Optimal distributed multiparameter estimation in noisy environments

We consider the task of multiple parameter estimation in the presence of strong correlated noise with a network of distributed sensors. We study how to find and improve noise-insensitive strategies. We show that sequentially probing GHZ states is optimal up to a factor of at most 4. This allows us to connect the problem to single parameter estimation, and to use techniques such as protection against correlated noise in a decoherence-free subspace, or read-out by local measurements.Comment: 8 pages, 2 figure

Improved visibility of character conflicts in quasi-median networks with the EMPOP NETWORK software

Aim To provide a valuable tool for graphical representation of mitochondrial DNA (mtDNA) data that enables visual emphasis on complex substructures within the network to highlight possible ambiguities and errors. Method We applied the new NETWORK graphical user interface, available via EMPOP (European DNA Profiling Group Mitochondrial DNA Population Database; www. empop.org) by means of two mtDNA data sets that were submitted for quality control. Results The quasi-median network torsi of the two data sets resulted in complex reticulations, suggesting ambiguous data. To check the corresponding raw data, accountable nodes and connecting branches of the network could be identified by highlighting induced subgraphs with concurrent dimming of their complements. This is achieved by accentuating the relevant substructures in the network: mouse clicking on a node displays a list of all mtDNA haplotypes included in that node; the selection of a branch specifies the mutation(s) connecting two nodes. It is indicated to evaluate these mutations by means of the raw data. Conclusion Inspection of the raw data confirmed the presence of phantom mutations due to suboptimal electrophoresis conditions and data misinterpretation. The network software proved to be a powerful tool to highlight problematic data and guide quality control of mtDNA data tables

The decoding of extended Reed-Solomon codes

AbstractCauchy codes are a class of maximum distance separable codes that include Reed-Solomon codes, singly- and doubly-extended Reed-Solomon codes, and reversible BCH over GF(2m) of length 2m+1. The decoding problem for Cauchy codes is studied by using an analogue of the classical theory of apolarity of binary forms, and Berlekamp's decoding algorithm for Reed-Solomon codes is extended to Cauchy codes. The covering radius of a Cauchy code over GF(q) of length n and minimum distance d is shown to be either d−2 or d−1, and the exact value is determined unless n = q + 1 and q⧸2+3<d<q. If n = q + 1 and d = q is even, the covering radius is q − 1, and the determination of all cosets with leaders of weight q − 1 is equivalent to the determination of all ovals with q + 2 points in the projective plane

Pathogenic Variant Filtering for Mitochondrial Genome Haplotype Reporting

Given the enhanced discriminatory power of the mitochondrial DNA (mtDNA) genome (mitogenome) over the commonly sequenced control region (CR) portion, the scientific merit of mitogenome sequencing is generally accepted. However, many laboratories remain beholden to CR sequencing due to privacy policies and legal requirements restricting the use of disease information or coding region (codR) information. In this report, we present an approach to obviate the reporting of sensitive codR data in forensic haplotypes. We consulted the MitoMap database to identify 92 mtDNA codR variants with confirmed pathogenicity. We determined the frequencies of these pathogenic variants in literature-quality and forensic-quality databases to be very low, at 1.2% and 0.36%, respectively. The observed effect of pathogenic variant filtering on random match statistics in 2488 forensic-quality mitogenome haplotypes from four populations was nil. We propose that pathogenic variant filtering should be incorporated into variant calling algorithms for mitogenome haplotype reporting to maximize the discriminatory power of the locus while minimizing the reveal of sensitive genetic information

SAM: String-based sequence search algorithm for mitochondrial DNA database queries

The analysis of the haploid mitochondrial (mt) genome has numerous applications in forensic and population genetics, as well as in disease studies. Although mtDNA haplotypes are usually determined by sequencing, they are rarely reported as a nucleotide string. Traditionally they are presented in a difference-coded position-based format relative to the corrected version of the first sequenced mtDNA. This convention requires recommendations for standardized sequence alignment that is known to vary between scientific disciplines, even between laboratories. As a consequence, database searches that are vital for the interpretation of mtDNA data can suffer from biased results when query and database haplotypes are annotated differently. In the forensic context that would usually lead to underestimation of the absolute and relative frequencies. To address this issue we introduce SAM, a string-based search algorithm that converts query and database sequences to position-free nucleotide strings and thus eliminates the possibility that identical sequences will be missed in a database query. The mere application of a BLAST algorithm would not be a sufficient remedy as it uses a heuristic approach and does not address properties specific to mtDNA, such as phylogenetically stable but also rapidly evolving insertion and deletion events. The software presented here provides additional flexibility to incorporate phylogenetic data, site-specific mutation rates, and other biologically relevant information that would refine the interpretation of mitochondrial DNA data. The manuscript is accompanied by freeware and example data sets that can be used to evaluate the new software (http://stringvalidation.org)