Trustworthiness Measurement Algorithm for TWfMS Based on Software Behaviour Entropy

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Qiang Han

2018-03-01

Full Text Available As the virtual mirror of complex real-time business processes of organisations’ underlying information systems, the workflow management system (WfMS has emerged in recent decades as a new self-autonomous paradigm in the open, dynamic, distributed computing environment. In order to construct a trustworthy workflow management system (TWfMS, the design of a software behaviour trustworthiness measurement algorithm is an urgent task for researchers. Accompanying the trustworthiness mechanism, the measurement algorithm, with uncertain software behaviour trustworthiness information of the WfMS, should be resolved as an infrastructure. Based on the framework presented in our research prior to this paper, we firstly introduce a formal model for the WfMS trustworthiness measurement, with the main property reasoning based on calculus operators. Secondly, this paper proposes a novel measurement algorithm from the software behaviour entropy of calculus operators through the principle of maximum entropy (POME and the data mining method. Thirdly, the trustworthiness measurement algorithm for incomplete software behaviour tests and runtime information is discussed and compared by means of a detailed explanation. Finally, we provide conclusions and discuss certain future research areas of the TWfMS.

A Comparison of Multiscale Permutation Entropy Measures in On-Line Depth of Anesthesia Monitoring.

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Su, Cui; Liang, Zhenhu; Li, Xiaoli; Li, Duan; Li, Yongwang; Ursino, Mauro

2016-01-01

Multiscale permutation entropy (MSPE) is becoming an interesting tool to explore neurophysiological mechanisms in recent years. In this study, six MSPE measures were proposed for on-line depth of anesthesia (DoA) monitoring to quantify the anesthetic effect on the real-time EEG recordings. The performance of these measures in describing the transient characters of simulated neural populations and clinical anesthesia EEG were evaluated and compared. Six MSPE algorithms-derived from Shannon permutation entropy (SPE), Renyi permutation entropy (RPE) and Tsallis permutation entropy (TPE) combined with the decomposition procedures of coarse-graining (CG) method and moving average (MA) analysis-were studied. A thalamo-cortical neural mass model (TCNMM) was used to generate noise-free EEG under anesthesia to quantitatively assess the robustness of each MSPE measure against noise. Then, the clinical anesthesia EEG recordings from 20 patients were analyzed with these measures. To validate their effectiveness, the ability of six measures were compared in terms of tracking the dynamical changes in EEG data and the performance in state discrimination. The Pearson correlation coefficient (R) was used to assess the relationship among MSPE measures. CG-based MSPEs failed in on-line DoA monitoring at multiscale analysis. In on-line EEG analysis, the MA-based MSPE measures at 5 decomposed scales could track the transient changes of EEG recordings and statistically distinguish the awake state, unconsciousness and recovery of consciousness (RoC) state significantly. Compared to single-scale SPE and RPE, MSPEs had better anti-noise ability and MA-RPE at scale 5 performed best in this aspect. MA-TPE outperformed other measures with faster tracking speed of the loss of unconsciousness. MA-based multiscale permutation entropies have the potential for on-line anesthesia EEG analysis with its simple computation and sensitivity to drug effect changes. CG-based multiscale permutation

Entropy of measurement and erasure: Szilard's membrane model revisited

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Leff, Harvey S.; Rex, Andrew F.

1994-11-01

It is widely believed that measurement is accompanied by irreversible entropy increase. This conventional wisdom is based in part on Szilard's 1929 study of entropy decrease in a thermodynamic system by intelligent intervention (i.e., a Maxwell's demon) and Brillouin's association of entropy with information. Bennett subsequently argued that information acquisition is not necessarily irreversible, but information erasure must be dissipative (Landauer's principle). Inspired by the ensuing debate, we revisit the membrane model introduced by Szilard and find that it can illustrate and clarify (1) reversible measurement, (2) information storage, (3) decoupling of the memory from the system being measured, and (4) entropy increase associated with memory erasure and resetting.

On Measuring the Complexity of Networks: Kolmogorov Complexity versus Entropy

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Mikołaj Morzy

2017-01-01

Full Text Available One of the most popular methods of estimating the complexity of networks is to measure the entropy of network invariants, such as adjacency matrices or degree sequences. Unfortunately, entropy and all entropy-based information-theoretic measures have several vulnerabilities. These measures neither are independent of a particular representation of the network nor can capture the properties of the generative process, which produces the network. Instead, we advocate the use of the algorithmic entropy as the basis for complexity definition for networks. Algorithmic entropy (also known as Kolmogorov complexity or K-complexity for short evaluates the complexity of the description required for a lossless recreation of the network. This measure is not affected by a particular choice of network features and it does not depend on the method of network representation. We perform experiments on Shannon entropy and K-complexity for gradually evolving networks. The results of these experiments point to K-complexity as the more robust and reliable measure of network complexity. The original contribution of the paper includes the introduction of several new entropy-deceiving networks and the empirical comparison of entropy and K-complexity as fundamental quantities for constructing complexity measures for networks.

Entropy Evaluation Based on Value Validity

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Tarald O. Kvålseth

2014-09-01

Full Text Available Besides its importance in statistical physics and information theory, the Boltzmann-Shannon entropy S has become one of the most widely used and misused summary measures of various attributes (characteristics in diverse fields of study. It has also been the subject of extensive and perhaps excessive generalizations. This paper introduces the concept and criteria for value validity as a means of determining if an entropy takes on values that reasonably reflect the attribute being measured and that permit different types of comparisons to be made for different probability distributions. While neither S nor its relative entropy equivalent S* meet the value-validity conditions, certain power functions of S and S* do to a considerable extent. No parametric generalization offers any advantage over S in this regard. A measure based on Euclidean distances between probability distributions is introduced as a potential entropy that does comply fully with the value-validity requirements and its statistical inference procedure is discussed.

Entropy of the Mixture of Sources and Entropy Dimension

OpenAIRE

Smieja, Marek; Tabor, Jacek

2011-01-01

We investigate the problem of the entropy of the mixture of sources. There is given an estimation of the entropy and entropy dimension of convex combination of measures. The proof is based on our alternative definition of the entropy based on measures instead of partitions.

IN-cross Entropy Based MAGDM Strategy under Interval Neutrosophic Set Environment

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Shyamal Dalapati

2017-12-01

Full Text Available Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. We define a new cross entropy measure under interval neutrosophic set (INS environment, which we call IN-cross entropy measure and prove its basic properties. We also develop weighted IN-cross entropy measure and investigats its basic properties. Based on the weighted IN-cross entropy measure, we develop a novel strategy for multi attribute group decision making (MAGDM strategy under interval neutrosophic environment. The proposed multi attribute group decision making strategy is compared with the existing cross entropy measure based strategy in the literature under interval neutrosophic set environment. Finally, an illustrative example of multi attribute group decision making problem is solved to show the feasibility, validity and efficiency of the proposed MAGDM strategy.

Measuring time series regularity using nonlinear similarity-based sample entropy

International Nuclear Information System (INIS)

Xie Hongbo; He Weixing; Liu Hui

2008-01-01

Sampe Entropy (SampEn), a measure quantifying regularity and complexity, is believed to be an effective analyzing method of diverse settings that include both deterministic chaotic and stochastic processes, particularly operative in the analysis of physiological signals that involve relatively small amount of data. However, the similarity definition of vectors is based on Heaviside function, of which the boundary is discontinuous and hard, may cause some problems in the validity and accuracy of SampEn. Sigmoid function is a smoothed and continuous version of Heaviside function. To overcome the problems SampEn encountered, a modified SampEn (mSampEn) based on nonlinear Sigmoid function was proposed. The performance of mSampEn was tested on the independent identically distributed (i.i.d.) uniform random numbers, the MIX stochastic model, the Rossler map, and the Hennon map. The results showed that mSampEn was superior to SampEn in several aspects, including giving entropy definition in case of small parameters, better relative consistency, robust to noise, and more independence on record length when characterizing time series generated from either deterministic or stochastic system with different regularities

Entropy-Based Algorithm for Supply-Chain Complexity Assessment

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Boris Kriheli

2018-03-01

Full Text Available This paper considers a graph model of hierarchical supply chains. The goal is to measure the complexity of links between different components of the chain, for instance, between the principal equipment manufacturer (a root node and its suppliers (preceding supply nodes. The information entropy is used to serve as a measure of knowledge about the complexity of shortages and pitfalls in relationship between the supply chain components under uncertainty. The concept of conditional (relative entropy is introduced which is a generalization of the conventional (non-relative entropy. An entropy-based algorithm providing efficient assessment of the supply chain complexity as a function of the SC size is developed.

Entanglement entropy after selective measurements in quantum chains

Energy Technology Data Exchange (ETDEWEB)

Najafi, Khadijeh [Department of Physics, Georgetown University,37th and O Sts. NW, Washington, DC 20057 (United States); Rajabpour, M.A. [Instituto de Física, Universidade Federal Fluminense,Av. Gal. Milton Tavares de Souza s/n, Gragoatá, 24210-346, Niterói, RJ (Brazil)

2016-12-22

We study bipartite post measurement entanglement entropy after selective measurements in quantum chains. We first study the quantity for the critical systems that can be described by conformal field theories. We find a connection between post measurement entanglement entropy and the Casimir energy of floating objects. Then we provide formulas for the post measurement entanglement entropy for open and finite temperature systems. We also comment on the Affleck-Ludwig boundary entropy in the context of the post measurement entanglement entropy. Finally, we also provide some formulas regarding modular hamiltonians and entanglement spectrum in the after measurement systems. After through discussion regarding CFT systems we also provide some predictions regarding massive field theories. We then discuss a generic method to calculate the post measurement entanglement entropy in the free fermion systems. Using the method we study the post measurement entanglement entropy in the XY spin chain. We check numerically the CFT and the massive field theory results in the transverse field Ising chain and the XX model. In particular, we study the post meaurement entanglement entropy in the infinite, periodic and open critical transverse field Ising chain and the critical XX model. The effect of the temperature and the gap is also discussed in these models.

Entanglement entropy after selective measurements in quantum chains

International Nuclear Information System (INIS)

Najafi, Khadijeh; Rajabpour, M.A.

2016-01-01

We study bipartite post measurement entanglement entropy after selective measurements in quantum chains. We first study the quantity for the critical systems that can be described by conformal field theories. We find a connection between post measurement entanglement entropy and the Casimir energy of floating objects. Then we provide formulas for the post measurement entanglement entropy for open and finite temperature systems. We also comment on the Affleck-Ludwig boundary entropy in the context of the post measurement entanglement entropy. Finally, we also provide some formulas regarding modular hamiltonians and entanglement spectrum in the after measurement systems. After through discussion regarding CFT systems we also provide some predictions regarding massive field theories. We then discuss a generic method to calculate the post measurement entanglement entropy in the free fermion systems. Using the method we study the post measurement entanglement entropy in the XY spin chain. We check numerically the CFT and the massive field theory results in the transverse field Ising chain and the XX model. In particular, we study the post meaurement entanglement entropy in the infinite, periodic and open critical transverse field Ising chain and the critical XX model. The effect of the temperature and the gap is also discussed in these models.

Definition and measurement of entropy in high energy heavy ion collisions

International Nuclear Information System (INIS)

Remler, E.A.

1986-01-01

This talk has two parts: the first on the definition and the second on the measurement of entropy. The connection to nuclear thermodynamics can be retained without the local equilibrium assumption via two steps. The first is relatively simple and goes as follows. The authors make the certainly reasonable assumption that in central collisions, at the moment of maximum compression, the state is similar to one or more fireballs and that the total entropy of each fireball approximates that of an equilibrated system at the same total energy and average density. This entropy, if measurable, would determine much of the thermodynamic properties of nuclear matter. The second step therefore concerns measurement of this entropy. This paper develops a method by which entropy may be measured using a minimum amount of theory. In particular, it is not based on any assumption local equilibrium

Entropy-based financial asset pricing.

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Mihály Ormos

Full Text Available We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return-entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy.

Entropy-based financial asset pricing.

Science.gov (United States)

Ormos, Mihály; Zibriczky, Dávid

2014-01-01

We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return-entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy.

Characterizing brain structures and remodeling after TBI based on information content, diffusion entropy.

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Fozouni, Niloufar; Chopp, Michael; Nejad-Davarani, Siamak P; Zhang, Zheng Gang; Lehman, Norman L; Gu, Steven; Ueno, Yuji; Lu, Mei; Ding, Guangliang; Li, Lian; Hu, Jiani; Bagher-Ebadian, Hassan; Hearshen, David; Jiang, Quan

2013-01-01

To overcome the limitations of conventional diffusion tensor magnetic resonance imaging resulting from the assumption of a Gaussian diffusion model for characterizing voxels containing multiple axonal orientations, Shannon's entropy was employed to evaluate white matter structure in human brain and in brain remodeling after traumatic brain injury (TBI) in a rat. Thirteen healthy subjects were investigated using a Q-ball based DTI data sampling scheme. FA and entropy values were measured in white matter bundles, white matter fiber crossing areas, different gray matter (GM) regions and cerebrospinal fluid (CSF). Axonal densities' from the same regions of interest (ROIs) were evaluated in Bielschowsky and Luxol fast blue stained autopsy (n = 30) brain sections by light microscopy. As a case demonstration, a Wistar rat subjected to TBI and treated with bone marrow stromal cells (MSC) 1 week after TBI was employed to illustrate the superior ability of entropy over FA in detecting reorganized crossing axonal bundles as confirmed by histological analysis with Bielschowsky and Luxol fast blue staining. Unlike FA, entropy was less affected by axonal orientation and more affected by axonal density. A significant agreement (r = 0.91) was detected between entropy values from in vivo human brain and histologically measured axonal density from post mortum from the same brain structures. The MSC treated TBI rat demonstrated that the entropy approach is superior to FA in detecting axonal remodeling after injury. Compared with FA, entropy detected new axonal remodeling regions with crossing axons, confirmed with immunohistological staining. Entropy measurement is more effective in distinguishing axonal remodeling after injury, when compared with FA. Entropy is also more sensitive to axonal density than axonal orientation, and thus may provide a more accurate reflection of axonal changes that occur in neurological injury and disease.

Characterizing Brain Structures and Remodeling after TBI Based on Information Content, Diffusion Entropy

Science.gov (United States)

Fozouni, Niloufar; Chopp, Michael; Nejad-Davarani, Siamak P.; Zhang, Zheng Gang; Lehman, Norman L.; Gu, Steven; Ueno, Yuji; Lu, Mei; Ding, Guangliang; Li, Lian; Hu, Jiani; Bagher-Ebadian, Hassan; Hearshen, David; Jiang, Quan

2013-01-01

Background To overcome the limitations of conventional diffusion tensor magnetic resonance imaging resulting from the assumption of a Gaussian diffusion model for characterizing voxels containing multiple axonal orientations, Shannon's entropy was employed to evaluate white matter structure in human brain and in brain remodeling after traumatic brain injury (TBI) in a rat. Methods Thirteen healthy subjects were investigated using a Q-ball based DTI data sampling scheme. FA and entropy values were measured in white matter bundles, white matter fiber crossing areas, different gray matter (GM) regions and cerebrospinal fluid (CSF). Axonal densities' from the same regions of interest (ROIs) were evaluated in Bielschowsky and Luxol fast blue stained autopsy (n = 30) brain sections by light microscopy. As a case demonstration, a Wistar rat subjected to TBI and treated with bone marrow stromal cells (MSC) 1 week after TBI was employed to illustrate the superior ability of entropy over FA in detecting reorganized crossing axonal bundles as confirmed by histological analysis with Bielschowsky and Luxol fast blue staining. Results Unlike FA, entropy was less affected by axonal orientation and more affected by axonal density. A significant agreement (r = 0.91) was detected between entropy values from in vivo human brain and histologically measured axonal density from post mortum from the same brain structures. The MSC treated TBI rat demonstrated that the entropy approach is superior to FA in detecting axonal remodeling after injury. Compared with FA, entropy detected new axonal remodeling regions with crossing axons, confirmed with immunohistological staining. Conclusions Entropy measurement is more effective in distinguishing axonal remodeling after injury, when compared with FA. Entropy is also more sensitive to axonal density than axonal orientation, and thus may provide a more accurate reflection of axonal changes that occur in neurological injury and disease

Multiscale sample entropy and cross-sample entropy based on symbolic representation and similarity of stock markets

Science.gov (United States)

Wu, Yue; Shang, Pengjian; Li, Yilong

2018-03-01

A modified multiscale sample entropy measure based on symbolic representation and similarity (MSEBSS) is proposed in this paper to research the complexity of stock markets. The modified algorithm reduces the probability of inducing undefined entropies and is confirmed to be robust to strong noise. Considering the validity and accuracy, MSEBSS is more reliable than Multiscale entropy (MSE) for time series mingled with much noise like financial time series. We apply MSEBSS to financial markets and results show American stock markets have the lowest complexity compared with European and Asian markets. There are exceptions to the regularity that stock markets show a decreasing complexity over the time scale, indicating a periodicity at certain scales. Based on MSEBSS, we introduce the modified multiscale cross-sample entropy measure based on symbolic representation and similarity (MCSEBSS) to consider the degree of the asynchrony between distinct time series. Stock markets from the same area have higher synchrony than those from different areas. And for stock markets having relative high synchrony, the entropy values will decrease with the increasing scale factor. While for stock markets having high asynchrony, the entropy values will not decrease with the increasing scale factor sometimes they tend to increase. So both MSEBSS and MCSEBSS are able to distinguish stock markets of different areas, and they are more helpful if used together for studying other features of financial time series.

System Entropy Measurement of Stochastic Partial Differential Systems

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Bor-Sen Chen

2016-03-01

Full Text Available System entropy describes the dispersal of a system’s energy and is an indication of the disorder of a physical system. Several system entropy measurement methods have been developed for dynamic systems. However, most real physical systems are always modeled using stochastic partial differential dynamic equations in the spatio-temporal domain. No efficient method currently exists that can calculate the system entropy of stochastic partial differential systems (SPDSs in consideration of the effects of intrinsic random fluctuation and compartment diffusion. In this study, a novel indirect measurement method is proposed for calculating of system entropy of SPDSs using a Hamilton–Jacobi integral inequality (HJII-constrained optimization method. In other words, we solve a nonlinear HJII-constrained optimization problem for measuring the system entropy of nonlinear stochastic partial differential systems (NSPDSs. To simplify the system entropy measurement of NSPDSs, the global linearization technique and finite difference scheme were employed to approximate the nonlinear stochastic spatial state space system. This allows the nonlinear HJII-constrained optimization problem for the system entropy measurement to be transformed to an equivalent linear matrix inequalities (LMIs-constrained optimization problem, which can be easily solved using the MATLAB LMI-toolbox (MATLAB R2014a, version 8.3. Finally, several examples are presented to illustrate the system entropy measurement of SPDSs.

Land quality, sustainable development and environmental degradation in agricultural districts: A computational approach based on entropy indexes

International Nuclear Information System (INIS)

Zambon, Ilaria; Colantoni, Andrea; Carlucci, Margherita; Morrow, Nathan; Sateriano, Adele; Salvati, Luca

2017-01-01

Land Degradation (LD) in socio-environmental systems negatively impacts sustainable development paths. This study proposes a framework to LD evaluation based on indicators of diversification in the spatial distribution of sensitive land. We hypothesize that conditions for spatial heterogeneity in a composite index of land sensitivity are more frequently associated to areas prone to LD than spatial homogeneity. Spatial heterogeneity is supposed to be associated with degraded areas that act as hotspots for future degradation processes. A diachronic analysis (1960–2010) was performed at the Italian agricultural district scale to identify environmental factors associated with spatial heterogeneity in the degree of land sensitivity to degradation based on the Environmentally Sensitive Area Index (ESAI). In 1960, diversification in the level of land sensitivity measured using two common indexes of entropy (Shannon's diversity and Pielou's evenness) increased significantly with the ESAI, indicating a high level of land sensitivity to degradation. In 2010, surface area classified as “critical” to LD was the highest in districts with diversification in the spatial distribution of ESAI values, confirming the hypothesis formulated above. Entropy indexes, based on observed alignment with the concept of LD, constitute a valuable base to inform mitigation strategies against desertification. - Highlights: • Spatial heterogeneity is supposed to be associated with degraded areas. • Entropy indexes can inform mitigation strategies against desertification. • Assessing spatial diversification in the degree of land sensitivity to degradation. • Mediterranean rural areas have an evident diversity in agricultural systems. • A diachronic analysis carried out at the Italian agricultural district scale.

Land quality, sustainable development and environmental degradation in agricultural districts: A computational approach based on entropy indexes

Energy Technology Data Exchange (ETDEWEB)

Zambon, Ilaria, E-mail: ilaria.zambon@unitus.it [Department of Agricultural and Forestry scieNcEs (DAFNE), Tuscia University, Via S. Camillo de Lellis, I-01100 Viterbo (Italy); Colantoni, Andrea [Department of Agricultural and Forestry scieNcEs (DAFNE), Tuscia University, Via S. Camillo de Lellis, I-01100 Viterbo (Italy); Carlucci, Margherita [Department of Social and Economic Science, University of Rome La Sapienza, Piazzale A. Moro 5, I-00185 Rome (Italy); Morrow, Nathan [Tulane University, Payson Program in International Development at the School of Law, New Orleans (United States); Sateriano, Adele; Salvati, Luca [Italian Council for Agricultural Research and Economics (CREA-RPS), Via della Navicella 2-4, I-00184 Rome (Italy)

2017-05-15

Land Degradation (LD) in socio-environmental systems negatively impacts sustainable development paths. This study proposes a framework to LD evaluation based on indicators of diversification in the spatial distribution of sensitive land. We hypothesize that conditions for spatial heterogeneity in a composite index of land sensitivity are more frequently associated to areas prone to LD than spatial homogeneity. Spatial heterogeneity is supposed to be associated with degraded areas that act as hotspots for future degradation processes. A diachronic analysis (1960–2010) was performed at the Italian agricultural district scale to identify environmental factors associated with spatial heterogeneity in the degree of land sensitivity to degradation based on the Environmentally Sensitive Area Index (ESAI). In 1960, diversification in the level of land sensitivity measured using two common indexes of entropy (Shannon's diversity and Pielou's evenness) increased significantly with the ESAI, indicating a high level of land sensitivity to degradation. In 2010, surface area classified as “critical” to LD was the highest in districts with diversification in the spatial distribution of ESAI values, confirming the hypothesis formulated above. Entropy indexes, based on observed alignment with the concept of LD, constitute a valuable base to inform mitigation strategies against desertification. - Highlights: • Spatial heterogeneity is supposed to be associated with degraded areas. • Entropy indexes can inform mitigation strategies against desertification. • Assessing spatial diversification in the degree of land sensitivity to degradation. • Mediterranean rural areas have an evident diversity in agricultural systems. • A diachronic analysis carried out at the Italian agricultural district scale.

Entropy as a measure of diffusion

International Nuclear Information System (INIS)

Aghamohammadi, Amir; Fatollahi, Amir H.; Khorrami, Mohammad; Shariati, Ahmad

2013-01-01

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.

Entropy as a measure of diffusion

Energy Technology Data Exchange (ETDEWEB)

Aghamohammadi, Amir, E-mail: mohamadi@alzahra.ac.ir; Fatollahi, Amir H., E-mail: fath@alzahra.ac.ir; Khorrami, Mohammad, E-mail: mamwad@mailaps.org; Shariati, Ahmad, E-mail: shariati@mailaps.org

2013-10-15

The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large times the entropy tends exponentially to a constant. For systems with no stationary density, at large times the entropy is logarithmic with a coefficient specifying the speed of the diffusion. As an example, the large-time behaviors of the entropy and the variance are compared for various types of fractional-derivative diffusions.

Multichannel interictal spike activity detection using time-frequency entropy measure.

Science.gov (United States)

Thanaraj, Palani; Parvathavarthini, B

2017-06-01

Localization of interictal spikes is an important clinical step in the pre-surgical assessment of pharmacoresistant epileptic patients. The manual selection of interictal spike periods is cumbersome and involves a considerable amount of analysis workload for the physician. The primary focus of this paper is to automate the detection of interictal spikes for clinical applications in epilepsy localization. The epilepsy localization procedure involves detection of spikes in a multichannel EEG epoch. Therefore, a multichannel Time-Frequency (T-F) entropy measure is proposed to extract features related to the interictal spike activity. Least squares support vector machine is used to train the proposed feature to classify the EEG epochs as either normal or interictal spike period. The proposed T-F entropy measure, when validated with epilepsy dataset of 15 patients, shows an interictal spike classification accuracy of 91.20%, sensitivity of 100% and specificity of 84.23%. Moreover, the area under the curve of Receiver Operating Characteristics plot of 0.9339 shows the superior classification performance of the proposed T-F entropy measure. The results of this paper show a good spike detection accuracy without any prior information about the spike morphology.

Entropy of the system formed in heavy ion collision

International Nuclear Information System (INIS)

Gudima, K.K.; Schulz, H.; Toneev, V.D.

1985-01-01

In frames of a cascade model the entropy evolution in a system producted in heavy ion collisions is investigated. Entropy calculation is based on smoothing of the distribution function over the momentum space by the temperature field introduction. The resulting entropy per one nucleon is shown to be rather sensitive to phase space subdivision into cells at the stage of free scattering of reaction products. Compared to recent experimental results for specific entropy values inferred from the composite particle yield of 4π measurements, it is found that cascade calculations do not favour some particular entropy model treatments and suggest smaller entropy values than following from consideration within equilibrium statistics

Changes in the Complexity of Heart Rate Variability with Exercise Training Measured by Multiscale Entropy-Based Measurements

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Frederico Sassoli Fazan

2018-01-01

Full Text Available Quantifying complexity from heart rate variability (HRV series is a challenging task, and multiscale entropy (MSE, along with its variants, has been demonstrated to be one of the most robust approaches to achieve this goal. Although physical training is known to be beneficial, there is little information about the long-term complexity changes induced by the physical conditioning. The present study aimed to quantify the changes in physiological complexity elicited by physical training through multiscale entropy-based complexity measurements. Rats were subject to a protocol of medium intensity training ( n = 13 or a sedentary protocol ( n = 12 . One-hour HRV series were obtained from all conscious rats five days after the experimental protocol. We estimated MSE, multiscale dispersion entropy (MDE and multiscale SDiff q from HRV series. Multiscale SDiff q is a recent approach that accounts for entropy differences between a given time series and its shuffled dynamics. From SDiff q , three attributes (q-attributes were derived, namely SDiff q m a x , q m a x and q z e r o . MSE, MDE and multiscale q-attributes presented similar profiles, except for SDiff q m a x . q m a x showed significant differences between trained and sedentary groups on Time Scales 6 to 20. Results suggest that physical training increases the system complexity and that multiscale q-attributes provide valuable information about the physiological complexity.

A STUDY OF WAVELET ENTROPY MEASURE DEFINITION AND ITS APPLICATION FOR FAULT FEATURE PICK-UP AND CLASSIFICATION

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

Shannon entropy in time domain is a measure of signal or system uncertainty. When based on spectrum entropy, Shannon entropy can be taken as a measure of signal or system complexity.Therefore, wavelet analysis based on wavelet entropy measure can signify the complexity of non-steady signal or system in both time and frequency domain. In this paper, in order to meet the requirements of post-analysis on abundant wavelet transform result data and the need of information mergence, the basic definition of wavelet entropy measure is proposed, corresponding algorithms of several wavelet entropies, such as wavelet average entropy, wavelet time-frequency entropy, wavelet distance entropy,etc. are put forward, and the physical meanings of these entropies are analyzed as well. The application principle of wavelet entropy measure in ElectroEncephaloGraphy (EEG) signal analysis, mechanical fault diagnosis, fault detection and classification in power system are analyzed. Finally, take the transmission line fault detection in power system for example, simulations in two different systems, a 10kV automatic blocking and continuous power transmission line and a 500kV Extra High Voltage (EHV) transmission line, are carried out, and the two methods, wavelet entropy and wavelet modulus maxima, are compared, the results show feasibility and application prospect of the six wavelet entropies.

Upper entropy axioms and lower entropy axioms

International Nuclear Information System (INIS)

Guo, Jin-Li; Suo, Qi

2015-01-01

The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak upper entropy axioms and weak lower entropy axioms. Their conditions are weaker than those of Shannon–Khinchin axioms and Tsallis axioms, while these conditions are stronger than those of the axiomatics based on the first three Shannon–Khinchin axioms. The subadditivity and strong subadditivity of entropy are obtained in the new axiomatics. Tsallis statistics is a special case of satisfying our axioms. Moreover, different forms of information measures, such as Shannon entropy, Daroczy entropy, Tsallis entropy and other entropies, can be unified under the same axiomatics

Entropy: A new measure of stock market volatility?

Science.gov (United States)

Bentes, Sonia R.; Menezes, Rui

2012-11-01

When uncertainty dominates understanding stock market volatility is vital. There are a number of reasons for that. On one hand, substantial changes in volatility of financial market returns are capable of having significant negative effects on risk averse investors. In addition, such changes can also impact on consumption patterns, corporate capital investment decisions and macroeconomic variables. Arguably, volatility is one of the most important concepts in the whole finance theory. In the traditional approach this phenomenon has been addressed based on the concept of standard-deviation (or variance) from which all the famous ARCH type models - Autoregressive Conditional Heteroskedasticity Models- depart. In this context, volatility is often used to describe dispersion from an expected value, price or model. The variability of traded prices from their sample mean is only an example. Although as a measure of uncertainty and risk standard-deviation is very popular since it is simple and easy to calculate it has long been recognized that it is not fully satisfactory. The main reason for that lies in the fact that it is severely affected by extreme values. This may suggest that this is not a closed issue. Bearing on the above we might conclude that many other questions might arise while addressing this subject. One of outstanding importance, from which more sophisticated analysis can be carried out, is how to evaluate volatility, after all? If the standard-deviation has some drawbacks shall we still rely on it? Shall we look for an alternative measure? In searching for this shall we consider the insight of other domains of knowledge? In this paper we specifically address if the concept of entropy, originally developed in physics by Clausius in the XIX century, which can constitute an effective alternative. Basically, what we try to understand is, which are the potentialities of entropy compared to the standard deviation. But why entropy? The answer lies on the fact

Entropy-Based Clutter Rejection for Intrawall Diagnostics

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Raffaele Solimene

2012-01-01

Full Text Available The intrawall diagnostic problem of detecting localized inhomogeneities possibly present within the wall is addressed. As well known, clutter arising from masonry structure can impair detection of embedded scatterers due to high amplitude reflections that wall front face introduces. Moreover, internal multiple reflections also can make it difficult ground penetrating radar images (radargramms interpretation. To counteract these drawbacks, a clutter rejection method, properly tailored on the wall features, is mandatory. To this end, here we employ a windowing strategy based on entropy measures of temporal traces “similarity.” Accordingly, instants of time for which radargramms exhibit entropy values greater than a prescribed threshold are “silenced.” Numerical results are presented in order to show the effectiveness of the entropy-based clutter rejection algorithm. Moreover, a comparison with the standard average trace subtraction is also included.

Investigating dynamical complexity in the magnetosphere using various entropy measures

Science.gov (United States)

Balasis, Georgios; Daglis, Ioannis A.; Papadimitriou, Constantinos; Kalimeri, Maria; Anastasiadis, Anastasios; Eftaxias, Konstantinos

2009-09-01

The complex system of the Earth's magnetosphere corresponds to an open spatially extended nonequilibrium (input-output) dynamical system. The nonextensive Tsallis entropy has been recently introduced as an appropriate information measure to investigate dynamical complexity in the magnetosphere. The method has been employed for analyzing Dst time series and gave promising results, detecting the complexity dissimilarity among different physiological and pathological magnetospheric states (i.e., prestorm activity and intense magnetic storms, respectively). This paper explores the applicability and effectiveness of a variety of computable entropy measures (e.g., block entropy, Kolmogorov entropy, T complexity, and approximate entropy) to the investigation of dynamical complexity in the magnetosphere. We show that as the magnetic storm approaches there is clear evidence of significant lower complexity in the magnetosphere. The observed higher degree of organization of the system agrees with that inferred previously, from an independent linear fractal spectral analysis based on wavelet transforms. This convergence between nonlinear and linear analyses provides a more reliable detection of the transition from the quiet time to the storm time magnetosphere, thus showing evidence that the occurrence of an intense magnetic storm is imminent. More precisely, we claim that our results suggest an important principle: significant complexity decrease and accession of persistency in Dst time series can be confirmed as the magnetic storm approaches, which can be used as diagnostic tools for the magnetospheric injury (global instability). Overall, approximate entropy and Tsallis entropy yield superior results for detecting dynamical complexity changes in the magnetosphere in comparison to the other entropy measures presented herein. Ultimately, the analysis tools developed in the course of this study for the treatment of Dst index can provide convenience for space weather

Entropies from Markov Models as Complexity Measures of Embedded Attractors

Directory of Open Access Journals (Sweden)

Julián D. Arias-Londoño

2015-06-01

Full Text Available This paper addresses the problem of measuring complexity from embedded attractors as a way to characterize changes in the dynamical behavior of different types of systems with a quasi-periodic behavior by observing their outputs. With the aim of measuring the stability of the trajectories of the attractor along time, this paper proposes three new estimations of entropy that are derived from a Markov model of the embedded attractor. The proposed estimators are compared with traditional nonparametric entropy measures, such as approximate entropy, sample entropy and fuzzy entropy, which only take into account the spatial dimension of the trajectory. The method proposes the use of an unsupervised algorithm to find the principal curve, which is considered as the “profile trajectory”, that will serve to adjust the Markov model. The new entropy measures are evaluated using three synthetic experiments and three datasets of physiological signals. In terms of consistency and discrimination capabilities, the results show that the proposed measures perform better than the other entropy measures used for comparison purposes.

Rényi entropy measure of noise-aided information transmission in a binary channel.

Science.gov (United States)

Chapeau-Blondeau, François; Rousseau, David; Delahaies, Agnès

2010-05-01

This paper analyzes a binary channel by means of information measures based on the Rényi entropy. The analysis extends, and contains as a special case, the classic reference model of binary information transmission based on the Shannon entropy measure. The extended model is used to investigate further possibilities and properties of stochastic resonance or noise-aided information transmission. The results demonstrate that stochastic resonance occurs in the information channel and is registered by the Rényi entropy measures at any finite order, including the Shannon order. Furthermore, in definite conditions, when seeking the Rényi information measures that best exploit stochastic resonance, then nontrivial orders differing from the Shannon case usually emerge. In this way, through binary information transmission, stochastic resonance identifies optimal Rényi measures of information differing from the classic Shannon measure. A confrontation of the quantitative information measures with visual perception is also proposed in an experiment of noise-aided binary image transmission.

Entropy-Based Privacy against Profiling of User Mobility

Directory of Open Access Journals (Sweden)

Alicia Rodriguez-Carrion

2015-06-01

Full Text Available Location-based services (LBSs flood mobile phones nowadays, but their use poses an evident privacy risk. The locations accompanying the LBS queries can be exploited by the LBS provider to build the user profile of visited locations, which might disclose sensitive data, such as work or home locations. The classic concept of entropy is widely used to evaluate privacy in these scenarios, where the information is represented as a sequence of independent samples of categorized data. However, since the LBS queries might be sent very frequently, location profiles can be improved by adding temporal dependencies, thus becoming mobility profiles, where location samples are not independent anymore and might disclose the user’s mobility patterns. Since the time dimension is factored in, the classic entropy concept falls short of evaluating the real privacy level, which depends also on the time component. Therefore, we propose to extend the entropy-based privacy metric to the use of the entropy rate to evaluate mobility profiles. Then, two perturbative mechanisms are considered to preserve locations and mobility profiles under gradual utility constraints. We further use the proposed privacy metric and compare it to classic ones to evaluate both synthetic and real mobility profiles when the perturbative methods proposed are applied. The results prove the usefulness of the proposed metric for mobility profiles and the need for tailoring the perturbative methods to the features of mobility profiles in order to improve privacy without completely loosing utility.

Automated EEG entropy measurements in coma, vegetative state/unresponsive wakefulness syndrome and minimally conscious state

Science.gov (United States)

Gosseries, Olivia; Schnakers, Caroline; Ledoux, Didier; Vanhaudenhuyse, Audrey; Bruno, Marie-Aurélie; Demertzi, Athéna; Noirhomme, Quentin; Lehembre, Rémy; Damas, Pierre; Goldman, Serge; Peeters, Erika; Moonen, Gustave; Laureys, Steven

Summary Monitoring the level of consciousness in brain-injured patients with disorders of consciousness is crucial as it provides diagnostic and prognostic information. Behavioral assessment remains the gold standard for assessing consciousness but previous studies have shown a high rate of misdiagnosis. This study aimed to investigate the usefulness of electroencephalography (EEG) entropy measurements in differentiating unconscious (coma or vegetative) from minimally conscious patients. Left fronto-temporal EEG recordings (10-minute resting state epochs) were prospectively obtained in 56 patients and 16 age-matched healthy volunteers. Patients were assessed in the acute (≤1 month post-injury; n=29) or chronic (>1 month post-injury; n=27) stage. The etiology was traumatic in 23 patients. Automated online EEG entropy calculations (providing an arbitrary value ranging from 0 to 91) were compared with behavioral assessments (Coma Recovery Scale-Revised) and outcome. EEG entropy correlated with Coma Recovery Scale total scores (r=0.49). Mean EEG entropy values were higher in minimally conscious (73±19; mean and standard deviation) than in vegetative/unresponsive wakefulness syndrome patients (45±28). Receiver operating characteristic analysis revealed an entropy cut-off value of 52 differentiating acute unconscious from minimally conscious patients (sensitivity 89% and specificity 90%). In chronic patients, entropy measurements offered no reliable diagnostic information. EEG entropy measurements did not allow prediction of outcome. User-independent time-frequency balanced spectral EEG entropy measurements seem to constitute an interesting diagnostic – albeit not prognostic – tool for assessing neural network complexity in disorders of consciousness in the acute setting. Future studies are needed before using this tool in routine clinical practice, and these should seek to improve automated EEG quantification paradigms in order to reduce the remaining false

Enhancement of Edge-based Image Quality Measures Using Entropy for Histogram Equalization-based Contrast Enhancement Techniques

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H. T. R. Kurmasha

2017-12-01

Full Text Available An Edge-based image quality measure (IQM technique for the assessment of histogram equalization (HE-based contrast enhancement techniques has been proposed that outperforms the Absolute Mean Brightness Error (AMBE and Entropy which are the most commonly used IQMs to evaluate Histogram Equalization based techniques, and also the two prominent fidelity-based IQMs which are Multi-Scale Structural Similarity (MSSIM and Information Fidelity Criterion-based (IFC measures. The statistical evaluation results show that the Edge-based IQM, which was designed for detecting noise artifacts distortion, has a Person Correlation Coefficient (PCC > 0.86 while the others have poor or fair correlation to human opinion, considering the Human Visual Perception (HVP. Based on HVP, this paper propose an enhancement to classic Edge-based IQM by taking into account the brightness saturation distortion which is the most prominent distortion in HE-based contrast enhancement techniques. It is tested and found to have significantly well correlation (PCC > 0.87, Spearman rank order correlation coefficient (SROCC > 0.92, Root Mean Squared Error (RMSE < 0.1054, and Outlier Ratio (OR = 0%.

Entropy and equilibrium via games of complexity

Science.gov (United States)

Topsøe, Flemming

2004-09-01

It is suggested that thermodynamical equilibrium equals game theoretical equilibrium. Aspects of this thesis are discussed. The philosophy is consistent with maximum entropy thinking of Jaynes, but goes one step deeper by deriving the maximum entropy principle from an underlying game theoretical principle. The games introduced are based on measures of complexity. Entropy is viewed as minimal complexity. It is demonstrated that Tsallis entropy ( q-entropy) and Kaniadakis entropy ( κ-entropy) can be obtained in this way, based on suitable complexity measures. A certain unifying effect is obtained by embedding these measures in a two-parameter family of entropy functions.

Entropy of Bit-Stuffing-Induced Measures for Two-Dimensional Checkerboard Constraints

DEFF Research Database (Denmark)

Forchhammer, Søren; Vaarby, Torben Strange

2007-01-01

A modified bit-stuffing scheme for two-dimensional (2-D) checkerboard constraints is introduced. The entropy of the scheme is determined based on a probability measure defined by the modified bit-stuffing. Entropy results of the scheme are given for 2-D constraints on a binary alphabet....... The constraints considered are 2-D RLL (d, infinity) for d = 2, 3 and 4 as well as for the constraint with a minimum 1-norm distance of 3 between Is. For these results the entropy is within 1-2% of an upper bound on the capacity for the constraint. As a variation of the scheme, periodic merging arrays are also...

