Statistical Entropy Research Articles

Evaluation Performance of Bloom Filter in Blockchain Network

A blockchain is a secret, scalability and decentralized p2p network in which all nodes follow similar protocols, preventing any single node from controlling the basic structure. In blockchain, Bloom filters are used to preserve the privacy of lightweight nodes. Bloom filter is a memory efficient randomized data structure to represent a set in order to support associate queries. Bloom filters offer a trade-off between (elements size in the network and bandwidth) and privacy metrics in untrusted environments. This paper proposes an analysis to evaluate the performance of Bloom filters. The evaluation results are based on the statistical distribution, standard deviation, entropy and y-deniability that are used by the attacker to analysis the leakage of the Bloom filter algorithm. Experimental results show that the degree of privacy in the network needs a large amount of elements and more bandwidth using the Bloom filter algorithm.

The free piston problem for pressureless Euler equations under the gravity

In this paper, the exact solutions of the free piston problem for the one-dimensional pressureless Euler equations under gravity are constructed in fully explicit forms. It is found that delta shock wave and vacuum state are contained in the solutions with appropriate initial condition. Furthermore, the trajectory function of the piston can be obtained in the combination of the generalized Rankine-Hugoniot conditions and Newton's second law, and it can be uniquely determined by the generalized entropy condition. We observe and analyze carefully some interesting nonlinear phenomena. For instance, delta shock wave absorbs the vacuum state and forms a new delta shock wave. In addition, some representative numerical simulations are presented to confirm the correctness of theoretical analysis.

Combined effects of temperature and confinement on the Shannon entropy of two-dimensional hydrogenic impurity states in the GaAs semiconductor quantum well

Understanding the quantum properties of two-dimensional (2-D) hydrogenic impurity states in the GaAs quantum well is essential for their applications in the semiconductor devices. Here, we report the combined effects of temperature and quantum confienment on the Shannon entropy of 2-D hydrogenic impurity states in the GaAs quantum well. First, by calculating the position and momentum space Shannon entropy (Sr and Sp), as well as the Shannon entropy sum (St), for the hydrogenic impurity states in the GaAs quantum well at room temperature, we show fascinating quantum confinement properties in the two conjugated spaces. Then, the effects of temperature on the Shannon entropy for different hydrogenic impurity states are examined and compared. Intriguingly, we discover that the Shannon entropy sum exhibits the property of translation invariance under the influence of temperature. Finally, with the radius of the quantum well fixed at a constant, we observe that the value of the Shannon entropy for a given quantum state is highly sensitive to the variations in temperature. While the size of circular quantum well is constrained by design parameters, such as the fabrication process and intended application, temperature adjustment emerges as a viable means to control the quantum properties of 2-D hydrogenic impurities in the quantum well. This research presents a pioneering method that employs temperature as a versatile tool for modulating the Shannon entropy of hydrogenic impurity states in the quantum well, and has potential applications in the field of semiconductor physics, material physics, chemical physics, etc.

Conformational analysis of the IQSEC2 protein by statistical thermodynamics

Mutations in the IQSEC2 gene result in severe intellectual disability, epilepsy and autism. The primary function of IQSEC2 is to serve as a guanine exchange factor (GEF) controlling the activation of ARF6 which in turn mediates membrane trafficking and synaptic connections between neurons. As IQSEC2 is a large intrinsically disordered protein little is known of the structure of the protein and how this influences its function. Understanding this structure and function relationship is critical for the development of novel therapies to treat IQSEC2 disease. We therefore sought to identify IQSEC2 conformers in unfolded and folded states and analyze how conformers differ when binding to ARF6 and thereby influence GEF catalysis. We simulated the folding process of IQSEC2 by accelerated molecular dynamics (aMD). Following the ensemble method of Gibbs, we proposed that the number of microstates in the ensemble replicating a protein macroscopic system is the total number of MD snapshots sampled on the production MD trajectory. We divided the entire range of reaction coordinate into a series of consecutive, non-overlapping bins. Thermal fluctuations of biomolecules in local equilibrium states are Gaussian in form. To predict the free energy and entropy of different conformational states using statistical thermodynamics, the density of states was estimated taking into account how many MD snapshots constitute each conformational state. IQSEC2 dimers derived from the most stable folded and unfolded conformers of IQSEC2 were generated by protein-protein docking and then used to construct IQSEC2-ARF6 encounter complexes. We suggest that IQSEC2 folding and dimerization are two competing processes that may be used by nature to regulate the process of GDP exchange on ARF6 catalyzed by IQSEC2.

