Diaphragm muscle adaptation to sustained hypoxia: lessons from animal models with relevance to high altitude and chronic respiratory diseases

The diaphragm is the primary inspiratory pump muscle of breathing. Notwithstanding its critical role in pulmonary ventilation, the diaphragm like other striated muscles is malleable in response to physiological and pathophysiological stressors, with potential implications for the maintenance of respiratory homeostasis. This review considers hypoxic adaptation of the diaphragm muscle, with a focus on functional, structural, and metabolic remodeling relevant to conditions such as high altitude and chronic respiratory disease. On the basis of emerging data in animal models, we posit that hypoxia is a significant driver of respiratory muscle plasticity, with evidence suggestive of both compensatory and deleterious adaptations in conditions of sustained exposure to low oxygen. Cellular strategies driving diaphragm remodeling during exposure to sustained hypoxia appear to confer hypoxic tolerance at the expense of peak force-generating capacity, a key functional parameter that correlates with patient morbidity and mortality. Changes include, but are not limited to: redox-dependent activation of hypoxia-inducible factor (HIF) and MAP kinases; time-dependent carbonylation of key metabolic and functional proteins; decreased mitochondrial respiration; activation of atrophic signaling and increased proteolysis; and altered functional performance. Diaphragm muscle weakness may be a signature effect of sustained hypoxic exposure. We discuss the putative role of reactive oxygen species as mediators of both advantageous and disadvantageous adaptations of diaphragm muscle to sustained hypoxia, and the role of antioxidants in mitigating adverse effects of chronic hypoxic stress on respiratory muscle function.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

Alcohol income and health: a complicated but desirable mix

The aim of this thesis is to examine if a difference exists in income for different categories of drinkers in Ireland using the 2007 Slán data set. The possible impact of alcohol consumption on health status and health care utilisation is also examined. Potential endogeneity and selection bias is accounted for throughout. Endogeneity is where an independent variable included in the model is determined within the context of the model (Chenhall and Moers, 2007). An endogenous relationship between income and alcohol and between health and alcohol is accounted for by the use of separate income equations and separate health status equations for each category of drinker similar to what was done in previous studies into the effects of alcohol on earnings (Hamilton and Hamilton, 1997; Barrett, 2002). Sample selection bias arises when a sector selection is non-random due to individuals choosing a particular sector because of their personal characteristics (Heckman, 1979; Zhang, 2004). In relation to alcohol consumption, selection bias may arise as people may select into a particular drinker group due to the fact that they know that by doing so it will not have a negative effect on their income or health (Hamilton and Hamilton, 1997; Di Pietro and Pedace, 2008; Barrett, 2002). Selection bias of alcohol consumption is accounted for by using the Multinomial Logit OLS Two Step Estimate as proposed by Lee (1982), which is an extension of the Heckman Probit OLS Two Step Estimate. Alcohol status as an ordered variable is examined and possible methods of estimation accounting for this ordinality while also accounting for selection bias are looked at. Limited Information Methods and Full Information Methods of estimation of simultaneous equations are assessed and compared. Findings show that in Ireland moderate drinkers have a higher income compared with abstainers or heavy drinkers. Some studies such as Barrett (2002) argue that this is as a consequence of alcohol improving ones health, which in turn can influence ones productivity which may ultimately be reflected in earnings, due to the fact that previous studies have found that moderate levels of alcohol consumption are beneficial towards ones health status. This study goes on to examine the relationship between health status and alcohol consumption and whether the correlation between income and the consumption of alcohol is similar in terms of sign and magnitude to the correlation between health status and the consumption of alcohol. Results indicate that moderate drinkers have a higher income than non or heavy drinkers, with the weekly household income of moderate drinkers being €660.10, non drinkers being €546.75 and heavy drinkers being €449.99. Moderate Drinkers also report having a better health status than non drinkers and a slightly better health status than heavy drinkers. More non-drinkers report poor health than either moderate or heavy drinkers. As part of the analysis into the effect of alcohol consumption on income and on health status, the relationship between other socio economic variables such as gender, age, education among others, with income, health and alcohol status is examined.

The effect of alcohol consumption on household income in Ireland

This paper presents a study of the effects of alcohol consumption on household income in Ireland using the Slán National Health and Lifestyle Survey 2007 dataset, accounting for endogeneity and selection bias. Drinkers are categorised into one of four categories based on the recommended weekly drinking levels by the Irish Health Promotion Unit; those who never drank, non-drinkers, moderate and heavy drinkers. A multinomial logit OLS Two Step Estimate is used to explain individual's choice of drinking status and to correct for selection bias which would result in the selection into a particular category of drinking being endogenous. Endogeneity which may arise through the simultaneity of drinking status and income either due to the reverse causation between the two variables, income affecting alcohol consumption or alcohol consumption affecting income, or due to unobserved heterogeneity, is addressed. This paper finds that the household income of drinkers is higher than that of non-drinkers and of those who never drank. There is very little difference between the household income of moderate and heavy drinkers, with heavy drinkers earning slightly more. Weekly household income for those who never drank is €454.20, non-drinkers is €506.26, compared with €683.36 per week for moderate drinkers and €694.18 for heavy drinkers.