Approximation Algorithms for Generalized MST and TSP in Grid Clusters

We consider a special case of the generalized minimum spanning tree problem (GMST) and the generalized travelling salesman problem (GTSP) where we are given a set of points inside the integer grid (in Euclidean plane) where each grid cell is $1 \times 1$. In the MST version of the problem, the goal is to find a minimum tree that contains exactly one point from each non-empty grid cell (cluster). Similarly, in the TSP version of the problem, the goal is to find a minimum weight cycle containing one point from each non-empty grid cell. We give a $(1+4\sqrt{2}+\epsilon)$ and $(1.5+8\sqrt{2}+\epsilon)$-approximation algorithm for these two problems in the described setting, respectively. Our motivation is based on the problem posed in [7] for a constant approximation algorithm. The authors designed a PTAS for the more special case of the GMST where non-empty cells are connected end dense enough. However, their algorithm heavily relies on this connectivity restriction and is unpractical. Our results develop the topic further

The Mean Absorption Line Spectra of a Selection of Luminous z~6 Lyman Break Galaxies

We examine the absorption-line spectra of a sample of 31 luminous (${M}_{\mathrm{UV}}\simeq -23$) Lyman break galaxies at redshift z sime 6 using data taken with the FOCAS and OSIRIS spectrographs on the Subaru and GTC telescopes. For two of these sources we present longer exposure data taken at higher spectral resolutions from ESO's X-shooter spectrograph. Using these data, we demonstrate the practicality of stacking our lower-resolution data to measure the depth of various interstellar and stellar absorption lines to probe the covering fraction of low-ionization gas and the gas phase and stellar metallicities near the end of the era of cosmic reionization. From maximum absorption-line depths of Si ii λ1260 and C ii λ1334, we infer a mean covering fraction of ≥0.85 ± 0.16 for our sample. This is larger than that determined using similar methods for lower-luminosity galaxies at slightly lower redshifts, suggesting that the most luminous galaxies appear to have a lower escape fraction than fainter galaxies, and therefore may not play a prominent role in concluding reionization. Using various interstellar absorption lines we deduce gas-phase metallicities close to solar, indicative of substantial early enrichment. Using selected stellar absorption lines, we model our spectra with a range of metallicities using techniques successfully employed at lower redshift and deduce a stellar metallicity of ${0.4}_{-0.1}^{+0.3}$ solar, consistent with the stellar mass—stellar metallicity relation recently found at z ~ 3–5. We discuss the implications of these metallicity estimates for the typical ages of our luminous galaxies and conclude our results imply initial star formation at redshifts z ~ 10, consistent with independent analyses of earlier objects

Software engineering standards and guides for very small entities: implementation in two start-ups

Very small entities, enterprises, organizations, projects or departments with up to 25 people, are very important to the worldwide economy. However it has ben established that such entities often do not utilize existing standards and frameworks. To address the needs of Very Small Entities (VSEs), a set of international standards and guides known as ISO/IEC 29110 has been developed. In this paper we present the results of early trials of this standard in two IT start-ups VSEs. A Peruvian VSE was recently audited and issued an ISO/IEC 29110 certificate of conformity

Compliance error compensation in robotic-based milling

The paper deals with the problem of compliance errors compensation in robotic-based milling. Contrary to previous works that assume that the forces/torques generated by the manufacturing process are constant, the interaction between the milling tool and the workpiece is modeled in details. It takes into account the tool geometry, the number of teeth, the feed rate, the spindle rotation speed and the properties of the material to be processed. Due to high level of the disturbing forces/torques, the developed compensation technique is based on the non-linear stiffness model that allows us to modify the target trajectory taking into account nonlinearities and to avoid the chattering effect. Illustrative example is presented that deals with robotic-based milling of aluminum alloy

Un assistant de mémoire pour les très petits projets d’ingénierie du logiciel

Nous proposons d’assister la mémoire des très petits projets d’ingénierie du logiciel avec une infrastructure la plus simple possible (un wiki sémantique) et des activités de gestion de connaissances intégrées dans deux processus issus de la norme ISO/IEC 29110, la gestion de projet et l’implémentation du logiciel. L’enregistrement, la réutilisation, la recherche et le partage de connaissances sont facilités par l’emploi d’un noyau ontologique basé sur le modèle de référence CIDOC CRM, enrichi par la modélisation du domaine de la norme 29110.We propose assisting the memory of very small software engineering projects thanks to an infrastructure kept as simple as possible (a semantic wiki) as well as knowledge management activities integrated into two  ISO/IEC 29110 standard processes, namely Project Management and Software Implementation. The recording, re-using, researching, and sharing of knowledge are facilitated by the use of an ontological core based on the CIDOC CRM and enhanced by the domain modeling of the 29110 standard

Draft Genome Sequence of the Putative Marine Pathogen Thalassobius sp. I31.1

Thalassobius sp. I31.1 is a putative pathogen involved in epizootic shell disease in the American lobster (Homarus americanus). We report here the draft genome sequence for Thalassobius sp. I31.1 and provide insight into its metabolism and links to environmental pollutant degradation

Fluorescent C II* 1335A emission spectroscopically resolved in a galaxy at z = 5.754

We report the discovery of the first spectroscopically resolved C II /C II* 1334, 1335A doublet in the Lyman-break galaxy J0215-0555 at z = 5.754. The separation of the resonant and fluorescent emission channels was possible thanks to the large redshift of the source and long integration time, as well as the small velocity width of the feature, 0.6 +- 0.2A. We model this emission and find that at least two components are required to reproduce the combination of morphologies of C II* emission, C II absorption and emission, and Lyman-alpha emission from the object. We suggest that the close alignment between the fluorescence and Lyman-alpha emission could indicate an ionisation escape channel within the object. While the faintness of such a C II /C II* doublet makes it prohibitively difficult to pursue for similar systems with current facilities, we suggest it can become a valuable porosity diagnostic in the era of JWST and the upcoming generations of ELTs

The QCD string and the generalised wave equation

The equation for QCD string proposed earlier is reviewed. This equation appears when we examine the gonihedric string model and the corresponding transfer matrix. Arguing that string equation should have a generalized Dirac form we found the corresponding infinite-dimensional gamma matrices as a symmetric solution of the Majorana commutation relations. The generalized gamma matrices are anticommuting and guarantee unitarity of the theory at all orders of $v/c$. In the second quantized form the equation does not have unwanted ghost states in Fock space. In the absence of Casimir mass terms the spectrum reminds hydrogen exitations. On every mass level $r=2,4,..$ there are different charged particles with spin running from $j=1/2$ up to $j_{max}=r-1/2$, and the degeneracy is equal to $d_{r}=2r-1 = 2j_{max}$. This is in contrast with the exponential degeneracy in superstring theory.Comment: 11 pages LaTeX, uses lamuphys.sty and bibnorm.sty,; Based on talks given at the 6th Hellenic School and Workshop on Elementary Particle Physics, Corfu, Greece, September 19-26, 1998 and at the International Workshop "ISMP", Tbilisi, Georgia, September 12-18, 199