Fractional Hardy-Sobolev type inequalities for half spaces and John domains

As our main result we prove a variant of the fractional Hardy-Sobolev-Maz'ya inequality for half spaces. This result contains a complete answer to a recent open question by Musina and Nazarov. In the proof we apply a new version of the fractional Hardy-Sobolev inequality that we establish also for more general unbounded John domains than half spaces

Energy spread of ultracold electron bunches extracted from a laser cooled gas

Ultrashort and ultracold electron bunches created by near-threshold femtosecond photoionization of a laser-cooled gas hold great promise for single-shot ultrafast diffraction experiments. In previous publications the transverse beam quality and the bunch length have been determined. Here the longitudinal energy spread of the generated bunches is measured for the first time, using a specially developed Wien filter. The Wien filter has been calibrated by determining the average deflection of the electron bunch as a function of magnetic field. The measured relative energy spread $\frac{\sigma_{U}}{U} = 0.64 \pm 0.09\%$ agrees well with the theoretical model which states that it is governed by the width of the ionization laser and the acceleration length

MOESM2 of Vitamin C induces specific demethylation of H3K9me2 in mouse embryonic stem cells via Kdm3a/b

Additional file 2: Figure S2. Analysis of H3K9me2 in G9a and GLP knockout ES cells treated with vitamin C. A) Western blot for H3K9me2 in wild-type parental TT2, G9a knockout, and GLP knockout ES cells ± vitamin C. B) Immunofluorescence for H3K9me2 in GiP ES cells ± vitamin C and untreated wild-type TT2, G9a knockout, and GLP knockout ES cells. GiP ES cells treated with vitamin C show a H3K9me2 staining pattern that is similar to G9a and GLP knockout ES cells. Scale bar represents 20 μm

MOESM4 of Vitamin C induces specific demethylation of H3K9me2 in mouse embryonic stem cells via Kdm3a/b

Additional file 4: Figure S4. Analysis of H3K9me2 at repetitive elements in ES cells treated with vitamin C. ChIP-qPCR for H3K9me2 in ES cells ± vitamin C at the repetitive element families indicated. ChIP for IgG was performed as a negative control. Data are mean ± SD. Asterisks represent P < 0.05 by t test

MOESM1 of Vitamin C induces specific demethylation of H3K9me2 in mouse embryonic stem cells via Kdm3a/b

Additional file 1: Figure S1. Evaluation of changes in H3 PTMs following vitamin C treatment. A) Western blot for several H3 PTMs in ES cells ± vitamin C. B) Immunofluorescence for H3K9me2 and corresponding DAPI staining in untreated and vitamin C-treated ES cells. Merged images show H3K9me2 in green and DAPI staining in red. H3K9me2 immunofluorescence is also shown in Fig. 1e. Scale bar represents 20 μm

Additional file 2: of The genomic and transcriptomic landscape of anaplastic thyroid cancer: implications for therapy

Supplementary file outlining the detailed sequencing methodology and additional figures. (DOCX 434 kb

Mutation Discovery in Regions of Segmental Cancer Genome Amplifications with CoNAn-SNV: A Mixture Model for Next Generation Sequencing of Tumors

<div><p>Next generation sequencing has now enabled a cost-effective enumeration of the full mutational complement of a tumor genome—in particular single nucleotide variants (SNVs). Most current computational and statistical models for analyzing next generation sequencing data, however, do not account for cancer-specific biological properties, including somatic segmental copy number alterations (CNAs)—which require special treatment of the data. Here we present CoNAn-SNV (<u>Co</u>py <u>N</u>umber <u>An</u>notated SNV): a novel algorithm for the inference of single nucleotide variants (SNVs) that overlap copy number alterations. The method is based on modelling the notion that genomic regions of segmental duplication and amplification induce an extended genotype space where a subset of genotypes will exhibit heavily skewed allelic distributions in SNVs (and therefore render them undetectable by methods that assume diploidy). We introduce the concept of modelling allelic counts from sequencing data using a panel of Binomial mixture models where the number of mixtures for a given locus in the genome is informed by a discrete copy number state given as input. We applied CoNAn-SNV to a previously published whole genome shotgun data set obtained from a lobular breast cancer and show that it is able to discover 21 experimentally revalidated somatic non-synonymous mutations in a lobular breast cancer genome that were not detected using copy number insensitive SNV detection algorithms. Importantly, ROC analysis shows that the increased sensitivity of CoNAn-SNV does not result in disproportionate loss of specificity. This was also supported by analysis of a recently published lymphoma genome with a relatively quiescent karyotype, where CoNAn-SNV showed similar results to other callers except in regions of copy number gain where increased sensitivity was conferred. Our results indicate that in genomically unstable tumors, copy number annotation for SNV detection will be critical to fully characterize the mutational landscape of cancer genomes.</p> </div

Discovery Flow Diagram.

<p>Discovery Flow Diagram.</p

Effect of copy number amplifications on germline alleles.

<p>These variants exhibit an amplification of the reference allele and show allelic skew, and as a result suggest an unbalanced allelic amplification over the tumor evolution.Impact refers to functional impact as determined by MutationAssessor.</p

Venn diagram of predictions made by samtools, SNVMix, CoNAn-SNV.

<p>Separating by CNA state shows an enrichment of CoNAn-SNV specific predictions in the GAIN, AMP and HLAMP segments of the genome.</p