Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture

The objective of this paper is to reconsider the Maximum Entropy Production conjecture (MEP) in the context of a very simple two-dimensional zonal-vertical climate model able to represent the total material entropy production due at the same time to both horizontal and vertical heat fluxes. MEP is applied first to a simple four-box model of climate which accounts for both horizontal and vertical material heat fluxes. It is shown that, under condition of fixed insolation, a MEP solution is found with reasonably realistic temperature and heat fluxes, thus generalising results from independent two-box horizontal or vertical models. It is also shown that the meridional and the vertical entropy production terms are independently involved in the maximisation and thus MEP can be applied to each subsystem with fixed boundary conditions. We then extend the four-box model by increasing its resolution, and compare it with GCM output. A MEP solution is found which is fairly realistic as far as the horizontal large scale organisation of the climate is concerned whereas the vertical structure looks to be unrealistic and presents seriously unstable features. This study suggest that the thermal meridional structure of the atmosphere is predicted fairly well by MEP once the insolation is given but the vertical structure of the atmosphere cannot be predicted satisfactorily by MEP unless constraints are imposed to represent the determination of longwave absorption by water vapour and clouds as a function of the state of the climate. Furthermore an order-of-magnitude estimate of contributions to the material entropy production due to horizontal and vertical processes within the climate system is provided by using two different methods. In both cases we found that approximately 40 mW m−2 K−1 of material entropy production is due to vertical heat transport and 5–7 mW m−2 K−1 to horizontal heat transport

Thermodynamic efficiency and entropy production in the climate system

We present an outlook on the climate system thermodynamics. First, we construct an equivalent Carnot engine with efficiency and frame the Lorenz energy cycle in a macroscale thermodynamic context. Then, by exploiting the second law, we prove that the lower bound to the entropy production is times the integrated absolute value of the internal entropy fluctuations. An exergetic interpretation is also proposed. Finally, the controversial maximum entropy production principle is reinterpreted as requiring the joint optimization of heat transport and mechanical work production. These results provide tools for climate change analysis and for climate models’ validation.

The conditional performance of UK property funds

The evaluation of investment fund performance has been one of the main developments of modern portfolio theory. Most studies employ the technique developed by Jensen (1968) that compares a particular fund's returns to a benchmark portfolio of equal risk. However, the standard measures of fund manager performance are known to suffer from a number of problems in practice. In particular previous studies implicitly assume that the risk level of the portfolio is stationary through the evaluation period. That is unconditional measures of performance do not account for the fact that risk and expected returns may vary with the state of the economy. Therefore many of the problems encountered in previous performance studies reflect the inability of traditional measures to handle the dynamic behaviour of returns. As a consequence Ferson and Schadt (1996) suggest an approach to performance evaluation called conditional performance evaluation which is designed to address this problem. This paper utilises such a conditional measure of performance on a sample of 27 UK property funds, over the period 1987-1998. The results of which suggest that once the time varying nature of the funds beta is corrected for, by the addition of the market indicators, the average fund performance show an improvement over that of the traditional methods of analysis.

Comment on ``Conditional Exceedance Probabilities''

In a recent paper, Mason et al. propose a reliability test of ensemble forecasts for a continuous, scalar verification. As noted in the paper, the test relies on a very specific interpretation of ensembles, namely, that the ensemble members represent quantiles of some underlying distribution. This quantile interpretation is not the only interpretation of ensembles, another popular one being the Monte Carlo interpretation. Mason et al. suggest estimating the quantiles in this situation; however, this approach is fundamentally flawed. Errors in the quantile estimates are not independent of the exceedance events, and consequently the conditional exceedance probabilities (CEP) curves are not constant, which is a fundamental assumption of the test. The test would reject reliable forecasts with probability much higher than the test size.

Conditional transgenic expression of fibroblast growth factor 9 in the adult mouse heart reduces heart failure mortality after myocardial infarction

BACKGROUND: Fibroblast growth factor 9 (FGF9) is secreted from bone marrow cells, which have been shown to improve systolic function after myocardial infarction (MI) in a clinical trial. FGF9 promotes cardiac vascularization during embryonic development but is only weakly expressed in the adult heart. METHODS AND RESULTS: We used a tetracycline-responsive binary transgene system based on the α-myosin heavy chain promoter to test whether conditional expression of FGF9 in the adult myocardium supports adaptation after MI. In sham-operated mice, transgenic FGF9 stimulated left ventricular hypertrophy with microvessel expansion and preserved systolic and diastolic function. After coronary artery ligation, transgenic FGF9 enhanced hypertrophy of the noninfarcted left ventricular myocardium with increased microvessel density, reduced interstitial fibrosis, attenuated fetal gene expression, and improved systolic function. Heart failure mortality after MI was markedly reduced by transgenic FGF9, whereas rupture rates were not affected. Adenoviral FGF9 gene transfer after MI similarly promoted left ventricular hypertrophy with improved systolic function and reduced heart failure mortality. Mechanistically, FGF9 stimulated proliferation and network formation of endothelial cells but induced no direct hypertrophic effects in neonatal or adult rat cardiomyocytes in vitro. FGF9-stimulated endothelial cell supernatants, however, induced cardiomyocyte hypertrophy via paracrine release of bone morphogenetic protein 6. In accord with this observation, expression of bone morphogenetic protein 6 and phosphorylation of its downstream targets SMAD1/5 were increased in the myocardium of FGF9 transgenic mice. CONCLUSIONS: Conditional expression of FGF9 promotes myocardial vascularization and hypertrophy with enhanced systolic function and reduced heart failure mortality after MI. These observations suggest a previously unrecognized therapeutic potential for FGF9 after MI.

Conditional mean functions of non-linear models of US output

We compare a number of models of post War US output growth in terms of the degree and pattern of non-linearity they impart to the conditional mean, where we condition on either the previous period's growth rate, or the previous two periods' growth rates. The conditional means are estimated non-parametrically using a nearest-neighbour technique on data simulated from the models. In this way, we condense the complex, dynamic, responses that may be present in to graphical displays of the implied conditional mean.

Forecasting exchange rate volatility using conditional variance models selected by information criteria

This paper uses appropriately modified information criteria to select models from the GARCH family, which are subsequently used for predicting US dollar exchange rate return volatility. The out of sample forecast accuracy of models chosen in this manner compares favourably on mean absolute error grounds, although less favourably on mean squared error grounds, with those generated by the commonly used GARCH(1, 1) model. An examination of the orders of models selected by the criteria reveals that (1, 1) models are typically selected less than 20% of the time.

Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics

We give an a posteriori analysis of a semidiscrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (2014, SIAM J. Math. Anal., 46, 3518–3539). This framework allows energy-type arguments to be applied to continuous functions. Since we advocate the use of discontinuous Galerkin methods we make use of two families of reconstructions, one set of discrete reconstructions and a set of elliptic reconstructions to apply the reduced relative entropy framework in this setting.

Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics

We give an a priori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (SIAM J Math Anal 46(5):3518–3539, 2014). The estimate we derive is optimal in the L∞(0,T;dG) norm for the strain and the L2(0,T;dG) norm for the velocity, where dG is an appropriate mesh dependent H1-like space.