On some entropy functionals derived from R\'enyi information divergence

We consider the maximum entropy problems associated with R\'enyi $Q$-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the generalized expectation as encountered in nonextensive statistics. The optimum maximum entropy probability distributions, which can exhibit a power-law behaviour, are derived and characterized. The R\'enyi entropy of the optimum distributions can be viewed as a function of the constraint. This defines two families of entropy functionals in the space of possible expected values. General properties of these functionals, including nonnegativity, minimum, convexity, are documented. Their relationships as well as numerical aspects are also discussed. Finally, we work out some specific cases for the reference measure $Q(x)$ and recover in a limit case some well-known entropies

Dietary Mg2+ Intake and the Na+/Mg2+ Exchanger SLC41A1 Influence Components of Mitochondrial Energetics in Murine Cardiomyocytes

Cardiomyocytes are among the most energy-intensive cell types. Interplay between the components of cellular magnesium (Mg) homeostasis and energy metabolism in cardiomyocytes is poorly understood. We have investigated the effects of dietary Mg content and presence/functionality of the Na+/Mg2+ exchanger SLC41A1 on enzymatic functions of selected constituents of the Krebs cycle and complexes of the electron transport chain (ETC). The activities of aconitate hydratase (ACON), isocitrate dehydrogenase (ICDH), α-ketoglutarate dehydrogenase (KGDH), and ETC complexes CI–CV have been determined in vitro in mitochondria isolated from hearts of wild-type (WT) and Slc41a1−/− mice fed a diet with either normal or low Mg content. Our data demonstrate that both, the type of Mg diet and the Slc41a1 genotype largely impact on the activities of enzymes of the Krebs cycle and ETC. Moreover, a compensatory effect of Slc41a1−/− genotype on the effect of low Mg diet on activities of the tested Krebs cycle enzymes has been identified. A machine-learning analysis identified activities of ICDH, CI, CIV, and CV as common predictors of the type of Mg diet and of CII as suitable predictor of Slc41a1 genotype. Thus, our data delineate the effect of dietary Mg content and of SLC41A1 functionality on the energy-production in cardiac mitochondria

Empirical Phi-Discrepancies and Quasi-Empirical Likelihood: Exponential Bounds

We review some recent extensions of the so-called generalized empirical likelihood method, when the Kullback distance is replaced by some general convex divergence. We propose to use, instead of empirical likelihood, some regularized form or quasi-empirical likelihood method, corresponding to a convex combination of Kullback and χ2 discrepancies. We show that for some adequate choice of the weight in this combination, the corresponding quasi-empirical likelihood is Bartlett-correctable. We also establish some non-asymptotic exponential bounds for the confidence regions obtained by using this method. These bounds are derived via bounds for self-normalized sums in the multivariate case obtained in a previous work by the authors. We also show that this kind of results may be extended to process valued infinite dimensional parameters. In this case some known results about self-normalized processes may be used to control the behavior of generalized empirical likelihood

Maximum-Entropy Weighting of Multi-Component Earth Climate Models

A maximum entropy-based framework is presented for the synthesis of projections from multiple Earth climate models. This identifies the most representative (most probable) model from a set of climate models -- as defined by specified constraints -- eliminating the need to calculate the entire set. Two approaches are developed, based on individual climate models or ensembles of models, subject to a single cost (energy) constraint or competing cost-benefit constraints. A finite-time limit on the minimum cost of modifying a model synthesis framework, at finite rates of change, is also reported.Comment: Inspired by discussions at the Mathematical and Statistical Approaches to Climate Modelling and Prediction workshop, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 11 Aug. to 22 Dec. 2010. Accepted for publication in Climate Dynamics, 8 August 201

Manipulating the alpha level cannot cure significance testing

We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p = 0.05 to p = 0.005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable alpha levels both are problematic, it is sensible to dispense with significance testing altogether. There are alternatives that address study design and sample size much more directly than significance testing does; but none of the statistical tools should be taken as the new magic method giving clear-cut mechanical answers. Inference should not be based on single studies at all, but on cumulative evidence from multiple independent studies. When evaluating the strength of the evidence, we should consider, for example, auxiliary assumptions, the strength of the experimental design, and implications for applications. To boil all this down to a binary decision based on a p-value threshold of 0.05, 0.01, 0.005, or anything else, is not acceptable

Community landscapes: an integrative approach to determine overlapping network module hierarchy, identify key nodes and predict network dynamics

Background: Network communities help the functional organization and evolution of complex networks. However, the development of a method, which is both fast and accurate, provides modular overlaps and partitions of a heterogeneous network, has proven to be rather difficult. Methodology/Principal Findings: Here we introduce the novel concept of ModuLand, an integrative method family determining overlapping network modules as hills of an influence function-based, centrality-type community landscape, and including several widely used modularization methods as special cases. As various adaptations of the method family, we developed several algorithms, which provide an efficient analysis of weighted and directed networks, and (1) determine pervasively overlapping modules with high resolution; (2) uncover a detailed hierarchical network structure allowing an efficient, zoom-in analysis of large networks; (3) allow the determination of key network nodes and (4) help to predict network dynamics. Conclusions/Significance: The concept opens a wide range of possibilities to develop new approaches and applications including network routing, classification, comparison and prediction.Comment: 25 pages with 6 figures and a Glossary + Supporting Information containing pseudo-codes of all algorithms used, 14 Figures, 5 Tables (with 18 module definitions, 129 different modularization methods, 13 module comparision methods) and 396 references. All algorithms can be downloaded from this web-site: http://www.linkgroup.hu/modules.ph

Therapeutic Drug Monitoring of Venlafaxine and Impact of Age, Gender, BMI, and Diagnosis

Depression is a common mental disorder affecting more than 264 million people in the world and 5.1% of the Slovak population. Although various antidepressant approaches have been used; still, about 40% of patients do not respond to a first-choice drug administration and one third of patients do not achieve total remission. Therapeutic drug monitoring (TDM) is a method used for quantification and interpreting the drug concentrations in plasma in order to optimize the pharmacotherapy. The aim of this study was to measure the plasma concentrations of venlafaxine, the fourth most prescribed antidepressant in Slovakia, as well as its active metabolite and interpret them with the relevant patients’ characteristics