Topological field theory approach to intermediate statistics

Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are conveniently characterized using the spectral form factor (SFF). Here, we calculate the SFF of unitary matrix ensembles of infinite order with the weight function satisfying the assumptions of Szeg\"o's limit theorem. We then consider a parameter-dependent critical ensemble which has intermediate statistics characteristic of ergodic-to-nonergodic transitions such as the Anderson localization transition. This same ensemble is the matrix model of $U(N)$ Chern-Simons theory on $S^3$, and the SFF of this ensemble is proportional to the HOMFLY invariant of $(2n,2)$-torus links with one component in the fundamental and one in the antifundamental representation. This is one of a large class of ensembles arising from topological field and string theories which exhibit intermediate statistics. Indeed, the absence of a local order parameter suggests that it is natural to characterize ergodic-to-nonergodic transitions using topological tools, such as we have done here.Comment: 41 pages, 3 figures. Changes: corrected typos and affiliations, resized figure 1. Submission to SciPos

Quantum Geometry of Non-Hermitian Topological Systems

Topological insulators have been studied intensively over the last decades. Earlier research focused on Hermitian Hamiltonians, but recently, peculiar and interesting properties were found by introducing non-Hermiticity. In this work, we apply a quantum geometric approach to various Hermitian and non-Hermitian versions of the Su-Schrieffer-Heeger (SSH) model. We find that this method allows one to correctly identify different topological phases and topological phase transitions for all SSH models, but only when using the metric tensor containing both left and right eigenvectors. Whereas the quantum geometry of Hermitian systems is Riemannian, introducing non-Hermiticity leads to pseudo-Riemannian and complex geometries, thus significantly generalizing from the quantum geometries studied thus far. One remarkable example of this is the mathematical agreement between topological phase transition curves and lightlike paths in general relativity, suggesting a possibility of simulating space-times in non-Hermitian systems. We find that the metric in non-Hermitian phases degenerates in such a way that it effectively reduces the dimensionality of the quantum geometry by one. This implies that within linear response theory, one can perturb the system by a particular change of parameters while maintaining a zero excitation rate.Comment: v2 has added a change in the acknowledgmen

Genome Analyses of an Aggressive and Invasive Lineage of the Irish Potato Famine Pathogen

Pest and pathogen losses jeopardise global food security and ever since the 19th century Irish famine, potato late blight has exemplified this threat. The causal oomycete pathogen, Phytophthora infestans, undergoes major population shifts in agricultural systems via the successive emergence and migration of asexual lineages. The phenotypic and genotypic bases of these selective sweeps are largely unknown but management strategies need to adapt to reflect the changing pathogen population. Here, we used molecular markers to document the emergence of a lineage, termed 13_A2, in the European P. infestans population, and its rapid displacement of other lineages to exceed 75% of the pathogen population across Great Britain in less than three years. We show that isolates of the 13_A2 lineage are among the most aggressive on cultivated potatoes, outcompete other aggressive lineages in the field, and overcome previously effective forms of plant host resistance. Genome analyses of a 13_A2 isolate revealed extensive genetic and expression polymorphisms particularly in effector genes. Copy number variations, gene gains and losses, amino-acid replacements and changes in expression patterns of disease effector genes within the 13_A2 isolate likely contribute to enhanced virulence and aggressiveness to drive this population displacement. Importantly, 13_A2 isolates carry intact and in planta induced Avrblb1, Avrblb2 and Avrvnt1 effector genes that trigger resistance in potato lines carrying the corresponding R immune receptor genes Rpi-blb1, Rpi-blb2, and Rpi-vnt1.1. These findings point towards a strategy for deploying genetic resistance to mitigate the impact of the 13_A2 lineage and illustrate how pathogen population monitoring, combined with genome analysis, informs the management of devastating disease epidemic

Functionally Redundant RXLR Effectors from <em>Phytophthora infestans</em> Act at Different Steps to Suppress Early flg22-Triggered Immunity

