Transductive-Inductive Cluster Approximation Via Multivariate Chebyshev Inequality

Approximating adequate number of clusters in multidimensional data is an open area of research, given a level of compromise made on the quality of acceptable results. The manuscript addresses the issue by formulating a transductive inductive learning algorithm which uses multivariate Chebyshev inequality. Considering clustering problem in imaging, theoretical proofs for a particular level of compromise are derived to show the convergence of the reconstruction error to a finite value with increasing (a) number of unseen examples and (b) the number of clusters, respectively. Upper bounds for these error rates are also proved. Non-parametric estimates of these error from a random sample of sequences empirically point to a stable number of clusters. Lastly, the generalization of algorithm can be applied to multidimensional data sets from different fields.Comment: 16 pages, 5 figure

Prioritizing 2nd and 3rd order interactions via support vector ranking using sensitivity indices on static Wnt measurements - Part A [work in progress]

It is widely known that the sensitivity analysis plays a major role in computing the strength of the influence of involved factors in any phenomena under investigation. When applied to expression profiles of various intra/extracellular factors that form an integral part of a signaling pathway, the variance and density based analysis yields a range of sensitivity indices for individual as well as various combinations of factors. These combinations denote the higher order interactions among the involved factors that might be of interest in the working mechanism of the pathway. For example, in a range of fourth order combinations among the various factors of the Wnt pathway, it would be easy to assess the influence of the destruction complex formed by APC, AXIN, CSKI and GSK3 interaction. In this work, after estimating the individual effects of factors for a higher order combination, the individual indices are considered as discriminative features. A combination, then is a multivariate feature set in higher order (&gt;2). With an excessively large number of factors involved in the pathway, it is difficult to search for important combinations in a wide search space over different orders. Exploiting the analogy of prioritizing webpages using ranking algorithms, for a particular order, a full set of combinations of interactions can then be prioritized based on these features using a powerful ranking algorithm via support vectors. The computational ranking sheds light on unexplored combinations that can further be investigated using hypothesis testing based on wet lab experiments. Here, the basic framework and results obtained on 2nd and 3rd order interactions on a toy example data set is presented. Subsequent manuscripts will examine higher order interactions in detail. Part B of this work deals with the time series data.</jats:p

protein phosphatase 2A catalytic subunit, alpha isoform (PPP2CA) : Time behavioural study of 3rd order combinations in WNT3A stimulated HEK 293 cells

PPP2CA encodes the phosphatase 2A catalytic subunit and is one of the four major Serine/threonine-protein phosphatases. It consists of a common heteromeric core enzyme, composed of a catalytic subunit and a constant regulatory subunit, that associates with a variety of regulatory subunits and it is implicated in the negative control of cell growth and division. Gujral and MacBeath [1] provides a quantitative, and dynamic study of WNT3A-mediated stimulation of HEK 293 cells, where they record time based expression profiles of several response genes which correlated significantly with proliferation and migration. By monitoring the dynamics of gene expression using self-organizing maps, they identified clusters of genes that exhibit similar expression dynamics and uncovered previously unrecognized positive and negative feedback loops. However, their study depicts/uses singular measurements of individual gene expression at different time snapshots/points to infer the system wide analysis of the pathway. At any particular time point, it is often the case that genes are working synergistically in combinations, even though their expression measurements are singular in nature. Here, I • enumerate and rank all 2415 PPP2CA related 3rd order combinations in a forest of 71C3 combinations using four different sensitivity methods; • show the conserved rankings for PPP2CA-X-X combinations, which point to existence of bio- logical synergy of some of these combinations across the different sensitivity methods; and • study the behaviour of some of these combinations related to WNT3A response genes that are ranked by the machine learning search engine (Sinha [2]) in time. Pat- terns of combinations emerge, some of which have been tested in wet lab, while others require further wet lab analysis

Buddhist perspectives

In the grand scale of cosmos, it is the human form, in which qualities (guna) exist which make it capable to understand and grasp the intricacies and work through to liberate itself from the limited cycles of birth and death and the coordinates governing them. That liberation has stages, which leads to fully liberated stage and is connoted by the term Buddha. And it is only in the human form that one can acquire the stage of Buddha, however, the journey is long. Articles in this project touch on various aspects of the journey into the realms of the absolute truth and the Buddha's teachings