A generalized complexity measure based on Rényi entropy

Science.gov (United States)

Sánchez-Moreno, Pablo; Angulo, Juan Carlos; Dehesa, Jesus S.

2014-08-01

The intrinsic statistical complexities of finite many-particle systems (i.e., those defined in terms of the single-particle density) quantify the degree of structure or patterns, far beyond the entropy measures. They are intuitively constructed to be minima at the opposite extremes of perfect order and maximal randomness. Starting from the pioneering LMC measure, which satisfies these requirements, some extensions of LMC-Rényi type have been published in the literature. The latter measures were shown to describe a variety of physical aspects of the internal disorder in atomic and molecular systems (e.g., quantum phase transitions, atomic shell filling) which are not grasped by their mother LMC quantity. However, they are not minimal for maximal randomness in general. In this communication, we propose a generalized LMC-Rényi complexity which overcomes this problem. Some applications which illustrate this fact are given.

Classicality condition on a system observable in a quantum measurement and a relative-entropy conservation law

Science.gov (United States)

Kuramochi, Yui; Ueda, Masahito

2015-03-01

We consider the information flow on a system observable X corresponding to a positive-operator-valued measure under a quantum measurement process Y described by a completely positive instrument from the viewpoint of the relative entropy. We establish a sufficient condition for the relative-entropy conservation law which states that the average decrease in the relative entropy of the system observable X equals the relative entropy of the measurement outcome of Y , i.e., the information gain due to measurement. This sufficient condition is interpreted as an assumption of classicality in the sense that there exists a sufficient statistic in a joint successive measurement of Y followed by X such that the probability distribution of the statistic coincides with that of a single measurement of X for the premeasurement state. We show that in the case when X is a discrete projection-valued measure and Y is discrete, the classicality condition is equivalent to the relative-entropy conservation for arbitrary states. The general theory on the relative-entropy conservation is applied to typical quantum measurement models, namely, quantum nondemolition measurement, destructive sharp measurements on two-level systems, a photon counting, a quantum counting, homodyne and heterodyne measurements. These examples except for the nondemolition and photon-counting measurements do not satisfy the known Shannon-entropy conservation law proposed by Ban [M. Ban, J. Phys. A: Math. Gen. 32, 1643 (1999), 10.1088/0305-4470/32/9/012], implying that our approach based on the relative entropy is applicable to a wider class of quantum measurements.

Entropy, Shannon’s Measure of Information and Boltzmann’s H-Theorem

Directory of Open Access Journals (Sweden)

Arieh Ben-Naim

2017-01-01

Full Text Available We start with a clear distinction between Shannon’s Measure of Information (SMI and the Thermodynamic Entropy. The first is defined on any probability distribution; and therefore it is a very general concept. On the other hand Entropy is defined on a very special set of distributions. Next we show that the Shannon Measure of Information (SMI provides a solid and quantitative basis for the interpretation of the thermodynamic entropy. The entropy measures the uncertainty in the distribution of the locations and momenta of all the particles; as well as two corrections due to the uncertainty principle and the indistinguishability of the particles. Finally we show that the H-function as defined by Boltzmann is an SMI but not entropy. Therefore; much of what has been written on the H-theorem is irrelevant to entropy and the Second Law of Thermodynamics.

Survey of sampling-based methods for uncertainty and sensitivity analysis

International Nuclear Information System (INIS)

Helton, J.C.; Johnson, J.D.; Sallaberry, C.J.; Storlie, C.B.

2006-01-01

Sampling-based methods for uncertainty and sensitivity analysis are reviewed. The following topics are considered: (i) definition of probability distributions to characterize epistemic uncertainty in analysis inputs (ii) generation of samples from uncertain analysis inputs (iii) propagation of sampled inputs through an analysis (iv) presentation of uncertainty analysis results, and (v) determination of sensitivity analysis results. Special attention is given to the determination of sensitivity analysis results, with brief descriptions and illustrations given for the following procedures/techniques: examination of scatterplots, correlation analysis, regression analysis, partial correlation analysis, rank transformations, statistical tests for patterns based on gridding, entropy tests for patterns based on gridding, nonparametric regression analysis, squared rank differences/rank correlation coefficient test, two-dimensional Kolmogorov-Smirnov test, tests for patterns based on distance measures, top down coefficient of concordance, and variance decomposition

Survey of sampling-based methods for uncertainty and sensitivity analysis.

Energy Technology Data Exchange (ETDEWEB)

Johnson, Jay Dean; Helton, Jon Craig; Sallaberry, Cedric J. PhD. (.; .); Storlie, Curt B. (Colorado State University, Fort Collins, CO)

2006-06-01

Sampling-based methods for uncertainty and sensitivity analysis are reviewed. The following topics are considered: (1) Definition of probability distributions to characterize epistemic uncertainty in analysis inputs, (2) Generation of samples from uncertain analysis inputs, (3) Propagation of sampled inputs through an analysis, (4) Presentation of uncertainty analysis results, and (5) Determination of sensitivity analysis results. Special attention is given to the determination of sensitivity analysis results, with brief descriptions and illustrations given for the following procedures/techniques: examination of scatterplots, correlation analysis, regression analysis, partial correlation analysis, rank transformations, statistical tests for patterns based on gridding, entropy tests for patterns based on gridding, nonparametric regression analysis, squared rank differences/rank correlation coefficient test, two dimensional Kolmogorov-Smirnov test, tests for patterns based on distance measures, top down coefficient of concordance, and variance decomposition.

Extending Entropy Stability Measure To External Debt Structure ...

African Journals Online (AJOL)

This study focuses on the measure of stability of external debt using entropy. This is achieved by modifying the conglomerate of Shannon and Boltzmann entropy. This modification rectifies the limitations of these models. Practical illustration of the modified model is also given to justify its use. Journal of Science ...

Value at risk estimation with entropy-based wavelet analysis in exchange markets

Science.gov (United States)

He, Kaijian; Wang, Lijun; Zou, Yingchao; Lai, Kin Keung

2014-08-01

In recent years, exchange markets are increasingly integrated together. Fluctuations and risks across different exchange markets exhibit co-moving and complex dynamics. In this paper we propose the entropy-based multivariate wavelet based approaches to analyze the multiscale characteristic in the multidimensional domain and improve further the Value at Risk estimation reliability. Wavelet analysis has been introduced to construct the entropy-based Multiscale Portfolio Value at Risk estimation algorithm to account for the multiscale dynamic correlation. The entropy measure has been proposed as the more effective measure with the error minimization principle to select the best basis when determining the wavelet families and the decomposition level to use. The empirical studies conducted in this paper have provided positive evidence as to the superior performance of the proposed approach, using the closely related Chinese Renminbi and European Euro exchange market.

The Shannon entropy as a measure of diffusion in multidimensional dynamical systems

Science.gov (United States)

Giordano, C. M.; Cincotta, P. M.

2018-05-01

In the present work, we introduce two new estimators of chaotic diffusion based on the Shannon entropy. Using theoretical, heuristic and numerical arguments, we show that the entropy, S, provides a measure of the diffusion extent of a given small initial ensemble of orbits, while an indicator related with the time derivative of the entropy, S', estimates the diffusion rate. We show that in the limiting case of near ergodicity, after an appropriate normalization, S' coincides with the standard homogeneous diffusion coefficient. The very first application of this formulation to a 4D symplectic map and to the Arnold Hamiltonian reveals very successful and encouraging results.

Relation Entropy and Transferable Entropy Think of Aggregation on Group Decision Making

Institute of Scientific and Technical Information of China (English)

CHENG Qi-yue; QIU Wan-hua; LIU Xiao-feng

2002-01-01

In this paper, aggregation question based on group decision making and a single decision making is studied. The theory of entropy is applied to the sets pair analysis. The system of relation entropy and the transferable entropy notion are put. The character is studied. An potential by the relation entropy and transferable entropy are defined. It is the consistency measure on the group between a single decision making. We gained a new aggregation effective definition on the group misjudge.

Application of entropy measurement technique in grey based ...

African Journals Online (AJOL)

For this study, four control variables are selected current, voltage, gas flow rate and ... Keywords: Metal Inert Gas (MIG) Welding, Grey-Taguchi Method, Entropy ...... of metal inert gas welding on the corrosion and mechanical behaviour of.

Entropy-based automated classification of independent components separated from fMCG

International Nuclear Information System (INIS)

Comani, S; Srinivasan, V; Alleva, G; Romani, G L

2007-01-01

Fetal magnetocardiography (fMCG) is a noninvasive technique suitable for the prenatal diagnosis of the fetal heart function. Reliable fetal cardiac signals can be reconstructed from multi-channel fMCG recordings by means of independent component analysis (ICA). However, the identification of the separated components is usually accomplished by visual inspection. This paper discusses a novel automated system based on entropy estimators, namely approximate entropy (ApEn) and sample entropy (SampEn), for the classification of independent components (ICs). The system was validated on 40 fMCG datasets of normal fetuses with the gestational age ranging from 22 to 37 weeks. Both ApEn and SampEn were able to measure the stability and predictability of the physiological signals separated with ICA, and the entropy values of the three categories were significantly different at p <0.01. The system performances were compared with those of a method based on the analysis of the time and frequency content of the components. The outcomes of this study showed a superior performance of the entropy-based system, in particular for early gestation, with an overall ICs detection rate of 98.75% and 97.92% for ApEn and SampEn respectively, as against a value of 94.50% obtained with the time-frequency-based system. (note)

Towards an entropy-based analysis of log variability

DEFF Research Database (Denmark)

Back, Christoffer Olling; Debois, Søren; Slaats, Tijs

2017-01-01

the development of hybrid miners: given a (sub-)log, can we determine a priori whether the log is best suited for imperative or declarative mining? We propose using the concept of entropy, commonly used in information theory. We consider different measures for entropy that could be applied and show through...... experimentation on both synthetic and real-life logs that these entropy measures do indeed give insights into the complexity of the log and can act as an indicator of which mining paradigm should be used....

Towards an Entropy-based Analysis of Log Variability

DEFF Research Database (Denmark)

Back, Christoffer Olling; Debois, Søren; Slaats, Tijs

2018-01-01

the development of hybrid miners: given a log, can we determine a priori whether the log is best suited for imperative or declarative mining? We propose using the concept of entropy, commonly used in information theory. We consider different measures for entropy that could be applied and show through...... experimentation on both synthetic and real-life logs that these entropy measures do indeed give insights into the complexity of the log and can act as an indicator of which mining paradigm should be used....

Lattice-Valued Possibilistic Entropy Measure

Czech Academy of Sciences Publication Activity Database

Kramosil, Ivan

2008-01-01

Roč. 16, č. 6 (2008), s. 829-846 ISSN 0218-4885 R&D Projects: GA AV ČR IAA100300503 Institutional research plan: CEZ:AV0Z10300504 Keywords : complete lattice * lattice-valued possibilistic distribution * entropy measure * product of possibilistic distribution Subject RIV: BA - General Mathematics Impact factor: 1.000, year: 2008

Financial time series analysis based on effective phase transfer entropy

Science.gov (United States)

Yang, Pengbo; Shang, Pengjian; Lin, Aijing

2017-02-01

Transfer entropy is a powerful technique which is able to quantify the impact of one dynamic system on another system. In this paper, we propose the effective phase transfer entropy method based on the transfer entropy method. We use simulated data to test the performance of this method, and the experimental results confirm that the proposed approach is capable of detecting the information transfer between the systems. We also explore the relationship between effective phase transfer entropy and some variables, such as data size, coupling strength and noise. The effective phase transfer entropy is positively correlated with the data size and the coupling strength. Even in the presence of a large amount of noise, it can detect the information transfer between systems, and it is very robust to noise. Moreover, this measure is indeed able to accurately estimate the information flow between systems compared with phase transfer entropy. In order to reflect the application of this method in practice, we apply this method to financial time series and gain new insight into the interactions between systems. It is demonstrated that the effective phase transfer entropy can be used to detect some economic fluctuations in the financial market. To summarize, the effective phase transfer entropy method is a very efficient tool to estimate the information flow between systems.

Information Entropy-Based Metrics for Measuring Emergences in Artificial Societies

Directory of Open Access Journals (Sweden)

Mingsheng Tang

2014-08-01

Full Text Available Emergence is a common phenomenon, and it is also a general and important concept in complex dynamic systems like artificial societies. Usually, artificial societies are used for assisting in resolving several complex social issues (e.g., emergency management, intelligent transportation system with the aid of computer science. The levels of an emergence may have an effect on decisions making, and the occurrence and degree of an emergence are generally perceived by human observers. However, due to the ambiguity and inaccuracy of human observers, to propose a quantitative method to measure emergences in artificial societies is a meaningful and challenging task. This article mainly concentrates upon three kinds of emergences in artificial societies, including emergence of attribution, emergence of behavior, and emergence of structure. Based on information entropy, three metrics have been proposed to measure emergences in a quantitative way. Meanwhile, the correctness of these metrics has been verified through three case studies (the spread of an infectious influenza, a dynamic microblog network, and a flock of birds with several experimental simulations on the Netlogo platform. These experimental results confirm that these metrics increase with the rising degree of emergences. In addition, this article also has discussed the limitations and extended applications of these metrics.

Two Notes on Measure-Theoretic Entropy of Random Dynamical Systems

Institute of Scientific and Technical Information of China (English)

YuJun ZHU

2009-01-01

In this paper, Brin-Katok local entropy formula and Katok's definition of the measure theoretic entropy using spanning set are established for the random dynamical system over an invertible ergodic system.

Inferring a Drive-Response Network from Time Series of Topological Measures in Complex Networks with Transfer Entropy

Directory of Open Access Journals (Sweden)

Xinbo Ai

2014-11-01

Full Text Available Topological measures are crucial to describe, classify and understand complex networks. Lots of measures are proposed to characterize specific features of specific networks, but the relationships among these measures remain unclear. Taking into account that pulling networks from different domains together for statistical analysis might provide incorrect conclusions, we conduct our investigation with data observed from the same network in the form of simultaneously measured time series. We synthesize a transfer entropy-based framework to quantify the relationships among topological measures, and then to provide a holistic scenario of these measures by inferring a drive-response network. Techniques from Symbolic Transfer Entropy, Effective Transfer Entropy, and Partial Transfer Entropy are synthesized to deal with challenges such as time series being non-stationary, finite sample effects and indirect effects. We resort to kernel density estimation to assess significance of the results based on surrogate data. The framework is applied to study 20 measures across 2779 records in the Technology Exchange Network, and the results are consistent with some existing knowledge. With the drive-response network, we evaluate the influence of each measure by calculating its strength, and cluster them into three classes, i.e., driving measures, responding measures and standalone measures, according to the network communities.

Entropy Measures as Geometrical Tools in the Study of Cosmology

Directory of Open Access Journals (Sweden)

Gilbert Weinstein

2017-12-01

Full Text Available Classical chaos is often characterized as exponential divergence of nearby trajectories. In many interesting cases these trajectories can be identified with geodesic curves. We define here the entropy by S = ln χ ( x with χ ( x being the distance between two nearby geodesics. We derive an equation for the entropy, which by transformation to a Riccati-type equation becomes similar to the Jacobi equation. We further show that the geodesic equation for a null geodesic in a double-warped spacetime leads to the same entropy equation. By applying a Robertson–Walker metric for a flat three-dimensional Euclidean space expanding as a function of time, we again reach the entropy equation stressing the connection between the chosen entropy measure and time. We finally turn to the Raychaudhuri equation for expansion, which also is a Riccati equation similar to the transformed entropy equation. Those Riccati-type equations have solutions of the same form as the Jacobi equation. The Raychaudhuri equation can be transformed to a harmonic oscillator equation, and it has been shown that the geodesic deviation equation of Jacobi is essentially equivalent to that of a harmonic oscillator. The Raychaudhuri equations are strong geometrical tools in the study of general relativity and cosmology. We suggest a refined entropy measure applicable in cosmology and defined by the average deviation of the geodesics in a congruence.

Constructing a Measurement Method of Differences in Group Preferences Based on Relative Entropy

Directory of Open Access Journals (Sweden)

Shiyu Zhang

2017-01-01

Full Text Available In the research and data analysis of the differences involved in group preferences, conventional statistical methods cannot reflect the integrity and preferences of human minds; in particular, it is difficult to exclude humans’ irrational factors. This paper introduces a preference amount model based on relative entropy theory. A related expansion is made based on the characteristics of the questionnaire data, and we also construct the parameters to measure differences in the data distribution of different groups on the whole. In this paper, this parameter is called the center distance, and it effectively reflects the preferences of human minds. Using the survey data of securities market participants as an example, this paper analyzes differences in market participants’ attitudes toward the effectiveness of securities regulation. Based on this method, differences between groups that were overlooked by analysis of variance are found, and certain aspects obscured by general data characteristics are also found.

Advancing Shannon Entropy for Measuring Diversity in Systems

Directory of Open Access Journals (Sweden)

R. Rajaram

2017-01-01

Full Text Available From economic inequality and species diversity to power laws and the analysis of multiple trends and trajectories, diversity within systems is a major issue for science. Part of the challenge is measuring it. Shannon entropy H has been used to rethink diversity within probability distributions, based on the notion of information. However, there are two major limitations to Shannon’s approach. First, it cannot be used to compare diversity distributions that have different levels of scale. Second, it cannot be used to compare parts of diversity distributions to the whole. To address these limitations, we introduce a renormalization of probability distributions based on the notion of case-based entropy Cc as a function of the cumulative probability c. Given a probability density p(x, Cc measures the diversity of the distribution up to a cumulative probability of c, by computing the length or support of an equivalent uniform distribution that has the same Shannon information as the conditional distribution of p^c(x up to cumulative probability c. We illustrate the utility of our approach by renormalizing and comparing three well-known energy distributions in physics, namely, the Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac distributions for energy of subatomic particles. The comparison shows that Cc is a vast improvement over H as it provides a scale-free comparison of these diversity distributions and also allows for a comparison between parts of these diversity distributions.

Entropy-based implied volatility and its information content

NARCIS (Netherlands)

X. Xiao (Xiao); C. Zhou (Chen)

2016-01-01

markdownabstractThis paper investigates the maximum entropy approach on estimating implied volatility. The entropy approach also allows to measure option implied skewness and kurtosis nonparametrically, and to construct confidence intervals. Simulations show that the en- tropy approach outperforms

Algorithmic randomness, physical entropy, measurements, and the second law

International Nuclear Information System (INIS)

Zurek, W.H.

1989-01-01

Algorithmic information content is equal to the size -- in the number of bits -- of the shortest program for a universal Turing machine which can reproduce a state of a physical system. In contrast to the statistical Boltzmann-Gibbs-Shannon entropy, which measures ignorance, the algorithmic information content is a measure of the available information. It is defined without a recourse to probabilities and can be regarded as a measure of randomness of a definite microstate. I suggest that the physical entropy S -- that is, the quantity which determines the amount of the work ΔW which can be extracted in the cyclic isothermal expansion process through the equation ΔW = k B TΔS -- is a sum of two contributions: the mission information measured by the usual statistical entropy and the known randomness measured by the algorithmic information content. The sum of these two contributions is a ''constant of motion'' in the process of a dissipation less measurement on an equilibrium ensemble. This conservation under a measurement, which can be traced back to the noiseless coding theorem of Shannon, is necessary to rule out existence of a successful Maxwell's demon. 17 refs., 3 figs

Can state or response entropy be used as a measure of sleep depth?

LENUS (Irish Health Repository)

Mahon, P

2012-02-03

SUMMARY: In this prospective observational study we examined the potential of the spectral entropy measures \\'state\\' and \\'response\\' entropy (Entropy monitor), as measures of sleep depth in 12 healthy adult subjects. Both median state and response entropy values varied significantly with sleep stage (p = 0.017 and p = 0.014 respectively; ANOVA). Median state or response entropy did not decrease significantly during the transition from awake to stage I sleep (p > 0.017). State entropy values decreased significantly between sleep stages I and II (p < 0.001). Both state and response entropy values were significantly less (40 and 45 arbitrary units respectively) in stage III (slow wave sleep) vs stage II sleep (p = 0.008). We conclude that state and response entropy values, when expressed as a function of time, may be a useful means of quantifying aspects of sleep.

New Fault Recognition Method for Rotary Machinery Based on Information Entropy and a Probabilistic Neural Network.

Science.gov (United States)

Jiang, Quansheng; Shen, Yehu; Li, Hua; Xu, Fengyu

2018-01-24

Feature recognition and fault diagnosis plays an important role in equipment safety and stable operation of rotating machinery. In order to cope with the complexity problem of the vibration signal of rotating machinery, a feature fusion model based on information entropy and probabilistic neural network is proposed in this paper. The new method first uses information entropy theory to extract three kinds of characteristics entropy in vibration signals, namely, singular spectrum entropy, power spectrum entropy, and approximate entropy. Then the feature fusion model is constructed to classify and diagnose the fault signals. The proposed approach can combine comprehensive information from different aspects and is more sensitive to the fault features. The experimental results on simulated fault signals verified better performances of our proposed approach. In real two-span rotor data, the fault detection accuracy of the new method is more than 10% higher compared with the methods using three kinds of information entropy separately. The new approach is proved to be an effective fault recognition method for rotating machinery.

A new entropy based method for computing software structural complexity

CERN Document Server

Roca, J L

2002-01-01

In this paper a new methodology for the evaluation of software structural complexity is described. It is based on the entropy evaluation of the random uniform response function associated with the so called software characteristic function SCF. The behavior of the SCF with the different software structures and their relationship with the number of inherent errors is investigated. It is also investigated how the entropy concept can be used to evaluate the complexity of a software structure considering the SCF as a canonical representation of the graph associated with the control flow diagram. The functions, parameters and algorithms that allow to carry out this evaluation are also introduced. After this analytic phase follows the experimental phase, verifying the consistency of the proposed metric and their boundary conditions. The conclusion is that the degree of software structural complexity can be measured as the entropy of the random uniform response function of the SCF. That entropy is in direct relation...

Defining and Measuring Cognitive-Entropy and Cognitive Self-Synchronization

Science.gov (United States)

2011-06-01

16th ICCRTS: “Collective C2 in Multinational Civil-Military Operations” Defining and Measuring Cognitive-Entropy and Cognitive Self- Synchronization ...shared awareness and enabling self- synchronization across the range of participating entities (Alberts and Hayes 2009, pp.106). We consider the...aspect of self- synchronization (Alberts and Hayes, 2006) a key one in the context of modern operations and in performing C2 assessments. Based on (Manso

Autonomous entropy-based intelligent experimental design

Science.gov (United States)

Malakar, Nabin Kumar

2011-07-01

The aim of this thesis is to explore the application of probability and information theory in experimental design, and to do so in a way that combines what we know about inference and inquiry in a comprehensive and consistent manner. Present day scientific frontiers involve data collection at an ever-increasing rate. This requires that we find a way to collect the most relevant data in an automated fashion. By following the logic of the scientific method, we couple an inference engine with an inquiry engine to automate the iterative process of scientific learning. The inference engine involves Bayesian machine learning techniques to estimate model parameters based upon both prior information and previously collected data, while the inquiry engine implements data-driven exploration. By choosing an experiment whose distribution of expected results has the maximum entropy, the inquiry engine selects the experiment that maximizes the expected information gain. The coupled inference and inquiry engines constitute an autonomous learning method for scientific exploration. We apply it to a robotic arm to demonstrate the efficacy of the method. Optimizing inquiry involves searching for an experiment that promises, on average, to be maximally informative. If the set of potential experiments is described by many parameters, the search involves a high-dimensional entropy space. In such cases, a brute force search method will be slow and computationally expensive. We develop an entropy-based search algorithm, called nested entropy sampling, to select the most informative experiment. This helps to reduce the number of computations necessary to find the optimal experiment. We also extended the method of maximizing entropy, and developed a method of maximizing joint entropy so that it could be used as a principle of collaboration between two robots. This is a major achievement of this thesis, as it allows the information-based collaboration between two robotic units towards a same

Direct measurements of the magnetic entropy change

DEFF Research Database (Denmark)

Nielsen, Kaspar Kirstein; Neves Bez, Henrique; von Moos, Lars

2015-01-01

An experimental device that can accurately measure the magnetic entropy change, Δs, as a function of temperature, T, and magnetic field, H, is presented. The magnetic field source is in this case a set of counter-rotating concentric Halbach-type magnets, which produce a highly homogeneous applied...... to the ambient are negligible in terms of the calorimetric determination of the magnetic entropy change, while the losses cannot be ignored when correcting for the actual sample temperature. We apply the device to two different types of samples; one is commercial grade Gd, i.e., a pure second-order phase...

Ranking DMUs by Comparing DEA Cross-Efficiency Intervals Using Entropy Measures

Directory of Open Access Journals (Sweden)

Tim Lu

2016-12-01

Full Text Available Cross-efficiency evaluation, an extension of data envelopment analysis (DEA, can eliminate unrealistic weighing schemes and provide a ranking for decision making units (DMUs. In the literature, the determination of input and output weights uniquely receives more attentions. However, the problem of choosing the aggressive (minimal or benevolent (maximal formulation for decision-making might still remain. In this paper, we develop a procedure to perform cross-efficiency evaluation without the need to make any specific choice of DEA weights. The proposed procedure takes into account the aggressive and benevolent formulations at the same time, and the choice of DEA weights can then be avoided. Consequently, a number of cross-efficiency intervals is obtained for each DMU. The entropy, which is based on information theory, is an effective tool to measure the uncertainty. We then utilize the entropy to construct a numerical index for DMUs with cross-efficiency intervals. A mathematical program is proposed to find the optimal entropy values of DMUs for comparison. With the derived entropy value, we can rank DMUs accordingly. Two examples are illustrated to show the effectiveness of the idea proposed in this paper.

Temperature multiscale entropy analysis: a promising marker for early prediction of mortality in septic patients

International Nuclear Information System (INIS)

Papaioannou, V E; Pneumatikos, I A; Chouvarda, I G; Maglaveras, N K; Baltopoulos, G I

2013-01-01

A few studies estimating temperature complexity have found decreased Shannon entropy, during severe stress. In this study, we measured both Shannon and Tsallis entropy of temperature signals in a cohort of critically ill patients and compared these measures with the sequential organ failure assessment (SOFA) score, in terms of intensive care unit (ICU) mortality. Skin temperature was recorded in 21 mechanically ventilated patients, who developed sepsis and septic shock during the first 24 h of an ICU-acquired infection. Shannon and Tsallis entropies were calculated in wavelet-based decompositions of the temperature signal. Statistically significant differences of entropy features were tested between survivors and non-survivors and classification models were built, for predicting final outcome. Significantly reduced Tsallis and Shannon entropies were found in non-survivors (seven patients, 33%) as compared to survivors. Wavelet measurements of both entropy metrics were found to predict ICU mortality better than SOFA, according to a combination of area under the curve, sensitivity and specificity values. Both entropies exhibited similar prognostic accuracy. Combination of SOFA and entropy presented improved the outcome of univariate models. We suggest that reduced wavelet Shannon and Tsallis entropies of temperature signals may complement SOFA in mortality prediction, during the first 24 h of an ICU-acquired infection. (paper)

Bubble Entropy: An Entropy Almost Free of Parameters.

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Manis, George; Aktaruzzaman, Md; Sassi, Roberto

2017-11-01

Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation entropy, where the vectors in the embedding space are ranked. We use the bubble sort algorithm for the ordering procedure and count instead the number of swaps performed for each vector. Doing so, we create a more coarse-grained distribution and then compute the entropy of this distribution. Results: Experimental results with both real and synthetic HRV signals showed that bubble entropy presents remarkable stability and exhibits increased descriptive and discriminating power compared to all other definitions, including the most popular ones. Conclusion: The definition proposed is almost free of parameters. The most common ones are the scale factor r and the embedding dimension m . In our definition, the scale factor is totally eliminated and the importance of m is significantly reduced. The proposed method presents increased stability and discriminating power. Significance: After the extensive use of some entropy measures in physiological signals, typical values for their parameters have been suggested, or at least, widely used. However, the parameters are still there, application and dataset dependent, influencing the computed value and affecting the descriptive power. Reducing their significance or eliminating them alleviates the problem, decoupling the method from the data and the application, and eliminating subjective factors. Objective : A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy . Bubble Entropy is based on permutation

Hepatic entropy and uniformity: additional parameters that can potentially increase the effectiveness of contrast enhancement during abdominal CT

International Nuclear Information System (INIS)

Ganeshan, B.; Miles, K.A.; Young, R.C.D.; Chatwin, C.R.

2007-01-01

Aim: To determine how hepatic entropy and uniformity of computed tomography (CT) images of the liver change after the administration of contrast material and to assess whether these additional parameters are more sensitive to tumour-related changes in the liver than measurements of hepatic attenuation or perfusion. Materials and methods: Hepatic attenuation, entropy, uniformity, and perfusion were measured using multi-phase CT following resection of colorectal cancer. Based on conventional CT and fluorodeoxyglucose positron emission tomography, 12 patients were classified as having no evidence of malignancy, eight with extra-hepatic tumours only, and eight with metastatic liver disease. Results: Hepatic attenuation and entropy increased after CM administration whereas uniformity decreased. Unlike hepatic attenuation, entropy and uniformity changed maximally in the arterial phase. No significant differences in hepatic perfusion or attenuation were found between patient groups, whereas arterial-phase entropy was lower (p = 0.034) and arterial-phase uniformity was higher (p = 0.034) in apparently disease-free areas of liver in patients with hepatic metastases compared with those with no metastases. Conclusion: Temporal changes in hepatic entropy and uniformity differ from those for hepatic attenuation. By reflecting the distribution of hepatic enhancement, these additional parameters are more sensitive to tumour-related changes in the liver than measurements of hepatic attenuation or perfusion

On entropy change measurements around first order phase transitions in caloric materials.

Science.gov (United States)

Caron, Luana; Ba Doan, Nguyen; Ranno, Laurent

2017-02-22

In this work we discuss the measurement protocols for indirect determination of the isothermal entropy change associated with first order phase transitions in caloric materials. The magneto-structural phase transitions giving rise to giant magnetocaloric effects in Cu-doped MnAs and FeRh are used as case studies to exemplify how badly designed protocols may affect isothermal measurements and lead to incorrect entropy change estimations. Isothermal measurement protocols which allow correct assessment of the entropy change around first order phase transitions in both direct and inverse cases are presented.

Variable screening and ranking using sampling-based sensitivity measures

International Nuclear Information System (INIS)

Wu, Y-T.; Mohanty, Sitakanta

2006-01-01

This paper presents a methodology for screening insignificant random variables and ranking significant important random variables using sensitivity measures including two cumulative distribution function (CDF)-based and two mean-response based measures. The methodology features (1) using random samples to compute sensitivities and (2) using acceptance limits, derived from the test-of-hypothesis, to classify significant and insignificant random variables. Because no approximation is needed in either the form of the performance functions or the type of continuous distribution functions representing input variables, the sampling-based approach can handle highly nonlinear functions with non-normal variables. The main characteristics and effectiveness of the sampling-based sensitivity measures are investigated using both simple and complex examples. Because the number of samples needed does not depend on the number of variables, the methodology appears to be particularly suitable for problems with large, complex models that have large numbers of random variables but relatively few numbers of significant random variables

A two-phase copula entropy-based multiobjective optimization approach to hydrometeorological gauge network design

Science.gov (United States)

Xu, Pengcheng; Wang, Dong; Singh, Vijay P.; Wang, Yuankun; Wu, Jichun; Wang, Lachun; Zou, Xinqing; Chen, Yuanfang; Chen, Xi; Liu, Jiufu; Zou, Ying; He, Ruimin

2017-12-01

Hydrometeorological data are needed for obtaining point and areal mean, quantifying the spatial variability of hydrometeorological variables, and calibration and verification of hydrometeorological models. Hydrometeorological networks are utilized to collect such data. Since data collection is expensive, it is essential to design an optimal network based on the minimal number of hydrometeorological stations in order to reduce costs. This study proposes a two-phase copula entropy- based multiobjective optimization approach that includes: (1) copula entropy-based directional information transfer (CDIT) for clustering the potential hydrometeorological gauges into several groups, and (2) multiobjective method for selecting the optimal combination of gauges for regionalized groups. Although entropy theory has been employed for network design before, the joint histogram method used for mutual information estimation has several limitations. The copula entropy-based mutual information (MI) estimation method is shown to be more effective for quantifying the uncertainty of redundant information than the joint histogram (JH) method. The effectiveness of this approach is verified by applying to one type of hydrometeorological gauge network, with the use of three model evaluation measures, including Nash-Sutcliffe Coefficient (NSC), arithmetic mean of the negative copula entropy (MNCE), and MNCE/NSC. Results indicate that the two-phase copula entropy-based multiobjective technique is capable of evaluating the performance of regional hydrometeorological networks and can enable decision makers to develop strategies for water resources management.

Microscopic insights into the NMR relaxation based protein conformational entropy meter

Science.gov (United States)

Kasinath, Vignesh; Sharp, Kim A.; Wand, A. Joshua

2013-01-01

Conformational entropy is a potentially important thermodynamic parameter contributing to protein function. Quantitative measures of conformational entropy are necessary for an understanding of its role but have been difficult to obtain. An empirical method that utilizes changes in conformational dynamics as a proxy for changes in conformational entropy has recently been introduced. Here we probe the microscopic origins of the link between conformational dynamics and conformational entropy using molecular dynamics simulations. Simulation of seven pro! teins gave an excellent correlation with measures of side-chain motion derived from NMR relaxation. The simulations show that the motion of methyl-bearing side-chains are sufficiently coupled to that of other side chains to serve as excellent reporters of the overall side-chain conformational entropy. These results tend to validate the use of experimentally accessible measures of methyl motion - the NMR-derived generalized order parameters - as a proxy from which to derive changes in protein conformational entropy. PMID:24007504

A Novel Entropy-Based Decoding Algorithm for a Generalized High-Order Discrete Hidden Markov Model

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Jason Chin-Tiong Chan

2018-01-01

Full Text Available The optimal state sequence of a generalized High-Order Hidden Markov Model (HHMM is tracked from a given observational sequence using the classical Viterbi algorithm. This classical algorithm is based on maximum likelihood criterion. We introduce an entropy-based Viterbi algorithm for tracking the optimal state sequence of a HHMM. The entropy of a state sequence is a useful quantity, providing a measure of the uncertainty of a HHMM. There will be no uncertainty if there is only one possible optimal state sequence for HHMM. This entropy-based decoding algorithm can be formulated in an extended or a reduction approach. We extend the entropy-based algorithm for computing the optimal state sequence that was developed from a first-order to a generalized HHMM with a single observational sequence. This extended algorithm performs the computation exponentially with respect to the order of HMM. The computational complexity of this extended algorithm is due to the growth of the model parameters. We introduce an efficient entropy-based decoding algorithm that used reduction approach, namely, entropy-based order-transformation forward algorithm (EOTFA to compute the optimal state sequence of any generalized HHMM. This EOTFA algorithm involves a transformation of a generalized high-order HMM into an equivalent first-order HMM and an entropy-based decoding algorithm is developed based on the equivalent first-order HMM. This algorithm performs the computation based on the observational sequence and it requires OTN~2 calculations, where N~ is the number of states in an equivalent first-order model and T is the length of observational sequence.

Assessment of sustainable urban transport development based on entropy and unascertained measure.

Science.gov (United States)

Li, Yancang; Yang, Jing; Shi, Huawang; Li, Yijie

2017-01-01

To find a more effective method for the assessment of sustainable urban transport development, the comprehensive assessment model of sustainable urban transport development was established based on the unascertained measure. On the basis of considering the factors influencing urban transport development, the comprehensive assessment indexes were selected, including urban economical development, transport demand, environment quality and energy consumption, and the assessment system of sustainable urban transport development was proposed. In view of different influencing factors of urban transport development, the index weight was calculated through the entropy weight coefficient method. Qualitative and quantitative analyses were conducted according to the actual condition. Then, the grade was obtained by using the credible degree recognition criterion from which the urban transport development level can be determined. Finally, a comprehensive assessment method for urban transport development was introduced. The application practice showed that the method can be used reasonably and effectively for the comprehensive assessment of urban transport development.

Entropy of Baker's Transformation

Institute of Scientific and Technical Information of China (English)

栾长福

2003-01-01

Four theorems about four different kinds of entropies for Baker's transformation are presented. The Kolmogorov entropy of Baker's transformation is sensitive to the initial flips by the time. The topological entropy of Baker's transformation is found to be log k. The conditions for the state of Baker's transformation to be forbidden are also derived. The relations among the Shanonn, Kolmogorov, topological and Boltzmann entropies are discussed in details.

Wavelet entropy of BOLD time series: An application to Rolandic epilepsy.

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Gupta, Lalit; Jansen, Jacobus F A; Hofman, Paul A M; Besseling, René M H; de Louw, Anton J A; Aldenkamp, Albert P; Backes, Walter H

2017-12-01

To assess the wavelet entropy for the characterization of intrinsic aberrant temporal irregularities in the time series of resting-state blood-oxygen-level-dependent (BOLD) signal fluctuations. Further, to evaluate the temporal irregularities (disorder/order) on a voxel-by-voxel basis in the brains of children with Rolandic epilepsy. The BOLD time series was decomposed using the discrete wavelet transform and the wavelet entropy was calculated. Using a model time series consisting of multiple harmonics and nonstationary components, the wavelet entropy was compared with Shannon and spectral (Fourier-based) entropy. As an application, the wavelet entropy in 22 children with Rolandic epilepsy was compared to 22 age-matched healthy controls. The images were obtained by performing resting-state functional magnetic resonance imaging (fMRI) using a 3T system, an 8-element receive-only head coil, and an echo planar imaging pulse sequence ( T2*-weighted). The wavelet entropy was also compared to spectral entropy, regional homogeneity, and Shannon entropy. Wavelet entropy was found to identify the nonstationary components of the model time series. In Rolandic epilepsy patients, a significantly elevated wavelet entropy was observed relative to controls for the whole cerebrum (P = 0.03). Spectral entropy (P = 0.41), regional homogeneity (P = 0.52), and Shannon entropy (P = 0.32) did not reveal significant differences. The wavelet entropy measure appeared more sensitive to detect abnormalities in cerebral fluctuations represented by nonstationary effects in the BOLD time series than more conventional measures. This effect was observed in the model time series as well as in Rolandic epilepsy. These observations suggest that the brains of children with Rolandic epilepsy exhibit stronger nonstationary temporal signal fluctuations than controls. 2 Technical Efficacy: Stage 3 J. Magn. Reson. Imaging 2017;46:1728-1737. © 2017 International Society for Magnetic

Entropy measures of collective cell migration

Science.gov (United States)

Whitby, Ariadne; Parrinello, Simona; Faisal, Aldo

2015-03-01

Collective cell migration is a critical process during tissue formation and repair. To this end there is a need to develop tools to quantitatively measure the dynamics of collective cell migration obtained from microscopy data. Drawing on statistical physics we use entropy of velocity fields derived from dense optic flow to quantitatively measure collective migration. Using peripheral nerve repair after injury as experimental system, we study how Schwann cells, guided by fibroblasts, migrate in cord-like structures across the cut, paving a highway for neurons. This process of emergence of organised behaviour is key for successful repair, yet the emergence of leader cells and transition from a random to ordered state is not understood. We find fibroblasts induce correlated directionality in migrating Schwann cells as measured by a decrease in the entropy of motion vector. We show our method is robust with respect to image resolution in time and space, giving a principled assessment of how various molecular mechanisms affect macroscopic features of collective cell migration. Finally, the generality of our method allows us to process both simulated cell movement and microscopic data, enabling principled fitting and comparison of in silico to in vitro. ICCS, Imperial College London & MRC Clinical Sciences Centre.

Gravel Image Segmentation in Noisy Background Based on Partial Entropy Method

Institute of Scientific and Technical Information of China (English)

无

2000-01-01

Because of wide variation in gray levels and particle dimensions and the presence of many small gravel objects in the background, as well as corrupting the image by noise, it is difficult o segment gravel objects. In this paper, we develop a partial entropy method and succeed to realize gravel objects segmentation. We give entropy principles and fur calculation methods. Moreover, we use minimum entropy error automaticly to select a threshold to segment image. We introduce the filter method using mathematical morphology. The segment experiments are performed by using different window dimensions for a group of gravel image and demonstrates that this method has high segmentation rate and low noise sensitivity.

Entropy in molecular recognition by proteins.

