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A special sorting operation called Context Directed Swap, and denoted \textbf{cds}, performs certain types of block interchanges on permutations. When a permutation is sortable by \textbf{cds}, then \textbf{cds} sorts it using the fewest possible block interchanges of any kind. This work introduces a classification of permutations based on their number of \textbf{cds}-eligible contexts. In prior work an object called the strategic pile of a permutation was discovered and shown to provide an efficient measure of the non-\textbf{cds}-sortability of a permutation. Focusing on the classification of permutations with maximal strategic pile, a complete characterization is given when the number of \textbf{cds}-eligible contexts is close to maximal as well as when the number of eligible contexts is minimal. A group action that preserves the number of \textbf{cds}-eligible contexts of a permutation provides, via the orbit-stabilizer theorem, enumerative results regarding the number of permutations with maximal strategic pile and a given number of \textbf{cds}-eligible contexts. Prior work introduced a natural two-person game on permutations that are not \textbf{cds}-sortable. The decision problem of which player has a winning strategy in a particular instance of the game appears to be of high computational complexity. Extending prior results, this work presents new conditions for player ONE to have a winning strategy in this combinatorial game., Comment: 22 pages

Borexino was the first experiment to detect solar neutrinos in real-time in the sub-MeV region. In order to achieve high precision in the determination of neutrino rates, the detector design includes an internal and an external calibration system. This paper describes both calibration systems and the calibration campaigns that were carried out in the period between 2008 and 2011. We discuss some of the results and show that the calibration procedures preserved the radiopurity of the scintillator. The calibrations provided a detailed understanding of the detector response and led to a significant reduction of the systematic uncertainties in the Borexino measurements.

Borexino is a large-volume liquid scintillator detector installed in the underground halls of the Laboratori Nazionali del Gran Sasso in Italy. After several years of construction, data taking started in May 2007. The Borexino phase I ended after about three years of data taking. Borexino provided the first real time measurement of the $^{7}$Be solar neutrino interaction rate with accuracy better than 5% and confirmed the absence of its day-night asymmetry with 1.4% precision. This latter Borexino results alone rejects the LOW region of solar neutrino oscillation parameters at more than 8.5 $\sigma$ C.L. Combined with the other solar neutrino data, Borexino measurements isolate the MSW-LMA solution of neutrino oscillations without assuming CPT invariance in the neutrino sector. Borexino has also directly observed solar neutrinos in the 1.0-1.5 MeV energy range, leading to the first direct evidence of the $pep$ solar neutrino signal and the strongest constraint of the CNO solar neutrino flux up to date. Borexino provided the measurement of the solar $^{8}$B neutrino rate with 3 MeV energy threshold., Comment: 6 pages, 4 figures, proceedings to Moriond 2012 EW session

We have measured the muon flux at the underground Gran Sasso National Laboratory (3800 m w.e.) to be (3.41 \pm 0.01) \times 10-4m-2s-1 using four years of Borexino data. A modulation of this signal is observed with a period of (366\pm3) days and a relative amplitude of (1.29 \pm 0.07)%. The measured phase is (179 \pm 6) days, corresponding to a maximum on the 28th of June. Using the most complete atmospheric data models available, muon rate fluctuations are shown to be positively correlated with atmospheric temperature, with an effective coefficient {\alpha}T = 0.93 \pm 0.04. This result represents the most precise study of the muon flux modulation for this site and is in good agreement with expectations., Comment: 14 pages, 8 figures, published on JCAP as JCAP05(2012)015 on May 15th 2012

In early 2010, the Long-Baseline Neutrino Experiment (LBNE) science collaboration initiated a study to investigate the physics potential of the experiment with a broad set of different beam, near- and far-detector configurations. Nine initial topics were identified as scientific areas that motivate construction of a long-baseline neutrino experiment with a very large far detector. We summarize the scientific justification for each topic and the estimated performance for a set of far detector reference configurations. We report also on a study of optimized beam parameters and the physics capability of proposed Near Detector configurations. This document was presented to the collaboration in fall 2010 and updated with minor modifications in early 2011., Comment: Corresponding author R.J.Wilson (Bob.Wilson@colostate.edu); 113 pages, 90 figures

