9,117 research outputs found
Cleanroom software development
The 'cleanroom' software development process is a technical and organizational approach to developing software with certifiable reliability. Key ideas behind the process are well structured software specifications, randomized testing methods and the introduction of statistical controls; but the main point is to deny entry for defects during the development of software. This latter point suggests the use of the term 'cleanroom' in analogy to the defect prevention controls used in the manufacturing of high technology hardware. In the 'cleanroom', the entire software development process is embedded within a formal statistical design, in contrast to executing selected tests and appealing to the randomness of operational settings for drawing statistical inferences. Instead, random testing is introduced as a part of the statistical design itself so that when development and testing are completed, statistical inferences are made about the operation of the system
Spatial Mixing of Coloring Random Graphs
We study the strong spatial mixing (decay of correlation) property of proper
-colorings of random graph with a fixed . The strong spatial
mixing of coloring and related models have been extensively studied on graphs
with bounded maximum degree. However, for typical classes of graphs with
bounded average degree, such as , an easy counterexample shows that
colorings do not exhibit strong spatial mixing with high probability.
Nevertheless, we show that for with and
sufficiently large , with high probability proper -colorings of
random graph exhibit strong spatial mixing with respect to an
arbitrarily fixed vertex. This is the first strong spatial mixing result for
colorings of graphs with unbounded maximum degree. Our analysis of strong
spatial mixing establishes a block-wise correlation decay instead of the
standard point-wise decay, which may be of interest by itself, especially for
graphs with unbounded degree
Rapid Mixing for Lattice Colorings with Fewer Colors
We provide an optimally mixing Markov chain for 6-colorings of the square
lattice on rectangular regions with free, fixed, or toroidal boundary
conditions. This implies that the uniform distribution on the set of such
colorings has strong spatial mixing, so that the 6-state Potts antiferromagnet
has a finite correlation length and a unique Gibbs measure at zero temperature.
Four and five are now the only remaining values of q for which it is not known
whether there exists a rapidly mixing Markov chain for q-colorings of the
square lattice.Comment: Appeared in Proc. LATIN 2004, to appear in JSTA
The energy dilemma and its impact on air transportation
The dimensions of the energy situation are discussed in relation to air travel. Energy conservation, fuel consumption, and combustion efficiency are examined, as well as the proposal for subsonic aircraft using hydrogen fuel
Quantum speedup of classical mixing processes
Most approximation algorithms for #P-complete problems (e.g., evaluating the
permanent of a matrix or the volume of a polytope) work by reduction to the
problem of approximate sampling from a distribution over a large set
. This problem is solved using the {\em Markov chain Monte Carlo} method: a
sparse, reversible Markov chain on with stationary distribution
is run to near equilibrium. The running time of this random walk algorithm, the
so-called {\em mixing time} of , is as shown
by Aldous, where is the spectral gap of and is the minimum
value of . A natural question is whether a speedup of this classical
method to , the diameter of the graph
underlying , is possible using {\em quantum walks}.
We provide evidence for this possibility using quantum walks that {\em
decohere} under repeated randomized measurements. We show: (a) decoherent
quantum walks always mix, just like their classical counterparts, (b) the
mixing time is a robust quantity, essentially invariant under any smooth form
of decoherence, and (c) the mixing time of the decoherent quantum walk on a
periodic lattice is , which is indeed
and is asymptotically no worse than the
diameter of (the obvious lower bound) up to at most a logarithmic
factor.Comment: 13 pages; v2 revised several part
Technical management techniques for identification and control of industrial safety and pollution hazards
Constructive recommendations are suggested for pollution problems from offshore energy resources industries on outer continental shelf. Technical management techniques for pollution identification and control offer possible applications to space engineering and management
Ablation debris control by means of closed thick film filtered water immersion
The performance of laser ablation generated debris control by means of open immersion techniques have been shown to be limited by flow surface ripple effects on the beam and the action of ablation plume pressure loss by splashing of the immersion fluid. To eradicate these issues a closed technique has been developed which ensured a controlled geometry for both the optical interfaces of the flowing liquid film. This had the action of preventing splashing, ensuring repeatable machining conditions and allowed for control of liquid flow velocity. To investigate the performance benefits of this closed immersion technique bisphenol A polycarbonate samples have been machined using filtered water at a number of flow velocities. The results demonstrate the efficacy of the closed immersion technique: a 93% decrease in debris is produced when machining under closed filtered water immersion; the average debris particle size becomes larger, with an equal proportion of small and medium sized debris being produced when laser machining under closed flowing filtered water immersion; large debris is shown to be displaced further by a given flow velocity than smaller debris, showing that the action of flow turbulence in the duct has more impact on smaller debris. Low flow velocities were found to be less effective at controlling the positional trend of deposition of laser ablation generated debris than high flow velocities; but, use of excessive flow velocities resulted in turbulence motivated deposition. This work is of interest to the laser micromachining community and may aide in the manufacture of 2.5D laser etched patterns covering large area wafers and could be applied to a range of wavelengths and laser types
Counting approximately-shortest paths in directed acyclic graphs
Given a directed acyclic graph with positive edge-weights, two vertices s and
t, and a threshold-weight L, we present a fully-polynomial time
approximation-scheme for the problem of counting the s-t paths of length at
most L. We extend the algorithm for the case of two (or more) instances of the
same problem. That is, given two graphs that have the same vertices and edges
and differ only in edge-weights, and given two threshold-weights L_1 and L_2,
we show how to approximately count the s-t paths that have length at most L_1
in the first graph and length at most L_2 in the second graph. We believe that
our algorithms should find application in counting approximate solutions of
related optimization problems, where finding an (optimum) solution can be
reduced to the computation of a shortest path in a purpose-built auxiliary
graph
Fast Genome-Wide QTL Association Mapping on Pedigree and Population Data
Since most analysis software for genome-wide association studies (GWAS)
currently exploit only unrelated individuals, there is a need for efficient
applications that can handle general pedigree data or mixtures of both
population and pedigree data. Even data sets thought to consist of only
unrelated individuals may include cryptic relationships that can lead to false
positives if not discovered and controlled for. In addition, family designs
possess compelling advantages. They are better equipped to detect rare
variants, control for population stratification, and facilitate the study of
parent-of-origin effects. Pedigrees selected for extreme trait values often
segregate a single gene with strong effect. Finally, many pedigrees are
available as an important legacy from the era of linkage analysis.
Unfortunately, pedigree likelihoods are notoriously hard to compute. In this
paper we re-examine the computational bottlenecks and implement ultra-fast
pedigree-based GWAS analysis. Kinship coefficients can either be based on
explicitly provided pedigrees or automatically estimated from dense markers.
Our strategy (a) works for random sample data, pedigree data, or a mix of both;
(b) entails no loss of power; (c) allows for any number of covariate
adjustments, including correction for population stratification; (d) allows for
testing SNPs under additive, dominant, and recessive models; and (e)
accommodates both univariate and multivariate quantitative traits. On a typical
personal computer (6 CPU cores at 2.67 GHz), analyzing a univariate HDL
(high-density lipoprotein) trait from the San Antonio Family Heart Study
(935,392 SNPs on 1357 individuals in 124 pedigrees) takes less than 2 minutes
and 1.5 GB of memory. Complete multivariate QTL analysis of the three
time-points of the longitudinal HDL multivariate trait takes less than 5
minutes and 1.5 GB of memory
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