Entropy Measures Research Articles

A scalable MapReduce-based design of an unsupervised entity resolution system.

Traditional data curation processes typically depend on human intervention. As data volume and variety grow exponentially, organizations are striving to increase efficiency of their data processes by automating manual processes and making them as unsupervised as possible. An additional challenge is to make these unsupervised processes scalable to meet the demands of increased data volume. This paper describes the parallelization of an unsupervised entity resolution (ER) process. ER is a component of many different data curation processes because it clusters records from multiple data sources that refer to the same real-world entity, such as the same customer, patient, or product. The ability to scale ER processes is particularly important because the computation effort of ER increases quadratically with data volume. The Data Washing Machine (DWM) is an already proposed unsupervised ER system which clusters references from diverse data sources. This work aims at solving the single-threaded nature of the DWM by adopting the parallelization nature of Hadoop MapReduce. However, the proposed parallelization method can be applied to both supervised systems, where matching rules are created by experts, and unsupervised systems, where expert intervention is not required. The DWM uses an entropy measure to self-evaluate the quality of record clustering. The current single-threaded implementations of the DWM in Python and Java are not scalable beyond a few 1,000 records and rely on large, shared memory. The objective of this research is to solve the major two shortcomings of the current design of the DWM which are the creation and usage of shared memory and lack of scalability by leveraging on the power of Hadoop MapReduce. We propose Hadoop Data Washing Machine (HDWM), a MapReduce implementation of the legacy DWM. The scalability of the proposed system is displayed using publicly available ER datasets. Based on results from our experiment, we conclude that HDWM can cluster from 1,000's to millions of equivalent references using multiple computational nodes with independent RAM and CPU cores.

A new flexible distribution: Statistical inference with application

A flexible distribution for the analysis of bounded data is proposed. The new model is generalized through the transmuted approach, and the resultant model is named “transmuted modified Lehmann-type II distribution.” A comprehensive analysis of key characteristics is performed, including the shape of the model, survival, and hazard function, analytical expressions of mode, quantile function, ordinary moments, quantile function, and stress–strength reliability. Some famous entropy measures are also derived. The model parameters have been estimated using four distinct methods, including maximum likelihood estimation, Anderson Darling, Cramer–von Misses, and ordinary least squares. A detailed simulation study is used to evaluate the behavior of all derived estimators. Finally, a dataset was used to demonstrate the utility of the proposed distribution.

Multi-attribute decision making based on VIKOR with probabilistic linguistic term sets: An application to the risk evaluation of foreign direct investment.

The multiple global environments have triggered changes in the international environment, leading to a sharp decline of foreign direct investment (FDI) compared to pre-pandemic level. To evaluate the investment risk of FDI and make optimal investment decision becomes the most important issue for investors. This paper focuses on the evaluation of investment risk for FDI. First, an index system for risk evaluation of FDI is constructed. Then, we introduce the probabilistic linguistic entropy and cross entropy measures, based on which, a programming model is developed to identify the objective attribute weights. A composite weight derivation method, which takes both the objective attribute weights and the subjective attribute weights into account, is further introduced. In view of attributes' uncertainty and fuzziness and the conflicting characteristics of some attributes, the VIKOR (the Serbian name: VlseKriterijumska Optimizacija I Kompromisno Resenje, means multi-criteria optimization and compromise solution) method is used to evaluate the risk of FDI under the probabilistic linguistic environment. Furthermore, a case study is presented to illustrate the proposed method. The comparative analysis and some further discussions verify the validity of the proposed method for the FDI risk evaluation.

