scholarly journals Proposed Framework for Comparison of Continuous Probabilistic Genotyping Systems amongst Different Laboratories

2021 ◽  
Vol 1 (1) ◽  
pp. 33-45
Author(s):  
Dennis McNevin ◽  
Kirsty Wright ◽  
Mark Barash ◽  
Sara Gomes ◽  
Allan Jamieson ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Analytical Solutions ◽  
Peak Height ◽  
Dna Profiling ◽  
Likelihood Ratios ◽  
Dna Mixtures ◽  
Individual Laboratory ◽  
Multiple Variables

Continuous probabilistic genotyping (PG) systems are becoming the default method for calculating likelihood ratios (LRs) for competing propositions about DNA mixtures. Calculation of the LR relies on numerical methods and simultaneous probabilistic simulations of multiple variables rather than on analytical solutions alone. Some also require modelling of individual laboratory processes that give rise to electropherogram artefacts and peak height variance. For these reasons, it has been argued that any LR produced by continuous PG is unique and cannot be compared with another. We challenge this assumption and demonstrate that there are a set of conditions defining specific DNA mixtures which can produce an aspirational LR and thereby provide a measure of reproducibility for DNA profiling systems incorporating PG. Such DNA mixtures could serve as the basis for inter-laboratory comparisons, even when different STR amplification kits are employed. We propose a procedure for an inter-laboratory comparison consistent with these conditions.

XVI.—Dual Series Relations. III. Dual Relations Involving Trigonometric Series

1963 ◽  
Vol 66 (3) ◽  
pp. 173-184 ◽  
Author(s):  
R. P. Srivastav
Keyword(s):  
Integral Equation ◽  
Numerical Methods ◽  
Integral Equations ◽  
Trigonometric Series ◽  
Analytical Solutions ◽  
Fredholm Integral Equation ◽  
Auxiliary Function

SynopsisThe methods developed in I, II of this series of papers are applied to a solution of a variety of dual series relations involving trigonometric series. In general the problem is reduced to one of solving (usually by numerical methods) a Fredholm integral equation of the second kind for an auxiliary function g(t), but for certain values of the parameters it is possible to obtain analytical solutions of the integral equations and these cases are considered in detail.

Fast Fourier Transform Based Numerical Methods for Elasto-Plastic Contacts of Nominally Flat Surfaces

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
W. Wayne Chen ◽  
Shuangbiao Liu ◽  
Q. Jane Wang
Keyword(s):  
Fourier Transform ◽  
Numerical Methods ◽  
Fast Fourier Transform ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Stress And Strain ◽  
Two Dimensional ◽  
Response Functions ◽  
Strain Fields ◽  
Flat Surfaces

This paper presents a three-dimensional numerical elasto-plastic model for the contact of nominally flat surfaces based on the periodic expandability of surface topography. This model is built on two algorithms: the continuous convolution and Fourier transform (CC-FT) and discrete convolution and fast Fourier transform (DC-FFT), modified with duplicated padding. This model considers the effect of asperity interactions and gives a detailed description of subsurface stress and strain fields caused by the contact of elasto-plastic solids with rough surfaces. Formulas of the frequency response functions (FRF) for elastic/plastic stresses and residual displacement are given in this paper. The model is verified by comparing the numerical results to several analytical solutions. The model is utilized to simulate the contacts involving a two-dimensional wavy surface and an engineering rough surface in order to examine its capability of evaluating the elasto-plastic contact behaviors of nominally flat surfaces.

scholarly journals Is peak height important for the statistical evaluation of the weight of evidence in DNA mixtures?

2015 ◽  
Vol 5 ◽  
pp. e395-e397
Author(s):  
A. Caglià ◽  
L. Baldassarri ◽  
I. Boschi ◽  
F. Scarnicci ◽  
V.L. Pascali
Keyword(s):  
Statistical Evaluation ◽  
Peak Height ◽  
Weight Of Evidence ◽  
Dna Mixtures

scholarly journals A Successive Linearization Method Approach to Solve Lane-Emden Type of Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
S. S. Motsa ◽  
S. Shateyi
Keyword(s):  
Numerical Methods ◽  
Boundary Value Problems ◽  
Analytical Solutions ◽  
Boundary Value ◽  
Linearization Method ◽  
Exact Analytical Solutions ◽  
Successive Linearization Method ◽  
Method Approach ◽  
Better Than

We propose a new application of the successive linearization method for solving singular initial and boundary value problems of Lane-Emden type. To demonstrate the reliability of the proposed method, a comparison is made with results from existing methods in the literature and with exact analytical solutions. It was found that the method is easy to implement, yields accurate results, and performs better than some numerical methods.

scholarly journals Probabilistic Genotyping of Single Cell Replicates from Complex DNA Mixtures Recovers Higher Contributor LRs than Standard Analysis

2021 ◽  
Author(s):  
Kaitlin Huffman ◽  
Erin Hanson ◽  
Jack Ballantyne
Keyword(s):  
Single Cell ◽  
Dna Typing ◽  
Complex Mixtures ◽  
Common Source ◽  
Single Source ◽  
Mixture Analysis ◽  
Likelihood Ratios ◽  
Dna Mixtures ◽  
Genotype Information ◽  
Dna Profiles

