Bayesian evidence for two companions orbiting HIP 5158

We present results of a Bayesian analysis of radial velocity (RV) data for the star HIP 5158, confirming the presence of two companions and also constraining their orbital parameters. Assuming Keplerian orbits, the two-companion model is found to be e^{48} times more probable than the one-planet model, although the orbital parameters of the second companion are only weakly constrained. The derived orbital periods are 345.6 +/- 2.0 d and 9017.8 +/- 3180.7 d respectively, and the corresponding eccentricities are 0.54 +/- 0.04 and 0.14 +/- 0.10. The limits on planetary mass (m \sin i) and semimajor axis are (1.44 +/- 0.14 M_{J}, 0.89 +/- 0.01 AU) and (15.04 +/- 10.55 M_{J}, 7.70 +/- 1.88 AU) respectively. Owing to large uncertainty on the mass of the second companion, we are unable to determine whether it is a planet or a brown dwarf. The remaining `noise' (stellar jitter) unaccounted for by the model is 2.28 +/- 0.31 m/s. We also analysed a three-companion model, but found it to be e^{8} times less probable than the two-companion model.Comment: 5 pages, 4 figures, 3 tables. Added a couple of figures showing the residuals after one and two companion fits. Accepted for publication in MNRAS Letter

BAMBI: blind accelerated multimodal Bayesian inference

In this paper we present an algorithm for rapid Bayesian analysis that combines the benefits of nested sampling and artificial neural networks. The blind accelerated multimodal Bayesian inference (BAMBI) algorithm implements the MultiNest package for nested sampling as well as the training of an artificial neural network (NN) to learn the likelihood function. In the case of computationally expensive likelihoods, this allows the substitution of a much more rapid approximation in order to increase significantly the speed of the analysis. We begin by demonstrating, with a few toy examples, the ability of a NN to learn complicated likelihood surfaces. BAMBI's ability to decrease running time for Bayesian inference is then demonstrated in the context of estimating cosmological parameters from Wilkinson Microwave Anisotropy Probe and other observations. We show that valuable speed increases are achieved in addition to obtaining NNs trained on the likelihood functions for the different model and data combinations. These NNs can then be used for an even faster follow-up analysis using the same likelihood and different priors. This is a fully general algorithm that can be applied, without any pre-processing, to other problems with computationally expensive likelihood functions.Comment: 12 pages, 8 tables, 17 figures; accepted by MNRAS; v2 to reflect minor changes in published versio

Pakistan: Ethnic Fragmentation or National Integration?

In light of the current ethnic polarisation, this paper briefly enumerates the elements of ethnic conflict in Pakistan. It, then, discusses the economic, demographic, political, and cultural developments taking place in Pakistan which tend to affect the inter-relationships among ethnic communities and between society as a whole and ethnic communities. Evidence is presented to support the argument that despite surface tensions and confrontations, there is an unmistakable trend of greater inter-dependence which can contribute to national integration. The paper further analyses the relationship between ethnicity, class, and the state. It identifies military, bureaucracy, capitalists, and landlords as the principal elements of the “ruling class”, and shows that the different ethnic groups have different class structures and differential participation in military and bureaucracy. It points out the near absence of “cross cutting cleavages” which tends to turn the class and power conflicts into ethnic conflicts. In conclusion, the paper, while underlining the shifting definitional boundaries and relative demographic and cultural homogenisation of the population, argues against the redrawing of provincial boundaries and constitutional recognition of “nationality rights” of fixed ethnic groups. However, it makes a case for the recognition of ethnic diversity in Pakistan, equal treatment of all ethnic groups, and protection and promotion of the languages and cultures of the different ethnic groups. It argues that national unity, security, and integrity will be achieved if the primary emphasis is placed on promoting equity and harmony rather than on suppression of ethnic differences in the name of unity.

Exploring Multi-Modal Distributions with Nested Sampling

In performing a Bayesian analysis, two difficult problems often emerge. First, in estimating the parameters of some model for the data, the resulting posterior distribution may be multi-modal or exhibit pronounced (curving) degeneracies. Secondly, in selecting between a set of competing models, calculation of the Bayesian evidence for each model is computationally expensive using existing methods such as thermodynamic integration. Nested Sampling is a Monte Carlo method targeted at the efficient calculation of the evidence, but also produces posterior inferences as a by-product and therefore provides means to carry out parameter estimation as well as model selection. The main challenge in implementing Nested Sampling is to sample from a constrained probability distribution. One possible solution to this problem is provided by the Galilean Monte Carlo (GMC) algorithm. We show results of applying Nested Sampling with GMC to some problems which have proven very difficult for standard Markov Chain Monte Carlo (MCMC) and down-hill methods, due to the presence of large number of local minima and/or pronounced (curving) degeneracies between the parameters. We also discuss the use of Nested Sampling with GMC in Bayesian object detection problems, which are inherently multi-modal and require the evaluation of Bayesian evidence for distinguishing between true and spurious detections.Comment: Refereed conference proceeding, presented at 32nd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineerin

