Capturing the ‘ome’ : the expanding molecular toolbox for RNA and DNA library construction

All sequencing experiments and most functional genomics screens rely on the generation of libraries to comprehensively capture pools of targeted sequences. In the past decade especially, driven by the progress in the field of massively parallel sequencing, numerous studies have comprehensively assessed the impact of particular manipulations on library complexity and quality, and characterized the activities and specificities of several key enzymes used in library construction. Fortunately, careful protocol design and reagent choice can substantially mitigate many of these biases, and enable reliable representation of sequences in libraries. This review aims to guide the reader through the vast expanse of literature on the subject to promote informed library generation, independent of the application

Cornerstones of Sampling of Operator Theory

This paper reviews some results on the identifiability of classes of operators whose Kohn-Nirenberg symbols are band-limited (called band-limited operators), which we refer to as sampling of operators. We trace the motivation and history of the subject back to the original work of the third-named author in the late 1950s and early 1960s, and to the innovations in spread-spectrum communications that preceded that work. We give a brief overview of the NOMAC (Noise Modulation and Correlation) and Rake receivers, which were early implementations of spread-spectrum multi-path wireless communication systems. We examine in detail the original proof of the third-named author characterizing identifiability of channels in terms of the maximum time and Doppler spread of the channel, and do the same for the subsequent generalization of that work by Bello. The mathematical limitations inherent in the proofs of Bello and the third author are removed by using mathematical tools unavailable at the time. We survey more recent advances in sampling of operators and discuss the implications of the use of periodically-weighted delta-trains as identifiers for operator classes that satisfy Bello's criterion for identifiability, leading to new insights into the theory of finite-dimensional Gabor systems. We present novel results on operator sampling in higher dimensions, and review implications and generalizations of the results to stochastic operators, MIMO systems, and operators with unknown spreading domains