219,877 research outputs found
A Closed-Form Shave from Occam's Quantum Razor: Exact Results for Quantum Compression
The causal structure of a stochastic process can be more efficiently
transmitted via a quantum channel than a classical one, an advantage that
increases with codeword length. While previously difficult to compute, we
express the quantum advantage in closed form using spectral decomposition,
leading to direct computation of the quantum communication cost at all encoding
lengths, including infinite. This makes clear how finite-codeword compression
is controlled by the classical process' cryptic order and allows us to analyze
structure within the length-asymptotic regime of infinite-cryptic order (and
infinite Markov order) processes.Comment: 21 pages, 13 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/eqc.ht
Cosmic-ray Acceleration at Ultrarelativistic Shock Waves: Effects of a "Realistic" Magnetic Field Structure
First-order Fermi acceleration processes at ultrarelativistic shocks are
studied with Monte Carlo simulations. The accelerated particle spectra are
derived by integrating the exact particle trajectories in a turbulent magnetic
field near the shock. ''Realistic'' features of the field structure are
included. We show that the main acceleration process at superluminal shocks is
the particle compression at the shock. Formation of energetic spectral tails is
possible in a limited energy range only for highly perturbed magnetic fields,
with cutoffs occuring at low energies within the resonance energy range
considered. These spectral features result from the anisotropic character of
particle transport in the downstream magnetic field, where field compression
produces effectively 2D perturbations. Because of the downstream field
compression, the acceleration process is inefficient in parallel shocks for
larger turbulence amplitudes, and features observed in oblique shocks are
recovered. For small-amplitude turbulence, wide-energy range particle spectra
are formed and modifications of the process due to the existence of long-wave
perturbations are observed. In both sub- and superluminal shocks, an increase
of \gamma leads to steeper spectra with lower cut-off energies. The spectra
obtained for the ``realistic'' background conditions assumed here do not
converge to the ``universal'' spectral index claimed in the literature. Thus
the role of the first-order Fermi process in astrophysical sources hosting
relativistic shocks requires serious reanalysis.Comment: submitted to Ap
Encoding dynamics for multiscale community detection: Markov time sweeping for the Map equation
The detection of community structure in networks is intimately related to
finding a concise description of the network in terms of its modules. This
notion has been recently exploited by the Map equation formalism (M. Rosvall
and C.T. Bergstrom, PNAS, 105(4), pp.1118--1123, 2008) through an
information-theoretic description of the process of coding inter- and
intra-community transitions of a random walker in the network at stationarity.
However, a thorough study of the relationship between the full Markov dynamics
and the coding mechanism is still lacking. We show here that the original Map
coding scheme, which is both block-averaged and one-step, neglects the internal
structure of the communities and introduces an upper scale, the `field-of-view'
limit, in the communities it can detect. As a consequence, Map is well tuned to
detect clique-like communities but can lead to undesirable overpartitioning
when communities are far from clique-like. We show that a signature of this
behavior is a large compression gap: the Map description length is far from its
ideal limit. To address this issue, we propose a simple dynamic approach that
introduces time explicitly into the Map coding through the analysis of the
weighted adjacency matrix of the time-dependent multistep transition matrix of
the Markov process. The resulting Markov time sweeping induces a dynamical
zooming across scales that can reveal (potentially multiscale) community
structure above the field-of-view limit, with the relevant partitions indicated
by a small compression gap.Comment: 10 pages, 6 figure
Magnetic Field Amplification in Galaxy Clusters and its Simulation
We review the present theoretical and numerical understanding of magnetic
field amplification in cosmic large-scale structure, on length scales of galaxy
clusters and beyond. Structure formation drives compression and turbulence,
which amplify tiny magnetic seed fields to the microGauss values that are
observed in the intracluster medium. This process is intimately connected to
the properties of turbulence and the microphysics of the intra-cluster medium.
Additional roles are played by merger induced shocks that sweep through the
intra-cluster medium and motions induced by sloshing cool cores. The accurate
simulation of magnetic field amplification in clusters still poses a serious
challenge for simulations of cosmological structure formation. We review the
current literature on cosmological simulations that include magnetic fields and
outline theoretical as well as numerical challenges.Comment: 60 pages, 19 Figure
- …