Science.gov (United States)

Caro, José A; Harpole, Kyle W; Kasinath, Vignesh; Lim, Jackwee; Granja, Jeffrey; Valentine, Kathleen G; Sharp, Kim A; Wand, A Joshua

2017-06-20

Molecular recognition by proteins is fundamental to molecular biology. Dissection of the thermodynamic energy terms governing protein-ligand interactions has proven difficult, with determination of entropic contributions being particularly elusive. NMR relaxation measurements have suggested that changes in protein conformational entropy can be quantitatively obtained through a dynamical proxy, but the generality of this relationship has not been shown. Twenty-eight protein-ligand complexes are used to show a quantitative relationship between measures of fast side-chain motion and the underlying conformational entropy. We find that the contribution of conformational entropy can range from favorable to unfavorable, which demonstrates the potential of this thermodynamic variable to modulate protein-ligand interactions. For about one-quarter of these complexes, the absence of conformational entropy would render the resulting affinity biologically meaningless. The dynamical proxy for conformational entropy or "entropy meter" also allows for refinement of the contributions of solvent entropy and the loss in rotational-translational entropy accompanying formation of high-affinity complexes. Furthermore, structure-based application of the approach can also provide insight into long-lived specific water-protein interactions that escape the generic treatments of solvent entropy based simply on changes in accessible surface area. These results provide a comprehensive and unified view of the general role of entropy in high-affinity molecular recognition by proteins.

Distance-Based Configurational Entropy of Proteins from Molecular Dynamics Simulations.

Science.gov (United States)

Fogolari, Federico; Corazza, Alessandra; Fortuna, Sara; Soler, Miguel Angel; VanSchouwen, Bryan; Brancolini, Giorgia; Corni, Stefano; Melacini, Giuseppe; Esposito, Gennaro

2015-01-01

Estimation of configurational entropy from molecular dynamics trajectories is a difficult task which is often performed using quasi-harmonic or histogram analysis. An entirely different approach, proposed recently, estimates local density distribution around each conformational sample by measuring the distance from its nearest neighbors. In this work we show this theoretically well grounded the method can be easily applied to estimate the entropy from conformational sampling. We consider a set of systems that are representative of important biomolecular processes. In particular: reference entropies for amino acids in unfolded proteins are obtained from a database of residues not participating in secondary structure elements;the conformational entropy of folding of β2-microglobulin is computed from molecular dynamics simulations using reference entropies for the unfolded state;backbone conformational entropy is computed from molecular dynamics simulations of four different states of the EPAC protein and compared with order parameters (often used as a measure of entropy);the conformational and rototranslational entropy of binding is computed from simulations of 20 tripeptides bound to the peptide binding protein OppA and of β2-microglobulin bound to a citrate coated gold surface. This work shows the potential of the method in the most representative biological processes involving proteins, and provides a valuable alternative, principally in the shown cases, where other approaches are problematic.

Fundamental limits on quantum dynamics based on entropy change

Science.gov (United States)

Das, Siddhartha; Khatri, Sumeet; Siopsis, George; Wilde, Mark M.

2018-01-01

It is well known in the realm of quantum mechanics and information theory that the entropy is non-decreasing for the class of unital physical processes. However, in general, the entropy does not exhibit monotonic behavior. This has restricted the use of entropy change in characterizing evolution processes. Recently, a lower bound on the entropy change was provided in the work of Buscemi, Das, and Wilde [Phys. Rev. A 93(6), 062314 (2016)]. We explore the limit that this bound places on the physical evolution of a quantum system and discuss how these limits can be used as witnesses to characterize quantum dynamics. In particular, we derive a lower limit on the rate of entropy change for memoryless quantum dynamics, and we argue that it provides a witness of non-unitality. This limit on the rate of entropy change leads to definitions of several witnesses for testing memory effects in quantum dynamics. Furthermore, from the aforementioned lower bound on entropy change, we obtain a measure of non-unitarity for unital evolutions.

Permutation Entropy for Random Binary Sequences

Directory of Open Access Journals (Sweden)

Lingfeng Liu

2015-12-01

Full Text Available In this paper, we generalize the permutation entropy (PE measure to binary sequences, which is based on Shannon’s entropy, and theoretically analyze this measure for random binary sequences. We deduce the theoretical value of PE for random binary sequences, which can be used to measure the randomness of binary sequences. We also reveal the relationship between this PE measure with other randomness measures, such as Shannon’s entropy and Lempel–Ziv complexity. The results show that PE is consistent with these two measures. Furthermore, we use PE as one of the randomness measures to evaluate the randomness of chaotic binary sequences.

Direct comparison of phase-sensitive vibrational sum frequency generation with maximum entropy method: case study of water.

Science.gov (United States)

de Beer, Alex G F; Samson, Jean-Sebastièn; Hua, Wei; Huang, Zishuai; Chen, Xiangke; Allen, Heather C; Roke, Sylvie

2011-12-14

We present a direct comparison of phase sensitive sum-frequency generation experiments with phase reconstruction obtained by the maximum entropy method. We show that both methods lead to the same complex spectrum. Furthermore, we discuss the strengths and weaknesses of each of these methods, analyzing possible sources of experimental and analytical errors. A simulation program for maximum entropy phase reconstruction is available at: http://lbp.epfl.ch/. © 2011 American Institute of Physics

Identification of Auditory Object-Specific Attention from Single-Trial Electroencephalogram Signals via Entropy Measures and Machine Learning

Directory of Open Access Journals (Sweden)

Yun Lu

2018-05-01

Full Text Available Existing research has revealed that auditory attention can be tracked from ongoing electroencephalography (EEG signals. The aim of this novel study was to investigate the identification of peoples’ attention to a specific auditory object from single-trial EEG signals via entropy measures and machine learning. Approximate entropy (ApEn, sample entropy (SampEn, composite multiscale entropy (CmpMSE and fuzzy entropy (FuzzyEn were used to extract the informative features of EEG signals under three kinds of auditory object-specific attention (Rest, Auditory Object1 Attention (AOA1 and Auditory Object2 Attention (AOA2. The linear discriminant analysis and support vector machine (SVM, were used to construct two auditory attention classifiers. The statistical results of entropy measures indicated that there were significant differences in the values of ApEn, SampEn, CmpMSE and FuzzyEn between Rest, AOA1 and AOA2. For the SVM-based auditory attention classifier, the auditory object-specific attention of Rest, AOA1 and AOA2 could be identified from EEG signals using ApEn, SampEn, CmpMSE and FuzzyEn as features and the identification rates were significantly different from chance level. The optimal identification was achieved by the SVM-based auditory attention classifier using CmpMSE with the scale factor τ = 10. This study demonstrated a novel solution to identify the auditory object-specific attention from single-trial EEG signals without the need to access the auditory stimulus.

Dynamic Cross-Entropy.

Science.gov (United States)

Aur, Dorian; Vila-Rodriguez, Fidel

2017-01-01

Complexity measures for time series have been used in many applications to quantify the regularity of one dimensional time series, however many dynamical systems are spatially distributed multidimensional systems. We introduced Dynamic Cross-Entropy (DCE) a novel multidimensional complexity measure that quantifies the degree of regularity of EEG signals in selected frequency bands. Time series generated by discrete logistic equations with varying control parameter r are used to test DCE measures. Sliding window DCE analyses are able to reveal specific period doubling bifurcations that lead to chaos. A similar behavior can be observed in seizures triggered by electroconvulsive therapy (ECT). Sample entropy data show the level of signal complexity in different phases of the ictal ECT. The transition to irregular activity is preceded by the occurrence of cyclic regular behavior. A significant increase of DCE values in successive order from high frequencies in gamma to low frequencies in delta band reveals several phase transitions into less ordered states, possible chaos in the human brain. To our knowledge there are no reliable techniques able to reveal the transition to chaos in case of multidimensional times series. In addition, DCE based on sample entropy appears to be robust to EEG artifacts compared to DCE based on Shannon entropy. The applied technique may offer new approaches to better understand nonlinear brain activity. Copyright © 2016 Elsevier B.V. All rights reserved.

Trajectories entropy in dynamical graphs with memory

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Francesco eCaravelli

2016-04-01

Full Text Available In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at a specific node. In particular, we study the model of reinforcement-decay graph dynamics, which leads to scale free graphs. We find that the node entropy characterizes the structure of the network in the two parameter phase-space describing the dynamical evolution of the weighted graph. We then apply an adapted version of the entropy measure to purely memristive circuits. We provide evidence that meanwhile in the case of DC voltage the entropy based on the forward probability is enough to characterize the graph properties, in the case of AC voltage generators one needs to consider both forward and backward based transition probabilities. We provide also evidence that the entropy highlights the self-organizing properties of memristive circuits, which re-organizes itself to satisfy the symmetries of the underlying graph.

Multiscale Permutation Entropy Based Rolling Bearing Fault Diagnosis

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Jinde Zheng

2014-01-01

Full Text Available A new rolling bearing fault diagnosis approach based on multiscale permutation entropy (MPE, Laplacian score (LS, and support vector machines (SVMs is proposed in this paper. Permutation entropy (PE was recently proposed and defined to measure the randomicity and detect dynamical changes of time series. However, for the complexity of mechanical systems, the randomicity and dynamic changes of the vibration signal will exist in different scales. Thus, the definition of MPE is introduced and employed to extract the nonlinear fault characteristics from the bearing vibration signal in different scales. Besides, the SVM is utilized to accomplish the fault feature classification to fulfill diagnostic procedure automatically. Meanwhile, in order to avoid a high dimension of features, the Laplacian score (LS is used to refine the feature vector by ranking the features according to their importance and correlations with the main fault information. Finally, the rolling bearing fault diagnosis method based on MPE, LS, and SVM is proposed and applied to the experimental data. The experimental data analysis results indicate that the proposed method could identify the fault categories effectively.

Spectrum unfolding, sensitivity analysis and propagation of uncertainties with the maximum entropy deconvolution code MAXED

CERN Document Server

Reginatto, M; Neumann, S

2002-01-01

MAXED was developed to apply the maximum entropy principle to the unfolding of neutron spectrometric measurements. The approach followed in MAXED has several features that make it attractive: it permits inclusion of a priori information in a well-defined and mathematically consistent way, the algorithm used to derive the solution spectrum is not ad hoc (it can be justified on the basis of arguments that originate in information theory), and the solution spectrum is a non-negative function that can be written in closed form. This last feature permits the use of standard methods for the sensitivity analysis and propagation of uncertainties of MAXED solution spectra. We illustrate its use with unfoldings of NE 213 scintillation detector measurements of photon calibration spectra, and of multisphere neutron spectrometer measurements of cosmic-ray induced neutrons at high altitude (approx 20 km) in the atmosphere.

A Dynamic and Adaptive Selection Radar Tracking Method Based on Information Entropy

Directory of Open Access Journals (Sweden)

Ge Jianjun

2017-12-01

Full Text Available Nowadays, the battlefield environment has become much more complex and variable. This paper presents a quantitative method and lower bound for the amount of target information acquired from multiple radar observations to adaptively and dynamically organize the detection of battlefield resources based on the principle of information entropy. Furthermore, for minimizing the given information entropy’s lower bound for target measurement at every moment, a method to dynamically and adaptively select radars with a high amount of information for target tracking is proposed. The simulation results indicate that the proposed method has higher tracking accuracy than that of tracking without adaptive radar selection based on entropy.

A Novel Entropy-Based Centrality Approach for Identifying Vital Nodes in Weighted Networks

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Tong Qiao

2018-04-01

Full Text Available Measuring centrality has recently attracted increasing attention, with algorithms ranging from those that simply calculate the number of immediate neighbors and the shortest paths to those that are complicated iterative refinement processes and objective dynamical approaches. Indeed, vital nodes identification allows us to understand the roles that different nodes play in the structure of a network. However, quantifying centrality in complex networks with various topological structures is not an easy task. In this paper, we introduce a novel definition of entropy-based centrality, which can be applicable to weighted directed networks. By design, the total power of a node is divided into two parts, including its local power and its indirect power. The local power can be obtained by integrating the structural entropy, which reveals the communication activity and popularity of each node, and the interaction frequency entropy, which indicates its accessibility. In addition, the process of influence propagation can be captured by the two-hop subnetworks, resulting in the indirect power. In order to evaluate the performance of the entropy-based centrality, we use four weighted real-world networks with various instance sizes, degree distributions, and densities. Correspondingly, these networks are adolescent health, Bible, United States (US airports, and Hep-th, respectively. Extensive analytical results demonstrate that the entropy-based centrality outperforms degree centrality, betweenness centrality, closeness centrality, and the Eigenvector centrality.

Entropy-Based Model for Interpreting Life Systems in Traditional Chinese Medicine

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Guo-lian Kang

2008-01-01

Full Text Available Traditional Chinese medicine (TCM treats qi as the core of the human life systems. Starting with a hypothetical correlation between TCM qi and the entropy theory, we address in this article a holistic model for evaluating and unveiling the rule of TCM life systems. Several new concepts such as acquired life entropy (ALE, acquired life entropy flow (ALEF and acquired life entropy production (ALEP are propounded to interpret TCM life systems. Using the entropy theory, mathematical models are established for ALE, ALEF and ALEP, which reflect the evolution of life systems. Some criteria are given on physiological activities and pathological changes of the body in different stages of life. Moreover, a real data-based simulation shows life entropies of the human body with different ages, Cold and Hot constitutions and in different seasons in North China are coincided with the manifestations of qi as well as the life evolution in TCM descriptions. Especially, based on the comparative and quantitative analysis, the entropy-based model can nicely describe the evolution of life entropies in Cold and Hot individuals thereby fitting the Yin–Yang theory in TCM. Thus, this work establishes a novel approach to interpret the fundamental principles in TCM, and provides an alternative understanding for the complex life systems.

Entropy method of measuring and evaluating periodicity of quasi-periodic trajectories

Science.gov (United States)

Ni, Yanshuo; Turitsyn, Konstantin; Baoyin, Hexi; Junfeng, Li

2018-06-01

This paper presents a method for measuring the periodicity of quasi-periodic trajectories by applying discrete Fourier transform (DFT) to the trajectories and analyzing the frequency domain within the concept of entropy. Having introduced the concept of entropy, analytical derivation and numerical results indicate that entropies increase as a logarithmic function of time. Periodic trajectories typically have higher entropies, and trajectories with higher entropies mean the periodicities of the motions are stronger. Theoretical differences between two trajectories expressed as summations of trigonometric functions are also derived analytically. Trajectories in the Henon-Heiles system and the circular restricted three-body problem (CRTBP) are analyzed with the indicator entropy and compared with orthogonal fast Lyapunov indicator (OFLI). The results show that entropy is a better tool for discriminating periodicity in quasiperiodic trajectories than OFLI and can detect periodicity while excluding the spirals that are judged as periodic cases by OFLI. Finally, trajectories in the vicinity of 243 Ida and 6489 Golevka are considered as examples, and the numerical results verify these conclusions. Some trajectories near asteroids look irregular, but their higher entropy values as analyzed by this method serve as evidence of frequency regularity in three directions. Moreover, these results indicate that applying DFT to the trajectories in the vicinity of irregular small bodies and calculating their entropy in the frequency domain provides a useful quantitative analysis method for evaluating orderliness in the periodicity of quasi-periodic trajectories within a given time interval.

Parameters Tuning of Model Free Adaptive Control Based on Minimum Entropy

Institute of Scientific and Technical Information of China (English)

Chao Ji; Jing Wang; Liulin Cao; Qibing Jin

2014-01-01

Dynamic linearization based model free adaptive control(MFAC) algorithm has been widely used in practical systems, in which some parameters should be tuned before it is successfully applied to process industries. Considering the random noise existing in real processes, a parameter tuning method based on minimum entropy optimization is proposed,and the feature of entropy is used to accurately describe the system uncertainty. For cases of Gaussian stochastic noise and non-Gaussian stochastic noise, an entropy recursive optimization algorithm is derived based on approximate model or identified model. The extensive simulation results show the effectiveness of the minimum entropy optimization for the partial form dynamic linearization based MFAC. The parameters tuned by the minimum entropy optimization index shows stronger stability and more robustness than these tuned by other traditional index,such as integral of the squared error(ISE) or integral of timeweighted absolute error(ITAE), when the system stochastic noise exists.

Characterizing time series via complexity-entropy curves

Science.gov (United States)

Ribeiro, Haroldo V.; Jauregui, Max; Zunino, Luciano; Lenzi, Ervin K.

2017-06-01

The search for patterns in time series is a very common task when dealing with complex systems. This is usually accomplished by employing a complexity measure such as entropies and fractal dimensions. However, such measures usually only capture a single aspect of the system dynamics. Here, we propose a family of complexity measures for time series based on a generalization of the complexity-entropy causality plane. By replacing the Shannon entropy by a monoparametric entropy (Tsallis q entropy) and after considering the proper generalization of the statistical complexity (q complexity), we build up a parametric curve (the q -complexity-entropy curve) that is used for characterizing and classifying time series. Based on simple exact results and numerical simulations of stochastic processes, we show that these curves can distinguish among different long-range, short-range, and oscillating correlated behaviors. Also, we verify that simulated chaotic and stochastic time series can be distinguished based on whether these curves are open or closed. We further test this technique in experimental scenarios related to chaotic laser intensity, stock price, sunspot, and geomagnetic dynamics, confirming its usefulness. Finally, we prove that these curves enhance the automatic classification of time series with long-range correlations and interbeat intervals of healthy subjects and patients with heart disease.

Option price calibration from Renyi entropy

International Nuclear Information System (INIS)

Brody, Dorje C.; Buckley, Ian R.C.; Constantinou, Irene C.

2007-01-01

The calibration of the risk-neutral density function for the future asset price, based on the maximisation of the entropy measure of Renyi, is proposed. Whilst the conventional approach based on the use of logarithmic entropy measure fails to produce the observed power-law distribution when calibrated against option prices, the approach outlined here is shown to produce the desired form of the distribution. Procedures for the maximisation of the Renyi entropy under constraints are outlined in detail, and a number of interesting properties of the resulting power-law distributions are also derived. The result is applied to efficiently evaluate prices of path-independent derivatives

Cross Entropy Measures of Bipolar and Interval Bipolar Neutrosophic Sets and Their Application for Multi-Attribute Decision-Making

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Surapati Pramanik

2018-03-01

Full Text Available The bipolar neutrosophic set is an important extension of the bipolar fuzzy set. The bipolar neutrosophic set is a hybridization of the bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent positive membership functions and three independent negative membership functions. In this paper, we develop cross entropy measures of bipolar neutrosophic sets and prove their basic properties. We also define cross entropy measures of interval bipolar neutrosophic sets and prove their basic properties. Thereafter, we develop two novel multi-attribute decision-making strategies based on the proposed cross entropy measures. In the decision-making framework, we calculate the weighted cross entropy measures between each alternative and the ideal alternative to rank the alternatives and choose the best one. We solve two illustrative examples of multi-attribute decision-making problems and compare the obtained result with the results of other existing strategies to show the applicability and effectiveness of the developed strategies. At the end, the main conclusion and future scope of research are summarized.

Entanglement generation and entropy growth due to intrinsic decoherence in the Jaynes-Cummings model

International Nuclear Information System (INIS)

Obada, A.-S.F.; Hessian, Hosny A.

2004-01-01

We study how intrinsic decoherence leads to growing entropy and a strong degradation of the maximal generated entanglement in the multiquanta Jaynes-Cummings model. We find an exact solution of the Milburn equation in multiquanta precesses and calculate the partial entropy of the particle (atom or trapped ion) and field subsystem as well as total entropy. As the total entropy is not conserved, and it is shown to increase as time develops, one cannot use the partial field or atomic entropy as a direct measure of particle-field entanglement. For a good entropy measure, we also calculate the negativity of the eigenvalues of the partially transposed density matrix. We find that, at least qualitatively, the difference of the total entropy to the sum of field and atom partial entropies can be also used as an entanglement measure. Our results show that the degree of entanglement is very sensitive to any change in the intrinsic decoherence parameter

Explaining the entropy concept and entropy components

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Marko Popovic

2018-04-01

Full Text Available Total entropy of a thermodynamic system consists of two components: thermal entropy due to energy, and residual entropy due to molecular orientation. In this article, a three-step method for explaining entropy is suggested. Step one is to use a classical method to introduce thermal entropy STM as a function of temperature T and heat capacity at constant pressure Cp: STM = ∫(Cp/T dT. Thermal entropy is the entropy due to uncertainty in motion of molecules and vanishes at absolute zero (zero-point energy state. It is also the measure of useless thermal energy that cannot be converted into useful work. The next step is to introduce residual entropy S0 as a function of the number of molecules N and the number of distinct orientations available to them in a crystal m: S0 = N kB ln m, where kB is the Boltzmann constant. Residual entropy quantifies the uncertainty in molecular orientation. Residual entropy, unlike thermal entropy, is independent of temperature and remains present at absolute zero. The third step is to show that thermal entropy and residual entropy add up to the total entropy of a thermodynamic system S: S = S0 + STM. This method of explanation should result in a better comprehension of residual entropy and thermal entropy, as well as of their similarities and differences. The new method was tested in teaching at Faculty of Chemistry University of Belgrade, Serbia. The results of the test show that the new method has a potential to improve the quality of teaching.

Fractal Image Compression Based on High Entropy Values Technique

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Douaa Younis Abbaas

2018-04-01

Full Text Available There are many attempts tried to improve the encoding stage of FIC because it consumed time. These attempts worked by reducing size of the search pool for pair range-domain matching but most of them led to get a bad quality, or a lower compression ratio of reconstructed image. This paper aims to present a method to improve performance of the full search algorithm by combining FIC (lossy compression and another lossless technique (in this case entropy coding is used. The entropy technique will reduce size of the domain pool (i. e., number of domain blocks based on the entropy value of each range block and domain block and then comparing the results of full search algorithm and proposed algorithm based on entropy technique to see each of which give best results (such as reduced the encoding time with acceptable values in both compression quali-ty parameters which are C. R (Compression Ratio and PSNR (Image Quality. The experimental results of the proposed algorithm proven that using the proposed entropy technique reduces the encoding time while keeping compression rates and reconstruction image quality good as soon as possible.

A novel evaluation of heat-electricity cost allocation in cogenerations based on entropy change method

International Nuclear Information System (INIS)

Ye, Xuemin; Li, Chunxi

2013-01-01

As one of the most significant measures to improve energy utilization efficiency and save energy, cogeneration or combined heat and power (CHP) has been widely applied and promoted with positive motivations in many countries. A rational cost allocation model should indicate the performance of cogenerations and balance the benefits between electricity generation and heat production. Based on the second law of thermodynamics, the present paper proposes an entropy change method for cost allocation by choosing exhaust steam entropy as a datum point, and the new model works in conjunction with entropy change and irreversibility during energy conversion processes. The allocation ratios of heat cost with the present and existing methods are compared for different types of cogenerations. Results show that the allocation ratios with the entropy change method are more rational and the cost allocation model can make up some limitations involved in other approaches. The future energy policies and innovational directions for cogenerations and heat consumers should be developed. - Highlights: • A rational model of cogeneration cost allocation is established. • Entropy change method integrates the relation of entropy change and exergy losses. • The unity of measuring energy quality and quantity is materialized. • The benefits between electricity generation and heat production are balanced

Detecting Genetic Interactions for Quantitative Traits Using m-Spacing Entropy Measure

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Jaeyong Yee

2015-01-01

Full Text Available A number of statistical methods for detecting gene-gene interactions have been developed in genetic association studies with binary traits. However, many phenotype measures are intrinsically quantitative and categorizing continuous traits may not always be straightforward and meaningful. Association of gene-gene interactions with an observed distribution of such phenotypes needs to be investigated directly without categorization. Information gain based on entropy measure has previously been successful in identifying genetic associations with binary traits. We extend the usefulness of this information gain by proposing a nonparametric evaluation method of conditional entropy of a quantitative phenotype associated with a given genotype. Hence, the information gain can be obtained for any phenotype distribution. Because any functional form, such as Gaussian, is not assumed for the entire distribution of a trait or a given genotype, this method is expected to be robust enough to be applied to any phenotypic association data. Here, we show its use to successfully identify the main effect, as well as the genetic interactions, associated with a quantitative trait.

Entropy-based critical reaction time for mixing-controlled reactive transport

DEFF Research Database (Denmark)

Chiogna, Gabriele; Rolle, Massimo

2017-01-01

Entropy-based metrics, such as the dilution index, have been proposed to quantify dilution and reactive mixing in solute transport problems. In this work, we derive the transient advection dispersion equation for the entropy density of a reactive plume. We restrict our analysis to the case where...... the concentration distribution of the transported species is Gaussian and we observe that, even in case of an instantaneous complete bimolecular reaction, dilution caused by dispersive processes dominates the entropy balance at early times and results in the net increase of the entropy density of a reactive species...

Entropy as a measure of the performance of phosphor materials used in medical imaging radiation detectors

International Nuclear Information System (INIS)

Cavouras, D.; Kandarakis, I.; Maris, T.; Panayiotakis, G.S.; Nomicos, C.D.

2001-01-01

In information theory, entropy expresses the information gain obtained after detection of a signal concerning the state of a parameter of interest. In this study, entropy has been expressed in terms of physical quantities (emitted optical fluence and MTF) related to the imaging performance of phosphor materials, which are employed in medical imaging radiation detectors. Four phosphor materials, used in the form of laboratory-prepared fluorescent layers (screens), were compared on the basis of their entropy performance. Measurements were performed using 30- and 80-kVp X-ray beams often employed in X-ray imaging. Results showed that phosphor materials with high density and effective atomic number exhibit high entropy performance, especially at the higher X-ray tube voltage of 80 kVp. Entropy values are also affected by the type of activator, which determines the intrinsic X-ray-to-light conversion efficiency, and the spectrum of emitted light. The proximity of the incident X-ray quanta energy to the energy of the K-shell threshold for photoelectric absorption is an additional important factor which increases entropy. This effect was more apparent in the performance of yttrium-based phosphors at the lower voltage of 30 kVp. (orig.)

Fault Detection and Diagnosis for Gas Turbines Based on a Kernelized Information Entropy Model

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Weiying Wang

2014-01-01

Full Text Available Gas turbines are considered as one kind of the most important devices in power engineering and have been widely used in power generation, airplanes, and naval ships and also in oil drilling platforms. However, they are monitored without man on duty in the most cases. It is highly desirable to develop techniques and systems to remotely monitor their conditions and analyze their faults. In this work, we introduce a remote system for online condition monitoring and fault diagnosis of gas turbine on offshore oil well drilling platforms based on a kernelized information entropy model. Shannon information entropy is generalized for measuring the uniformity of exhaust temperatures, which reflect the overall states of the gas paths of gas turbine. In addition, we also extend the entropy to compute the information quantity of features in kernel spaces, which help to select the informative features for a certain recognition task. Finally, we introduce the information entropy based decision tree algorithm to extract rules from fault samples. The experiments on some real-world data show the effectiveness of the proposed algorithms.

Fault detection and diagnosis for gas turbines based on a kernelized information entropy model.

Science.gov (United States)

Wang, Weiying; Xu, Zhiqiang; Tang, Rui; Li, Shuying; Wu, Wei

2014-01-01

Gas turbines are considered as one kind of the most important devices in power engineering and have been widely used in power generation, airplanes, and naval ships and also in oil drilling platforms. However, they are monitored without man on duty in the most cases. It is highly desirable to develop techniques and systems to remotely monitor their conditions and analyze their faults. In this work, we introduce a remote system for online condition monitoring and fault diagnosis of gas turbine on offshore oil well drilling platforms based on a kernelized information entropy model. Shannon information entropy is generalized for measuring the uniformity of exhaust temperatures, which reflect the overall states of the gas paths of gas turbine. In addition, we also extend the entropy to compute the information quantity of features in kernel spaces, which help to select the informative features for a certain recognition task. Finally, we introduce the information entropy based decision tree algorithm to extract rules from fault samples. The experiments on some real-world data show the effectiveness of the proposed algorithms.

Multi-Level Wavelet Shannon Entropy-Based Method for Single-Sensor Fault Location

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Qiaoning Yang

2015-10-01

Full Text Available In actual application, sensors are prone to failure because of harsh environments, battery drain, and sensor aging. Sensor fault location is an important step for follow-up sensor fault detection. In this paper, two new multi-level wavelet Shannon entropies (multi-level wavelet time Shannon entropy and multi-level wavelet time-energy Shannon entropy are defined. They take full advantage of sensor fault frequency distribution and energy distribution across multi-subband in wavelet domain. Based on the multi-level wavelet Shannon entropy, a method is proposed for single sensor fault location. The method firstly uses a criterion of maximum energy-to-Shannon entropy ratio to select the appropriate wavelet base for signal analysis. Then multi-level wavelet time Shannon entropy and multi-level wavelet time-energy Shannon entropy are used to locate the fault. The method is validated using practical chemical gas concentration data from a gas sensor array. Compared with wavelet time Shannon entropy and wavelet energy Shannon entropy, the experimental results demonstrate that the proposed method can achieve accurate location of a single sensor fault and has good anti-noise ability. The proposed method is feasible and effective for single-sensor fault location.

A new entropy based method for computing software structural complexity

International Nuclear Information System (INIS)

Roca, Jose L.

2002-01-01

In this paper a new methodology for the evaluation of software structural complexity is described. It is based on the entropy evaluation of the random uniform response function associated with the so called software characteristic function SCF. The behavior of the SCF with the different software structures and their relationship with the number of inherent errors is investigated. It is also investigated how the entropy concept can be used to evaluate the complexity of a software structure considering the SCF as a canonical representation of the graph associated with the control flow diagram. The functions, parameters and algorithms that allow to carry out this evaluation are also introduced. After this analytic phase follows the experimental phase, verifying the consistency of the proposed metric and their boundary conditions. The conclusion is that the degree of software structural complexity can be measured as the entropy of the random uniform response function of the SCF. That entropy is in direct relationship with the number of inherent software errors and it implies a basic hazard failure rate for it, so that a minimum structure assures a certain stability and maturity of the program. This metric can be used, either to evaluate the product or the process of software development, as development tool or for monitoring the stability and the quality of the final product. (author)

Measuring the quality of a quantum reference frame: The relative entropy of frameness

International Nuclear Information System (INIS)

Gour, Gilad; Marvian, Iman; Spekkens, Robert W.

2009-01-01

In the absence of a reference frame for transformations associated with group G, any quantum state that is noninvariant under the action of G may serve as a token of the missing reference frame. We here present a measure of the quality of such a token: the relative entropy of frameness. This is defined as the relative entropy distance between the state of interest and the nearest G-invariant state. Unlike the relative entropy of entanglement, this quantity is straightforward to calculate, and we find it to be precisely equal to the G-asymmetry, a measure of frameness introduced by Vaccaro et al. It is shown to provide an upper bound on the mutual information between the group element encoded into the token and the group element that may be extracted from it by measurement. In this sense, it quantifies the extent to which the token successfully simulates a full reference frame. We also show that despite a suggestive analogy from entanglement theory, the regularized relative entropy of frameness is zero and therefore does not quantify the rate of interconversion between the token and some standard form of quantum reference frame. Finally, we show how these investigations yield an approach to bounding the relative entropy of entanglement.

Minimal entropy approximation for cellular automata

International Nuclear Information System (INIS)

Fukś, Henryk

2014-01-01

We present a method for the construction of approximate orbits of measures under the action of cellular automata which is complementary to the local structure theory. The local structure theory is based on the idea of Bayesian extension, that is, construction of a probability measure consistent with given block probabilities and maximizing entropy. If instead of maximizing entropy one minimizes it, one can develop another method for the construction of approximate orbits, at the heart of which is the iteration of finite-dimensional maps, called minimal entropy maps. We present numerical evidence that the minimal entropy approximation sometimes outperforms the local structure theory in characterizing the properties of cellular automata. The density response curve for elementary CA rule 26 is used to illustrate this claim. (paper)

Nonlinear digital signal processing in mental health: characterization of major depression using instantaneous entropy measures of heartbeat dynamics.

Science.gov (United States)

Valenza, Gaetano; Garcia, Ronald G; Citi, Luca; Scilingo, Enzo P; Tomaz, Carlos A; Barbieri, Riccardo

2015-01-01

Nonlinear digital signal processing methods that address system complexity have provided useful computational tools for helping in the diagnosis and treatment of a wide range of pathologies. More specifically, nonlinear measures have been successful in characterizing patients with mental disorders such as Major Depression (MD). In this study, we propose the use of instantaneous measures of entropy, namely the inhomogeneous point-process approximate entropy (ipApEn) and the inhomogeneous point-process sample entropy (ipSampEn), to describe a novel characterization of MD patients undergoing affective elicitation. Because these measures are built within a nonlinear point-process model, they allow for the assessment of complexity in cardiovascular dynamics at each moment in time. Heartbeat dynamics were characterized from 48 healthy controls and 48 patients with MD while emotionally elicited through either neutral or arousing audiovisual stimuli. Experimental results coming from the arousing tasks show that ipApEn measures are able to instantaneously track heartbeat complexity as well as discern between healthy subjects and MD patients. Conversely, standard heart rate variability (HRV) analysis performed in both time and frequency domains did not show any statistical significance. We conclude that measures of entropy based on nonlinear point-process models might contribute to devising useful computational tools for care in mental health.

Permutation Entropy: New Ideas and Challenges

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Karsten Keller

2017-03-01

Full Text Available Over recent years, some new variants of Permutation entropy have been introduced and applied to EEG analysis, including a conditional variant and variants using some additional metric information or being based on entropies that are different from the Shannon entropy. In some situations, it is not completely clear what kind of information the new measures and their algorithmic implementations provide. We discuss the new developments and illustrate them for EEG data.

Breaking the glass ceiling: Configurational entropy measurements in extremely supercooled liquids

Science.gov (United States)

Berthier, Ludovic

Liquids relax extremely slowly on approaching the glass state. One explanation is that an entropy crisis, due to the rarefaction of available states, makes it increasingly arduous to reach equilibrium in that regime. Validating this scenario is challenging, because experiments offer limited resolution, while numerical studies lag more than eight orders of magnitude behind experimentally-relevant timescales. In this work we not only close the colossal gap between experiments and simulations but manage to create in-silico configurations that have no experimental analog yet. Deploying a range of computational tools, we obtain four independent estimates of their configurational entropy. These measurements consistently indicate that the steep entropy decrease observed in experiments is found in simulations even beyond the experimental glass transition. Our numerical results thus open a new observational window into the physics of glasses and reinforce the relevance of an entropy crisis for understanding their formation.

Low-algorithmic-complexity entropy-deceiving graphs

KAUST Repository

Zenil, Hector

2017-07-08

In estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graphand information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these measures are not independent of the way in which an object, such as a graph, can be described or observed. From observations that can reconstruct the same graph and are therefore essentially translations of the same description, we see that when applying a computable measure such as the Shannon entropy, not only is it necessary to preselect a feature of interest where there is one, and to make an arbitrary selection where there is not, but also more general properties, such as the causal likelihood of a graph as a measure (opposed to randomness), can be largely misrepresented by computable measures such as the entropy and entropy rate. We introduce recursive and nonrecursive (uncomputable) graphs and graph constructions based on these integer sequences, whose different lossless descriptions have disparate entropy values, thereby enabling the study and exploration of a measure\\'s range of applications and demonstrating the weaknesses of computable measures of complexity.

A gravitational entropy proposal

International Nuclear Information System (INIS)

Clifton, Timothy; Tavakol, Reza; Ellis, George F R

2013-01-01

We propose a thermodynamically motivated measure of gravitational entropy based on the Bel–Robinson tensor, which has a natural interpretation as the effective super-energy–momentum tensor of free gravitational fields. The specific form of this measure differs depending on whether the gravitational field is Coulomb-like or wave-like, and reduces to the Bekenstein–Hawking value when integrated over the interior of a Schwarzschild black hole. For scalar perturbations of a Robertson–Walker geometry we find that the entropy goes like the Hubble weighted anisotropy of the gravitational field, and therefore increases as structure formation occurs. This is in keeping with our expectations for the behaviour of gravitational entropy in cosmology, and provides a thermodynamically motivated arrow of time for cosmological solutions of Einstein’s field equations. It is also in keeping with Penrose’s Weyl curvature hypothesis. (paper)

Entropy of a system formed in the collision of heavy ions

International Nuclear Information System (INIS)

Gudima, K.K.; Roepke, G.; Toneev, V.D.; Schulz, H.

1987-01-01

In the framework of the cascade model, we study the evolution of the entropy of a system formed in the collision of heavy ions. The method of calculating the entropy is based on a smoothing of the momentum distribution function by means of introducing a temperature field. It is shown that the resulting entropy per nucleon is very sensitive to the specific partitioning of phase space into cells in the free-expansion phase of the reaction. From comparison with experiment it is found that the cascade calculations do not show a preference for a particular model calculation of the entropy, but predict that the entropy is smaller than the values following from equilibrium statistics

Multidimensional scaling analysis of financial time series based on modified cross-sample entropy methods

Science.gov (United States)

He, Jiayi; Shang, Pengjian; Xiong, Hui

2018-06-01

Stocks, as the concrete manifestation of financial time series with plenty of potential information, are often used in the study of financial time series. In this paper, we utilize the stock data to recognize their patterns through out the dissimilarity matrix based on modified cross-sample entropy, then three-dimensional perceptual maps of the results are provided through multidimensional scaling method. Two modified multidimensional scaling methods are proposed in this paper, that is, multidimensional scaling based on Kronecker-delta cross-sample entropy (MDS-KCSE) and multidimensional scaling based on permutation cross-sample entropy (MDS-PCSE). These two methods use Kronecker-delta based cross-sample entropy and permutation based cross-sample entropy to replace the distance or dissimilarity measurement in classical multidimensional scaling (MDS). Multidimensional scaling based on Chebyshev distance (MDSC) is employed to provide a reference for comparisons. Our analysis reveals a clear clustering both in synthetic data and 18 indices from diverse stock markets. It implies that time series generated by the same model are easier to have similar irregularity than others, and the difference in the stock index, which is caused by the country or region and the different financial policies, can reflect the irregularity in the data. In the synthetic data experiments, not only the time series generated by different models can be distinguished, the one generated under different parameters of the same model can also be detected. In the financial data experiment, the stock indices are clearly divided into five groups. Through analysis, we find that they correspond to five regions, respectively, that is, Europe, North America, South America, Asian-Pacific (with the exception of mainland China), mainland China and Russia. The results also demonstrate that MDS-KCSE and MDS-PCSE provide more effective divisions in experiments than MDSC.

Harmonic analysis of electric locomotive and traction power system based on wavelet singular entropy

Science.gov (United States)

Dun, Xiaohong

2018-05-01

With the rapid development of high-speed railway and heavy-haul transport, the locomotive and traction power system has become the main harmonic source of China's power grid. In response to this phenomenon, the system's power quality issues need timely monitoring, assessment and governance. Wavelet singular entropy is an organic combination of wavelet transform, singular value decomposition and information entropy theory, which combines the unique advantages of the three in signal processing: the time-frequency local characteristics of wavelet transform, singular value decomposition explores the basic modal characteristics of data, and information entropy quantifies the feature data. Based on the theory of singular value decomposition, the wavelet coefficient matrix after wavelet transform is decomposed into a series of singular values that can reflect the basic characteristics of the original coefficient matrix. Then the statistical properties of information entropy are used to analyze the uncertainty of the singular value set, so as to give a definite measurement of the complexity of the original signal. It can be said that wavelet entropy has a good application prospect in fault detection, classification and protection. The mat lab simulation shows that the use of wavelet singular entropy on the locomotive and traction power system harmonic analysis is effective.

Low-algorithmic-complexity entropy-deceiving graphs

KAUST Repository

Zenil, Hector; Kiani, Narsis A.; Tegner, Jesper

2017-01-01

In estimating the complexity of objects, in particular, of graphs, it is common practice to rely on graphand information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these measures are not independent of the way in which an object, such as a graph, can be described or observed. From observations that can reconstruct the same graph and are therefore essentially translations of the same description, we see that when applying a computable measure such as the Shannon entropy, not only is it necessary to preselect a feature of interest where there is one, and to make an arbitrary selection where there is not, but also more general properties, such as the causal likelihood of a graph as a measure (opposed to randomness), can be largely misrepresented by computable measures such as the entropy and entropy rate. We introduce recursive and nonrecursive (uncomputable) graphs and graph constructions based on these integer sequences, whose different lossless descriptions have disparate entropy values, thereby enabling the study and exploration of a measure's range of applications and demonstrating the weaknesses of computable measures of complexity.

