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A two-dimensional helium atom (2D-helium) is a real subject for current studies, particularly regarding a hot topic of negatively charged excitons (trions) in semiconducting monolayers. The present study considers a 2D-helium-like atom in a homogeneous magnetic field. We are able to rewrite its Schrödinger equation into a polynomial form concerning dynamic variables. This form is useful for utilizing the algebraic calculation by annihilation and creation operators, enabling the successful application of the Feranchuk-Komarov (FK) operator method to obtain numerically exact solutions (energies and wave functions) for this system. The polynomialization of the equation allows obtaining analytical expressions of all matrix elements, which saves the computational resources significantly. Numerical results for the case without a magnetic field are comparable to other calculations. Moreover, the precise separation of the center-of-mass motion, as provided in this study, leads to an equation for the relative motion of the electrons in a magnetic field, incorporating all previously neglected terms. This result is useful for further study of trions where the electron effective mass is comparable with the hole effective mass. Additionally, we provide a FORTRAN program designed to solve the problems above. Program Title: CHeAMF CPC Library link to program files: https://doi.org/10.17632/mp8tf2dz67.1 Licensing provisions: BSD 3-clause Programming language: FORTRAN90 Nature of problem: The Schrödinger equation for a 2D-helium-like atom in a homogeneous magnetic field is transformed into a polynomial form using the Levi-Civita transformation twice. This transformation results in a structure more conductive to applying algebraic methods based on annihilation and creation operators. Consequently, we employ the FK operator method [1] to obtain numerically exact solutions, ensuring that the calculated energies converge to a high level of precision, up to 15 decimal places in this study. This method is developed to cover a broad range of magnetic field intensities, extending up to 0.1 a.u. (2.35 × 10 4 Tesla). Moreover, it is applicable not only for the ground state but also for highly excited states. Solution method: The modified FK operator method, as introduced in reference [2], has been developed and applied to obtain precise numerical solutions for a 2D-helium-like atom. Concurrently, algebraic techniques have been employed to compute matrix elements. Subsequently, we transformed the Schrödinger equation into a linear matrix equation, which we solved using the 'dsygvx.f' subroutine from the LAPACK library [3]. This subroutine has been optimized for improved accuracy by employing real*16 variables instead of real*8. Furthermore, we have incorporated an optimal free parameter into the FORTRAN program, enhancing convergence speed. Additional comments including restrictions and unusual features: Operating system: Linux. RAM: at least 4 GByte per core. We recommend using the gFortran compiler for this program. The runtime varies from a few minutes to hours, depending on the required precision. Particularly for strong magnetic fields (γ ≥ 0.01 a.u.) or when working with excited levels, the runtime may extend to several hours to achieve a precision of 16 decimal places. In such cases, it is advisable to have at least 60 GB of RAM per core. [1] I. Feranchuk, A. Ivanov, Van-Hoang Le, A. Ulyanenkov, Non-perturbative Description of Quantum Systems, Springer, Switzerland, 2015, https://doi.org/10.1007/978-3-319-13006-4. [2] Thanh-Xuan H. Cao, Duy-Nhat Ly, Ngoc-Tram D. Hoang, Van-Hoang Le, High-accuracy numerical calculations of the bound states of a hydrogen atom in a constant magnetic field with arbitrary strength, Comput. Phys. Commun. (2019), https://doi.org/10.1016/j.cpc.2019.02.013. [3] Netlib.org. LAPACK: Linear Algebra PACKage, Subroutine dsygvx.f, https://netlib.org/lapack/explore-3.1.1-html/dsygvx.f.html. [ABSTRACT FROM AUTHOR]

The Receiver Operating Characteristics (ROC) method is used to evaluate the diagnostic accuracy of binary quantitative tests in a broad spectrum of disciplines, including medicine, physics of complex systems, geophysics, meteorology, etc. The estimation of the significance of the examined prediction method is of high importance and it's usually approximated by Monte Carlo calculations. To simplify this problem, a F O R T R A N code called VISROC was submitted to the CPC Program Library in 2014. VISROC evaluates the significance of binary diagnostic and prognostic tools for a family of k -ellipses which are based on confidence ellipses and cover the whole ROC space. Since that time, the code has been significantly improved and several new capabilities have been added. Most importantly, a Graphical User Interface (GUI) has been implemented, which can be invoked using either the R shiny web application or the P y t h o n application available for Windows, Mac, and Linux operating systems, both of which are described here. Program Title: VISROC 2.0 CPC Library link to program files: https://doi.org/10.17632/dktybrydvf.1 Licensing provisions: AGPLv3 Programming language: R and P y t h o n Journal reference of previous version: N.V. Sarlis, S.