The spectral form factor in the ‘t Hooft limit – Intermediacy versus universality

The Spectral Form Factor (SFF) is a convenient tool for the characterization of eigenvalue statistics of systems with discrete spectra, and thus serves as a proxy for quantum chaoticity. This work presents an analytical calculation of the SFF of the Chern-Simons Matrix Model (CSMM), which was first introduced to describe the intermediate level statistics of disordered electrons at the mobility edge. The CSMM is characterized by a parameter $0 \leq q\leq 1$, where the Circular Unitary Ensemble (CUE) is recovered for $q\to 0$. The CSMM was later found as a matrix model description of $U(N)$ Chern-Simons theory on $S^3$, which is dual to a topological string theory characterized by string coupling $g_s=-\log q$. The spectral form factor is proportional to a colored HOMFLY invariant of a $(2n,2)$-torus link with its two components carrying the fundamental and antifundamental representations, respectively. We check that taking $N \to \infty$ whilst keeping $q<1$ reduces the connected SFF to an exact linear ramp of unit slope, confirming the main result from arXiv:2012.11703 for the specific case of the CSMM. We then consider the `t Hooft limit, where $N \to \infty$ and $q \to 1^-$ such that $y = q^N$ remains finite. As we take $q\to 1^-$, this constitutes the opposite extreme of the CUE limit. In the `t Hooft limit, the connected SFF turns into a remarkable sequence of polynomials which, as far as the authors are aware, have not appeared in the literature thus far. A gap opens in the spectrum and, after unfolding by a constant rescaling, the connected SFF approximates a linear ramp of unit slope for all $y$ except $y \approx 1$, where the connected SFF goes to zero. We thus find that, although the CSMM was introduced to describe intermediate statistics and the `t Hooft limit is the opposite limit of the CUE, we still recover Wigner-Dyson universality for all $y$ except $y\approx 1$.Comment: Changes: 1. Added a treatment of unfolding and revised our conclusions, changed title, abstract, introduction, and conclusion. 2. Removed comparison with linear fit to connected SFF 3. Changed commas to decimal points 4. Added figures on level density and unfolded SFF 5. Added references 6. Corrected typos 30 pages, 6 figure

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

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

High resolution mapping of a novel late blight resistance gene Rpi-avll, from the wild Bolivian species Solanum avilesii

Both Mexico and South America are rich in Solanum species that might be valuable sources of resistance (R) genes to late blight (Phytophthora infestans). Here, we focus on an R gene present in the diploid Bolivian species S. avilesii. The genotype carrying the R gene was resistant to eight out of 10 Phytophthora isolates of various provenances. The identification of a resistant phenotype and the generation of a segregating population allowed the mapping of a single dominant R gene, Rpi-avl1, which is located in an R gene cluster on chromosome 11. This R gene cluster is considered as an R gene “hot spot”, containing R genes to at least five different pathogens. High resolution mapping of the Rpi-avl1 gene revealed a marker co-segregating in 3890 F1 individuals, which may be used for marker assisted selection in breeding programs and for further cloning of Rpi-avl

The Lectin Receptor Kinase LecRK-I.9 Is a Novel Phytophthora Resistance Component and a Potential Host Target for a RXLR Effector

In plants, an active defense against biotrophic pathogens is dependent on a functional continuum between the cell wall (CW) and the plasma membrane (PM). It is thus anticipated that proteins maintaining this continuum also function in defense. The legume-like lectin receptor kinase LecRK-I.9 is a putative mediator of CW-PM adhesions in Arabidopsis and is known to bind in vitro to the Phytophthora infestans RXLR-dEER effector IPI-O via a RGD cell attachment motif present in IPI-O. Here we show that LecRK-I.9 is associated with the plasma membrane, and that two T-DNA insertions lines deficient in LecRK-I.9 (lecrk-I.9) have a ‘gain-of-susceptibility’ phenotype specifically towards the oomycete Phytophthora brassicae. Accordingly, overexpression of LecRK-I.9 leads to enhanced resistance to P. brassicae. A similar ‘gain-of-susceptibility’ phenotype was observed in transgenic Arabidopsis lines expressing ipiO (35S-ipiO1). This phenocopy behavior was also observed with respect to other defense-related functions; lecrk-I.9 and 35S-ipiO1 were both disturbed in pathogen- and MAMP-triggered callose deposition. By site-directed mutagenesis, we demonstrated that the RGD cell attachment motif in IPI-O is not only essential for disrupting the CW-PM adhesions, but also for disease suppression. These results suggest that destabilizing the CW-PM continuum is one of the tactics used by Phytophthora to promote infection. As countermeasure the host may want to strengthen CW-PM adhesions and the novel Phytophthora resistance component LecRK-I.9 seems to function in this process

Computational models in plant-pathogen interactions: the case of Phytophthora infestans

<p>Abstract</p> <p>Background</p> <p><it>Phytophthora infestans </it>is a devastating oomycete pathogen of potato production worldwide. This review explores the use of computational models for studying the molecular interactions between <it>P. infestans </it>and one of its hosts, <it>Solanum tuberosum</it>.</p> <p>Modeling and conclusion</p> <p>Deterministic logistics models have been widely used to study pathogenicity mechanisms since the early 1950s, and have focused on processes at higher biological resolution levels. In recent years, owing to the availability of high throughput biological data and computational resources, interest in stochastic modeling of plant-pathogen interactions has grown. Stochastic models better reflect the behavior of biological systems. Most modern approaches to plant pathology modeling require molecular kinetics information. Unfortunately, this information is not available for many plant pathogens, including <it>P. infestans</it>. Boolean formalism has compensated for the lack of kinetics; this is especially the case where comparative genomics, protein-protein interactions and differential gene expression are the most common data resources.</p

Computational Prediction and Molecular Characterization of an Oomycete Effector and the Cognate Arabidopsis Resistance Gene

Hyaloperonospora arabidopsidis (Hpa) is an obligate biotroph oomycete pathogen of the model plant Arabidopsis thaliana and contains a large set of effector proteins that are translocated to the host to exert virulence functions or trigger immune responses. These effectors are characterized by conserved amino-terminal translocation sequences and highly divergent carboxyl-terminal functional domains. The availability of the Hpa genome sequence allowed the computational prediction of effectors and the development of effector delivery systems enabled validation of the predicted effectors in Arabidopsis. In this study, we identified a novel effector ATR39-1 by computational methods, which was found to trigger a resistance response in the Arabidopsis ecotype Weiningen (Wei-0). The allelic variant of this effector, ATR39-2, is not recognized, and two amino acid residues were identified and shown to be critical for this loss of recognition. The resistance protein responsible for recognition of the ATR39-1 effector in Arabidopsis is RPP39 and was identified by map-based cloning. RPP39 is a member of the CC-NBS-LRR family of resistance proteins and requires the signaling gene NDR1 for full activity. Recognition of ATR39-1 in Wei-0 does not inhibit growth of Hpa strains expressing the effector, suggesting complex mechanisms of pathogen evasion of recognition, and is similar to what has been shown in several other cases of plant-oomycete interactions. Identification of this resistance gene/effector pair adds to our knowledge of plant resistance mechanisms and provides the basis for further functional analyses

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

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