Optimal Investment with Risk Controlled by Weighted Entropic Risk Measures

Optimal Investment with Risk Controlled by Weighted Entropic Risk Measures

Shifts of finite type on locally finite groups

Abstract In this work we prove that every shift of finite type (SFT), sofic shift, and strongly irreducible shift on locally finite groups has strong dynamical properties. These properties include that every sofic shift is an SFT, every SFT is strongly irreducible, every strongly irreducible shift is an SFT, every SFT is entropy minimal, and every SFT has a unique measure of maximal entropy, among others. In addition, we show that if every SFT on a group is strongly irreducible, or if every sofic shift is an SFT, then the group must be locally finite, and this extends to all of the properties we explore. These results are collected in two main theorems which characterize the local finiteness of groups by purely dynamical properties. In pursuit of these results, we present a formal construction of free extension shifts on a group G, which takes a shift on a subgroup H of G, and naturally extends it to a shift on all of G.

Measurement of Enthalpy and Entropy of a Model Electrocatalyst for the Oxygen Evolution Reaction

AbstractExperimentally determined thermodynamic parameters are rarely reported for electrocatalytic reactions including the oxygen evolution reaction (OER). Yet, they contain unique and valuable mechanistic insight and present a missing link to theoretical investigations. Herein, a protocol for determining thermodynamic properties of the rate determining state and intermediate (RDSI) of the OER is presented. Cobalt oxide is investigated at pH 7 as a case study. Two different approaches are employed: steady state polarization (SSP) that uses chronopotentiometry at different temperatures and current values, and potentiostatic electrochemical impedance spectroscopy (PEIS) at different DC voltages and temperatures. The data is used to fit a 3D plane from which entropy and enthalpy of the RDSI are obtained. The data analysis requires an appropriate filtering of the data. Hence, we discuss suitable figures of merit for establishing appropriate filtering criteria. The values obtained are 0.72 and −0.39 eV (at 298 K) for enthalpic and entropic contributions, respectively. The obtained values are reproducible for both approaches and consistent with literature.

A novel q-rung orthopair fuzzy best-worst method, Shannon entropy and MARCOS method for mobile medical app service quality evaluation

In this study, we propose a new hybrid multi-criteria decision-making (MCDM) methodology based on q-rung orthopair fuzzy sets (q-ROFSs) by integrating best-worst method (BWM), Shannon entropy method (SEM) and measurement of alternatives and ranking according to compromise solution (MARCOS). The methodology consists of two main phases: weight determination and alternative ranking. Firstly, the determination of the weight is mainly from both subjective and objective aspects. To determine the subjective weights, we propose a q-rung orthopair fuzzy best-worst method (q-ROF-BWM) satisfying additive consistency, which requires fewer comparisons for more reliable results, and define a new consistency ratio (CR) to test the consistency of comparisons. Additionally, objective weights are obtained using SEM extended to q-ROFSs, which are ignored by many MCDM methods. In the second stage, a new integrated alternative ranking approach called q-ROF-MARCOS is proposed, which does not become more complex with the increase in the number of criteria or alternatives. Finally, the proposed method is applied to the evaluation problem of mobile medical app service quality, and a new mobile medical app service quality evaluation index system based on SERVQUAL model is established. Sensitivity and comparative analysis validate the method’s effectiveness, rationality, superiority, and robustness.

Measures of maximal entropy of bounded density shifts

Abstract We find sufficient conditions for bounded density shifts to have a unique measure of maximal entropy. We also prove that every measure of maximal entropy of a bounded density shift is fully supported. As a consequence of this, we obtain that bounded density shifts are surjunctive.

Avenues of decarbonisation in the dynamics of processed food supply chains: Towards responsible production consumption

Nowadays, the demand for processed food items is surging. To fulfil the enhanced demand, a significant impact is laid on the environment, which enhances the carbon footprint being generated. Hence, to overcome this, the avenues of decarbonisation need to be explored. The presented work is aimed at promoting the decarbonisation of the existing practices within the processed food supply chains. It finds strong compliance with the sustainable development goal (SDG-12), focusing on responsible production-consumption mechanisms. For the same, key enactors of decarbonisation are identified and mapped with the practices at various stages of food supply chains, i.e. upstream, downstream, and other allied practices. Based upon these enactors, a relational, hierarchical framework is developed to provide a comprehensive perspective on complex intricacies. This framework is analysed with an innovative approach which comprises the fundamentals of Interval-Valued Intuitionistic Hesitant Fuzzy Set with the Entropy measures. It results in the outranking of the enactors relative to its importance in the decarbonisation of processed food supply chains. Furthermore, the empirical findings are validated by the sensitivity analysis to felicitate robust decision-making. The outcomes of the presented work provide a roadmap and stepped approach to achieve the decarbonisation goals and make production-consumption mechanisms sustainable. It finds implications in the development of the framework, policy formulation, and decisional attributes for the decarbonisation of food supply chains. It focuses on the adoption of strategies that align with global efforts to mitigate climate change and promote a sustainable future.

