Rigorous confidence intervals for critical probabilities

We use the method of Balister, Bollobas and Walters to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedean lattices. In our computer calculations, the emphasis is on simplicity and ease of verification, rather than obtaining the best possible results. Nevertheless, we obtain intervals of width at most 0.0005 in all cases

Assessing policy stability in Iraq: a fuzzy approach to modeling preferences

The first Council of Representatives elected under the new Iraqi Constitution was unable to pass legislation required to achieve the political benchmarks set by the government. We argue that the exercise of a qualified veto by the three-member Presidency Council essentially required near unanimity among the nine parties of the governing coalition. Given the policy positions of these parties, unanimity was not possible. Our analysis makes use of a fuzzy veto players model. The placement of the government parties along a single dimension based on fuzzy preference measures derived from party text data reveals no common area of agreement

Commissioning of the vacuum system of the KATRIN Main Spectrometer

The KATRIN experiment will probe the neutrino mass by measuring the beta-electron energy spectrum near the endpoint of tritium beta-decay. An integral energy analysis will be performed by an electro-static spectrometer (Main Spectrometer), an ultra-high vacuum vessel with a length of 23.2 m, a volume of 1240 m^3, and a complex inner electrode system with about 120000 individual parts. The strong magnetic field that guides the beta-electrons is provided by super-conducting solenoids at both ends of the spectrometer. Its influence on turbo-molecular pumps and vacuum gauges had to be considered. A system consisting of 6 turbo-molecular pumps and 3 km of non-evaporable getter strips has been deployed and was tested during the commissioning of the spectrometer. In this paper the configuration, the commissioning with bake-out at 300{\deg}C, and the performance of this system are presented in detail. The vacuum system has to maintain a pressure in the 10^{-11} mbar range. It is demonstrated that the performance of the system is already close to these stringent functional requirements for the KATRIN experiment, which will start at the end of 2016.Comment: submitted for publication in JINST, 39 pages, 15 figure

The design, construction, and commissioning of the KATRIN experiment

The KArlsruhe TRItium Neutrino (KATRIN) experiment, which aims to make a direct and model-independent determination of the absolute neutrino mass scale, is a complex experiment with many components. More than 15 years ago, we published a technical design report (TDR) [1] to describe the hardware design and requirements to achieve our sensitivity goal of 0.2 eV at 90% C.L. on the neutrino mass. Since then there has been considerable progress, culminating in the publication of first neutrino mass results with the entire beamline operating [2]. In this paper, we document the current state of all completed beamline components (as of the first neutrino mass measurement campaign), demonstrate our ability to reliably and stably control them over long times, and present details on their respective commissioning campaigns

Commissioning of the vacuum system of the KATRIN Main Spectrometer

The KATRIN experiment will probe the neutrino mass by measuring the -electron energy spectrum near the endpoint of tritium -decay. An integral energy analysis will be performed by an electro-static spectrometer (“Main Spectrometer”), an ultra-high vacuum vessel with a length of 23.2 m, a volume of 1240m3, and a complex inner electrode system with about 120 000 individual parts. The strong magnetic field that guides the -electrons is provided by super-conducting solenoids at both ends of the spectrometer. Its influence on turbo-molecular pumps and vacuum gauges had to be considered. A system consisting of 6 turbo-molecular pumps and 3 km of non-evaporable getter strips has been deployed and was tested during the commissioning of the spectrometer. In this paper the configuration, the commissioning with bake-out at 300 C, and the performance of this system are presented in detail. The vacuum system has to maintain a pressure in the 10$^{-11}$ mbar range. It is demonstrated that the performance of the system is already close to these stringent functional requirements for the KATRIN experiment, which will start at the end of 2016

Improved Upper Limit on the Neutrino Mass from a Direct Kinematic Method by KATRIN

We report on the neutrino mass measurement result from the first four-week science run of the Karlsruhe Tritium Neutrino experiment KATRIN in spring 2019. Beta-decay electrons from a high-purity gaseous molecular tritium source are energy analyzed by a high-resolution MAC-E filter. A fit of the integrated electron spectrum over a narrow interval around the kinematic end point at 18.57 keV gives an effective neutrino mass square value of $(−1.0^{+0.9}_{−1.1}) eV^2$. From this, we derive an upper limit of 1.1 eV (90% confidence level) on the absolute mass scale of neutrinos. This value coincides with the KATRIN sensitivity. It improves upon previous mass limits from kinematic measurements by almost a factor of 2 and provides model-independent input to cosmological studies of structure formation

Measurement theory and subsethood

The connection between logical implication and the subsethood relationship is apparent when bivalent logic and crisp set theory are examined. When fuzzy logic and fuzzy set theory are examined, however the connection is not always clear. Ragin Ragin (1987) introduced fuzzy subsethood into the social sciences as a tool for detecting necessary and sufficient conditions. Unfortunately, Ragin\u27s efforts were dismissed by social scientists becasue of the problem of scale. This paper examines the use of fuzzy subsethood as tools for detecting causality. © 2010 IEEE

Agreement, agreement distributions, and distance

Data collected by ordered category, i.e. a Likert scale, can be both challenging to understand and difficult to compare with other similar kinds of data. Building on the agreement measure we extend the application to include the calculation of a distance by which comparisons between agreement distributions can be made. This is useful in decision making when it is necessary to determine group positional changes over time, or proximity to agreement among separate teams. ©2008 IEEE

E-business decision making by agreement

Gathering customer data over the Internet is largely limited to collecting the responses to a set of easily answerable questions, such as Yes/No questions and Likert scale questions. These data are then analyzed to identify customer trends or other items of interest to management. The data can be useful but key to their usage is the application of suitable mathematical tools. Traditionally little more than standard statistics has been used in the analysis of ordinal, or category, data. This can be inaccurate and in some cases, misleading. This paper introduces measures of agreement and dissent to the field of eBusiness analysis and shows how ordinal data can be analyzed in more meaningful ways. Copyright © 2008, IGI Global