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

Shallow-Water Habitats as Sources of Fallback Foods for Hominins

Underground storage organs (USOs) have been proposed as critical fallback foods for early hominins in savanna, but there has been little discussion as to which habitats would have been important sources of USOs. USOs consumed by hominins could have included both underwater and underground storage organs, i.e., from both aquatic and terrestrial habitats. Shallow aquatic habitats tend to offer high plant growth rates, high USO densities, and relatively continuous USO availability throughout the year. Baboons in the Okavango delta use aquatic USOs as a fallback food, and aquatic or semiaquatic USOs support high-density human populations in various parts of the world. As expected given fossilization requisites, the African early- to mid-Pleistocene shows an association of Homo and Paranthropus fossils with shallow-water and flooded habitats where high densities of plant-bearing USOs are likely to have occurred. Given that early hominins in the tropics lived in relatively dry habitats, while others occupied temperate latitudes, ripe, fleshy fruits of the type preferred by African apes would not normally have been available year round. We therefore suggest that water-associated USOs were likely to have been key fallback foods, and that dry-season access to aquatic habitats would have been an important predictor of hominin home range quality. This study differs from traditional savanna chimpanzee models of hominin origins by proposing that access to aquatic habitats was a necessary condition for adaptation to savanna habitats. It also raises the possibility that harvesting efficiency in shallow water promoted adaptations for habitual bipedality in early hominins.Human Evolutionary Biolog

Negative thermal expansion of MgB2_{2} in the superconducting state and anomalous behavior of the bulk Gr\"uneisen function

The thermal expansion coefficient $\alpha$ of MgB$_2$ is revealed to change from positive to negative on cooling through the superconducting transition temperature $T_c$. The Gr\"uneisen function also becomes negative at $T_c$ followed by a dramatic increase to large positive values at low temperature. The results suggest anomalous coupling between superconducting electrons and low-energy phonons.Comment: 5 figures. submitted to Phys. Rev. Let

A New Method of Synthesizing Black Birnessite Nanoparticles: From Brown to Black Birnessite with Nanostructures

A new method for preparing black birnessite nanoparticles is introduced. The initial synthesis process resembles the classical McKenzie method of preparing brown birnessite except for slower cooling and closing the system from the ambient air. Subsequent process, including wet-aging at 7◦C for 48 hours, overnight freezing, and lyophilization, is shown to convert the brown birnessite into black birnessite with complex nanomorphology with folded sheets and spirals. Characterization of the product is performed by X-ray diffraction (XRD), transmission electron microscopy (TEM), high-resolution transmission electron microscopy (HRTEM), thermogravimetric analysis (TGA), and N2 adsorption (BET) techniques. Wet-aging and lyophilization times are shown to affect the architecture of the product. XRD patterns show a single phase corresponding to a semicrystalline birnessite-based manganese oxide. TEM studies suggest its fibrous and petal-like structures. The HRTEM images at 5 and 10 nm length scales reveal the fibrils in folding sheets and also show filamentary breaks. The BET surface area of this nanomaterial was found to be 10.6m2/g. The TGA measurement demonstrated that it possessed an excellent thermal stability up to 400◦C. Layerstructured black birnessite nanomaterial containing sheets, spirals, and filamentary breaks can be produced at low temperature (−49◦C) from brown birnessite without the use of cross-linking reagents

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

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

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

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 Proposed Industrial Arts Program for Harry P. Harding High School of Charlotte, North Carolina

(From Introduction) In September 1949, the writer became a member of the staff at Harry P. Harding High School in Charlotte, North Carolina, as Instructor in Industrial Arts. In conference with administrators, it was revealed that they were interested in further development of Industrial Arts Education in the school. Without any implied criticisms or previous efforts, it is felt that the expansion of present offerings is in order. School authorities are favorable toward a study of the situation which might cast more light on the present services being offered and might point to the possibilities of enlarged services. In any event it is believed that the results of such a study would receive careful consideration at the hands of local administrators and with this thought in mind the problem has been attacked