Application of maximum statistical entropy in formulating a non-gaussian probability density function in flow uncertainty analysis with prior measurement knowledge

In mechanical, civil and chemical engineering systems the accuracies of flow measurement instruments is conventionally specified by certified measurement capabilities (CMCs) that are symmetric, however it is physically possible for some flow instruments and equipment to exhibit asymmetric non-Gaussian behaviour. In this paper the influence of non-Gaussian uncertainties is investigated using direct Monte Carlo simulations to construct a probability density function (PDF) using representative non-Gaussian surface roughness data for a commercial steel pipe friction factor. Actual PDF results are compared and contrasted with a symmetric Gaussian PDF, and reveal inconsistencies in the statistical distributions that cannot be neglected in high accuracy flow measurements. The non-Gaussian PDF is visualized with a kernel density estimate (KDE) scheme to infer an initial qualitative shape of the actual PDF using the approximate locations of the normalized peaks as a initial metrologist estimate of the measurement density. This is then utilized as inputs in a maximum statistical entropy functional to optimize the actual non-Gaussian PDF using a nonlinear optimization of Lagrange multipliers for a mathematically unique PDE. Novelties in the present study is that a new methodology has been developed for statistical sampling from non-monotonic non-Gaussian distributions with accompanying Python and Matlab/GNU Octave computer codes, and a new methodology for utilizing metrologist's expert prior knowledge of PDF peaks and locations for constructing an a priori estimate of the shape of unknown density have been incorporated into the maximum statistical entropy nonlinear optimization problem for a faster and more efficient approach for generating statistical information and insights in constructing high accuracy non-Gaussian PDFs of real world messy engineering measurements.

Fast Convergence on Perfect Classification for Functional Data

We investigate the availability of approaching perfect classification on functional data with finite samples. The seminal work (Delaigle and Hall (2012)) showed that perfect classification for functional data is easier to achieve than for finite-dimensional data. This result is based on their finding that a sufficient condition for the existence of a perfect classifier, named a Delaigle--Hall condition, is only available for functional data. However, there is a danger that a large sample size is required to achieve the perfect classification even though the Delaigle--Hall condition holds, because a minimax convergence rate of errors with functional data has a logarithm order in sample size. This study solves this complication by proving that the Delaigle--Hall condition also achieves fast convergence of the misclassification error in sample size, under the bounded entropy condition on functional data. We study a reproducing kernel Hilbert space-based classifier under the Delaigle--Hall condition, and show that a convergence rate of its misclassification error has an exponential order in sample size. Technically, our proof is based on (i) connecting the Delaigle--Hall condition and a margin of classifiers, and (ii) handling metric entropy of functional data. Our experiments support our result, and also illustrate that some other classifiers for functional data have a similar property.

Smallest unit of maximal entropy as novel experimental criterion for parametric characterization of middle- and high-entropy materials.

Materials with multiple principal elements (middle- and high-entropy materials), are used in emerging applications in various fields due to their unique properties, driven by configuration entropy. Improved understanding and experimental investigations of the impact of the entropy of mixing on the properties of these materials are of large practical interest. Here we show a simplified limited area calculation approach for assessing the entropy of mixing using a CoCuFeNi model nanoalloy. Based on our calculations we propose a new parametric entropy-based criterion, which defines critical scale parameter transition from the maximal entropy state to the entropy-depleted state of the system. The criterion could be used for generalized mechanistic assessment of the effect of the entropy of mixing on the characteristics of the materials with multiple principal elements and for the development and characterization of existing and new middle- and high-entropy materials with both simple single-, and more complex, multiple-sublattice structures.

Novel Entropy-Based Metrics for Long-Term Atrial Fibrillation Recurrence Prediction Following Surgical Ablation: Insights from Preoperative Electrocardiographic Analysis.