The improvement of Clausius entropy and its application in entropy analysis

Institute of Scientific and Technical Information of China (English)

WU Jing; GUO ZengYuan

2008-01-01

The defects of Cleusius entropy which Include s premise of reversible process and a process quantlty of heat in Its definition are discussed in this paper. Moreover, the heat temperature quotient under reversible conditions, i.e. (δQ/T)rev, is essentially a process quantity although it is numerically equal to the entropy change. The sum of internal energy temperature quotient and work temperature quotient is defined as the improved form of Clausius entropy and it can be further proved to be a state funcllon. Unlike Clausius entropy, the improved deflnltion consists of system properties wlthout premise just like other state functions, for example, pressure p and enthalpy h, etc. it is unnecessary to invent reversible paths when calculating entropy change for irreversible processes based on the improved form of entropy since it is independent of process. Furthermore, entropy balance equations for internally and externally irreversible processes are deduced respectively based on the concepts of thermal reservoir entropy transfer and system entropy transfer. Finally, some examples are presented to show that the improved deflnitlon of Clausius entropy provides a clear concept as well as a convenient method for en-tropy change calculation.

Heart rate variability analysis based on time–frequency representation and entropies in hypertrophic cardiomyopathy patients

International Nuclear Information System (INIS)

Clariá, F; Vallverdú, M; Caminal, P; Baranowski, R; Chojnowska, L

2008-01-01

In hypertrophic cardiomyopathy (HCM) patients there is an increased risk of premature death, which can occur with little or no warning. Furthermore, classification for sudden cardiac death on patients with HCM is very difficult. The aim of our study was to improve the prognostic value of heart rate variability (HRV) in HCM patients, giving insight into changes of the autonomic nervous system. In this way, the suitability of linear and nonlinear measures was studied to assess the HRV. These measures were based on time–frequency representation (TFR) and on Shannon and Rényi entropies, and compared with traditional HRV measures. Holter recordings of 64 patients with HCM and 55 healthy subjects were analyzed. The HCM patients consisted of two groups: 13 high risk patients, after aborted sudden cardiac death (SCD); 51 low risk patients, without SCD. Five-hour RR signals, corresponding to the sleep period of the subjects, were considered for the analysis as a comparable standard situation. These RR signals were filtered in the three frequency bands: very low frequency band (VLF, 0–0.04 Hz), low frequency band (LF, 0.04–0.15 Hz) and high frequency band (HF, 0.15–0.45 Hz). TFR variables based on instantaneous frequency and energy functions were able to classify HCM patients and healthy subjects (control group). Results revealed that measures obtained from TFR analysis of the HRV better classified the groups of subjects than traditional HRV parameters. However, results showed that nonlinear measures improved group classification. It was observed that entropies calculated in the HF band showed the highest statistically significant levels comparing the HCM group and the control group, p-value < 0.0005. The values of entropy measures calculated in the HCM group presented lower values, indicating a decreasing of complexity, than those calculated from the control group. Moreover, similar behavior was observed comparing high and low risk of premature death, the values of

Driver Fatigue Detection System Using Electroencephalography Signals Based on Combined Entropy Features

Directory of Open Access Journals (Sweden)

Zhendong Mu

2017-02-01

Full Text Available Driver fatigue has become one of the major causes of traffic accidents, and is a complicated physiological process. However, there is no effective method to detect driving fatigue. Electroencephalography (EEG signals are complex, unstable, and non-linear; non-linear analysis methods, such as entropy, maybe more appropriate. This study evaluates a combined entropy-based processing method of EEG data to detect driver fatigue. In this paper, 12 subjects were selected to take part in an experiment, obeying driving training in a virtual environment under the instruction of the operator. Four types of enthrones (spectrum entropy, approximate entropy, sample entropy and fuzzy entropy were used to extract features for the purpose of driver fatigue detection. Electrode selection process and a support vector machine (SVM classification algorithm were also proposed. The average recognition accuracy was 98.75%. Retrospective analysis of the EEG showed that the extracted features from electrodes T5, TP7, TP8 and FP1 may yield better performance. SVM classification algorithm using radial basis function as kernel function obtained better results. A combined entropy-based method demonstrates good classification performance for studying driver fatigue detection.

Selection of entropy-measure parameters for knowledge discovery in heart rate variability data.

Science.gov (United States)

Mayer, Christopher C; Bachler, Martin; Hörtenhuber, Matthias; Stocker, Christof; Holzinger, Andreas; Wassertheurer, Siegfried

2014-01-01

Heart rate variability is the variation of the time interval between consecutive heartbeats. Entropy is a commonly used tool to describe the regularity of data sets. Entropy functions are defined using multiple parameters, the selection of which is controversial and depends on the intended purpose. This study describes the results of tests conducted to support parameter selection, towards the goal of enabling further biomarker discovery. This study deals with approximate, sample, fuzzy, and fuzzy measure entropies. All data were obtained from PhysioNet, a free-access, on-line archive of physiological signals, and represent various medical conditions. Five tests were defined and conducted to examine the influence of: varying the threshold value r (as multiples of the sample standard deviation σ, or the entropy-maximizing rChon), the data length N, the weighting factors n for fuzzy and fuzzy measure entropies, and the thresholds rF and rL for fuzzy measure entropy. The results were tested for normality using Lilliefors' composite goodness-of-fit test. Consequently, the p-value was calculated with either a two sample t-test or a Wilcoxon rank sum test. The first test shows a cross-over of entropy values with regard to a change of r. Thus, a clear statement that a higher entropy corresponds to a high irregularity is not possible, but is rather an indicator of differences in regularity. N should be at least 200 data points for r = 0.2 σ and should even exceed a length of 1000 for r = rChon. The results for the weighting parameters n for the fuzzy membership function show different behavior when coupled with different r values, therefore the weighting parameters have been chosen independently for the different threshold values. The tests concerning rF and rL showed that there is no optimal choice, but r = rF = rL is reasonable with r = rChon or r = 0.2σ. Some of the tests showed a dependency of the test significance on the data at hand. Nevertheless, as the medical

Structural contributions to the third-law entropy of uranyl phases

International Nuclear Information System (INIS)

Chen, F.; Ewing, R.C.

1999-01-01

Entropies that are used in geochemical calculations are usually based on calorimetric measurements. However, because of the contributions of neglected residual entropies which cannot be determined by calorimetric measurements, the true third-law entropies for many phases may be quite different from those derived from thermal data. The residual entropies are caused by site-mixing, structural disorder and magnetic spin disorder and may result in a considerable contribution to the third-law entropy of solid phases. Magnetic spin-configurational entropy is not expected to be significant in uranyl phases. However, because most uranyl phases are based on sheet or chain structures and usually contain several molecular water groups, site-mixing, vacancies, as well as disorder in the orientation of hydrogen bonds and the polar H 2 O molecules may occur. Calculations of the ideal site-mixing configurational entropy for some uranyl phases indicate that the residual contributions that arise from substitution and vacancies to the third-law entropies of uranyl phases may be large. A brief examination of the crystal chemistry of water molecules in uranyl phases suggests that considerable residual entropy may be caused by the disorder of hydrogen bonds associated with interstitial H 2 O groups

Logarithmic black hole entropy corrections and holographic Renyi entropy

Energy Technology Data Exchange (ETDEWEB)

Mahapatra, Subhash [The Institute of Mathematical Sciences, Chennai (India); KU Leuven - KULAK, Department of Physics, Kortrijk (Belgium)

2018-01-15

The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G{sub D}{sup 0}. The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)

Logarithmic black hole entropy corrections and holographic Renyi entropy

International Nuclear Information System (INIS)

Mahapatra, Subhash

2018-01-01

The entanglement and Renyi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Renyi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order G D 0 . The entropic c-function and the inequalities of the Renyi entropy are also satisfied even with the correction terms. (orig.)

The Grading Entropy-based Criteria for Structural Stability of Granular Materials and Filters

Directory of Open Access Journals (Sweden)

Janos Lőrincz

2015-05-01

Full Text Available This paper deals with three grading entropy-based rules that describe different soil structure stability phenomena: an internal stability rule, a filtering rule and a segregation rule. These rules are elaborated on the basis of a large amount of laboratory testing and from existing knowledge in the field. Use is made of the theory of grading entropy to derive parameters which incorporate all of the information of the grading curve into a pair of entropy-based parameters that allow soils with common behaviours to be grouped into domains on an entropy diagram. Applications of the derived entropy-based rules are presented by examining the reason of a dam failure, by testing against the existing filter rules from the literature, and by giving some examples for the design of non-segregating grading curves (discrete particle size distributions by dry weight. A physical basis for the internal stability rule is established, wherein the higher values of base entropy required for granular stability are shown to reflect the closeness between the mean and maximum grain diameters, which explains how there are sufficient coarser grains to achieve a stable grain skeleton.

The improvement of Clausius entropy and its application in entropy analysis

Institute of Scientific and Technical Information of China (English)

2008-01-01

The defects of Clausius entropy which include a premise of reversible process and a process quantity of heat in its definition are discussed in this paper. Moreover, the heat temperature quotient under reversible conditions, i.e. (δQ/T)rev, is essentially a process quantity although it is numerically equal to the entropy change. The sum of internal energy temperature quotient and work temperature quotient is defined as the improved form of Clausius entropy and it can be further proved to be a state function. Unlike Clausius entropy, the improved definition consists of system properties without premise just like other state functions, for example, pressure p and enthalpy h, etc. It is unnecessary to invent reversible paths when calculating entropy change for irreversible processes based on the improved form of entropy since it is independent of process. Furthermore, entropy balance equations for internally and externally irreversible processes are deduced respectively based on the concepts of thermal reservoir entropy transfer and system entropy transfer. Finally, some examples are presented to show that the improved definition of Clausius entropy provides a clear concept as well as a convenient method for en- tropy change calculation.

Empirical study on entropy models of cellular manufacturing systems

Institute of Scientific and Technical Information of China (English)

Zhifeng Zhang; Renbin Xiao

2009-01-01

From the theoretical point of view,the states of manufacturing resources can be monitored and assessed through the amount of information needed to describe their technological structure and operational state.The amount of information needed to describe cellular manufacturing systems is investigated by two measures:the structural entropy and the operational entropy.Based on the Shannon entropy,the models of the structural entropy and the operational entropy of cellular manufacturing systems are developed,and the cognizance of the states of manufacturing resources is also illustrated.Scheduling is introduced to measure the entropy models of cellular manufacturing systems,and the feasible concepts of maximum schedule horizon and schedule adherence are advanced to quantitatively evaluate the effectiveness of schedules.Finally,an example is used to demonstrate the validity of the proposed methodology.

Tsallis-like entropies in quantum scattering

International Nuclear Information System (INIS)

Ion, D.B.; Ion, M.L.

1998-01-01

In this work, the following entropies in quantum scattering are defined: the informational angular entropy, S θ ; Tsallis-like angular entropies, S q (θ); the angular momentum entropy, S L ; the Tsallis-like angular momentum entropies, S q (L); the angle-angular momentum entropy, S θL . These entropies are defined as natural measures of the uncertainties corresponding to the distribution probabilities. If we are interested in obtaining a measure of uncertainty of the simultaneous realization of the probability distributions, than, we have to calculate the entropy corresponding to these distributions. The expression of angle-angular momentum entropy is given. The relation between the Tsallis entropies and the angle-angular momentum entropy is derived

An Entropy-Based Network Anomaly Detection Method

Directory of Open Access Journals (Sweden)

Przemysław Bereziński

2015-04-01

Full Text Available Data mining is an interdisciplinary subfield of computer science involving methods at the intersection of artificial intelligence, machine learning and statistics. One of the data mining tasks is anomaly detection which is the analysis of large quantities of data to identify items, events or observations which do not conform to an expected pattern. Anomaly detection is applicable in a variety of domains, e.g., fraud detection, fault detection, system health monitoring but this article focuses on application of anomaly detection in the field of network intrusion detection.The main goal of the article is to prove that an entropy-based approach is suitable to detect modern botnet-like malware based on anomalous patterns in network. This aim is achieved by realization of the following points: (i preparation of a concept of original entropy-based network anomaly detection method, (ii implementation of the method, (iii preparation of original dataset, (iv evaluation of the method.

Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling

Science.gov (United States)

Berthier, Ludovic; Charbonneau, Patrick; Coslovich, Daniele; Ninarello, Andrea; Ozawa, Misaki; Yaida, Sho

2017-10-01

Liquids relax extremely slowly on approaching the glass state. One explanation is that an entropy crisis, because of the rarefaction of available states, makes it increasingly arduous to reach equilibrium in that regime. Validating this scenario is challenging, because experiments offer limited resolution, while numerical studies lag more than eight orders of magnitude behind experimentally relevant timescales. In this work, we not only close the colossal gap between experiments and simulations but manage to create in silico configurations that have no experimental analog yet. Deploying a range of computational tools, we obtain four estimates of their configurational entropy. These measurements consistently confirm that the steep entropy decrease observed in experiments is also found in simulations, even beyond the experimental glass transition. Our numerical results thus extend the observational window into the physics of glasses and reinforce the relevance of an entropy crisis for understanding their formation.

Monte Carlo evaluation of derivative-based global sensitivity measures

International Nuclear Information System (INIS)

Kucherenko, S.; Rodriguez-Fernandez, M.; Pantelides, C.; Shah, N.

2009-01-01

A novel approach for evaluation of derivative-based global sensitivity measures (DGSM) is presented. It is compared with the Morris and the Sobol' sensitivity indices methods. It is shown that there is a link between DGSM and Sobol' sensitivity indices. DGSM are very easy to implement and evaluate numerically. The computational time required for numerical evaluation of DGSM is many orders of magnitude lower than that for estimation of the Sobol' sensitivity indices. It is also lower than that for the Morris method. Efficiencies of Monte Carlo (MC) and quasi-Monte Carlo (QMC) sampling methods for calculation of DGSM are compared. It is shown that the superiority of QMC over MC depends on the problem's effective dimension, which can also be estimated using DGSM.

Statistical region based active contour using a fractional entropy descriptor: Application to nuclei cell segmentation in confocal \\ud microscopy images

OpenAIRE

Histace, A; Meziou, B J; Matuszewski, Bogdan; Precioso, F; Murphy, M F; Carreiras, F

2013-01-01

We propose an unsupervised statistical region based active contour approach integrating an original fractional entropy measure for image segmentation with a particular application to single channel actin tagged fluorescence confocal microscopy image segmentation. Following description of statistical based active contour segmentation and the mathematical definition of the proposed fractional entropy descriptor, we demonstrate comparative segmentation results between the proposed approach and s...

Biological Aging and Life Span Based on Entropy Stress via Organ and Mitochondrial Metabolic Loading

Directory of Open Access Journals (Sweden)

Kalyan Annamalai

2017-10-01

mass over life time. The corresponding life time entropy stresses of organs are: 1.2; 60.5; 110.5; 110.5; 50.5; 3.5; 3.0 MJ/K per kg organ mass. Thus, among vital organs highest stress is for heart and kidney and lowest stress is for liver. The 5-organ model (BHKL and R5 also shows similar ranking. Based on mitochondrial volume and 5-organ model, the entropy stresses of organs expressed in kJ/K per cm3 of Mito volume are: 12,670; 5465; 2855; 4730 kJ/cm3 of Mito for BHKL indicating brain to be highly stressed and liver to be least stressed. Thus, the organ entropy stress ranking based on unit volume of mitochondria within an organ (kJ/(K cm3 of Mito of organ k differs from entropy stress based on unit mass of organ. Based on metabolic loading, the brains of athletes already under extreme mitochondrial stress and facing reduced metabolic efficiency under concussion are subjected to more increased stress. In the absence of non-intrusive measurements for estimating organ-based metabolic rates which can serve as metabolism-based biomarkers for biological aging (BA of whole body, alternate methods are suggested for estimating the biological aging rate.

Prediction Model of Collapse Risk Based on Information Entropy and Distance Discriminant Analysis Method

Directory of Open Access Journals (Sweden)

Hujun He

2017-01-01

Full Text Available The prediction and risk classification of collapse is an important issue in the process of highway construction in mountainous regions. Based on the principles of information entropy and Mahalanobis distance discriminant analysis, we have produced a collapse hazard prediction model. We used the entropy measure method to reduce the influence indexes of the collapse activity and extracted the nine main indexes affecting collapse activity as the discriminant factors of the distance discriminant analysis model (i.e., slope shape, aspect, gradient, and height, along with exposure of the structural face, stratum lithology, relationship between weakness face and free face, vegetation cover rate, and degree of rock weathering. We employ postearthquake collapse data in relation to construction of the Yingxiu-Wolong highway, Hanchuan County, China, as training samples for analysis. The results were analyzed using the back substitution estimation method, showing high accuracy and no errors, and were the same as the prediction result of uncertainty measure. Results show that the classification model based on information entropy and distance discriminant analysis achieves the purpose of index optimization and has excellent performance, high prediction accuracy, and a zero false-positive rate. The model can be used as a tool for future evaluation of collapse risk.

Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causality

Science.gov (United States)

Ito, Sosuke

2016-01-01

The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the backward time series called the backward transfer entropy, and show that the backward transfer entropy quantifies how far it is from dynamics to a hidden Markov model. Furthermore, we discuss physical interpretations of the backward transfer entropy in completely different settings of thermodynamics for information processing and the gambling with side information. In both settings of thermodynamics and the gambling, the backward transfer entropy characterizes a possible loss of some benefit, where the conventional transfer entropy characterizes a possible benefit. Our result implies the deep connection between thermodynamics and the gambling in the presence of information flow, and that the backward transfer entropy would be useful as a novel measure of information flow in nonequilibrium thermodynamics, biochemical sciences, economics and statistics. PMID:27833120

Entropy Viscosity and L1-based Approximations of PDEs: Exploiting Sparsity

Science.gov (United States)

2015-10-23

AFRL-AFOSR-VA-TR-2015-0337 Entropy Viscosity and L1-based Approximations of PDEs: Exploiting Sparsity Jean-Luc Guermond TEXAS A & M UNIVERSITY 750...REPORT DATE (DD-MM-YYYY) 09-05-2015 2. REPORT TYPE Final report 3. DATES COVERED (From - To) 01-07-2012 - 30-06-2015 4. TITLE AND SUBTITLE Entropy ...conservation equations can be stabilized by using the so-called entropy viscosity method and we proposed to to investigate this new technique. We

On the Entropy Based Associative Memory Model with Higher-Order Correlations

Directory of Open Access Journals (Sweden)

Masahiro Nakagawa

2010-01-01

Full Text Available In this paper, an entropy based associative memory model will be proposed and applied to memory retrievals with an orthogonal learning model so as to compare with the conventional model based on the quadratic Lyapunov functional to be minimized during the retrieval process. In the present approach, the updating dynamics will be constructed on the basis of the entropy minimization strategy which may be reduced asymptotically to the above-mentioned conventional dynamics as a special case ignoring the higher-order correlations. According to the introduction of the entropy functional, one may involve higer-order correlation effects between neurons in a self-contained manner without any heuristic coupling coefficients as in the conventional manner. In fact we shall show such higher order coupling tensors are to be uniquely determined in the framework of the entropy based approach. From numerical results, it will be found that the presently proposed novel approach realizes much larger memory capacity than that of the quadratic Lyapunov functional approach, e.g., associatron.

EEG entropy measures indicate decrease of cortical information processing in Disorders of Consciousness.

Science.gov (United States)

Thul, Alexander; Lechinger, Julia; Donis, Johann; Michitsch, Gabriele; Pichler, Gerald; Kochs, Eberhard F; Jordan, Denis; Ilg, Rüdiger; Schabus, Manuel

2016-02-01

Clinical assessments that rely on behavioral responses to differentiate Disorders of Consciousness are at times inapt because of some patients' motor disabilities. To objectify patients' conditions of reduced consciousness the present study evaluated the use of electroencephalography to measure residual brain activity. We analyzed entropy values of 18 scalp EEG channels of 15 severely brain-damaged patients with clinically diagnosed Minimally-Conscious-State (MCS) or Unresponsive-Wakefulness-Syndrome (UWS) and compared the results to a sample of 24 control subjects. Permutation entropy (PeEn) and symbolic transfer entropy (STEn), reflecting information processes in the EEG, were calculated for all subjects. Participants were tested on a modified active own-name paradigm to identify correlates of active instruction following. PeEn showed reduced local information content in the EEG in patients, that was most pronounced in UWS. STEn analysis revealed altered directed information flow in the EEG of patients, indicating impaired feed-backward connectivity. Responses to auditory stimulation yielded differences in entropy measures, indicating reduced information processing in MCS and UWS. Local EEG information content and information flow are affected in Disorders of Consciousness. This suggests local cortical information capacity and feedback information transfer as neural correlates of consciousness. The utilized EEG entropy analyses were able to relate to patient groups with different Disorders of Consciousness. Copyright © 2015 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Monte Carlo evaluation of derivative-based global sensitivity measures

Energy Technology Data Exchange (ETDEWEB)

Kucherenko, S. [Centre for Process Systems Engineering, Imperial College London, London SW7 2AZ (United Kingdom)], E-mail: s.kucherenko@ic.ac.uk; Rodriguez-Fernandez, M. [Process Engineering Group, Instituto de Investigaciones Marinas, Spanish Council for Scientific Research (C.S.I.C.), C/ Eduardo Cabello, 6, 36208 Vigo (Spain); Pantelides, C.; Shah, N. [Centre for Process Systems Engineering, Imperial College London, London SW7 2AZ (United Kingdom)

2009-07-15

A novel approach for evaluation of derivative-based global sensitivity measures (DGSM) is presented. It is compared with the Morris and the Sobol' sensitivity indices methods. It is shown that there is a link between DGSM and Sobol' sensitivity indices. DGSM are very easy to implement and evaluate numerically. The computational time required for numerical evaluation of DGSM is many orders of magnitude lower than that for estimation of the Sobol' sensitivity indices. It is also lower than that for the Morris method. Efficiencies of Monte Carlo (MC) and quasi-Monte Carlo (QMC) sampling methods for calculation of DGSM are compared. It is shown that the superiority of QMC over MC depends on the problem's effective dimension, which can also be estimated using DGSM.

The impulse cutoff an entropy functional measure on trajectories of Markov diffusion process integrating in information path functional

OpenAIRE

Lerner, Vladimir S.

2012-01-01

The impulses, cutting entropy functional (EF) measure on trajectories Markov diffusion process, integrate information path functional (IPF) composing discrete information Bits extracted from observing random process. Each cut brings memory of the cutting entropy, which provides both reduction of the process entropy and discrete unit of the cutting entropy a Bit. Consequently, information is memorized entropy cutting in random observations which process interactions. The origin of information ...

Entropy equilibrium equation and dynamic entropy production in environment liquid

Institute of Scientific and Technical Information of China (English)

无

2002-01-01

The entropy equilibrium equation is the basis of the nonequilibrium state thermodynamics. But the internal energy implies the kinetic energy of the fluid micelle relative to mass center in the classical entropy equilibrium equation at present. This internal energy is not the mean kinetic energy of molecular movement in thermodynamics. Here a modified entropy equilibrium equation is deduced, based on the concept that the internal energy is just the mean kinetic energy of the molecular movement. A dynamic entropy production is introduced into the entropy equilibrium equation to describe the dynamic process distinctly. This modified entropy equilibrium equation can describe not only the entropy variation of the irreversible processes but also the reversible processes in a thermodynamic system. It is more reasonable and suitable for wider applications.

Quantum key distribution with finite resources: Smooth Min entropy vs. Smooth Renyi entropy

Energy Technology Data Exchange (ETDEWEB)

Mertz, Markus; Abruzzo, Silvestre; Bratzik, Sylvia; Kampermann, Hermann; Bruss, Dagmar [Institut fuer Theoretische Physik III, Duesseldorf (Germany)

2010-07-01

We consider different entropy measures that play an important role in the analysis of the security of QKD with finite resources. The smooth min entropy leads to an optimal bound for the length of a secure key. Another bound on the secure key length was derived by using Renyi entropies. Unfortunately, it is very hard or even impossible to calculate these entropies for realistic QKD scenarios. To estimate the security rate it becomes important to find computable bounds on these entropies. Here, we compare a lower bound for the smooth min entropy with a bound using Renyi entropies. We compare these entropies for the six-state protocol with symmetric attacks.

A Method of Rotating Machinery Fault Diagnosis Based on the Close Degree of Information Entropy

Institute of Scientific and Technical Information of China (English)

GENG Jun-bao; HUANG Shu-hong; JIN Jia-shan; CHEN Fei; LIU Wei

2006-01-01

This paper presents a method of rotating machinery fault diagnosis based on the close degree of information entropy. In the view of the information entropy, we introduce four information entropy features of the rotating machinery, which describe the vibration condition of the machinery. The four features are, respectively, denominated as singular spectrum entropy, power spectrum entropy, wavelet space state feature entropy and wavelet power spectrum entropy. The value scopes of the four information entropy features of the rotating machinery in some typical fault conditions are gained by experiments, which can be acted as the standard features of fault diagnosis. According to the principle of the shorter distance between the more similar models, the decision-making method based on the close degree of information entropy is put forward to deal with the recognition of fault patterns. We demonstrate the effectiveness of this approach in an instance involving the fault pattern recognition of some rotating machinery.

Multiscale analysis of heart rate dynamics: entropy and time irreversibility measures.

Science.gov (United States)

Costa, Madalena D; Peng, Chung-Kang; Goldberger, Ary L

2008-06-01

Cardiovascular signals are largely analyzed using traditional time and frequency domain measures. However, such measures fail to account for important properties related to multiscale organization and non-equilibrium dynamics. The complementary role of conventional signal analysis methods and emerging multiscale techniques, is, therefore, an important frontier area of investigation. The key finding of this presentation is that two recently developed multiscale computational tools--multiscale entropy and multiscale time irreversibility--are able to extract information from cardiac interbeat interval time series not contained in traditional methods based on mean, variance or Fourier spectrum (two-point correlation) techniques. These new methods, with careful attention to their limitations, may be useful in diagnostics, risk stratification and detection of toxicity of cardiac drugs.

On Single-Valued Neutrosophic Entropy of order α

Directory of Open Access Journals (Sweden)

Harish Garg, Nancy

2016-12-01

Full Text Available Entropy is one of the measures which is used for measuring the fuzziness of the set. In this article, we have presented an entropy measure of order α under the single-valued neutrosophic set environment by considering the pair of their membership functions as well as the hesitation degree between them. Based on this measure, some of its desirable properties have been proposed and validated by taking an example of structure linguistic variable.

Multiattribute Decision Making Based on Entropy under Interval-Valued Intuitionistic Fuzzy Environment

Directory of Open Access Journals (Sweden)

Yingjun Zhang

2013-01-01

Full Text Available Multiattribute decision making (MADM is one of the central problems in artificial intelligence, specifically in management fields. In most cases, this problem arises from uncertainty both in the data derived from the decision maker and the actions performed in the environment. Fuzzy set and high-order fuzzy sets were proven to be effective approaches in solving decision-making problems with uncertainty. Therefore, in this paper, we investigate the MADM problem with completely unknown attribute weights in the framework of interval-valued intuitionistic fuzzy (IVIF set (IVIFS. We first propose a new definition of IVIF entropy and some calculation methods for IVIF entropy. Furthermore, we propose an entropy-based decision-making method to solve IVIF MADM problems with completely unknown attribute weights. Particular emphasis is put on assessing the attribute weights based on IVIF entropy. Instead of the traditional methods, which use divergence among attributes or the probabilistic discrimination of attributes to obtain attribute weights, we utilize the IVIF entropy to assess the attribute weights based on the credibility of the decision-making matrix for solving the problem. Finally, a supplier selection example is given to demonstrate the feasibility and validity of the proposed MADM method.

Logarithmic black hole entropy corrections and holographic Rényi entropy

Science.gov (United States)

Mahapatra, Subhash

2018-01-01

The entanglement and Rényi entropies for spherical entangling surfaces in CFTs with gravity duals can be explicitly calculated by mapping these entropies first to the thermal entropy on hyperbolic space and then, using the AdS/CFT correspondence, to the Wald entropy of topological black holes. Here we extend this idea by taking into account corrections to the Wald entropy. Using the method based on horizon symmetries and the asymptotic Cardy formula, we calculate corrections to the Wald entropy and find that these corrections are proportional to the logarithm of the area of the horizon. With the corrected expression for the entropy of the black hole, we then find corrections to the Rényi entropies. We calculate these corrections for both Einstein and Gauss-Bonnet gravity duals. Corrections with logarithmic dependence on the area of the entangling surface naturally occur at the order GD^0. The entropic c-function and the inequalities of the Rényi entropy are also satisfied even with the correction terms.

Holographic charged Rényi entropies

Science.gov (United States)

Belin, Alexandre; Hung, Ling-Yan; Maloney, Alexander; Matsuura, Shunji; Myers, Robert C.; Sierens, Todd

2013-12-01

We construct a new class of entanglement measures by extending the usual definition of Rényi entropy to include a chemical potential. These charged Rényi entropies measure the degree of entanglement in different charge sectors of the theory and are given by Euclidean path integrals with the insertion of a Wilson line encircling the entangling surface. We compute these entropies for a spherical entangling surface in CFT's with holographic duals, where they are related to entropies of charged black holes with hyperbolic horizons. We also compute charged Rényi entropies in free field theories.

Sensitivity evaluation of dynamic speckle activity measurements using clustering methods

International Nuclear Information System (INIS)

Etchepareborda, Pablo; Federico, Alejandro; Kaufmann, Guillermo H.

2010-01-01

We evaluate and compare the use of competitive neural networks, self-organizing maps, the expectation-maximization algorithm, K-means, and fuzzy C-means techniques as partitional clustering methods, when the sensitivity of the activity measurement of dynamic speckle images needs to be improved. The temporal history of the acquired intensity generated by each pixel is analyzed in a wavelet decomposition framework, and it is shown that the mean energy of its corresponding wavelet coefficients provides a suited feature space for clustering purposes. The sensitivity obtained by using the evaluated clustering techniques is also compared with the well-known methods of Konishi-Fujii, weighted generalized differences, and wavelet entropy. The performance of the partitional clustering approach is evaluated using simulated dynamic speckle patterns and also experimental data.

Towards an entropy-based detached-eddy simulation

Science.gov (United States)

Zhao, Rui; Yan, Chao; Li, XinLiang; Kong, WeiXuan

2013-10-01

A concept of entropy increment ratio ( s¯) is introduced for compressible turbulence simulation through a series of direct numerical simulations (DNS). s¯ represents the dissipation rate per unit mechanical energy with the benefit of independence of freestream Mach numbers. Based on this feature, we construct the shielding function f s to describe the boundary layer region and propose an entropy-based detached-eddy simulation method (SDES). This approach follows the spirit of delayed detached-eddy simulation (DDES) proposed by Spalart et al. in 2005, but it exhibits much better behavior after their performances are compared in the following flows, namely, pure attached flow with thick boundary layer (a supersonic flat-plate flow with high Reynolds number), fully separated flow (the supersonic base flow), and separated-reattached flow (the supersonic cavity-ramp flow). The Reynolds-averaged Navier-Stokes (RANS) resolved region is reliably preserved and the modeled stress depletion (MSD) phenomenon which is inherent in DES and DDES is partly alleviated. Moreover, this new hybrid strategy is simple and general, making it applicable to other models related to the boundary layer predictions.

Entropy factor for randomness quantification in neuronal data.

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Rajdl, K; Lansky, P; Kostal, L

2017-11-01

A novel measure of neural spike train randomness, an entropy factor, is proposed. It is based on the Shannon entropy of the number of spikes in a time window and can be seen as an analogy to the Fano factor. Theoretical properties of the new measure are studied for equilibrium renewal processes and further illustrated on gamma and inverse Gaussian probability distributions of interspike intervals. Finally, the entropy factor is evaluated from the experimental records of spontaneous activity in macaque primary visual cortex and compared to its theoretical behavior deduced for the renewal process models. Both theoretical and experimental results show substantial differences between the Fano and entropy factors. Rather paradoxically, an increase in the variability of spike count is often accompanied by an increase of its predictability, as evidenced by the entropy factor. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

Local conditional entropy in measure for covers with respect to a fixed partition

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Romagnoli, Pierre-Paul

2018-05-01

In this paper we introduce two measure theoretical notions of conditional entropy for finite measurable covers conditioned to a finite measurable partition and prove that they are equal. Using this we state a local variational principle with respect to the notion of conditional entropy defined by Misiurewicz (1976 Stud. Math. 55 176–200) for the case of open covers. This in particular extends the work done in Romagnoli (2003 Ergod. Theor. Dynam. Syst. 23 1601–10), Glasner and Weiss (2006 Handbook of Dynamical Systems vol 1B (Amsterdam: Elsevier)) and Huang et al (2006 Ergod. Theor. Dynam. Syst. 26 219–45).

Special Issue on Entropy-Based Applied Cryptography and Enhanced Security for Ubiquitous Computing

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James (Jong Hyuk Park

2016-09-01

Full Text Available Entropy is a basic and important concept in information theory. It is also often used as a measure of the unpredictability of a cryptographic key in cryptography research areas. Ubiquitous computing (Ubi-comp has emerged rapidly as an exciting new paradigm. In this special issue, we mainly selected and discussed papers related with ore theories based on the graph theory to solve computational problems on cryptography and security, practical technologies; applications and services for Ubi-comp including secure encryption techniques, identity and authentication; credential cloning attacks and countermeasures; switching generator with resistance against the algebraic and side channel attacks; entropy-based network anomaly detection; applied cryptography using chaos function, information hiding and watermark, secret sharing, message authentication, detection and modeling of cyber attacks with Petri Nets, and quantum flows for secret key distribution, etc.

Cooperative Localization for Multi-AUVs Based on GM-PHD Filters and Information Entropy Theory

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Lichuan Zhang

2017-10-01

Full Text Available Cooperative localization (CL is considered a promising method for underwater localization with respect to multiple autonomous underwater vehicles (multi-AUVs. In this paper, we proposed a CL algorithm based on information entropy theory and the probability hypothesis density (PHD filter, aiming to enhance the global localization accuracy of the follower. In the proposed framework, the follower carries lower cost navigation systems, whereas the leaders carry better ones. Meanwhile, the leaders acquire the followers’ observations, including both measurements and clutter. Then, the PHD filters are utilized on the leaders and the results are communicated to the followers. The followers then perform weighted summation based on all received messages and obtain a final positioning result. Based on the information entropy theory and the PHD filter, the follower is able to acquire a precise knowledge of its position.

Statistical inference based on divergence measures

CERN Document Server

Pardo, Leandro

2005-01-01

The idea of using functionals of Information Theory, such as entropies or divergences, in statistical inference is not new. However, in spite of the fact that divergence statistics have become a very good alternative to the classical likelihood ratio test and the Pearson-type statistic in discrete models, many statisticians remain unaware of this powerful approach.Statistical Inference Based on Divergence Measures explores classical problems of statistical inference, such as estimation and hypothesis testing, on the basis of measures of entropy and divergence. The first two chapters form an overview, from a statistical perspective, of the most important measures of entropy and divergence and study their properties. The author then examines the statistical analysis of discrete multivariate data with emphasis is on problems in contingency tables and loglinear models using phi-divergence test statistics as well as minimum phi-divergence estimators. The final chapter looks at testing in general populations, prese...

Characterization of complexity in the electroencephalograph activity of Alzheimer's disease based on fuzzy entropy.

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Cao, Yuzhen; Cai, Lihui; Wang, Jiang; Wang, Ruofan; Yu, Haitao; Cao, Yibin; Liu, Jing

2015-08-01

In this paper, experimental neurophysiologic recording and statistical analysis are combined to investigate the nonlinear characteristic and the cognitive function of the brain. Fuzzy approximate entropy and fuzzy sample entropy are applied to characterize the model-based simulated series and electroencephalograph (EEG) series of Alzheimer's disease (AD). The effectiveness and advantages of these two kinds of fuzzy entropy are first verified through the simulated EEG series generated by the alpha rhythm model, including stronger relative consistency and robustness. Furthermore, in order to detect the abnormality of irregularity and chaotic behavior in the AD brain, the complexity features based on these two fuzzy entropies are extracted in the delta, theta, alpha, and beta bands. It is demonstrated that, due to the introduction of fuzzy set theory, the fuzzy entropies could better distinguish EEG signals of AD from that of the normal than the approximate entropy and sample entropy. Moreover, the entropy values of AD are significantly decreased in the alpha band, particularly in the temporal brain region, such as electrode T3 and T4. In addition, fuzzy sample entropy could achieve higher group differences in different brain regions and higher average classification accuracy of 88.1% by support vector machine classifier. The obtained results prove that fuzzy sample entropy may be a powerful tool to characterize the complexity abnormalities of AD, which could be helpful in further understanding of the disease.

Spatial-dependence recurrence sample entropy

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Pham, Tuan D.; Yan, Hong

2018-03-01

Measuring complexity in terms of the predictability of time series is a major area of research in science and engineering, and its applications are spreading throughout many scientific disciplines, where the analysis of physiological signals is perhaps the most widely reported in literature. Sample entropy is a popular measure for quantifying signal irregularity. However, the sample entropy does not take sequential information, which is inherently useful, into its calculation of sample similarity. Here, we develop a method that is based on the mathematical principle of the sample entropy and enables the capture of sequential information of a time series in the context of spatial dependence provided by the binary-level co-occurrence matrix of a recurrence plot. Experimental results on time-series data of the Lorenz system, physiological signals of gait maturation in healthy children, and gait dynamics in Huntington's disease show the potential of the proposed method.

On quantum Rényi entropies

DEFF Research Database (Denmark)

Müller-Lennert, Martin; Dupont-Dupuis, Fréderic; Szehr, Oleg

2013-01-01

The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in in...

Sample Entropy-Based Approach to Evaluate the Stability of Double-Wire Pulsed MIG Welding

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Ping Yao

2014-01-01

Full Text Available According to the sample entropy, this paper deals with a quantitative method to evaluate the current stability in double-wire pulsed MIG welding. Firstly, the sample entropy of current signals with different stability but the same parameters is calculated. The results show that the more stable the current, the smaller the value and the standard deviation of sample entropy. Secondly, four parameters, which are pulse width, peak current, base current, and frequency, are selected for four-level three-factor orthogonal experiment. The calculation and analysis of desired signals indicate that sample entropy values are affected by welding current parameters. Then, a quantitative method based on sample entropy is proposed. The experiment results show that the method can preferably quantify the welding current stability.

2D Tsallis Entropy for Image Segmentation Based on Modified Chaotic Bat Algorithm

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Zhiwei Ye

2018-03-01

Full Text Available Image segmentation is a significant step in image analysis and computer vision. Many entropy based approaches have been presented in this topic; among them, Tsallis entropy is one of the best performing methods. However, 1D Tsallis entropy does not consider make use of the spatial correlation information within the neighborhood results might be ruined by noise. Therefore, 2D Tsallis entropy is proposed to solve the problem, and results are compared with 1D Fisher, 1D maximum entropy, 1D cross entropy, 1D Tsallis entropy, fuzzy entropy, 2D Fisher, 2D maximum entropy and 2D cross entropy. On the other hand, due to the existence of huge computational costs, meta-heuristics algorithms like genetic algorithm (GA, particle swarm optimization (PSO, ant colony optimization algorithm (ACO and differential evolution algorithm (DE are used to accelerate the 2D Tsallis entropy thresholding method. In this paper, considering 2D Tsallis entropy as a constrained optimization problem, the optimal thresholds are acquired by maximizing the objective function using a modified chaotic Bat algorithm (MCBA. The proposed algorithm has been tested on some actual and infrared images. The results are compared with that of PSO, GA, ACO and DE and demonstrate that the proposed method outperforms other approaches involved in the paper, which is a feasible and effective option for image segmentation.

Research and Measurement of Software Complexity Based on Wuli, Shili, Renli (WSR and Information Entropy

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Rong Jiang

2015-04-01

Full Text Available Complexity is an important factor throughout the software life cycle. It is increasingly difficult to guarantee software quality, cost and development progress with the increase in complexity. Excessive complexity is one of the main reasons for the failure of software projects, so effective recognition, measurement and control of complexity becomes the key of project management. At first, this paper analyzes the current research situation of software complexity systematically and points out existing problems in current research. Then, it proposes a WSR framework of software complexity, which divides the complexity of software into three levels of Wuli (WL, Shili (SL and Renli (RL, so that the staff in different roles may have a better understanding of complexity. Man is the main source of complexity, but the current research focuses on WL complexity, and the research of RL complexity is extremely scarce, so this paper emphasizes the research of RL complexity of software projects. This paper not only analyzes the composing factors of RL complexity, but also provides the definition of RL complexity. Moreover, it puts forward a quantitative measurement method of the complexity of personnel organization hierarchy and the complexity of personnel communication information based on information entropy first and analyzes and validates the scientificity and rationality of this measurement method through a large number of cases.

Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

Energy Technology Data Exchange (ETDEWEB)

Xu, Kaixuan, E-mail: kaixuanxubjtu@yeah.net; Wang, Jun

2017-02-26

In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model. - Highlights: • Two new entropy approaches for estimation of nonlinear complexity are proposed for the financial market. • Effectiveness analysis of proposed methods is presented and their respective features are studied. • Empirical research of proposed analysis on seven world financial market indices. • Numerical simulation of Potts financial dynamics is preformed for nonlinear complexity behaviors.

Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

International Nuclear Information System (INIS)

Xu, Kaixuan; Wang, Jun

2017-01-01

In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model. - Highlights: • Two new entropy approaches for estimation of nonlinear complexity are proposed for the financial market. • Effectiveness analysis of proposed methods is presented and their respective features are studied. • Empirical research of proposed analysis on seven world financial market indices. • Numerical simulation of Potts financial dynamics is preformed for nonlinear complexity behaviors.

[Identification of special quality eggs with NIR spectroscopy technology based on symbol entropy feature extraction method].

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Zhao, Yong; Hong, Wen-Xue

2011-11-01

Fast, nondestructive and accurate identification of special quality eggs is an urgent problem. The present paper proposed a new feature extraction method based on symbol entropy to identify near infrared spectroscopy of special quality eggs. The authors selected normal eggs, free range eggs, selenium-enriched eggs and zinc-enriched eggs as research objects and measured the near-infrared diffuse reflectance spectra in the range of 12 000-4 000 cm(-1). Raw spectra were symbolically represented with aggregation approximation algorithm and symbolic entropy was extracted as feature vector. An error-correcting output codes multiclass support vector machine classifier was designed to identify the spectrum. Symbolic entropy feature is robust when parameter changed and the highest recognition rate reaches up to 100%. The results show that the identification method of special quality eggs using near-infrared is feasible and the symbol entropy can be used as a new feature extraction method of near-infrared spectra.

Shannon versus Kullback-Leibler entropies in nonequilibrium random motion

International Nuclear Information System (INIS)

Garbaczewski, Piotr

2005-01-01

We analyze dynamical properties of the Shannon information entropy of a continuous probability distribution, which is driven by a standard diffusion process. This entropy choice is confronted with another option, employing the conditional Kullback-Leibler entropy. Both entropies discriminate among various probability distributions, either statically or in the time domain. An asymptotic approach towards equilibrium is typically monotonic in terms of the Kullback entropy. The Shannon entropy time rate needs not to be positive and is a sensitive indicator of the power transfer processes (removal/supply) due to an active environment. In the case of Smoluchowski diffusions, the Kullback entropy time rate coincides with the Shannon entropy 'production' rate

Fuzzy 2-partition entropy threshold selection based on Big Bang–Big Crunch Optimization algorithm

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Baljit Singh Khehra

2015-03-01

Full Text Available The fuzzy 2-partition entropy approach has been widely used to select threshold value for image segmenting. This approach used two parameterized fuzzy membership functions to form a fuzzy 2-partition of the image. The optimal threshold is selected by searching an optimal combination of parameters of the membership functions such that the entropy of fuzzy 2-partition is maximized. In this paper, a new fuzzy 2-partition entropy thresholding approach based on the technology of the Big Bang–Big Crunch Optimization (BBBCO is proposed. The new proposed thresholding approach is called the BBBCO-based fuzzy 2-partition entropy thresholding algorithm. BBBCO is used to search an optimal combination of parameters of the membership functions for maximizing the entropy of fuzzy 2-partition. BBBCO is inspired by the theory of the evolution of the universe; namely the Big Bang and Big Crunch Theory. The proposed algorithm is tested on a number of standard test images. For comparison, three different algorithms included Genetic Algorithm (GA-based, Biogeography-based Optimization (BBO-based and recursive approaches are also implemented. From experimental results, it is observed that the performance of the proposed algorithm is more effective than GA-based, BBO-based and recursion-based approaches.

Development of a task difficulty measure for emergency operating procedures using entropy concepts

International Nuclear Information System (INIS)

Park, Jinkyun; Jung, Wondea; Kim, Jaewhan; Ha Jaejoo

2000-01-01

In this paper, a method to quantify the degree of step complexity (SC) of an EOP step is developed based on entropy measures that have been used to evaluate software complexity in software engineering. Developed measure consists of three sub-measures that can quantify step complexity from various viewpoints. To verify developed SC measure, estimated SC values are compared with subjective task load scores obtained from the NASA-TLX (task load index) technique and the step performance time data obtained from a full scope simulator. From these comparisons, it can be concluded that the SC measure seems be appropriate for step difficulty evaluations because estimated SC values generally agree with the results of subjective task load scores the step performance time data. (author)

An entropy-based analysis of lane changing behavior: An interactive approach.

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Kosun, Caglar; Ozdemir, Serhan

2017-05-19

As a novelty, this article proposes the nonadditive entropy framework for the description of driver behaviors during lane changing. The authors also state that this entropy framework governs the lane changing behavior in traffic flow in accordance with the long-range vehicular interactions and traffic safety. The nonadditive entropy framework is the new generalized theory of thermostatistical mechanics. Vehicular interactions during lane changing are considered within this framework. The interactive approach for the lane changing behavior of the drivers is presented in the traffic flow scenarios presented in the article. According to the traffic flow scenarios, 4 categories of traffic flow and driver behaviors are obtained. Through the scenarios, comparative analyses of nonadditive and additive entropy domains are also provided. Two quadrants of the categories belong to the nonadditive entropy; the rest are involved in the additive entropy domain. Driving behaviors are extracted and the scenarios depict that nonadditivity matches safe driving well, whereas additivity corresponds to unsafe driving. Furthermore, the cooperative traffic system is considered in nonadditivity where the long-range interactions are present. However, the uncooperative traffic system falls into the additivity domain. The analyses also state that there would be possible traffic flow transitions among the quadrants. This article shows that lane changing behavior could be generalized as nonadditive, with additivity as a special case, based on the given traffic conditions. The nearest and close neighbor models are well within the conventional additive entropy framework. In this article, both the long-range vehicular interactions and safe driving behavior in traffic are handled in the nonadditive entropy domain. It is also inferred that the Tsallis entropy region would correspond to mandatory lane changing behavior, whereas additive and either the extensive or nonextensive entropy region would

Entropy Based Analysis of DNS Query Traffic in the Campus Network

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Dennis Arturo Ludeña Romaña

2008-10-01

Full Text Available We carried out the entropy based study on the DNS query traffic from the campus network in a university through January 1st, 2006 to March 31st, 2007. The results are summarized, as follows: (1 The source IP addresses- and query keyword-based entropies change symmetrically in the DNS query traffic from the outside of the campus network when detecting the spam bot activity on the campus network. On the other hand (2, the source IP addresses- and query keywordbased entropies change similarly each other when detecting big DNS query traffic caused by prescanning or distributed denial of service (DDoS attack from the campus network. Therefore, we can detect the spam bot and/or DDoS attack bot by only watching DNS query access traffic.

Entropy-based Probabilistic Fatigue Damage Prognosis and Algorithmic Performance Comparison

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National Aeronautics and Space Administration — In this paper, a maximum entropy-based general framework for probabilistic fatigue damage prognosis is investigated. The proposed methodology is based on an...

Entropy-based probabilistic fatigue damage prognosis and algorithmic performance comparison

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National Aeronautics and Space Administration — In this paper, a maximum entropy-based general framework for probabilistic fatigue damage prognosis is investigated. The proposed methodology is based on an...

Entropy based fingerprint for local crystalline order

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Piaggi, Pablo M.; Parrinello, Michele

2017-09-01

We introduce a new fingerprint that allows distinguishing between liquid-like and solid-like atomic environments. This fingerprint is based on an approximate expression for the entropy projected on individual atoms. When combined with local enthalpy, this fingerprint acquires an even finer resolution and it is capable of discriminating between different crystal structures.

Measuring Coupling of Rhythmical Time Series Using Cross Sample Entropy and Cross Recurrence Quantification Analysis

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John McCamley

2017-01-01

Full Text Available The aim of this investigation was to compare and contrast the use of cross sample entropy (xSE and cross recurrence quantification analysis (cRQA measures for the assessment of coupling of rhythmical patterns. Measures were assessed using simulated signals with regular, chaotic, and random fluctuations in frequency, amplitude, and a combination of both. Biological data were studied as models of normal and abnormal locomotor-respiratory coupling. Nine signal types were generated for seven frequency ratios. Fifteen patients with COPD (abnormal coupling and twenty-one healthy controls (normal coupling walked on a treadmill at three speeds while breathing and walking were recorded. xSE and the cRQA measures of percent determinism, maximum line, mean line, and entropy were quantified for both the simulated and experimental data. In the simulated data, xSE, percent determinism, and entropy were influenced by the frequency manipulation. The 1 : 1 frequency ratio was different than other frequency ratios for almost all measures and/or manipulations. The patients with COPD used a 2 : 3 ratio more often and xSE, percent determinism, maximum line, mean line, and cRQA entropy were able to discriminate between the groups. Analysis of the effects of walking speed indicated that all measures were able to discriminate between speeds.

Transfer Entropy as a Log-Likelihood Ratio

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Barnett, Lionel; Bossomaier, Terry

2012-09-01

Transfer entropy, an information-theoretic measure of time-directed information transfer between joint processes, has steadily gained popularity in the analysis of complex stochastic dynamics in diverse fields, including the neurosciences, ecology, climatology, and econometrics. We show that for a broad class of predictive models, the log-likelihood ratio test statistic for the null hypothesis of zero transfer entropy is a consistent estimator for the transfer entropy itself. For finite Markov chains, furthermore, no explicit model is required. In the general case, an asymptotic χ2 distribution is established for the transfer entropy estimator. The result generalizes the equivalence in the Gaussian case of transfer entropy and Granger causality, a statistical notion of causal influence based on prediction via vector autoregression, and establishes a fundamental connection between directed information transfer and causality in the Wiener-Granger sense.

Novel Application of a Multiscale Entropy Index as a Sensitive Tool for Detecting Subtle Vascular Abnormalities in the Aged and Diabetic

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Hsien-Tsai Wu

2013-01-01

Full Text Available Although previous studies have shown the successful use of pressure-induced reactive hyperemia as a tool for the assessment of endothelial function, its sensitivity remains questionable. This study aims to investigate the feasibility and sensitivity of a novel multiscale entropy index (MEI in detecting subtle vascular abnormalities in healthy and diabetic subjects. Basic anthropometric and hemodynamic parameters, serum lipid profiles, and glycosylated hemoglobin levels were recorded. Arterial pulse wave signals were acquired from the wrist with an air pressure sensing system (APSS, followed by MEI and dilatation index (DI analyses. MEI succeeded in detecting significant differences among the four groups of subjects: healthy young individuals, healthy middle-aged or elderly individuals, well-controlled diabetic individuals, and poorly controlled diabetic individuals. A reduction in multiscale entropy reflected age- and diabetes-related vascular changes and may serve as a more sensitive indicator of subtle vascular abnormalities compared with DI in the setting of diabetes.

n-Order and maximum fuzzy similarity entropy for discrimination of signals of different complexity: Application to fetal heart rate signals.

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Zaylaa, Amira; Oudjemia, Souad; Charara, Jamal; Girault, Jean-Marc

2015-09-01

This paper presents two new concepts for discrimination of signals of different complexity. The first focused initially on solving the problem of setting entropy descriptors by varying the pattern size instead of the tolerance. This led to the search for the optimal pattern size that maximized the similarity entropy. The second paradigm was based on the n-order similarity entropy that encompasses the 1-order similarity entropy. To improve the statistical stability, n-order fuzzy similarity entropy was proposed. Fractional Brownian motion was simulated to validate the different methods proposed, and fetal heart rate signals were used to discriminate normal from abnormal fetuses. In all cases, it was found that it was possible to discriminate time series of different complexity such as fractional Brownian motion and fetal heart rate signals. The best levels of performance in terms of sensitivity (90%) and specificity (90%) were obtained with the n-order fuzzy similarity entropy. However, it was shown that the optimal pattern size and the maximum similarity measurement were related to intrinsic features of the time series. Copyright © 2015 Elsevier Ltd. All rights reserved.

Relations Among Some Fuzzy Entropy Formulae

Institute of Scientific and Technical Information of China (English)

卿铭

2004-01-01

Fuzzy entropy has been widely used to analyze and design fuzzy systems, and many fuzzy entropy formulae have been proposed. For further in-deepth analysis of fuzzy entropy, the axioms and some important formulae of fuzzy entropy are introduced. Some equivalence results among these fuzzy entropy formulae are proved, and it is shown that fuzzy entropy is a special distance measurement.

Differentiating epileptic from non-epileptic high frequency intracerebral EEG signals with measures of wavelet entropy.

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Mooij, Anne H; Frauscher, Birgit; Amiri, Mina; Otte, Willem M; Gotman, Jean

2016-12-01

To assess whether there is a difference in the background activity in the ripple band (80-200Hz) between epileptic and non-epileptic channels, and to assess whether this difference is sufficient for their reliable separation. We calculated mean and standard deviation of wavelet entropy in 303 non-epileptic and 334 epileptic channels from 50 patients with intracerebral depth electrodes and used these measures as predictors in a multivariable logistic regression model. We assessed sensitivity, positive predictive value (PPV) and negative predictive value (NPV) based on a probability threshold corresponding to 90% specificity. The probability of a channel being epileptic increased with higher mean (p=0.004) and particularly with higher standard deviation (pentropy is likely to be epileptic; with a threshold corresponding to 90% specificity our model can reliably select a subset of epileptic channels. Most studies have concentrated on brief ripple events. We showed that background activity in the ripple band also has some ability to discriminate epileptic channels. Copyright © 2016 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Entropy: Order or Information

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Ben-Naim, Arieh

2011-01-01

Changes in entropy can "sometimes" be interpreted in terms of changes in disorder. On the other hand, changes in entropy can "always" be interpreted in terms of changes in Shannon's measure of information. Mixing and demixing processes are used to highlight the pitfalls in the association of entropy with disorder. (Contains 3 figures.)

Multiscale entropy based study of the pathological time series

International Nuclear Information System (INIS)

Wang Jun; Ma Qianli

2008-01-01

This paper studies the multiscale entropy (MSE) of electrocardiogram's ST segment and compares the MSE results of ST segment with that of electrocardiogram in the first time. Electrocardiogram complexity changing characteristics has important clinical significance for early diagnosis. Study shows that the average MSE values and the varying scope fluctuation could be more effective to reveal the heart health status. Particularly the multiscale values varying scope fluctuation is a more sensitive parameter for early heart disease detection and has a clinical diagnostic significance. (general)

The generalized Simpson's entropy is a measure of biodiversity.

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Michael Grabchak

Full Text Available Modern measures of diversity satisfy reasonable axioms, are parameterized to produce diversity profiles, can be expressed as an effective number of species to simplify their interpretation, and come with estimators that allow one to apply them to real-world data. We introduce the generalized Simpson's entropy as a measure of diversity and investigate its properties. We show that it has many useful features and can be used as a measure of biodiversity. Moreover, unlike most commonly used diversity indices, it has unbiased estimators, which allow for sound estimation of the diversity of poorly sampled, rich communities.

Exploring the effects of climatic variables on monthly precipitation variation using a continuous wavelet-based multiscale entropy approach.

Science.gov (United States)

Roushangar, Kiyoumars; Alizadeh, Farhad; Adamowski, Jan

2018-08-01

Understanding precipitation on a regional basis is an important component of water resources planning and management. The present study outlines a methodology based on continuous wavelet transform (CWT) and multiscale entropy (CWME), combined with self-organizing map (SOM) and k-means clustering techniques, to measure and analyze the complexity of precipitation. Historical monthly precipitation data from 1960 to 2010 at 31 rain gauges across Iran were preprocessed by CWT. The multi-resolution CWT approach segregated the major features of the original precipitation series by unfolding the structure of the time series which was often ambiguous. The entropy concept was then applied to components obtained from CWT to measure dispersion, uncertainty, disorder, and diversification of subcomponents. Based on different validity indices, k-means clustering captured homogenous areas more accurately, and additional analysis was performed based on the outcome of this approach. The 31 rain gauges in this study were clustered into 6 groups, each one having a unique CWME pattern across different time scales. The results of clustering showed that hydrologic similarity (multiscale variation of precipitation) was not based on geographic contiguity. According to the pattern of entropy across the scales, each cluster was assigned an entropy signature that provided an estimation of the entropy pattern of precipitation data in each cluster. Based on the pattern of mean CWME for each cluster, a characteristic signature was assigned, which provided an estimation of the CWME of a cluster across scales of 1-2, 3-8, and 9-13 months relative to other stations. The validity of the homogeneous clusters demonstrated the usefulness of the proposed approach to regionalize precipitation. Further analysis based on wavelet coherence (WTC) was performed by selecting central rain gauges in each cluster and analyzing against temperature, wind, Multivariate ENSO index (MEI), and East Atlantic (EA) and

Local entropy as a measure for sampling solutions in constraint satisfaction problems

International Nuclear Information System (INIS)

Baldassi, Carlo; Ingrosso, Alessandro; Lucibello, Carlo; Saglietti, Luca; Zecchina, Riccardo

2016-01-01

We introduce a novel entropy-driven Monte Carlo (EdMC) strategy to efficiently sample solutions of random constraint satisfaction problems (CSPs). First, we extend a recent result that, using a large-deviation analysis, shows that the geometry of the space of solutions of the binary perceptron learning problem (a prototypical CSP), contains regions of very high-density of solutions. Despite being sub-dominant, these regions can be found by optimizing a local entropy measure. Building on these results, we construct a fast solver that relies exclusively on a local entropy estimate, and can be applied to general CSPs. We describe its performance not only for the perceptron learning problem but also for the random K-satisfiabilty problem (another prototypical CSP with a radically different structure), and show numerically that a simple zero-temperature Metropolis search in the smooth local entropy landscape can reach sub-dominant clusters of optimal solutions in a small number of steps, while standard Simulated Annealing either requires extremely long cooling procedures or just fails. We also discuss how the EdMC can heuristically be made even more efficient for the cases we studied. (paper: disordered systems, classical and quantum)

Entropy Generation Across Earth's Bow Shock

Science.gov (United States)

Parks, George K.; McCarthy, Michael; Fu, Suiyan; Lee E. s; Cao, Jinbin; Goldstein, Melvyn L.; Canu, Patrick; Dandouras, Iannis S.; Reme, Henri; Fazakerley, Andrew;

Optimization and large scale computation of an entropy-based moment closure

Science.gov (United States)

Kristopher Garrett, C.; Hauck, Cory; Hill, Judith

2015-12-01

We present computational advances and results in the implementation of an entropy-based moment closure, MN, in the context of linear kinetic equations, with an emphasis on heterogeneous and large-scale computing platforms. Entropy-based closures are known in several cases to yield more accurate results than closures based on standard spectral approximations, such as PN, but the computational cost is generally much higher and often prohibitive. Several optimizations are introduced to improve the performance of entropy-based algorithms over previous implementations. These optimizations include the use of GPU acceleration and the exploitation of the mathematical properties of spherical harmonics, which are used as test functions in the moment formulation. To test the emerging high-performance computing paradigm of communication bound simulations, we present timing results at the largest computational scales currently available. These results show, in particular, load balancing issues in scaling the MN algorithm that do not appear for the PN algorithm. We also observe that in weak scaling tests, the ratio in time to solution of MN to PN decreases.

Towards operational interpretations of generalized entropies

Science.gov (United States)

Topsøe, Flemming

2010-12-01

The driving force behind our study has been to overcome the difficulties you encounter when you try to extend the clear and convincing operational interpretations of classical Boltzmann-Gibbs-Shannon entropy to other notions, especially to generalized entropies as proposed by Tsallis. Our approach is philosophical, based on speculations regarding the interplay between truth, belief and knowledge. The main result demonstrates that, accepting philosophically motivated assumptions, the only possible measures of entropy are those suggested by Tsallis - which, as we know, include classical entropy. This result constitutes, so it seems, a more transparent interpretation of entropy than previously available. However, further research to clarify the assumptions is still needed. Our study points to the thesis that one should never consider the notion of entropy in isolation - in order to enable a rich and technically smooth study, further concepts, such as divergence, score functions and descriptors or controls should be included in the discussion. This will clarify the distinction between Nature and Observer and facilitate a game theoretical discussion. The usefulness of this distinction and the subsequent exploitation of game theoretical results - such as those connected with the notion of Nash equilibrium - is demonstrated by a discussion of the Maximum Entropy Principle.

Towards operational interpretations of generalized entropies

International Nuclear Information System (INIS)

Topsoee, Flemming

2010-01-01

The driving force behind our study has been to overcome the difficulties you encounter when you try to extend the clear and convincing operational interpretations of classical Boltzmann-Gibbs-Shannon entropy to other notions, especially to generalized entropies as proposed by Tsallis. Our approach is philosophical, based on speculations regarding the interplay between truth, belief and knowledge. The main result demonstrates that, accepting philosophically motivated assumptions, the only possible measures of entropy are those suggested by Tsallis - which, as we know, include classical entropy. This result constitutes, so it seems, a more transparent interpretation of entropy than previously available. However, further research to clarify the assumptions is still needed. Our study points to the thesis that one should never consider the notion of entropy in isolation - in order to enable a rich and technically smooth study, further concepts, such as divergence, score functions and descriptors or controls should be included in the discussion. This will clarify the distinction between Nature and Observer and facilitate a game theoretical discussion. The usefulness of this distinction and the subsequent exploitation of game theoretical results - such as those connected with the notion of Nash equilibrium - is demonstrated by a discussion of the Maximum Entropy Principle.

Combined Forecasting of Rainfall Based on Fuzzy Clustering and Cross Entropy

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Baohui Men

2017-12-01

Full Text Available Rainfall is an essential index to measure drought, and it is dependent upon various parameters including geographical environment, air temperature and pressure. The nonlinear nature of climatic variables leads to problems such as poor accuracy and instability in traditional forecasting methods. In this paper, the combined forecasting method based on data mining technology and cross entropy is proposed to forecast the rainfall with full consideration of the time-effectiveness of historical data. In view of the flaws of the fuzzy clustering method which is easy to fall into local optimal solution and low speed of operation, the ant colony algorithm is adopted to overcome these shortcomings and, as a result, refine the model. The method for determining weights is also improved by using the cross entropy. Besides, the forecast is conducted by analyzing the weighted average rainfall based on Thiessen polygon in the Beijing–Tianjin–Hebei region. Since the predictive errors are calculated, the results show that improved ant colony fuzzy clustering can effectively select historical data and enhance the accuracy of prediction so that the damage caused by extreme weather events like droughts and floods can be greatly lessened and even kept at bay.

Entropy squeezing of the field interacting with a nearly degenerate V-type three-level atom

Institute of Scientific and Technical Information of China (English)

Zhou Qing-Chun; Zhu Shi-Ning

2005-01-01

The position- and momentum-entopic squeezing properties of the optical field in the system of a nearly degenerate three-level atom interacting with a single-mode field are investigated. Calculation results indicate that when the field is initially in the vacuum state, it may lead to squeezing of the position entropy or the momentum entropy of the field if the atom is prepared properly. The effects of initial atomic state and the splitting of the excited levels of the atom on field entropies are discussed in this case. When the initial field is in a coherent state, we find that position-entropy squeezing of the field is present even if the atom is prepared in the ground state. By comparing the variance squeezing and entropy squeezing of the field we confirm that entropy is more sensitive than variance in measuring quantum fluctuations.

Computing derivative-based global sensitivity measures using polynomial chaos expansions

International Nuclear Information System (INIS)

Sudret, B.; Mai, C.V.

2015-01-01

In the field of computer experiments sensitivity analysis aims at quantifying the relative importance of each input parameter (or combinations thereof) of a computational model with respect to the model output uncertainty. Variance decomposition methods leading to the well-known Sobol' indices are recognized as accurate techniques, at a rather high computational cost though. The use of polynomial chaos expansions (PCE) to compute Sobol' indices has allowed to alleviate the computational burden though. However, when dealing with large dimensional input vectors, it is good practice to first use screening methods in order to discard unimportant variables. The derivative-based global sensitivity measures (DGSMs) have been developed recently in this respect. In this paper we show how polynomial chaos expansions may be used to compute analytically DGSMs as a mere post-processing. This requires the analytical derivation of derivatives of the orthonormal polynomials which enter PC expansions. Closed-form expressions for Hermite, Legendre and Laguerre polynomial expansions are given. The efficiency of the approach is illustrated on two well-known benchmark problems in sensitivity analysis. - Highlights: • Derivative-based global sensitivity measures (DGSM) have been developed for screening purpose. • Polynomial chaos expansions (PC) are used as a surrogate model of the original computational model. • From a PC expansion the DGSM can be computed analytically. • The paper provides the derivatives of Hermite, Legendre and Laguerre polynomials for this purpose

The criteria for selecting a method for unfolding neutron spectra based on the information entropy theory

International Nuclear Information System (INIS)

Zhu, Qingjun; Song, Fengquan; Ren, Jie; Chen, Xueyong; Zhou, Bin

2014-01-01

To further expand the application of an artificial neural network in the field of neutron spectrometry, the criteria for choosing between an artificial neural network and the maximum entropy method for the purpose of unfolding neutron spectra was presented. The counts of the Bonner spheres for IAEA neutron spectra were used as a database, and the artificial neural network and the maximum entropy method were used to unfold neutron spectra; the mean squares of the spectra were defined as the differences between the desired and unfolded spectra. After the information entropy of each spectrum was calculated using information entropy theory, the relationship between the mean squares of the spectra and the information entropy was acquired. Useful information from the information entropy guided the selection of unfolding methods. Due to the importance of the information entropy, the method for predicting the information entropy using the Bonner spheres' counts was established. The criteria based on the information entropy theory can be used to choose between the artificial neural network and the maximum entropy method unfolding methods. The application of an artificial neural network to unfold neutron spectra was expanded. - Highlights: • Two neutron spectra unfolding methods, ANN and MEM, were compared. • The spectrum's entropy offers useful information for selecting unfolding methods. • For the spectrum with low entropy, the ANN was generally better than MEM. • The spectrum's entropy was predicted based on the Bonner spheres' counts

Measurement Uncertainty Relations for Discrete Observables: Relative Entropy Formulation

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Barchielli, Alberto; Gregoratti, Matteo; Toigo, Alessandro

2018-02-01

We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate joint measurement of two target discrete observables, we define the entropic divergence as the maximal total loss of information occurring in the approximation at hand. For fixed target observables, we study the joint measurements minimizing the entropic divergence, and we prove the general properties of its minimum value. Such a minimum is our uncertainty lower bound: the total information lost by replacing the target observables with their optimal approximations, evaluated at the worst possible state. The bound turns out to be also an entropic incompatibility degree, that is, a good information-theoretic measure of incompatibility: indeed, it vanishes if and only if the target observables are compatible, it is state-independent, and it enjoys all the invariance properties which are desirable for such a measure. In this context, we point out the difference between general approximate joint measurements and sequential approximate joint measurements; to do this, we introduce a separate index for the tradeoff between the error of the first measurement and the disturbance of the second one. By exploiting the symmetry properties of the target observables, exact values, lower bounds and optimal approximations are evaluated in two different concrete examples: (1) a couple of spin-1/2 components (not necessarily orthogonal); (2) two Fourier conjugate mutually unbiased bases in prime power dimension. Finally, the entropic incompatibility degree straightforwardly generalizes to the case of many observables, still maintaining all its relevant properties; we explicitly compute it for three orthogonal spin-1/2 components.

An Entropy-Based Adaptive Hybrid Particle Swarm Optimization for Disassembly Line Balancing Problems

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Shanli Xiao

2017-11-01

Full Text Available In order to improve the product disassembly efficiency, the disassembly line balancing problem (DLBP is transformed into a problem of searching for the optimum path in the directed and weighted graph by constructing the disassembly hierarchy information graph (DHIG. Then, combining the characteristic of the disassembly sequence, an entropy-based adaptive hybrid particle swarm optimization algorithm (AHPSO is presented. In this algorithm, entropy is introduced to measure the changing tendency of population diversity, and the dimension learning, crossover and mutation operator are used to increase the probability of producing feasible disassembly solutions (FDS. Performance of the proposed methodology is tested on the primary problem instances available in the literature, and the results are compared with other evolutionary algorithms. The results show that the proposed algorithm is efficient to solve the complex DLBP.

Irreversible entropy model for damage diagnosis in resistors

Energy Technology Data Exchange (ETDEWEB)

Cuadras, Angel, E-mail: angel.cuadras@upc.edu; Crisóstomo, Javier; Ovejas, Victoria J.; Quilez, Marcos [Instrumentation, Sensor and Interfaces Group, Electronic Engineering Department, Escola d' Enginyeria de Telecomunicació i Aeronàutica de Castelldefels EETAC, Universitat Politècnica de Catalunya, Barcelona Tech (UPC), Castelldefels-Barcelona (Spain)

2015-10-28

We propose a method to characterize electrical resistor damage based on entropy measurements. Irreversible entropy and the rate at which it is generated are more convenient parameters than resistance for describing damage because they are essentially positive in virtue of the second law of thermodynamics, whereas resistance may increase or decrease depending on the degradation mechanism. Commercial resistors were tested in order to characterize the damage induced by power surges. Resistors were biased with constant and pulsed voltage signals, leading to power dissipation in the range of 4–8 W, which is well above the 0.25 W nominal power to initiate failure. Entropy was inferred from the added power and temperature evolution. A model is proposed to understand the relationship among resistance, entropy, and damage. The power surge dissipates into heat (Joule effect) and damages the resistor. The results show a correlation between entropy generation rate and resistor failure. We conclude that damage can be conveniently assessed from irreversible entropy generation. Our results for resistors can be easily extrapolated to other systems or machines that can be modeled based on their resistance.

Irreversible entropy model for damage diagnosis in resistors

International Nuclear Information System (INIS)

Cuadras, Angel; Crisóstomo, Javier; Ovejas, Victoria J.; Quilez, Marcos

2015-01-01

We propose a method to characterize electrical resistor damage based on entropy measurements. Irreversible entropy and the rate at which it is generated are more convenient parameters than resistance for describing damage because they are essentially positive in virtue of the second law of thermodynamics, whereas resistance may increase or decrease depending on the degradation mechanism. Commercial resistors were tested in order to characterize the damage induced by power surges. Resistors were biased with constant and pulsed voltage signals, leading to power dissipation in the range of 4–8 W, which is well above the 0.25 W nominal power to initiate failure. Entropy was inferred from the added power and temperature evolution. A model is proposed to understand the relationship among resistance, entropy, and damage. The power surge dissipates into heat (Joule effect) and damages the resistor. The results show a correlation between entropy generation rate and resistor failure. We conclude that damage can be conveniently assessed from irreversible entropy generation. Our results for resistors can be easily extrapolated to other systems or machines that can be modeled based on their resistance

Symbolic transfer entropy-based premature signal analysis

International Nuclear Information System (INIS)

Wang Jun; Yu Zheng-Feng

2012-01-01

In this paper, we use symbolic transfer entropy to study the coupling strength between premature signals. Numerical experiments show that three types of signal couplings are in the same direction. Among them, normal signal coupling is the strongest, followed by that of premature ventricular contractions, and that of atrial premature beats is the weakest. The T test shows that the entropies of the three signals are distinct. Symbolic transfer entropy requires less data, can distinguish the three types of signals and has very good computational efficiency. (interdisciplinary physics and related areas of science and technology)

Adjoint-based sensitivity analysis of low-order thermoacoustic networks using a wave-based approach

Science.gov (United States)

Aguilar, José G.; Magri, Luca; Juniper, Matthew P.

2017-07-01

Strict pollutant emission regulations are pushing gas turbine manufacturers to develop devices that operate in lean conditions, with the downside that combustion instabilities are more likely to occur. Methods to predict and control unstable modes inside combustion chambers have been developed in the last decades but, in some cases, they are computationally expensive. Sensitivity analysis aided by adjoint methods provides valuable sensitivity information at a low computational cost. This paper introduces adjoint methods and their application in wave-based low order network models, which are used as industrial tools, to predict and control thermoacoustic oscillations. Two thermoacoustic models of interest are analyzed. First, in the zero Mach number limit, a nonlinear eigenvalue problem is derived, and continuous and discrete adjoint methods are used to obtain the sensitivities of the system to small modifications. Sensitivities to base-state modification and feedback devices are presented. Second, a more general case with non-zero Mach number, a moving flame front and choked outlet, is presented. The influence of the entropy waves on the computed sensitivities is shown.

Algorithmic randomness and physical entropy

International Nuclear Information System (INIS)

Zurek, W.H.

1989-01-01

Algorithmic randomness provides a rigorous, entropylike measure of disorder of an individual, microscopic, definite state of a physical system. It is defined by the size (in binary digits) of the shortest message specifying the microstate uniquely up to the assumed resolution. Equivalently, algorithmic randomness can be expressed as the number of bits in the smallest program for a universal computer that can reproduce the state in question (for instance, by plotting it with the assumed accuracy). In contrast to the traditional definitions of entropy, algorithmic randomness can be used to measure disorder without any recourse to probabilities. Algorithmic randomness is typically very difficult to calculate exactly but relatively easy to estimate. In large systems, probabilistic ensemble definitions of entropy (e.g., coarse-grained entropy of Gibbs and Boltzmann's entropy H=lnW, as well as Shannon's information-theoretic entropy) provide accurate estimates of the algorithmic entropy of an individual system or its average value for an ensemble. One is thus able to rederive much of thermodynamics and statistical mechanics in a setting very different from the usual. Physical entropy, I suggest, is a sum of (i) the missing information measured by Shannon's formula and (ii) of the algorithmic information content---algorithmic randomness---present in the available data about the system. This definition of entropy is essential in describing the operation of thermodynamic engines from the viewpoint of information gathering and using systems. These Maxwell demon-type entities are capable of acquiring and processing information and therefore can ''decide'' on the basis of the results of their measurements and computations the best strategy for extracting energy from their surroundings. From their internal point of view the outcome of each measurement is definite

Absolute entropy of ions in methanol

International Nuclear Information System (INIS)

Abakshin, V.A.; Kobenin, V.A.; Krestov, G.A.

1978-01-01

By measuring the initial thermoelectromotive forces of chains with bromo-silver electrodes in tetraalkylammonium bromide solutions the absolute entropy of bromide-ion in methanol is determined in the 298.15-318.15 K range. The anti Ssub(Brsup(-))sup(0) = 9.8 entropy units value is used for calculation of the absolute partial molar entropy of alkali metal ions and halogenide ions. It has been found that, absolute entropy of Cs + =12.0 entropy units, I - =14.0 entropy units. The obtained ion absolute entropies in methanol at 298.15 K within 1-2 entropy units is in an agreement with published data

Adjoint entropy vs topological entropy

OpenAIRE

Giordano Bruno, Anna

2012-01-01

Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied. We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic entropy is defined using the family of all finite-index subgroups, while we take only the subfamily of all open finite-index subgroups to define the topological adjoint entropy. This allows us to compare the (topological) adjoint entropy with the known topologic...

Possible extended forms of thermodynamic entropy

International Nuclear Information System (INIS)

Sasa, Shin-ichi

2014-01-01

Thermodynamic entropy is determined by a heat measurement through the Clausius equality. The entropy then formalizes a fundamental limitation of operations by the second law of thermodynamics. The entropy is also expressed as the Shannon entropy of the microscopic degrees of freedom. Whenever an extension of thermodynamic entropy is attempted, we must pay special attention to how its three different aspects just mentioned are altered. In this paper, we discuss possible extensions of the thermodynamic entropy. (paper)

Misuse of thermodynamic entropy in economics

International Nuclear Information System (INIS)

Kovalev, Andrey V.

2016-01-01

The direct relationship between thermodynamic entropy and economic scarcity is only valid for a thermodynamically isolated economy. References to the second law of thermodynamics in economics within the context of scarcity ignore the fact that the earth is not an isolated system. The earth interacts with external sources and sinks of entropy and the resulting total entropy fluctuates around a constant. Even if the mankind finally proves unable to recycle industrial waste and close the technological cycle, the economic disruption caused by the depletion of natural resources may happen while the total thermodynamic entropy of the ecosystem remains essentially at the present level, because the transfer of chemically refined products may not increase significantly the total entropy, but it may decrease their recyclability. The inutility of industrial waste is not connected with its entropy, which may be exemplified with the case of alumina production. The case also demonstrates that industrially generated entropy is discharged into surroundings without being accumulated in ‘thermodynamically unavailable matter’. Material entropy, as a measure of complexity and economic dispersal of resources, can be a recyclability metric, but it is not a thermodynamic parameter, and its growth is not equivalent to the growth of thermodynamic entropy. - Highlights: • Entropy cannot be used as a measure of economic scarcity. • There is no anthropogenic entropy separate from the entropy produced naturally. • Inutility of industrial waste is not connected with its thermodynamic entropy. • Industrially generated entropy may or may not be accumulated in industrial waste. • Recyclability is more important than thermodynamic entropy of a product.

Calculating the Entropy of Solid and Liquid Metals, Based on Acoustic Data

Science.gov (United States)

Tekuchev, V. V.; Kalinkin, D. P.; Ivanova, I. V.

2018-05-01

The entropies of iron, cobalt, rhodium, and platinum are studied for the first time, based on acoustic data and using the Debye theory and rigid-sphere model, from 298 K up to the boiling point. A formula for the melting entropy of metals is validated. Good agreement between the research results and the literature data is obtained.

Multiple Sclerosis Identification Based on Fractional Fourier Entropy and a Modified Jaya Algorithm

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Shui-Hua Wang

2018-04-01

Full Text Available Aim: Currently, identifying multiple sclerosis (MS by human experts may come across the problem of “normal-appearing white matter”, which causes a low sensitivity. Methods: In this study, we presented a computer vision based approached to identify MS in an automatic way. This proposed method first extracted the fractional Fourier entropy map from a specified brain image. Afterwards, it sent the features to a multilayer perceptron trained by a proposed improved parameter-free Jaya algorithm. We used cost-sensitivity learning to handle the imbalanced data problem. Results: The 10 × 10-fold cross validation showed our method yielded a sensitivity of 97.40 ± 0.60%, a specificity of 97.39 ± 0.65%, and an accuracy of 97.39 ± 0.59%. Conclusions: We validated by experiments that the proposed improved Jaya performs better than plain Jaya algorithm and other latest bioinspired algorithms in terms of classification performance and training speed. In addition, our method is superior to four state-of-the-art MS identification approaches.

Non-Gaussian Systems Control Performance Assessment Based on Rational Entropy

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Jinglin Zhou

2018-05-01

Full Text Available Control loop Performance Assessment (CPA plays an important role in system operations. Stochastic statistical CPA index, such as a minimum variance controller (MVC-based CPA index, is one of the most widely used CPA indices. In this paper, a new minimum entropy controller (MEC-based CPA method of linear non-Gaussian systems is proposed. In this method, probability density function (PDF and rational entropy (RE are respectively used to describe the characteristics and the uncertainty of random variables. To better estimate the performance benchmark, an improved EDA algorithm, which is used to estimate the system parameters and noise PDF, is given. The effectiveness of the proposed method is illustrated through case studies on an ARMAX system.

Nonsymmetric entropy and maximum nonsymmetric entropy principle

International Nuclear Information System (INIS)

Liu Chengshi

2009-01-01

Under the frame of a statistical model, the concept of nonsymmetric entropy which generalizes the concepts of Boltzmann's entropy and Shannon's entropy, is defined. Maximum nonsymmetric entropy principle is proved. Some important distribution laws such as power law, can be derived from this principle naturally. Especially, nonsymmetric entropy is more convenient than other entropy such as Tsallis's entropy in deriving power laws.

Scaling-Laws of Flow Entropy with Topological Metrics of Water Distribution Networks

OpenAIRE

Giovanni Francesco Santonastaso; Armando Di Nardo; Michele Di Natale; Carlo Giudicianni; Roberto Greco

2018-01-01

Robustness of water distribution networks is related to their connectivity and topological structure, which also affect their reliability. Flow entropy, based on Shannon’s informational entropy, has been proposed as a measure of network redundancy and adopted as a proxy of reliability in optimal network design procedures. In this paper, the scaling properties of flow entropy of water distribution networks with their size and other topological metrics are studied. To such aim, flow entropy, ma...

Relative entropy as a measure of entanglement for Gaussian states

Institute of Scientific and Technical Information of China (English)

Lu Huai-Xin; Zhao Bo

2006-01-01

In this paper, we derive an explicit analytic expression of the relative entropy between two general Gaussian states. In the restriction of the set for Gaussian states and with the help of relative entropy formula and Peres-Simon separability criterion, one can conveniently obtain the relative entropy entanglement for Gaussian states. As an example,the relative entanglement for a two-mode squeezed thermal state has been obtained.

