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How to Use Entropy Download to Learn Information Theory and Entropy



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Lead Investigator, Brigham and Women's HospitalResearch Director, Medical Biodynamics Program (MBP)Contact NewsResearchPublicationsPresentationsVideosResourcesPeopleLinks HOME / RESOURCES / EZ Entropy: A MATLAB App for the entropy analysis of physiological signals This page shares the MATLAB application EZ Entropy that I developed for easing the use of entropy analysis. This App has been published in the following paper:




entropy download



It has long been a norm that researchers extract knowledge from literature to design materials. However, the avalanche of publications makes the norm challenging to follow. Text mining (TM) is efficient in extracting information from corpora. Still, it cannot discover materials not present in the corpora, hindering its broader applications in exploring novel materials, such as high-entropy alloys (HEAs). Here we introduce a concept of context similarity" for selecting chemical elements for HEAs, based on TM models that analyze the abstracts of 6.4 million papers. The method captures the similarity of chemical elements in the context used by scientists. It overcomes the limitations of TM and identifies the Cantor and Senkov HEAs. We demonstrate its screening capability for six- and seven-component lightweight HEAs by finding nearly 500 promising alloys out of 2.6 million candidates. The method thus brings an approach to the development of ultrahigh-entropy alloys and multicomponent materials.


Text mining (TM) is an artificial intelligence method to analyze and discover scientific knowledge in literature. It has been used in several fields, such as materials science1,2,3,4,5, political science6,7, public health8,9,10,11, etc. TM has the potential for automatic materials discovery given sufficiently large corpora, such as for the material group of high- and medium-entropy alloys (HEAs, MEAs)12,13,14,15,16,17,18, where more than 10,000 papers have been published19. Several TM methods have been suggested that build on corpora as training data20. One group of TM algorithms uses vectors to represent words, known as word-embedding algorithms21,22,23,24. Operations on the vectors provide meaningful information. For example, the difference between vector FCC" and vector Al" is approximately equal to that between vector W" and vector BCC", since the chemical element Al" is commonly found with a face-centered-cubic (FCC) crystal structure and W" with a body-centered-cubic (BCC) structure. These vectors are determined by maximizing the co-occurrence probability of an embedded word and its neighbors within the corpora. The cosine of two vectors measures the similarity of the words they represent. When increasing the frequency of the word CoCrFeNiV" as the neighbor of CoCrFeMnNi" by 10 times in a TM (skip-gram) model, its similarity ranking increases by 13 (Supplementary Fig. 1). TM models trained on specially selected corpora are predictive, as the presence of less relevant text items can reduce the relative frequency of keywords1.


It has a neural-network structure but with only one hidden layer between the input and output layers21,22 (a). The training data fed into the model are the processed corpora downloaded from an online database41. The corpora are first tokenized into separate words or phrases (combinations of two or more words with unique meanings) and then translated into vectors. In the one-hot representative of a word vector, each word is represented by a sparse vector with only one nonzero element. The word vectors are connected to all neurons in the hidden layer; the latter is also fully connected with the output layer which represents the appearance probabilities of words in their context. For a given window size of the words that define their context, the skip-gram algorithm maximizes the probability of the word that appeared in that context. Once the neural network is optimized, the key information is stored in the hidden layer. As examples of its application, similar words of Fe" and Ni" are shown in b, c, respectively.


Similar to the BCC HEAs, the averaged context similarity \(\barS\) is calculated for a group of FCC HEAs and shown in Supplementary Figure 2. Again, we limit the constitutional elements to the transition-metal elements from V to Cu of the third group. Taking the five-component alloys as an example, we show the similarity \(\barS\) for individual years in Supplementary Fig. 2a. This test protocol shows that the concept effectively identifies HEAs long before they were found by conventional alloy-design methods. The Cantor alloy was first reported in 2004, but it was ranked as the second most promising solid-solution HEA by our method already before 2004. The seminal paper of Cantor et al. did not receive much attention immediately after its publication, but its impact has increased exponentially since the last decade19. This trend is correctly reflected by its ranking in Supplementary Fig. 2a. The second and third most promising HEAs are MnFeCoNiCu31 and CrFeCoNiCu13, which were also synthesized. We also calculate their tendency to form solid solutions by using the γ parameter30. As presented in Supplementary Fig. 2b, the two quantities are linearly correlated, similar to the case of the BCC HEAs. This trend further confirms the significance of the \(\barS\) parameter in screening for high-entropy solid solutions.


The method of context similarity" picks element candidates for HEAs, which is the first step for designing high-entropy solid solutions. Then, various procedures can be developed for further screening, refining, and filtering the results, assisted by the methods grouped under the umbrella of ICME (integrated computational materials engineering)32,33 and included in the materials genome initiative34. ICME is an approach for designing materials and microstructures using mean-field thermodynamics and kinetics tools as well as ab-initio and structure-property simulation methods. A few examples are provided below to show how to integrate the context-similarity method with ICME to accelerate the design process.


Scientific texts appear in various formats, such as books, journals, etc., either in printed or electronic versions. The first step for corpora collection is to unify all these texts in a single digital format that can be directly used in machine-learning models (Fig. 1a of the main text). Here the training corpora of 6.4 million abstracts are downloaded through the ELSEVIER Scopus API41. The latter can retrieve abstracts in bulk with the journal ISSN and publishing year as input. We use the ISSN list generated by Tshitoyan et al.1 as the starting point. The abstracts are stored in JSON format along with the metadata, such as authors, years of publication, keywords, journals, etc. In addition, we also manually add important journals and abstracts for HEAs that are absent in the first round of abstract collections. The representative journals for metallic materials of the past two decades include Acta Mater., Journal of Alloys and Compound, Materials Science and Engineering: A, and Advanced Engineering Materials. Note that there is a weekly download quota for regular Scopus developer API. The entire collection process of 6.4 million abstracts can take several months.


The article DOIs used to generate the training corpora in this study have been deposited in our GitHub repository under the accession link ( ). The raw training corpora data are protected and not shared due to the data privacy rules of Elsevier. Users can download it after they open an Elsevier account since all the papers are stored in their database. Details and guidelines to use the API and papers provided by Elsevier are here: Any reader can register there and receive an API account to reproduce the results. All copyright rules explained by Elsevier on that webpage must be followed.


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.


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:


entropy:EQ+ is the perfect tool when it comes to complex mixing tasks. The highly specialized signal processing of entropy:EQ+ allows mixing engineers to get a tight drum sound or crispy bass within seconds.


From subtle modifications of natural sounds to the excessive reshaping of complex audio material - entropy:EQ+ is a great creative tool for designing sounds or customizing soundscapes for movies or games.


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. 2ff7e9595c


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