Atrial fibrillation (AF) is a prevalent cardiac arrhythmia often treated concomitantly with other cardiac interventions through the Cox-Maze procedure. This highly invasive intervention is still linked to a long-term recurrence rate of approximately 35% in permanent AF patients. The aim of this study is to preoperatively predict long-term AF recurrence post-surgery through the analysis of atrial activity (AA) organization from non-invasive electrocardiographic (ECG) recordings. A dataset comprising ECGs from 53 patients with permanent AF who had undergone Cox-Maze concomitant surgery was analyzed. The AA was extracted from the lead V1 of these recordings and then characterized using novel predictors, such as the mean and standard deviation of the relative wavelet energy (RWEm and RWEs) across different scales, and an entropy-based metric that computes the stationary wavelet entropy variability (SWEnV). The individual predictors exhibited limited predictive capabilities to anticipate the outcome of the procedure, with the SWEnV yielding a classification accuracy (Acc) of 68.07%. However, the assessment of the RWEs for the seventh scale (RWEs7), which encompassed frequencies associated with the AA, stood out as the most promising individual predictor, with sensitivity (Se) and specificity (Sp) values of 80.83% and 67.09%, respectively, and an Acc of almost 75%. Diverse multivariate decision tree-based models were constructed for prediction, giving priority to simplicity in the interpretation of the forecasting methodology. In fact, the combination of the SWEnV and RWEs7 consistently outperformed the individual predictors and excelled in predicting post-surgery outcomes one year after the Cox-Maze procedure, with Se, Sp, and Acc values of approximately 80%, thus surpassing the results of previous studies based on anatomical predictors associated with atrial function or clinical data. These findings emphasize the crucial role of preoperative patient-specific ECG signal analysis in tailoring post-surgical care, enhancing clinical decision making, and improving long-term clinical outcomes.

A novel extended inverse‐exponential distribution and its application to COVID‐19 data

AbstractThe aim of this article is to define a new flexible statistical model to examine the COVID‐19 data sets that cannot be modeled by the inverse exponential distribution. A novel extended distribution with one scale and three shape parameters is proposed using the generalized alpha power family of distributions to derive the generalized alpha power exponentiated inverse exponential distribution. Some important statistical properties of the new distribution such as the survival function, hazard function, quantile function, moment, Rényi entropy, and order statistics are all derived. The method of maximum likelihood estimation is used to estimate the parameters of the new distribution. The performance of the estimators are assessed through Monte Carlo simulation, which shows that the maximum likelihood method works well in estimating the parameters. The GAPEIEx distribution was applied to COVID‐19 data sets in order to access the flexibility and adaptability of the distribution, and it happens to perform better than its submodels and other well‐known distributions.

PROFILES OF OLDER INCARCERATED PERSONS WHO ATTEMPT SUICIDE FOLLOWING RELEASE

Abstract Release from incarceration is a strong risk factor for suicide. Yet little is known regarding factors associated with suicide attempt among older adults who reentered the community following incarceration. Leveraging a national cohort of U.S. veterans age ≥50 released from incarceration between FY2007 and FY2018 (N=30,584), we conducted a 1:3 matched case-control study and compared demographic and comorbidity factors between those who attempted suicide (cases, N=643) and those with no suicide attempt (controls, N=1,929) up to 13 years post-release. Comorbidity profiles were determined using latent class analysis. As compared with controls, cases had higher proportions of chronic illnesses (e.g., chronic lung disease [35.2% vs. 19.6%], diabetes [32.2% vs. 19.4%], Hepatitis C [24.9% vs. 9.6%]); depression (75% vs. 28.7%); substance use disorders (SUDS) (83.0% vs. 39.4%); and other serious mental illnesses (SMI) (e.g., schizophrenia [34.2% vs. 13.2%], psychotic illness [39.5% vs. 12.5%]). We found four distinct latent clusters among cases (entropy statistic = 0.80): (1) “Minimal Comorbidity” (18%); (2) “PTSD/SUD” (35%); (3) “High Psychiatric/SMI” (32%); and (4) “High Medical/Psychiatric Comorbidity” (15%), and four clusters among controls (entropy statistic = 0.84): (1) “Minimal Comorbidity” (50%); (2) “SMI” (8%); (3) “Tobacco dependence/SUD” (33%); and (4) “High Medical/Psychiatric Comorbidity” (9%). Compared with controls, fewer cases were likely to have the “Minimal Comorbidity” profile (18% vs. 50%), whereas more were likely to have profiles with SMI (32% vs. 8%). Establishing comorbidity profiles of older persons reentering the community after incarceration may help determine who is more likely to die by suicide, thus informing prevention efforts.

