Nonlinear mm-sectorial operators and time-dependent Ginzburg-Landau equations(Nonlinear Evolution Equations and Applications)

<p>(a) Z-stack photo of ‘exploded’ appearance to the ventral side of the perforations on the artefact. (b) Replica perforation with the same ‘exploded’ appearance produced from using a core tool to peck through the crania.</p

Sagittal CT view of the skull, showing the development state of the teeth.

<p>Sagittal CT view of the skull, showing the development state of the teeth.</p

Map of Denmark indicating the Skrydstrup and the Egtved sites.

<p>Map of Denmark indicating the Skrydstrup and the Egtved sites.</p

CT images (axial, coronal, and sagittal views) and 3D visualization of the skull.

<p>CT images (axial, coronal, and sagittal views) and 3D visualization of the skull.</p

Overview of the postcranial skeleton.

<p>Overview of the postcranial skeleton.</p

Strontium isotope ratios of tooth enamel and hair from the Skrydstrup Woman.

<p>Strontium isotope ratios of tooth enamel and hair from the Skrydstrup Woman.</p

The Skrydstrup Woman as she is exhibited today at the National Museum of Denmark (Photo: Courtesy of The National Museum of Denmark).

<p>The Skrydstrup Woman as she is exhibited today at the National Museum of Denmark (Photo: Courtesy of The National Museum of Denmark).</p

A close up image of the Skrydstrup Woman’s facial remains (Photo: Lennart Larsen, National Museum of Denmark).

<p>A close up image of the Skrydstrup Woman’s facial remains (Photo: Lennart Larsen, National Museum of Denmark).</p

Strontium isotope diagram depicting the results of the human remains of the Skrydtsrup Woman (hair segments and tooth enamel).

<p>The area between the horizontal green dotted lines indicate the bioavailable strontium isotopic range of the area of Skrydstrup calculated from the values in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0178834#pone.0178834.t002" target="_blank">Table 2</a>. The area between the horizontal green solid lines indicate the bioavailable strontium isotopic range for territorial Denmark.</p

Direct validation of imputed non-synonymous SNP alleles.

<p><b>A</b>) Genetically variant peptides (GVPs) that contained single amino-acid polymorphisms (SAPs) were identified in both European-American cohorts (EA1 and EA2) and collated for each subject. Imputed nsSNP alleles (Gene Name = GN, SNP accession number = rs#, allele nucleotide = nuc) were directly compared to the genotype resulting from direct Sanger sequencing (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0160653#pone.0160653.s011" target="_blank">S1 Methods</a>). Correctly imputed nsSNP alleles (TP, true positives) are indicated by a blue square. Imputed alleles that were incorrectly predicted (FP, false positive) are indicated by red squares. Alleles that were identified using Sanger sequencing, but did not contain a resulting GVP in the matching proteomic dataset (FN, false negative) are indicated by light green squares. Alleles absent in both subjects DNA and in resulting proteomic datasets (TN, true negatives) are indicated by white squares[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0160653#pone.0160653.ref049" target="_blank">49</a>]. Failed Sanger sequencing determination of nsSNP allelic status is indicated by grey. <b>B</b>) The effectiveness of each SAP-containing peptide to impute nsSNP alleles was also quantified. The sensitivity of each genetically variant peptide, measured as the proportion of nsSNP-alleles that are correctly detected and imputed (TP/(TP+FN)), was calculated as a percentage (log₁₀(%). The positive predictive value (PPV) of genetically variant peptide-based SNP imputations was calculated as the percentage of correct validated SNP imputations of all imputations (TP/(TP + FP); log₁₀(%))[<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0160653#pone.0160653.ref049" target="_blank">49</a>]. <b>C</b>)</p