Superstrings with multiplicities

A superstring of a set of words P = s1, · · · , sp is a string that contains each word of P as substring. Given P, the well known Shortest Linear Superstring problem (SLS), asks for a shortest superstring of P. In a variant of SLS, called Multi-SLS, each word si comes with an integer m(i), its multiplicity, that sets a constraint on its number of occurrences, and the goal is to find a shortest superstring that contains at least m(i) occurrences of si. Multi-SLS generalizes SLS and is obviously as hard to solve, but it has been studied only in special cases (with words of length 2 or with a fixed number of words). The approximability of Multi-SLS in the general case remains open. Here, we study the approximability of Multi-SLS and that of the companion problem Multi-SCCS, which asks for a shortest cyclic cover instead of shortest superstring. First, we investigate the approximation of a greedy algorithm for maximizing the compression offered by a superstring or by a cyclic cover: the approximation ratio is 1/2 for Multi-SLS and 1 for Multi-SCCS. Then, we exhibit a linear time approximation algorithm, Concat-Greedy, and show it achieves a ratio of 4 regarding the superstring length. This demonstrates that for both measures Multi-SLS belongs to the class of APX problems. © 2018 Yoshifumi Sakai; licensed under Creative Commons License CC-BY.Peer reviewe

Linking BWT and XBW via Aho-Corasick automaton : Applications to run-length encoding

Peer reviewe

Pore evolution in interstellar ice analogues: simulating the effects of temperature increase

Context. The level of porosity of interstellar ices - largely comprised of amorphous solid water (ASW) - contains clues on the trapping capacity of other volatile species and determines the surface accessibility that is needed for solid state reactions to take place. Aims. Our goal is to simulate the growth of amorphous water ice at low temperature (10 K) and to characterize the evolution of the porosity (and the specific surface area) as a function of temperature (from 10 to 120 K). Methods. Kinetic Monte Carlo simulations are used to mimic the formation and the thermal evolution of pores in amorphous water ice. We follow the accretion of gas-phase water molecules as well as their migration on surfaces with different grid sizes, both at the top growing layer and within the bulk. Results. We show that the porosity characteristics change substantially in water ice as the temperature increases. The total surface of the pores decreases strongly while the total volume decreases only slightly for higher temperatures. This will decrease the overall reaction efficiency, but in parallel, small pores connect and merge, allowing trapped molecules to meet and react within the pores network, providing a pathway to increase the reaction efficiency. We introduce pore coalescence as a new solid state process that may boost the solid state formation of new molecules in space and has not been considered so far.Comment: 9 pages, 8 figures Accepted for publication in A&

Practical lower and upper bounds for the Shortest Linear Superstring

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The first frost in the Pipe Nebula

Spectroscopic studies of ices in nearby star-forming regions indicate that ice mantles form on dust grains in two distinct steps, starting with polar ice formation (H2O rich) and switching to apolar ice (CO rich). We test how well the picture applies to more diffuse and quiescent clouds where the formation of the first layers of ice mantles can be witnessed. Medium-resolution near-infrared spectra are obtained toward background field stars behind the Pipe Nebula. The water ice absorption is positively detected at 3.0 micron in seven lines of sight out of 21 sources for which observed spectra are successfully reduced. The peak optical depth of the water ice is significantly lower than those in Taurus with the same visual extinction. The source with the highest water-ice optical depth shows CO ice absorption at 4.7 micron as well. The fractional abundance of CO ice with respect to water ice is 16+7-6 %, and about half as much as the values typically seen in low-mass star-forming regions. A small fractional abundance of CO ice is consistent with some of the existing simulations. Observations of CO2 ice in the early diffuse phase of a cloud play a decisive role in understanding the switching mechanism between polar and apolar ice formation.Comment: 17 pages, 8 figures, accepted by A&

Design to reliability shielded vertical interconnection applied to microwave Chip Scale Packaging

This paper presents the electrical design, measurement and reliability ests of a shielded vertical interconnection dedicated to microwave solder-mount packages. Electromagnetic simulations show very good results up to 20 GHz. Test samples have been designed and manufactured. Electrical results are in accordance with the simulations with insertion loss lower than 0.1 dB up to 20 GHz for the proposed interconnection. Reliability tests of present no degradation of the after 500 thermal cycles in the [-55°C, +125°C] temperature range

