No abstract

This paper probabilistically explores a class of stationary count time series models built by superpositioning (or otherwise combining) independent copies of a binary stationary sequence of zeroes and ones. Superpositioning methods have proven useful in devising stationary count time series having prespecified marginal distributions. Here, basic properties of this model class are established and the idea is further developed. Specifically, stationary series with binomial, Poisson, negative binomial, discrete uniform, and multinomial marginal distributions are constructed; other marginal distributions are possible. Our primary goal is to derive the autocovariance function of the resulting series.

Mammals with increased requirements for adipose tissue stores, such as marine mammals, have altered nutrient allocation priorities compared to many terrestrial mammals and thus the physiological response to undernutrition (low nutritional status) and realimentation (refeeding) may differ. Key regulators of nutrient allocation and tissue specific growth include metabolic hormones of the somatotropic axis, growth hormone (GH) and insulin-like growth factor (IGF)-I, as well as satiety and adipose promoting ghrelin and the stress hormone cortisol. Longitudinal measurements of metabolic hormones, blood metabolites, and morphometrics were collected over a 10-week period in twelve (male n = 3, female n = 9) harbor seal pups (< 6 weeks of age). Blood metabolites were used to indicate metabolic response during realimentation while morphometrics estimated tissue specific growth priorities. Harbor seal pups undergoing refeeding after nutritional deprivation show a preference for protein sparing despite severe malnutrition. Both BUN and total protein were negatively associated with GH and positively associated with IGF-I and ghrelin highlighting the importance of these metabolic hormones in the regulation of protein metabolism. While the response of the somatotropic axis to realimentation was typical of the mammalian pattern, the surprising increase of ghrelin across the study period suggests the priority of adipose accretion in addition to a possible mechanism regulating compensatory growth of vital adipose stores in a species, which prioritizes adipose accretion for survival.

This paper develops a mathematical model and statistical methods to quantify trends in presence/absence observations of snow cover (not depths) and applies these in an analysis of Northern Hemispheric observations extracted from satellite flyovers during 1967-2021. A two-state Markov chain model with periodic dynamics is introduced to analyze changes in the data in a cell by cell fashion. Trends, converted to the number of weeks of snow cover lost/gained per century, are estimated for each study cell. Uncertainty margins for these trends are developed from the model and used to assess the significance of the trend estimates. Cells with questionable data quality are explicitly identified. Among trustworthy cells, snow presence is seen to be declining in almost twice as many cells as it is advancing. While Arctic and southern latitude snow presence is found to be rapidly receding, other locations, such as Eastern Canada, are experiencing advancing snow cover.