Towards an information extraction and knowledge formation framework based on Shannon entropy

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Iliescu Dragoș

2017-01-01

Full Text Available Information quantity subject is approached in this paperwork, considering the specific domain of nonconforming product management as information source. This work represents a case study. Raw data were gathered from a heavy industrial works company, information extraction and knowledge formation being considered herein. Involved method for information quantity estimation is based on Shannon entropy formula. Information and entropy spectrum are decomposed and analysed for extraction of specific information and knowledge-that formation. The result of the entropy analysis point out the information needed to be acquired by the involved organisation, this being presented as a specific knowledge type.

Fault detection of the connection of lithium-ion power batteries based on entropy for electric vehicles

Science.gov (United States)

Yao, Lei; Wang, Zhenpo; Ma, Jun

2015-10-01

This paper proposes a method of fault detection of the connection of Lithium-Ion batteries based on entropy for electric vehicle. In electric vehicle operation process, some factors, such as road conditions, driving habits, vehicle performance, always affect batteries by vibration, which easily cause loosing or virtual connection between batteries. Through the simulation of the battery charging and discharging experiment under vibration environment, the data of voltage fluctuation can be obtained. Meanwhile, an optimal filtering method is adopted using discrete cosine filter method to analyze the characteristics of system noise, based on the voltage set when batteries are working under different vibration frequency. Experimental data processed by filtering is analyzed based on local Shannon entropy, ensemble Shannon entropy and sample entropy. And the best way to find a method of fault detection of the connection of lithium-ion batteries based on entropy is presented for electric vehicle. The experimental data shows that ensemble Shannon entropy can predict the accurate time and the location of battery connection failure in real time. Besides electric-vehicle industry, this method can also be used in other areas in complex vibration environment.

Keeping the entropy of measurement: Szilard revisited

International Nuclear Information System (INIS)

Lubkin, E.

1987-01-01

The Second Law of Thermodynamics forbids a net gain of information. Yet a measurement provides information. Measurement itself thus becomes paradoxical, until one reflects that the gain in information about the system of interest might be offset by a gain in entropy of some garbage can gc. Indeed, it must be so offset to save the bookkeeping of the Second Law. This apparent and paradoxical gain in information attendant upon observation, presumably due to neglect of some dissipant gc, has long prompted aberrant speculation that intelligent beings and even life in general somehow indeed violate the Second Law, an erroneous view he cites only for perspective. For some time he has fallen prey to a version of this paradox, developed in the context of standard quantum theory of measurement as delineated by von Neumann (1955), a trap he has recently been able to escape with the help of Szilard (1929), the celebrated paper in which the related paradox of Maxwell's demon is broken. Here he describes a precise formulation, then resolution of his paradox of information through measurement

Connections between classical and parametric network entropies.

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Matthias Dehmer

Full Text Available This paper explores relationships between classical and parametric measures of graph (or network complexity. Classical measures are based on vertex decompositions induced by equivalence relations. Parametric measures, on the other hand, are constructed by using information functions to assign probabilities to the vertices. The inequalities established in this paper relating classical and parametric measures lay a foundation for systematic classification of entropy-based measures of graph complexity.

Three faces of entropy for complex systems: Information, thermodynamics, and the maximum entropy principle

Science.gov (United States)

Thurner, Stefan; Corominas-Murtra, Bernat; Hanel, Rudolf

2017-09-01

There are at least three distinct ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a means for statistical inference on multinomial processes (Jaynes maximum entropy principle). Even though these notions represent fundamentally different concepts, the functional form of the entropy for thermodynamic systems in equilibrium, for ergodic sources in information theory, and for independent sampling processes in statistical systems, is degenerate, H (p ) =-∑ipilogpi . For many complex systems, which are typically history-dependent, nonergodic, and nonmultinomial, this is no longer the case. Here we show that for such processes, the three entropy concepts lead to different functional forms of entropy, which we will refer to as SEXT for extensive entropy, SIT for the source information rate in information theory, and SMEP for the entropy functional that appears in the so-called maximum entropy principle, which characterizes the most likely observable distribution functions of a system. We explicitly compute these three entropy functionals for three concrete examples: for Pólya urn processes, which are simple self-reinforcing processes, for sample-space-reducing (SSR) processes, which are simple history dependent processes that are associated with power-law statistics, and finally for multinomial mixture processes.

Entropy and information causality in general probabilistic theories

International Nuclear Information System (INIS)

Barnum, Howard; Leifer, Matthew; Spekkens, Robert; Barrett, Jonathan; Clark, Lisa Orloff; Stepanik, Nicholas; Wilce, Alex; Wilke, Robin

2010-01-01

We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality (IC) recently proposed by Pawlowski et al (2009 arXiv:0905.2292). We consider two entropic quantities, which we term measurement and mixing entropy. In the context of classical and quantum theory, these coincide, being given by the Shannon and von Neumann entropies, respectively; in general, however, they are very different. In particular, while measurement entropy is easily seen to be concave, mixing entropy need not be. In fact, as we show, mixing entropy is not concave whenever the state space is a non-simplicial polytope. Thus, the condition that measurement and mixing entropies coincide is a strong constraint on possible theories. We call theories with this property monoentropic. Measurement entropy is subadditive, but not in general strongly subadditive. Equivalently, if we define the mutual information between two systems A and B by the usual formula I(A: B)=H(A)+H(B)-H(AB), where H denotes the measurement entropy and AB is a non-signaling composite of A and B, then it can happen that I(A:BC)< I(A:B). This is relevant to IC in the sense of Pawlowski et al: we show that any monoentropic non-signaling theory in which measurement entropy is strongly subadditive, and also satisfies a version of the Holevo bound, is informationally causal, and on the other hand we observe that Popescu-Rohrlich boxes, which violate IC, also violate strong subadditivity. We also explore the interplay between measurement and mixing entropy and various natural conditions on theories that arise in quantum axiomatics.

Entropy, complexity, and Markov diagrams for random walk cancer models.

Science.gov (United States)

Newton, Paul K; Mason, Jeremy; Hurt, Brian; Bethel, Kelly; Bazhenova, Lyudmila; Nieva, Jorge; Kuhn, Peter

2014-12-19

The notion of entropy is used to compare the complexity associated with 12 common cancers based on metastatic tumor distribution autopsy data. We characterize power-law distributions, entropy, and Kullback-Liebler divergence associated with each primary cancer as compared with data for all cancer types aggregated. We then correlate entropy values with other measures of complexity associated with Markov chain dynamical systems models of progression. The Markov transition matrix associated with each cancer is associated with a directed graph model where nodes are anatomical locations where a metastatic tumor could develop, and edge weightings are transition probabilities of progression from site to site. The steady-state distribution corresponds to the autopsy data distribution. Entropy correlates well with the overall complexity of the reduced directed graph structure for each cancer and with a measure of systemic interconnectedness of the graph, called graph conductance. The models suggest that grouping cancers according to their entropy values, with skin, breast, kidney, and lung cancers being prototypical high entropy cancers, stomach, uterine, pancreatic and ovarian being mid-level entropy cancers, and colorectal, cervical, bladder, and prostate cancers being prototypical low entropy cancers, provides a potentially useful framework for viewing metastatic cancer in terms of predictability, complexity, and metastatic potential.

Fault Diagnosis Method Based on Information Entropy and Relative Principal Component Analysis

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Xiaoming Xu

2017-01-01

Full Text Available In traditional principle component analysis (PCA, because of the neglect of the dimensions influence between different variables in the system, the selected principal components (PCs often fail to be representative. While the relative transformation PCA is able to solve the above problem, it is not easy to calculate the weight for each characteristic variable. In order to solve it, this paper proposes a kind of fault diagnosis method based on information entropy and Relative Principle Component Analysis. Firstly, the algorithm calculates the information entropy for each characteristic variable in the original dataset based on the information gain algorithm. Secondly, it standardizes every variable’s dimension in the dataset. And, then, according to the information entropy, it allocates the weight for each standardized characteristic variable. Finally, it utilizes the relative-principal-components model established for fault diagnosis. Furthermore, the simulation experiments based on Tennessee Eastman process and Wine datasets demonstrate the feasibility and effectiveness of the new method.

Entropy, neutro-entropy and anti-entropy for neutrosophic information

OpenAIRE

Vasile Patrascu

2017-01-01

This approach presents a multi-valued representation of the neutrosophic information. It highlights the link between the bifuzzy information and neutrosophic one. The constructed deca-valued structure shows the neutrosophic information complexity. This deca-valued structure led to construction of two new concepts for the neutrosophic information: neutro-entropy and anti-entropy. These two concepts are added to the two existing: entropy and non-entropy. Thus, we obtained the following triad: e...

Local curvature entropy-based 3D terrain representation using a comprehensive Quadtree

Science.gov (United States)

Chen, Qiyu; Liu, Gang; Ma, Xiaogang; Mariethoz, Gregoire; He, Zhenwen; Tian, Yiping; Weng, Zhengping

2018-05-01

Large scale 3D digital terrain modeling is a crucial part of many real-time applications in geoinformatics. In recent years, the improved speed and precision in spatial data collection make the original terrain data more complex and bigger, which poses challenges for data management, visualization and analysis. In this work, we presented an effective and comprehensive 3D terrain representation based on local curvature entropy and a dynamic Quadtree. The Level-of-detail (LOD) models of significant terrain features were employed to generate hierarchical terrain surfaces. In order to reduce the radical changes of grid density between adjacent LODs, local entropy of terrain curvature was regarded as a measure of subdividing terrain grid cells. Then, an efficient approach was presented to eliminate the cracks among the different LODs by directly updating the Quadtree due to an edge-based structure proposed in this work. Furthermore, we utilized a threshold of local entropy stored in each parent node of this Quadtree to flexibly control the depth of the Quadtree and dynamically schedule large-scale LOD terrain. Several experiments were implemented to test the performance of the proposed method. The results demonstrate that our method can be applied to construct LOD 3D terrain models with good performance in terms of computational cost and the maintenance of terrain features. Our method has already been deployed in a geographic information system (GIS) for practical uses, and it is able to support the real-time dynamic scheduling of large scale terrain models more easily and efficiently.

Physical entropy, information entropy and their evolution equations

Institute of Scientific and Technical Information of China (English)

无

2001-01-01

Inspired by the evolution equation of nonequilibrium statistical physics entropy and the concise statistical formula of the entropy production rate, we develop a theory of the dynamic information entropy and build a nonlinear evolution equation of the information entropy density changing in time and state variable space. Its mathematical form and physical meaning are similar to the evolution equation of the physical entropy: The time rate of change of information entropy density originates together from drift, diffusion and production. The concise statistical formula of information entropy production rate is similar to that of physical entropy also. Furthermore, we study the similarity and difference between physical entropy and information entropy and the possible unification of the two statistical entropies, and discuss the relationship among the principle of entropy increase, the principle of equilibrium maximum entropy and the principle of maximum information entropy as well as the connection between them and the entropy evolution equation.

Entropy of Fluidized Bed - a Measure of Particles Mixing

Czech Academy of Sciences Publication Activity Database

Punčochář, Miroslav; Drahoš, Jiří

2003-01-01

Roč. 58, č. 12 (2003), s. 2515-2518 ISSN 0009-2509 R&D Projects: GA ČR GA104/97/S002 Institutional research plan: CEZ:AV0Z4072921 Keywords : entropy * fluidization * Kolmogorov entropy Subject RIV: CI - Industrial Chemistry, Chemical Engineering Impact factor: 1.562, year: 2003

Entropy and Digital Installation

Directory of Open Access Journals (Sweden)

Susan Ballard

2005-01-01

Full Text Available This paper examines entropy as a process which introduces ideas of distributed materiality to digital installation. Beginning from an analysis of entropy as both force and probability measure within information theory and it’s extension in Ruldof Arnheim’s text ‘Entropy and Art” it develops an argument for the positive rather thannegative forces of entropy. The paper centres on a discussion of two recent works by New Zealand artists Ronnie van Hout (“On the Run”, Wellington City Gallery, NZ, 2004 and Alex Monteith (“Invisible Cities”, Physics Room Contemporary Art Space, Christchurch, NZ, 2004. Ballard suggests that entropy, rather than being a hindrance to understanding or a random chaotic force, discloses a necessary and material politics of noise present in digital installation.

Entropy, neutro-entropy and anti-entropy for neutrosophic information

OpenAIRE

Vasile Patrascu

2017-01-01

This article shows a deca-valued representation of neutrosophic information in which are defined the following features: truth, falsity, weak truth, weak falsity, ignorance, contradiction, saturation, neutrality, ambiguity and hesitation. Using these features, there are constructed computing formulas for entropy, neutro-entropy and anti-entropy.

Generalized composite multiscale permutation entropy and Laplacian score based rolling bearing fault diagnosis

Science.gov (United States)

Zheng, Jinde; Pan, Haiyang; Yang, Shubao; Cheng, Junsheng

2018-01-01

Multiscale permutation entropy (MPE) is a recently proposed nonlinear dynamic method for measuring the randomness and detecting the nonlinear dynamic change of time series and can be used effectively to extract the nonlinear dynamic fault feature from vibration signals of rolling bearing. To solve the drawback of coarse graining process in MPE, an improved MPE method called generalized composite multiscale permutation entropy (GCMPE) was proposed in this paper. Also the influence of parameters on GCMPE and its comparison with the MPE are studied by analyzing simulation data. GCMPE was applied to the fault feature extraction from vibration signal of rolling bearing and then based on the GCMPE, Laplacian score for feature selection and the Particle swarm optimization based support vector machine, a new fault diagnosis method for rolling bearing was put forward in this paper. Finally, the proposed method was applied to analyze the experimental data of rolling bearing. The analysis results show that the proposed method can effectively realize the fault diagnosis of rolling bearing and has a higher fault recognition rate than the existing methods.

The density process of the minimal entropy Martingale measure in a ...

African Journals Online (AJOL)

In a stochastic volatility market the Radon-Nikodym density of the minimal entropy martingale measure can be expressed in terms of the solution of a semilinear partial differential equation (PDE). This fact has been explored and illustrated for the time-homogeneous case in a recent paper by Benth and Karlsen [3]. However ...

Expected Shannon Entropy and Shannon Differentiation between Subpopulations for Neutral Genes under the Finite Island Model.

Directory of Open Access Journals (Sweden)

Anne Chao

Full Text Available Shannon entropy H and related measures are increasingly used in molecular ecology and population genetics because (1 unlike measures based on heterozygosity or allele number, these measures weigh alleles in proportion to their population fraction, thus capturing a previously-ignored aspect of allele frequency distributions that may be important in many applications; (2 these measures connect directly to the rich predictive mathematics of information theory; (3 Shannon entropy is completely additive and has an explicitly hierarchical nature; and (4 Shannon entropy-based differentiation measures obey strong monotonicity properties that heterozygosity-based measures lack. We derive simple new expressions for the expected values of the Shannon entropy of the equilibrium allele distribution at a neutral locus in a single isolated population under two models of mutation: the infinite allele model and the stepwise mutation model. Surprisingly, this complex stochastic system for each model has an entropy expressable as a simple combination of well-known mathematical functions. Moreover, entropy- and heterozygosity-based measures for each model are linked by simple relationships that are shown by simulations to be approximately valid even far from equilibrium. We also identify a bridge between the two models of mutation. We apply our approach to subdivided populations which follow the finite island model, obtaining the Shannon entropy of the equilibrium allele distributions of the subpopulations and of the total population. We also derive the expected mutual information and normalized mutual information ("Shannon differentiation" between subpopulations at equilibrium, and identify the model parameters that determine them. We apply our measures to data from the common starling (Sturnus vulgaris in Australia. Our measures provide a test for neutrality that is robust to violations of equilibrium assumptions, as verified on real world data from starlings.

Expected Shannon Entropy and Shannon Differentiation between Subpopulations for Neutral Genes under the Finite Island Model.

Science.gov (United States)

Chao, Anne; Jost, Lou; Hsieh, T C; Ma, K H; Sherwin, William B; Rollins, Lee Ann

2015-01-01

Shannon entropy H and related measures are increasingly used in molecular ecology and population genetics because (1) unlike measures based on heterozygosity or allele number, these measures weigh alleles in proportion to their population fraction, thus capturing a previously-ignored aspect of allele frequency distributions that may be important in many applications; (2) these measures connect directly to the rich predictive mathematics of information theory; (3) Shannon entropy is completely additive and has an explicitly hierarchical nature; and (4) Shannon entropy-based differentiation measures obey strong monotonicity properties that heterozygosity-based measures lack. We derive simple new expressions for the expected values of the Shannon entropy of the equilibrium allele distribution at a neutral locus in a single isolated population under two models of mutation: the infinite allele model and the stepwise mutation model. Surprisingly, this complex stochastic system for each model has an entropy expressable as a simple combination of well-known mathematical functions. Moreover, entropy- and heterozygosity-based measures for each model are linked by simple relationships that are shown by simulations to be approximately valid even far from equilibrium. We also identify a bridge between the two models of mutation. We apply our approach to subdivided populations which follow the finite island model, obtaining the Shannon entropy of the equilibrium allele distributions of the subpopulations and of the total population. We also derive the expected mutual information and normalized mutual information ("Shannon differentiation") between subpopulations at equilibrium, and identify the model parameters that determine them. We apply our measures to data from the common starling (Sturnus vulgaris) in Australia. Our measures provide a test for neutrality that is robust to violations of equilibrium assumptions, as verified on real world data from starlings.

Structure of a Global Network of Financial Companies Based on Transfer Entropy

Directory of Open Access Journals (Sweden)

Leonidas Sandoval

2014-08-01

Full Text Available This work uses the stocks of the 197 largest companies in the world, in terms of market capitalization, in the financial area, from 2003 to 2012. We study the causal relationships between them using Transfer Entropy, which is calculated using the stocks of those companies and their counterparts lagged by one day. With this, we can assess which companies influence others according to sub-areas of the financial sector, which are banks, diversified financial services, savings and loans, insurance, private equity funds, real estate investment companies, and real estate trust funds. We also analyze the exchange of information between those stocks as seen by Transfer Entropy and the network formed by them based on this measure, verifying that they cluster mainly according to countries of origin, and then by industry and sub-industry. Then we use data on the stocks of companies in the financial sector of some countries that are suffering the most with the current credit crisis, namely Greece, Cyprus, Ireland, Spain, Portugal, and Italy, and assess, also using Transfer Entropy, which companies from the largest 197 are most affected by the stocks of these countries in crisis. The aim is to map a network of influences that may be used in the study of possible contagions originating in those countries in financial crisis.

Entropy for the Complexity of Physiological Signal Dynamics.

Science.gov (United States)

Zhang, Xiaohua Douglas

2017-01-01

Recently, the rapid development of large data storage technologies, mobile network technology, and portable medical devices makes it possible to measure, record, store, and track analysis of biological dynamics. Portable noninvasive medical devices are crucial to capture individual characteristics of biological dynamics. The wearable noninvasive medical devices and the analysis/management of related digital medical data will revolutionize the management and treatment of diseases, subsequently resulting in the establishment of a new healthcare system. One of the key features that can be extracted from the data obtained by wearable noninvasive medical device is the complexity of physiological signals, which can be represented by entropy of biological dynamics contained in the physiological signals measured by these continuous monitoring medical devices. Thus, in this chapter I present the major concepts of entropy that are commonly used to measure the complexity of biological dynamics. The concepts include Shannon entropy, Kolmogorov entropy, Renyi entropy, approximate entropy, sample entropy, and multiscale entropy. I also demonstrate an example of using entropy for the complexity of glucose dynamics.

Structured chaos shapes spike-response noise entropy in balanced neural networks

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Guillaume eLajoie

2014-10-01

Full Text Available Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. For many models of these networks, a striking feature is that their dynamics are chaotic and thus, are sensitive to small perturbations. How does this chaos manifest in the neural code? Specifically, how variable are the spike patterns that such a network produces in response to an input signal? To answer this, we derive a bound for a general measure of variability -- spike-train entropy. This leads to important insights on the variability of multi-cell spike pattern distributions in large recurrent networks of spiking neurons responding to fluctuating inputs. The analysis is based on results from random dynamical systems theory and is complemented by detailed numerical simulations. We find that the spike pattern entropy is an order of magnitude lower than what would be extrapolated from single cells. This holds despite the fact that network coupling becomes vanishingly sparse as network size grows -- a phenomenon that depends on ``extensive chaos, as previously discovered for balanced networks without stimulus drive. Moreover, we show how spike pattern entropy is controlled by temporal features of the inputs. Our findings provide insight into how neural networks may encode stimuli in the presence of inherently chaotic dynamics.

Entropy measurements in paroxysmal and persistent atrial fibrillation

International Nuclear Information System (INIS)

Cervigón, R; Moreno, J; Pérez-Villacastín, J; Reilly, R B; Millet, J; Castells, F

2010-01-01

Recent studies on atrial fibrillation (AF) have identified different activation patterns in paroxysmal and persistent AF. In this study, bipolar intra-atrial registers from 28 patients (14 paroxysmal AF and 14 persistent AF) were analyzed in order to find out regional differences in the organization in both types of arrhythmias. The organization of atrial electrical activity was assessed in terms of nonlinear parameters, such as entropy measurements. Results showed differences between the atrial chambers with a higher disorganization in the left atrium in paroxysmal AF patients and a more homogenous behavior along the atria in persistent AF patients

A Markovian Entropy Measure for the Analysis of Calcium Activity Time Series.

Science.gov (United States)

Marken, John P; Halleran, Andrew D; Rahman, Atiqur; Odorizzi, Laura; LeFew, Michael C; Golino, Caroline A; Kemper, Peter; Saha, Margaret S

2016-01-01

Methods to analyze the dynamics of calcium activity often rely on visually distinguishable features in time series data such as spikes, waves, or oscillations. However, systems such as the developing nervous system display a complex, irregular type of calcium activity which makes the use of such methods less appropriate. Instead, for such systems there exists a class of methods (including information theoretic, power spectral, and fractal analysis approaches) which use more fundamental properties of the time series to analyze the observed calcium dynamics. We present a new analysis method in this class, the Markovian Entropy measure, which is an easily implementable calcium time series analysis method which represents the observed calcium activity as a realization of a Markov Process and describes its dynamics in terms of the level of predictability underlying the transitions between the states of the process. We applied our and other commonly used calcium analysis methods on a dataset from Xenopus laevis neural progenitors which displays irregular calcium activity and a dataset from murine synaptic neurons which displays activity time series that are well-described by visually-distinguishable features. We find that the Markovian Entropy measure is able to distinguish between biologically distinct populations in both datasets, and that it can separate biologically distinct populations to a greater extent than other methods in the dataset exhibiting irregular calcium activity. These results support the benefit of using the Markovian Entropy measure to analyze calcium dynamics, particularly for studies using time series data which do not exhibit easily distinguishable features.

A Markovian Entropy Measure for the Analysis of Calcium Activity Time Series.

Directory of Open Access Journals (Sweden)

John P Marken

Full Text Available Methods to analyze the dynamics of calcium activity often rely on visually distinguishable features in time series data such as spikes, waves, or oscillations. However, systems such as the developing nervous system display a complex, irregular type of calcium activity which makes the use of such methods less appropriate. Instead, for such systems there exists a class of methods (including information theoretic, power spectral, and fractal analysis approaches which use more fundamental properties of the time series to analyze the observed calcium dynamics. We present a new analysis method in this class, the Markovian Entropy measure, which is an easily implementable calcium time series analysis method which represents the observed calcium activity as a realization of a Markov Process and describes its dynamics in terms of the level of predictability underlying the transitions between the states of the process. We applied our and other commonly used calcium analysis methods on a dataset from Xenopus laevis neural progenitors which displays irregular calcium activity and a dataset from murine synaptic neurons which displays activity time series that are well-described by visually-distinguishable features. We find that the Markovian Entropy measure is able to distinguish between biologically distinct populations in both datasets, and that it can separate biologically distinct populations to a greater extent than other methods in the dataset exhibiting irregular calcium activity. These results support the benefit of using the Markovian Entropy measure to analyze calcium dynamics, particularly for studies using time series data which do not exhibit easily distinguishable features.

Entropy as a measure of the noise extent in a two-level quantum feedback controlled system

Institute of Scientific and Technical Information of China (English)

Wang Tao-Bo; Fang Mao-Fa; Hu Yao-Hua

2007-01-01

By introducing the von Neumann entropy as a measure of the extent of noise, this paper discusses the entropy evolution in a two-level quantum feedback controlled system. The results show that the feedback control can induce the reduction of the degree of noise, and different control schemes exhibit different noise controlling ability, the extent of the reduction also related with the position of the target state on the Bloch sphere. It is shown that the evolution of entropy can provide a real time noise observation and a systematic guideline to make reasonable choice of control strategy.

Risk Contagion in Chinese Banking Industry: A Transfer Entropy-Based Analysis

Directory of Open Access Journals (Sweden)

Jianping Li

2013-12-01

Full Text Available What is the impact of a bank failure on the whole banking industry? To resolve this issue, the paper develops a transfer entropy-based method to determine the interbank exposure matrix between banks. This method constructs the interbank market structure by calculating the transfer entropy matrix using bank stock price sequences. This paper also evaluates the stability of Chinese banking system by simulating the risk contagion process. This paper contributes to the literature on interbank contagion mainly in two ways: it establishes a convincing connection between interbank market and transfer entropy, and exploits the market information (stock price rather than presumptions to determine the interbank exposure matrix. Second, the empirical analysis provides an in depth understanding of the stability of the current Chinese banking system.

Conflict management based on belief function entropy in sensor fusion.

Science.gov (United States)

Yuan, Kaijuan; Xiao, Fuyuan; Fei, Liguo; Kang, Bingyi; Deng, Yong

2016-01-01

Wireless sensor network plays an important role in intelligent navigation. It incorporates a group of sensors to overcome the limitation of single detection system. Dempster-Shafer evidence theory can combine the sensor data of the wireless sensor network by data fusion, which contributes to the improvement of accuracy and reliability of the detection system. However, due to different sources of sensors, there may be conflict among the sensor data under uncertain environment. Thus, this paper proposes a new method combining Deng entropy and evidence distance to address the issue. First, Deng entropy is adopted to measure the uncertain information. Then, evidence distance is applied to measure the conflict degree. The new method can cope with conflict effectually and improve the accuracy and reliability of the detection system. An example is illustrated to show the efficiency of the new method and the result is compared with that of the existing methods.

A Pilot Directional Protection for HVDC Transmission Line Based on Relative Entropy of Wavelet Energy

Directory of Open Access Journals (Sweden)

Sheng Lin

2015-07-01

Full Text Available On the basis of analyzing high-voltage direct current (HVDC transmission system and its fault superimposed circuit, the direction of the fault components of the voltage and the current measured at one end of transmission line is certified to be different for internal faults and external faults. As an estimate of the differences between two signals, relative entropy is an effective parameter for recognizing transient signals in HVDC transmission lines. In this paper, the relative entropy of wavelet energy is applied to distinguish internal fault from external fault. For internal faults, the directions of fault components of voltage and current are opposite at the two ends of the transmission line, indicating a huge difference of wavelet energy relative entropy; for external faults, the directions are identical, indicating a small difference. The simulation results based on PSCAD/EMTDC show that the proposed pilot protection system acts accurately for faults under different conditions, and its performance is not affected by fault type, fault location, fault resistance and noise.

Entropy of Iterated Function Systems and Their Relations with Black Holes and Bohr-Like Black Holes Entropies

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Christian Corda

2018-01-01

Full Text Available In this paper we consider the metric entropies of the maps of an iterated function system deduced from a black hole which are known the Bekenstein–Hawking entropies and its subleading corrections. More precisely, we consider the recent model of a Bohr-like black hole that has been recently analysed in some papers in the literature, obtaining the intriguing result that the metric entropies of a black hole are created by the metric entropies of the functions, created by the black hole principal quantum numbers, i.e., by the black hole quantum levels. We present a new type of topological entropy for general iterated function systems based on a new kind of the inverse of covers. Then the notion of metric entropy for an Iterated Function System ( I F S is considered, and we prove that these definitions for topological entropy of IFS’s are equivalent. It is shown that this kind of topological entropy keeps some properties which are hold by the classic definition of topological entropy for a continuous map. We also consider average entropy as another type of topological entropy for an I F S which is based on the topological entropies of its elements and it is also an invariant object under topological conjugacy. The relation between Axiom A and the average entropy is investigated.

Image coding based on maximum entropy partitioning for identifying ...

Indian Academy of Sciences (India)

A new coding scheme based on maximum entropy partitioning is proposed in our work, particularly to identify the improbable intensities related to different emotions. The improbable intensities when used as a mask decode the facial expression correctly, providing an effectiveplatform for future emotion categorization ...

Permutation entropy analysis of financial time series based on Hill's diversity number

Science.gov (United States)

Zhang, Yali; Shang, Pengjian

2017-12-01

In this paper the permutation entropy based on Hill's diversity number (Nn,r) is introduced as a new way to assess the complexity of a complex dynamical system such as stock market. We test the performance of this method with simulated data. Results show that Nn,r with appropriate parameters is more sensitive to the change of system and describes the trends of complex systems clearly. In addition, we research the stock closing price series from different data that consist of six indices: three US stock indices and three Chinese stock indices during different periods, Nn,r can quantify the changes of complexity for stock market data. Moreover, we get richer information from Nn,r, and obtain some properties about the differences between the US and Chinese stock indices.

A Note on Quantum Entropy

International Nuclear Information System (INIS)

Hansen, Frank

2016-01-01

Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We present a truly elementary proof of this fact in the context of the broader family of matrix entropies introduced by Chen and Tropp.

A Note on Quantum Entropy

Energy Technology Data Exchange (ETDEWEB)

Hansen, Frank, E-mail: frank.hansen@m.tohoku.ac.jp [Tohoku University, Institute for Excellence in Higher Education (Japan)

2016-06-15

Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We present a truly elementary proof of this fact in the context of the broader family of matrix entropies introduced by Chen and Tropp.

The Maximum Entropy Principle and the Modern Portfolio Theory

Directory of Open Access Journals (Sweden)

Ailton Cassetari

2003-12-01

Full Text Available In this work, a capital allocation methodology base don the Principle of Maximum Entropy was developed. The Shannons entropy is used as a measure, concerning the Modern Portfolio Theory, are also discuted. Particularly, the methodology is tested making a systematic comparison to: 1 the mean-variance (Markovitz approach and 2 the mean VaR approach (capital allocations based on the Value at Risk concept. In principle, such confrontations show the plausibility and effectiveness of the developed method.

Secondary structural entropy in RNA switch (Riboswitch) identification.

Science.gov (United States)

Manzourolajdad, Amirhossein; Arnold, Jonathan

2015-04-28

RNA regulatory elements play a significant role in gene regulation. Riboswitches, a widespread group of regulatory RNAs, are vital components of many bacterial genomes. These regulatory elements generally function by forming a ligand-induced alternative fold that controls access to ribosome binding sites or other regulatory sites in RNA. Riboswitch-mediated mechanisms are ubiquitous across bacterial genomes. A typical class of riboswitch has its own unique structural and biological complexity, making de novo riboswitch identification a formidable task. Traditionally, riboswitches have been identified through comparative genomics based on sequence and structural homology. The limitations of structural-homology-based approaches, coupled with the assumption that there is a great diversity of undiscovered riboswitches, suggests the need for alternative methods for riboswitch identification, possibly based on features intrinsic to their structure. As of yet, no such reliable method has been proposed. We used structural entropy of riboswitch sequences as a measure of their secondary structural dynamics. Entropy values of a diverse set of riboswitches were compared to that of their mutants, their dinucleotide shuffles, and their reverse complement sequences under different stochastic context-free grammar folding models. Significance of our results was evaluated by comparison to other approaches, such as the base-pairing entropy and energy landscapes dynamics. Classifiers based on structural entropy optimized via sequence and structural features were devised as riboswitch identifiers and tested on Bacillus subtilis, Escherichia coli, and Synechococcus elongatus as an exploration of structural entropy based approaches. The unusually long untranslated region of the cotH in Bacillus subtilis, as well as upstream regions of certain genes, such as the sucC genes were associated with significant structural entropy values in genome-wide examinations. Various tests show that there

Giant irreversible positive to large reversible negative magnetic entropy change evolution in Tb-based bulk metallic glass

International Nuclear Information System (INIS)

Luo Qiang; Schwarz, Bjoern; Mattern, Norbert; Eckert, Juergen

2010-01-01

We study the effects of amorphous structure and random anisotropy on the magnetic entropy change in a series of Tb-based amorphous alloys. The amorphous structure broadens the peak of magnetic entropy change and facilitates the adjustment of properties. The peak magnetic entropy change above the spin freezing temperature first depends on the average magnetic moment approximately linearly and second on the exchange interaction and random anisotropy. Large and broad reversible negative magnetic entropy changes are observed above the spin freezing temperature and giant positive irreversible magnetic entropy changes which associate with the internal entropy production are obtained well below.

Measuring sensitivity in pharmacoeconomic studies. Refining point sensitivity and range sensitivity by incorporating probability distributions.

Science.gov (United States)

Nuijten, M J

1999-07-01

The aim of the present study is to describe a refinement of a previously presented method, based on the concept of point sensitivity, to deal with uncertainty in economic studies. The original method was refined by the incorporation of probability distributions which allow a more accurate assessment of the level of uncertainty in the model. In addition, a bootstrap method was used to create a probability distribution for a fixed input variable based on a limited number of data points. The original method was limited in that the sensitivity measurement was based on a uniform distribution of the variables and that the overall sensitivity measure was based on a subjectively chosen range which excludes the impact of values outside the range on the overall sensitivity. The concepts of the refined method were illustrated using a Markov model of depression. The application of the refined method substantially changed the ranking of the most sensitive variables compared with the original method. The response rate became the most sensitive variable instead of the 'per diem' for hospitalisation. The refinement of the original method yields sensitivity outcomes, which greater reflect the real uncertainty in economic studies.

Quartz crystal microbalance-based system for high-sensitivity differential sputter yield measurements

International Nuclear Information System (INIS)

Rubin, B.; Topper, J. L.; Farnell, C. C.; Yalin, A. P.

2009-01-01

We present a quartz crystal microbalance-based system for high sensitivity differential sputter yield measurements of different target materials due to ion bombardment. The differential sputter yields can be integrated to find total yields. Possible ion beam conditions include ion energies in the range of 30-350 eV and incidence angles of 0 deg. - 70 deg. from normal. A four-grid ion optics system is used to achieve a collimated ion beam at low energy (<100 eV) and a two-grid ion optics is used for higher energies (up to 750 eV). A complementary weight loss approach is also used to measure total sputter yields. Validation experiments are presented that confirm high sensitivity and accuracy of sputter yield measurements.

Optimizing an estuarine water quality monitoring program through an entropy-based hierarchical spatiotemporal Bayesian framework

Science.gov (United States)

Alameddine, Ibrahim; Karmakar, Subhankar; Qian, Song S.; Paerl, Hans W.; Reckhow, Kenneth H.

2013-10-01

The total maximum daily load program aims to monitor more than 40,000 standard violations in around 20,000 impaired water bodies across the United States. Given resource limitations, future monitoring efforts have to be hedged against the uncertainties in the monitored system, while taking into account existing knowledge. In that respect, we have developed a hierarchical spatiotemporal Bayesian model that can be used to optimize an existing monitoring network by retaining stations that provide the maximum amount of information, while identifying locations that would benefit from the addition of new stations. The model assumes the water quality parameters are adequately described by a joint matrix normal distribution. The adopted approach allows for a reduction in redundancies, while emphasizing information richness rather than data richness. The developed approach incorporates the concept of entropy to account for the associated uncertainties. Three different entropy-based criteria are adopted: total system entropy, chlorophyll-a standard violation entropy, and dissolved oxygen standard violation entropy. A multiple attribute decision making framework is adopted to integrate the competing design criteria and to generate a single optimal design. The approach is implemented on the water quality monitoring system of the Neuse River Estuary in North Carolina, USA. The model results indicate that the high priority monitoring areas identified by the total system entropy and the dissolved oxygen violation entropy criteria are largely coincident. The monitoring design based on the chlorophyll-a standard violation entropy proved to be less informative, given the low probabilities of violating the water quality standard in the estuary.

Research on Sustainable Development Level Evaluation of Resource-based Cities Based on Shapely Entropy and Chouqet Integral

Science.gov (United States)

Zhao, Hui; Qu, Weilu; Qiu, Weiting

2018-03-01

In order to evaluate sustainable development level of resource-based cities, an evaluation method with Shapely entropy and Choquet integral is proposed. First of all, a systematic index system is constructed, the importance of each attribute is calculated based on the maximum Shapely entropy principle, and then the Choquet integral is introduced to calculate the comprehensive evaluation value of each city from the bottom up, finally apply this method to 10 typical resource-based cities in China. The empirical results show that the evaluation method is scientific and reasonable, which provides theoretical support for the sustainable development path and reform direction of resource-based cities.

Applying Improved Multiscale Fuzzy Entropy for Feature Extraction of MI-EEG

Directory of Open Access Journals (Sweden)

Ming-ai Li

2017-01-01

Full Text Available Electroencephalography (EEG is considered the output of a brain and it is a bioelectrical signal with multiscale and nonlinear properties. Motor Imagery EEG (MI-EEG not only has a close correlation with the human imagination and movement intention but also contains a large amount of physiological or disease information. As a result, it has been fully studied in the field of rehabilitation. To correctly interpret and accurately extract the features of MI-EEG signals, many nonlinear dynamic methods based on entropy, such as Approximate Entropy (ApEn, Sample Entropy (SampEn, Fuzzy Entropy (FE, and Permutation Entropy (PE, have been proposed and exploited continuously in recent years. However, these entropy-based methods can only measure the complexity of MI-EEG based on a single scale and therefore fail to account for the multiscale property inherent in MI-EEG. To solve this problem, Multiscale Sample Entropy (MSE, Multiscale Permutation Entropy (MPE, and Multiscale Fuzzy Entropy (MFE are developed by introducing scale factor. However, MFE has not been widely used in analysis of MI-EEG, and the same parameter values are employed when the MFE method is used to calculate the fuzzy entropy values on multiple scales. Actually, each coarse-grained MI-EEG carries the characteristic information of the original signal on different scale factors. It is necessary to optimize MFE parameters to discover more feature information. In this paper, the parameters of MFE are optimized independently for each scale factor, and the improved MFE (IMFE is applied to the feature extraction of MI-EEG. Based on the event-related desynchronization (ERD/event-related synchronization (ERS phenomenon, IMFE features from multi channels are fused organically to construct the feature vector. Experiments are conducted on a public dataset by using Support Vector Machine (SVM as a classifier. The experiment results of 10-fold cross-validation show that the proposed method yields

An entropy-assisted musculoskeletal shoulder model.

Science.gov (United States)

Xu, Xu; Lin, Jia-Hua; McGorry, Raymond W

2017-04-01

Optimization combined with a musculoskeletal shoulder model has been used to estimate mechanical loading of musculoskeletal elements around the shoulder. Traditionally, the objective function is to minimize the summation of the total activities of the muscles with forces, moments, and stability constraints. Such an objective function, however, tends to neglect the antagonist muscle co-contraction. In this study, an objective function including an entropy term is proposed to address muscle co-contractions. A musculoskeletal shoulder model is developed to apply the proposed objective function. To find the optimal weight for the entropy term, an experiment was conducted. In the experiment, participants generated various 3-D shoulder moments in six shoulder postures. The surface EMG of 8 shoulder muscles was measured and compared with the predicted muscle activities based on the proposed objective function using Bhattacharyya distance and concordance ratio under different weight of the entropy term. The results show that a small weight of the entropy term can improve the predictability of the model in terms of muscle activities. Such a result suggests that the concept of entropy could be helpful for further understanding the mechanism of muscle co-contractions as well as developing a shoulder biomechanical model with greater validity. Copyright © 2017 Elsevier Ltd. All rights reserved.

Entropy-Based Video Steganalysis of Motion Vectors

Directory of Open Access Journals (Sweden)

Elaheh Sadat Sadat

2018-04-01

Full Text Available In this paper, a new method is proposed for motion vector steganalysis using the entropy value and its combination with the features of the optimized motion vector. In this method, the entropy of blocks is calculated to determine their texture and the precision of their motion vectors. Then, by using a fuzzy cluster, the blocks are clustered into the blocks with high and low texture, while the membership function of each block to a high texture class indicates the texture of that block. These membership functions are used to weight the effective features that are extracted by reconstructing the motion estimation equations. Characteristics of the results indicate that the use of entropy and the irregularity of each block increases the precision of the final video classification into cover and stego classes.

