Stability of 2-D characteristic polynomials

This paper derives some new conditions for the bivariate characteristic polynomial of an uncertain matrix to be very strict Hurwitz. The uncertainties are assumed of the structured and unstructured type. By using the two-dimensional (2-D) inverse Laplace transform, the bounds on the uncertainties are derived which will ensure that the bivariate characteristic polynomial to be very strict Hurwitz. Two numerical examples are given to illustrate the results.

On the permutation behaviour of Dickson polynomials of the second kind

The known permutation behaviour of the Dickson polynomials of the second kind in characteristic 3 is expanded and simplified.

Conditions to ensure the 2-D characteristic polynomial of uncertain matrix is very strict Hurwitz

This article derives some new conditions for the bivariate characteristic
polynomial of an uncertain matrix to be very strict Hurwitz. The uncertainties are assumed of the structured and unstructured type. Using the two-dimensional inverse Laplace transform, we derive the bounds on the uncertainties, which will ensure that the bivariate characteristic polynomial is very strict Hurwitz. Two numerical examples are given to illustrate the results.

Fractional polynomials and model selection in generalized estimating equations analysis, with an application to a longitudinal epidemiologic study in Australia

In epidemiologic studies, researchers often need to establish a nonlinear exposure-response relation between a continuous risk factor and a health outcome. Furthermore, periodic interviews are often conducted to take repeated measurements from an individual. The authors proposed to use fractional polynomial models to jointly analyze the effects of 2 continuous risk factors on a health outcome. This method was applied to an analysis of the effects of age and cumulative fluoride exposure on forced vital capacity in a longitudinal study of lung function carried out among aluminum workers in Australia (1995-2003). Generalized estimating equations and the quasi-likelihood under the independence model criterion were used. The authors found that the second-degree fractional polynomial models for age and fluoride fitted the data best. The best model for age was robust across different models for fluoride, and the best model for fluoride was also robust. No evidence was found to suggest that the effects of smoking and cumulative fluoride exposure on change in forced vital capacity over time were significant. The trend 1 model, which included the unexposed persons in the analysis of trend in forced vital capacity over tertiles of fluoride exposure, did not fit the data well, and caution should be exercised when this method is used.

Bivariate variance-component analysis, with application to systolic blood pressure and total cholesterol levels in the Framingham Heart Study

Background :
The correlations between systolic blood pressure (SBP) and total cholesterol levels (CHOL) might result from genetic or environmental factors that determine variation in the phenotypes and are shared by family members. Based on 330 nuclear families in the Framingham Heart Study, we used a multivariate normal model, implemented in the software FISHER, to estimate genetic and shared environmental components of variation and genetic and shared environmental correlation between the phenotypes. The natural logarithm of the phenotypes measured at the last visit in both Cohort 1 and 2 was used in the analyses. The antihypertensive treatment effect was corrected before adjustment of the systolic blood pressure for age, sex, and cohort.
Results :
The univariate correlation coefficient was statistically significant for sibling pairs and parent-offspring pairs, but not significant for spouse pairs. In the bivariate analysis, the cross-trait correlation coefficients were not statistically significant for all relative pairs. The shared environmental correlation was statistically significant, but the genetic correlation was not significant.
Conclusion :
There is no significant evidence for a close genetic correlation between systolic blood pressure and total cholesterol levels. However, some shared environmental factors may determine the variation of both phenotypes.

Non-homogeneous volatility correlations in the bivariate multifractal model

In this paper, we consider an extension of the recently proposed bivariate Markov-switching multifractal model of Calvet, Fisher, and Thompson [2006. "Volatility Comovement: A Multifrequency Approach." Journal of Econometrics {131}: 179-215]. In particular, we allow correlations between volatility components to be non-homogeneous with two different parameters governing the volatility correlations at high and low frequencies. Specification tests confirm the added explanatory value of this specification. In order to explore its practical performance, we apply the model for computing value-at-risk statistics for different classes of financial assets and compare the results with the baseline, homogeneous bivariate multifractal model and the bivariate DCC-GARCH of Engle [2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models." Journal of Business & Economic Statistics 20 (3): 339-350]. As it turns out, the multifractal model with heterogeneous volatility correlations provides more reliable results than both the homogeneous benchmark and the DCC-GARCH model. © 2014 Taylor & Francis.

