7,309 research outputs found
Toward 2^W beyond Web 2.0
From its inception as a global hypertext system, the Web has evolved into a universal platform for deploying loosely coupled distributed applications. 2^W is a result of the exponentially growing Web building on itself to move from a Web of content to a Web of applications
Quantum and Classical Dynamics of a BEC in a Large-Period Optical Lattice
We experimentally investigate diffraction of a Rb-87 Bose-Einstein condensate
from a 1D optical lattice. We use a range of lattice periods and timescales,
including those beyond the Raman-Nath limit. We compare the results to quantum
mechanical and classical simulations, with quantitative and qualitative
agreement, respectively. The classical simulation predicts that the envelope of
the time-evolving diffraction pattern is shaped by caustics: singularities in
the phase space density of classical trajectories. This behavior becomes
increasingly clear as the lattice period grows.Comment: 7 pages, 6 figure
Delineating Parameter Unidentifiabilities in Complex Models
Scientists use mathematical modelling to understand and predict the
properties of complex physical systems. In highly parameterised models there
often exist relationships between parameters over which model predictions are
identical, or nearly so. These are known as structural or practical
unidentifiabilities, respectively. They are hard to diagnose and make reliable
parameter estimation from data impossible. They furthermore imply the existence
of an underlying model simplification. We describe a scalable method for
detecting unidentifiabilities, and the functional relations defining them, for
generic models. This allows for model simplification, and appreciation of which
parameters (or functions thereof) cannot be estimated from data. Our algorithm
can identify features such as redundant mechanisms and fast timescale
subsystems, as well as the regimes in which such approximations are valid. We
base our algorithm on a novel quantification of regional parametric
sensitivity: multiscale sloppiness. Traditionally, the link between parametric
sensitivity and the conditioning of the parameter estimation problem is made
locally, through the Fisher Information Matrix. This is valid in the regime of
infinitesimal measurement uncertainty. We demonstrate the duality between
multiscale sloppiness and the geometry of confidence regions surrounding
parameter estimates made where measurement uncertainty is non-negligible.
Further theoretical relationships are provided linking multiscale sloppiness to
the Likelihood-ratio test. From this, we show that a local sensitivity analysis
(as typically done) is insufficient for determining the reliability of
parameter estimation, even with simple (non)linear systems. Our algorithm
provides a tractable alternative. We finally apply our methods to a
large-scale, benchmark Systems Biology model of NF-B, uncovering
previously unknown unidentifiabilities
Succinct Indexable Dictionaries with Applications to Encoding -ary Trees, Prefix Sums and Multisets
We consider the {\it indexable dictionary} problem, which consists of storing
a set for some integer , while supporting the
operations of \Rank(x), which returns the number of elements in that are
less than if , and -1 otherwise; and \Select(i) which returns
the -th smallest element in . We give a data structure that supports both
operations in O(1) time on the RAM model and requires bits to store a set of size , where {\cal B}(n,m) = \ceil{\lg
{m \choose n}} is the minimum number of bits required to store any -element
subset from a universe of size . Previous dictionaries taking this space
only supported (yes/no) membership queries in O(1) time. In the cell probe
model we can remove the additive term in the space bound,
answering a question raised by Fich and Miltersen, and Pagh.
We present extensions and applications of our indexable dictionary data
structure, including:
An information-theoretically optimal representation of a -ary cardinal
tree that supports standard operations in constant time,
A representation of a multiset of size from in bits that supports (appropriate generalizations of) \Rank
and \Select operations in constant time, and
A representation of a sequence of non-negative integers summing up to
in bits that supports prefix sum queries in constant
time.Comment: Final version of SODA 2002 paper; supersedes Leicester Tech report
2002/1
Experimental study of the effects of secondary air on the emissions and stability of a lean premixed combustor
Tests were run using a perforated plate flameholder with a relatively short attached recirculation zone and a vee gutter flameholder with a relatively long attached recirculation zone. Combustor streamlines were traced in cold flow tests at ambient pressure. The amount of secondary air entrainment in the recirculation zones of the flameholders was determined by tracer gas testing at cold flow ambient pressure conditions. Combustion tests were caried out at entrance conditions of 0.5 MPa/630K and emission of NOx, CO and unburned hydrocarbons were measured along with lean stability and flashback limits. The degree of entrainment increases as dilution air injection decreases. Flashback appears to be a function of overall equivalence ratio and resistance to flashback increases with increasing combustor entrance velocity. Lean stability limit appears to be a function of both primary zone and flameholder recirculation zone equivalence ratios and resistance to lean blowout increases with increasing combustor entrance velocity
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