The Parameterized Complexity of Domination-type Problems and Application to Linear Codes

We study the parameterized complexity of domination-type problems. (sigma,rho)-domination is a general and unifying framework introduced by Telle: a set D of vertices of a graph G is (sigma,rho)-dominating if for any v in D, |N(v)\cap D| in sigma and for any $v\notin D, |N(v)\cap D| in rho. We mainly show that for any sigma and rho the problem of (sigma,rho)-domination is W[2] when parameterized by the size of the dominating set. This general statement is optimal in the sense that several particular instances of (sigma,rho)-domination are W[2]-complete (e.g. Dominating Set). We also prove that (sigma,rho)-domination is W[2] for the dual parameterization, i.e. when parameterized by the size of the dominated set. We extend this result to a class of domination-type problems which do not fall into the (sigma,rho)-domination framework, including Connected Dominating Set. We also consider problems of coding theory which are related to domination-type problems with parity constraints. In particular, we prove that the problem of the minimal distance of a linear code over Fq is W[2] for both standard and dual parameterizations, and W[1]-hard for the dual parameterization. To prove W[2]-membership of the domination-type problems we extend the Turing-way to parameterized complexity by introducing a new kind of non deterministic Turing machine with the ability to perform `blind' transitions, i.e. transitions which do not depend on the content of the tapes. We prove that the corresponding problem Short Blind Multi-Tape Non-Deterministic Turing Machine is W[2]-complete. We believe that this new machine can be used to prove W[2]-membership of other problems, not necessarily related to dominationComment: 19 pages, 2 figure

Suppression of Penning discharges between the KATRIN spectrometers

Artículo escrito por un elevado número de autores, solo se referencian el que aparece en primer lugar, el nombre del grupo de colaboración, si le hubiere, y los autores pertenecientes a la UAMThe KArlsruhe TRItium Neutrino experiment (KATRIN) aims to determine the effective electron (anti)-neutrino mass with a sensitivity of 0.2eV/c2 by precisely measuring the endpoint region of the tritium β-decay spectrum. It uses a tandem of electrostatic spectrometers working as magnetic adiabatic collimation combined with an electrostatic (MAC-E) filters. In the space between the pre-spectrometer and the main spectrometer, creating a Penning trap is unavoidable when the superconducting magnet between the two spectrometers, biased at their respective nominal potentials, is energized. The electrons accumulated in this trap can lead to discharges, which create additional background electrons and endanger the spectrometer and detector section downstream. To counteract this problem, “electron catchers” were installed in the beamline inside the magnet bore between the two spectrometers. These catchers can be moved across the magnetic-flux tube and intercept on a sub-ms time scale the stored electrons along their magnetron motion paths. In this paper, we report on the design and the successful commissioning of the electron catchers and present results on their efficiency in reducing the experimental backgroun

New constraint on the local relic neutrino background overdensity with the first KATRIN data runs

Artículo escrito por un elevado número de autores, solo se referencian el que aparece en primer lugar, el nombre del grupo de colaboración, si le hubiere, y los autores pertenecientes a la UAMWe report on the direct search for cosmic relic neutrinos using data acquired during the first two science campaigns of the KATRIN experiment in 2019. Beta-decay electrons from a high-purity molecular tritium gas source are analyzed by a high-resolution MAC-E filter around the end point at 18.57 keV. The analysis is sensitive to a local relic neutrino overdensity ratio of η < 9.7 × 1010/α (1.1 × 1011/α) at a 90% (95%) confidence level with α = 1 (0.5) for Majorana (Dirac) neutrinos. A fit of the integrated electron spectrum over a narrow interval around the end point accounting for relic neutrino captures in the tritium source reveals no significant overdensity. This work improves the results obtained by the previous neutrino mass experiments at Los Alamos and Troitsk. We furthermore update the projected final sensitivity of the KATRIN experiment to η < 1 × 1010/α at 90% confidence level, by relying on updated operational condition

First operation of the KATRIN experiment with tritium

Artículo escrito por un elevado número de autores, solo se referencian el que aparece en primer lugar, el nombre del grupo de colaboración, si le hubiere, y los autores pertenecientes a la UA

Precision measurement of the electron energy-loss function in tritium and deuterium gas for the KATRIN experiment