Computation of Structural Descriptors of Pyrene Cored Dendrimers through Quotient Graph Approach and Its Graph Entropy Measures

Dendrimers are highly defined hyperbranched artificial macromolecules, synthesised by convergent or divergent approach with specific applications in various fields. Dendrimers can be represented as graph models, from which a quantitative description can be drawn in relation with their structural properties. The distance-based and the degree-based descriptors have great importance and huge applications in structural chemistry. These indices together with entropy measures are found to be more effective and have found application in scientific fields. The idea of graph entropy is to characterise the complexity of graphs. The use of these graph invariants in quantitative structure property relationship and quantitative structure activity relationship studies has become of major interest in recent years. In this paper, the distance-based molecular descriptors of pyrene cored dendrimers are studied applying the technique of converting original graph into quotient graphs using Θ∗-classes. It is to be noted that, since the pyrene cored dendrimer, Gn is not a partial cube, usual cut method is not applicable. Further, various degree-based descriptors and their corresponding graph entropies of the pyrene cored dendrimers are also studied. Based on the obtained results, a comparative analysis as well as a regression analysis was carried out.

Optimizing the measurement of sample entropy in resting-state fMRI data.

The complexity of brain signals may hold clues to understand brain-based disorders. Sample entropy, an index that captures the predictability of a signal, is a promising tool to measure signal complexity. However, measurement of sample entropy from fMRI signals has its challenges, and numerous questions regarding preprocessing and parameter selection require research to advance the potential impact of this method. For one example, entropy may be highly sensitive to the effects of motion, yet standard approaches to addressing motion (e.g., scrubbing) may be unsuitable for entropy measurement. For another, the parameters used to calculate entropy need to be defined by the properties of data being analyzed, an issue that has frequently been ignored in fMRI research. The current work sought to rigorously address these issues and to create methods that could be used to advance this field. We developed and tested a novel windowing approach to select and concatenate (ignoring connecting volumes) low-motion windows in fMRI data to reduce the impact of motion on sample entropy estimates. We created utilities (implementing autoregressive models and a grid search function) to facilitate selection of the matching length m parameter and the error tolerance r parameter. We developed an approach to apply these methods at every grayordinate of the brain, creating a whole-brain dense entropy map. These methods and tools have been integrated into a publicly available R package ("powseR"). We demonstrate these methods using data from the ABCD study. After applying the windowing procedure to allow sample entropy calculation on the lowest-motion windows from runs 1 and 2 (combined) and those from runs 3 and 4 (combined), we identified the optimal m and r parameters for these data. To confirm the impact of the windowing procedure, we compared entropy values and their relationship with motion when entropy was calculated using the full set of data vs. those calculated using the windowing procedure. We then assessed reproducibility of sample entropy calculations using the windowed procedure by calculating the intraclass correlation between the earlier and later entropy measurements at every grayordinate. When applying these optimized methods to the ABCD data (from the subset of individuals who had enough windows of continuous "usable" volumes), we found that the novel windowing procedure successfully mitigated the large inverse correlation between entropy values and head motion seen when using a standard approach. Furthermore, using the windowed approach, entropy values calculated early in the scan (runs 1 and 2) are largely reproducible when measured later in the scan (runs 3 and 4), although there is some regional variability in reproducibility. We developed an optimized approach to measuring sample entropy that addresses concerns about motion and that can be applied across datasets through user-identified adaptations that allow the method to be tailored to the dataset at hand. We offer preliminary results regarding reproducibility. We also include recommendations for fMRI data acquisition to optimize sample entropy measurement and considerations for the field.

