On axiomatic characterization of information-theoretic measures

1974 ◽  
Vol 10 (4) ◽  
pp. 337-346 ◽  
Author(s):  
Bhu Dev Sharma ◽  
Inder Jeet Taneja
Keyword(s):  
Axiomatic Characterization ◽  
Information Theoretic ◽  
Information Theoretic Measures

scholarly journals Using time causal quantifiers to characterize sleep stages

2019 ◽  
Author(s):  
Diego M. Mateos ◽  
Jaime Gómez-Ramírez ◽  
Osvaldo A. Rosso
Keyword(s):  
Temporal Dynamics ◽  
Single Channel ◽  
Well Being ◽  
Sleep Stages ◽  
Eeg Signals ◽  
Information Theoretic ◽  
Information Theoretic Measures ◽  
Sleep Recording ◽  
Vector Approach

AbstractSleep plays substantial role in daily cognitive performance, mood and memory. The study of sleep has attracted the interest of neuroscientists, clinicans and the overall population, with increasing number of adults suffering from insufficient amounts of sleep. Sleep is an activity composed of different stages whose temporal dynamics, cycles and inter dependencies are not fully understood. Healthy body function and personal well being, however, depends on proper unfolding and continuance of the sleep cycles. The characterization of the different sleep stages can be undertaken with the development of biomarkers derived from sleep recording. For this purpose, in this work we analyzed single-channel EEG signals from 106 healthy subjects. The signals were quantified using the permutation vector approach using five different information theoretic measures: i) Shannon’s entropy, ii) MPR statistical complexity, iii) Fisher information, iv) Renyí Min-entropy and v) Lempel-Ziv complexity. The results show that all five information theory-based measures make possible to quantify and classify the underlying dynamics of the different sleep stages. In addition to this, we combine these measures to show that planes containing pairs of measures, such as the plane composed of Lempel-Ziv and Shannon, have a better performance for differentiating sleep states than measures used individually for the same purpose.

Large-sample confidence intervals of information-theoretic measures in linguistics

2020 ◽  
Vol 6 (1) ◽  
pp. 19-54
Author(s):  
Ryan Ka Yau Lai ◽  
Youngah Do
Keyword(s):  
Maximum Likelihood ◽  
Corpus Linguistics ◽  
Delta Method ◽  
Confidence Bounds ◽  
Likelihood Estimator ◽  
Information Theoretic ◽  
Leibler Divergence ◽  
Information Theoretic Measures ◽  
Data Points ◽  
Measure Of Uncertainty

This article explores a method of creating confidence bounds for information-theoretic measures in linguistics, such as entropy, Kullback-Leibler Divergence (KLD), and mutual information. We show that a useful measure of uncertainty can be derived from simple statistical principles, namely the asymptotic distribution of the maximum likelihood estimator (MLE) and the delta method. Three case studies from phonology and corpus linguistics are used to demonstrate how to apply it and examine its robustness against common violations of its assumptions in linguistics, such as insufficient sample size and non-independence of data points.

scholarly journals Optimized permutation testing for information theoretic measures of multi-gene interactions

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
James M. Kunert-Graf ◽  
Nikita A. Sakhanenko ◽  
David J. Galas
Keyword(s):  
Large Scale ◽  
Permutation Test ◽  
Association Studies ◽  
Genome Wide Association Studies ◽  
Permutation Testing ◽  
Exact Test ◽  
Information Theoretic ◽  
Information Theoretic Measures ◽  
Full Analysis ◽  
Computational Bottleneck

Abstract Background Permutation testing is often considered the “gold standard” for multi-test significance analysis, as it is an exact test requiring few assumptions about the distribution being computed. However, it can be computationally very expensive, particularly in its naive form in which the full analysis pipeline is re-run after permuting the phenotype labels. This can become intractable in multi-locus genome-wide association studies (GWAS), in which the number of potential interactions to be tested is combinatorially large. Results In this paper, we develop an approach for permutation testing in multi-locus GWAS, specifically focusing on SNP–SNP-phenotype interactions using multivariable measures that can be computed from frequency count tables, such as those based in Information Theory. We find that the computational bottleneck in this process is the construction of the count tables themselves, and that this step can be eliminated at each iteration of the permutation testing by transforming the count tables directly. This leads to a speed-up by a factor of over 103 for a typical permutation test compared to the naive approach. Additionally, this approach is insensitive to the number of samples making it suitable for datasets with large number of samples. Conclusions The proliferation of large-scale datasets with genotype data for hundreds of thousands of individuals enables new and more powerful approaches for the detection of multi-locus genotype-phenotype interactions. Our approach significantly improves the computational tractability of permutation testing for these studies. Moreover, our approach is insensitive to the large number of samples in these modern datasets. The code for performing these computations and replicating the figures in this paper is freely available at https://github.com/kunert/permute-counts.

An Axiomatic Characterization of a Class of Petri Nets

1991 ◽  
Vol 14 (4) ◽  
pp. 477-491
Author(s):  
Waldemar Korczynski
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Axiomatic Characterization ◽  
Algebraic Characterization

In this paper an algebraic characterization of a class of Petri nets is given. The nets are characterized by a kind of algebras, which can be considered as a generalization of the concept of the case graph of a (marked) Petri net.