Space-time evolution of electron cascades in diamond

Here we describe model calculations to follow the spatio-temporal evolution of secondary electron cascades in diamond. The band structure of the insulator has been explicitly incorporated into the calculations as it affects ionizations from the valence band. A Monte-Carlo model was constructed to describe the path of electrons following the impact of a single electron of energy E 250 eV. The results show the evolution of the secondary electron cascades in terms of the number of electrons liberated, the spatial distribution of these electrons, and the energy distribution among the electrons as a function of time. The predicted ionization rates (5-13 electrons in 100 fs) lie within the limits given by experiments and phenomenological models. Calculation of the local electron density and the corresponding Debye length shows that the latter is systematically larger than the radius of the electron cloud. This means that the electron gas generated does not represent a plasma in a single impact cascade triggered by an electron of E 250 eV energy. This is important as it justifies the independent-electron approximation used in the model. At 1 fs, the (average) spatial distribution of secondary electrons is anisotropic with the electron cloud elongated in the direction of the primary impact. The maximal radius of the cascade is about 50 A at this time. As the system cools, energy is distributed more equally, and the spatial distribution of the electron cloud becomes isotropic. At 90 fs maximal radius is about 150 A. The Monte-Carlo model described here could be adopted for the investigation of radiation damage in other insulators and has implications for planned experiments with intense femtosecond X-ray sources.Comment: 26 pages, latex, 13 figure

Finding all maximal perfect haplotype blocks in linear time

Recent large-scale community sequencing efforts allow at an unprecedented level of detail the identification of genomic regions that show signatures of natural selection. Traditional methods for identifying such regions from individuals' haplotype data, however, require excessive computing times and therefore are not applicable to current datasets. In 2019, Cunha et al. (Advances in bioinformatics and computational biology: 11th Brazilian symposium on bioinformatics, BSB 2018, Niteroi, Brazil, October 30 - November 1, 2018, Proceedings, 2018. 10.1007/978-3-030-01722-4_3) suggested the maximal perfect haplotype block as a very simple combinatorial pattern, forming the basis of a new method to perform rapid genome-wide selection scans. The algorithm they presented for identifying these blocks, however, had a worst-case running time quadratic in the genome length. It was posed as an open problem whether an optimal, linear-time algorithm exists. In this paper we give two algorithms that achieve this time bound, one conceptually very simple one using suffix trees and a second one using the positional Burrows-Wheeler Transform, that is very efficient also in practice.Peer reviewe

Porosity measurements of interstellar ice mixtures using optical laser interference and extended effective medium approximations

Aims. This article aims to provide an alternative method of measuring the porosity of multi-phase composite ices from their refractive indices and of characterising how the abundance of a premixed contaminant (e.g., CO2) affects the porosity of water-rich ice mixtures during omni-directional deposition. Methods. We combine optical laser interference and extended effective medium approximations (EMAs) to measure the porosity of three astrophysically relevant ice mixtures: H2O:CO2=10:1, 4:1, and 2:1. Infrared spectroscopy is used as a benchmarking test of this new laboratory-based method. Results. By independently monitoring the O-H dangling modes of the different water-rich ice mixtures, we confirm the porosities predicted by the extended EMAs. We also demonstrate that CO2 premixed with water in the gas phase does not significantly affect the ice morphology during omni-directional deposition, as long as the physical conditions favourable to segregation are not reached. We propose a mechanism in which CO2 molecules diffuse on the surface of the growing ice sample prior to being incorporated into the bulk and then fill the pores partly or completely, depending on the relative abundance and the growth temperature.Comment: 9 pages, 6 figures, 1 table. Accepted for publication in A&

Near-arcsecond resolution observations of the hot corino of the solar type protostar IRAS 16293-2422

Complex organic molecules have previously been discovered in solar type protostars, raising the questions of where and how they form in the envelope. Possible formation mechanisms include grain mantle evaporation, interaction of the outflow with its surroundings or the impact of UV/X-rays inside the cavities. In this Letter we present the first interferometric observations of two complex molecules, CH3CN and HCOOCH3, towards the solar type protostar IRAS16293-2422. The images show that the emission originates from two compact regions centered on the two components of the binary system. We discuss how these results favor the grain mantle evaporation scenario and we investigate the implications of these observations for the chemical composition and physical and dynamical state of the two components.Comment: 5 pages (apjemulate), 2 figures; accepted by ApJ