Identification and mapping of loci controlling viability in Vitis vinifera crosses

The present research work is part of the NOVABREED project, funded by the European Research Council (ERC). The focus of NOVABREED is the concept of pan-genome as a comprehensive representation of a species genome: its main aim is to characterise the dispensable portion that arises as a consequence of structural variation, and its contribution to the intra-specific genetic and phenotypic variation (Morgante, De Paoli, & Radovic, 2007). The focus of the present work is on the Vitis vinifera genome. The goal of the present research is to understand the genetic bases of inbreeding depression in grapevine through the identification of loci controlling viability and survival and their relationship with structural variation. Vitis vinifera is a very variable species with high levels of both nucleotide diversity and structural variation (Gabriele Magris, PhD thesis, 2016). Cultivated varieties are highly heterozygous (Jaillon et al., 2007) and are expected to carry a large mutational load that is reflected in rather severe inbreeding depression observed upon crossing of related individuals or selfing. We set out to identify loci that are responsible for inbreeding depression both individually as well as a consequence of epistatic interactions. Through the analysis of segregation distortion, defined as deviation of segregation ratio from the expected Mendelian ratio, we explored progenies segregation pattern with the goal of isolating causative mutations of the distortion. In order to characterize segregation distortion in Vitis vinifera, progenies obtained from self-crosses of six varieties and from one out-cross were genotyped using a Genotyping-by-Sequencing approach. The technique used, known as double digest Restriction Site Associated DNA Sequencing (ddRAD-seq) (Peterson, Weber, Kay, Fisher, & Hoekstra, 2012), subsamples the genome at homologous locations among individuals by coupling double restriction enzyme digestion to a selection of genomic fragments by size, allowing fine-scale control of the fraction of regions represented in the final library. SNP genotyping, by means of the software Stacks (Catchen, Hohenlohe, Bassham, Amores, & Cresko, 2013), allowed the identification of several regions of single locus distortion in each progeny assessed. Progenies deriving from self-fertilization of the six cultivars Cabernet franc, Pinot Noir, Primitivo, Rkatsiteli, Sangiovese and Schiava Grossa, showed distortion in 12 different loci. Progeny of the out-cross between Schiava Grossa and Rkatsiteli did not show any locus of segregation distortion. Overall, ten loci of distortion revealed lethal effects, whereas two loci revealed severe deleterious effects. Among loci with lethal effect, seven showed the complete absence of a homozygous genotype, corresponding to the action of recessive alleles; two showed the action of partially dominant alleles and one showed nearly complete dominance of the lethal allele. Deleterious loci exhibited recessive and overdominant allelic effect on distortion, respectively. In three different varieties, chromosome 8 was revealed to harbour non overlapping loci of distortion with different allelic effects. Analysis of selected progenies over two vegetative seasons showed that five loci caused embryo or seedling lethality in early stages of growth, while two loci exerted their lethal effects on growth only after the first wintering. Fine mapping of the distorted regions allowed to narrow down the causal locus to less than 34 Kbp, in the best case. Genotype data of the progeny of Rkatsiteli self-cross and of the progeny of Schiava Grossa and Rkatsiteli out-cross was used to build genetic linkage maps of the parental varieties. The three genetic maps were used to analyse recombination frequency along the genome of Vitis vinifera. To identify structural variants (SVs), single nucleotide polymorphisms (SNPs) and small insertion-deletion polymorphisms (INDELs) contributing to the genetic load in the grapevine genome and leading to segregation distortion in the progenies of selfing, candidate loci were screened for mutations affecting genes. Haplotype phasing of alleles allowed to identify mutations belonging to the haplotype that generated segregation distortion in the progenies of selfing. Furthermore, expression of genes affected by such variation was evaluated in a panel of six varieties in three different tissues (leaf, berry and tendril). The analysis of two-loci segregation distortion was also performed in order to identify epistatic interactions. Fisher\u2019s test of independence revealed one strong signal of interaction between loci on chromosome 1 and chromosome 11 in the variety Rkatsiteli, evidenced also by the pseudo-linkage signal in the genetic map. Further evidences showed that the interaction was actually due to a balanced translocation, which was validated through a PCR-based assay. In order to evaluate gene expression differences between the haplotype carrying the translocation and the normal haplotype in Rkatsiteli, we performed allele specific expression (ASE) analysis for each of the three tissues. Interestingly, the analysis revealed no significant difference in the allele-specific expression profile in the tissues. In order to detect the balanced translocation in other grapevine varieties, a panel of 196 cultivars was tested, revealing that three varieties - Alexandroouli, Mtsvane Kachuri and Gorula - carried the rearrangement. All four varieties originated from Georgia and belonged to the Proles pontica, although not all the varieties of this Proles showed the translocation. This suggests that Georgian varieties are distinct and genetically variable from western one and that translocation could be an ancient event never imported to the West and Central Europe varieties (Proles occidentalis). Our study showed that self-fertilization of Vitis vinifera cultivars lead to high levels of segregation distortion in the progenies due to the presence of unfavourable alleles in genes. Future studies will be oriented to the characterization of the identified genes. Furthermore, we generated a fine-scale map of recombination frequency along the genome of Vitis vinifera. Lastly, we detected and validated a balanced translocation involving chromosome 1 and chromosome 11 in the variety Rkatsiteli and we found the chromosomal rearrangement in other three grapevine varietie

