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Special Functions: Fractional Calculus and the Pathway for Entropy

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ISBN: 9783038426653 9783038426646 Year: Pages: 304 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General)
Added to DOAB on : 2018-01-24 13:53:41
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Historically, the notion of entropy emerged in conceptually very distinct contexts. This book deals with the connection between entropy, probability, and fractional dynamics as they appeared, for example, in solar neutrino astrophysics since the 1970's (Mathai and Rathie 1975, Mathai and Pederzoli 1977, Mathai and Saxena 1978, Mathai, Saxena, and Haubold 2010).The original solar neutrino problem, experimentally and theoretically, was resolved through the discovery of neutrino oscillations and was recently enriched by neutrino entanglement entropy. To reconsider possible new physics of solar neutrinos, diffusion entropy analysis, utilizing Boltzmann entropy, and standard deviation analysis was undertaken with Super-Kamiokande solar neutrino data. This analysis revealed a non-Gaussian signal with harmonic content. The Hurst exponent is different from the scaling exponent of the probability density function and both Hurst exponent and scaling exponent of the Super-Kamiokande data deviate considerably from the value of ½, which indicates that the statistics of the underlying phenomenon is anomalous. Here experiment may provide guidance about the generalization of theory of Boltzmann statistical mechanics. Arguments in the so-called Boltzmann-Planck-Einstein discussion related to Planck's discovery of the black-body radiation law are recapitulated mathematically and statistically and emphasize from this discussion is pursued that a meaningful implementation of the complex ‘entropy-probability-dynamics’ may offer two ways for explaining the results of diffusion entropy analysis and standard deviation analysis. One way is to consider an anomalous diffusion process that needs to use the fractional space-time diffusion equation (Gorenflo and Mainardi) and the other way is to consider a generalized Boltzmann entropy by assuming a power law probability density function. Here new mathematical framework, invented by sheer thought, may provide guidance for the generalization of Boltzmann statistical mechanics. In this book Boltzmann entropy, generalized by Tsallis and Mathai, is considered. The second one contains a varying parameter that is used to construct an entropic pathway covering generalized type-1 beta, type-2 beta, and gamma families of densities. Similarly, pathways for respective distributions and differential equations can be developed. Mathai's entropy is optimized under various conditions reproducing the well-known Boltzmann distribution, Raleigh distribution, and other distributions used in physics. Properties of the entropy measure for the generalized entropy are examined. In this process the role of special functions of mathematical physics, particularly the H-function, is highlighted.

Beyond the simple contrastive analysis: Appropriate experimental approaches for unraveling the neural basis of conscious experience

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Book Series: Frontiers Research Topics ISSN: 16648714 ISBN: 9782889195473 Year: Pages: 129 DOI: 10.3389/978-2-88919-547-3 Language: English
Publisher: Frontiers Media SA
Subject: Psychology --- Science (General)
Added to DOAB on : 2016-01-19 14:05:46
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Contrasting conditions with and without conscious experience has served consciousness research well. However, research based on this simple contrast has led to controversies about the neural basis of conscious experience. One key reason for these ongoing debates seems to be that the simple contrast between conditions with and without consciousness is not specific for unraveling the neural basis of conscious experience, but rather also leads to other processes that precede or follow it. Acknowledging this methodological problem implies that some of the previous research findings about the neural underpinnings of conscious experience are actually reflecting the prerequisites and consequences rather than the direct correlates of conscious perception. Thus, it is required to re-evaluate the previous results to find out which of them are telling us anything about the neural basis of consciousness. But first and foremost, to overcome this methodological problem we need new experimental paradigms that go beyond the simple contrastive analysis or find the ways how some older but well forgotten paradigms may foster a new look at this emerging problem. Accordingly, this research topic is looking for empirical and theoretical contributions that: 1) envision new and suitable experimental approaches to study consciousness that are free from the limitations of the simple contrastive analysis; 2) provide empirical data that help to separate the neural correlates of conscious experience from the prerequisites and consequences of it; 3) help to re-assess previous research findings about the neural correlates of conscious perception in the light of the methodological problems with the traditional contrastive analysis. We hope that the theoretical insights and experimental approaches collected within this Research Topic help us to gain a more refined understanding of the neural basis of conscious experience.

