Molecular crystal global phase diagrams. II. Reference lattices

In the first part of this series [Keith et al. (2004). Cryst. Growth Des. 4, 1009-1012; Mettes et al. (2004). Acta Cryst. A60, 621-636], a method was developed for constructing global phase diagrams (GPDs) for molecular crystals in which crystal structure is presented as a function of intermolecular potential parameters. In that work, a face-centered-cubic center-of-mass lattice was arbitrarily adopted as a reference state. In part two of the series, experimental crystal structures composed of tetrahedral point group molecules are classified to determine what fraction of structures are amenable to inclusion in the GPDs and the number of reference lattices necessary to span the observed structures. It is found that 60% of crystal structures composed of molecules with T_d point-group symmetry are amenable and that eight reference lattices are sufficient to span the observed structures. Similar results are expected for other cubic point groups

Structural Relationship between Negative Thermal Expansion and Quartic Anharmonicity of Cubic ScF_3

Cubic scandium trifluoride (ScF_3) has a large negative thermal expansion over a wide range of temperatures. Inelastic neutron scattering experiments were performed to study the temperature dependence of the lattice dynamics of ScF3 from 7 to 750 K. The measured phonon densities of states show a large anharmonic contribution with a thermal stiffening of modes around 25 meV. Phonon calculations with first-principles methods identified the individual modes in the densities of states, and frozen phonon calculations showed that some of the modes with motions of F atoms transverse to their bond direction behave as quantum quartic oscillators. The quartic potential originates from harmonic interatomic forces in the DO_9 structure of ScF_3, and accounts for phonon stiffening with the temperature and a significant part of the negative thermal expansion

Exponential Smoothing for Inventory Control: Means and Variances of Lead-Time Demand

Exponential smoothing is often used to forecast lead-time demand for inventory control. In this paper, formulae are provided for calculating means and variances of lead-time demand for a wide variety of exponential smoothing methods. A feature of many of the formulae is that variances, as well as the means, depend on trends and seasonal effects. Thus, these formulae provide the opportunity to implement methods that ensure that safety stocks adjust to changes in trend or changes in season.Forecasting; inventory control; lead-time demand; exponential smoothing; forecast variance.

Monitoring Processes with Changing Variances

Statistical process control (SPC) has evolved beyond its classical applications in manufacturing to monitoring economic and social phenomena. This extension requires consideration of autocorrelated and possibly non-stationary time series. Less attention has been paid to the possibility that the variance of the process may also change over time. In this paper we use the innovations state space modeling framework to develop conditionally heteroscedastic models. We provide examples to show that the incorrect use of homoscedastic models may lead to erroneous decisions about the nature of the process. The framework is extended to include counts data, when we also introduce a new type of chart, the P-value chart, to accommodate the changes in distributional form from one period to the next.Control charts, count data, GARCH, heteroscedasticity, innovations, state space, statistical process control

A Bayesian Estimate of the Primordial Helium Abundance

We introduce a new statistical method to estimate the primordial helium abundance, Y_p from observed abundances in a sample of galaxies which have experienced stellar helium enrichment. Rather than using linear regression on metal abundance we construct a likelihood function using a Bayesian prior, where the key assumption is that the true helium abundance must always exceed the primordial value. Using a sample of measurements compiled from the literature we find estimates of Y_p between 0.221 and 0.236, depending on the specific subsample and prior adopted, consistent with previous estimates either from a linear extrapolation of the helium abundance with respect to metallicity, or from the helium abundance of the lowest metallicity HII region, I Zw 18. We also find an upper limit which is insensitive to the specific subsample or prior, and estimate a model-independent bound Y_p < 0.243 at 95% confidence, favoring a low cosmic baryon density and a high primordial deuterium abundance. The main uncertainty is not the model of stellar enrichment but possible common systematic biases in the estimate of Y in each individual HII region.Comment: 14 pages, latex, 3 ps figure

Trispectrum versus Bispectrum in Single-Field Inflation

In the standard slow-roll inflationary cosmology, quantum fluctuations in a single field, the inflaton, generate approximately Gaussian primordial density perturbations. At present, the bispectrum and trispectrum of the density perturbations have not been observed and the probability distribution for these perturbations is consistent with Gaussianity. However, Planck satellite data will bring a new level of precision to bear on this issue, and it is possible that evidence for non-Gaussian effects in the primordial distribution will be discovered. One possibility is that a trispectrum will be observed without evidence for a non-zero bispectrum. It is not difficult for this to occur in inflationary models where quantum fluctuations in a field other than the inflaton contribute to the density perturbations. A natural question to ask is whether such an observation would rule out the standard scenarios. We explore this issue and find that it is possible to construct single-field models in which inflaton-generated primordial density perturbations have an observable trispectrum, but a bispectrum that is too small to be observed by the Planck satellite. However, an awkward fine tuning seems to be unavoidable.Comment: 15 pages, 3 figures; journal versio