Genome sequences of several economically important phytopathogenic oomycetes have revealed the presence of large families of so-called RXLR effectors. Functional screens have identified RXLR effector repertoires that either compromise or induce plant defense responses. However, limited information is available about the molecular mechanisms underlying the modes of action of these effectors in planta. The perception of highly conserved pathogen- or microbe-associated molecular patterns (PAMPs/MAMPs), such as flg22, triggers converging signaling pathways recruiting MAP kinase cascades and inducing transcriptional re-programming, yielding a generic anti-microbial response. We used a highly synchronizable, pathogen-free protoplast-based assay to identify a set of RXLR effectors from Phytophthora infestans (PiRXLRs), the causal agent of potato and tomato light blight that manipulate early stages of flg22-triggered signaling. Of thirty-three tested PiRXLR effector candidates, eight, called Suppressor of early Flg22-induced Immune response (SFI), significantly suppressed flg22-dependent activation of a reporter gene under control of a typical MAMP-inducible promoter (pFRK1-Luc) in tomato protoplasts. We extended our analysis to Arabidopsis thaliana, a non-host plant species of P. infestans. From the aforementioned eight SFI effectors, three appeared to share similar functions in both Arabidopsis and tomato by suppressing transcriptional activation of flg22-induced marker genes downstream of post-translational MAP kinase activation. A further three effectors interfere with MAMP signaling at, or upstream of, the MAP kinase cascade in tomato, but not in Arabidopsis. Transient expression of the SFI effectors in Nicotiana benthamiana enhances susceptibility to P. infestans and, for the most potent effector, SFI1, nuclear localization is required for both suppression of MAMP signaling and virulence function. The present study provides a framework to decipher the molecular mechanisms underlying the manipulation of host MAMP-triggered immunity (MTI) by P. infestans and to understand the basis of host versus non-host resistance in plants towards P. infestans

Characterisation of pathogen-specific regions and novel effector candidates in Fusarium oxysporum f. sp. cepae

A reference-quality assembly of Fusarium oxysporum f. sp. cepae (Foc), the causative agent of onion basal rot has been generated along with genomes of additional pathogenic and non-pathogenic isolates of onion. Phylogenetic analysis confirmed a single origin of the Foc pathogenic lineage. Genome alignments with other F. oxysporum ff. spp. and non pathogens revealed high levels of syntenic conservation of core chromosomes but little synteny between lineage specific (LS) chromosomes. Four LS contigs in Foc totaling 3.9 Mb were designated as pathogen-specific (PS). A two-fold increase in segmental duplication events was observed between LS regions of the genome compared to within core regions or from LS regions to the core. RNA-seq expression studies identified candidate effectors expressed in planta, consisting of both known effector homologs and novel candidates. FTF1 and a subset of other transcription factors implicated in regulation of effector expression were found to be expressed in planta

A temporal assessment of nematode community structure and diversity in the rhizosphere of cisgenic Phytophthora infestans-resistant potatoes

This is publication No. 18 produced within the framework of the project Assessing and Monitoring the Impacts of Genetically Modified Plants on Agro-ecosystems (AMIGA), funded by the European Commission in the Framework programme 7. THEME [KBBE.2011.3.5-01].peer-reviewedBackground Nematodes play a key role in soil processes with alterations in the nematode community structure having the potential to considerably influence ecosystem functioning. As a result fluctuations in nematode diversity and/or community structure can be gauged as a ‘barometer’ of a soil’s functional biodiversity. However, a deficit exists in regards to baseline knowledge and on the impact of specific GM crops on soil nematode populations and in particular in regard to the impact of GM potatoes on the diversity of nematode populations in the rhizosphere. The goal of this project was to begin to address this knowledge gap in regards to a GM potato line, cisgenically engineered for resistance to Phytophthora infestans (responsible organism of the Irish potato famine causing late blight disease). For this, a 3 year (2013, 2014, 2015) field experimental study was completed, containing two conventional genotypes (cvs. Desiree and Sarpo Mira) and a cisgenic genotype (cv. Desiree + Rpi-vnt1). Each potato genotype was treated with different disease management strategies (weekly chemical applications and corresponding no spray control). Hence affording the opportunity to investigate the temporal impact of potato genotype, disease management strategy (and their interaction) on the potato rhizosphere nematode community. Results Nematode structure and diversity were measured through established indices, accounts and taxonomy with factors recording a significant effect limited to the climatic conditions across the three seasons of the study and chemical applications associated with the selected disease management strategy. Based on the metrics studied, the cultivation of the cisgenic potato genotype exerted no significant effect (P > 0.05) on nematode community diversity or structure. The disease management treatments led to a reduction of specific trophic groups (e.g. Predacious c–p = 4), which of interest appeared to be counteracted by a potato genotype with vigorous growth phenotype e.g. cv. Sarpo Mira. The fluctuating climates led to disparate conditions, with enrichment conditions (bacterial feeding c–p = 1) dominating during the wet seasons of 2014 and 2015 versus the dry season of 2013 which induced an environmental stress (functional guild c–p = 2) on nematode communities. Conclusions Overall the functional guild indices in comparison to other indices or absolutes values, delivered the most accurate quantitative measurement with which to determine the occurrence of a specific disturbance relative to the cultivation of the studied cisgenic P. infestans-resistant potatoes.European Unio

