22,011 research outputs found
Stochastic expansions using continuous dictionaries: L\'{e}vy adaptive regression kernels
This article describes a new class of prior distributions for nonparametric
function estimation. The unknown function is modeled as a limit of weighted
sums of kernels or generator functions indexed by continuous parameters that
control local and global features such as their translation, dilation,
modulation and shape. L\'{e}vy random fields and their stochastic integrals are
employed to induce prior distributions for the unknown functions or,
equivalently, for the number of kernels and for the parameters governing their
features. Scaling, shape, and other features of the generating functions are
location-specific to allow quite different function properties in different
parts of the space, as with wavelet bases and other methods employing
overcomplete dictionaries. We provide conditions under which the stochastic
expansions converge in specified Besov or Sobolev norms. Under a Gaussian error
model, this may be viewed as a sparse regression problem, with regularization
induced via the L\'{e}vy random field prior distribution. Posterior inference
for the unknown functions is based on a reversible jump Markov chain Monte
Carlo algorithm. We compare the L\'{e}vy Adaptive Regression Kernel (LARK)
method to wavelet-based methods using some of the standard test functions, and
illustrate its flexibility and adaptability in nonstationary applications.Comment: Published in at http://dx.doi.org/10.1214/11-AOS889 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Unparticle Self-Interactions and Their Collider Implications
In unparticle physics, operators of the conformal sector have
self-interactions, and these are unsuppressed for strong coupling. The 3-point
interactions are completely determined by conformal symmetry, up to a constant.
We do not know of any theoretical upper bounds on this constant. Imposing
current experimental constraints, we find that these interactions mediate
spectacular collider signals, such as , , , , , and
, with cross sections of picobarns or larger at the Large Hadron Collider.
Self-interactions may therefore provide the leading discovery prospects for
unparticle physics.Comment: 12 pages, 5 figures; v2: published versio
Hidden Charged Dark Matter
Can dark matter be stabilized by charge conservation, just as the electron is
in the standard model? We examine the possibility that dark matter is hidden,
that is, neutral under all standard model gauge interactions, but charged under
an exact U(1) gauge symmetry of the hidden sector. Such candidates are
predicted in WIMPless models, supersymmetric models in which hidden dark matter
has the desired thermal relic density for a wide range of masses. Hidden
charged dark matter has many novel properties not shared by neutral dark
matter: (1) bound state formation and Sommerfeld-enhanced annihilation after
chemical freeze out may reduce its relic density, (2) similar effects greatly
enhance dark matter annihilation in protohalos at redshifts of z ~ 30, (3)
Compton scattering off hidden photons delays kinetic decoupling, suppressing
small scale structure, and (4) Rutherford scattering makes such dark matter
self-interacting and collisional, potentially impacting properties of the
Bullet Cluster and the observed morphology of galactic halos. We analyze all of
these effects in a WIMPless model in which the hidden sector is a simplified
version of the minimal supersymmetric standard model and the dark matter is a
hidden sector stau. We find that charged hidden dark matter is viable and
consistent with the correct relic density for reasonable model parameters and
dark matter masses in the range 1 GeV < m_X < 10 TeV. At the same time, in the
preferred range of parameters, this model predicts cores in the dark matter
halos of small galaxies and other halo properties that may be within the reach
of future observations. These models therefore provide a viable and
well-motivated framework for collisional dark matter with Sommerfeld
enhancement, with novel implications for astrophysics and dark matter searches.Comment: 29 pages; v2: references added; v3: published versio
Radiance and Doppler shift distributions across the network of the quiet Sun
The radiance and Doppler-shift distributions across the solar network provide
observational constraints of two-dimensional modeling of transition-region
emission and flows in coronal funnels. Two different methods, dispersion plots
and average-profile studies, were applied to investigate these distributions.
In the dispersion plots, we divided the entire scanned region into a bright and
a dark part according to an image of Fe xii; we plotted intensities and Doppler
shifts in each bin as determined according to a filtered intensity of Si ii. We
also studied the difference in height variations of the magnetic field as
extrapolated from the MDI magnetogram, in and outside network. For the
average-profile study, we selected 74 individual cases and derived the average
profiles of intensities and Doppler shifts across the network. The dispersion
plots reveal that the intensities of Si ii and C iv increase from network
boundary to network center in both parts. However, the intensity of Ne viii
shows different trends, namely increasing in the bright part and decreasing in
the dark part. In both parts, the Doppler shift of C iv increases steadily from
internetwork to network center. The average-profile study reveals that the
intensities of the three lines all decline from the network center to
internetwork region. The binned intensities of Si ii and Ne viii have a good
correlation. We also find that the large blue shift of Ne viii does not
coincide with large red shift of C iv. Our results suggest that the network
structure is still prominent at the layer where Ne viii is formed in the quiet
Sun, and that the magnetic structures expand more strongly in the dark part
than in the bright part of this quiet Sun region.Comment: 10 pages,9 figure
Bandwidth and density for block graphs
The bandwidth of a graph G is the minimum of the maximum difference between
adjacent labels when the vertices have distinct integer labels. We provide a
polynomial algorithm to produce an optimal bandwidth labeling for graphs in a
special class of block graphs (graphs in which every block is a clique), namely
those where deleting the vertices of degree one produces a path of cliques. The
result is best possible in various ways. Furthermore, for two classes of graphs
that are ``almost'' caterpillars, the bandwidth problem is NP-complete.Comment: 14 pages, 9 included figures. Note: figures did not appear in
original upload; resubmission corrects thi
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