A confining, Goldstone theorem preserving, separable Ansatz for the ladder kernel of the two-body Bethe-Salpeter equation is constructed from phenomenologically efficacious u, d and s dressed-quark propagators. The simplicity of the approach is its merit. It provides a good description of the ground-state isovector-pseudoscalar, vector and axial-vector meson spectrum; facilitates an exploration of the relative importance of various components of the two-body Bethe-Salpeter amplitudes, showing that sub-leading Dirac components are quantitatively important in the isovector-pseudoscalar meson channels; and allows a scrutiny of the domain of applicability of ladder truncation studies. A colour-antitriplet diquark spectrum is obtained. Shortcomings of separable Ansätze and the ladder kernel are highlighted.

BackgroundRNA sequencing (RNA-Seq) has emerged as a powerful approach for the detection of differential gene expression with both high-throughput and high resolution capabilities possible depending upon the experimental design chosen. Multiplex experimental designs are now readily available, these can be utilised to increase the numbers of samples or replicates profiled at the cost of decreased sequencing depth generated per sample. These strategies impact on the power of the approach to accurately identify differential expression. This study presents a detailed analysis of the power to detect differential expression in a range of scenarios including simulated null and differential expression distributions with varying numbers of biological or technical replicates, sequencing depths and analysis methods.ResultsDifferential and non-differential expression datasets were simulated using a combination of negative binomial and exponential distributions derived from real RNA-Seq data. These datasets were used to evaluate the performance of three commonly used differential expression analysis algorithms and to quantify the changes in power with respect to true and false positive rates when simulating variations in sequencing depth, biological replication and multiplex experimental design choices.ConclusionsThis work quantitatively explores comparisons between contemporary analysis tools and experimental design choices for the detection of differential expression using RNA-Seq. We found that the DESeq algorithm performs more conservatively than edgeR and NBPSeq. With regard to testing of various experimental designs, this work strongly suggests that greater power is gained through the use of biological replicates relative to library (technical) replicates and sequencing depth. Strikingly, sequencing depth could be reduced as low as 15% without substantial impacts on false positive or true positive rates.

Euclidean lattice fermions are examined in odd dimensions. The continuum flavours are identified and it is found that the flavours fall into two equal groups requiring inequivalent representations of the Dirac matrices. The relationship of this result to the parity transformation and the role of chiral symmetry are elucidated.

The charged and neutral kaon form factors are calculated as a phenomenological application of the QCD Dyson-Schwinger equations. The results are compared with the pion form factor calculated in the same framework and yield F K ± (Q 2 ) > F π ± (Q 2 ) on Q 2 ∈ [0, 3] GeV 2 ; and a neutral kaon form factor that is similar in form and magnitude to the neutron charge form factor. These results are sensitive to the difference between the kaon and pion Bethe-Salpeter amplitude and the u-and s-quark propagation characteristics.