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A Divergence Formula for Randomness and Dimension
"... If S is an infinite sequence over a finite alphabet Σ and β is a probability measure on Σ, then the dimension of S with respect to β, written dim β (S), is a constructive version of Billingsley dimension that coincides with the (constructive Hausdorff) dimension dim(S) when β is the uniform probabil ..."
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Cited by 1 (1 self)
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probability measure. This paper shows that dim β (S) and its dual Dim β (S), the strong dimension of S with respect to β, can be used in conjunction with randomness to measure the similarity of two probability measures α and β on Σ. Specifically, we prove that the divergence formula dim β (R) = Dim β (R) =
A Divergence Formula for Randomness and Dimension (Short Version)
, 906
"... If S is an infinite sequence over a finite alphabet Σ and β is a probability measure on Σ, then the dimension of S with respect to β, written dim β (S), is a constructive version of Billingsley dimension that coincides with the (constructive Hausdorff) dimension dim(S) when β is the uniform probabil ..."
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probability measure. This paper shows that dim β (S) and its dual Dim β (S), the strong dimension of S with respect to β, can be used in conjunction with randomness to measure the similarity of two probability measures α and β on Σ. Specifically, we prove that the divergence formula dim β (R) = Dim β (R) =
Usability Analysis of Visual Programming Environments: a `cognitive dimensions' framework
 JOURNAL OF VISUAL LANGUAGES AND COMPUTING
, 1996
"... The cognitive dimensions framework is a broadbrush evaluation technique for interactive devices and for noninteractive notations. It sets out a small vocabulary of terms designed to capture the cognitivelyrelevant aspects of structure, and shows how they can be traded off against each other. T ..."
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Cited by 510 (13 self)
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The cognitive dimensions framework is a broadbrush evaluation technique for interactive devices and for noninteractive notations. It sets out a small vocabulary of terms designed to capture the cognitivelyrelevant aspects of structure, and shows how they can be traded off against each other
Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
, 2004
"... Suppose we are given a vector f in RN. How many linear measurements do we need to make about f to be able to recover f to within precision ɛ in the Euclidean (ℓ2) metric? Or more exactly, suppose we are interested in a class F of such objects— discrete digital signals, images, etc; how many linear m ..."
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Cited by 1513 (20 self)
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law), then it is possible to reconstruct f to within very high accuracy from a small number of random measurements. typical result is as follows: we rearrange the entries of f (or its coefficients in a fixed basis) in decreasing order of magnitude f  (1) ≥ f  (2) ≥... ≥ f  (N), and define the weakℓp ball
Segmentation of brain MR images through a hidden Markov random field model and the expectationmaximization algorithm
 IEEE TRANSACTIONS ON MEDICAL. IMAGING
, 2001
"... The finite mixture (FM) model is the most commonly used model for statistical segmentation of brain magnetic resonance (MR) images because of its simple mathematical form and the piecewise constant nature of ideal brain MR images. However, being a histogrambased model, the FM has an intrinsic limi ..."
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Cited by 619 (14 self)
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based methods produce unreliable results. In this paper, we propose a novel hidden Markov random field (HMRF) model, which is a stochastic process generated by a MRF whose state sequence cannot be observed directly but which can be indirectly estimated through observations. Mathematically, it can be shown
Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test
 REVIEW OF FINANCIAL STUDIES
, 1988
"... In this article we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at different frequencies. The random walk model is strongly rejected for the entire sample period (19621985) and for all subperiod for a variety of aggrega ..."
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Cited by 492 (18 self)
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In this article we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at different frequencies. The random walk model is strongly rejected for the entire sample period (19621985) and for all subperiod for a variety
Statistical mechanics of complex networks
 Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
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Cited by 2083 (10 self)
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Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled
A New Kind of Science
, 2002
"... “Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplit ..."
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Cited by 850 (0 self)
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“Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical
Results 1  10
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337,302