-R. G. Christopoulos, Comput. Phys. Commun. 185 (2014) 1172. Does the new version supersede the previous version?: Yes Reasons for the new version: Overcome previous version's limitations and implement GUI. Summary of revisions: R and P y t h o n applications, GUI, ability to input files containing ROC data. Nature of problem: The Receiver Operating Characteristics (ROC) [1] is a method used to evaluate the diagnostic ability of binary tests and prediction methods in a broad spectrum of disciplines. Apart from the sensitivity (or True Positive rate, TPr) and specificity (which is complementary to False Positive rate, FPr, i.e., specificity=1-FPr) measures, the estimation of the statistical significance of the examined method is of high importance. VISROC evaluates the significance of binary diagnostic and prognostic tools for a family of k -ellipses which are based on confidence ellipses and cover the whole ROC space. Solution method: Using the statistics of random binary predictions for a given value of the predictor threshold ϵ t , one can construct the corresponding confidence ellipses. The envelope of these confidence ellipses is estimated by varying ϵ t in the interval [ 0 , 1 ] and one obtains a new family of ellipses, called k -ellipses [2]. They cover the whole ROC space and lead to a well defined Area Under the Curve (AUC). Mason and Graham [3] have shown that AUC follows the Mann-Whitney U-statistics [4] which can be used [5] to estimate the statistical significance of each k -ellipse. As the transformation is invertible, any point on the ROC plane corresponds to a unique value of k , hence it belongs to a unique k -ellipse that allows the estimation of the probability (p -value) to obtain this point by chance. The present GUI applications provide the p -value on the ROC plane as well as the k -ellipses corresponding to the (p =)10%, 5% and 1% significance levels using as input the number of the positive (P) and negative (Q) cases to be predicted. [1] T. Fawcett, Pattern Recognit. Lett. 27 (8) (2006) 861–874, 1172. [2] N.V. Sarlis, S.-R.G. Christopoulos, Comput. Phys. Commun. 185 (2014) 1172. [3] S.J. Mason, N.E. Graham, Q. J. R. Meteorol. Soc. 128 (2002) 2145. [4] H.B. Mann, D.R. Whitney, Ann. Math. Stat.. 18 (1947) 50. Program Summary section. [5] L.C. Dinneen, B.C. Blakesley, J. R. Stat. Soc., Ser. C, Appl. Stat. 22 (1973) 269. [ABSTRACT FROM AUTHOR]

In this release note we describe the 1.2 update to NLOX , a computer program for calculations in high-energy particle physics. New features since the 1.0 release and other changes are described, along with usage documentation. Program title: NLOX CPC Library link to program files: https://doi.org/10.17632/y7jth5hznv.2 Developer's repository link: http://www.hep.fsu.edu/~nlox Licensing provisions: CC BY NC 3.0 Programming language: C++. Fortran interface available, and Fortran compiler required for dependencies. Journal reference of previous version: Comput. Phys. Commun. 257 (2020) 107284 Does the new version supersede the previous version?: Yes Reasons for the new version: We have added several new features to NLOX , and made significant stability and efficiency improvements. The new features provide new types of output, and more flexibility for user input. These features are largely motivated to simplify interfacing NLOX with other automated tools, Monte Carlo and real-radiation providers in particular. Occasionally in a Monte Carlo run using NLOX instabilities are discovered in the loop results of NLOX in certain corners of phase space. While the original version had methods to detect these instabilities, and partially correct for them, the latest version has additional methods of detecting instabilities, and existing methods are improved. This version has better reliability and specificity of detection, and a higher success rate of correction. Summary of revisions: We have added new output modes. The first new mode allows the user to isolate contributing pieces in the amplitude-squared in powers of the constants α e and α s. NLOX is also now capable of producing color-correlated output for Born-level matrix elements, required for interfacing to real-radiation providers. We have added support for the Les Houches standard interface function, OLP_SetParameter, implemented as NLOX_OLP_SetParameter. This allows users to set certain parameters, for our purposes coupling constants, masses, widths, the number of light and heavy quark flavors, and the renormalization scale. Previously these were runtime constants in NLOX , requiring editing an input file, or specialized functions to set after program initialization. We have improved the numerical stability of NLOX substantially in this release. First, the stability tests performed internally by the TRed library have been improved. In particular, we have devised a better metric for determining configurations of phase space where the Gram determinant is small, and therefore the default reduction numerically unstable, by