44,502 research outputs found
A rigorous definition of axial lines: ridges on isovist fields
We suggest that 'axial lines' defined by (Hillier and Hanson, 1984) as lines
of uninterrupted movement within urban streetscapes or buildings, appear as
ridges in isovist fields (Benedikt, 1979). These are formed from the maximum
diametric lengths of the individual isovists, sometimes called viewsheds, that
make up these fields (Batty and Rana, 2004). We present an image processing
technique for the identification of lines from ridges, discuss current
strengths and weaknesses of the method, and show how it can be implemented
easily and effectively.Comment: 18 pages, 5 figure
Log Skeletons: A Classification Approach to Process Discovery
To test the effectiveness of process discovery algorithms, a Process
Discovery Contest (PDC) has been set up. This PDC uses a classification
approach to measure this effectiveness: The better the discovered model can
classify whether or not a new trace conforms to the event log, the better the
discovery algorithm is supposed to be. Unfortunately, even the state-of-the-art
fully-automated discovery algorithms score poorly on this classification. Even
the best of these algorithms, the Inductive Miner, scored only 147 correct
classified traces out of 200 traces on the PDC of 2017. This paper introduces
the rule-based log skeleton model, which is closely related to the Declare
constraint model, together with a way to classify traces using this model. This
classification using log skeletons is shown to score better on the PDC of 2017
than state-of-the-art discovery algorithms: 194 out of 200. As a result, one
can argue that the fully-automated algorithm to construct (or: discover) a log
skeleton from an event log outperforms existing state-of-the-art
fully-automated discovery algorithms.Comment: 16 pages with 9 figures, followed by an appendix of 14 pages with 17
figure
Semiclassical Series from Path Integrals
We derive the semiclassical series for the partition function in Quantum
Statistical Mechanics (QSM) from its path integral representation. Each term of
the series is obtained explicitly from the (real) minima of the classical
action. The method yields a simple derivation of the exact result for the
harmonic oscillator, and an accurate estimate of ground-state energy and
specific heat for a single-well quartic anharmonic oscillator. As QSM can be
regarded as finite temperature field theory at a point, we make use of Feynman
diagrams to illustrate the non-perturbative character of the series: it
contains all powers of and graphs with any number of loops; the usual
perturbative series corresponds to a subset of the diagrams of the
semiclassical series. We comment on the application of our results to other
potentials, to correlation functions and to field theories in higher
dimensions.Comment: 18 pages, 4 figures. References update
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