Generalized entropy for general subregions in quantum gravity

We consider quantum algebras of observables associated with subregions in theories of Einstein gravity coupled to matter in the GN → 0 limit. When the subregion is spatially compact or encompasses an asymptotic boundary, we argue that the algebra is a type II von Neumann factor. To do so in the former case we introduce a model of an observer living in the region; in the latter, the ADM Hamiltonian effectively serves as an observer. In both cases the entropy of states on which this algebra acts is UV finite, and we find that it agrees, up to a state-independent constant, with the generalized entropy. For spatially compact regions the algebra is type II1, implying the existence of an entropy maximizing state, which realizes a version of Jacobson’s entanglement equilibrium hypothesis. The construction relies on the existence of well-motivated but conjectural states whose modular flow is geometric at an instant in time. Our results generalize the recent work of Chandrasekaran, Longo, Penington, and Witten on an algebra of operators for the static patch of de Sitter space.

Statistical investigations of profile error impact on flow and performance of a low-pressure turbine cascade

Profile error impacts on turbomachinery flow and blade performance have been attracting widespread attention. In the study, the characteristics of profile error of about one thousand real low-pressure turbine blades are extracted. Sensitivities of total pressure loss coefficient (ζ), outflow angle (β), and Zweifel lift coefficient (zw) of the blade to the basis modes of profile error are calculated. Flow solutions of the blades considering specified basis modes with high sensitivities illustrate that profile error contributes much to the variations of transition onset and flow acceleration on the suction side and flow mixing intensity in the wake. Uncertainty quantification of performance changes is then implemented by the method of moment (MM) using second-order sensitivities. With only 5% computational cost of that by Monte Carlo simulation (MCS), the MM-based statistical results are close to MCS ones with maximum relative error not exceeding 1.07%. The statistical results reveal that the variations of both β and zw are linearly dependent, whereas the variation of ζ is nonlinearly dependent on profile error. As the variation range of profile error increases, the standard deviation and skewness increase, indicating that the performance is more dispersive and the nonlinear dependence of ζ on profile error is intensified. Finally, the MCS flow fields are analyzed. Statistical shear stress near the leading edge and transition onset, statistical boundary layer momentum thickness near transition onset, statistical intermittency near transition onset, and statistical entropy in the wake are more considerable. The impact mechanisms of profile error on turbine flow and performance changes are demonstrated.

Semiclassical asymptotics and entropy

We study the entanglement of quantum states associated with submanifolds of Kaehler manifolds. As a motivating example, we discuss the semiclassical asymptotics of entanglement entropy of pure states on the two dimensional sphere with the standard metric.

Characterizing EEG signals of meditative states using persistent homology and Hodge spectral entropy

We present a novel topological characterization of EEG time series signals associated with two meditative states: autobiographical self-reflection and mantra-based meditation. The results demonstrate significant information geometric differences among the two groups of meditators and the control group for two brain regions, namely anterior frontal (AF) and temporoparietal (TP). The analysis involves global topological invariants and persistent homology features of the point cloud data constructed from the EEG time series using Takens’s embedding. While traditional EEG analyses face the well-known issues of noise and artefacts, the persistent homology approach is robust to them due to its emphasis on the overall topological changes rather than the transient structures. We analyse the characteristics of the Betti areas, peak location of Betti curves, persistent entropy, persistent amplitude and Hodge spectral entropy of the meditative states for up to the second homology dimension. We find that the mantra- based meditative state is rich in persistent features compared to autobiographical self-reflection. Also, the entropic measures indicate reduced chaotic dynamics and enhanced topological structure formation for the former. Moreover, the correlation of Hodge spectral entropy with persistent entropy or Betti area in a group is a key feature in differentiating the TP and AF channels. These topological features can be used to classify the meditative states with more than 95% accuracy.

Influencer identification of dynamical networks based on an information entropy dimension reduction method

Identifying critical nodes or sets in large-scale networks is a fundamental scientific problem and one of the key research directions in the fields of data mining and network science when implementing network attacks, defense, repair and control. Traditional methods usually begin from the centrality, node location or the impact on the largest connected component after node destruction, mainly based on the network structure. However, these algorithms do not consider network state changes. We applied a model that combines a random connectivity matrix and minimal low-dimensional structures to represent network connectivity. By using mean field theory and information entropy to calculate node activity, we calculated the overlap between the random parts and fixed low-dimensional parts to quantify the influence of node impact on network state changes and ranked them by importance. We applied this algorithm and the proposed importance algorithm to the overall analysis and stratified analysis of the C. elegans neural network. We observed a change in the critical entropy of the network state and by utilizing the proposed method we can calculate the nodes that indirectly affect muscle cells through neural layers.