Artículo escrito por un elevado número de autores, solo se referencian el que aparece en primer lugar, el nombre del grupo de colaboración, si le hubiere, y los autores pertenecientes a la UAMThe KATRIN experiment is designed for a direct and model-independent determination of the effective electron anti-neutrino mass via a high-precision measurement of the tritium β-decay endpoint region with a sensitivity on mν of 0.2 eV /c 2 (90% CL). For this purpose, the β-electrons from a high-luminosity windowless gaseous tritium source traversing an electrostatic retarding spectrometer are counted to obtain an integral spectrum around the endpoint energy of 18.6 keV. A dominant systematic effect of the response of the experimental setup is the energy loss of β -electrons from elastic and inelastic scattering off tritium molecules within the source. We determined the energy-loss function in-situ with a pulsed angular-selective and monoenergetic photoelectron source at various tritium-source densities. The data was recorded in integral and differential modes; the latter was achieved by using a novel time-of-flight technique. We developed a semi-empirical parametrization for the energy-loss function for the scattering of 18.6-keV electrons from hydrogen isotopologs. This model was fit to measurement data with a 95% T 2 gas mixture at 30 K, as used in the first KATRIN neutrino-mass analyses, as well as a D 2 gas mixture of 96% purity used in KATRIN commissioning runs. The achieved precision on the energy-loss function has abated the corresponding uncertainty of σ(mν2) < 10-2eV2 [1] in the KATRIN neutrino-mass measurement to a subdominant leve

Versatile Confocal Raman Imaging Microscope Built from Off-the-Shelf Opto-Mechanical Components

Confocal Raman microscopic (CRM) imaging has evolved to become a key tool for spatially resolved, compositional analysis and imaging, down to the μm-scale, and nowadays one may choose between numerous commercial instruments. That notwithstanding, situations may arise which exclude the use of a commercial instrument, e.g., if the analysis involves toxic or radioactive samples/environments; one may not wish to render an expensive instrument unusable for other uses, due to contamination. Therefore, custom-designed CRM instrumentation—being adaptable to hazardous conditions and providing operational flexibility—may be beneficial. Here, we describe a CRM setup, which is constructed nearly in its entirety from off-the-shelf optomechanical and optical components. The original aim was to develop a CRM suitable for the investigation of samples exposed to tritium. For increased flexibility, the CRM system incorporates optical fiber coupling to both the Raman excitation laser and the spectrometer. Lateral raster scans and axial profiling of samples are facilitated by the use of a motorized xyz-translation assembly. Besides the description of the construction and alignment of the CRM system, we also provide (i) the experimental evaluation of system performance (such as, e.g., spatial resolution) and (ii) examples of Raman raster maps and axial profiles of selected thin-film samples (such as, e.g., graphene sheets)

Improved eV-scale sterile-neutrino constraints from the second KATRIN measurement campaign

Artículo escrito por un elevado número de autores, solo se referencian el que aparece en primer lugar, el nombre del grupo de colaboración, si le hubiere, y los autores pertenecientes a la UAMWe present the results of the light sterile neutrino search from the second Karlsruhe Tritium Neutrino (KATRIN) measurement campaign in 2019. Approaching nominal activity, 3.76 × 106 tritium β-electrons are analyzed in an energy window extending down to 40 eV below the tritium end point at E0 = 18.57 keV. We consider the 3ν + 1 framework with three active and one sterile neutrino flavors. The analysis is sensitive to a fourth mass eigenstate m42 ≲ 1600 eV2 and active-to-sterile mixing |Ue4|2 ≳ 6 × 10-3. As no sterile-neutrino signal was observed, we provide improved exclusion contours on m42 and |Ue4|2 at 95% C.L. Our results supersede the limits from the Mainz and Troitsk experiments. Furthermore, we are able to exclude the large Δm412 solutions of the reactor antineutrino and gallium anomalies to a great extent. The latter has recently been reaffirmed by the BEST Collaboration and could be explained by a sterile neutrino with large mixing. While the remaining solutions at small Δm412 are mostly excluded by short-baseline reactor experiments, KATRIN is the only ongoing laboratory experiment to be sensitive to relevant solutions at large Δm412 through a robust spectral shape analysi