Borexino, a liquid scintillator detector at LNGS, is designed for the detection of neutrinos and antineutrinos from the Sun, supernovae, nuclear reactors, and the Earth. The feeble nature of these signals requires a strong suppression of backgrounds below a few MeV. Very low intrinsic radiogenic contamination of all detector components needs to be accompanied by the efficient identification of muons and of muon-induced backgrounds. Muons produce unstable nuclei by spallation processes along their trajectory through the detector whose decays can mimic the expected signals; for isotopes with half-lives longer than a few seconds, the dead time induced by a muon-related veto becomes unacceptably long, unless its application can be restricted to a sub-volume along the muon track. Consequently, not only the identification of muons with very high efficiency but also a precise reconstruction of their tracks is of primary importance for the physics program of the experiment. The Borexino inner detector is surrounded by an outer water-Cherenkov detector that plays a fundamental role in accomplishing this task. The detector design principles and their implementation are described. The strategies adopted to identify muons are reviewed and their efficiency is evaluated. The overall muon veto efficiency is found to be 99.992% or better. Ad-hoc track reconstruction algorithms developed are presented. Their performance is tested against muon events of known direction such as those from the CNGS neutrino beam, test tracks available from a dedicated External Muon Tracker and cosmic muons whose angular distribution reflects the local overburden profile. The achieved angular resolution is 3-5 deg and the lateral resolution is 35-50 cm, depending on the impact parameter of the crossing muon. The methods implemented to efficiently tag cosmogenic neutrons are also presented., Comment: 42 pages. 32 figures on 37 files. Uses JINST.cls. 1 auxiliary file (defines.tex) with TEX macros. submitted to Journal of Instrumentation

Short baseline oscillations of neutrinos (nue and nuebar) due to active-sterile (a-s) mixing can be observed explicitly using MeV neutrino beams and existing/planned neutrino detectors. The typical baseline/energy (L/E) of this approach allows flavor survival waves to be observed in the spatial distribution of events inside the detector itself. Single/multiple oscillations can be tested using a variety of sources of nue and nuebar matched to Cerenkov (C), liquid scintillator (LS) and LENS (In-LS) detectors. Distinct tags for nue (from In) and nuebar (from p in the LS) in LENS allow access to nue and nuebar for probing (a-s) mixing, CPT symmetry and in a new way, limits on lepton number violation (LNV) via wrong helicity neutrino reactions comparable to limits for neutrinoless double beta decay via right handed currents., Comment: Typos corrected. Discussion on LNV revised. Conclusions unchanged

It was recently pointed out that mono-energetic neutrino lines from the 2-body decay of tritium (tau ~ 18-y) can be emitted, a significant fraction, with natural line width (~10-24 eV) for hypersharp resonance transitions 3H--> <--3He. The very long lifetime typical of a neutrino transition, encountered for the first time in resonance, is the key to this surprising effect which is not intuitive from perspectives of line broadening in resonances of short lived (tau ~ microsec) states., Comment: Corrected citation for ref. 10

The role of quantum mechanical time-energy uncertainty (TEU) is central in resonant neutrino (nue) reactions (3H to 3He to 3H) because of the unusual 18 y lifetime of 3H. The TEU explicitly manifests itself by a non-intuitive but quantitatively predictable spontaneous temporal growth of the nue resonance signal. A slower growth rate signifies violation of TEU via a larger than natural width of 3H, possibly imposed by a fundamental length in nature. Strong limits on TEU violation can be set in the unprobed virgin energy regime of ~10-24 eV.

The 18.6 keV antineutrino line from 2-body decay of 3H in crystals can be emitted with natural width because of motional averaging by lattice vibrations despite the very long lifetime of 3H and contrary to commonly held views of linewidths in such a case. It can be resonantly captured in 3He with geometrical cross section sigma ~10-17 cm2. Using its hypersharp sensitivity DELTAE/E ~10-29 and the method of time-filtered resonance, the basic energy width ~10-24 eV expected of the 3H state can be measured to test if ultimate nuclear widths are limited by the Planck length rather than time-energy uncertainty., Comment: To apppear in Physical Review Letters

Recent ideas suggest that the 18.6 keV antineutrino (nuebar) line from 2-body decay of 3H in crystals is emitted with natural width, motionally narrowed by lattice vibrations as in recoilless emission. It can be resonantly captured in 3He with geometrical cross section sigma ~10 ^ -17 cm2. A key technique solves a basic obstacle for achieving resonance--the chemical difference of H and He in metals. The low nue energy, the high sigma and the hypersharp sensitivity DELTA E/E ~10^--29 make an extraordinary tool for bench scale tests of nue theta13 oscillations and predicted Planck length limits on nuclear level widths in models of quantum gravity., Comment: 4p, 1fig, 3tables

