We examine the thermodynamic stability of large black holes in four-dimensional antide Sitter space, and we demonstrate numerically that black holes which lack local thermodynamic stability often also lack stability against small perturbations. This shows that no-hair theorems do not apply in anti-de Sitter space. A heuristic argument, based on thermodynamics only, suggests that if there are any violations of Cosmic Censorship in the evolution of unstable black holes in anti-de Sitter space, they are beyond the reach of a perturbative analysis.

We perform a one-loop calculation of the vacuum energy of a tachyon field in anti de-Sitter space with boundary conditions corresponding to the presence of a double-trace operator in the dual field theory. Such an operator can lead to a renormalization group flow between two different conformal field theories related to each other by a Legendre transformation in the large N limit. The calculation of the one-loop vacuum energy enables us to verify the holographic c-theorem one step beyond the classical supergravity approximation.

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Quantitative structure-property relationship (QSPR) models used for prediction of property of untested chemicals can be utilized for prioritization plan of synthesis and experimental testing of new compounds. Validation of QSPR models plays a crucial role for judgment of the reliability of predictions of such models. In the QSPR literature, serious attention is now given to external validation for checking reliability of QSPR models, and predictive quality is in the most cases judged based on the quality of predictions of property of a single test set as reflected in one or more external validation metrics. Here, we have shown that a single QSPR model may show a variable degree of prediction quality as reflected in some variants of external validation metrics like Q²(F1), Q²(F2), Q²(F3), CCC, and r²(m) (all of which are differently modified forms of predicted variance, which theoretically may attain a maximum value of 1), depending on the test set composition and test set size. Thus, this report questions the appropriateness of the common practice of the "classic" approach of external validation based on a single test set and thereby derives a conclusion about predictive quality of a model on the basis of a particular validation metric. The present work further demonstrates that among the considered external validation metrics, r²(m) shows statistically significantly different numerical values from others among which CCC is the most optimistic or less stringent. Furthermore, at a given level of threshold value of acceptance for external validation metrics, r²(m) provides the most stringent criterion (especially with Δr²(m) at highest tolerated value of 0.2) of external validation, which may be adopted in the case of regulatory decision support processes.

Quantitative structure-activity relationship (QSAR) techniques have found wide application in the fields of drug design, property modeling, and toxicity prediction of untested chemicals. A rigorous validation of the developed models plays the key role for their successful application in prediction for new compounds. The r(m)(2) metrics introduced by Roy et al. have been extensively used by different research groups for validation of regression-based QSAR models. This concept has been further advanced here with introduction of scaling of response data prior to computation of r(m)(2). Further, a web application (accessible from http://aptsoftware.co.in/rmsquare/ and http://203.200.173.43:8080/rmsquare/) for calculation of the r(m)(2) metrics has been introduced here. The present study reports that the web application can be easily used for computation of r(m)(2) metrics provided observed and QSAR-predicted data for a set of compounds are available. Further, scaling of response data is recommended prior to r(m)(2) calculation.