Ewens measures on compact groups and hypergeometric kernels

On unitary compact groups the decomposition of a generic element into product of reflections induces a decomposition of the characteristic polynomial into a product of factors. When the group is equipped with the Haar probability measure, these factors become independent random variables with explicit distributions. Beyond the known results on the orthogonal and unitary groups (O(n) and U(n)), we treat the symplectic case. In U(n), this induces a family of probability changes analogous to the biassing in the Ewens sampling formula known for the symmetric group. Then we study the spectral properties of these measures, connected to the pure Fisher-Hartvig symbol on the unit circle. The associated orthogonal polynomials give rise, as $n$ tends to infinity to a limit kernel at the singularity.Comment: New version of the previous paper "Hua-Pickrell measures on general compact groups". The article has been completely re-written (the presentation has changed and some proofs have been simplified). New references added

The Characteristic Polynomial of a Random Permutation Matrix at Different Points

We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show that the behavior at different points is independent in the limit and are asymptotically normal. Our methods enables us to study more general matrices, closely related to permutation matrices, and multiplicative class functions.Comment: 30 pages, 2 figures. Differences to Version 1: We have improved the presentation and add some references Stochastic Processes and their Applications, 201

Is the Riemann zeta function in a short interval a 1-RSB spin glass ?

Fyodorov, Hiary & Keating established an intriguing connection between the maxima of log-correlated processes and the ones of the Riemann zeta function on a short interval of the critical line. In particular, they suggest that the analogue of the free energy of the Riemann zeta function is identical to the one of the Random Energy Model in spin glasses. In this paper, the connection between spin glasses and the Riemann zeta function is explored further. We study a random model of the Riemann zeta function and show that its two-overlap distribution corresponds to the one of a one-step replica symmetry breaking (1-RSB) spin glass. This provides evidence that the local maxima of the zeta function are strongly clustered.Comment: 20 pages, 1 figure, Minor corrections, References update

Reverse engineering synthetic antiviral amyloids

Human amyloids have been shown to interact with viruses and interfere with viral replication. Based on this observation, we employed a synthetic biology approach in which we engineered virus-specific amyloids against influenza A and Zika proteins. Each amyloid shares a homologous aggregation-prone fragment with a specific viral target protein. For influenza we demonstrate that a designer amyloid against PB2 accumulates in influenza A-infected tissue in vivo. Moreover, this amyloid acts specifically against influenza A and its common PB2 polymorphisms, but not influenza B, which lacks the homologous fragment. Our model amyloid demonstrates that the sequence specificity of amyloid interactions has the capacity to tune amyloid-virus interactions while allowing for the flexibility to maintain activity on evolutionary diverging variants. Some human amyloid proteins have been shown to interact with viral proteins, suggesting that they may have potential as therapeutic agents. Here the authors design synthetic amyloids specific for influenza A and Zika virus proteins, respectively, and show that they can inhibit viral replication

X-ray imaging in an environment with high-neutron background on National Ignition Facility

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Immune monitoring and TCR sequencing of CD4 T cells in a long term responsive patient with metastasized pancreatic ductal carcinoma treated with individualized, neoepitope-derived multipeptide vaccines : a case report

Abstract Background Cancer vaccines can effectively establish clinically relevant tumor immunity. Novel sequencing approaches rapidly identify the mutational fingerprint of tumors, thus allowing to generate personalized tumor vaccines within a few weeks from diagnosis. Here, we report the case of a 62-year-old patient receiving a four-peptide-vaccine targeting the two sole mutations of his pancreatic tumor, identified via exome sequencing. Methods Vaccination started during chemotherapy in second complete remission and continued monthly thereafter. We tracked IFN-γ+ T cell responses against vaccine peptides in peripheral blood after 12, 17 and 34 vaccinations by analyzing T-cell receptor (TCR) repertoire diversity and epitope-binding regions of peptide-reactive T-cell lines and clones. By restricting analysis to sorted IFN-γ-producing T cells we could assure epitope-specificity, functionality, and TH1 polarization. Results A peptide-specific T-cell response against three of the four vaccine peptides could be detected sequentially. Molecular TCR analysis revealed a broad vaccine-reactive TCR repertoire with clones of discernible specificity. Four identical or convergent TCR sequences could be identified at more than one time-point, indicating timely persistence of vaccine-reactive T cells. One dominant TCR expressing a dual TCRVα chain could be found in three T-cell clones. The observed T-cell responses possibly contributed to clinical outcome: The patient is alive 6 years after initial diagnosis and in complete remission for 4 years now. Conclusions Therapeutic vaccination with a neoantigen-derived four-peptide vaccine resulted in a diverse and long-lasting immune response against these targets which was associated with prolonged clinical remission. These data warrant confirmation in a larger proof-of concept clinical trial

The Porphyromonas gingivalis/host interactome shows enrichment in GWASdb genes related to Alzheimer’s disease, diabetes and cardiovascular diseases

Periodontal disease is of established aetiology in which polymicrobial synergistic ecology has become dysbiotic under the influence of Porphyromonas gingivalis. Following breakdown of the host’s protective oral tissue barriers, P. gingivalis migrates to developing inflammatory pathologies that associate with Alzheimer’s disease (AD). Periodontal disease is a risk factor for cardiovascular disorders (CVD), type II diabetes mellitus (T2DM), AD and other chronic diseases, whilst T2DM exacerbates periodontitis. This study analysed the relationship between the P. gingivalis/host interactome and the genes identified in genome-wide association studies (GWAS) for the aforementioned conditions using data from GWASdb (P<1E-03) and, in some cases, from the NCBI/EBI GWAS database (P< 1E-05). Gene expression data from periodontitis or P. gingivalis microarray was compared to microarray datasets from the AD hippocampus and/or from carotid artery plaques. The results demonstrated that the host genes of the P. gingivalis interactome were significantly enriched in genes deposited in GWASdb genes related to cognitive disorders, AD and dementia, and its co-morbid conditions T2DM, obesity, and CVD. The P. gingivalis/host interactome was also enriched in GWAS genes from the more stringent NCBI-EBI database for AD, atherosclerosis and T2DM. The misregulated genes in periodontitis tissue or P. gingivalis infected macrophages also matched those in the AD hippocampus or atherosclerotic plaques. Together, these data suggest important gene/environment interactions between P. gingivalis and susceptibility genes or gene expression changes in conditions where periodontal disease is a contributory factor

Lawson criterion for ignition exceeded in an inertial fusion experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion