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EMPOP—A forensic mtDNA database

Mitochondrial DNA databases stand as the basis for frequency estimations of mtDNA sequences that became relevant in a case. The establishment of mtDNA databases sounds trivial; however, it has been shown in the past that this undertaking is prone to error for several reasons, particularly human error. We have established a concept for mtDNA data generation, analysis, transfer and quality control that meets forensic standards. Due to the complexity of mtDNA population data tables it is often difficult if not impossible to detect errors, especially for the untrained eye. We developed software based on quasi-median network analysis that visualizes mtDNA data tables and thus signposts sequencing, interpretation and transcription errors. The mtDNA data (N=5173; release 1) are stored and made publicly available via the Internet in the form of the EDNAP mtDNA Population Database, short EMPOP. This website also facilitates quasi-median network analysis and provides results that can be used to check the quality of mtDNA sequence data. EMPOP has been launched on 16 October 2006 and is since then available at http://www.empop.org.

Concept for estimating mitochondrial DNA haplogroups using a maximum likelihood approach (EMMA)

The assignment of haplogroups to mitochondrial DNA haplotypes contributes substantial value for quality control, not only in forensic genetics but also in population and medical genetics. The availability of Phylotree, a widely accepted phylogenetic tree of human mitochondrial DNA lineages, led to the development of several (semi-)automated software solutions for haplogrouping. However, currently existing haplogrouping tools only make use of haplogroup-defining mutations, whereas private mutations (beyond the haplogroup level) can be additionally informative allowing for enhanced haplogroup assignment. This is especially relevant in the case of (partial) control region sequences, which are mainly used in forensics. The present study makes three major contributions toward a more reliable, semi-automated estimation of mitochondrial haplogroups. First, a quality-controlled database consisting of 14,990 full mtGenomes downloaded from GenBank was compiled. Together with Phylotree, these mtGenomes serve as a reference database for haplogroup estimates. Second, the concept of fluctuation rates, i.e. a maximum likelihood estimation of the stability of mutations based on 19,171 full control region haplotypes for which raw lane data is available, is presented. Finally, an algorithm for estimating the haplogroup of an mtDNA sequence based on the combined database of full mtGenomes and Phylotree, which also incorporates the empirically determined fluctuation rates, is brought forward. On the basis of examples from the literature and EMPOP, the algorithm is not only validated, but both the strength of this approach and its utility for quality control of mitochondrial haplotypes is also demonstrated.

On the Optimality of the Discrete Karhunen--Loève Expansion

A short proof of the optimality of the discrete Karhunen--Loeve expansion as the best linear approximation in the quadratic mean is presented.

An Improved Normalization for the Ward Reflectance Model

We analyze the energy balance of Wards empirical reflection model and calculate the distribution of Wards Monte-Carlo importance sampling used in the Radiance Lighting Simulation and Rendering System. Both results suggest a different normalization of the bidirectional reflection distribution function proposed by Ward.

A new ward BRDF model with bounded albedo

Due to its realistic appearance, computational convenience, and efficient Monte Carlo sampling, Wards anisotropic BRDF is widely used in computer graphics for modeling specular reflection. Incorporating the criticism that the Ward and the Ward‐Dür model do not meet energy balance at grazing angles, we propose a modified BRDF that is energy conserving and preserves Helmholtz reciprocity. The new BRDF is computationally cheap to evaluate, admits efficient importance sampling, and thus sustains the main benefits of the Ward model. We show that the proposed BRDF is better suited for fitting measured reflectance data of a linoleum floor used in a real‐world building than the Ward and the Ward‐Dür model.

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).

On the computation of the performance probabilities for block codes with a bounded-distance decoding rule

The invention relates to a flexible probe for non-destructive inspection of long tubes. The measuring head is connected to the electrical connection by means of a body constituted by a sheath, whose particular characteristic is that it has a limited elongation strain and a low degree of deformation on compression, so that it does not deform either during the introduction of the probe into the tube or during its extraction from the tube, no matter what the tube length. The invention is more particularly applicable to the inspection for faults within long tubes by the eddy current method.When a block code is used on a discrete memoryless channel with an incomplete decoding rule that is based on a generalized distance, the probability of decoding failure, the probability of erroneous decoding, and the expected number of symbol decoding errors can be expressed in terms of the generalized weight enumerator polynomials of the code. For the symmetric erasure channel, numerically stable methods to compute these probabilities or expectations are proposed for binary codes whose distance distributions are known, and for linear maximum distance separable (MDS) codes. The method for linear MDS codes saves the computation of the weight distribution and yields upper bounds for the probability of erroneous decoding and for the symbol error rate by the cumulative binomial distribution. Numerical examples include a triple-error-correcting Bose-Chaudhuri-Hocquenghem (BCH) code of length 63 and a Reed-Solomon code of length 1023 and minimum distance 31. >

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.

Finite linear recurring sequences and homogeneous ideals

The linear recurrence relations satisfied by finitely many sequences of finite length over a ground field are described by homogeneous ideals in the polynomial ring in two variables by using Macaulays theory of inverse systems. The class of these ideals is shown to be precisely the class of homogeneous primary ideals the associated prime of which is the irrelevant maximal ideal. In the case of a single sequence, the classical Berlekamp-Massey algorithm for linear feedback shift register synthesis can be applied to obtain a minimal Gröbner basis of the ideal. The case of multiple sequences is reduced to the case of single sequences by ideal intersection, and the set of all linear recurrence relations of minimal order for the given sequences is generated by the low degree polynomials of the Gröbner basis.

A fast algorithm to determine the burst-correcting limit of cyclic or shortened cyclic codes

A novel fast algorithm is developed for computing the burst-correcting limit of a cyclic or shortened cyclic code from the parity-check polynomial of the cyclic code. The algorithm is similar to the algorithm of H.J. Matt and J.L. Massey (1980) which, up to now, has been the most efficient method for determining the burst-correcting limit of a cyclic code, but is based on apolarity of binary forms instead of linear complexity. The running times of implementations in C of both algorithms on an IBM RISC System/6000 are compared for several binary cyclic codes of practical interest. A table of the burst-correcting limit of primitive binary BCH codes of length up to 1023 is included. >