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Open clusters are unique tracers of the history of our own Galaxy's disc. According to our membership analysis based on Gaia astrometry, out of the 226 potential clusters falling in the footprint of the GALactic Archaeology with HERMES (GALAH) survey or the Apache Point Observatory Galactic Evolution Experiment (APOGEE) survey, we find that 205 have secure members that were observed by at least one of the surveys. Furthermore, members of 134 clusters have high-quality spectroscopic data that we use to determine their chemical composition. We leverage this information to study the chemical distribution throughout the Galactic disc of 21 elements, from C to Eu. The radial metallicity gradient obtained from our analysis is −0.076 ± 0.009 dex kpc−1, which is in agreement with previous works based on smaller samples. Furthermore, the gradient in the [Fe/H]–guiding radius (r guid) plane is −0.073 ± 0.008 dex kpc−1. We show consistently that open clusters trace the distribution of chemical elements throughout the Galactic disc differently than field stars. In particular, at the given radius, open clusters show an age–metallicity relation that has less scatter than field stars. As such scatter is often interpreted as an effect of radial migration, we suggest that these differences are due to the physical selection effect imposed by our Galaxy: clusters that would have migrated significantly also had higher chances to get destroyed. Finally, our results reveal trends in the [X/Fe]– r guid–age space, which are important to understand production rates of different elements as a function of space and time. [ABSTRACT FROM AUTHOR]

A bordering of Gaussian unitary ensemble matrices is considered, in which the bordered row consists of zero mean complex Gaussians N[0, σ/2] + iN[0, σ/2] off the diagonal and the real Gaussian N[formula] on the diagonal. We compute the explicit form of the eigenvalue probability function for such matrices as well as that for matrices obtained by repeating the bordering. The correlations are in general determinantal, and in the single bordering case the explicit form of the correlation kernel is computed. In the large N limit it is shown that μ and/or σ can be tuned to induce a separation of the largest eigenvalue. This effect is shown to be controlled by a single parameter, universal correlation kernel. [ABSTRACT FROM AUTHOR]

The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semicircle law. If the Gaussian entries are all shifted by a constant amount s/(2N)1/2, where N is the size of the matrix, in the large N limit a single eigenvalue will separate from the support of the Wigner semicircle provided s>1. In this study, using an asymptotic analysis of the secular equation for the eigenvalue condition, we compare this effect to analogous effects occurring in general variance Wishart matrices and matrices from the shifted mean chiral ensemble. We undertake an analogous comparative study of eigenvalue separation properties when the sizes of the matrices are fixed and s→∞, and higher rank analogs of this setting. This is done using exact expressions for eigenvalue probability densities in terms of generalized hypergeometric functions and using the interpretation of the latter as a Green function in the Dyson Brownian motion model. For the shifted mean Gaussian unitary ensemble and its analogs, an alternative approach is to use exact expressions for the correlation functions in terms of classical orthogonal polynomials and associated multiple generalizations. By using these exact expressions to compute and plot the eigenvalue density, illustrations of the various eigenvalue separation effects are obtained. [ABSTRACT FROM AUTHOR]

A survey of linearized cosmological fluid equations with a number of different matter components is made. To begin with, the one-component case is reconsidered to illustrate some important mathematical and physical points rarely discussed in the literature. The work of some previous studies of two-component systems are examined and reanalyzed to point out some deficiencies of solutions, and further solutions and physical interpretation are then presented. This leads into a general two-component model with variable velocity dispersion parameters and mass density fractions of each component. The equations, applicable to both hot dark matter (HDM) and cold dark matter (CDM) universes are solved in the long wavelength limit. This region is of interest, because some modes in this range of wave numbers are Jeans unstable. The mixture Jeans wave number of the two-component system is introduced and interpreted, and the solutions are discussed, particularly in comparison to analogous solutions previously derived for plasma modes. This work is applicable to that region in the early Universe (20

The equations describing a two-component cosmological fluid with linearized density perturbations are investigated in the small wavelength or large k limit. The equations are formulated to include a baryonic component, as well as either a hot dark matter (HDM) or cold dark matter (CDM) component. Previous work done on such a system in static space–time is extended to reveal some interesting physical properties, such as the Jeans wave number of the mixture, and resonant mode amplitudes. A WKB technique is then developed to study the expanding universe equations in detail, and to see whether such physical properties are also of relevance in this more realistic scenario. The Jeans wave number of the mixture is reinterpreted for the case of an expanding background space–time. The various modes are obtained to leading order, and the amplitudes of the modes are examined in detail to compare to the resonances observed in the static space–time results. It is found that some conclusions made in the literature about static space–time results cannot be carried over to an expanding cosmology. [ABSTRACT FROM AUTHOR]