Neutrino lines from very long lived nuclei in simple crystals such as metals have hypersharp natural width, motionally narrowed by lattice vibrations in analogy to recoilless emission. A generalized hypersharp line fraction including the recoilless part can be derived in a frequency modulation approach. The nue lines of natural width in 3H to 3He 2-body beta-decay can then be resonantly captured with geometrical cross section. The extreme sharpness DeltaE/E~10-29 of the tritium nue line can probe the Planck length L via its limits on the widths of states, DeltaE/E(L) =L(L/R)beta =10-20(beta ~1) to 10-40 (beta= L/R(fm)). Stringent limits can be set on beta, thus, on models of quantum gravity.

Sterile neutrino ($\nu_s$) conversion in meter scale baselines can be sensitively probed using mono-energetic, sub-MeV, flavor pure $\nu_e$'s from an artificial MCi source and the unique technology of the LENS low energy solar $\nu_e$ detector. Active-sterile {\em oscillations} can be directly observed in the granular LENS detector itself to critically test and extend results of short baseline accelerator and reactor experiments., Comment: Submitted to the proceedings of the XII International Workshop on Neutrino Telescopes, March 6-9, 2007, Venice

Paper withdrawn by author. Theoretical formalism employed is inappropriate to the problem considered., Comment: Paper withdrawn by author. Theoretical formalism employed is inappropriate to the problem considered

Sterile neutrino conversion in meter scale baselines can be sensitively probed using monoenergetic, sub-MeV, flavor pure e-neutrinos from an artificial MCi source and the unique technology of LENS designed to oberve the low energy solar neutrino spectrum via tagged CC e-neutrino capture in 115-In. Active-sterile oscillations can be directly observed in the granular LENS detector itself to critically test and extend resuls of short baseline accelerator and reactor experiments., Comment: 4pages, 4 figures, text and figure changes

The particle kinetic energies of pp fusion in the sun (Gamow Energy) produce small changes in the energies of pp solar neutrinos relative to those due only to exothermal energetics. Observation of this effect may be possible via the unique tools of the upcoming LENS solar neutrino detector. The temperature profile of energy production in the sun may thus be directly probed for the first time.

Monoenergetic antineutrinos emitted in the bound state beta-decay of H can be resonantly captured in 3He. Favorable conditions are offered by tritide technology for ultra sharp recoilless resonant capture of the 18.6 keV nubare with sigma~5x10-32 cm2, 11 orders of magnitude larger than sigma(nubare +p). The gravitational red shift of neutrinos and the mixing angle theta13 may be measurable in bench scale baselines., Comment: Technical parts updated and revised

The time dependence that appears to be hinted by the data from the first 13 years of the solar neutrino Gallium experiments is viewed as resulting from a partial conversion of active neutrinos to light sterile ones through the resonant interaction between the magnetic moment of the neutrino and a varying solar field. A summary of the model and its predictions are presented for the forthcoming experiments Borexino and LENS., Comment: 6 pages, 3 figures, contribution to 12th Lomonosov Conference in Elementary Particle Physics, Moscow, Aug 24-31 (2005)

Resonant capture of antineutrinos can be accomplished by exploiting the monoenergetic antineutrinos emitted in bound state beta-decay. Extending this idea, I explore conditions for recoilless resonant capture in the system 3H - 3He. Observation of such transitions can set the stage for placing stringent limits on the neutrino parameter theta-13 on an ultra-short baseline of ~9 m and for observing the gravitational red shift of neutrinos

The possibility that the Gallium data effectively indicates a time modulation of the solar active neutrino flux in possible connection to solar activity is examined on the light of spin flavour precession to sterile neutrinos as a subdominant process in addition to oscillations. We distinguish two sets of Gallium data, relating them to high and low solar activity. Such modulation affects principally the low energy neutrinos ($pp$ and $^7 Be$) so that the effect, if it exists, will become most clear in the forthcoming Borexino and LENS experiments and will provide evidence for a neutrino magnetic moment. Using a model previously developed, we perform two separate fits in relation to low and high activity periods to all solar neutrino data. These fits include the very recent charged current spectrum from the SNO experiment. We also derive the model predictions for Borexino and LENS experiments., Comment: 20 pages, 5 ps figures, 1 eps figure, final version to be published in JHEP