Extension of bivariate means to weighted means of several arguments by using binary trees

ABSTRACTAveraging aggregation functions are valuable in building decision making and fuzzy logic systems and in handling uncertainty. Some interesting classes of averages are bivariate and not easily extended to the multivariate case. We propose a generic method for extending bivariate symmetric means to n-variate weighted means by recursively applying the specified bivariate mean in a binary tree construction. We prove that the resulting extension inherits many desirable properties of the base mean and design an efficient numerical algorithm by pruning the binary tree. We show that the proposed method is numerically competitive to the explicit analytical formulas and hence can be used in various computational intelligence systems which rely on aggregation functions.

The determination of all syzygies for the dependent polynomial invariants of the Riemann Tensor. II. mixed invariants of Eeven degree in the Ricci Spinor

We continue our analysis of the polynomial invariants of the Riemann tensor in a four-dimensional Lorentzian space. We concentrate on the mixed invariants of even degree in the Ricci spinor Φ_ABȦḂ and show how, using constructive graph-theoretic methods, arbitrary scalar contractions between copies of the Weyl spinor ψ_ABCD, its conjugate ψ_ȦḂĊḊ and an even number of Ricci spinors can be expressed in terms of paired contractions between these spinors. This leads to an algorithm for the explicit expression of dependent invariants as polynomials of members of the complete set. Finally, we rigorously prove that the complete set as given by Sneddon [J. Math. Phys. 39, 1659-1679 (1998)] for this case is both complete and minimal.

Time-varying hedge ratios: an application to the Indian stock futures market

This paper investigates time-varying optimal hedge ratios in individual stock futures markets in India. The analysis employs data on individual stock futures from an unexplored but highly traded (both in terms of volume and quantity) emerging market. The hedge ratios derived in this study incorporate mean reversion in volatility, which is an important extension of the bivariate BEKK-GARCH model of Engle and Kroner. This extension generates improved optimal hedge ratios over the traditional BEKK-GARCH model and static error correction type alternatives.

Spatial and temporal distribution of solute leaching in heterogeneous soils: analysis and application to multisampler lysimeter data

Accurate assessment of the fate of salts, nutrients, and pollutants in natural, heterogeneous soils requires a proper quantification of both spatial and temporal solute spreading during solute movement. The number of experiments with multisampler devices that measure solute leaching as a function of space and time is increasing. The breakthrough curve (BTC) can characterize the temporal aspect of solute leaching, and recently the spatial solute distribution curve (SSDC) was introduced to describe the spatial solute distribution. We combined and extended both concepts to develop a tool for the comprehensive analysis of the full spatio-temporal behavior of solute leaching. The sampling locations are ranked in order of descending amount of total leaching (defined as the cumulative leaching from an individual compartment at the end of the experiment), thus collapsing both spatial axes of the sampling plane into one. The leaching process can then be described by a curved surface that is a function of the single spatial coordinate and time. This leaching surface is scaled to integrate to unity, and termed S can efficiently represent data from multisampler solute transport experiments or simulation results from multidimensional solute transport models. The mathematical relationships between the scaled leaching surface S, the BTC, and the SSDC are established. Any desired characteristic of the leaching process can be derived from S. The analysis was applied to a chloride leaching experiment on a lysimeter with 300 drainage compartments of 25 cm2 each. The sandy soil monolith in the lysimeter exhibited fingered flow in the water-repellent top layer. The observed S demonstrated the absence of a sharp separation between fingers and dry areas, owing to diverging flow in the wettable soil below the fingers. Times-to-peak, maximum solute fluxes, and total leaching varied more in high-leaching than in low-leaching compartments. This suggests a stochastic–convective transport process in the high-flow streamtubes, while convection–dispersion is predominant in the low-flow areas. S can be viewed as a bivariate probability density function. Its marginal distributions are the BTC of all sampling locations combined, and the SSDC of cumulative solute leaching at the end of the experiment. The observed S cannot be represented by assuming complete independence between its marginal distributions, indicating that S contains information about the leaching process that cannot be derived from the combination of the BTC and the SSDC.