comparing the determinant, a measure of the "volume" of the matrix, to a maximal volume spanned by the vectors of the matrix. Second, we have interfaced with higher-precision external libraries where available and necessary. The thresholds for recomputation in higher precision and warning flags for internal failure have been adjusted accordingly, allowing for fewer recomputations, a higher sensitivity to phase space points giving numerically incorrect results, and more specificity to flagging points as failed to the user. Finally, we have implemented new routines that compute the IR pole structure of the real emission corresponding to the virtual routines of NLOX , as a final check of the amplitude squared. These routines are used automatically to determine an estimated accuracy of the result returned through the standard Les Houches flag acc of the user function NLOX_OLP_EvalSubProcess. We have retooled the generation of processes provided in downloadable packages to reduce expression sizes and eliminate some common structures, resulting in significantly smaller code sizes, sometimes a factor of two smaller than in the 1.0 version. For a more complete discussion of the changes in this release, please see the accompanying document in the package, nlox-1.2.0.pdf. Nature of problem: The computation of higher-order terms in the coupling expansion of Standard Model scattering amplitudes is required for precision studies in collider experiments. Techniques for computing the first corrections are well-known, and are now suited to automation. We wish to provide code that calculates virtual (one-loop) quantum chromodynamics and electroweak corrections for desired amplitudes using a package that automates the production of this code. Solution method: We use Python scripts and a computer algebra system, FORM , to reduce virtual amplitudes to C++ code and data based on Feynman rules of the Standard Model. The scripts perform a tensor decomposition of the one loop integrals to reduce each amplitude to a dependence on tensor integral coefficients. These coefficients are called at runtime by the provided library TRed, which performs tensor reduction into base (scalar) coefficients at runtime. The scripts identify repeated structures to be calculated once in the produced code for efficiency. The tensor reduction code is designed such that needed tensor coefficients need to be computed only once per evaluation of the desired amplitude, and are built recursively from other needed coefficients. Additional comments including restrictions and unusual features: The code-producing scripts are not provided in this release, only fixed libraries such as TRed and required interface code for pre-generated processes. Some processes are provided with this release, with others available upon request. • Required External Dependencies: QCDLoop 1.95, OneLOop 3.6 (available for download in utility tarball). • Required Compilers: gcc 4.6 or higher. Interface to certain optional libraries requires C++ 11 support found in gcc 4.7 or higher. • Operating System: Linux, MacOS. [ABSTRACT FROM AUTHOR]

We present VAH , a (3+1)–dimensional simulation that evolves the far-from-equilibrium quark-gluon plasma produced in ultrarelativistic heavy-ion collisions with anisotropic fluid dynamics. We solve the hydrodynamic equations on an Eulerian grid using the Kurganov–Tadmor algorithm in combination with a new adaptive Runge–Kutta method. Our numerical scheme allows us to start the simulation soon after the nuclear collision, largely avoiding the need to integrate it with a separate pre-equilibrium dynamics module. We test the code's performance by simulating on the Eulerian grid conformal and non-conformal Bjorken flow as well as conformal Gubser flow, whose (0+1)–dimensional solutions are precisely known. Finally, we compare non-conformal anisotropic hydrodynamics to second-order viscous hydrodynamics in central Pb+Pb collisions and find that the former's longitudinal flow profile responds more consistently to the fluid's gradients along the spacetime rapidity direction. Manuscript Title: Anisotropic fluid dynamical simulations of heavy-ion collisions Authors: Mike McNelis, Dennis Bazow, Ulrich Heinz Program Title: VAH Licensing provisions: GPLv3 Programming Language: C++ Computer: Laptop, desktop, cluster Operating System: GNU/Linux distributions, Mac OS X Global memory usage: 1.2 GB (for a 129 × 129 × 63 grid) Keywords: Ultrarelativistic heavy-ion collisions, quark-gluon plasma, relativistic hydrodynamics, computational fluid dynamics Classification: 12 Gases and Fluids, 17 Nuclear physics External routines/libraries: GNU Scientific Library (GSL) Nature of problem: Modeling the far-from-equilibrium dynamics of quark-gluon plasma produced in ultrarelativistic heavy-ion collisions. Solution method: Kurganov–Tadmor algorithm, adaptive stepsize method Running time: A (3+1)–d non-conformal anisotropic fluid dynamical simulation of a central Pb+Pb collision on a 129 × 129 × 63 grid takes about 530 s for an Intel Xeon E5-2680 v4 multi-core processor with OpenMP acceleration (see Sec. 5.3). [ABSTRACT FROM AUTHOR]