Some combinatorial identities related to commuting varieties and Hilbert schemes

In this article we explore some of the combinatorial consequences of recent results relating the isospectral commuting variety and the Hilbert scheme of points in the plane

Meiotic recombination profiling of interspecific hybrid F1 tomato pollen by linked read sequencing

Genome wide screening of pooled pollen samples from a single interspecific F1 hybrid obtained from a cross between tomato, Solanum lycopersicum and its wild relative, Solanum pimpinellifolium using linked read sequencing of the haploid nuclei, allowed profiling of the crossover (CO) and gene conversion (GC) landscape. We observed a striking overlap between cold regions of CO in the male gametes and our previously established F6 recombinant inbred lines (RILs) population. COs were overrepresented in non‐coding regions in the gene promoter and 5′UTR regions of genes. Poly‐A/T and AT rich motifs were found enriched in 1 kb promoter regions flanking the CO sites. Non‐crossover associated allelic and ectopic GCs were detected in most chromosomes, confirming that besides CO, GC represents also a source for genetic diversity and genome plasticity in tomato. Furthermore, we identified processed break junctions pointing at the involvement of both homology directed and non‐homology directed repair pathways, suggesting a recombination machinery in tomato that is more complex than currently anticipated

Meiotic recombination profiling of interspecific hybrid F1 tomato pollen by linked read sequencing

Genome wide screening of pooled pollen samples from a single interspecific F1 hybrid obtained from a cross between tomato, Solanum lycopersicum and its wild relative, Solanum pimpinellifolium using linked read sequencing of the haploid nuclei, allowed profiling of the crossover (CO) and gene conversion (GC) landscape. We observed a striking overlap between cold regions of CO in the male gametes and our previously established F6 recombinant inbred lines (RILs) population. COs were overrepresented in non‐coding regions in the gene promoter and 5′UTR regions of genes. Poly‐A/T and AT rich motifs were found enriched in 1 kb promoter regions flanking the CO sites. Non‐crossover associated allelic and ectopic GCs were detected in most chromosomes, confirming that besides CO, GC represents also a source for genetic diversity and genome plasticity in tomato. Furthermore, we identified processed break junctions pointing at the involvement of both homology directed and non‐homology directed repair pathways, suggesting a recombination machinery in tomato that is more complex than currently anticipated

The 12C(e, e′p) and 12C(e, e′pp) reactions in the Δ-resonance region

Coincidence cross sections for the 12C(e, e′pp) and 12C(e, e′p) reactions have been measured in the Δ-resonance region. The 12C(e, e′pp) reaction has been measured at three different angular settings of the proton detectors to investigate the angular correlation between the emitted protons. The data, which have a low statistical accuracy, are compared with a calculation based on the direct-knockout mechanism, which includes one- and two-body currents. NN-correlations are accounted for via a correlation function, Δ-excitation via a two-body current and final-state interactions of the emitted protons via an optical potential. The 12C(e, e′p) data, taken at large proton-emission angles, cover the region of high missing-energy values (145-275 MeV). The data are compared to results of a calculation taking into account meson exchange, intermediate Δ-excitation and pion production. This comparison shows that there is ample evidence for processes leading to multi-nucleon knockout