An Algorithm for the Longest Common Subsequence and Substring Problem

In this note, we first introduce a new problem called the longest common subsequence and substring problem. Let $X$ and $Y$ be two strings over an alphabet $\Sigma$. The longest common subsequence and substring problem for $X$ and $Y$ is to find the longest string which is a subsequence of $X$ and a substring of $Y$. We propose an algorithm to solve the problem

An Algorithm for the Constrained Longest Common Subsequence and Substring Problem

Let $\Sigma$ be an alphabet. For two strings $X$, $Y$, and a constrained string $P$ over the alphabet $\Sigma$, the constrained longest common subsequence and substring problem for two strings $X$ and $Y$ with respect to $P$ is to find a longest string $Z$ which is a subsequence of $X$, a substring of $Y$, and has $P$ as a subsequence. In this paper, we propose an algorithm for the constrained longest common subsequence and substring problem for two strings with a constrained string.Comment: arXiv admin note: text overlap with arXiv:2308.0092

Efficient numerical methods for Anisotropic Diffusion of Galactic Cosmic Rays

Anisotropic diffusion is imperative in understanding cosmic ray diffusion across the Galaxy, the heliosphere, and the interplay of cosmic rays with the Galactic magnetic field. This diffusion term contributes to the highly stiff nature of the cosmic ray transport equation. To conduct numerical simulations of time-dependent cosmic ray transport, implicit integrators (namely, Crank-Nicolson (CN)) have been traditionally favoured over the CFL-bound explicit integrators in order to be able to take large step sizes. We propose exponential methods to treat the linear anisotropc diffusion equation in the presence of advection and time-independent and time-dependent sources. These methods allow us to take even larger step sizes that can substantially speed-up the simulations whilst generating highly accurate solutions. In or subsequent work, we will use these exponential solvers in the Picard code to study anisotropic cosmic ray diffusion and we will consider additional physical processes such as continuous momentum losses and reacceleration.Comment: The 38th International Cosmic Ray Conference (ICRC2023

LeXInt: Package for Exponential Integrators employing Leja interpolation

We present a publicly available software for exponential integrators that computes the $\varphi_l(z)$ functions using polynomial interpolation. The interpolation method at Leja points have recently been shown to be competitive with the traditionally-used Krylov subspace method. The developed framework facilitates easy adaptation into any Python software package for time integration.Comment: Publicly available software available at https://github.com/Pranab-JD/LeXInt, in submissio

Tracking Advanced Planetary Systems (TAPAS) with HARPS-N. V.: A Massive Jupiter orbiting the very low metallicity giant star BD+03 2562 and a possible planet around HD~103485

We present two evolved stars from the TAPAS (Tracking Advanced PlAnetary Systems) with HARPS-N project devoted to RV precision measurements of identified candidates within the PennState - Torun Centre for Astronomy Planet Search. Evolved stars with planets are crucial to understand the dependency of the planet formation mechanism on the mass and metallicity of the parent star and to study star-planet interactions. The paper is based on precise radial velocity (RV) measurements, for HD 103485 we collected 57 epochs over 3317 days with the Hobby-Eberly Telescope and its High Resolution Spectrograph and 18 ultra-precise HARPS-N data over 919 days. For BD+03 2562 we collected 46 epochs of HET data over 3380 days and 19 epochs of HARPS-N data over 919 days. We present the analysis of the data and the search for correlations between the RV signal and stellar activity, stellar rotation and photometric variability. Based on the available data, we interpret the RV variations measured in both stars as Keplerian motion. Both stars have masses close to Solar (1.11 and 1.14), very low metallicities ([Fe/H]=-0.50 and -0.71), and, both have Jupiter planetary mass companions (m sin i=7 and 6.4 Mj), in close to terrestrial orbits (1.4 and 1.3~au), with moderate eccentricities (e=0.34 and 0.2). However, we cannot totally exclude that the signal in the case of HD~103485 is due to rotational modulation of active regions. Based on the current data, we conclude that BD+03 2562 has a bona fide planetary companion while for HD 103485 we cannot totally exclude that the best explanation for the RV signal modulations is not the existence of a planet but stellar activity. If, the interpretation remains that both stars have planetary companions they represent systems orbiting very evolved stars with very low metallicities, a challenge to the conditions required for the formation of massive giant gas planets.Comment: Acepted A&A 12 pages, 11 figure

Revisit of non-linear Landau damping for electrostatic instability driven by blazar-induced pair beams

We revisit the effect of non-linear Landau (NL) damping on the electrostatic instability of blazar-induced pair beams, using a realistic pair-beam distribution. We employ a simplified 2D model in ${\bf k}$-space to study the evolution of the electric-field spectrum and to calculate the relaxation time of the beam. We demonstrate that the 2D model is an adequate representation of the 3D physics. We find that non-linear Landau damping, once it operates efficiently, transports essentially the entire wave energy to small wavenumbers where wave driving is weak or absent. The relaxation time also strongly depends on the IGM temperature, $T_\mathrm{IGM}$, and for $T_\mathrm{IGM}\ll10$ eV, and in the absence of any other damping mechanism, the relaxation time of the pair beam is longer than the inverse Compton (IC) scattering time. The weak late-time beam energy losses arise from the accumulation of wave energy at small $k$, that non-linearly drains the wave energy at the resonant $\mathbf{k}$ of the pair-beam instability. Any other dissipation process operating at small $k$ would reduce that wave-energy drain and hence lead to stronger pair-beam energy losses. As an example, collisions reduce the relaxation time by an order of magnitude, although their rate is very small. Other non-linear processes, such as the modulation instability, could provide additional damping of the non-resonant waves and dramatically reduce the relaxation time of the pair beam. An accurate description of the spectral evolution of the electrostatic waves is crucial for calculating the relaxation time of the pair beam