345,496 research outputs found
Relative entropy as a measure of inhomogeneity in general relativity
We introduce the notion of relative volume entropy for two spacetimes with
preferred compact spacelike foliations. This is accomplished by applying the
notion of Kullback-Leibler divergence to the volume elements induced on
spacelike slices. The resulting quantity gives a lower bound on the number of
bits which are necessary to describe one metric given the other. For
illustration, we study some examples, in particular gravitational waves, and
conclude that the relative volume entropy is a suitable device for quantitative
comparison of the inhomogeneity of two spacetimes.Comment: 15 pages, 7 figure
Entropy as a Measure of Quality of XML Schema Document
In this paper, a metric for the assessment of the structural complexity of eXtensible Markup Language schema
document is formulated. The present metric ‘Schema Entropy is based on entropy concept and intended to measure the
complexity of the schema documents written in W3C XML Schema Language due to diversity in the structures of its elements. The SE is useful in evaluating the efficiency of the design of Schemas. A good design reduces the maintainability efforts. Therefore, our metric provides valuable information about the reliability and maintainability of systems. In this respect, this
metric is believed to be a valuable contribution for improving the quality of XML-based systems. It is demonstrated with examples and validated empirically through actual test cases
Increment entropy as a measure of complexity for time series
Entropy has been a common index to quantify the complexity of time series in
a variety of fields. Here, we introduce increment entropy to measure the
complexity of time series in which each increment is mapped into a word of two
letters, one letter corresponding to direction and the other corresponding to
magnitude. The Shannon entropy of the words is termed as increment entropy
(IncrEn). Simulations on synthetic data and tests on epileptic EEG signals have
demonstrated its ability of detecting the abrupt change, regardless of
energetic (e.g. spikes or bursts) or structural changes. The computation of
IncrEn does not make any assumption on time series and it can be applicable to
arbitrary real-world data.Comment: 12pages,7figure,2 table
On Classical Analogues of Free Entropy Dimension
We define a classical probability analogue of Voiculescu's free entropy
dimension that we shall call the classical probability entropy dimension of a
probability measure on . We show that the classical probability
entropy dimension of a measure is related with diverse other notions of
dimension. First, it can be viewed as a kind of fractal dimension. Second, if
one extends Bochner's inequalities to a measure by requiring that microstates
around this measure asymptotically satisfy the classical Bochner's
inequalities, then we show that the classical probability entropy dimension
controls the rate of increase of optimal constants in Bochner's inequality for
a measure regularized by convolution with the Gaussian law as the
regularization is removed. We introduce a free analogue of the Bochner
inequality and study the related free entropy dimension quantity. We show that
it is greater or equal to the non-microstates free entropy dimension
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