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We give a comprehensive description of the functions and variables defined in the authors GAP code file OrbOrd.txt, which serve mainly to compute (bounds on) the number of $operatorname{Aut}(S)$-orbits on $S$, or the set or number of element orders in $S$ for nonabelian finite simple groups of Lie type $S$.
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Aspects ([asp{epsilon}], ASsociation PositionnellE/ProbabilistE de CaTalogues de Sources in French) is a Fortran 95 code for the cross-identification of astrophysical sources. Its source files are freely available. Given the coordinates and positional uncertainties of all the sources in two catalogs K and K, Aspects computes the probability that an object in K and one in K are the same or that they have no counterpart. Three exclusive assumptions are considered: (1) Several-to-one associations: a K-source has at most one counterpart in K, but a K-source may have several counterparts in K; (2) One-to-several associations: the same with K and K swapped; (3) One-to-one associations: a K-source has at most one counterpart in K and vice versa. To compute the probabilities of association, Aspects needs the a priori (i.e. ignoring positions) probability that an object has a counterpart. The code obtains estimates of this quantity by maximizing the likelihood to observe all the sources at their effective positions under each assumption. The likelihood may also be used to determine the most appropriate model, given the data, or to estimate the typical positional uncertainty if unknown.
Pegase.3 is a Fortran 95 code modeling the spectral evolution of galaxies from the far-ultraviolet to submillimeter wavelengths. It also follows the chemical evolution of their stars, gas and dust. For a given scenario (a set of parameters defining the history of mass assembly, the star formation law, the initial mass function...), Pegase.3 consistently computes the following: * the star formation, infall, outflow and supernova rates from 0 to 20 Gyr; * the stellar metallicity, the abundances of main elements in the gas and the composition of dust; * the unattenuated stellar spectral energy distribution (SED); * the nebular SED, using nebular continua and emission lines precomputed with code Cloudy (Ferland et al. 2017); * the attenuation in star-forming clouds and the diffuse interstellar medium, by absorption and scattering on dust grains, of the stellar and nebular SEDs. For this, the code uses grids of the transmittance for spiral and spheroidal galaxies. We precomputed these grids through Monte Carlo simulations of radiative transfer based on the method of virtual interactions; * the re-emission by grains of the light they absorbed, taking into account stochastic heating. The main innovation compared to Pegase.2 is the modeling of dust emission and its evolution. The computation of nebular emission has also been entirely upgraded to take into account metallicity effects and infrared lines. Other major differences are that complex scenarios of evolution (derived for instance from cosmological simulations), with several episodes of star formation, infall or outflow, may now be implemented, and that the detailed evolution of the most important elements -- not only the overall metallicity -- is followed.
Let $S_n$ denote the symmetric group on $n$ elements, and $Sigmasubseteq S_{n}$ a symmetric subset of permutations. Aldous spectral gap conjecture, proved by Caputo, Liggett and Richthammer [arXiv:0906.1238], states that if $Sigma$ is a set of transpositions, then the second eigenvalue of the Cayley graph $mathrm{Cay}left(S_{n},Sigmaright)$ is identical to the second eigenvalue of the Schreier graph on $n$ vertices depicting the action of $S_{n}$ on $left{ 1,ldots,nright}$. Inspired by this seminal result, we study similar questions for other types of sets in $S_{n}$. Specifically, we consider normal sets: sets that are invariant under conjugation. Relying on character bounds due to Larsen and Shalev [2008], we show that for large enough $n$, if $Sigmasubset S_{n}$ is a full conjugacy class, then the second eigenvalue of $mathrm{Cay}left(S_{n},Sigmaright)$ is roughly identical to the second eigenvalue of the Schreier graph depicting the action of $S_{n}$ on ordered $4$-tuples of elements from $left{ 1,ldots,nright}$. We further show that this type of result does not hold when $Sigma$ is an arbitrary normal set, but a slightly weaker one does hold. We state a conjecture in the same spirit regarding an arbitrary symmetric set $Sigmasubset S_{n}$, which yields surprisingly strong consequences.
The Algorithms for Lattice Fermions package provides a general code for the finite-temperature and projective auxiliary-field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to a bosonic field with given dynamics. The package includes five pre-defined model classes: SU(N) Kondo, SU(N) Hubbard, SU(N) t-V and SU(N) models with long range Coulomb repulsion on honeycomb, square and N-leg lattices, as well as $Z_2$ unconstrained lattice gauge theories coupled to fermionic and $Z_2$ matter. An implementation of the stochastic Maximum Entropy method is also provided. One can download the code from our Git instance at https://git.physik.uni-wuerzburg.de/ALF/ALF/-/tree/ALF-2.0 and sign in to file issues.
Jupyter notebook allows data scientists to write machine learning code together with its documentation in cells. In this paper, we propose a new task of code documentation generation (CDG) for computational notebooks. In contrast to the previous CDG tasks which focus on generating documentation for single code snippets, in a computational notebook, one documentation in a markdown cell often corresponds to multiple code cells, and these code cells have an inherent structure. We proposed a new model (HAConvGNN) that uses a hierarchical attention mechanism to consider the relevant code cells and the relevant code tokens information when generating the documentation. Tested on a new corpus constructed from well-documented Kaggle notebooks, we show that our model outperforms other baseline models.
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