Disentangling the stigma of HIV/AIDS from the stigmas of drugs use, commercial sex and commercial blood donation - a factorial survey of medical students in China

Background
HIV/AIDS related stigma interferes with the provision of appropriate care and support for people living with HIV/AIDS. Currently, programs to address the stigma approach it as if it occurs in isolation, separate from the co-stigmas related to the various modes of disease transmission including injection drug use (IDU) and commercial sex (CS). In order to develop better programs to address HIV/AIDS related stigma, the inter-relationship (or 'layering') between HIV/AIDS stigma and the co-stigmas needs to be better understood. This paper describes an experimental study for disentangling the layering of HIV/AIDS related stigmas.

Methods
The study used a factorial survey design. 352 medical students from Guangzhou were presented with four random vignettes each describing a hypothetical male. The vignettes were identical except for the presence of a disease diagnosis (AIDS, leukaemia, or no disease) and a co-characteristic (IDU, CS, commercial blood donation (CBD), blood transfusion or no co-characteristic). After reading each vignette, participants completed a measure of social distance that assessed the level of stigmatising attitudes.

Results
Bivariate and multivariable analyses revealed statistically significant levels of stigma associated with AIDS, IDU, CS and CBD. The layering of stigma was explored using a recently developed technique. Strong interactions between the stigmas of AIDS and the co-characteristics were also found. AIDS was significantly less stigmatising than IDU or CS. Critically, the stigma of AIDS in combination with either the stigmas of IDU or CS was significantly less than the stigma of IDU alone or CS alone.

Conclusion
The findings pose several surprising challenges to conventional beliefs about HIV/AIDS related stigma and stigma interventions that have focused exclusively on the disease stigma. Contrary to the belief that having a co-stigma would add to the intensity of stigma attached to people with HIV/AIDS, the findings indicate the presence of an illness might have a moderating effect on the stigma of certain co-characteristics like IDU. The strong interdependence between the stigmas of HIV/AIDS and the co-stigmas of IDU and CS suggest that reducing the co-stigmas should be an integral part of HIV/AIDS stigma intervention within this context.

Time varying hedge ratios : an application to the Indian stock futures market

This paper investigates time-varying optimal hedge ratios in individual stock futures markets in India. The analysis employs data on individual stock futures from an unexplored but highly traded (both in terms of volume and quantity) emerging market. The hedge ratios derived in this study incorporate mean reversion in volatility, which is an important extension of the bivariate BEKK-GARCH model of Engle and Kroner. This extension generates improved optimal hedge ratios over the traditional BEKK-GARCH model and static error correction type alternatives.

Associations between the home food environment and obesity-promoting eating behaviors in adolescence

Objective: This study examines relationships between multiple aspects of the home food environment and obesity-promoting characteristics of 12- to 13-year-old adolescents' diets, specifically frequency of consumption of high-energy fluids, sweet snacks, savory snacks, and take-out foods.

Research Methods: This was a cross-sectional study including 347 adolescents 12 to 13 years of age and their parents. Data were collected via self-completed surveys. The adolescents' diets were assessed using a Food Frequency Questionnaire derived from existing age-appropriate National Nutrition Survey data. An extensive range of domains within the home food environment were assessed. Bivariate linear regression analyses were run split by gender. Forced entry multiple linear regression analyses (adjusting for all variables significant in bivariate analyses as well as for maternal education) were also performed, stratified by the sex of the child.

Results: The influence of mothers, either as models for eating behaviors or as the providers of food, was pervasive. Mothers' intake of high-energy fluids (p = 0.003), sweet snacks (p = 0.010), savory snacks (p = 0.008), and take-out food (p = 0.007) was positively associated with boys' intake of all these foods. In addition, mothers' intake of high-energy fluids was positively associated with daughters' consumption of these drinks (p = 0.025). Furthermore, availability of unhealthy foods at home was positively associated with girls' sweet snack (p = 0.001), girls' savory snack (p < 0.001), boys' savory snack (p = 0.002), and, in the bivariate analyses, girls' high-energy fluid consumption (p = 0.002).

Discussion: This study of home food environment influences on adolescent diet highlights the pervasive influence of mothers in determining adolescents' obesity-promoting eating, providing direction for obesity prevention strategies and future research.