Approximations from Anywhere and General Rough Sets

Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present author in her earlier papers. From the practical perspective, a few (as opposed to one) theoretical frameworks may be suitable for formulating the problem itself. \emph{Granular operator spaces} have been recently introduced and investigated by the present author in her recent work in the context of antichain based and dialectical semantics for general rough sets. The nature of the inverse problem is examined from number-theoretic and combinatorial perspectives in a higher order variant of granular operator spaces and some necessary conditions are proved. The results and the novel approach would be useful in a number of unsupervised and semi supervised learning contexts and algorithms.Comment: 20 Pages. Scheduled to appear in IJCRS'2017 LNCS Proceedings, Springe

Limits on uranium and thorium bulk content in GERDA Phase I detectors

Internal contaminations of $^{238}$U, $^{235}$U and $^{232}$Th in the bulk of high purity germanium detectors are potential backgrounds for experiments searching for neutrinoless double beta decay of $^{76}$Ge. The data from GERDA Phase~I have been analyzed for alpha events from the decay chain of these contaminations by looking for full decay chains and for time correlations between successive decays in the same detector. No candidate events for a full chain have been found. Upper limits on the activities in the range of a few nBq/kg for $^{226}$Ra, $^{227}$Ac and $^{228}$Th, the long-lived daughter nuclides of $^{238}$U, $^{235}$U and $^{232}$Th, respectively, have been derived. With these upper limits a background index in the energy region of interest from $^{226}$Ra and $^{228}$Th contamination is estimated which satisfies the prerequisites of a future ton scale germanium double beta decay experiment.Comment: 2 figures, 7 page

Limit on the Radiative Neutrinoless Double Electron Capture of 36^{36}Ar from GERDA Phase I

Neutrinoless double electron capture is a process that, if detected, would give evidence of lepton number violation and the Majorana nature of neutrinos. A search for neutrinoless double electron capture of $^{36}$Ar has been performed with germanium detectors installed in liquid argon using data from Phase I of the GERmanium Detector Array (GERDA) experiment at the Gran Sasso Laboratory of INFN, Italy. No signal was observed and an experimental lower limit on the half-life of the radiative neutrinoless double electron capture of $^{36}$Ar was established: $T_{1/2} >$ 3.6 $\times$ 10$^{21}$ yr at 90 % C.I.Comment: 7 pages, 3 figure

2νββ2\nu\beta\beta decay of 76^{76}Ge into excited states with GERDA Phase I

Two neutrino double beta decay of $^{76}$Ge to excited states of $^{76}$Se has been studied using data from Phase I of the GERDA experiment. An array composed of up to 14 germanium detectors including detectors that have been isotopically enriched in $^{76}$Ge was deployed in liquid argon. The analysis of various possible transitions to excited final states is based on coincidence events between pairs of detectors where a de-excitation $\gamma$ ray is detected in one detector and the two electrons in the other. No signal has been observed and an event counting profile likelihood analysis has been used to determine Frequentist 90\,\% C.L. bounds for three transitions: ${0^+_{\rm g.s.}-2^+_1}$: $T^{2\nu}_{1/2}>$1.6$\cdot10^{23}$ yr, ${0^+_{\rm g.s.}-0^+_1}$: $T^{2\nu}_{1/2}>$3.7$\cdot10^{23}$ yr and ${0^+_{\rm g.s.}-2^+_2}$: $T^{2\nu}_{1/2}>$2.3$\cdot10^{23}$ yr. These bounds are more than two orders of magnitude larger than those reported previously. Bayesian 90\,\% credibility bounds were extracted and used to exclude several models for the ${0^+_{\rm g.s.}-0^+_1}$ transition

Results on ββ\beta\beta decay with emission of two neutrinos or Majorons in 76^{76}Ge from GERDA Phase I

A search for neutrinoless $\beta\beta$ decay processes accompanied with Majoron emission has been performed using data collected during Phase I of the GERmanium Detector Array (GERDA) experiment at the Laboratori Nazionali del Gran Sasso of INFN (Italy). Processes with spectral indices n = 1, 2, 3, 7 were searched for. No signals were found and lower limits of the order of 10$^{23}$ yr on their half-lives were derived, yielding substantially improved results compared to previous experiments with $^{76}$Ge. A new result for the half-life of the neutrino-accompanied $\beta\beta$ decay of $^{76}$Ge with significantly reduced uncertainties is also given, resulting in $T^{2\nu}_{1/2} = (1.926 \pm 0.095)\cdot10^{21}$ yr.Comment: 3 Figure

Flux Modulations seen by the Muon Veto of the GERDA Experiment

The GERDA experiment at LNGS of INFN is equipped with an active muon veto. The main part of the system is a water Cherenkov veto with 66~PMTs in the water tank surrounding the GERDA cryostat. The muon flux recorded by this veto shows a seasonal modulation. Two effects have been identified which are caused by secondary muons from the CNGS neutrino beam (2.2 %) and a temperature modulation of the atmosphere (1.4 %). A mean cosmic muon rate of $I^0_{\mu} = (3.477 \pm 0.002_{\textrm{stat}} \pm 0.067_{\textrm{sys}}) \times 10^{-4}$/(s$\cdot$m$^2$) was found in good agreement with other experiments at LNGS at a depth of 3500~meter water equivalent.Comment: 7 pages, 6 figure

133In: A Rosetta Stone for decays of r-process nuclei

The $\beta$ decays from both the ground state and a long-lived isomer of $^{133}$In were studied at the ISOLDE Decay Station (IDS). With a hybrid detection system sensitive to $\beta$, $\gamma$, and neutron spectroscopy, the comparative partial half-lives (logft) have been measured for all their dominant $\beta$-decay channels for the first time, including a low-energy Gamow-Teller transition and several First-Forbidden (FF) transitions. Uniquely for such a heavy neutron-rich nucleus, their $\beta$ decays selectively populate only a few isolated neutron unbound states in $^{133}$Sn. Precise energy and branching-ratio measurements of those resonances allow us to benchmark $\beta$-decay theories at an unprecedented level in this region of the nuclear chart. The results show good agreement with the newly developed large-scale shell model (LSSM) calculations. The experimental findings establish an archetype for the $\beta$ decay of neutron-rich nuclei southeast of $^{132}$Sn and will serve as a guide for future theoretical development aiming to describe accurately the key $\beta$ decays in the rapid-neutron capture (r-) process

Beta-delayed neutron spectroscopy of 133^{133}In

The decay properties of $^{133}$In were studied in detail at the ISOLDE Decay Station (IDS). The implementation of the Resonance Ionization Laser Ion Source (RILIS) allowed separate measurements of its $9/2^+$ ground state ($^{133g}$In) and $1/2^-$ isomer ($^{133m}$In). With the use of $\beta$-delayed neutron and $\gamma$ spectroscopy, the decay strengths above the neutron separation energy were quantified in this neutron-rich nucleus for the first time. The allowed Gamow-Teller transition $9/2^+\rightarrow7/2^+$ was located at 5.92 MeV in the $^{133g}$In decay with a logft = 4.7(1). In addition, several neutron-unbound states were populated at lower excitation energies by the First-Forbidden decays of $^{133g,m}$In. We assigned spins and parities to those neutron-unbound states based on the $\beta$-decay selection rules, the logft values, and systematics