Ordering of Random Walks: The Leader and the Laggard

We investigate two complementary problems related to maintaining the relative positions of N random walks on the line: (i) the leader problem, that is, the probability {\cal L}_N(t) that the leftmost particle remains the leftmost as a function of time and (ii) the laggard problem, the probability {\cal R}_N(t) that the rightmost particle never becomes the leftmost. We map these ordering problems onto an equivalent (N-1)-dimensional electrostatic problem. From this construction we obtain a very accurate estimate for {\cal L}_N(t) for N=4, the first case that is not exactly soluble: {\cal L}_4(t) ~ t^{-\beta_4}, with \beta_4=0.91342(8). The probability of being the laggard also decays algebraically, {\cal R}_N(t) ~ t^{-\gamma_N}; we derive \gamma_2=1/2, \gamma_3=3/8, and argue that \gamma_N--> ln N/N$ as N-->oo.Comment: 7 pages, 4 figures, 2-column revtex 4 forma

Livetime and sensitivity of the ARIANNA Hexagonal Radio Array

The ARIANNA collaboration completed the installation of the hexagonal radio array (HRA) in December 2014, serving as a pilot program for a planned high energy neutrino telescope located about 110 km south of McMurdo Station on the Ross Ice Shelf near the coast of Antarctica. The goal of ARIANNA is to measure both diffuse and point fluxes of astrophysical neutrinos at energies in excess of 1016 eV. Upgraded hardware has been installed during the 2014 deployment season and stations show a livetime of better than 90% between commissioning and austral sunset. Though designed to observe radio pulses from neutrino interactions originating within the ice below each detector, one station was modified to study the low-frequency environment and signals from above. We provide evidence that the HRA observed both continuous emission from the Galaxy and a transient solar burst. Preliminary work on modeling the (weak) Galactic signal confirm the absolute sensitivity of the HRA detector system.Comment: Proceedings from the 34th ICRC2015, http://icrc2015.nl/, 8 pages, 6 figure

Exact, time-independent estimation of clone size distributions in normal and mutated cells

Biological tools such as genetic lineage tracing, three dimensional confocal microscopy and next generation DNA sequencing are providing new ways to quantify the distribution of clones of normal and mutated cells. Population-wide clone size distributions in vivo are complicated by multiple cell types, and overlapping birth and death processes. This has led to the increased need for mathematically informed models to understand their biological significance. Standard approaches usually require knowledge of clonal age. We show that modelling on clone size independent of time is an alternative method that offers certain analytical advantages; it can help parameterize these models, and obtain distributions for counts of mutated or proliferating cells, for example. When applied to a general birth-death process common in epithelial progenitors this takes the form of a gamblers ruin problem, the solution of which relates to counting Motzkin lattice paths. Applying this approach to mutational processes, an alternative, exact, formulation of the classic Luria Delbruck problem emerges. This approach can be extended beyond neutral models of mutant clonal evolution, and also describe some distributions relating to sub-clones within a tumour. The approaches above are generally applicable to any Markovian branching process where the dynamics of different "coloured" daughter branches are of interest

Performance of the ARIANNA Hexagonal Radio Array

Installation of the ARIANNA Hexagonal Radio Array (HRA) on the Ross Ice Shelf of Antarctica has been completed. This detector serves as a pilot program to the ARIANNA neutrino telescope, which aims to measure the diffuse flux of very high energy neutrinos by observing the radio pulse generated by neutrino-induced charged particle showers in the ice. All HRA stations ran reliably and took data during the entire 2014-2015 austral summer season. A new radio signal direction reconstruction procedure is described, and is observed to have a resolution better than a degree. The reconstruction is used in a preliminary search for potential neutrino candidate events in the data from one of the newly installed detector stations. Three cuts are used to separate radio backgrounds from neutrino signals. The cuts are found to filter out all data recorded by the station during the season while preserving 85.4% of simulated neutrino events that trigger the station. This efficiency is similar to that found in analyses of previous HRA data taking seasons.Comment: Proceedings from the 34th ICRC2015, http://icrc2015.nl/ . 8 pages, 6 figure

A First Search for Cosmogenic Neutrinos with the ARIANNA Hexagonal Radio Array

The ARIANNA experiment seeks to observe the diffuse flux of neutrinos in the 10^8 - 10^10 GeV energy range using a grid of radio detectors at the surface of the Ross Ice Shelf of Antarctica. The detector measures the coherent Cherenkov radiation produced at radio frequencies, from about 100 MHz to 1 GHz, by charged particle showers generated by neutrino interactions in the ice. The ARIANNA Hexagonal Radio Array (HRA) is being constructed as a prototype for the full array. During the 2013-14 austral summer, three HRA stations collected radio data which was wirelessly transmitted off site in nearly real-time. The performance of these stations is described and a simple analysis to search for neutrino signals is presented. The analysis employs a set of three cuts that reject background triggers while preserving 90% of simulated cosmogenic neutrino triggers. No neutrino candidates are found in the data and a model-independent 90% confidence level Neyman upper limit is placed on the all flavor neutrino+antineutrino flux in a sliding decade-wide energy bin. The limit reaches a minimum of 1.9x10^-23 GeV^-1 cm^-2 s^-1 sr^-1 in the 10^8.5 - 10^9.5 GeV energy bin. Simulations of the performance of the full detector are also described. The sensitivity of the full ARIANNA experiment is presented and compared with current neutrino flux models.Comment: 22 pages, 22 figures. Published in Astroparticle Physic

