661 research outputs found
The classical umbral calculus: Sheffer sequences
Following the approach of Rota and Taylor \cite{SIAM}, we present an
innovative theory of Sheffer sequences in which the main properties are encoded
by using umbrae. This syntax allows us noteworthy computational simplifications
and conceptual clarifications in many results involving Sheffer sequences. To
give an indication of the effectiveness of the theory, we describe applications
to the well-known connection constants problem, to Lagrange inversion formula
and to solving some recurrence relations
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
New constraints on supersymmetry using neutrino telescopes
We demonstrate that megaton-mass neutrino telescopes are able to observe the signal from long-lived particles beyond the Standard Model, in particular the stau, the supersymmetric partner of the tau lepton. Its signature is an excess of charged particle tracks with horizontal arrival directions and energy deposits between 0.1 and 1 TeV inside the detector. We exploit this previously-overlooked signature to search for stau particles in the publicly available IceCube data. The data shows no evidence of physics beyond the Standard Model. We derive a new lower limit on the stau mass of 320 GeV (95% C.L.) and estimate that this new approach, when applied to the full data set available to the IceCube collaboration, will reach word-leading sensitivity to the stau mass (m_{\tilde{t}}
= 450GeV)
Families of Vicious Walkers
We consider a generalisation of the vicious walker problem in which N random
walkers in R^d are grouped into p families. Using field-theoretic
renormalisation group methods we calculate the asymptotic behaviour of the
probability that no pairs of walkers from different families have met up to
time t. For d>2, this is constant, but for d<2 it decays as a power t^(-alpha),
which we compute to O(epsilon^2) in an expansion in epsilon=2-d. The second
order term depends on the ratios of the diffusivities of the different
families. In two dimensions, we find a logarithmic decay (ln t)^(-alpha'), and
compute alpha' exactly.Comment: 20 pages, 5 figures. v.2: minor additions and correction
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
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
Search for non-relativistic Magnetic Monopoles with IceCube
The IceCube Neutrino Observatory is a large Cherenkov detector instrumenting
of Antarctic ice. The detector can be used to search for
signatures of particle physics beyond the Standard Model. Here, we describe the
search for non-relativistic, magnetic monopoles as remnants of the GUT (Grand
Unified Theory) era shortly after the Big Bang. These monopoles may catalyze
the decay of nucleons via the Rubakov-Callan effect with a cross section
suggested to be in the range of to
. In IceCube, the Cherenkov light from nucleon decays
along the monopole trajectory would produce a characteristic hit pattern. This
paper presents the results of an analysis of first data taken from May 2011
until May 2012 with a dedicated slow-particle trigger for DeepCore, a
subdetector of IceCube. A second analysis provides better sensitivity for the
brightest non-relativistic monopoles using data taken from May 2009 until May
2010. In both analyses no monopole signal was observed. For catalysis cross
sections of the flux of non-relativistic
GUT monopoles is constrained up to a level of at a 90% confidence level,
which is three orders of magnitude below the Parker bound. The limits assume a
dominant decay of the proton into a positron and a neutral pion. These results
improve the current best experimental limits by one to two orders of magnitude,
for a wide range of assumed speeds and catalysis cross sections.Comment: 20 pages, 20 figure
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