Islands and dynamics at the interface

We investigate a family of models described by two holographic CFT2s coupled along a shared interface. The bulk dual geometry consists of two AdS3 spacetimes truncated by a shared Karch-Randall end-of-the-world (EOW) brane. A lower dimensional effective model comprising of JT gravity coupled to two flat CFT2 baths is subsequently realized by considering small fluctuations on the EOW brane and implementing a partial Randall-Sundrum reduction where the transverse fluctuations of the EOW brane are identified as the dilaton field. We compute the generalized entanglement entropy for bipartite states through the island prescription in the effective lower dimensional picture and obtain precise agreement in the limit of large brane tension with the corresponding doubly holographic computations in the bulk geometry. Furthermore, we obtain the corresponding Page curves for the Hawking radiation in this JT braneworld.

Riemann problem for a 2times 2 hyperbolic system with time-gradually-degenerate damping

This paper is focused on the Riemann problem for a 2times 2 hyperbolic system of conservation laws with a time-gradually-degenerate damping. Two kinds of non-self-similar solutions involving the delta-shocks and vacuum are obtained using the variable substitution method. The generalized Rankine-Hugoniot relation and entropy condition are clarified for the delta-shock. Furthermore, the vanishing viscosity method proves the existence, uniqueness, and stability of non-self-similar solutions.

Statistical Analysis of Covid-19 Data using the Odd Log Logistic Kumaraswamy Distribution

This paper presents a statistical analysis of Covid-19 data using the Odd log logistic kumaraswamy Kumaraswamy (OLLK) distribution. Some mathematical properties of the proposed OLLK distribution such as the survival and hazard functions, quantile function, ordinary and incomplete moments, moment generating function, probability weighted moment, distribution of order statistic and Renyi entropy were derived. Five estimators are examined for unknown model parameters. The performance of the estimators is compared using an extensive simulation study based on the bias and mean square error criteria. Two Covid-19 data sets representing the percentage of daily recoveries of Covid-19 patients are used to illustrate the applicability of the proposed OLLK distribution. Results revealed that the OLLK distribution is a better alternative to some existing models with bounded support.

The Topp-Leone Odd Burr X-G Family of Distributions: Properties and Applications

This paper proposes a new generalized family of distributions called the Topp-Leone odd Burr X-G (TLOBX-G) distribution and its special model, Topp-Leone odd Burr X-Weibull (TLOBX-W) is studied in detail. Structural properties are derived, including the hazard rate function, quantile function, density expansion, moments, R'enyi entropy, and order statistics. The maximum likelihood technique is used to estimate the parameters of the new family of distributions and a simulation study was carried out to assess the accuracy and consistency of these estimators. Finally, the applicability, usefulness, and flexibility of TLOBX-W distribution are illustrated using two real-life datasets.

Entanglement Entropy of Ground States of the Three-Dimensional Ideal Fermi Gas in a Magnetic Field

We study the asymptotic growth of the entanglement entropy of ground states of non-interacting (spinless) fermions in R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb {R}}}^3$$\\end{document} subject to a constant magnetic field perpendicular to a plane. As for the case with no magnetic field we find, to leading order L2ln(L)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2\\ln (L)$$\\end{document}, a logarithmically enhanced area law of this entropy for a bounded, piecewise Lipschitz region LΛ⊂R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L\\Lambda \\subset {{\\mathbb {R}}}^3$$\\end{document} as the scaling parameter L tends to infinity. This is in contrast to the two-dimensional case since particles can now move freely in the direction of the magnetic field, which causes the extra ln(L)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ln (L)$$\\end{document} factor. The explicit expression for the coefficient of the leading order contains a surface integral similar to the Widom–Sobolev formula in the non-magnetic case. It differs, however, in the sense that the dependence on the boundary, ∂Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial \\Lambda $$\\end{document}, is not solely on its area but on the “surface perpendicular to the direction of the magnetic field”. We utilize a two-term asymptotic expansion by Widom (up to an error term of order one) of certain traces of one-dimensional Wiener–Hopf operators with a discontinuous symbol. This leads to an improved error term of the order L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2$$\\end{document} of the relevant trace for piecewise C1,α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{C}^{1,\\alpha }$$\\end{document} smooth surfaces ∂Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial \\Lambda $$\\end{document}.