20,348 research outputs found
Theoretical and computational aspects of clumps
Chapter 1 of this paper contains the general theory of clumps, chapter 2 deals with three applications of this theory in associative information retrieval, and chapter 3 presents a procedure for computing clumps
Stable super-resolution limit and smallest singular value of restricted Fourier matrices
Super-resolution refers to the process of recovering the locations and
amplitudes of a collection of point sources, represented as a discrete measure,
given of its noisy low-frequency Fourier coefficients. The recovery
process is highly sensitive to noise whenever the distance between the
two closest point sources is less than . This paper studies the {\it
fundamental difficulty of super-resolution} and the {\it performance guarantees
of a subspace method called MUSIC} in the regime that .
The most important quantity in our theory is the minimum singular value of
the Vandermonde matrix whose nodes are specified by the source locations. Under
the assumption that the nodes are closely spaced within several well-separated
clumps, we derive a sharp and non-asymptotic lower bound for this quantity. Our
estimate is given as a weighted sum, where each term only depends on
the configuration of each individual clump. This implies that, as the noise
increases, the super-resolution capability of MUSIC degrades according to a
power law where the exponent depends on the cardinality of the largest clump.
Numerical experiments validate our theoretical bounds for the minimum singular
value and the resolution limit of MUSIC.
When there are point sources located on a grid with spacing , the
fundamental difficulty of super-resolution can be quantitatively characterized
by a min-max error, which is the reconstruction error incurred by the best
possible algorithm in the worst-case scenario. We show that the min-max error
is closely related to the minimum singular value of Vandermonde matrices, and
we provide a non-asymptotic and sharp estimate for the min-max error, where the
dominant term is .Comment: 47 pages, 8 figure
Mass loss from inhomogeneous hot star winds II. Constraints from a combined optical/UV study
Mass-loss rates currently in use for hot, massive stars have recently been
seriously questioned, mainly because of the effects of wind clumping. We
investigate the impact of clumping on diagnostic ultraviolet resonance and
optical recombination lines. Optically thick clumps, a non-void interclump
medium, and a non-monotonic velocity field are all accounted for in a single
model. We used 2D and 3D stochastic and radiation-hydrodynamic (RH) wind
models, constructed by assembling 1D snapshots in radially independent slices.
To compute synthetic spectra, we developed and used detailed radiative transfer
codes for both recombination lines (solving the "formal integral") and
resonance lines (using a Monte-Carlo approach). In addition, we propose an
analytic method to model these lines in clumpy winds, which does not rely on
optically thin clumping. Results: Synthetic spectra calculated directly from
current RH wind models of the line-driven instability are unable to in parallel
reproduce strategic optical and ultraviolet lines for the Galactic O-supergiant
LCep. Using our stochastic wind models, we obtain consistent fits essentially
by increasing the clumping in the inner wind. A mass-loss rate is derived that
is approximately two times lower than predicted by the line-driven wind theory,
but much higher than the corresponding rate derived from spectra when assuming
optically thin clumps. Our analytic formulation for line formation is used to
demonstrate the potential impact of optically thick clumping in weak-winded
stars and to confirm recent results that resonance doublets may be used as
tracers of wind structure and optically thick clumping. (Abridged)Comment: 14 pages+1 Appendix, 8 figures, 3 tables. Accepted for publication in
Astronomy and Astrophysics. One reference updated, minor typo in Appendix
correcte
Large-amplitude isothermal fluctuations and high-density dark-matter clumps
Large-amplitude isothermal fluctuations in the dark matter energy density,
parameterized by \Phi\equiv\delta\rhodm/\rhodm, are studied within the
framework of a spherical collapse model. For \Phi \ga 1, a fluctuation
collapses in the radiation-dominated epoch and produces a dense dark-matter
object. The final density of the virialized object is found to be \rho_F
\approx 140\, \Phi^3 (\Phi+1) \rhoeq, where \rhoeq is the matter density at
equal matter and radiation energy density. This expression is valid for the
entire range of possible values of , both for and . Some astrophysical consequences of high-density dark-matter clumps are
discussed.Comment: 15 pages plus 3 figures (included at the end as a uuencoded
postscript file), LaTeX, FNAL--PUB--94/055--
Lumpy species coexistence arises robustly in fluctuating resource environments
The effect of life-history traits on resource competition outcomes is well understood in the context of a constant resource supply. However, almost all natural systems are subject to fluctuations of resources driven by cyclical processes such as seasonality and tidal hydrology. To understand community composition, it is therefore imperative to study the impact of resource fluctuations on interspecies competition. We adapted a well-established resource-competition model to show that fluctuations in inflow concentrations of two limiting resources lead to the survival of species in clumps along the trait axis, consistent with observations of “lumpy coexistence” [Scheffer M, van Nes EH (2006) Proc Natl Acad Sci USA 103:6230–6235]. A complex dynamic pattern in the available ambient resources arose very early in the self-organization process and dictated the locations of clumps along the trait axis by creating niches that promoted the growth of species with specific traits. This dynamic pattern emerged as the combined result of fluctuations in the inflow of resources and their consumption by the most competitive species that accumulated the bulk of biomass early in assemblage organization. Clumps emerged robustly across a range of periodicities, phase differences, and amplitudes. Given the ubiquity in the real world of asynchronous fluctuations of limiting resources, our findings imply that assemblage organization in clumps should be a common feature in nature
On the Number of Clumps Resulting from the Overlap of Randomly Placed Figures in a Plane
When two-dimensional figures, called laminae, are randomly placed on a plane domains result that can either be aggregates or individual laminae. The intersection of the union, U, of these domains with a specified field of view, F, in the plane is considered. The separate elements of the intersection are called clumps; they may be laminae, aggregates or partial laminae and aggregates. A formula is derived for the expected number of clumps minus enclosed voids. For bounded laminae homeomorphic to a closed disc with isotropic random direction the formula contains only their mean area and mean perimeter, the area and perimeter of F, and the intensity of the Poisson process
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