A New Logic, a New Information Measure, and a New Information-Based Approach to Interpreting Quantum Mechanics.

The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of partitions. Or, putting it the other way around, the math of partitions is a skeletal version of the math of QM. The key concepts throughout this progression from logic, to logical information, to quantum theory are distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. The distinctions of a partition are the ordered pairs of elements from the underlying set that are in different blocks of the partition and logical entropy is defined (initially) as the normalized number of distinctions. The cognate notions of definiteness and distinguishability run throughout the math of QM, e.g., in the key non-classical notion of superposition (=ontic indefiniteness) and in the Feynman rules for adding amplitudes (indistinguishable alternatives) versus adding probabilities (distinguishable alternatives).

Information entropy facilitates (not impedes) lexical processing during language comprehension.

It is well known that contextual predictability facilitates word identification, but it is less clear whether the uncertainty associated with the current context (i.e., its lexical entropy) influences sentence processing. On the one hand, high entropy contexts may lead to interference due to greater number of lexical competitors. On the other hand, predicting multiple lexical competitors may facilitate processing through the preactivation of shared semantic features. In this study, we examined whether entropy measured at the trial level (i.e., for each participant, for each item) corresponds to facilitatory or inhibitory effects. Trial-level entropy captures each individual's knowledge about specific contexts and is therefore a more valid and sensitive measure of entropy (relative to the commonly employed item-level entropy). Participants (N = 112) completed two experimental sessions (with counterbalanced orders) that were separated by a 3- to 14-day interval. In one session, they produced up to 10 completions for sentence fragments (N = 647). In another session, they read the same sentences including a target word (whose entropy value was calculated based on the produced completions) while reading times were measured. We observed a facilitatory (not inhibitory) effect of trial-level entropy on lexical processing over and above item-level measures of lexical predictability (including cloze probability, surprisal, and semantic constraint). Extra analyses revealed that greater semantic overlap between the target and the produced responses facilitated target processing. Thus, the results lend support to theories of lexical prediction maintaining that prediction involves broad activation of semantic features rather than activation of full lexical forms.

Uncertainty measurement for incomplete lattice-valued information system

We analyze the properties and characteristics of the information structure in incomplete lattice-valued information system (ILIS), we redefine the information structure and the dependence and information distance between the two information structures. In addition, in order to evaluate the uncertainty of ILIS, the concepts of granular measure and entropy measure are expounded, including information granulation, information quantity, rough entropy and information entropy. Finally, we carry out numerical experiments to verify the feasibility of the method, and carry out effective statistical analysis. These results are conducive to the establishment of granular computing framework in ILIS.

On K-Banhatti, Revan Indices and Entropy Measures of MgO(111) Nanosheets via Linear Regression

The structure and topology of chemical compounds can be determined using chemical graph theory. Using topological indices, we may uncover much about connectivity, complexity, and other important aspects of molecules. Numerous research investigations have been conducted on the K-Banhatti indices and entropy measurements in various fields, including the study of natural polymers, nanotubes, and catalysts. At the same time, the Shannon entropy of a graph is widely used in network science. It is employed in evaluating several networks, including social networks, neural networks, and transportation systems. The Shannon entropy enables the analysis of a network’s topology and structure, facilitating the identification of significant nodes or structures that substantially impact network operation and stability. In the past decade, there has been a considerable focus on investigating a range of nanostructures, such as nanosheets and nanoparticles, in both experimental and theoretical domains. As a very effective catalyst and inert substrate, the MgO nanostructure has received a lot of interest. The primary objective of this research is to study different indices and employ them to look at entropy measures of magnesium oxide(111) nanosheets over a wide range of p values, including p=1,2,3,…,j. Additionally, we conducted a linear regression analysis to establish the correlation between indices and entropies.