The coupling analysis between stock market indices based on permutation measures

Science.gov (United States)

Shi, Wenbin; Shang, Pengjian; Xia, Jianan; Yeh, Chien-Hung

2016-04-01

Many information-theoretic methods have been proposed for analyzing the coupling dependence between time series. And it is significant to quantify the correlation relationship between financial sequences since the financial market is a complex evolved dynamic system. Recently, we developed a new permutation-based entropy, called cross-permutation entropy (CPE), to detect the coupling structures between two synchronous time series. In this paper, we extend the CPE method to weighted cross-permutation entropy (WCPE), to address some of CPE's limitations, mainly its inability to differentiate between distinct patterns of a certain motif and the sensitivity of patterns close to the noise floor. It shows more stable and reliable results than CPE does when applied it to spiky data and AR(1) processes. Besides, we adapt the CPE method to infer the complexity of short-length time series by freely changing the time delay, and test it with Gaussian random series and random walks. The modified method shows the advantages in reducing deviations of entropy estimation compared with the conventional one. Finally, the weighted cross-permutation entropy of eight important stock indices from the world financial markets is investigated, and some useful and interesting empirical results are obtained.

Real-time tricolor phase measuring profilometry based on CCD sensitivity calibration

Science.gov (United States)

Zhu, Lin; Cao, Yiping; He, Dawu; Chen, Cheng

2017-02-01

A real-time tricolor phase measuring profilometry (RTPMP) based on charge coupled device (CCD) sensitivity calibration is proposed. Only one colour fringe pattern whose red (R), green (G) and blue (B) components are, respectively, coded as three sinusoidal phase-shifting gratings with an equivalent shifting phase of 2π/3 is needed and sent to an appointed flash memory on a specialized digital light projector (SDLP). A specialized time-division multiplexing timing sequence actively controls the SDLP to project the fringe patterns in R, G and B channels sequentially onto the measured object in one over seventy-two of a second and meanwhile actively controls a high frame rate monochrome CCD camera to capture the corresponding deformed patterns synchronously with the SDLP. So the sufficient information for reconstructing the three-dimensional (3D) shape in one over twenty-four of a second is obtained. Due to the different spectral sensitivity of the CCD camera to RGB lights, the captured deformed patterns from R, G and B channels cannot share the same peak and valley, which will lead to lower accuracy or even failing to reconstruct the 3D shape. So a deformed pattern amending method based on CCD sensitivity calibration is developed to guarantee the accurate 3D reconstruction. The experimental results verify the feasibility of the proposed RTPMP method. The proposed RTPMP method can obtain the 3D shape at over the video frame rate of 24 frames per second, avoid the colour crosstalk completely and be effective for measuring real-time changing object.

Symbolic phase transfer entropy method and its application

Science.gov (United States)

Zhang, Ningning; Lin, Aijing; Shang, Pengjian

2017-10-01

In this paper, we introduce symbolic phase transfer entropy (SPTE) to infer the direction and strength of information flow among systems. The advantages of the proposed method are investigated by simulations on synthetic signals and real-world data. We demonstrate that symbolic phase transfer entropy is a robust and efficient tool to infer the information flow between complex systems. Based on the study of the synthetic data, we find a significant advantage of SPTE is its reduced sensitivity to noise. In addition, SPTE requires less amount of data than symbolic transfer entropy(STE). We analyze the direction and strength of information flow between six stock markets during the period from 2006 to 2016. The results indicate that the information flow among stocks varies over different periods. We also find that the interaction network pattern among stocks undergoes hierarchial reorganization with transition from one period to another. It is shown that the clusters are mainly classified according to period, and then by region. The stocks during the same time period are shown to drop into the same cluster.

A High-Precision Time-Frequency Entropy Based on Synchrosqueezing Generalized S-Transform Applied in Reservoir Detection

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Hui Chen

2018-06-01

Full Text Available According to the fact that high frequency will be abnormally attenuated when seismic signals travel across reservoirs, a new method, which is named high-precision time-frequency entropy based on synchrosqueezing generalized S-transform, is proposed for hydrocarbon reservoir detection in this paper. First, the proposed method obtains the time-frequency spectra by synchrosqueezing generalized S-transform (SSGST, which are concentrated around the real instantaneous frequency of the signals. Then, considering the characteristics and effects of noises, we give a frequency constraint condition to calculate the entropy based on time-frequency spectra. The synthetic example verifies that the entropy will be abnormally high when seismic signals have an abnormal attenuation. Besides, comparing with the GST time-frequency entropy and the original SSGST time-frequency entropy in field data, the results of the proposed method show higher precision. Moreover, the proposed method can not only accurately detect and locate hydrocarbon reservoirs, but also effectively suppress the impact of random noises.

On variational definition of quantum entropy

International Nuclear Information System (INIS)

Belavkin, Roman V.

2015-01-01

Entropy of distribution P can be defined in at least three different ways: 1) as the expectation of the Kullback-Leibler (KL) divergence of P from elementary δ-measures (in this case, it is interpreted as expected surprise); 2) as a negative KL-divergence of some reference measure ν from the probability measure P; 3) as the supremum of Shannon’s mutual information taken over all channels such that P is the output probability, in which case it is dual of some transportation problem. In classical (i.e. commutative) probability, all three definitions lead to the same quantity, providing only different interpretations of entropy. In non-commutative (i.e. quantum) probability, however, these definitions are not equivalent. In particular, the third definition, where the supremum is taken over all entanglements of two quantum systems with P being the output state, leads to the quantity that can be twice the von Neumann entropy. It was proposed originally by V. Belavkin and Ohya [1] and called the proper quantum entropy, because it allows one to define quantum conditional entropy that is always non-negative. Here we extend these ideas to define also quantum counterpart of proper cross-entropy and cross-information. We also show inequality for the values of classical and quantum information

Bayesian and maximum entropy methods for fusion diagnostic measurements with compact neutron spectrometers

International Nuclear Information System (INIS)

Reginatto, Marcel; Zimbal, Andreas

2008-01-01

In applications of neutron spectrometry to fusion diagnostics, it is advantageous to use methods of data analysis which can extract information from the spectrum that is directly related to the parameters of interest that describe the plasma. We present here methods of data analysis which were developed with this goal in mind, and which were applied to spectrometric measurements made with an organic liquid scintillation detector (type NE213). In our approach, we combine Bayesian parameter estimation methods and unfolding methods based on the maximum entropy principle. This two-step method allows us to optimize the analysis of the data depending on the type of information that we want to extract from the measurements. To illustrate these methods, we analyze neutron measurements made at the PTB accelerator under controlled conditions, using accelerator-produced neutron beams. Although the methods have been chosen with a specific application in mind, they are general enough to be useful for many other types of measurements

Entropy statistics and information theory

NARCIS (Netherlands)

Frenken, K.; Hanusch, H.; Pyka, A.

2007-01-01

Entropy measures provide important tools to indicate variety in distributions at particular moments in time (e.g., market shares) and to analyse evolutionary processes over time (e.g., technical change). Importantly, entropy statistics are suitable to decomposition analysis, which renders the

Transfer Entropy for Nonparametric Granger Causality Detection : An Evaluation of Different Resampling Methods

NARCIS (Netherlands)

Diks, C.; Fang, H.

2017-01-01

The information-theoretical concept transfer entropy is an ideal measure for detecting conditional independence, or Granger causality in a time series setting. The recent literature indeed witnesses an increased interest in applications of entropy-based tests in this direction. However, those tests

Brain entropy and human intelligence: A resting-state fMRI study

Science.gov (United States)

Calderone, Daniel; Morales, Leah J.

2018-01-01

Human intelligence comprises comprehension of and reasoning about an infinitely variable external environment. A brain capable of large variability in neural configurations, or states, will more easily understand and predict variable external events. Entropy measures the variety of configurations possible within a system, and recently the concept of brain entropy has been defined as the number of neural states a given brain can access. This study investigates the relationship between human intelligence and brain entropy, to determine whether neural variability as reflected in neuroimaging signals carries information about intellectual ability. We hypothesize that intelligence will be positively associated with entropy in a sample of 892 healthy adults, using resting-state fMRI. Intelligence is measured with the Shipley Vocabulary and WASI Matrix Reasoning tests. Brain entropy was positively associated with intelligence. This relation was most strongly observed in the prefrontal cortex, inferior temporal lobes, and cerebellum. This relationship between high brain entropy and high intelligence indicates an essential role for entropy in brain functioning. It demonstrates that access to variable neural states predicts complex behavioral performance, and specifically shows that entropy derived from neuroimaging signals at rest carries information about intellectual capacity. Future work in this area may elucidate the links between brain entropy in both resting and active states and various forms of intelligence. This insight has the potential to provide predictive information about adaptive behavior and to delineate the subdivisions and nature of intelligence based on entropic patterns. PMID:29432427

Brain entropy and human intelligence: A resting-state fMRI study.

Science.gov (United States)

Saxe, Glenn N; Calderone, Daniel; Morales, Leah J

2018-01-01

Human intelligence comprises comprehension of and reasoning about an infinitely variable external environment. A brain capable of large variability in neural configurations, or states, will more easily understand and predict variable external events. Entropy measures the variety of configurations possible within a system, and recently the concept of brain entropy has been defined as the number of neural states a given brain can access. This study investigates the relationship between human intelligence and brain entropy, to determine whether neural variability as reflected in neuroimaging signals carries information about intellectual ability. We hypothesize that intelligence will be positively associated with entropy in a sample of 892 healthy adults, using resting-state fMRI. Intelligence is measured with the Shipley Vocabulary and WASI Matrix Reasoning tests. Brain entropy was positively associated with intelligence. This relation was most strongly observed in the prefrontal cortex, inferior temporal lobes, and cerebellum. This relationship between high brain entropy and high intelligence indicates an essential role for entropy in brain functioning. It demonstrates that access to variable neural states predicts complex behavioral performance, and specifically shows that entropy derived from neuroimaging signals at rest carries information about intellectual capacity. Future work in this area may elucidate the links between brain entropy in both resting and active states and various forms of intelligence. This insight has the potential to provide predictive information about adaptive behavior and to delineate the subdivisions and nature of intelligence based on entropic patterns.

Scintigraphic acquisition entropy (2). A new approach in the quality control of the scintillation camera performances

International Nuclear Information System (INIS)

Elloumi, I.; Bouhdima, M.S.

2002-01-01

A new approach in the survey of the performances of gamma camera based on the entropy associated to the scintigraphic acquisition is presented. We take into account the sensitivity, the variation of the collimator response in function of the depth, the uncertainty on the number of counts, the multiplex effect and the spatial uncertainty. This entropy function is expressed in function of all the acquisition parameters: intrinsic crystal resolution, collimator characteristics, emitter object parameters and the source activity. The application of this method to the study of the influence of the collimation shows that the entropy associated to a collimator permits a best appreciation of the quality of the acquisition and therefore a better analysis of collimator performances. Likewise, the evolution of the entropy associated to the acquisition of a uniform source image is in agreement with the variation of the quality of image histogram. One shows, thus, that nor the spatial resolution, nor the sensitivity and nor the signal to noise ratio are able detect a variation of the image quality, when analysed one by one. (author)

Connectivity in the human brain dissociates entropy and complexity of auditory inputs.

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Nastase, Samuel A; Iacovella, Vittorio; Davis, Ben; Hasson, Uri

2015-03-01

Complex systems are described according to two central dimensions: (a) the randomness of their output, quantified via entropy; and (b) their complexity, which reflects the organization of a system's generators. Whereas some approaches hold that complexity can be reduced to uncertainty or entropy, an axiom of complexity science is that signals with very high or very low entropy are generated by relatively non-complex systems, while complex systems typically generate outputs with entropy peaking between these two extremes. In understanding their environment, individuals would benefit from coding for both input entropy and complexity; entropy indexes uncertainty and can inform probabilistic coding strategies, whereas complexity reflects a concise and abstract representation of the underlying environmental configuration, which can serve independent purposes, e.g., as a template for generalization and rapid comparisons between environments. Using functional neuroimaging, we demonstrate that, in response to passively processed auditory inputs, functional integration patterns in the human brain track both the entropy and complexity of the auditory signal. Connectivity between several brain regions scaled monotonically with input entropy, suggesting sensitivity to uncertainty, whereas connectivity between other regions tracked entropy in a convex manner consistent with sensitivity to input complexity. These findings suggest that the human brain simultaneously tracks the uncertainty of sensory data and effectively models their environmental generators. Copyright © 2014. Published by Elsevier Inc.

An entropy-based improved k-top scoring pairs (TSP) method for ...

African Journals Online (AJOL)

An entropy-based improved k-top scoring pairs (TSP) (Ik-TSP) method was presented in this study for the classification and prediction of human cancers based on gene-expression data. We compared Ik-TSP classifiers with 5 different machine learning methods and the k-TSP method based on 3 different feature selection ...

Entropy generation method to quantify thermal comfort

Science.gov (United States)

Boregowda, S. C.; Tiwari, S. N.; Chaturvedi, S. K.

2001-01-01

The present paper presents a thermodynamic approach to assess the quality of human-thermal environment interaction and quantify thermal comfort. The approach involves development of entropy generation term by applying second law of thermodynamics to the combined human-environment system. The entropy generation term combines both human thermal physiological responses and thermal environmental variables to provide an objective measure of thermal comfort. The original concepts and definitions form the basis for establishing the mathematical relationship between thermal comfort and entropy generation term. As a result of logic and deterministic approach, an Objective Thermal Comfort Index (OTCI) is defined and established as a function of entropy generation. In order to verify the entropy-based thermal comfort model, human thermal physiological responses due to changes in ambient conditions are simulated using a well established and validated human thermal model developed at the Institute of Environmental Research of Kansas State University (KSU). The finite element based KSU human thermal computer model is being utilized as a "Computational Environmental Chamber" to conduct series of simulations to examine the human thermal responses to different environmental conditions. The output from the simulation, which include human thermal responses and input data consisting of environmental conditions are fed into the thermal comfort model. Continuous monitoring of thermal comfort in comfortable and extreme environmental conditions is demonstrated. The Objective Thermal Comfort values obtained from the entropy-based model are validated against regression based Predicted Mean Vote (PMV) values. Using the corresponding air temperatures and vapor pressures that were used in the computer simulation in the regression equation generates the PMV values. The preliminary results indicate that the OTCI and PMV values correlate well under ideal conditions. However, an experimental study

The Effect of Threshold Values and Weighting Factors on the Association between Entropy Measures and Mortality after Myocardial Infarction in the Cardiac Arrhythmia Suppression Trial (CAST

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Christopher Mayer

2016-04-01

Full Text Available Heart rate variability (HRV is a non-invasive measurement based on the intervals between normal heart beats that characterize cardiac autonomic function. Decreased HRV is associated with increased risk of cardiovascular events. Characterizing HRV using only moment statistics fails to capture abnormalities in regulatory function that are important aspects of disease risk. Thus, entropy measures are a promising approach to quantify HRV for risk stratification. The purpose of this study was to investigate this potential for approximate, corrected approximate, sample, fuzzy, and fuzzy measure entropy and its dependency on the parameter selection. Recently, published parameter sets and further parameter combinations were investigated. Heart rate data were obtained from the "Cardiac Arrhythmia Suppression Trial (CAST RR Interval Sub-Study Database" (Physionet. Corresponding outcomes and clinical data were provided by one of the investigators. The use of previously-reported parameter sets on the pre-treatment data did not significantly add to the identification of patients at risk for cardiovascular death on follow-up. After arrhythmia suppression treatment, several parameter sets predicted outcomes for all patients and patients without coronary artery bypass grafting (CABG. The strongest results were seen using the threshold parameter as a multiple of the data’s standard deviation ( r = 0 . 2 · σ . Approximate and sample entropy provided significant hazard ratios for patients without CABG and without diabetes for an entropy maximizing threshold approximation. Additional parameter combinations did not improve the results for pre-treatment data. The results of this study illustrate the influence of parameter selection on entropy measures’ potential for cardiovascular risk stratification and support the potential use of entropy measures in future studies.

Feedback structure based entropy approach for multiple-model estimation

Institute of Scientific and Technical Information of China (English)

Shen-tu Han; Xue Anke; Guo Yunfei

2013-01-01

The variable-structure multiple-model (VSMM) approach, one of the multiple-model (MM) methods, is a popular and effective approach in handling problems with mode uncertainties. The model sequence set adaptation (MSA) is the key to design a better VSMM. However, MSA methods in the literature have big room to improve both theoretically and practically. To this end, we propose a feedback structure based entropy approach that could find the model sequence sets with the smallest size under certain conditions. The filtered data are fed back in real time and can be used by the minimum entropy (ME) based VSMM algorithms, i.e., MEVSMM. Firstly, the full Markov chains are used to achieve optimal solutions. Secondly, the myopic method together with particle filter (PF) and the challenge match algorithm are also used to achieve sub-optimal solutions, a trade-off between practicability and optimality. The numerical results show that the proposed algorithm provides not only refined model sets but also a good robustness margin and very high accuracy.

Entropy-based derivation of generalized distributions for hydrometeorological frequency analysis

Science.gov (United States)

Chen, Lu; Singh, Vijay P.

2018-02-01

Frequency analysis of hydrometeorological and hydrological extremes is needed for the design of hydraulic and civil infrastructure facilities as well as water resources management. A multitude of distributions have been employed for frequency analysis of these extremes. However, no single distribution has been accepted as a global standard. Employing the entropy theory, this study derived five generalized distributions for frequency analysis that used different kinds of information encoded as constraints. These distributions were the generalized gamma (GG), the generalized beta distribution of the second kind (GB2), and the Halphen type A distribution (Hal-A), Halphen type B distribution (Hal-B) and Halphen type inverse B distribution (Hal-IB), among which the GG and GB2 distribution were previously derived by Papalexiou and Koutsoyiannis (2012) and the Halphen family was first derived using entropy theory in this paper. The entropy theory allowed to estimate parameters of the distributions in terms of the constraints used for their derivation. The distributions were tested using extreme daily and hourly rainfall data. Results show that the root mean square error (RMSE) values were very small, which indicated that the five generalized distributions fitted the extreme rainfall data well. Among them, according to the Akaike information criterion (AIC) values, generally the GB2 and Halphen family gave a better fit. Therefore, those general distributions are one of the best choices for frequency analysis. The entropy-based derivation led to a new way for frequency analysis of hydrometeorological extremes.

Esscher transforms and the minimal entropy martingale measure for exponential Lévy models

DEFF Research Database (Denmark)

Hubalek, Friedrich; Sgarra, C.

In this paper we offer a systematic survey and comparison of the Esscher martingale transform for linear processes, the Esscher martingale transform for exponential processes, and the minimal entropy martingale measure for exponential lévy models and present some new results in order to give...

Prediction of Protein Configurational Entropy (Popcoen).

Science.gov (United States)

Goethe, Martin; Gleixner, Jan; Fita, Ignacio; Rubi, J Miguel

2018-03-13

A knowledge-based method for configurational entropy prediction of proteins is presented; this methodology is extremely fast, compared to previous approaches, because it does not involve any type of configurational sampling. Instead, the configurational entropy of a query fold is estimated by evaluating an artificial neural network, which was trained on molecular-dynamics simulations of ∼1000 proteins. The predicted entropy can be incorporated into a large class of protein software based on cost-function minimization/evaluation, in which configurational entropy is currently neglected for performance reasons. Software of this type is used for all major protein tasks such as structure predictions, proteins design, NMR and X-ray refinement, docking, and mutation effect predictions. Integrating the predicted entropy can yield a significant accuracy increase as we show exemplarily for native-state identification with the prominent protein software FoldX. The method has been termed Popcoen for Prediction of Protein Configurational Entropy. An implementation is freely available at http://fmc.ub.edu/popcoen/ .

A review of entropy generation in microchannels

Directory of Open Access Journals (Sweden)

Mohamed M Awad

2015-12-01

Full Text Available In this study, a critical review of thermodynamic optimum of microchannels based on entropy generation analysis is presented. Using entropy generation analysis as evaluation parameter of microchannels has been reported by many studies in the literature. In these studies, different working fluids such as nanofluids, air, water, engine oil, aniline, ethylene glycol, and non-Newtonian fluids have been used. For the case of nanofluids, “nanoparticles” has been used in various kinds such as Al2O3 and Cu, and “base fluid” has been used in various kinds such as water and ethylene glycol. Furthermore, studies on thermodynamic optimum of microchannels based on entropy generation analysis are summarized in a table. At the end, recommendations of future work for thermodynamic optimum of microchannels based on entropy generation analysis are given. As a result, this article can not only be used as the starting point for the researcher interested in entropy generation in microchannels, but it also includes recommendations for future studies on entropy generation in microchannels.

Particle swarm optimization-based local entropy weighted histogram equalization for infrared image enhancement

Science.gov (United States)

Wan, Minjie; Gu, Guohua; Qian, Weixian; Ren, Kan; Chen, Qian; Maldague, Xavier

2018-06-01

Infrared image enhancement plays a significant role in intelligent urban surveillance systems for smart city applications. Unlike existing methods only exaggerating the global contrast, we propose a particle swam optimization-based local entropy weighted histogram equalization which involves the enhancement of both local details and fore-and background contrast. First of all, a novel local entropy weighted histogram depicting the distribution of detail information is calculated based on a modified hyperbolic tangent function. Then, the histogram is divided into two parts via a threshold maximizing the inter-class variance in order to improve the contrasts of foreground and background, respectively. To avoid over-enhancement and noise amplification, double plateau thresholds of the presented histogram are formulated by means of particle swarm optimization algorithm. Lastly, each sub-image is equalized independently according to the constrained sub-local entropy weighted histogram. Comparative experiments implemented on real infrared images prove that our algorithm outperforms other state-of-the-art methods in terms of both visual and quantized evaluations.

On Thermodynamic Interpretation of Transfer Entropy

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Don C. Price

2013-02-01

Full Text Available We propose a thermodynamic interpretation of transfer entropy near equilibrium, using a specialised Boltzmann’s principle. The approach relates conditional probabilities to the probabilities of the corresponding state transitions. This in turn characterises transfer entropy as a difference of two entropy rates: the rate for a resultant transition and another rate for a possibly irreversible transition within the system affected by an additional source. We then show that this difference, the local transfer entropy, is proportional to the external entropy production, possibly due to irreversibility. Near equilibrium, transfer entropy is also interpreted as the difference in equilibrium stabilities with respect to two scenarios: a default case and the case with an additional source. Finally, we demonstrated that such a thermodynamic treatment is not applicable to information flow, a measure of causal effect.

Development of the step complexity measure for emergency operating procedures using entropy concepts

International Nuclear Information System (INIS)

Park, Jinkyun; Jung, Wondea; Ha, Jaejoo

2001-01-01

For a nuclear power plant (NPP), symptom-based emergency operating procedures (EOPs) have been adopted to enhance the safety of NPPs through reduction of operators' workload under emergency conditions. Symptom-based EOPs, however, could place a workload on operators because they have to not only identify related symptoms, but also understand the context of steps that should be carried out. Therefore, many qualitative checklists are suggested to ensure the appropriateness of steps included in EOPs. However, since these qualitative evaluations have some drawbacks, a quantitative measure that can roughly estimate the complexity of EOP steps is imperative to compensate for them. In this paper, a method to evaluate the complexity of an EOP step is developed based on entropy measures that have been used in software engineering. Based on these, step complexity (SC) measure that can evaluate SC from various viewpoints (such as the amount of information/operators' actions included in each EOP step, and the logic structure of each EOP step) was developed. To verify the suitableness of the SC measure, estimated SC values are compared with subjective task load scores obtained from the NASA-TLX (task load index) method and step performance time obtained from a full scope simulator. From these comparisons, it was observed that estimated SC values generally agree with the NASA-TLX scores and step performance time data. Thus, it could be concluded that the developed SC measure would be considered for evaluating SC of an EOP step

Entropy: From Thermodynamics to Hydrology

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Demetris Koutsoyiannis

2014-02-01

Full Text Available Some known results from statistical thermophysics as well as from hydrology are revisited from a different perspective trying: (a to unify the notion of entropy in thermodynamic and statistical/stochastic approaches of complex hydrological systems and (b to show the power of entropy and the principle of maximum entropy in inference, both deductive and inductive. The capability for deductive reasoning is illustrated by deriving the law of phase change transition of water (Clausius-Clapeyron from scratch by maximizing entropy in a formal probabilistic frame. However, such deductive reasoning cannot work in more complex hydrological systems with diverse elements, yet the entropy maximization framework can help in inductive inference, necessarily based on data. Several examples of this type are provided in an attempt to link statistical thermophysics with hydrology with a unifying view of entropy.

An exploration for the macroscopic physical meaning of entropy

Institute of Scientific and Technical Information of China (English)

无

2010-01-01

The macroscopic physical meaning of entropy is analyzed based on the exergy (availability) of a combined system (a closed system and its environment), which is the maximum amount of useful work obtainable from the system and the environment as the system is brought into equilibrium with the environment. The process the system experiences can be divided in two sequent sub-processes, the process at constant volume, which represents the heat interaction of the system with the environment, and the adiabatic process, which represents the work interaction of the system with the environment. It is shown that the macroscopic physical meaning of entropy is a measure of the unavailable energy of a closed system for doing useful work through heat interaction. This statement is more precise than those reported in prior literature. The unavailability function of a closed system can be defined as T0S and p0V in volume constant process and adiabatic process, respectively. Their changes, that is, AiTgS) and A (p0V) represent the unusable parts of the internal energy of a closed system for doing useful work in corresponding processes. Finally, the relation between Clausius entropy and Boltzmann entropy is discussed based on the comparison of their expressions for absolute entropy.

Entropy Measures for Stochastic Processes with Applications in Functional Anomaly Detection

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Gabriel Martos

2018-01-01

Full Text Available We propose a definition of entropy for stochastic processes. We provide a reproducing kernel Hilbert space model to estimate entropy from a random sample of realizations of a stochastic process, namely functional data, and introduce two approaches to estimate minimum entropy sets. These sets are relevant to detect anomalous or outlier functional data. A numerical experiment illustrates the performance of the proposed method; in addition, we conduct an analysis of mortality rate curves as an interesting application in a real-data context to explore functional anomaly detection.

On a Generalized Entropy Measure Leading to the Pathway Model with a Preliminary Application to Solar Neutrino Data

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Hans J. Haubold

2013-09-01

Full Text Available An entropy for the scalar variable case, parallel to Havrda-Charvat entropy, was introduced by the first author, and the properties and its connection to Tsallis non-extensive statistical mechanics and the Mathai pathway model were examined by the authors in previous papers. In the current paper, we extend the entropy to cover the scalar case, multivariable case, and matrix variate case. Then, this measure is optimized under different types of restrictions, and a number of models in the multivariable case and matrix variable case are obtained. Connections of these models to problems in statistical and physical sciences are pointed out. An application of the simplest case of the pathway model to the interpretation of solar neutrino data by applying standard deviation analysis and diffusion entropy analysis is provided.

A Real-Time Analysis Method for Pulse Rate Variability Based on Improved Basic Scale Entropy

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Yongxin Chou

2017-01-01

Full Text Available Base scale entropy analysis (BSEA is a nonlinear method to analyze heart rate variability (HRV signal. However, the time consumption of BSEA is too long, and it is unknown whether the BSEA is suitable for analyzing pulse rate variability (PRV signal. Therefore, we proposed a method named sliding window iterative base scale entropy analysis (SWIBSEA by combining BSEA and sliding window iterative theory. The blood pressure signals of healthy young and old subjects are chosen from the authoritative international database MIT/PhysioNet/Fantasia to generate PRV signals as the experimental data. Then, the BSEA and the SWIBSEA are used to analyze the experimental data; the results show that the SWIBSEA reduces the time consumption and the buffer cache space while it gets the same entropy as BSEA. Meanwhile, the changes of base scale entropy (BSE for healthy young and old subjects are the same as that of HRV signal. Therefore, the SWIBSEA can be used for deriving some information from long-term and short-term PRV signals in real time, which has the potential for dynamic PRV signal analysis in some portable and wearable medical devices.

A Connection Entropy Approach to Water Resources Vulnerability Analysis in a Changing Environment

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Zhengwei Pan

2017-11-01

Full Text Available This paper establishes a water resources vulnerability framework based on sensitivity, natural resilience and artificial adaptation, through the analyses of the four states of the water system and its accompanying transformation processes. Furthermore, it proposes an analysis method for water resources vulnerability based on connection entropy, which extends the concept of contact entropy. An example is given of the water resources vulnerability in Anhui Province of China, which analysis illustrates that, overall, vulnerability levels fluctuated and showed apparent improvement trends from 2001 to 2015. Some suggestions are also provided for the improvement of the level of water resources vulnerability in Anhui Province, considering the viewpoint of the vulnerability index.

Entropy Production of Stars

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Leonid M. Martyushev

2015-06-01

Full Text Available The entropy production (inside the volume bounded by a photosphere of main-sequence stars, subgiants, giants, and supergiants is calculated based on B–V photometry data. A non-linear inverse relationship of thermodynamic fluxes and forces as well as an almost constant specific (per volume entropy production of main-sequence stars (for 95% of stars, this quantity lies within 0.5 to 2.2 of the corresponding solar magnitude is found. The obtained results are discussed from the perspective of known extreme principles related to entropy production.

Enthalpy-entropy compensation in protein unfolding

Institute of Scientific and Technical Information of China (English)

无

2000-01-01

Enthalpy-entropy compensation was found to be a universal law in protein unfolding based on over 3 000 experimental data. Water molecular reorganization accompanying the protein unfolding was suggested as the origin of the enthalpy-entropy compensation in protein unfolding. It is indicated that the enthalpy-entropy compensation constitutes the physical foundation that satisfies the biological need of the small free energy changes in protein unfolding, without the sacrifice of the bio-diversity of proteins. The enthalpy-entropy compensation theory proposed herein also provides valuable insights into the Privalov's puzzle of enthalpy and entropy convergence in protein unfolding.

Black hole entropy functions and attractor equations

International Nuclear Information System (INIS)

Lopes Cardoso, Gabriel; Wit, Bernard de; Mahapatra, Swapna

2007-01-01

The entropy and the attractor equations for static extremal black hole solutions follow from a variational principle based on an entropy function. In the general case such an entropy function can be derived from the reduced action evaluated in a near-horizon geometry. BPS black holes constitute special solutions of this variational principle, but they can also be derived directly from a different entropy function based on supersymmetry enhancement at the horizon. Both functions are consistent with electric/magnetic duality and for BPS black holes their corresponding OSV-type integrals give identical results at the semi-classical level. We clarify the relation between the two entropy functions and the corresponding attractor equations for N = 2 supergravity theories with higher-derivative couplings in four space-time dimensions. We discuss how non-holomorphic corrections will modify these entropy functions

Entropy generation in a condenser and related correlations

Directory of Open Access Journals (Sweden)

Askowski Rafał

2015-06-01

Full Text Available The paper presents an analysis of relations describing entropy generation in a condenser of a steam unit. Connections between entropy generation, condenser ratio, and heat exchanger effectiveness, as well as relations implied by them are shown. Theoretical considerations allowed to determine limits of individual parameters which describe the condenser operation. Various relations for average temperature of the cold fluid were compared. All the proposed relations were verified against data obtained using a simulator and actual measurement data from a 200 MW unit condenser. Based on data from a simulator it was examined how the sum of entropy rates, steam condenser effectiveness, terminal temperature difference and condenser ratio vary with the change in the inlet cooling water temperature, mass flow rate of steam and the cooling water mass flow rate.

Entropy and Entropy Production: Old Misconceptions and New Breakthroughs

Directory of Open Access Journals (Sweden)

Leonid M. Martyushev

2013-03-01

Full Text Available Persistent misconceptions existing for dozens of years and influencing progress in various fields of science are sometimes encountered in the scientific and especially, the popular-science literature. The present brief review deals with two such interrelated misconceptions (misunderstandings. The first misunderstanding: entropy is a measure of disorder. This is an old and very common opinion. The second misconception is that the entropy production minimizes in the evolution of nonequilibrium systems. However, as it has recently become clear, evolution (progress in Nature demonstrates the opposite, i.e., maximization of the entropy production. The principal questions connected with this maximization are considered herein. The two misconceptions mentioned above can lead to the apparent contradiction between the conclusions of modern thermodynamics and the basic conceptions of evolution existing in biology. In this regard, the analysis of these issues seems extremely important and timely as it contributes to the deeper understanding of the laws of development of the surrounding World and the place of humans in it.

Receiver function estimated by maximum entropy deconvolution

Institute of Scientific and Technical Information of China (English)

吴庆举; 田小波; 张乃铃; 李卫平; 曾融生

2003-01-01

Maximum entropy deconvolution is presented to estimate receiver function, with the maximum entropy as the rule to determine auto-correlation and cross-correlation functions. The Toeplitz equation and Levinson algorithm are used to calculate the iterative formula of error-predicting filter, and receiver function is then estimated. During extrapolation, reflective coefficient is always less than 1, which keeps maximum entropy deconvolution stable. The maximum entropy of the data outside window increases the resolution of receiver function. Both synthetic and real seismograms show that maximum entropy deconvolution is an effective method to measure receiver function in time-domain.

Multivariate refined composite multiscale entropy analysis

International Nuclear Information System (INIS)

Humeau-Heurtier, Anne

2016-01-01

Multiscale entropy (MSE) has become a prevailing method to quantify signals complexity. MSE relies on sample entropy. However, MSE may yield imprecise complexity estimation at large scales, because sample entropy does not give precise estimation of entropy when short signals are processed. A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. Nevertheless, RCMSE is for univariate signals only. The simultaneous analysis of multi-channel (multivariate) data often over-performs studies based on univariate signals. We therefore introduce an extension of RCMSE to multivariate data. Applications of multivariate RCMSE to simulated processes reveal its better performances over the standard multivariate MSE. - Highlights: • Multiscale entropy quantifies data complexity but may be inaccurate at large scale. • A refined composite multiscale entropy (RCMSE) has therefore recently been proposed. • Nevertheless, RCMSE is adapted to univariate time series only. • We herein introduce an extension of RCMSE to multivariate data. • It shows better performances than the standard multivariate multiscale entropy.

Activity-Based Approach for Teaching Aqueous Solubility, Energy, and Entropy

Science.gov (United States)

Eisen, Laura; Marano, Nadia; Glazier, Samantha

2014-01-01

We describe an activity-based approach for teaching aqueous solubility to introductory chemistry students that provides a more balanced presentation of the roles of energy and entropy in dissolution than is found in most general chemistry textbooks. In the first few activities, students observe that polar substances dissolve in water, whereas…

The vibrational and configurational entropy of α-brass

International Nuclear Information System (INIS)

Benisek, Artur; Dachs, Edgar; Salihović, Miralem; Paunovic, Aleksandar; Maier, Maria E.

2014-01-01

Highlights: • The heat capacity of two α-brass samples was measured from T = 5 K to 300 K. • Above T = 300 K, the ordering/disordering processes were investigated calorimetrically. • The vibrational and configurational entropies of α-brass were calculated. • A volume vs. bulk modulus approach describing the excess entropy was tested. -- Abstract: The heat capacities of two samples of a fcc Cu–Zn alloy with the composition CuZn15 and CuZn34 were measured from T = 5 K to 573 K using relaxation and differential scanning calorimetry. Below ∼90 K, they are characterised by negative excess heat capacities deviating from ideal mixing by up to −0.20 and −0.44 J · mol −1 · K −1 for CuZn15 and CuZn34, respectively. The excess heat capacities produce excess vibrational entropies, which are less negative compared to the excess entropy available from the literature. Since the literature entropy data contain both, the configurational and the vibrational part of the entropy, the difference is attributed to the excess configurational entropy. The thermodynamics of different short-range ordered samples was also investigated. The extent of the short-range order had no influence on the heat capacity below T = 300 K. Above T = 300 K, where the ordering changed during the measurement, the heat capacity depended strongly on the thermal history of the samples. From these data, the heat and entropy of ordering was calculated. The results on the vibrational entropy of this study were also used to test a relationship for estimating the excess vibrational entropy of mixing

Gibbs Measures Over Locally Tree-Like Graphs and Percolative Entropy Over Infinite Regular Trees

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Austin, Tim; Podder, Moumanti

2018-03-01

Consider a statistical physical model on the d-regular infinite tree Td described by a set of interactions Φ . Let Gn be a sequence of finite graphs with vertex sets V_n that locally converge to Td. From Φ one can construct a sequence of corresponding models on the graphs G_n. Let μ_n be the resulting Gibbs measures. Here we assume that μ n converges to some limiting Gibbs measure μ on Td in the local weak^* sense, and study the consequences of this convergence for the specific entropies |V_n|^{-1}H(μ _n). We show that the limit supremum of |V_n|^{-1}H(μ _n) is bounded above by the percolative entropy H_{it{perc}}(μ ), a function of μ itself, and that |V_n|^{-1}H(μ _n) actually converges to H_{it{perc}}(μ ) in case Φ exhibits strong spatial mixing on T_d. When it is known to exist, the limit of |V_n|^{-1}H(μ _n) is most commonly shown to be given by the Bethe ansatz. Percolative entropy gives a different formula, and we do not know how to connect it to the Bethe ansatz directly. We discuss a few examples of well-known models for which the latter result holds in the high temperature regime.

Entropy correlation distance method. The Euro introduction effect on the Consumer Price Index

Science.gov (United States)

Miśkiewicz, Janusz

2010-04-01

The idea of entropy was introduced in thermodynamics, but it can be used in time series analysis. There are various ways to define and measure the entropy of a system. Here the so called Theil index, which is often used in economy and finance, is applied as it were an entropy measure. In this study the time series are remapped through the Theil index. Then the linear correlation coefficient between the remapped time series is evaluated as a function of time and time window size and the corresponding statistical distance is defined. The results are compared with the the usual correlation distance measure for the time series themselves. As an example this entropy correlation distance method (ECDM) is applied to several series, as those of the Consumer Price Index (CPI) in order to test some so called globalisation processes. Distance matrices are calculated in order to construct two network structures which are next analysed. The role of two different time scales introduced by the Theil index and a correlation coefficient is also discussed. The evolution of the mean distance between the most developed countries is presented and the globalisation periods of the prices discussed. It is finally shown that the evolution of mean distance between the most developed countries on several networks follows the process of introducing the European currency - the Euro. It is contrasted to the GDP based analysis. It is stressed that the entropy correlation distance measure is more suitable in detecting significant changes, like a globalisation process than the usual statistical (correlation based) measure.

Time Dependence of Entropy Flux and Entropy Production of a Dissipative Dynamical System Driven by Non-Gaussian Noise

International Nuclear Information System (INIS)

Guo Yongfeng; Xu Wei; Li Dongxi; Xie Wenxian

2008-01-01

A stochastic dissipative dynamical system driven by non-Gaussian noise is investigated. A general approximate Fokker-Planck equation of the system is derived through a path-integral approach. Based on the definition of Shannon's information entropy, the exact time dependence of entropy flux and entropy production of the system is calculated both in the absence and in the presence of non-equilibrium constraint. The present calculation can be used to interpret the interplay of the dissipative constant and non-Gaussian noise on the entropy flux and entropy production

Interim heterogeneity changes measured using entropy texture features on T2-weighted MRI at 3.0 T are associated with pathological response to neoadjuvant chemotherapy in primary breast cancer

Energy Technology Data Exchange (ETDEWEB)

Henderson, Shelley; Lerski, Richard [Ninewells Hospital and Medical School, Department of Medical Physics, Dundee (United Kingdom); Purdie, Colin [Ninewells Hospital and Medical School, Department of Pathology, Dundee (United Kingdom); Michie, Caroline [Ninewells Hospital and Medical School, Department of Oncology, Dundee (United Kingdom); Evans, Andrew; Vinnicombe, Sarah [University of Dundee, Division of Imaging and Technology, Ninewells Hospital and Medical School, Dundee (United Kingdom); Johnston, Marilyn [Ninewells Hospital and Medical School, Department of Clinical Radiology, Dundee (United Kingdom); Thompson, Alastair M. [University of Texas MD Anderson Cancer Centre, Department of Breast Surgical Oncology, Houston, TX (United States)

2017-11-15

To investigate whether interim changes in hetereogeneity (measured using entropy features) on MRI were associated with pathological residual cancer burden (RCB) at final surgery in patients receiving neoadjuvant chemotherapy (NAC) for primary breast cancer. This was a retrospective study of 88 consenting women (age: 30-79 years). Scanning was performed on a 3.0 T MRI scanner prior to NAC (baseline) and after 2-3 cycles of treatment (interim). Entropy was derived from the grey-level co-occurrence matrix, on slice-matched baseline/interim T2-weighted images. Response, assessed using RCB score on surgically resected specimens, was compared statistically with entropy/heterogeneity changes and ROC analysis performed. Association of pCR within each tumour immunophenotype was evaluated. Mean entropy percent differences between examinations, by response category, were: pCR: 32.8%, RCB-I: 10.5%, RCB-II: 9.7% and RCB-III: 3.0%. Association of ultimate pCR with coarse entropy changes between baseline/interim MRI across all lesions yielded 85.2% accuracy (area under ROC curve: 0.845). Excellent sensitivity/specificity was obtained for pCR prediction within each immunophenotype: ER+: 100%/100%; HER2+: 83.3%/95.7%, TNBC: 87.5%/80.0%. Lesion T2 heterogeneity changes are associated with response to NAC using RCB scores, particularly for pCR, and can be useful across all immunophenotypes with good diagnostic accuracy. (orig.)

