A model for bimodal rates and proportions.

The beta model is the most important distribution for fitting data with the unit interval. However, the beta distribution is not suitable to model bimodal unit interval data. In this paper, we propose a bimodal beta distribution constructed by using an approach based on the alpha-skew-normal model. We discuss several properties of this distribution, such as bimodality, real moments, entropies and identifiability. Furthermore, we propose a new regression model based on the proposed model and discuss residuals. Estimation is performed by maximum likelihood. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. An application is provided to show the modelling competence of the proposed distribution when the data sets show bimodality.

Stable and metastable crystal structures and ammonia dynamics in strontium chloride ammines.

Metal halide ammines are promising ammonia storage materials due to their high ammonia densities and suitable decomposition properties. Here, we studied the polymorphism of ammines with a general formula of Sr(NH3)nCl2 (n = 1, 2, 4, 6, and 8) by combining the Fast and Flexible CrystAl Structure Predictor (FFCASP) with density functional theory (DFT) calculations. Furthermore, the lattice stability and the minimum energy paths for bulk and surface diffusion of NH3 were investigated by performing phonon and nudged elastic band (NEB) calculations. In addition to the successful reproduction of the reported experimental crystal structures of octammine (Pnma (IT number 62)), diammine (Aem2 (IT number 39)) and monoammine (Cmcm (IT number 63)), several isoenergetic polymorphs for each phase were also found. Not only the experimentally determined octammine and monoammine structures, but also the proposed structures for the hexammine and tetrammine phases were found to be metastable. While phonon calculations show instability for the experimental diammine structure, some of the proposed structures for the diammine phase showed thermodynamical stability. Moreover, NEB paths examining the bulk and surface diffusion of NH3 are in accordance with the experimental desorption enthalpies.

A bimodal Weibull distribution: properties and inference.

Modelling is challenging topic and using parametric models is important stage to reach flexible function for modelling. Weibull distribution has shape and scale parameters which play the main role for modelling. Bimodality parameter is added and so bimodal Weibull distribution can capture real data set with bimodality which can be actually combination of two populations. The properties of the proposed distribution and estimation method are examined extensively to show its usability in modelling accurately and safely for practitioners. After examination as first stage in modelling issue, it is appropriate to use bimodal Weibull for modelling bimodality in real data sets if it exists. Two estimation methods including objective functions are used to estimate the parameters of shape, scale and bimodality parameters of function. The second stage in modelling is overcome by using heuristic algorithms for optimization of function according to parameters due to the fact that converging to global point of objective function is performed by heuristic algorithms from stochastic optimization. Real data sets are provided to show the modelling competence of objective functions from bimodal forms of Weibull and Gamma distributions having well defined shape, scale and bimodality parameters and potentially less parameters when compared with the existing distributions.

Fractional q-deformed chaotic maps: A weight function approach.

The fractional derivative holds long-time memory effects or non-locality. It successfully depicts the dynamical systems with long-range interactions. However, it becomes challenging to investigate chaos in the deformed fractional discrete-time systems. This study turns to fractional quantum calculus on the time scale and reports chaos in fractional q-deformed maps. The discrete memory kernels are used, and a weight function approach is proposed for fractional modeling. Rich q-deformed dynamics are demonstrated, which shows the methodology's efficiency.

Symmetry-adapted perturbation theory potential for the adenine dimer.

A new intermolecular interaction potential for the adenine dimer has been developed with the help of a combination of symmetry-adapted perturbation theory and density functional theory (DFT-SAPT). Supermolecular intermolecular interaction energy computations on hydrogen-bonded and stacked adenine dimers at B3LYP-D, MP2, SCS-MP2, SCS-MI-MP2 and CCSD(T) levels showed that DFT-SAPT is in a very good agreement with CCSD(T). The developed ab initio intermolecular potential has been used to predict the cluster structure of adenine dimers, trimers and tetramers. These global cluster optimizations reproduced adenine dimers reported in the literature and moreover new low-energy structures were also located. For trimers and tetramers, new hydrogen-bonded and stacked low-energy structures have also been found. The current findings suggest that the new ab initio potential can further be exploited to reveal the structure and energy of much larger supramolecular adenine clusters.

The informational entropy endowed in cortical oscillations.

A two-dimensional shadow may encompass more information than its corresponding three-dimensional object. Indeed, if we rotate the object, we achieve a pool of observed shadows from different angulations, gradients, shapes and variable length contours that make it possible for us to increase our available information. Starting from this simple observation, we show how informational entropies might turn out to be useful in the evaluation of scale-free dynamics in the brain. Indeed, brain activity exhibits a scale-free distribution that leads to the variations in the power law exponent typical of different functional neurophysiological states. Here we show that modifications in scaling slope are associated with variations in Rényi entropy, a generalization of Shannon informational entropy. From a three-dimensional object's perspective, by changing its orientation (standing for the cortical scale-free exponent), we detect different two-dimensional shadows from different perception angles (standing for Rényi entropy in different brain areas). We show how, starting from known values of Rényi entropy (easily detectable in brain fMRIs or EEG traces), it is feasible to calculate the scaling slope in a given moment and in a given brain area. Because changes in scale-free cortical dynamics modify brain activity, this issue points towards novel approaches to mind reading and description of the forces required for transcranial stimulation.

Asymmetric Bimodal Exponential Power Distribution on the Real Line.

The asymmetric bimodal exponential power (ABEP) distribution is an extension of the generalized gamma distribution to the real line via adding two parameters that fit the shape of peakedness in bimodality on the real line. The special values of peakedness parameters of the distribution are a combination of half Laplace and half normal distributions on the real line. The distribution has two parameters fitting the height of bimodality, so capacity of bimodality is enhanced by using these parameters. Adding a skewness parameter is considered to model asymmetry in data. The location-scale form of this distribution is proposed. The Fisher information matrix of these parameters in ABEP is obtained explicitly. Properties of ABEP are examined. Real data examples are given to illustrate the modelling capacity of ABEP. The replicated artificial data from maximum likelihood estimates of parameters of ABEP and other distributions having an algorithm for artificial data generation procedure are provided to test the similarity with real data. A brief simulation study is presented.

Estimation of cerebral surface area using vertical sectioning and magnetic resonance imaging: a stereological study.

Stereological techniques using isotropic uniform random and vertical uniform random sections have been used for surface area estimation. However, there are a few studies in which the surface area of the brain is estimated using the vertical section technique in a stereological approach. The objective of the current study was to apply the vertical section technique using cycloid test probes for estimation of cerebral surface area in magnetic resonance imaging (MRI). In this study, cerebral surface areas were estimated in a total of 13 young subjects (6 males, 7 females) who were free of any neurological symptoms and signs. The means (+/-S.D.) of the surface areas were 1619.92+/-140. 97 cm (2), 1625.69+/-147. 58 cm(2) and 1674.69+/-160. 60 cm(2) for 36, 18 and 12 vertical sections, respectively. The mean coefficient of error obtained by applying cycloid test lines that use a 2. 8-cm ratio of area associated with each cycloid was estimated at <7% for the three models. No significant difference was found for each of the 36, 18 and 12 vertical sections (p>0.05). In addition, the three models correlated well with each other. From these results, it is concluded that the vertical section technique is an unbiased, efficient and reliable method and is ideally suited to in vivo examination of MRI data for estimating the surface area of the brain. Hence, we suggest that estimation of surface area using MRI and stereology may be clinically relevant for assessing cortical atrophy as well as for investigating the structure and function of cerebral hemispheres.