The real Ginibre ensemble consists of random N ×N matrices formed from i.i.d. standard Gaussian entries. By using the method of skew orthogonal polynomials, the general n-point correlations for the real eigenvalues, and for the complex eigenvalues, are given as n × n Pfaffians with explicit entries. A computationally tractable formula for the cumulative probability density of the largest real eigenvalue is presented. This is relevant to May's stability analysis of biological webs. Dyson's three fold way [1] is a viewpoint on the foundations of random matrix theory, showing how consideration of time reversal symmetry leads to three classes of ensembles of relevance to quantum mechanics. The three ensembles are catalogued by the classes of unitary matrices which leave the ensemble invariant -orthogonal (time reversal symmetry is an involution), unitary (no time reversal symmetry), and symplectic (time reversal symmetry is an anti-involution). For an ensemble theory of Hermitian matrices, an equivalent characterization is that the matrix elements be real, complex and real quaternion respectively.Both as a concept, and as a calculational tool, the three fold way has been highly successful. As a concept, allowing for global symmetries in addition to that of time reversal gives a classification of the former in terms of the ten infinite families of matrix Lie algebras [2]. This classification now provides theoretical underpinning to fundamental phenomena in mesoscopic physics [3], disordered systems [4], and low energy QCD [5], in additional to the study of the statistical properties of quantum spectra for which it was originally intended. A good deal of the success relates to the matrix ensembles of the three fold way and its generalization being exactly solvable -analytic forms are available for all key statistical quantities, allowing for quantitative theoretical predictions.Soon after the formulation of the three fold way, Ginibre [6] presented as a mathematical extension an analogous theory of non-Hermitian random matrices. The entries are taken to be either real, complex or real quaternion. Like their Hermitian counterparts, it transpires that such random matrices have physical relevance.Consider the complex case first. Then the joint eigenvalue probability density function (PDF) is proportional to

For the orthogonal-unitary and symplectic-unitary transitions in random matrix theory, the general parameter dependent distribution between two sets of eigenvalues with two different parameter values can be expressed as a quaternion determinant. For the parameter dependent Gaussian and Laguerre ensembles the matrix elements of the determinant are expressed in terms of corresponding skew-orthogonal polynomials, and their limiting value for infinite matrix dimension are computed in the vicinity of the soft and hard edges respectively. A connection formula relating the distributions at the hard and soft edge is obtained, and a universal asymptotic behaviour of the two point correlation is identified.

The conformation and dynamics of melittin bound to the dimyristoylphosphatidylcholine (DMPC) bilayer and the magnetic orientation in the lipid bilayer systems were investigated by solid-state (31)P and (13)C NMR spectroscopy. Using (31)P NMR, it was found that melittin-lipid bilayers form magnetically oriented elongated vesicles with the long axis parallel to the magnetic field above the liquid crystalline-gel phase transition temperature (T(m) = 24 degrees C). The conformation, orientation, and dynamics of melittin bound to the membrane were further determined by using this magnetically oriented lipid bilayer system. For this purpose, the (13)C NMR spectra of site-specifically (13)C-labeled melittin bound to the membrane in the static, fast magic angle spinning (MAS) and slow MAS conditions were measured. Subsequently, we analyzed the (13)C chemical shift tensors of carbonyl carbons in the peptide backbone under the conditions where they form an alpha-helix and reorient rapidly about the average helical axis. Finally, it was found that melittin adopts a transmembrane alpha-helix whose average axis is parallel to the bilayer normal. The kink angle between the N- and C-terminal helical rods of melittin in the lipid bilayer is approximately 140 degrees or approximately 160 degrees, which is larger than the value of 120 degrees determined by x-ray diffraction studies. Pore formation was clearly observed below the T(m) in the initial stage of lysis by microscope. This is considered to be caused by the association of melittin molecules in the lipid bilayer.

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Himawari‐8, a next‐generation geostationary meteorological satellite, was launched on 7 October 2014 and became operational on 7 July 2015. The advanced imager on board Himawari‐8 is equipped with 16 observational bands (including three visible and three near‐infrared bands) that enable retrieval of full‐disk aerosol optical properties at 10 min intervals from geostationary (GEO) orbit. Here we show the first application of aerosol optical properties (AOPs) derived from Himawari‐8 data to aerosol data assimilation. Validation of the assimilation experiment by comparison with independent observations demonstrated successful modeling of continental pollution that was not predicted by simulation without assimilation and reduced overestimates of dust front concentrations. These promising results suggest that AOPs derived from Himawari‐8/9 and other planned GEO satellites will considerably improve forecasts of air quality, inverse modeling of emissions, and aerosol reanalysis through assimilation techniques.

We developed a common algorithm to retrieve aerosol properties, such as aerosol optical thickness, single-scattering albedo, and Ångström exponent for various satellite sensors over land and ocean. The three main features of this algorithm are: (1) automatic selection of the optimum channels for aerosol retrieval by introducing a weight for each channel to the object function, (2) setting common candidate aerosol models over land and ocean, and (3) preparing lookup tables for every 1 nm in the range of 300 to 2500 nm in the wavelength and weighting the radiance using the response function for each sensor. This method was applied to the Advanced Himawari Imager (AHI) on board the Japan Meteorological Agency's geostationary satellite Himawari-8, and the results depicted a continuous estimate of aerosol optical thickness over land and ocean. Furthermore, the aerosol optical thickness estimated using our algorithm was generally consistent with the products of the Moderate Resolution Imaging Spectroradiometer (MODIS) and Aerosol Robotic Network (AERONET). In addition, we applied our algorithm to MODIS on board the Aqua satellite and compared the retrieval results to the results obtained from AHI. The comparisons of the aerosol optical thickness, retrieved from different sensors with the different viewing angles onboard the geostationary and polar-orbiting satellites, suggest an underestimation of aerosol optical thickness at the backscattering direction (or overestimated in other directions). The retrieval of aerosol properties using a common algorithm allows in identifying a weakness in the algorithm, such as the assumptions in the aerosol model (e.g., sphericity or size distribution).

We investigate the spectral properties of the product of M complex non-Hermitian random matrices that are obtained by removing L rows and columns of larger unitary random matrices uniformly distributed on the group U (N + L). Such matrices are called truncated unitary matrices or random contractions. We first derive the joint probability distribution for the complex eigenvalues of the product matrix for fixed N, L, and M , given by a standard determinantal point process in the complex plane. The weight however is non-standard and can be expressed in terms of the Meijer G-function. The explicit knowledge of all eigenvalue correlation functions and the corresponding kernel allows us to take various large N (and L) limits at fixed M . At strong non-unitarity, with L/N finite, the eigenvalues condense on a domain inside the unit circle. At the edge and in the bulk we find the same universal microscopic kernel as for a single complex non-Hermitian matrix from the Ginibre ensemble. At the origin we find the same new universality classes labelled by M as for the product of M matrices from the Ginibre ensemble. Keeping a fixed size of truncation, L, when N goes to infinity leads to weak non-unitarity, with most eigenvalues on the unit circle as for unitary matrices. Here we find a new microscopic edge kernel that generalizes the known results for M = 1. We briefly comment on the case when each product matrix results from a truncation of different size L j .