scholarly journals Rényi Entropy Power Inequalities via Normal Transport and Rotation

2018 ◽  
Author(s):  
Olivier Rioul
Keyword(s):  
Shannon’S Entropy ◽  
Shannon's Entropy ◽  
Change Of Variable ◽  
Power Inequality ◽  
Multiplicative Form ◽  
Normal Transport ◽  
Comprehensive Framework

Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Rényi entropy is presented that uses transport arguments from normal densities and a change of variable by rotation. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.

scholarly journals Rényi Entropy Power Inequalities via Normal Transport and Rotation

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 641 ◽  
Author(s):  
Olivier Rioul
Keyword(s):  
Shannon’S Entropy ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Shannon's Entropy ◽  
Change Of Variable ◽  
Power Inequality ◽  
Multiplicative Form ◽  
Normal Transport ◽  
Comprehensive Framework

Following a recent proof of Shannon’s entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Rényi entropy is presented that uses transport arguments from normal densities and a change of variable by rotation. Simple arguments are given to recover the previously known Rényi EPIs and derive new ones, by unifying a multiplicative form with constant c and a modification with exponent α of previous works. In particular, for log-concave densities, we obtain a simple transportation proof of a sharp varentropy bound.

scholarly journals Rényi Entropy Power Inequalities via Normal Transport and Rotation

2018 ◽  
Author(s):  
Olivier Rioul
Keyword(s):  
Shannon’S Entropy ◽  
Shannon's Entropy ◽  
Change Of Variable ◽  
Power Inequality ◽  
Normal Transport ◽  
Comprehensive Framework

Following a recent proof of Shannon's entropy power inequality (EPI), a comprehensive framework for deriving various EPIs for the Rényi entropy is presented, that uses transport arguments from normal densities and a change of variable by rotation.

scholarly journals ASSESSMENT OF URBAN SPRAWL USING SHANNON’S ENTROPY AND FRACTAL ANALYSIS: A CASE STUDY OF ATAKUM, ILKADIM AND CANIK (SAMSUN, TURKEY)

2017 ◽  
Vol 25 (3) ◽  
pp. 264-276 ◽  
Author(s):  
Derya OZTURK
Keyword(s):  
Urban Sprawl ◽  
Fractal Analysis ◽  
Urban Form ◽  
Entropy Method ◽  
Shannon’S Entropy ◽  
Analysis Method ◽  
Maximum Likelihood Classification ◽  
Shannon's Entropy ◽  
Box Counting

Urban sprawl is one of the most important problems in urban development due to its negative environmental and societal impacts. Therefore, the spatial pattern of urban growth should be accurately analyzed and well understood for effective urban planning. This paper focuses on urban sprawl analysis in the Atakum, Ilkadim and Canik districts of Samsun, Turkey. In this study, urban sprawl was examined over a period of 24 years using Shannon's entropy and fractal analysis based on remote sensing and Geographic Information System (GIS). The built-up areas in 1989, 2000 and 2013 were extracted from Landsat TM/ETM+/OLI images using the maximum likelihood classification method, and urban form changes in the 1989–2013 period were investigated. The Shannon's entropy method was used to determine the degree of urban sprawl, and a fractal analysis method based on box counting was used to characterize the urban sprawl. The results show that Atakum, Ilkadim and Canik experienced important changes and have considerable sprawl and complex characteristics now. The study also revealed that there is no monotonic relationship between Shannon's entropy and fractal dimension.

Durational contrast in gemination and informativity

2018 ◽  
Vol 4 (s2) ◽  
Author(s):  
Shin-Ichiro Sano
Keyword(s):  
Shannon’S Entropy ◽  
Minimal Pair ◽  
Shannon's Entropy ◽  
Linguistic Behavior ◽  
Manner Of Articulation

AbstractRecent studies in Message Oriented Phonology (MOP) have provided increasing evidence that informativity plays a non-trivial role in linguistic behavior. This paper provides a case study of MOP focusing on the durational contrast of singleton and geminate consonants in spoken Japanese. In modern Japanese, short consonants (singletons) and long consonants (geminates) are lexically contrastive, and the durational properties of these consonants are affected by a variety of factors. This provides a useful test of the assumptions of MOP. Based on the assumption that the higher the informativity, the more robustly the contrast is phonetically implemented, this study examines the hypothesis that the durations of singletons and geminates increase or decrease according to the informativity of their durational contrast. The study confirms that (i) the distribution of singletons and geminates is affected by the manner of articulation and positional differences (morpheme-initial, medial, and final); (ii) the distributional differences follow from the informativity of contrasts as represented by Shannon’s entropy; and (iii) the durational contrast is enhanced by the presence or absence of a minimal pair.

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