Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery

PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The problem of subspace learning or PCA in the presence of outliers is called robust subspace learning or robust PCA (RPCA). For long data sequences, if one tries to use a single lower dimensional subspace to represent the data, the required subspace dimension may end up being quite large. For such data, a better model is to assume that it lies in a low-dimensional subspace that can change over time, albeit gradually. The problem of tracking such data (and the subspaces) while being robust to outliers is called robust subspace tracking (RST). This article provides a magazine-style overview of the entire field of robust subspace learning and tracking. In particular solutions for three problems are discussed in detail: RPCA via sparse+low-rank matrix decomposition (S+LR), RST via S+LR, and "robust subspace recovery (RSR)". RSR assumes that an entire data vector is either an outlier or an inlier. The S+LR formulation instead assumes that outliers occur on only a few data vector indices and hence are well modeled as sparse corruptions.Comment: To appear, IEEE Signal Processing Magazine, July 201

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Intergenerational Mobility: Evidence from Pakistan Panel Household Survey

Pakistan over the years, since its independence in 1947, had a rather erratic growth profile but on average GDP growth rate hovered around 5 percent per annum with per capita income growth ranging between 2 to 3 percent. The structure of the economy graduated from being predominantly agriculture in 1950s to being service sector orientated since the turn of the century. The manufacturing sector grew from almost insignificance in 1947 to a reasonable level accounting for around one third of the GDP. The demographic inertia associated with unchecked population growth and emergence of job opportunities in urban areas led to massive rural to urban migration, which resulted in a rather high level of urbanisation. Concomitant changes in both the urban and rural labour markets are visible too. Not only did average years of schooling of the labour force rise but also changes in occupational classification suggest a relative ris

Jameel Jalibi’s History of Urdu Literature; The Techniques, Standard and Limitations, A Critical and Research Analyses

History of Urdu literature has been a very phenomenal subject of Urdu research. Our book-shelves are adorned and well equipped with esteemed writings of esteemed historians of Urdu language and literature. It is the subject of keen importance to analyze, compare, value and put them on the touch-stone of modern research that invites the critic to highlight the right areas where the historians have done exceedingly well and find genuine requisitions, still deemed necessary to revise the existing history works. Jameel Jalibi is the most famous and well-read historian of Urdu language and literature among the all. His (book series) “Tareekh-e-Adab-e-Urdu” consisting of 4 volumes keeps the place amongst highest ranks of history of Urdu. In this article, the technique of all of his four volumes has been discussed chronologically, critically and analytically. It has been studied in the liaison with modern trends and needs of research and criticism. The right amendments, displacements and additions, wherever are deemed mandatory to be done, in the historic study of Jameel Jalibi have been discussed. This article will offer the critics and researchers to revise the standards of historic mode of research and put the rational approach of research in literary work

A Hybrid Variational Iteration Method for Blasius Equation

The objective of this paper is to present the hybrid variational iteration method. The proposed algorithm is based on the combination of variational iteration and shooting methods. In the proposed algorithm the entire domain is divided into subintervals to establish the accuracy and convergence of the approximate solution. It is found that in each subinterval a three term approximate solution using variational iteration method is sufficient. The proposed hybrid variational iteration method offers not only numerical values, but also closed form analytic solutions in each subinterval. The method is implemented using an example of the Blasius equation. The results show that a hybrid variational iteration method is a powerful technique for solving nonlinear problems

Potential role of gut microbiota in induction and regulation of innate immune memory

The gut microbiota significantly regulates the development and function of the innate and adaptive immune system. The attribute of immunological memory has long been linked only with adaptive immunity. Recent evidence indicates that memory is also present in the innate immune cells such as monocytes/macrophages and natural killer cells. These cells exhibit pattern recognition receptors (PRRs) that recognize microbe- or pathogen-associated molecular patterns (MAMPs or PAMPs) expressed by the microbes. Interaction between PRRs and MAMPs is quite crucial since it triggers the sequence of signaling events and epigenetic rewiring that not only play a cardinal role in modulating the activation and function of the innate cells but also impart a sense of memory response. We discuss here how gut microbiota can influence the generation of innate memory and functional reprogramming of bone marrow progenitors that helps in protection against infections. This article will broaden our current perspective of association between the gut microbiome and innate memory. In the future, this knowledge may pave avenues for development and designing of novel immunotherapies and vaccination strategies