DNA mixtures are a common source of crime scene evidence and are often one of the more difficult sources of biological evidence to interpret. With the implementation of probabilistic genotyping (PG), mixture analysis has been revolutionized allowing previously unresolvable mixed profiles to be analyzed and probative genotype information from contributors to be recovered. However, due to allele overlap, artifacts, or low-level minor contributors, genotype information loss inevitably occurs. In order to reduce the potential loss of significant DNA information from donors in complex mixtures, an alternative approach is to physically separate individual cells from mixtures prior to performing DNA typing thus obtaining single source profiles from contributors. In the present work, a simplified micro-manipulation technique combined with enhanced single-cell DNA typing was used to collect one or few cells, referred to as direct single-cell subsampling (DSCS). Using this approach, single and 2-cell subsamples were collected from 2-6 person mixtures. Single-cell subsamples resulted in single source DNA profiles while the 2-cell subsamples returned either single source DNA profiles or new mini-mixtures that are less complex than the original mixture due to the presence of fewer contributors. PG (STRmixTM) was implemented, after appropriate validation, to analyze the original bulk mixtures, single source cell subsamples, and the 2-cell mini mixture subsamples from the original 2-6-person mixtures. PG further allowed replicate analysis to be employed which, in many instances, resulted in a significant gain of genotype information such that the returned donor likelihood ratios (LRs) were comparable to that seen in their single source reference profiles (i.e., the reciprocal of their random match probabilities). In every mixture, the DSCS approach gave improved results for each donor compared to standard bulk mixture analysis. With the 5- and 6- person complex mixtures, DSCS recovered highly probative LRs (> 1020) from donors that had returned non-probative LRs (<103) by standard methods.

scholarly journals Differential Models, Numerical Simulations and Applications

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 260
Author(s):  
Gabriella Bretti
Keyword(s):  
Applied Sciences ◽  
Numerical Methods ◽  
Computer Simulations ◽  
Analytical Solutions ◽  
Real World ◽  
Measured Data ◽  
Model Parameters ◽  
Special Issue ◽  
Efficient Simulation ◽  
Real World Applications

Differential models, numerical methods and computer simulations play a fundamental role in applied sciences. Since most of the differential models inspired by real world applications have no analytical solutions, the development of numerical methods and efficient simulation algorithms play a key role in the computation of the solutions to many relevant problems. Moreover, since the model parameters in mathematical models have interesting scientific interpretations and their values are often unknown, estimation techniques need to be developed for parameter identification against the measured data of observed phenomena. In this respect, this Special Issue collects some important developments in different areas of application.

scholarly journals Calculating likelihoods and likelihood ratios at SNPs-based mixtures. A reappraisal of the binomial inference, as applied to forensic identity tests

2021 ◽  
Author(s):  
Vincenzo L. Pascali
Keyword(s):  
Peak Height ◽  
Empirical Method ◽  
Peak Height Ratio ◽  
Nucleotide Polymorphisms ◽  
Likelihood Ratios ◽  
Single Nucleotide ◽  
Genotype Combination ◽  
Empirical Procedure ◽  
Typing Result ◽  
Number Of Individuals

AbstractSingle nucleotide polymorphisms (SNPs) are useful forensic markers. When a SNPs-based forensic protocol targets a body fluid stain, it returns elementary evidence regardless of the number of individuals that might have contributed to the stain deposition. Therefore, drawing inference from a mixed stain with SNPs is different than drawing it while using multinomial polymorphisms. We here revisit this subject, with a view to contribute to a fresher insight into it. First, we manage to model conditional semi-continuous likelihoods in terms of matrices of genotype permutations vs number of contributors (NTZsc). Secondly, we redefine some algebraic formulas to approach the semi-continuous calculation. To address allelic dropouts, we introduce a peak height ratio index (‘h’, or: the minor read divided by the major read at any NGS-based typing result) into the semi-continuous formulas, for they to act as an acceptable proxy of the ‘split drop’ (Haned et al, 2012) model of calculation. Secondly, we introduce a new, empirical method to deduct the expected quantitative ratio at which the contributors of a mixture have originally mixed and the observed ratio generated by each genotype combination at each locus. Compliance between observed and expected quantity ratios is measured in terms of (1-χ2) values at each state of a locus deconvolution. These probability values are multiplied, along with the h index, to the relevant population probabilities to weigh the overall plausibility of each combination according to the quantitative perspective. We compare calculation performances of our empirical procedure (NITZq) with those of the EUROFORMIX software ver. 3.0.3. NITZq generates LR values a few orders of magnitude lower than EUROFORMIX when true contributors are used as POIs, but much lower LR values when false contributors are used as POIs. NITZ calculation routines may be useful, especially in combination with mass genomics typing protocols.

scholarly journals Analytical Estimates of Critical Taylor Number for Motion between Rotating Coaxial Cylinders Based on Theory of Stochastic Equations and Equivalence of Measures

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 306
Author(s):  
Artur V. Dmitrenko
Keyword(s):  
Experimental Data ◽  
Numerical Methods ◽  
Analytical Solutions ◽  
Scientific Literature ◽  
Stochastic Equations ◽  
Taylor Number ◽  
Coaxial Cylinders ◽  
Equivalence Of Measures ◽  
Special Value ◽  
Mathematical Relationships

The purpose of this article was to present the solution for the critical Taylor number in the case of the motion between rotating coaxial cylinders based on the theory of stochastic equations of continuum laws and the equivalence of measures between random and deterministic motions. Analytical solutions are currently of special value, as the solutions obtained by modern numerical methods require verification. At present, in the scientific literature, there are no mathematical relationships connecting the critical Taylor number with the parameters of the initial disturbances in the flow. The result of the solution shows a satisfactory correspondence of the obtained analytical dependence for the critical Taylor number to the experimental data.

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