Mutually Uncorrelated Primers for DNA-Based Data Storage

We introduce the notion of weakly mutually uncorrelated (WMU) sequences, motivated by applications in DNA-based data storage systems and for synchronization of communication devices. WMU sequences are characterized by the property that no sufficiently long suffix of one sequence is the prefix of the same or another sequence. WMU sequences used for primer design in DNA-based data storage systems are also required to be at large mutual Hamming distance from each other, have balanced compositions of symbols, and avoid primer-dimer byproducts. We derive bounds on the size of WMU and various constrained WMU codes and present a number of constructions for balanced, error-correcting, primer-dimer free WMU codes using Dyck paths, prefix-synchronized and cyclic codes.Comment: 14 pages, 3 figures, 1 Table. arXiv admin note: text overlap with arXiv:1601.0817

Semistable modifications of families of curves and compactified Jacobians

Given a family of nodal curves, a semistable modification of it is another family made up of curves obtained by inserting chains of rational curves of any given length at certain nodes of certain curves of the original family. We give comparison theorems between torsion-free, rank-1 sheaves in the former family and invertible sheaves in the latter. We apply them to show that there are functorial isomorphisms between the compactifications of relative Jacobians of families of nodal curves constructed through Caporaso's approach and those constructed through Pandharipande's approach.Comment: 27 pages. arXiv admin note: substantial text overlap with arXiv:1212.112

Integrality of hook ratios

We study integral ratios of hook products of quotient partitions. This question is motivated by an analogous question in number theory concerning integral factorial ratios. We prove an analogue of a theorem of Landau that already applied in the factorial case. Under the additional condition that the ratio has one more factor on the denominator than the numerator, we provide a complete classification. Ultimately this relies on Kneser's theorem in additive combinatorics.Comment: 13 pages, 3 figures Keywords: partitions, hook products, Kneser's theorem, McKay numbers, Beurling-Nyman criterio

An ESPC algorithm based approach to solve inventory deployment problem

Global competitiveness has enforced the hefty industries to become more customized. To compete in the market they are targeting the customers who want exotic products, and faster and reliable deliveries. Industries are exploring the option of satisfying a portion of their demand by converting strategically placed products, this helps in increasing the variability of product produced by them in short lead time. In this paper, authors have proposed a new hybrid evolutionary algorithm named Endosymbiotic-Psychoclonal (ESPC) algorithm to determine the amount and type of product to stock as a semi product in inventory. In the proposed work the ability of previously proposed Psychoclonal algorithm to exploit the search space has been increased by making antibodies and antigen more cooperative interacting species. The efficacy of the proposed algorithm has been tested on randomly generated datasets and the results obtained, are compared with other evolutionary algorithms such as Genetic Algorithm (GA) and Simulated Annealing (SA). The comparison of ESPC with GA and SA proves the superiority of the proposed algorithm both in terms of quality of the solution obtained, and convergence time required to reach the optimal /near optimal value of the solution