211 research outputs found
A dichotomy theory for height functions
Height functions are random functions on a given graph, in our case
integer-valued functions on the two-dimensional square lattice. We consider
gradient potentials which (informally) lie between the discrete Gaussian and
solid-on-solid model (inclusive). The phase transition in this model, known as
the roughening transition, Berezinskii-Kosterlitz-Thouless transition, or
localisation-delocalisation transition, was established rigorously in the 1981
breakthrough work of Fr\"ohlich and Spencer. It was not until 2005 that
Sheffield derived continuity of the phase transition. First, we establish
sharpness, in the sense that covariances decay exponentially in the localised
phase. Second, we show that the model is delocalised at criticality, in the
sense that the set of potentials inducing localisation is open in a natural
topology. Third, we prove that the pointwise variance of the height function is
at least in the delocalised regime, where is the distance to the
boundary, and where denotes a universal constant. This implies that the
effective temperature of any potential cannot lie in the interval
(whenever it is well-defined), and jumps from to at least at the
critical point. We call this range of forbidden values the effective
temperature gap.Comment: 68 pages, 20 figures; added definition of correlation length and
improved presentatio
Parameter Synthesis for Markov Models
Markov chain analysis is a key technique in reliability engineering. A
practical obstacle is that all probabilities in Markov models need to be known.
However, system quantities such as failure rates or packet loss ratios, etc.
are often not---or only partially---known. This motivates considering
parametric models with transitions labeled with functions over parameters.
Whereas traditional Markov chain analysis evaluates a reliability metric for a
single, fixed set of probabilities, analysing parametric Markov models focuses
on synthesising parameter values that establish a given reliability or
performance specification . Examples are: what component failure rates
ensure the probability of a system breakdown to be below 0.00000001?, or which
failure rates maximise reliability? This paper presents various analysis
algorithms for parametric Markov chains and Markov decision processes. We focus
on three problems: (a) do all parameter values within a given region satisfy
?, (b) which regions satisfy and which ones do not?, and (c)
an approximate version of (b) focusing on covering a large fraction of all
possible parameter values. We give a detailed account of the various
algorithms, present a software tool realising these techniques, and report on
an extensive experimental evaluation on benchmarks that span a wide range of
applications.Comment: 38 page
The ABAG biogenic emissions inventory project
The ability to identify the role of biogenic hydrocarbon emissions in contributing to overall ozone production in the Bay Area, and to identify the significance of that role, were investigated in a joint project of the Association of Bay Area Governments (ABAG) and NASA/Ames Research Center. Ozone, which is produced when nitrogen oxides and hydrocarbons combine in the presence of sunlight, is a primary factor in air quality planning. In investigating the role of biogenic emissions, this project employed a pre-existing land cover classification to define areal extent of land cover types. Emission factors were then derived for those cover types. The land cover data and emission factors were integrated into an existing geographic information system, where they were combined to form a Biogenic Hydrocarbon Emissions Inventory. The emissions inventory information was then integrated into an existing photochemical dispersion model
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