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10.3390/e16115838 http://scihub22266oqcxt.onion/10.3390/e16115838 C5365032!5365032!28344436     free     free     free Deprecated: Implicit conversion from float 209.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 209.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 209.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 209.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534 Deprecated: Implicit conversion from float 209.6 to int loses precision in C:\Inetpub\vhosts\kidney.de\httpdocs\pget.php on line 534       Entropy+(Basel) 2014 ; 16 (11): 5838-52 Nephropedia Template TP {{tp|p=28344436|t=2014. New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis |pdf=|usr=}}{{28344436}} gab.com Text New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis JO: Entropy (Basel) http://www.kidney.de/pget.php?&tw=1&pmid=28344436 #FOAvip Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag?Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient. Twit Text FOAVip New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis ????Entropy (Basel) http://www.kidney.de/pget.php?&tw=1&pmid=28344436 #FOAvip Twit Text # Free Paper on # # # # # LINK http://www.kidney.de/pget.php?&tw=1&pmid=28344436 #FOAvip English Wikipedia <ref>{{Cite pmid|28344436}}</ref> New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis #MMPMID28344436 Ingo C; Magin RL; Parrish TB Entropy (Basel) 2014[Nov]; 16 (11): 5838-52 PMID28344436show ga Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag?Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient. äNew Insights into the Fractional Order Diffusion Equation Using Entrop(epmc).pdf DeepDyve Pubget Overpricing