Subcritical multiplicative chaos for regularized counting statistics from random matrix theory

For an N×N random unitary matrix U_N, we consider the random field defined by counting the number of eigenvalues of U_N in a mesoscopic arc of the unit circle, regularized at an N-dependent scale Ɛ_N>0. We prove that the renormalized exponential of this field converges as N → ∞ to a Gaussian multiplicative chaos measure in the whole subcritical phase. In addition, we show that the moments of the total mass converge to a Selberg-like integral and by taking a further limit as the size of the arc diverges, we establish part of the conjectures in [55]. By an analogous construction, we prove that the multiplicative chaos measure coming from the sine process has the same distribution, which strongly suggests that this limiting object should be universal. The proofs are based on the asymptotic analysis of certain Toeplitz or Fredholm determinants using the Borodin-Okounkov formula or a Riemann-Hilbert problem for integrable operators. Our approach to the L¹-phase is based on a generalization of the construction in Berestycki [5] to random fields which are only asymptotically Gaussian. In particular, our method could have applications to other random fields coming from either random matrix theory or a different context

Experimental Evidence of a Variant Neutron Spectrum from the T(t,2n)α Reaction at Center-of-Mass Energies in the Range of 16–50 keV

Full calculations of six-nucleon reactions with a three-body final state have been elusive and a long-standing issue. We present neutron spectra from the T(t,2n)α (TT) reaction measured in inertial confinement fusion experiments at the OMEGA laser facility at ion temperatures from 4 to 18 keV, corresponding to center-of-mass energies (E[subscript c.m.]) from 16 to 50 keV. A clear difference in the shape of the TT-neutron spectrum is observed between the two E[subscript c.m.], with the ⁵He ground state resonant peak at 8.6 MeV being significantly stronger at the higher than at the lower energy. The data provide the first conclusive evidence of a variant TT-neutron spectrum in this E[subscript c.m.] range. In contrast to earlier available data, this indicates a reaction mechanism that must involve resonances and/or higher angular momenta than L=0. This finding provides an important experimental constraint on theoretical efforts that explore this and complementary six-nucleon systems, such as the solar ³He(³He,2p)α reaction

Diagnostic Components in Harsh Radiation Environments: Possible Overlap in R&D Requirements of IC and MF Systems

The next generation of large scale fusion devices--ITER/LMJ/NIF--will require diagnostic components to operate in environments far more severe than those encountered in present facilities. This harsh environment will be induced by fluxes of neutrons, gamma rays, energetic ions, electromagnetic radiation, and in some cases debris and shrapnel, at levels several orders of magnitude higher than those experienced in today's devices. For several years the question of possible synergy between inertial and the magnetic confinement research has been pursued by members of the respective communities. A first joint workshop specifically devoted to the identification and promotion of these synergies was organized in France, at Aix-en-Provence from June 27th to 29th, 2007. The workshop was attended by about 50 invited specialists. The participants identified a number of subject areas where common overlapping interests could benefit from additional interactions and meetings: windows, optical fibers, mirrors, cables, electronic components and 14 MeV neutron sources. In this paper we summarize the findings of these working groups. We put the discussion into context by including a brief description of the environments and the physical effects that have to be handled

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

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

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

Moments of the Position of the Maximum for GUE Characteristic Polynomials and for Log-Correlated Gaussian Processes

We study three instances of log-correlated processes on the interval: the logarithm of the Gaussian unitary ensemble (GUE) characteristic polynomial, the Gaussian log-correlated potential in presence of edge charges, and the Fractional Brownian motion with Hurst index $H \to 0$ (fBM0). In previous collaborations we obtained the probability distribution function (PDF) of the value of the global minimum (equivalently maximum) for the first two processes, using the {\it freezing-duality conjecture} (FDC). Here we study the PDF of the position of the maximum $x_m$ through its moments. Using replica, this requires calculating moments of the density of eigenvalues in the $\beta$-Jacobi ensemble. Using Jack polynomials we obtain an exact and explicit expression for both positive and negative integer moments for arbitrary $\beta >0$ and positive integer $n$ in terms of sums over partitions. For positive moments, this expression agrees with a very recent independent derivation by Mezzadri and Reynolds. We check our results against a contour integral formula derived recently by Borodin and Gorin (presented in the Appendix A from these authors). The duality necessary for the FDC to work is proved, and on our expressions, found to correspond to exchange of partitions with their dual. Performing the limit $n \to 0$ and to negative Dyson index $\beta \to -2$, we obtain the moments of $x_m$ and give explicit expressions for the lowest ones. Numerical checks for the GUE polynomials, performed independently by N. Simm, indicate encouraging agreement. Some results are also obtained for moments in Laguerre, Hermite-Gaussian, as well as circular and related ensembles. The correlations of the position and the value of the field at the minimum are also analyzed.Comment: 64 page, 5 figures, with Appendix A written by Alexei Borodin and Vadim Gorin; The appendix H in the ArXiv version is absent in the published versio