38,030 research outputs found
Bayesian inferences of galaxy formation from the K-band luminosity and HI mass functions of galaxies: constraining star formation and feedback
We infer mechanisms of galaxy formation for a broad family of semi-analytic
models (SAMs) constrained by the K-band luminosity function and HI mass
function of local galaxies using tools of Bayesian analysis. Even with a broad
search in parameter space the whole model family fails to match to constraining
data. In the best fitting models, the star formation and feedback parameters in
low-mass haloes are tightly constrained by the two data sets, and the analysis
reveals several generic failures of models that similarly apply to other
existing SAMs. First, based on the assumption that baryon accretion follows the
dark matter accretion, large mass-loading factors are required for haloes with
circular velocities lower than 200 km/s, and most of the wind mass must be
expelled from the haloes. Second, assuming that the feedback is powered by
Type-II supernovae with a Chabrier IMF, the outflow requires more than 25% of
the available SN kinetic energy. Finally, the posterior predictive
distributions for the star formation history are dramatically inconsistent with
observations for masses similar to or smaller than the Milky-Way mass. The
inferences suggest that the current model family is still missing some key
physical processes that regulate the gas accretion and star formation in
galaxies with masses below that of the Milky Way.Comment: 17 pages, 9 figures, 1 table, accepted for publication in MNRA
Bits from Photons: Oversampled Image Acquisition Using Binary Poisson Statistics
We study a new image sensor that is reminiscent of traditional photographic
film. Each pixel in the sensor has a binary response, giving only a one-bit
quantized measurement of the local light intensity. To analyze its performance,
we formulate the oversampled binary sensing scheme as a parameter estimation
problem based on quantized Poisson statistics. We show that, with a
single-photon quantization threshold and large oversampling factors, the
Cram\'er-Rao lower bound (CRLB) of the estimation variance approaches that of
an ideal unquantized sensor, that is, as if there were no quantization in the
sensor measurements. Furthermore, the CRLB is shown to be asymptotically
achievable by the maximum likelihood estimator (MLE). By showing that the
log-likelihood function of our problem is concave, we guarantee the global
optimality of iterative algorithms in finding the MLE. Numerical results on
both synthetic data and images taken by a prototype sensor verify our
theoretical analysis and demonstrate the effectiveness of our image
reconstruction algorithm. They also suggest the potential application of the
oversampled binary sensing scheme in high dynamic range photography
Phase Retrieval for Sparse Signals: Uniqueness Conditions
In a variety of fields, in particular those involving imaging and optics, we
often measure signals whose phase is missing or has been irremediably
distorted. Phase retrieval attempts the recovery of the phase information of a
signal from the magnitude of its Fourier transform to enable the reconstruction
of the original signal. A fundamental question then is: "Under which conditions
can we uniquely recover the signal of interest from its measured magnitudes?"
In this paper, we assume the measured signal to be sparse. This is a natural
assumption in many applications, such as X-ray crystallography, speckle imaging
and blind channel estimation. In this work, we derive a sufficient condition
for the uniqueness of the solution of the phase retrieval (PR) problem for both
discrete and continuous domains, and for one and multi-dimensional domains.
More precisely, we show that there is a strong connection between PR and the
turnpike problem, a classic combinatorial problem. We also prove that the
existence of collisions in the autocorrelation function of the signal may
preclude the uniqueness of the solution of PR. Then, assuming the absence of
collisions, we prove that the solution is almost surely unique on 1-dimensional
domains. Finally, we extend this result to multi-dimensional signals by solving
a set of 1-dimensional problems. We show that the solution of the
multi-dimensional problem is unique when the autocorrelation function has no
collisions, significantly improving upon a previously known result.Comment: submitted to IEEE TI
On the origin of cold dark matter halo density profiles
N-body simulations predict that CDM halo-assembly occurs in two phases: 1) a
fast accretion phase with a rapidly deepening potential well; and 2) a slow
accretion phase characterised by a gentle addition of mass to the outer halo
with little change in the inner potential well. We demonstrate, using
one-dimensional simulations, that this two-phase accretion leads to CDM halos
of the NFW form and provides physical insight into the properties of the mass
accretion history that influence the final profile. Assuming that the
velocities of CDM particles are effectively isotropised by fluctuations in the
gravitational potential during the fast accretion phase, we show that
gravitational collapse in this phase leads to an inner profile rho(r) ~ r^{-1}.
Slow accretion onto an established potential well leads to an outer profile
with rho(r) ~ r^{-3}. The concentration of a halo is determined by the fraction
of mass that is accreted during the fast accretion phase. Using an ensemble of
realistic mass accretion histories, we show that the model predictions of the
dependence of halo concentration on halo formation time, and hence the
dependence of halo concentration on halo mass, and the distribution of halo
concentrations all match those found in cosmological N-body simulations. Using
a simple analytic model that captures much of the important physics we show
that the inner r^{-1} profile of CDM halos is a natural result of hierarchical
mass assembly with a initial phase of rapid accretion.Comment: Accepted for publication in MNRAS, references added, 11 pages, 8
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