In a recent study we have obtained correction terms to the large N asymptotic expansions of the eigenvalue density for the Gaussian unitary and Laguerre unitary ensembles of random N×N matrices, both in the bulk and at the soft edge of the spectrum. In the present study these results are used to similarly analyze the eigenvalue density for Gaussian and Laguerre random matrix ensembles with orthogonal and symplectic symmetry. As in the case of unitary symmetry, a matching is exhibited between the asymptotic expansion of the bulk density, expanded about the edge, and the asymptotic expansion of the edge density, expanded into the bulk. In addition, aspects of the asymptotic expansion of the smoothed density, which involves delta functions at the endpoints of the support, are interpreted microscopically. [ABSTRACT FROM AUTHOR]

We obtain correction terms to the large N asymptotic expansions of the eigenvalue density for the Gaussian unitary and Laguerre unitary ensembles of random N×N matrices, both in the bulk of the spectrum and near the spectral edge. This is achieved by using the well known orthogonal polynomial expression for the kernel to construct a double contour integral representation for the density, to which we apply the saddle point method. The main correction to the bulk density is oscillatory in N and depends on the distribution function of the limiting density, while the corrections to the Airy kernel at the soft edge are again expressed in terms of the Airy function and its first derivative. We demonstrate numerically that these expansions are very accurate. A matching is exhibited between the asymptotic expansion of the bulk density, expanded about the edge, and the asymptotic expansion of the edge density, expanded into the bulk. [ABSTRACT FROM AUTHOR]

Fisher–Hartwig asymptotics refers to the large n form of a class of Toeplitz determinants with singular generating functions. This class of Toeplitz determinants occurs in the study of the spin–spin correlations for the two-dimensional Ising model, and the ground state density matrix of the impenetrable Bose gas, amongst other problems in mathematical physics. We give a new application of the original Fisher–Hartwig formula to the asymptotic decay of the Ising correlations above Tc, while the study of the Bose gas density matrix leads us to generalize the Fisher–Hartwig formula to the asymptotic form of random matrix averages over the classical groups and the Gaussian and Laguerre unitary matrix ensembles. Another viewpoint of our generalizations is that they extend to Hankel determinants the Fisher–Hartwig asymptotic form known for Toeplitz determinants.© 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The density matrix for the impenetrable Bose gas in Dirichlet and Neumann boundary conditions can be written in terms of &land;Π[SUBl=1][SUPn]|cos ø[SUB1]-cos&thetas; [SUBl]|| cos ø [SUB2]-cos &thetas;[SUBl]|&rand, where the average is with respect to the eigenvalue probability density function for random unitary matrices from the classical groups Sp(n) and O[SUP+] (2n), respectively. In the large n limit log-gas considerations imply that the average factorizes into the product of averages of the form &land;Π[SUBl=1][SUPn]|cos ø- cos &thetas;[SUBl]|&rand. By changing variables this average in turn is a special case of the function of t obtained by averaging Π[SUBl=1][SUPn]|t-x[SUBl]|[SUP2q] over the Jacobi unitary ensemble from random matrix theory. The latter task is accomplished by a duality formula from the theory of Selberg correlation integrals, and the large n asymptotic form is obtained. The corresponding large n asymptotic form of the density matrix is used, via the exact solution of a particular integral equation, to compute the asymptotic form of the low lying effective single particle states and their occupations, which are proportional to √N. [ABSTRACT FROM AUTHOR]

We present here an overview of the history, applications and important properties of a function which we refer to as the Lévy integral. For certain values of its characteristic parameter, the Lévy integral defines the symmetric Lévy stable probability density function. As we discuss however, the Lévy integral has applications to a number of other fields besides probability, including random matrix theory, number theory and asymptotics beyond all orders. We exhibit a direct relationship between the Lévy integral and a number theoretic series which we refer to as the generalized Euler-Jacobi series. The complete asymptotic expansions for all natural values of its parameter are presented, and in particular it is pointed out that the intricate exponentially small series become dominant for certain parameter values. [ABSTRACT FROM AUTHOR]

Presents letters to the editor of the 'Archives of Internal Medicine,' commenting on articles published in the periodical as of January 27, 2003. C-reactive protein screening for cardiovascular disease; Use of ephebiatrics in adolescent medicine; D-dimer tests for assessment of pulmonary medicine.