Insights into codeswitching from online communication: Effects of language preference and conditions arising from vocabulary richness

2021 ◽  
pp. 1-7
Author(s):  
Laurie Beth Feldman ◽  
Vidhushini Srinivasan ◽  
Rachel B. Fernandes ◽  
Samira Shaikh
Keyword(s):  
Online Communication ◽  
Language Preference ◽  
Lexical Diversity ◽  
Information Theoretic ◽  
Vocabulary Richness ◽  
Twitter Data ◽  
Language Mixing ◽  
Communication Effects ◽  
Information Theoretic Measures ◽  
Spanish Bilinguals

Abstract Twitter data from a crisis that impacted many English–Spanish bilinguals show that the direction of codeswitches is associated with the statistically documented tendency of single speakers to prefer one language over another in their tweets, as gleaned from their tweeting history. Further, lexical diversity, a measure of vocabulary richness derived from information-theoretic measures of uncertainty in communication, is greater in proximity to a codeswitch than in productions remote from a switch. The prospects of a role for lexical diversity in characterizing the conditions for a language switch suggest that communicative precision may induce conditions that attenuate constraints against language mixing.

scholarly journals Information-Theoretic Measures and Modeling Stock Market Volatility: A Comparative Approach

Risks ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 89
Author(s):  
Muhammad Sheraz ◽  
Imran Nasir
Keyword(s):  
Stock Market ◽  
Stock Returns ◽  
Stock Exchange ◽  
Approximate Entropy ◽  
Market Volatility ◽  
Comparative Approach ◽  
Stock Market Volatility ◽  
Information Theoretic ◽  
Information Theoretic Measures ◽  
Garch Modeling

The volatility analysis of stock returns data is paramount in financial studies. We investigate the dynamics of volatility and randomness of the Pakistan Stock Exchange (PSX-100) and obtain insights into the behavior of investors during and before the coronavirus disease (COVID-19 pandemic). The paper aims to present the volatility estimations and quantification of the randomness of PSX-100. The methodology includes two approaches: (i) the implementation of EGARCH, GJR-GARCH, and TGARCH models to estimate the volatilities; and (ii) analysis of randomness in volatilities series, return series, and PSX-100 closing prices for pre-pandemic and pandemic period by using Shannon’s, Tsallis, approximate and sample entropies. Volatility modeling suggests the existence of the leverage effect in both the underlying periods of study. The results obtained using GARCH modeling reveal that the stock market volatility has increased during the pandemic period. However, information-theoretic results based on Shannon and Tsallis entropies do not suggest notable variation in the estimated volatilities series and closing prices. We have examined regularity and randomness based on the approximate entropy and sample entropy. We have noticed both entropies are extremely sensitive to choices of the parameters.

Information-theoretic characterization of eye-tracking signals with relation to cognitive tasks

2021 ◽  
Vol 31 (3) ◽  
pp. 033107
Author(s):  
F. R. Iaconis ◽  
A. A. Jiménez Gandica ◽  
J. A. Del Punta ◽  
C. A. Delrieux ◽  
G. Gasaneo
Keyword(s):  
Eye Tracking ◽  
Cognitive Tasks ◽  
Information Theoretic ◽  
Theoretic Characterization

Measuring the Complexity of Additive Manufacturing Supply Chains

2017 ◽  
Author(s):  
Ardeshir Raihanian Mashhadi ◽  
Sara Behdad
Keyword(s):  
Supply Chain ◽  
Additive Manufacturing ◽  
Supply Chains ◽  
Product Complexity ◽  
Information Theoretic ◽  
Manufacturing Method ◽  
Management Domain ◽  
Information Theoretic Measures ◽  
Production Cycles ◽  
Supply Planning

Complexity has been one of the focal points of attention in the supply chain management domain, as it deteriorates the performance of the supply chain and makes controlling it problematic. The complexity of supply chains has been significantly increased over the past couple of decades. Meanwhile, Additive Manufacturing (AM) not only revolutionizes the way that the products are made, but also brings a paradigm shift to the whole production system. The influence of AM extends to product design and supply chain as well. The unique capabilities of AM suggest that this manufacturing method can significantly affect the supply chain complexity. More product complexity and demand heterogeneity, faster production cycles, higher levels of automation and shorter supply paths are among the features of additive manufacturing that can directly influence the supply chain complexity. Comparison of additive manufacturing supply chain complexity to its traditional counterpart requires a profound comprehension of the transformative effects of AM on the supply chain. This paper first extracts the possible effects of AM on the supply chain and then tries to connect these effects to the drivers of complexity under three main categories of 1) market, 2) manufacturing technology, and 3) supply, planning and infrastructure. Possible impacts of additive manufacturing adoption on the supply chain complexity have been studied using information theoretic measures. An Agent-based Simulation (ABS) model has been developed to study and compare two different supply chain configurations. The findings of this study suggest that the adoption of AM can decrease the supply chain complexity, particularly when product customization is considered.

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