Membrane and Membrane Reactors Operations in Chemical Engineering

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ISBN: 9783039210220 / 9783039210237 Year: Pages: 154 DOI: 10.3390/books978-3-03921-023-7 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering --- Environmental Engineering
Added to DOAB on : 2019-06-26 10:09:00
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This Special Issue is aimed at highlighting the potentialities of membrane and membrane reactor operations in various sectors of chemical engineering, based on application of the process intensification strategy. In all of the contributions, the principles of process intensification were pursued during the adoption of membrane technology, demonstrating how it may lead to the development of redesigned processes that are more compact and efficient while also being more environmental friendly, energy saving, and amenable to integration with other green processes. This Special Issue comprises a number of experimental and theoretical studies dealing with the application of membrane and membrane reactor technology in various scientific fields of chemical engineering, such as membrane distillation for wastewater treatment, hydrogen production from reforming reactions via inorganic membrane and membrane photoassisted reactors, membrane desalination, gas/liquid phase membrane separation of CO2, and membrane filtration for the recovery of antioxidants from agricultural byproducts, contributing to valorization of the potentialities of membrane operations.

Forest Insects and Pathogens in a Changing Environment: Ecology, Monitoring & Genetics (IUFRO Joint Meeting of WP7.03.05 & 7.03.10)

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ISBN: 9783039215119 / 9783039215126 Year: Pages: 158 DOI: 10.3390/books978-3-03921-512-6 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Environmental Sciences
Added to DOAB on : 2019-12-09 11:49:15
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After the successful conclusion of the Joint Meeting of IUFRO’s 7.03.05 & 7.03.10 working parties and given the exciting and novel studies that have been presented in the framework of this meeting, we decided to present some of these studies in the current Special Issue of Forests. To make this issue more appealing and interesting to everyone in the field of Forest Protection, studies that cover a wide range of topics were selected, ranging from ecology and phylogeography to forest management and protection. More importantly, as these studies refer to pests and pathogens from different parts of the world, it is expected that the knowledge gained can be further used in the protection of natural environment worldwide.

Extractable and Non-Extractable Antioxidants

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ISBN: 9783039214372 / 9783039214389 Year: Pages: 234 DOI: 10.3390/books978-3-03921-438-9 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Biology --- Nutrition and Food Sciences
Added to DOAB on : 2019-12-09 11:49:15
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The Special Issue “Extractable and Non-Extractable Antioxidants” gives an updated view on antioxidants—both in their extractable and non-extractable form—in the different food groups, their products thereof, and food preparations as well as byproducts and biomass waste. The potential beneficial properties of these compounds and nutraceutical formulations are described in the various studies covered in this Special Issue.

Keywords

anthocyanins --- polyphenolic compounds --- classic extraction --- ultrasound assisted extraction --- antioxidant capacity --- daidzein --- cyclodextrin --- inclusion complex --- antioxidant activity --- trans-cinnamaldehyde --- ?-cyclodextrin --- self-inclusion --- anti-inflammation --- antioxidant --- Pleurotus ostreatus --- antioxidant activity --- polyphenols --- digestibility --- fermentation --- cereals --- legumes --- Chinese mistletoes --- phenolics --- phenolic contents --- antioxidant activity --- forest residues --- phenolic compounds --- natural antioxidants --- quercitrin --- value-added by-products --- Camellia sinensis --- black teas --- catechins --- antioxidant activity --- LC-ESI-Q-TOF-MS --- principal component analysis --- extractable --- non-extractable --- antioxidant activity --- agglomerative hierarchical clustering --- principal component analysis --- multivariate analysis --- nuclear magnetic spectroscopy --- nitric oxide scavengers --- pre-column HPLC method --- Aloysia triphylla --- phenolics --- antioxidants --- dietary supplements --- botanicals --- bioactive compounds --- antioxidants --- study approach --- integrated food research --- dedicated databases --- dietary assessment. --- biorefinery --- circular economy --- grape seed --- bio-based --- chemometrics --- Cagnulari marc --- Naviglio Extractor® --- green extraction --- endothelial cell --- oxidative stress --- polyphenols --- berries jam --- phenolic acids --- flavonols glycosides --- degradation --- HPLC-ESI/MS --- antioxidant properties --- digestive enzyme --- nutrient --- polymerization --- proanthocyanidins --- eggplant --- flour --- phenolics --- antioxidant activity --- functional ingredient --- sour cherry --- anthocyanins --- extractable polyphenols --- non-extractable polyphenols --- Italian popular recipes --- food composition database --- antioxidant properties --- extractable compounds --- non-extractable compounds --- ferric reducing antioxidant power (FRAP) --- total polyphenol content (TPC) --- n/a

