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Implements various estimators of entropy for discrete random variables, including the shrinkage estimator by Hausser and Strimmer (2009), the maximum likelihood and the Millow-Madow estimator, various Bayesian estimators, and the Chao-Shen estimator. It also offers an R interface to the NSB estimator. Furthermore, the package provides functions for estimating the Kullback-Leibler divergence, the chi-squared divergence, mutual information, and the chi-squared divergence of independence. It also computes the G statistic and the chi-squared statistic and corresponding p-values. Furthermore, there are functions for discretizing continuous random variables.
In a multicomponent system, a GB can certainly be compositionally complex. In fact, even if the bulk phase a conventional multicomponent alloy that is a dilute solid solution of multiple solute components, the GB can be a concentrated multi-principal component solution (Fig. 1c), thereby potentially being high entropy even if the bulk alloy is not. Here, we need to first discuss what is GB entropy and thermodynamic characters of HEGBs based on rigorous interfacial thermodynamics.
To illustrate GB and bulk high-entropy effects, we can use a statistical thermodynamic model for multicomponent GB segregation (a.k.a. adsorption)8 that is a generalization of the binary Wynblatt-Chatain model24 with a few simplifications. Considering a general twist GB with segregation limited to the two layers at the GB core and further assuming an ideal solution for simplicity (that can be further refined to include multilayer adsorption and regular-solution interactions8), we can obtain:
Furthermore, a first-order premelting transition can result in a discontinuous increase in the GB excess entropy to accelerate the GB energy reduction with increasing temperature (Fig. 1a, albeit that studies showed GB structural disordering can often increase GB mobilities44.). Likewise, a first-order adsorption transitions can also cause a discontinuous increase in the GB adsorption (a.k.a. segregation), which accelerates the GB energy reduction with increasing chemical potential (Fig. 2b)23, 29, 47. It will be exciting to seek coupled GB disordering or adsorption transitions in HEGBs to further accelerate the \(\gamma _GB\) reduction (i.e., increase the effective GB entropy) to potentially achieve zero GB energy within the solid solubility limit (to realize nanoalloys with equilibrium grain sizes at a true thermodynamic equilibrium).
A further extension is to investigate other types of high-entropy interfaces beyond GBs. For example, can we use high-entropy surfaces to stabilize nanoparticles for high-temperature catalysis or other applications?52 Do high-entropy surfaces (or solid-solid heterointerfaces) have unique properties?
This Recommendation specifies the design principles and requirements for the entropy sources used by Random Bit Generators, and the tests for the validation of entropy sources. These entropy sources are intended to be combined with Deterministic Random Bit Generator mechanisms that are specified in SP 800-90A to construct Random Bit Generators, as specified in SP 800-90C.
Once you have the required PGP keys, you can verify the release. Download borderwallets.txt and borderwallets.txt.asc from the links above to the same directory (for example, your Downloads directory). In your terminal, change directory (cd) to the one where the downloaded files are, for example:
New software package added to PhysioToolkit: TEWP (March 4, 2016, 1 a.m.) The Transfer Entropy With Partitioning package is a repository of MATLAB functions that can estimate transfer entropy (information flow) from one time series to another using a non-parametric partitioning algorithm. Also included is an example data set that the implemented algorithms can be applied to.
This is a repository of MATLAB functions that can estimate transfer entropy (information flow) from one time series to another using a non-parametric partitioning algorithm. Also included is an example data set that the implemented algorithms can be applied to. The functions were tested in MATLAB R2016b on 03 March 2016.
The high entropy alloys (HEAs), which are also often referred to as complex concentrated alloys (CCAs) and multi-principal element alloys (MPEAs), form a new concept for alloy design. Many empirical rules were proposed to predict the stability of solid solution phases in HEAs, yet the CALPHAD method provides the most convenient and reliable solution in this regard. Here we will use a few examples to demonstrate how one can use Pandat software and PanHEA database to optimize the alloy chemistry and processing conditions to achieve the desired properties for high entropy alloys.
Calphad based high-throughput calculation (HTC) provides a powerful tool for explore high-entropy alloys (HEA) with targeted properties. The potential alloy compositions can be screened out from thousands of initial compositions. This figure shows the flowchart and results of the high-throughput calculations in the Al-Cr-Fe-Mn-Ti system. Eight promising alloys are determined from more than three thousand initial alloy compositions. In this example, all the HTC calculations and results analysis are carried out in the PanPhaseDiagram module.
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For an image, local entropy is related to the complexity contained in a givenneighborhood, typically defined by a structuring element. The entropy filter candetect subtle variations in the local gray level distribution.
In the first example, the image is composed of two surfaces with two slightlydifferent distributions. The image has a uniform random distribution in therange [-15, +15] in the middle of the image and a uniform random distribution inthe range [-14, 14] at the image borders, both centered at a gray value of 128.To detect the central square, we compute the local entropy measure using acircular structuring element of a radius big enough to capture the local graylevel distribution. The second example shows how to detect texture in the cameraimage using a smaller structuring element.
More about this item Keywords inequality; diversity; concentration; entropy; Shannon; Simpson; Gini; Herfindahl; Hirschman; Turing; Stata; All these keywords.Statistics Access and download statistics Corrections All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:boc:bocode:s458272. See general information about how to correct material in RePEc.
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The first one is increasing the number of molecules in a reaction, OK? So any reaction that's going to make more moles of molecules or more equivalents of molecules after the reaction is over is going to be entropically favored, why? Because what it does is it allows us to arrange these molecules in more ways, alright? So here's a really good example, thermal cracking OK? This is used by the petroleum industry to take large hydrocarbons ones that don't really do anything you can't put them in your car or anything then they put them with hydrogen in high heat, OK? And what happens is that these long hydrocarbons spontaneously start breaking into smaller pieces, OK? Why would this be a favored reaction, OK? It actually takes energy to break those bonds so why would these long hydrocarbons break? The reason is because at high enough temperature what starts to happen is that if we can break one molecule into ten molecule, right? That's going to be in entropically favored because now I can arrange those molecules in different orders, OK? So what that means is that the chances are that if I have two systems that are of equal energy one is that I have all the molecules perfectly arranged that they're all in a line or all of the molecules scattered all over the place which one is going to be more probable? The one where it's scattered, OK? And that's why thermal cracking is favored you take large hydrocarbons and you turn them into smaller ones by using high heat, high heat then makes the entropy part of the equation very very favored so now the more pieces that can break it into the more entropically favored that is, alright? This is just one example but there's lots of examples in organic chemistry of reactions that make more molecules than they start off with meaning that they're entropically favored, OK? 041b061a72