Dynamic Weighted Cumulative Residual Entropy Estimators for Laplace Distribution: Bayesian Approach

Objectives: To develop Bayesian estimators of dynamic weighted cumulative residual entropy (DWCRE) for Laplace distribution and to investigate posterior risks using various priors and loss functions. Methods: Weighted entropy measure of information is provided by a probabilistic experiment whose basic events are described by their objective probabilities and some qualitative (objective or subjective) weights. In this paper, we have used priors (Jeffrey’s, Hartigan, Uniform and Gumble Type II) and several loss functions. Findings: Bayesian estimators and associated posterior risks for Laplace distribution have been derived for different priors and loss functions. Monte Carlo Simulation study and graphical analyses have also been presented along with the conclusion. Through the comprehensive simulation study in the paper, it has been observed that Hartigan prior is better than other priors in terms of the posterior risk whereas Uniform prior has always higher posterior risk. Novelty: The introduction of new Bayesian estimators and their posterior risks for dynamic weighted cumulative residual entropy (DWCRE) of Laplace distribution. Keywords: Bayesian estimators, Laplace distribution, Fisher information matrix, Loss functions, Priors

Fractal dimensions and machine learning for detection of Parkinson’s disease in resting-state electroencephalography

Parkinson’s disease (PD) is an incurable neurological disorder that degenerates the cerebrospinal nervous system and hinders motor functions. Electroencephalography (EEG) signal analysis can provide reliable information regarding PD conditions. However, EEG is a complex, multichannel, and nonlinear signal with noise that problematizes identifying PD symptoms. A few studies have employed fractal dimension (FD) to extract distinguishing PD features from EEG signals. However, no exploratory study exists, as per our knowledge, on the efficiency of the different FD measures. We aim to conduct a comparative analysis of the various FDs that, as feature extraction measures, can discriminate PD patients who are ON and OFF medication from healthy controls using ML architecture. This study has implemented and analyzed several techniques for segmentation, feature extraction, and ML models. The results show that k-nearest neighbors (KNN) classifier with Higuchi FD and 90% overlap for segmented window delivers the highest accuracies, yielding a mean accuracy of 99.65±0.15%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$99.65\\pm 0.15\\%$$\\end{document} for PD patients ON medication and 99.45±0.18%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$99.45\\pm 0.18\\%$$\\end{document} for PD patients OFF medication, respectively. The model accurately identifies the signs of the disease in resting-state EEG with almost equivalent accuracy in both OFF and ON medication patients. To enhance the interpretability in our study, we leveraged XGB’s feature importance to generate brain topographic plots. This integration of explainable AI (XAI) enhanced the transparency and comprehensibility of our model’s classifications. Additionally, a comparison between the performance of FD and a few entropy measures has also been drawn to validate the significance of FD as a superior feature extraction measure. This study contributes to the body of knowledge with an architectural pipeline for detecting PD in resting-state EEG while emphasizing fractal dimension as an effective way of extracting salient features from EEG signals.

The confined helium atom: An information–theoretic approach

AbstractIn this article, we study the helium atom confined in a spherical impenetrable cavity by using informational measures. We use the Ritz variational method to obtain the energies and wave functions of the confined helium atom as a function of the cavity radius . As trial wave functions we use one uncorrelated function and five explicitly correlated basis sets in Hylleraas coordinates with different degrees of electronic correlation. We computed the Shannon entropy, Fisher information, Kullback–Leibler entropy, Tsallis entropy, disequilibrium and Fisher–Shannon complexity, as a function of . We found that these entropic measures are sensitive to electronic correlation and can be used to measure it. As expected these entropic measures are less sensitive to electron correlation in the strong confinement regime ( a.u.).

