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Criteria are proposed for assessing the robustness of a binary block design against the loss of whole blocks, based on summing entries of selected upper non-principal sections of the concurrence matrix. These criteria improve on the minimal concurrence concept that has been used previously and provide new conditions for measuring the robustness status of a design. The robustness properties of two-associate partially balanced designs are considered and it is shown that two categories of group divisible designs are maximally robust. These results expand a classic result in the literature, obtained by Ghosh, which established maximal robustness for the class of balanced block designs. [ABSTRACT FROM AUTHOR]

Sequence libraries that cover all k-mers enable universal, unbiased measurements of binding to both oligonucleotides and peptides. While the number of k-mers grows exponentially in k, space on all experimental platforms is limited. Here, we shrink k-mer library sizes by using joker characters, which represent all characters in the alphabet simultaneously. We present the JokerCAKE (joker covering all k-mers) algorithm for generating a short sequence such that each k-mer appears at least p times with at most one joker character per k-mer. By running our algorithm on a range of parameters and alphabets, we show that JokerCAKE produces near-optimal sequences. Moreover, through comparison with data from hundreds of DNA-protein binding experiments and with new experimental results for both standard and JokerCAKE libraries, we establish that accurate binding scores can be inferred for high-affinity k-mers using JokerCAKE libraries. JokerCAKE libraries allow researchers to search a significantly larger sequence space using the same number of experimental measurements and at the same cost., (Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.)