The analytic and asymptotic properties of the spherically symmetric d-dimensional Lévy stable probability density function, p[sup d, sub α](r), are discussed in detail. These isotropic stable probability density functions (pdfs) are analogous to the onedimensional symmetric Lévy stable pdfs previously studied by the present authors [J. Math. Phys. 43, 2670 (2002)]. We construct a hypergeometric representation of p[sup d, sub α](r) when α is rational, and find a number of new representations of p[sup d, sub α](r) in terms of special functions for various values of d and α. A recursion relation is found between p[sup d, sub α](r) and p[sup d+2, sub α](r), which, in particular, implies there exists a simple map between p¹[sub α](r) and p³[sub α](r). As in our previous paper, we discuss the properties of p[sup d, sub α](r) for both the cases α ≤ 2 and α > 2. We demonstrate the existence of intricate exponentially small series in the large r asymptotics of p[sup d, sub α](r) when α is an integer, which are dominant when α is even. We explicitly construct this beyond all orders expansion of p[sup d, sub α](r) for arbitrary integral α and d. [ABSTRACT FROM AUTHOR]

A comprehensive study of the symmetric Le´vy stable probability density function is presented. This is performed for orders both less than 2, and greater than 2. The latter class of functions are traditionally neglected because of a failure to satisfy non-negativity. The complete asymptotic expansions of the symmetric Le´vy stable densities of order greater than 2 are constructed, and shown to exhibit intricate series of transcendentally small terms—asymptotics beyond all orders. It is demonstrated that the symmetric Le´vy stable densities of any arbitrary rational order can be written in terms of generalized hypergeometric functions, and a number of new special cases are given representations in terms of special functions. A link is shown between the symmetric Le´vy stable density of order 4, and Pearcey’s integral, which is used widely in problems of optical diffraction and wave propagation. This suggests the existence of applications for the symmetric Le´vy stable densities of order greater than 2, despite their failure to define a probability density function. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The asymptotic expansions for the Kummer function obtained in the study of the linear response of magnetized Bose plasmas at T=0 K are presented for large and small values of its parameter, thereby displaying the function’s asymptotic nonuniformity. The large parameter expansion plays a determining role in the behavior of these Bose systems in the limit that the external magnetic field B→0. This particular expansion is generalized herein and its validity tested by determining the asymptotic expansion for the Hurwitz zeta function. [ABSTRACT FROM AUTHOR]

The complete asymptotic expansions, that is to say expansions which include any exponentially small terms lying beyond all orders of the asymptotic power series, are calculated for the Fermi-Dirac integrals. We present two methods to accomplish this, the first in the complex plane utilizing Mellin transforms and Hankel's representation of the gamma function, and the second on the real line using the known asymptotic expansions of the confluent hypergeometric functions. The complete expansions of F[sub p](η) are then used to investigate the effect that these traditionally neglected exponentially small terms have on physical systems. It is shown that for a 2 dimensional nonrelativistic ideal Fermi gas, the subdominant exponentially small series becomes dominant. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Understanding the evolutionary potential of mutations in gene regulatory networks is essential to furthering the study of evolution and development. However, in multicellular systems, genetic manipulation of regulatory networks in a targeted and high-throughput way remains challenging. In this study, we designed TF-High-Evolutionary (HighEvo), a transcription factor (TF) fused with a base editor (activation-induced deaminase), to continuously induce germline mutations at TF-binding sites across regulatory networks in Drosophila. Populations of flies expressing TF-HighEvo in their germlines accumulated mutations at rates an order of magnitude higher than natural populations. Importantly, these mutations accumulated around the targeted TF-binding sites across the genome, leading to distinct morphological phenotypes consistent with the developmental roles of the tagged TFs. As such, this TF-HighEvo method allows the interrogation of the mutational space of gene regulatory networks at scale and can serve as a powerful reagent for experimental evolution and genetic screens focused on the regulatory genome., Competing Interests: Conflict of Interest The authors declare no competing interests., (© The Author(s) 2024. Published by Oxford University Press on behalf of Society for Molecular Biology and Evolution.)