Graph Entropy for Adjacently and Non-Adjacently Configured Pentagonal Structure of Carbon Nanocones

aims: Carbon nanocones possess exceptional properties compared to other nanomaterials, such as nanotubes, graphene etc. Hence they can be used as an alternative to other nanostructures. This work helps in determining various properties of the nanocone structure through topological descriptors. In this paper, various degree based topological descriptors along with its entropy measures are evaluated for adjacently and non-adjacently configured pentagonal structure of carbon nanocones. background: Carbon nanoparticles are gaining much importance in the contemporary world. Among which carbon nanocones have wide range of acceptance in the field of nanotechnology due to its effective properties and applications. Nanocones, also known as nanohorns are carbon networks which are planar in structure and has majority of hexagonal faces along with some nonhexagonal faces, which are most commonly pentagons. Nanocones which include pentagons in their structure can be referred to as adjacently or non- adjacently configured pentagonal structure of nanocones. Various topological descriptors for few nanocone classes were derived by researchers earlier, but not for the class of nanocones in this paper. Through this work, we try to vanish the research gap in this field. objective: : The degree based descriptors and corresponding graph entropies for the adjacently and non-adjacently configured pentagonal structure of nanocones were determined, which further can be applied in quantitative structure – activity – property relationship studies. The concept of graph entropy is to assign a probability function to the edges in the chemical graph using the topological descriptor and it helps to characterise the complexity of graphs. method: We have employed the degree counting method and edge partition based on the vertices and edges of the adjacently and non-adjacently configured pentagonal nanocone structures to obtain the edge partitions and then using the corresponding mathematical expression, the degree based descriptors and its corresponding entropies were determined. result: Result: The analytically closed formulas to compute the degree based topological descriptors and graph entropies for any generation of the class of nanocone structures were obtained. conclusion: In this work, the degree based descriptors and the corresponding graph entropies for the adjacently and non-adjacently configured pentagonal structure of carbon nanocones are determined applying the degree counting method and edge partition based on the vertices and edges. Also a graphical comparative study was also done with the help of obtained results. other: end.

Scale based entropy measures and deep learning methods for analyzing the dynamical characteristics of cardiorespiratory control system in COVID-19 subjects during and after recovery

COVID-19, known as Coronavirus Disease 2019 primarily targets the respiratory system and can impact the cardiovascular system, leading to a range of cardiorespiratory complications. The current forefront in analyzing the dynamical characteristics of physiological systems and aiding clinical decision-making involves the integration of entropy-based complexity techniques with artificial intelligence. Entropy-based measures offer promising prospects for identifying disturbances in cardiorespiratory control system (CRCS) among COVID-19 patients by assessing the oxygen saturation variability (OSV) signals. In this investigation, we employ scale-based entropy (SBE) methods, including multiscale entropy (MSE), multiscale permutation entropy (MPE), and multiscale fuzzy entropy (MFE), to characterize the dynamical characteristics of OSV signals. These measurements serve as features for the application of traditional machine learning (ML) and deep learning (DL) approaches in the context of classifying OSV signals from COVID-19 patients during their illness and subsequent recovery. We use the Beurer PO-80 pulse oximeter which non-invasively acquired OSV and pulse rate data from COVID-19 infected patients during the active infection phase and after a two-month recovery period. The dataset comprises of 88 recordings collected from 44 subjects(26 men and 18 women), both during their COVID-19 illness and two months post-recovery. Prior to analysis, data preprocessing is performed to remove artifacts and outliers. The application of SBE measures to OSV signals unveils a reduction in signal complexity during the course of COVID-19. Leveraging these SBE measures as feature sets, we employ two DL techniques, namely the radial basis function network (RBFN) and RBFN with dynamic delay algorithm (RBFNDDA), for the classification of OSV data collected during and after COVID-19 recovery. To evaluate the classification performance, we employ standard metrics such as sensitivity, specificity, false positive rate (FPR), and the area under the receiver operator characteristic curve (AUC). Among the three scale-based entropy measures, MFE outperformed MSE and MPE by achieving the highest classification performance using RBFN with 13 best features having sensitivity (0.84), FPR (0.30), specificity (0.70) and AUC (0.77). The outcomes of our study demonstrate that SBE measures combined with DL methods offer a valuable approach for categorizing OSV signals obtained during and after COVID-19, ultimately aiding in the detection of CRCS dysfunction.