees of freedom are included this is not the case, and the class of `multi-photon' states is much broader than the class of `Fock' states. We discuss the criteria for a state to be considered a Fock state. We then address the decomposition of general multi-photon states into bases of orthogonal eigenmodes, building on existing multi-mode theory, and introduce an occupation number representation that provides an elegant description of such states that in many situations simplifies calculations. Finally we apply this technique to several example situations, which are highly relevant for state of the art experiments. These include Hong-Ou-Mandel interference, spectral filtering, finite bandwidth photo-detection, homodyne detection and the conditional preparation of Schr\"odinger Kitten and Fock states. Our techniques allow for very simple descriptions of each of these examples.Comment: 12 page

A Nutrient-Regulated Cyclic Diguanylate Phosphodiesterase Controls Clostridium difficile Biofilm and Toxin Production during Stationary Phase

ABSTRACT The signaling molecule cyclic diguanylate (c-di-GMP) mediates physiological adaptation to extracellular stimuli in a wide range of bacteria. The complex metabolic pathways governing c-di-GMP synthesis and degradation are highly regulated, but the specific cues that impact c-di-GMP signaling are largely unknown. In the intestinal pathogen Clostridium difficile , c-di-GMP inhibits flagellar motility and toxin production and promotes pilus-dependent biofilm formation, but no specific biological functions have been ascribed to any of the individual c-di-GMP synthases or phosphodiesterases (PDEs). Here, we report the functional and biochemical characterization of a c-di-GMP PDE, PdcA, 1 of 37 confirmed or putative c-di-GMP metabolism proteins in C. difficile 630. Our studies reveal that pdcA transcription is controlled by the nutrient-regulated transcriptional regulator CodY and accordingly increases during stationary phase. In addition, PdcA PDE activity is allosterically regulated by GTP, further linking c-di-GMP levels to nutrient availability. Mutation of pdcA increased biofilm formation and reduced toxin biosynthesis without affecting swimming motility or global intracellular c-di-GMP. Analysis of the transcriptional response to pdcA mutation indicates that PdcA-dependent phenotypes manifest during stationary phase, consistent with regulation by CodY. These results demonstrate that inactivation of this single PDE gene is sufficient to impact multiple c-di-GMP-dependent phenotypes, including the production of major virulence factors, and suggest a link between c-di-GMP signaling and nutrient availability

Positive approximations of the inverse of fractional powers of SPD M-matrices

This study is motivated by the recent development in the fractional calculus and its applications. During last few years, several different techniques are proposed to localize the nonlocal fractional diffusion operator. They are based on transformation of the original problem to a local elliptic or pseudoparabolic problem, or to an integral representation of the solution, thus increasing the dimension of the computational domain. More recently, an alternative approach aimed at reducing the computational complexity was developed. The linear algebraic system $\cal A^\alpha \bf u=\bf f$, $0< \alpha <1$ is considered, where $\cal A$ is a properly normalized (scalded) symmetric and positive definite matrix obtained from finite element or finite difference approximation of second order elliptic problems in $\Omega\subset\mathbb{R}^d$, $d=1,2,3$. The method is based on best uniform rational approximations (BURA) of the function $t^{\beta-\alpha}$ for $0 < t \le 1$ and natural $\beta$. The maximum principles are among the major qualitative properties of linear elliptic operators/PDEs. In many studies and applications, it is important that such properties are preserved by the selected numerical solution method. In this paper we present and analyze the properties of positive approximations of $\cal A^{-\alpha}$ obtained by the BURA technique. Sufficient conditions for positiveness are proven, complemented by sharp error estimates. The theoretical results are supported by representative numerical tests

A Nutrient-Regulated Cyclic Diguanylate Phosphodiesterase Controls Clostridium difficile Biofilm and Toxin Production During Stationary Phase

The signaling molecule cyclic diguanylate (c-di-GMP) mediates physiological adaptation to extracellular stimuli in a wide range of bacteria. The complex metabolic pathways governing c-di-GMP synthesis and degradation are highly regulated, but the specific cues that impact c-di-GMP signaling are largely unknown. In the intestinal pathogen Clostridium difficile, c-di-GMP inhibits flagellar motility and toxin production and promotes pilus-dependent biofilm formation, but no specific biological functions have been ascribed to any of the individual c-di-GMP synthases or phosphodiesterases (PDEs). Here, we report the functional and biochemical characterization of a c-di-GMP PDE, PdcA, 1 of 37 confirmed or putative c-di-GMP metabolism proteins in C. difficile 630. Our studies reveal that pdcA transcription is controlled by the nutrient-regulated transcriptional regulator CodY and accordingly increases during stationary phase. In addition, PdcA PDE activity is allosterically regulated by GTP, further linking c-di-GMP levels to nutrient availability. Mutation of pdcA increased biofilm formation and reduced toxin biosynthesis without affecting swimming motility or global intracellular c-di-GMP. Analysis of the transcriptional response to pdcA mutation indicates that PdcA-dependent phenotypes manifest during stationary phase, consistent with regulation by CodY. These results demonstrate that inactivation of this single PDE gene is sufficient to impact multiple c-di-GMP-dependent phenotypes, including the production of major virulence factors, and suggest a link between c-di-GMP signaling and nutrient availability