Distortion maps for genus two curves

Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated since the full torsion subgroup has rank 2g. In this paper we prove that distortion maps always exist for supersingular curves of genus g>1 and we construct distortion maps in genus 2 (for embedding degrees 4,5,6 and 12).Comment: 16 page

Analysis of a hysteresis-controlled self-oscillating class-D amplifier

This paper gives the first systematic perturbation analysis of the audio distortion and mean switching period for a self-oscillating class-D amplifier. Explicit expressions are given for all the principal components of audio distortion, for a general audio input signal; the specific example of a sinusoidal input is also discussed in some detail, yielding an explicit closed-form expression for the total harmonic distortion (THD). A class-D amplifier works by converting a low-frequency audio input signal to a high-frequency train of rectangular pulses, whose widths are slowly modulated according to the audio signal. The audiofrequency components of the pulse-train are designed to agree with those of the audio signal. In many varieties of class-D amplifier, the pulse-train is generated using a carrier wave of fixed frequency, well above the audio range. In other varieties, as here, there is no such fixed-frequency clock, and the local frequency of the pulse-train varies in response to the audio input. Such self-oscillating designs pose a particular challenge for comprehensive mathematical modelling; we show that in order to properly account for the local frequency variations, a warped-time transformation is necessary. The systematic nature of our calculation means it can potentially be applied to a range of other self-oscillating topologies. Our results for a general input allow ready calculation of distortion diagnostics such as the intermodulation distortion (IMD), which prior analyses, based on sinusoidal input, cannot provide

Finite TYCZ expansions and cscK metrics

Let $(M, g)$ be a Kaehler manifold whose associated Kaehler form $\omega$ is integral and let $(L, h)\rightarrow (M, \omega)$ be a quantization hermitian line bundle. In this paper we study those Kaehler manifolds $(M, g)$ admitting a finite TYCZ expansion. We show that if the TYCZ expansion is finite then $T_{mg}$ is indeed a polynomial in $m$ of degree $n$, $n=dim M$, and the log-term of the Szeg\"{o} kernel of the disc bundle $D\subset L^*$ vanishes (where $L^*$ is the dual bundle of $L$). Moreover, we provide a complete classification of the Kaehler manifolds admitting finite TYCZ expansion either when $M$ is a complex curve or when $M$ is a complex surface with a cscK metric which admits a radial Kaehler potential

Trade Policy: Home Market Effect vs Terms of Trade Externality

We study trade policy in a two-sector Krugman type model of trade. We conduct a general analysis allowing for three different instruments: tariffs, export taxes and production subsidies. For each instrument we consider unilateral trade policy without retaliation. When carefully disentangling the different effects that determine policy makers' choices and modeling general equilibrium effects of taxes/tariffs, we find that production subsidies are always inefficiently low and driven by terms of trade effects. In the cases of tariffs and export taxes the home market effect prevails for some parameter combinations but mostly trade policy is determined by terms of trade effects and the desire to reduce distortions arising from monopolistic competition. Hence, our analysis sheds new light on trade policy in a model of intra-industry trade.Home Market Effect, Terms of Trade, Tariffs and Subsidies