The Future of Hyperspectral Imaging

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ISBN: 9783039218226 / 9783039218233 Year: Pages: 220 DOI: 10.3390/books978-3-03921-823-3 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Chemistry (General)
Added to DOAB on : 2019-12-09 16:39:37
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Keywords

hyperspectral imaging --- Raman --- fluorescence --- sorting --- quality control --- black polymers --- PZT --- classification --- machine learning --- alternating direction method of multipliers --- Cramer–Rao lower bound --- forward observation model --- linear mixture model --- maximum likelihood --- multiband image fusion --- total variation --- fingerprints --- blood detection --- age determination --- hyperspectral imaging --- lossless compression --- multitemporal hyperspectral images --- information theoretic analysis --- predictive coding --- hyperspectral imaging --- plant phenotyping --- disease detection --- spectral tracking --- time series --- hyperspectral imaging --- principal component analysis --- oxygen saturation --- wound healing --- diabetic foot ulcer --- Raman spectroscopy --- chemical imaging --- compressive detection --- spatial light modulators (SLM) --- digital micromirror device (DMD) --- digital light processor (DLP) --- optimal binary filters --- Chemometrics --- multivariate data analysis --- compressive sensing --- hyperspectral imaging --- multiplexing system --- liquid crystal --- three-dimensional imaging --- integral imaging --- remote sensing --- point target detection --- CS-MUSI --- hyperspectral --- video --- imaging --- coastal dynamics --- moving vehicle imaging --- bi-directional reflectance distribution function (BRDF) --- hemispherical conical reflectance factor (HCRF) --- stereo imaging --- digital elevation model --- Virginia Coast Reserve Long Term Ecological Research (VCR LTER) --- Hyperspectral imaging --- painting samples --- retouching pigments --- watercolours --- multivariate analysis --- potatoes --- sprouting --- primordial leaf count --- hyperspectral imaging --- spectroscopy --- fusion --- wavelength selection --- PLSR --- interval partial least squares --- deep learning --- hyperspectral imaging --- neural networks --- machine learning --- image processing --- hyperspectral imaging --- medical imaging by HSI --- HSI for biology --- remote sensing --- hyperspectral microscopy --- fluorescence hyperspectral imaging --- Raman hyperspectral imaging --- infrared hyperspectral imaging --- statistical methods for HSI --- hyperspectral data mining and compression --- statistical methods for HSI --- hyperspectral data mining and compression

Entropy Measures for Data Analysis: Theory, Algorithms and Applications

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ISBN: 9783039280322 / 9783039280339 Year: Pages: 260 DOI: 10.3390/books978-3-03928-033-9 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering --- Environmental Engineering
Added to DOAB on : 2020-01-07 09:21:22
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Entropies and entropy-like quantities play an increasing role in modern non-linear data analysis. Fields that benefit from this application range from biosignal analysis to econophysics and engineering. This issue is a collection of papers touching on different aspects of entropy measures in data analysis, as well as theoretical and computational analyses. The relevant topics include the difficulty to achieve adequate application of entropy measures and the acceptable parameter choices for those entropy measures, entropy-based coupling, and similarity analysis, along with the utilization of entropy measures as features in automatic learning and classification. Various real data applications are given.

Keywords

experiment of design --- empirical mode decomposition --- signal analysis --- similarity indices --- synchronization analysis --- auditory attention --- entropy measure --- linear discriminant analysis (LDA) --- support vector machine (SVM) --- auditory attention classifier --- electroencephalography (EEG) --- vague entropy --- distance induced vague entropy --- distance --- complex fuzzy set --- complex vague soft set --- entropy, entropy visualization --- entropy balance equation --- Shannon-type relations --- multivariate analysis --- machine learning evaluation --- data transformation --- sample entropy --- treadmill walking --- center of pressure displacement --- dual-tasking --- analog circuit --- fault diagnosis --- cross wavelet transform --- Tsallis entropy --- parametric t-distributed stochastic neighbor embedding --- support vector machine --- information transfer --- Chinese stock sectors --- effective transfer entropy --- market crash --- system coupling --- cross-visibility graphs --- image entropy --- geodesic distance --- Dempster-Shafer evidence theory --- uncertainty of basic probability assignment --- belief entropy --- plausibility transformation --- weighted Hartley entropy --- Shannon entropy --- learning --- information --- novelty detection --- non-probabilistic entropy --- learning systems --- permutation entropy --- embedded dimension --- short time records --- signal classification --- relevance analysis --- global optimization --- meta-heuristic --- firefly algorithm --- cross-entropy method --- co-evolution --- symbolic analysis --- ordinal patterns --- Permutation entropy --- conditional entropy of ordinal patterns --- Kolmogorov-Sinai entropy --- algorithmic complexity --- information entropy --- particle size distribution --- selfsimilar measure --- simulation --- data analysis --- entropy --- entropy measures --- automatic learning

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