Decomposing elements of a right self-injective ring

It was proved independently by both Wolfson [An ideal theoretic characterization of the ring of all linear transformations, Amer. J. Math. 75 (1953), 358-386] and Zelinsky [Every Linear Transformation is Sum of Nonsingular Ones, Proc. Amer. Math. Soc. 5 (1954), 627-630] that every linear transformation of a vector space $V$ over a division ring $D$ is the sum of two invertible linear transformations except when $V$ is one-dimensional over $\mathbb Z_2$. This was extended by Khurana and Srivastava [Right self-injective rings in which each element is sum of two units, J. Algebra and its Appl., Vol. 6, No. 2 (2007), 281-286] who proved that every element of a right self-injective ring $R$ is the sum of two units if and only if $R$ has no factor ring isomorphic to $\mathbb Z_2$. In this paper we prove that if $R$ is a right self-injective ring, then for each element $a\in R$ there exists a unit $u\in R$ such that both $a+u$ and $a-u$ are units if and only if $R$ has no factor ring isomorphic to $\mathbb Z_2$ or $\mathbb Z_3$.Comment: To appear in J. Algebra and App

ANN Based Virtual Classification Model for Discriminating Active and Inactive Withanolide E Analogs against Human Breast Cancer Cell Line MCF-7

Withanolides are a group of natural C-28 steroids built on an ergostane skeleton and classified into two major groups according to their structural skeleton: (a) compounds with a beta-oriented side chain and (b) compounds with an alpha-oriented side chain. Withanolide E represents one of the members of the latter group. Classification of active compounds on the basis of pharmacophore against specific cancer cell line poses a serious concern at the primary stage of virtual screening. To overcome this problem we have developed an artificial neural network based virtual screening model for discriminating active and non-active Withanolide-E-like derivatives or analogs against human breast cancer cell line MCF-7. In the present work, a 2D chemical descriptors ensemble pharmacophore has been modelled on the basis of withanolide E structural featured molecules. The ANN structure activity based classification model could be useful for identification of active withanolide analogs as anticancer leads against MCF-7. This model can be used for predicting possible growth inhibitory concentration (logGI50) against breast cancer cell line MCF-7. The virtual screening tool “CanWithaANN” can be accessed at local network of CIMAP

Weight matrix based identification of terpene synthases conserved motifs in Arabidopsis thaliana proteome

Terpenes comprise the most diverse collection of natural products. Out of more than 30,000 individual terpenoids identified, at least half are synthesized by plants. A relatively small, but quantitatively significant, number of terpenoids are involved in primary plant metabolism. However, the vast majorities are classified as secondary metabolites; compounds not required for plant growth and development but presumed to have an ecological function in communication or defense and are widely used in industrial applications. Terpene hydrocarbon scaffolds are generated by the action of the mechanistically intriguing family of mono-, sesqui-, and diterpene synthases collectively termed as terpene synthases, that catalyze multistep reactions with diphosphorylated substrates of 10 (geranyl diphosphate), 15 (farnesyl diphosphate) or 20 (geranylgeranyl diphosphate) carbons. In the studied work, we performed a computational study on proteome wide identification of terpene synthase motifs in Arabidopsis thaliana proteome on the basis of weight matrix approach. We have developed an optimal weight matrix for the identification of terpene synthase motifs in the plant’s proteome. Weight matrix was constructed by aligning orthologous sequences of known terpene synthases originated from diverse plant species viz., Abies grandis, Nicotiana tobaccum etc. Sequences of detected domains & motifs were retrieved through SwissProtKB/NCBI on the basis of specific conservation IDs of Prosite, Pfam, Interpro, Prodom, COG, TIGR databases, while position specific scoring matrices were made through MEME, MotifSampler, PossuMsearch tools. Weight matrix based search of conserved motifs in the proteome of A. thaliana was done through ESA, Lahead and Simple algorithm based search tools of PossuMsearch biosuite in Linux system. Prediction was first validated by using positive control data set and optimized the method to reach prediction accuracy upto >90%. After tool performance evaluation, prediction was made on whole proteome at specific threshold/score value. Significant results were found in A. thaliana with motif similarity ranges from 80% to 100%. This proteome wide search model paves the path to identify more terpene synthases genes in A. thaliana, as well as in other plant systems

Weak lensing by triaxial galaxy clusters

Weak gravitational lensing studies of galaxy clusters often assume a spherical cluster model to simplify the analysis, but some recent studies have suggested this simplifying assumption may result in large biases in estimated cluster masses and concentration values, since clusters are expected to exhibit triaxiality. Several such analyses have, however, quoted expressions for the spatial derivatives of the lensing potential in triaxial models, which are open to misinterpretation. In this paper, we give a clear description of weak lensing by triaxial NFW galaxy clusters and also present an efficient and robust method to model these clusters and obtain parameter estimates. By considering four highly triaxial NFW galaxy clusters, we re-examine the impact of simplifying spherical assumptions and found that while the concentration estimates are largely unbiased except in one of our traixial NFW simulated clusters, for which the concentration is only slightly biased, the masses are significantly biased, by up to 40%, for all the clusters we analysed. Moreover, we find that such assumptions can lead to the erroneous conclusion that some substructure is present in the galaxy clusters or, even worse, that multiple galaxy clusters are present in the field. Our cluster fitting method also allows one to answer the question of whether a given cluster exhibits triaxiality or a simple spherical model is good enough.Comment: 8 pages, 3 figures, 2 tables, minor changes in response to referee's comments, accepted for publication in MNRA