Quantum Geometry of Non-Hermitian Topological Systems

Topological insulators have been studied intensively over the last decades. Earlier research focused on Hermitian Hamiltonians, but recently, peculiar and interesting properties were found by introducing non-Hermiticity. In this work, we apply a quantum geometric approach to various Hermitian and non-Hermitian versions of the Su-Schrieffer-Heeger (SSH) model. We find that this method allows one to correctly identify different topological phases and topological phase transitions for all SSH models, but only when using the metric tensor containing both left and right eigenvectors. Whereas the quantum geometry of Hermitian systems is Riemannian, introducing non-Hermiticity leads to pseudo-Riemannian and complex geometries, thus significantly generalizing from the quantum geometries studied thus far. One remarkable example of this is the mathematical agreement between topological phase transition curves and lightlike paths in general relativity, suggesting a possibility of simulating space-times in non-Hermitian systems. We find that the metric in non-Hermitian phases degenerates in such a way that it effectively reduces the dimensionality of the quantum geometry by one. This implies that within linear response theory, one can perturb the system by a particular change of parameters while maintaining a zero excitation rate

Expression profiling during arabidopsis/downy mildew interaction reveals a highly-expressed effector that attenuates responses to salicylic acid

Plants have evolved strong innate immunity mechanisms, but successful pathogens evade or suppress plant immunity via effectors delivered into the plant cell. Hyaloperonospora arabidopsidis (Hpa) causes downy mildew on Arabidopsis thaliana, and a genome sequence is available for isolate Emoy2. Here, we exploit the availability of genome sequences for Hpa and Arabidopsis to measure gene-expression changes in both Hpa and Arabidopsis simultaneously during infection. Using a high-throughput cDNA tag sequencing method, we reveal expression patterns of Hpa predicted effectors and Arabidopsis genes in compatible and incompatible interactions, and promoter elements associated with Hpa genes expressed during infection. By resequencing Hpa isolate Waco9, we found it evades Arabidopsis resistance gene RPP1 through deletion of the cognate recognized effector ATR1. Arabidopsis salicylic acid (SA)-responsive genes including PR1 were activated not only at early time points in the incompatible interaction but also at late time points in the compatible interaction. By histochemical analysis, we found that Hpa suppresses SA-inducible PR1 expression, specifically in the haustoriated cells into which host-translocated effectors are delivered, but not in non-haustoriated adjacent cells. Finally, we found a highly-expressed Hpa effector candidate that suppresses responsiveness to SA. As this approach can be easily applied to host-pathogen interactions for which both host and pathogen genome sequences are available, this work opens the door towards transcriptome studies in infection biology that should help unravel pathogen infection strategies and the mechanisms by which host defense responses are overcome

A novel approach to locate Phytophthora infestans resistance genes on the potato genetic map

Mapping resistance genes is usually accomplished by phenotyping a segregating population for the resistance trait and genotyping it using a large number of markers. Most resistance genes are of the NBS-LRR type, of which an increasing number is sequenced. These genes and their analogs (RGAs) are often organized in clusters. Clusters tend to be rather homogenous, viz. containing genes that show high sequence similarity with each other. From many of these clusters the map position is known. In this study we present and test a novel method to quickly identify to which cluster a new resistance gene belongs and to produce markers that can be used for introgression breeding. We used NBS profiling to identify markers in bulked DNA samples prepared from resistant and susceptible genotypes of small segregating populations. Markers co-segregating with resistance can be tested on individual plants and directly used for breeding. To identify the resistance gene cluster a gene belongs to, the fragments were sequenced and the sequences analyzed using bioinformatics tools. Putative map positions arising from this analysis were validated using markers mapped in the segregating population. The versatility of the approach is demonstrated with a number of populations derived from wild Solanum species segregating for P. infestans resistance. Newly identified P. infestans resistance genes originating from S. verrucosum, S. schenckii, and S. capsicibaccatum could be mapped to potato chromosomes 6, 4, and 11, respectively