95,923 research outputs found
Real-time and Probabilistic Temporal Logics: An Overview
Over the last two decades, there has been an extensive study on logical
formalisms for specifying and verifying real-time systems. Temporal logics have
been an important research subject within this direction. Although numerous
logics have been introduced for the formal specification of real-time and
complex systems, an up to date comprehensive analysis of these logics does not
exist in the literature. In this paper we analyse real-time and probabilistic
temporal logics which have been widely used in this field. We extrapolate the
notions of decidability, axiomatizability, expressiveness, model checking, etc.
for each logic analysed. We also provide a comparison of features of the
temporal logics discussed
An Algebraic Framework for Compositional Program Analysis
The purpose of a program analysis is to compute an abstract meaning for a
program which approximates its dynamic behaviour. A compositional program
analysis accomplishes this task with a divide-and-conquer strategy: the meaning
of a program is computed by dividing it into sub-programs, computing their
meaning, and then combining the results. Compositional program analyses are
desirable because they can yield scalable (and easily parallelizable) program
analyses.
This paper presents algebraic framework for designing, implementing, and
proving the correctness of compositional program analyses. A program analysis
in our framework defined by an algebraic structure equipped with sequencing,
choice, and iteration operations. From the analysis design perspective, a
particularly interesting consequence of this is that the meaning of a loop is
computed by applying the iteration operator to the loop body. This style of
compositional loop analysis can yield interesting ways of computing loop
invariants that cannot be defined iteratively. We identify a class of
algorithms, the so-called path-expression algorithms [Tarjan1981,Scholz2007],
which can be used to efficiently implement analyses in our framework. Lastly,
we develop a theory for proving the correctness of an analysis by establishing
an approximation relationship between an algebra defining a concrete semantics
and an algebra defining an analysis.Comment: 15 page
Maximum-a-posteriori estimation with Bayesian confidence regions
Solutions to inverse problems that are ill-conditioned or ill-posed may have
significant intrinsic uncertainty. Unfortunately, analysing and quantifying
this uncertainty is very challenging, particularly in high-dimensional
problems. As a result, while most modern mathematical imaging methods produce
impressive point estimation results, they are generally unable to quantify the
uncertainty in the solutions delivered. This paper presents a new general
methodology for approximating Bayesian high-posterior-density credibility
regions in inverse problems that are convex and potentially very
high-dimensional. The approximations are derived by using recent concentration
of measure results related to information theory for log-concave random
vectors. A remarkable property of the approximations is that they can be
computed very efficiently, even in large-scale problems, by using standard
convex optimisation techniques. In particular, they are available as a
by-product in problems solved by maximum-a-posteriori estimation. The
approximations also have favourable theoretical properties, namely they
outer-bound the true high-posterior-density credibility regions, and they are
stable with respect to model dimension. The proposed methodology is illustrated
on two high-dimensional imaging inverse problems related to tomographic
reconstruction and sparse deconvolution, where the approximations are used to
perform Bayesian hypothesis tests and explore the uncertainty about the
solutions, and where proximal Markov chain Monte Carlo algorithms are used as
benchmark to compute exact credible regions and measure the approximation
error
A Statistical Modeling Approach to Computer-Aided Quantification of Dental Biofilm
Biofilm is a formation of microbial material on tooth substrata. Several
methods to quantify dental biofilm coverage have recently been reported in the
literature, but at best they provide a semi-automated approach to
quantification with significant input from a human grader that comes with the
graders bias of what are foreground, background, biofilm, and tooth.
Additionally, human assessment indices limit the resolution of the
quantification scale; most commercial scales use five levels of quantification
for biofilm coverage (0%, 25%, 50%, 75%, and 100%). On the other hand, current
state-of-the-art techniques in automatic plaque quantification fail to make
their way into practical applications owing to their inability to incorporate
human input to handle misclassifications. This paper proposes a new interactive
method for biofilm quantification in Quantitative light-induced fluorescence
(QLF) images of canine teeth that is independent of the perceptual bias of the
grader. The method partitions a QLF image into segments of uniform texture and
intensity called superpixels; every superpixel is statistically modeled as a
realization of a single 2D Gaussian Markov random field (GMRF) whose parameters
are estimated; the superpixel is then assigned to one of three classes
(background, biofilm, tooth substratum) based on the training set of data. The
quantification results show a high degree of consistency and precision. At the
same time, the proposed method gives pathologists full control to post-process
the automatic quantification by flipping misclassified superpixels to a
different state (background, tooth, biofilm) with a single click, providing
greater usability than simply marking the boundaries of biofilm and tooth as
done by current state-of-the-art methods.Comment: 10 pages, 7 figures, Journal of Biomedical and Health Informatics
2014. keywords: {Biomedical imaging;Calibration;Dentistry;Estimation;Image
segmentation;Manuals;Teeth},
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6758338&isnumber=636350
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