Forecasting Compositional Time Series with Exponential Smoothing Methods

Compositional time series are formed from measurements of proportions that sum to one in each period of time. We might be interested in forecasting the proportion of home loans that have adjustable rates, the proportion of nonagricultural jobs in manufacturing, the proportion of a rock's geochemical composition that is a specific oxide, or the proportion of an election betting market choosing a particular candidate. A problem may involve many related time series of proportions. There could be several categories of nonagricultural jobs or several oxides in the geochemical composition of a rock that are of interest. In this paper we provide a statistical framework for forecasting these special kinds of time series. We build on the innovations state space framework underpinning the widely used methods of exponential smoothing. We couple this with a generalized logistic transformation to convert the measurements from the unit interval to the entire real line. The approach is illustrated with two applications: the proportion of new home loans in the U.S. that have adjustable rates; and four probabilities for specified candidates winning the 2008 democratic presidential nomination.compositional time series, innovations state space models, exponential smoothing, forecasting proportions

Time Series Forecasting: The Case for the Single Source of Error State Space

The state space approach to modelling univariate time series is now widely used both in theory and in applications. However, the very richness of the framework means that quite different model formulations are possible, even when they purport to describe the same phenomena. In this paper, we examine the single source of error [SSOE] scheme, which has perfectly correlated error components. We then proceed to compare SSOE to the more common version of the state space models, for which all the error terms are independent; we refer to this as the multiple source of error [MSOE] scheme. As expected, there are many similarities between the MSOE and SSOE schemes, but also some important differences. Both have ARIMA models as their reduced forms, although the mapping is more transparent for SSOE. Further, SSOE does not require a canonical form to complete its specification. An appealing feature of SSOE is that the estimates of the state variables converge in probability to their true values, thereby leading to a formal inferential structure for the ad-hoc exponential smoothing methods for forecasting. The parameter space for SSOE models may be specified to match that of the corresponding ARIMA scheme, or it may be restricted to meaningful sub-spaces, as for MSOE but with somewhat different outcomes. The SSOE formulation enables straightforward extensions to certain classes of non-linear models, including a linear trend with multiplicative seasonals version that underlies the Holt-Winters forecasting method. Conditionally heteroscedastic models may be developed in a similar manner. Finally we note that smoothing and decomposition, two crucial practical issues, may be performed within the SSOE framework.ARIMA, Dynamic Linear Models, Equivalence, Exponential Smoothing, Forecasting, GARCH, Holt's Method, Holt-Winters Method, Kalman Filter, Prediction Intervals.

Towards a mechanistic understanding of fish species niche divergence along a river continuum

Citation: Troia, M. J., & Gido, K. B. (2014). Towards a mechanistic understanding of fish species niche divergence along a river continuum. Ecosphere, 5(4), art41. https://doi.org/10.1890/ES13-00399.1Environmental niche modeling is a valuable tool but it often fails to identify causal links between environmental gradients and individual- or population-level performance that drive species' distributions. Correlation between the abundances of stream fish species and longitudinal position in stream networks is well documented and is hypothesized to occur through differential environmental filtering of trophic traits. Still, trophically similar congeners often exhibit complementary distributions along stream size gradients, suggesting that other mechanisms are important. We present niche models to test the hypothesis that four congeneric pairs (Teleostei: Cyprinidae) exhibit complementary distributions along a gradient of stream size in the central Great Plains of Kansas, USA. Stream size was the strongest predictor of abundance compared to five other environmental variables tested and three of the four species pairs exhibited complementary distributions along a stream size gradient. We carried out field experiments to quantify potentially causal environmental gradients (food resources, temperature, and turbidity) and four measures of individual performance (adult spawning success and juvenile survival, condition, and growth) along a stream size gradient for one congeneric pair: Pimephales notatus, a tributary species and P. vigilax, a river mainstem species. These experiments revealed an increase in temperature and food resources with stream size, along with a corresponding increase in adult spawning success, juvenile condition, and juvenile growth for both species. We conclude that these congeners respond similarly to abiotic gradients associated with the river continuum and that complementary distributions are a consequence of biotic interactions, differential environmental filtering evident in an unmeasured performance metric, or differential environmental filtering by a direct environmental gradient operating at longer timescales