Flavor Ratio of Astrophysical Neutrinos above 35 TeV in IceCube

A diffuse flux of astrophysical neutrinos above $100\,\mathrm{TeV}$ has been observed at the IceCube Neutrino Observatory. Here we extend this analysis to probe the astrophysical flux down to $35\,\mathrm{TeV}$ and analyze its flavor composition by classifying events as showers or tracks. Taking advantage of lower atmospheric backgrounds for shower-like events, we obtain a shower-biased sample containing 129 showers and 8 tracks collected in three years from 2010 to 2013. We demonstrate consistency with the $(f_e:f_{\mu}:f_\tau)_\oplus\approx(1:1:1)_\oplus$ flavor ratio at Earth commonly expected from the averaged oscillations of neutrinos produced by pion decay in distant astrophysical sources. Limits are placed on non-standard flavor compositions that cannot be produced by averaged neutrino oscillations but could arise in exotic physics scenarios. A maximally track-like composition of $(0:1:0)_\oplus$ is excluded at $3.3\sigma$, and a purely shower-like composition of $(1:0:0)_\oplus$ is excluded at $2.3\sigma$.Comment: 8 pages, 3 figures. Submitted to PR

Search for a diffuse flux of astrophysical muon neutrinos with the IceCube 59-string configuration

A search for high-energy neutrinos was performed using data collected by the IceCube Neutrino Observatory from May 2009 to May 2010, when the array was running in its 59-string configuration. The data sample was optimized to contain muon neutrino induced events with a background contamination of atmospheric muons of less than 1%. These data, which are dominated by atmospheric neutrinos, are analyzed with a global likelihood fit to search for possible contributions of prompt atmospheric and astrophysical neutrinos, neither of which have yet been identified. Such signals are expected to follow a harder energy spectrum than conventional atmospheric neutrinos. In addition, the zenith angle distribution differs for astrophysical and atmospheric signals. A global fit of the reconstructed energies and directions of observed events is performed, including possible neutrino flux contributions for an astrophysical signal and atmospheric backgrounds as well as systematic uncertainties of the experiment and theoretical predictions. The best fit yields an astrophysical signal flux for nu(mu) + (nu) over bar (mu) of E-2. Phi(E) = 0.25 x 10(-8) GeV cm(-2) s(-1) sr(-1), and a zero prompt component. Although the sensitivity of this analysis for astrophysical neutrinos surpasses the Waxman and Bahcall upper bound, the experimental limit at 90% confidence level is a factor of 1.5 above at a flux of E-2 . Phi(E) = 1.44 x 10(-8) GeV cm(-2) s(-1) sr(-1)

Determining neutrino oscillation parameters from atmospheric muon neutrino disappearance with three years of IceCube DeepCore data

We present a measurement of neutrino oscillations via atmospheric muon neutrino disappearance with three years of data of the completed IceCube neutrino detector. DeepCore, a region of denser instrumentation, enables the detection and reconstruction of atmospheric muon neutrinos between 10 GeV and 100 GeV, where a strong disappearance signal is expected. The detector volume surrounding DeepCore is used as a veto region to suppress the atmospheric muon background. Neutrino events are selected where the detected Cherenkov photons of the secondary particles minimally scatter, and the neutrino energy and arrival direction are reconstructed. Both variables are used to obtain the neutrino oscillation parameters from the data, with the best fit given by $\Delta m^2_{32}=2.72^{+0.19}_{-0.20}\times 10^{-3}\,\mathrm{eV}^2$ and $\sin^2\theta_{23} = 0.53^{+0.09}_{-0.12}$ (normal mass hierarchy assumed). The results are compatible and comparable in precision to those of dedicated oscillation experiments.Comment: 10 pages, 7 figure

Search for Prompt Neutrino Emission from Gamma-Ray Bursts with IceCube

We present constraints derived from a search of four years of IceCube data for a prompt neutrino flux from gamma-ray bursts (GRBs). A single low-significance neutrino, compatible with the atmospheric neutrino background, was found in coincidence with one of the 506 observed bursts. Although GRBs have been proposed as candidate sources for ultra-high energy cosmic rays, our limits on the neutrino flux disfavor much of the parameter space for the latest models. We also find that no more than $\sim1\%$ of the recently observed astrophysical neutrino flux consists of prompt emission from GRBs that are potentially observable by existing satellites.Comment: 15 pages, 3 figure