1,566 research outputs found
Strongly Contracting Geodesics in Outer Space
We study the Lipschitz metric on Outer Space and prove that fully irreducible
elements of Out(F_n) act by hyperbolic isometries with axes which are strongly
contracting. As a corollary, we prove that the axes of fully irreducible
automorphisms in the Cayley graph of Out(F_n) are stable, meaning that a
quasi-geodesic with endpoints on the axis stays within a bounded distance from
the axis.Comment: 37 pages. Revised applications chapte
Cosmic ray propagation time scales: lessons from radioactive nuclei and positron data
We take a fresh look at high energy radioactive nuclei data reported in the
90's and at the positron data recently reported by PAMELA. Our aim is to study
the model independent implications of these data for the propagation time
scales of cosmic rays in the Galaxy. Considering radioactive nuclei, using
decaying charge to decayed charge ratios -- the only directly relevant data
available at relativistic energies -- we show that a rigidity independent
residence time is consistent with observations. The data for all nuclei can be
described by f_{s,i}=(t_i/100 Myr)^{0.7}, where f_{s,i} is the suppression of
the flux due to decay and t_i is the observer frame lifetime for nucleus specie
i. Considering positron measurements, we argue that the positron flux is
consistent with a secondary origin. Comparing the positron data with
radioactive nuclei at the same energy range, we derive an upper bound on the
mean electromagnetic energy density traversed by the positrons, \bar U_T<1.25
eV/cm^3 at a rigidity of R=40 GV. Charge ratio measurements within easy reach
of the AMS-02 experiment, most notably a determination of the Cl/Ar ratio
extending up to R\sim100 GV, will constrain the energy dependence of the
positron cooling time. Such constraints can be used to distinguish between
different propagation scenarios, as well as to test the secondary origin
hypothesis for the positrons in detail.Comment: 16 pages, 10 figure
The Model Selection Curse
A "statistician" takes an action on behalf of an agent, based on the agent's
self-reported personal data and a sample involving other people. The action
that he takes is an estimated function of the agent's report. The estimation
procedure involves model selection. We ask the following question: Is
truth-telling optimal for the agent given the statistician's procedure? We
analyze this question in the context of a simple example that highlights the
role of model selection. We suggest that our simple exercise may have
implications for the broader issue of human interaction with "machine learning"
algorithms
Nuclear coalescence from correlation functions
We derive a simple formula relating the cross section for light cluster
production (defined via a coalescence factor) to the two-proton correlation
function measured in heavy-ion collisions. The formula generalises earlier
coalescence-correlation relations found by Scheibl & Heinz and by Mrowczynski
for Gaussian source models. It motivates joint experimental analyses of Hanbury
Brown-Twiss (HBT) and cluster yield measurements in existing and future data
sets.Comment: 10 pages, 4 figures. v2: some clarifications. A missing (2\pi)^3
normalization factor, relating diff cross sec to density matrix traces, is
corrected in Secs.II.A and II.B. It does not affect any of the result
Parallel vs. Sequential Belief Propagation Decoding of LDPC Codes over GF(q) and Markov Sources
A sequential updating scheme (SUS) for belief propagation (BP) decoding of
LDPC codes over Galois fields, , and correlated Markov sources is
proposed, and compared with the standard parallel updating scheme (PUS). A
thorough experimental study of various transmission settings indicates that the
convergence rate, in iterations, of the BP algorithm (and subsequently its
complexity) for the SUS is about one half of that for the PUS, independent of
the finite field size . Moreover, this 1/2 factor appears regardless of the
correlations of the source and the channel's noise model, while the error
correction performance remains unchanged. These results may imply on the
'universality' of the one half convergence speed-up of SUS decoding
- …