Calculation of Configurational Entropy in Complex Landscapes

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Samuel A Cushman

2018-04-01

configurational entropy of a landscape is highly related to the dimensionality of the landscape, the number of cover classes, the evenness of landscape composition across classes, and landscape heterogeneity. These advances provide a means for researchers to directly estimate the frequency distribution of all possible macrostates of any observed landscape, and then directly calculate the relative configurational entropy of the observed macrostate, and to understand the ecological meaning of different amounts of configurational entropy. These advances enable scientists to take configurational entropy from a concept to an applied tool to measure and compare the disorder of real landscapes with an objective and unbiased measure based on entropy and the second law.

Application of the entropy generation minimization method to a solar heat exchanger: A pseudo-optimization design process based on the analysis of the local entropy generation maps

International Nuclear Information System (INIS)

Giangaspero, Giorgio; Sciubba, Enrico

2013-01-01

This paper presents an application of the entropy generation minimization method to the pseudo-optimization of the configuration of the heat exchange surfaces in a Solar Rooftile. An initial “standard” commercial configuration is gradually improved by introducing design changes aimed at the reduction of the thermodynamic losses due to heat transfer and fluid friction. Different geometries (pins, fins and others) are analysed with a commercial CFD (Computational Fluid Dynamics) code that also computes the local entropy generation rate. The design improvement process is carried out on the basis of a careful analysis of the local entropy generation maps and the rationale behind each step of the process is discussed in this perspective. The results are compared with other entropy generation minimization techniques available in the recent technical literature. It is found that the geometry with pin-fins has the best performance among the tested ones, and that the optimal pin array shape parameters (pitch and span) can be determined by a critical analysis of the integrated and local entropy maps and of the temperature contours. - Highlights: ► An entropy generation minimization method is applied to a solar heat exchanger. ► The approach is heuristic and leads to a pseudo-optimization process with CFD as main tool. ► The process is based on the evaluation of the local entropy generation maps. ► The geometry with pin-fins in general outperforms all other configurations. ► The entropy maps and temperature contours can be used to determine the optimal pin array design parameters

Entropy Analysis of RR and QT Interval Variability during Orthostatic and Mental Stress in Healthy Subjects

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Mathias Baumert

2014-12-01

Full Text Available Autonomic activity affects beat-to-beat variability of heart rate and QT interval. The aim of this study was to explore whether entropy measures are suitable to detect changes in neural outflow to the heart elicited by two different stress paradigms. We recorded short-term ECG in 11 normal subjects during an experimental protocol that involved head-up tilt and mental arithmetic stress and computed sample entropy, cross-sample entropy and causal interactions based on conditional entropy from RR and QT interval time series. Head-up tilt resulted in a significant reduction in sample entropy of RR intervals and cross-sample entropy, while mental arithmetic stress resulted in a significant reduction in coupling directed from RR to QT. In conclusion, measures of entropy are suitable to detect changes in neural outflow to the heart and decoupling of repolarisation variability from heart rate variability elicited by orthostatic or mental arithmetic stress.

Determination of Sample Entropy and Fuzzy Measure Entropy Parameters for Distinguishing Congestive Heart Failure from Normal Sinus Rhythm Subjects

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Lina Zhao

2015-09-01

Full Text Available Entropy provides a valuable tool for quantifying the regularity of physiological time series and provides important insights for understanding the underlying mechanisms of the cardiovascular system. Before any entropy calculation, certain common parameters need to be initialized: embedding dimension m, tolerance threshold r and time series length N. However, no specific guideline exists on how to determine the appropriate parameter values for distinguishing congestive heart failure (CHF from normal sinus rhythm (NSR subjects in clinical application. In the present study, a thorough analysis on the selection of appropriate values of m, r and N for sample entropy (SampEn and recently proposed fuzzy measure entropy (FuzzyMEn is presented for distinguishing two group subjects. 44 long-term NRS and 29 long-term CHF RR interval recordings from http://www.physionet.org were used as the non-pathological and pathological data respectively. Extreme (>2 s and abnormal heartbeat RR intervals were firstly removed from each RR recording and then the recording was segmented with a non-overlapping segment length N of 300 and 1000, respectively. SampEn and FuzzyMEn were performed for each RR segment under different parameter combinations: m of 1, 2, 3 and 4, and r of 0.10, 0.15, 0.20 and 0.25 respectively. The statistical significance between NSR and CHF groups under each combination of m, r and N was observed. The results demonstrated that the selection of m, r and N plays a critical role in determining the SampEn and FuzzyMEn outputs. Compared with SampEn, FuzzyMEn shows a better regularity when selecting the parameters m and r. In addition, FuzzyMEn shows a better relative consistency for distinguishing the two groups, that is, the results of FuzzyMEn in the NSR group were consistently lower than those in the CHF group while SampEn were not. The selections of m of 2 and 3 and r of 0.10 and 0.15 for SampEn and the selections of m of 1 and 2 whenever r (herein

Extended VIKOR Method for Intuitionistic Fuzzy Multiattribute Decision-Making Based on a New Distance Measure

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Xiao Luo

2017-01-01

Full Text Available An intuitionistic fuzzy VIKOR (IF-VIKOR method is proposed based on a new distance measure considering the waver of intuitionistic fuzzy information. The method aggregates all individual decision-makers’ assessment information based on intuitionistic fuzzy weighted averaging operator (IFWA, determines the weights of decision-makers and attributes objectively using intuitionistic fuzzy entropy, calculates the group utility and individual regret by the new distance measure, and then reaches a compromise solution. It can be effectively applied to multiattribute decision-making (MADM problems where the weights of decision-makers and attributes are completely unknown and the attribute values are intuitionistic fuzzy numbers (IFNs. The validity and stability of this method are verified by example analysis and sensitivity analysis, and its superiority is illustrated by the comparison with the existing method.

Residual and Past Entropy for Concomitants of Ordered Random Variables of Morgenstern Family

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M. M. Mohie EL-Din

2015-01-01

Full Text Available For a system, which is observed at time t, the residual and past entropies measure the uncertainty about the remaining and the past life of the distribution, respectively. In this paper, we have presented the residual and past entropy of Morgenstern family based on the concomitants of the different types of generalized order statistics (gos and give the linear transformation of such model. Characterization results for these dynamic entropies for concomitants of ordered random variables have been considered.

Sensitivity to mental effort and test-retest reliability of heart rate variability measures in healthy seniors.

Science.gov (United States)

Mukherjee, Shalini; Yadav, Rajeev; Yung, Iris; Zajdel, Daniel P; Oken, Barry S

2011-10-01

To determine (1) whether heart rate variability (HRV) was a sensitive and reliable measure in mental effort tasks carried out by healthy seniors and (2) whether non-linear approaches to HRV analysis, in addition to traditional time and frequency domain approaches were useful to study such effects. Forty healthy seniors performed two visual working memory tasks requiring different levels of mental effort, while ECG was recorded. They underwent the same tasks and recordings 2 weeks later. Traditional and 13 non-linear indices of HRV including Poincaré, entropy and detrended fluctuation analysis (DFA) were determined. Time domain, especially mean R-R interval (RRI), frequency domain and, among non-linear parameters - Poincaré and DFA were the most reliable indices. Mean RRI, time domain and Poincaré were also the most sensitive to different mental effort task loads and had the largest effect size. Overall, linear measures were the most sensitive and reliable indices to mental effort. In non-linear measures, Poincaré was the most reliable and sensitive, suggesting possible usefulness as an independent marker in cognitive function tasks in healthy seniors. A large number of HRV parameters was both reliable as well as sensitive indices of mental effort, although the simple linear methods were the most sensitive. Copyright © 2011 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Parametric optimization of CNC end milling using entropy ...

African Journals Online (AJOL)

Parametric optimization of CNC end milling using entropy measurement technique combined with grey-Taguchi method. ... International Journal of Engineering, Science and Technology ... Keywords: CNC end milling, surface finish, material removal rate (MRR), entropy measurement technique, Taguchi method ...

ENTROPY FUNCTIONAL FOR CONTINUOUS SYSTEMS OF FINITE ENTROPY

Institute of Scientific and Technical Information of China (English)

M. Rahimi A. Riazi

2012-01-01

In this article,we introduce the concept of entropy functional for continuous systems on compact metric spaces,and prove some of its properties.We also extract the Kolmogorov entropy from the entropy functional.

Entropy and Information Approaches to Genetic Diversity and its Expression: Genomic Geography

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William B. Sherwin

2010-07-01

Full Text Available This article highlights advantages of entropy-based genetic diversity measures, at levels from gene expression to landscapes. Shannon’s entropy-based diversity is the standard for ecological communities. The exponentials of Shannon’s and the related “mutual information” excel in their ability to express diversity intuitively, and provide a generalised method of considering microscopic behaviour to make macroscopic predictions, under given conditions. The hierarchical nature of entropy and information allows integrated modeling of diversity along one DNA sequence, and between different sequences within and among populations, species, etc. The aim is to identify the formal connections between genetic diversity and the flow of information to and from the environment.

COLLAGE-BASED INVERSE PROBLEMS FOR IFSM WITH ENTROPY MAXIMIZATION AND SPARSITY CONSTRAINTS

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Herb Kunze

2013-11-01

Full Text Available We consider the inverse problem associated with IFSM: Given a target function f, find an IFSM, such that its invariant fixed point f is sufficiently close to f in the Lp distance. In this paper, we extend the collage-based method developed by Forte and Vrscay (1995 along two different directions. We first search for a set of mappings that not only minimizes the collage error but also maximizes the entropy of the dynamical system. We then include an extra term in the minimization process which takes into account the sparsity of the set of mappings. In this new formulation, the minimization of collage error is treated as multi-criteria problem: we consider three different and conflicting criteria i.e., collage error, entropy and sparsity. To solve this multi-criteria program we proceed by scalarization and we reduce the model to a single-criterion program by combining all objective functions with different trade-off weights. The results of some numerical computations are presented. Numerical studies indicate that a maximum entropy principle exists for this approximation problem, i.e., that the suboptimal solutions produced by collage coding can be improved at least slightly by adding a maximum entropy criterion.

Rapid estimation of fatigue entropy and toughness in metals

Energy Technology Data Exchange (ETDEWEB)

Liakat, M.; Khonsari, M.M., E-mail: khonsari@me.lsu.edu

2014-10-15

Highlights: • A correlation is developed to predict fatigue entropy and toughness of metals. • Predictions are made based on the thermal response of the materials. • The trend of hysteresis energy and temperature evolutions is discussed. • Predicted results are found to be in good agreement to those measured. - Abstract: An analytical model and an experimental procedure are presented for estimating the rate and accumulation of thermodynamic entropy and fatigue toughness in metals subjected to cyclic uniaxial tension–compression tests. Entropy and plastic strain energy generations are predicted based on the thermal response of a specimen at different levels of material damage. Fatigue tests are performed with cylindrical dogbone specimens made of tubular low-carbon steel 1018 and solid medium-carbon steel 1045, API 5L X52, and Al 6061. The evolution of the plastic strain energy generation, temperature, and thermal response throughout a fatigue process are presented and discussed. Predicted entropy accumulation and fatigue toughness obtained from the proposed method are found to be in good agreement to those obtained using a load cell and an extensometer over the range of experimental and environmental conditions considered.

Rapid estimation of fatigue entropy and toughness in metals

International Nuclear Information System (INIS)

Liakat, M.; Khonsari, M.M.

2014-01-01

Highlights: • A correlation is developed to predict fatigue entropy and toughness of metals. • Predictions are made based on the thermal response of the materials. • The trend of hysteresis energy and temperature evolutions is discussed. • Predicted results are found to be in good agreement to those measured. - Abstract: An analytical model and an experimental procedure are presented for estimating the rate and accumulation of thermodynamic entropy and fatigue toughness in metals subjected to cyclic uniaxial tension–compression tests. Entropy and plastic strain energy generations are predicted based on the thermal response of a specimen at different levels of material damage. Fatigue tests are performed with cylindrical dogbone specimens made of tubular low-carbon steel 1018 and solid medium-carbon steel 1045, API 5L X52, and Al 6061. The evolution of the plastic strain energy generation, temperature, and thermal response throughout a fatigue process are presented and discussed. Predicted entropy accumulation and fatigue toughness obtained from the proposed method are found to be in good agreement to those obtained using a load cell and an extensometer over the range of experimental and environmental conditions considered

Entropy type complexity of quantum processes

International Nuclear Information System (INIS)

Watanabe, Noboru

2014-01-01

von Neumann entropy represents the amount of information in the quantum state, and this was extended by Ohya for general quantum systems [10]. Umegaki first defined the quantum relative entropy for σ-finite von Neumann algebras, which was extended by Araki, and Uhlmann, for general von Neumann algebras and *-algebras, respectively. In 1983 Ohya introduced the quantum mutual entropy by using compound states; this describes the amount of information correctly transmitted through the quantum channel, which was also extended by Ohya for general quantum systems. In this paper, we briefly explain Ohya's S-mixing entropy and the quantum mutual entropy for general quantum systems. By using structure equivalent class, we will introduce entropy type functionals based on quantum information theory to improve treatment for the Gaussian communication process. (paper)

HIV-1 envelope sequence-based diversity measures for identifying recent infections.

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Alexis Kafando

Full Text Available Identifying recent HIV-1 infections is crucial for monitoring HIV-1 incidence and optimizing public health prevention efforts. To identify recent HIV-1 infections, we evaluated and compared the performance of 4 sequence-based diversity measures including percent diversity, percent complexity, Shannon entropy and number of haplotypes targeting 13 genetic segments within the env gene of HIV-1. A total of 597 diagnostic samples obtained in 2013 and 2015 from recently and chronically HIV-1 infected individuals were selected. From the selected samples, 249 (134 from recent versus 115 from chronic infections env coding regions, including V1-C5 of gp120 and the gp41 ectodomain of HIV-1, were successfully amplified and sequenced by next generation sequencing (NGS using the Illumina MiSeq platform. The ability of the four sequence-based diversity measures to correctly identify recent HIV infections was evaluated using the frequency distribution curves, median and interquartile range and area under the curve (AUC of the receiver operating characteristic (ROC. Comparing the median and interquartile range and evaluating the frequency distribution curves associated with the 4 sequence-based diversity measures, we observed that the percent diversity, number of haplotypes and Shannon entropy demonstrated significant potential to discriminate recent from chronic infections (p<0.0001. Using the AUC of ROC analysis, only the Shannon entropy measure within three HIV-1 env segments could accurately identify recent infections at a satisfactory level. The env segments were gp120 C2_1 (AUC = 0.806, gp120 C2_3 (AUC = 0.805 and gp120 V3 (AUC = 0.812. Our results clearly indicate that the Shannon entropy measure represents a useful tool for predicting HIV-1 infection recency.

Topological nearly entropy

Science.gov (United States)

Gulamsarwar, Syazwani; Salleh, Zabidin

2017-08-01

The purpose of this paper is to generalize the notions of Adler's topological entropy along with their several fundamental properties. A function f : X → Y is said to be R-map if f-1 (V) is regular open in X for every regular open set V in Y. Thus, we initiated a notion of topological nearly entropy for topological R-dynamical systems which is based on nearly compact relative to the space by using R-map.

Feasible Histories, Maximum Entropy

International Nuclear Information System (INIS)

Pitowsky, I.

1999-01-01

We consider the broadest possible consistency condition for a family of histories, which extends all previous proposals. A family that satisfies this condition is called feasible. On each feasible family of histories we choose a probability measure by maximizing entropy, while keeping the probabilities of commuting histories to their quantum mechanical values. This procedure is justified by the assumption that decoherence increases entropy. Finally, a criterion for identifying the nearly classical families is proposed

A numerically research on energy loss evaluation in a centrifugal pump system based on local entropy production method

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Hou Hucan

2017-01-01

Full Text Available Inspired by wide application of the second law of thermodynamics to flow and heat transfer devices, local entropy production analysis method was creatively introduced into energy assessment system of centrifugal water pump. Based on Reynolds stress turbulent model and energy equation model, the steady numerical simulation of the whole flow passage of one IS centrifugal pump was carried out. The local entropy production terms were calculated by user defined functions, mainly including wall entropy production, turbulent entropy production, and viscous entropy production. The numerical results indicated that the irreversible energy loss calculated by the local entropy production method agreed well with that calculated by the traditional method but with some deviations which were probably caused by high rotatability and high curvature of impeller and volute. The wall entropy production and turbulent entropy production took up large part of the whole entropy production about 48.61% and 47.91%, respectively, which indicated that wall friction and turbulent fluctuation were the major factors in affecting irreversible energy loss. Meanwhile, the entropy production rate distribution was discussed and compared with turbulent kinetic energy dissipation rate distribution, it showed that turbulent entropy production rate increased sharply at the near wall regions and both distributed more uniformly. The blade region in leading edge near suction side, trailing edge and volute tongue were the main regions to generate irreversible exergy loss. This research broadens a completely new view in evaluating energy loss and further optimizes pump using entropy production minimization.

Entanglement entropy and differential entropy for massive flavors

International Nuclear Information System (INIS)

Jones, Peter A.R.; Taylor, Marika

2015-01-01

In this paper we compute the holographic entanglement entropy for massive flavors in the D3-D7 system, for arbitrary mass and various entangling region geometries. We show that the universal terms in the entanglement entropy exactly match those computed in the dual theory using conformal perturbation theory. We derive holographically the universal terms in the entanglement entropy for a CFT perturbed by a relevant operator, up to second order in the coupling; our results are valid for any entangling region geometry. We present a new method for computing the entanglement entropy of any top-down brane probe system using Kaluza-Klein holography and illustrate our results with massive flavors at finite density. Finally we discuss the differential entropy for brane probe systems, emphasising that the differential entropy captures only the effective lower-dimensional Einstein metric rather than the ten-dimensional geometry.

Time dependence of entropy flux and entropy production for a dynamical system driven by noises with coloured cross-correlation

Institute of Scientific and Technical Information of China (English)

Xie Wen-Xian; Xu Wei; Cai Li

2007-01-01

This paper shows the Fokker-Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker-Planck equation and the definition of Shannon's information entropy, the time dependence of entropy flux and entropy production can be calculated. The present results can be used to explain the extremal behaviour of time dependence of entropy flux and entropy production in view of the dissipative parameter γ of the system, coloured cross-correlation time τ and coloured cross-correlation strength λ.

Chatter detection in milling process based on VMD and energy entropy

Science.gov (United States)

Liu, Changfu; Zhu, Lida; Ni, Chenbing

2018-05-01

This paper presents a novel approach to detect the milling chatter based on Variational Mode Decomposition (VMD) and energy entropy. VMD has already been employed in feature extraction from non-stationary signals. The parameters like number of modes (K) and the quadratic penalty (α) need to be selected empirically when raw signal is decomposed by VMD. Aimed at solving the problem how to select K and α, the automatic selection method of VMD's based on kurtosis is proposed in this paper. When chatter occurs in the milling process, energy will be absorbed to chatter frequency bands. To detect the chatter frequency bands automatically, the chatter detection method based on energy entropy is presented. The vibration signal containing chatter frequency is simulated and three groups of experiments which represent three cutting conditions are conducted. To verify the effectiveness of method presented by this paper, chatter feather extraction has been successfully employed on simulation signals and experimental signals. The simulation and experimental results show that the proposed method can effectively detect the chatter.

Epileptic seizure detection using DWT-based approximate entropy, Shannon entropy and support vector machine: a case study.

Science.gov (United States)

Sharmila, A; Aman Raj, Suman; Shashank, Pandey; Mahalakshmi, P

2018-01-01

In this work, we have used a time-frequency domain analysis method called discrete wavelet transform (DWT) technique. This method stand out compared to other proposed methods because of its algorithmic elegance and accuracy. A wavelet is a mathematical function based on time-frequency analysis in signal processing. It is useful particularly because it allows a weak signal to be recovered from a noisy signal without much distortion. A wavelet analysis works by analysing the image and converting it to mathematical function which is decoded by the receiver. Furthermore, we have used Shannon entropy and approximate entropy (ApEn) for extracting the complexities associated with electroencephalographic (EEG) signals. The ApEn is a suitable feature to characterise the EEGs because its value drops suddenly due to excessive synchronous discharge of neurons in the brain during epileptic activity in this study. EEG signals are decomposed into six EEG sub-bands namely D1-D5 and A5 using DWT technique. Non-linear features such as ApEn and Shannon entropy are calculated from these sub-bands and support vector machine classifiers are used for classification purpose. This scheme is tested using EEG data recorded from five healthy subjects and five epileptic patients during the inter-ictal and ictal periods. The data are acquired from University of Bonn, Germany. The proposed method is evaluated through 15 classification problems, and obtained high classification accuracy of 100% for two cases and it indicates the good classifying performance of the proposed method.

Entropy and Compression Capture Different Complexity Features: The Case of Fetal Heart Rate

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João Monteiro-Santos

2017-12-01

Full Text Available Entropy and compression have been used to distinguish fetuses at risk of hypoxia from their healthy counterparts through the analysis of Fetal Heart Rate (FHR. Low correlation that was observed between these two approaches suggests that they capture different complexity features. This study aims at characterizing the complexity of FHR features captured by entropy and compression, using as reference international guidelines. Single and multi-scale approaches were considered in the computation of entropy and compression. The following physiologic-based features were considered: FHR baseline; percentage of abnormal long (%abLTV and short (%abSTV term variability; average short term variability; and, number of acceleration and decelerations. All of the features were computed on a set of 68 intrapartum FHR tracings, divided as normal, mildly, and moderately-severely acidemic born fetuses. The correlation between entropy/compression features and the physiologic-based features was assessed. There were correlations between compressions and accelerations and decelerations, but neither accelerations nor decelerations were significantly correlated with entropies. The %abSTV was significantly correlated with entropies (ranging between −0.54 and −0.62, and to a higher extent with compression (ranging between −0.80 and −0.94. Distinction between groups was clearer in the lower scales using entropy and in the higher scales using compression. Entropy and compression are complementary complexity measures.

Symplectic entropy

International Nuclear Information System (INIS)

De Nicola, Sergio; Fedele, Renato; Man'ko, Margarita A; Man'ko, Vladimir I

2007-01-01

The tomographic-probability description of quantum states is reviewed. The symplectic tomography of quantum states with continuous variables is studied. The symplectic entropy of the states with continuous variables is discussed and its relation to Shannon entropy and information is elucidated. The known entropic uncertainty relations of the probability distribution in position and momentum of a particle are extended and new uncertainty relations for symplectic entropy are obtained. The partial case of symplectic entropy, which is optical entropy of quantum states, is considered. The entropy associated to optical tomogram is shown to satisfy the new entropic uncertainty relation. The example of Gaussian states of harmonic oscillator is studied and the entropic uncertainty relations for optical tomograms of the Gaussian state are shown to minimize the uncertainty relation

Scaling-Laws of Flow Entropy with Topological Metrics of Water Distribution Networks

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Giovanni Francesco Santonastaso

2018-01-01

Full Text Available Robustness of water distribution networks is related to their connectivity and topological structure, which also affect their reliability. Flow entropy, based on Shannon’s informational entropy, has been proposed as a measure of network redundancy and adopted as a proxy of reliability in optimal network design procedures. In this paper, the scaling properties of flow entropy of water distribution networks with their size and other topological metrics are studied. To such aim, flow entropy, maximum flow entropy, link density and average path length have been evaluated for a set of 22 networks, both real and synthetic, with different size and topology. The obtained results led to identify suitable scaling laws of flow entropy and maximum flow entropy with water distribution network size, in the form of power–laws. The obtained relationships allow comparing the flow entropy of water distribution networks with different size, and provide an easy tool to define the maximum achievable entropy of a specific water distribution network. An example of application of the obtained relationships to the design of a water distribution network is provided, showing how, with a constrained multi-objective optimization procedure, a tradeoff between network cost and robustness is easily identified.

Time-dependent entropy evolution in microscopic and macroscopic electromagnetic relaxation

International Nuclear Information System (INIS)

Baker-Jarvis, James

2005-01-01

This paper is a study of entropy and its evolution in the time and frequency domains upon application of electromagnetic fields to materials. An understanding of entropy and its evolution in electromagnetic interactions bridges the boundaries between electromagnetism and thermodynamics. The approach used here is a Liouville-based statistical-mechanical theory. I show that the microscopic entropy is reversible and the macroscopic entropy satisfies an H theorem. The spectral entropy development can be very useful for studying the frequency response of materials. Using a projection-operator based nonequilibrium entropy, different equations are derived for the entropy and entropy production and are applied to the polarization, magnetization, and macroscopic fields. I begin by proving an exact H theorem for the entropy, progress to application of time-dependent entropy in electromagnetics, and then apply the theory to relevant applications in electromagnetics. The paper concludes with a discussion of the relationship of the frequency-domain form of the entropy to the permittivity, permeability, and impedance

Deconstructing Cross-Entropy for Probabilistic Binary Classifiers

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Daniel Ramos

2018-03-01

Full Text Available In this work, we analyze the cross-entropy function, widely used in classifiers both as a performance measure and as an optimization objective. We contextualize cross-entropy in the light of Bayesian decision theory, the formal probabilistic framework for making decisions, and we thoroughly analyze its motivation, meaning and interpretation from an information-theoretical point of view. In this sense, this article presents several contributions: First, we explicitly analyze the contribution to cross-entropy of (i prior knowledge; and (ii the value of the features in the form of a likelihood ratio. Second, we introduce a decomposition of cross-entropy into two components: discrimination and calibration. This decomposition enables the measurement of different performance aspects of a classifier in a more precise way; and justifies previously reported strategies to obtain reliable probabilities by means of the calibration of the output of a discriminating classifier. Third, we give different information-theoretical interpretations of cross-entropy, which can be useful in different application scenarios, and which are related to the concept of reference probabilities. Fourth, we present an analysis tool, the Empirical Cross-Entropy (ECE plot, a compact representation of cross-entropy and its aforementioned decomposition. We show the power of ECE plots, as compared to other classical performance representations, in two diverse experimental examples: a speaker verification system, and a forensic case where some glass findings are present.

Crane Safety Assessment Method Based on Entropy and Cumulative Prospect Theory

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Aihua Li

2017-01-01

Full Text Available Assessing the safety status of cranes is an important problem. To overcome the inaccuracies and misjudgments in such assessments, this work describes a safety assessment method for cranes that combines entropy and cumulative prospect theory. Firstly, the proposed method transforms the set of evaluation indices into an evaluation vector. Secondly, a decision matrix is then constructed from the evaluation vectors and evaluation standards, and an entropy-based technique is applied to calculate the index weights. Thirdly, positive and negative prospect value matrices are established from reference points based on the positive and negative ideal solutions. Thus, this enables the crane safety grade to be determined according to the ranked comprehensive prospect values. Finally, the safety status of four general overhead traveling crane samples is evaluated to verify the rationality and feasibility of the proposed method. The results demonstrate that the method described in this paper can precisely and reasonably reflect the safety status of a crane.

A Note on Burg’s Modified Entropy in Statistical Mechanics

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Amritansu Ray

2016-02-01

Full Text Available Burg’s entropy plays an important role in this age of information euphoria, particularly in understanding the emergent behavior of a complex system such as statistical mechanics. For discrete or continuous variable, maximization of Burg’s Entropy subject to its only natural and mean constraint always provide us a positive density function though the Entropy is always negative. On the other hand, Burg’s modified entropy is a better measure than the standard Burg’s entropy measure since this is always positive and there is no computational problem for small probabilistic values. Moreover, the maximum value of Burg’s modified entropy increases with the number of possible outcomes. In this paper, a premium has been put on the fact that if Burg’s modified entropy is used instead of conventional Burg’s entropy in a maximum entropy probability density (MEPD function, the result yields a better approximation of the probability distribution. An important lemma in basic algebra and a suitable example with tables and graphs in statistical mechanics have been given to illustrate the whole idea appropriately.

Controlling the Shannon Entropy of Quantum Systems

Science.gov (United States)

Xing, Yifan; Wu, Jun

2013-01-01

This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking. PMID:23818819

Controlling the Shannon Entropy of Quantum Systems

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Yifan Xing

2013-01-01

Full Text Available This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.

Entropy for Mechanically Vibrating Systems

Science.gov (United States)

Tufano, Dante

, which demonstrates the applicability of entropy-based approaches to real-world systems. Three systems are considered to demonstrate these findings: 1) a rod end-coupled to a simple oscillator, 2) two end-coupled rods, and 3) two end-coupled beams. The aforementioned work utilizes the weak coupling assumption to determine the entropy of composite systems. Following this discussion, a direct method of finding entropy is developed which does not rely on this limiting assumption. The resulting entropy provides a useful benchmark for evaluating the accuracy of the weak coupling approach, and is validated using systems of coupled oscillators. The later chapters of this work discuss Khinchin's entropy as applied to nonlinear and nonconservative systems, respectively. The discussion of entropy for nonlinear systems is motivated by the desire to expand the applicability of SEA techniques beyond the linear regime. The discussion of nonconservative systems is also crucial, since real-world systems interact with their environment, and it is necessary to confirm the validity of an entropy approach for systems that are relevant in the context of SEA. Having developed a mathematical framework for determining entropy under a number of previously unexplored cases, the relationship between thermodynamics and statistical vibroacoustics can be better understood. Specifically, vibroacoustic temperatures can be obtained for systems that are not necessarily linear or weakly coupled. In this way, entropy provides insight into how the power flow proportionality of statistical energy analysis (SEA) can be applied to a broader class of vibroacoustic systems. As such, entropy is a useful tool for both justifying and expanding the foundational results of SEA.

Entanglement entropy in top-down models

Energy Technology Data Exchange (ETDEWEB)

Jones, Peter A.R.; Taylor, Marika [Mathematical Sciences and STAG Research Centre, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom)

2016-08-26

We explore holographic entanglement entropy in ten-dimensional supergravity solutions. It has been proposed that entanglement entropy can be computed in such top-down models using minimal surfaces which asymptotically wrap the compact part of the geometry. We show explicitly in a wide range of examples that the holographic entanglement entropy thus computed agrees with the entanglement entropy computed using the Ryu-Takayanagi formula from the lower-dimensional Einstein metric obtained from reduction over the compact space. Our examples include not only consistent truncations but also cases in which no consistent truncation exists and Kaluza-Klein holography is used to identify the lower-dimensional Einstein metric. We then give a general proof, based on the Lewkowycz-Maldacena approach, of the top-down entanglement entropy formula.

Entanglement entropy in top-down models

International Nuclear Information System (INIS)

Jones, Peter A.R.; Taylor, Marika

2016-01-01

We explore holographic entanglement entropy in ten-dimensional supergravity solutions. It has been proposed that entanglement entropy can be computed in such top-down models using minimal surfaces which asymptotically wrap the compact part of the geometry. We show explicitly in a wide range of examples that the holographic entanglement entropy thus computed agrees with the entanglement entropy computed using the Ryu-Takayanagi formula from the lower-dimensional Einstein metric obtained from reduction over the compact space. Our examples include not only consistent truncations but also cases in which no consistent truncation exists and Kaluza-Klein holography is used to identify the lower-dimensional Einstein metric. We then give a general proof, based on the Lewkowycz-Maldacena approach, of the top-down entanglement entropy formula.

Chain rules for smooth min-and max-entropies

DEFF Research Database (Denmark)

Vitanov, Alexande; Dupont-Dupuis, Fréderic; Tomamichel, Marco

2013-01-01

The chain rule for the Shannon and von Neumann en- tropy, which relates the total entropy of a system to the entropies of its parts, is of central importance to information theory. Here, we consider the chain rule for the more general smooth min- and max-entropies, used in one-shot in formation...... theory. For these en- tropy measures, the chain rule no longer holds as an equality. How- ever, the standard chain rule for the von Neum ann entropy is re- trieved asymptotically when evaluating the smooth entropies for many identical and independently distributed states....

Hypoglycemia-Related Electroencephalogram Changes Assessed by Multiscale Entropy

DEFF Research Database (Denmark)

Fabris, C.; Sparacino, G.; Sejling, A. S.

2014-01-01

derivation in the two glycemic intervals was assessed using the multiscale entropy (MSE) approach, obtaining measures of sample entropy (SampEn) at various temporal scales. The comparison of how signal irregularity measured by SampEn varies as the temporal scale increases in the two glycemic states provides...

Amplitude-aware permutation entropy: Illustration in spike detection and signal segmentation.

Science.gov (United States)

Azami, Hamed; Escudero, Javier

2016-05-01

Signal segmentation and spike detection are two important biomedical signal processing applications. Often, non-stationary signals must be segmented into piece-wise stationary epochs or spikes need to be found among a background of noise before being further analyzed. Permutation entropy (PE) has been proposed to evaluate the irregularity of a time series. PE is conceptually simple, structurally robust to artifacts, and computationally fast. It has been extensively used in many applications, but it has two key shortcomings. First, when a signal is symbolized using the Bandt-Pompe procedure, only the order of the amplitude values is considered and information regarding the amplitudes is discarded. Second, in the PE, the effect of equal amplitude values in each embedded vector is not addressed. To address these issues, we propose a new entropy measure based on PE: the amplitude-aware permutation entropy (AAPE). AAPE is sensitive to the changes in the amplitude, in addition to the frequency, of the signals thanks to it being more flexible than the classical PE in the quantification of the signal motifs. To demonstrate how the AAPE method can enhance the quality of the signal segmentation and spike detection, a set of synthetic and realistic synthetic neuronal signals, electroencephalograms and neuronal data are processed. We compare the performance of AAPE in these problems against state-of-the-art approaches and evaluate the significance of the differences with a repeated ANOVA with post hoc Tukey's test. In signal segmentation, the accuracy of AAPE-based method is higher than conventional segmentation methods. AAPE also leads to more robust results in the presence of noise. The spike detection results show that AAPE can detect spikes well, even when presented with single-sample spikes, unlike PE. For multi-sample spikes, the changes in AAPE are larger than in PE. We introduce a new entropy metric, AAPE, that enables us to consider amplitude information in the

Problems in black-hole entropy interpretation

International Nuclear Information System (INIS)

Liberati, S.

1997-01-01

In this work some proposals for black-hole entropy interpretation are exposed and investigated. In particular, the author will firstly consider the so-called 'entanglement entropy' interpretation, in the framework of the brick wall model and the divergence problem arising in the one-loop calculations of various thermodynamical quantities, like entropy, internal energy and heat capacity. It is shown that the assumption of equality of entanglement entropy and Bekenstein-Hawking one appears to give inconsistent results. These will be a starting point for a different interpretation of black.hole entropy based on peculiar topological structures of manifolds with 'intrinsic' thermodynamical features. It is possible to show an exact relation between black-hole gravitational entropy and topology of these Euclidean space-times. the expression for the Euler characteristic, through the Gauss-Bonnet integral, and the one for entropy for gravitational instantons are proposed in a form which makes the relation between these self-evident. Using this relation he propose a generalization of the Bekenstein-Hawking entropy in which the former and Euler characteristic are related in the equation S = χA / 8. Finally, he try to expose some conclusions and hypotheses about possible further development of this research

An Integrated Dictionary-Learning Entropy-Based Medical Image Fusion Framework

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Guanqiu Qi

2017-10-01

Full Text Available Image fusion is widely used in different areas and can integrate complementary and relevant information of source images captured by multiple sensors into a unitary synthetic image. Medical image fusion, as an important image fusion application, can extract the details of multiple images from different imaging modalities and combine them into an image that contains complete and non-redundant information for increasing the accuracy of medical diagnosis and assessment. The quality of the fused image directly affects medical diagnosis and assessment. However, existing solutions have some drawbacks in contrast, sharpness, brightness, blur and details. This paper proposes an integrated dictionary-learning and entropy-based medical image-fusion framework that consists of three steps. First, the input image information is decomposed into low-frequency and high-frequency components by using a Gaussian filter. Second, low-frequency components are fused by weighted average algorithm and high-frequency components are fused by the dictionary-learning based algorithm. In the dictionary-learning process of high-frequency components, an entropy-based algorithm is used for informative blocks selection. Third, the fused low-frequency and high-frequency components are combined to obtain the final fusion results. The results and analyses of comparative experiments demonstrate that the proposed medical image fusion framework has better performance than existing solutions.

Wavelet entropy characterization of elevated intracranial pressure.

Science.gov (United States)

Xu, Peng; Scalzo, Fabien; Bergsneider, Marvin; Vespa, Paul; Chad, Miller; Hu, Xiao

2008-01-01

Intracranial Hypertension (ICH) often occurs for those patients with traumatic brain injury (TBI), stroke, tumor, etc. Pathology of ICH is still controversial. In this work, we used wavelet entropy and relative wavelet entropy to study the difference existed between normal and hypertension states of ICP for the first time. The wavelet entropy revealed the similar findings as the approximation entropy that entropy during ICH state is smaller than that in normal state. Moreover, with wavelet entropy, we can see that ICH state has the more focused energy in the low wavelet frequency band (0-3.1 Hz) than the normal state. The relative wavelet entropy shows that the energy distribution in the wavelet bands between these two states is actually different. Based on these results, we suggest that ICH may be formed by the re-allocation of oscillation energy within brain.

The effects of cardiorespiratory fitness and acute aerobic exercise on executive functioning and EEG entropy in adolescents

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Michael John Hogan

2015-10-01

Full Text Available The current study examined the effects of cardiorespiratory fitness, identified with a continuous graded cycle ergometry, and aerobic exercise on cognitive functioning and entropy of the electroencephalogram (EEG in 30 adolescents between the ages of 13 and 14 years. Higher and lower fit participants performed an executive function task after a bout of acute exercise and after rest while watching a film. EEG entropy, using the sample entropy measure, was repeatedly measured during the 1500ms post-stimulus interval to evaluate changes in entropy over time. Analysis of the behavioural data for lower and higher fit groups revealed an interaction between fitness levels and acute physical exercise. Notably, lower fit, but not higher fit, participants had higher error rates for NoGo relative to Go trials in the rest condition, whereas in the acute exercise condition there were no differences in error rates between groups; higher fit participants also had significantly faster reaction times in the exercise condition in comparison with the rest condition. Analysis of EEG data revealed that higher fit participants demonstrated lower entropy post-stimulus than lower fit participants in the left frontal hemisphere, possibly indicating increased efficiency of early stage stimulus processing and more efficient allocation of cognitive resources to the task demands. The results suggest that EEG entropy is sensitive to stimulus processing demands and varies as a function of physical fitness levels, but not acute exercise. Physical fitness, in turn, may enhance cognition in adolescence by facilitating higher functionality of the attentional system in the context of lower levels of frontal EEG entropy.

Analysis of complex time series using refined composite multiscale entropy

International Nuclear Information System (INIS)

Wu, Shuen-De; Wu, Chiu-Wen; Lin, Shiou-Gwo; Lee, Kung-Yen; Peng, Chung-Kang

2014-01-01

Multiscale entropy (MSE) is an effective algorithm for measuring the complexity of a time series that has been applied in many fields successfully. However, MSE may yield an inaccurate estimation of entropy or induce undefined entropy because the coarse-graining procedure reduces the length of a time series considerably at large scales. Composite multiscale entropy (CMSE) was recently proposed to improve the accuracy of MSE, but it does not resolve undefined entropy. Here we propose a refined composite multiscale entropy (RCMSE) to improve CMSE. For short time series analyses, we demonstrate that RCMSE increases the accuracy of entropy estimation and reduces the probability of inducing undefined entropy.

Intra-Tumour Signalling Entropy Determines Clinical Outcome in Breast and Lung Cancer

Science.gov (United States)

Banerji, Christopher R. S.; Severini, Simone; Caldas, Carlos; Teschendorff, Andrew E.

2015-01-01

The cancer stem cell hypothesis, that a small population of tumour cells are responsible for tumorigenesis and cancer progression, is becoming widely accepted and recent evidence has suggested a prognostic and predictive role for such cells. Intra-tumour heterogeneity, the diversity of the cancer cell population within the tumour of an individual patient, is related to cancer stem cells and is also considered a potential prognostic indicator in oncology. The measurement of cancer stem cell abundance and intra-tumour heterogeneity in a clinically relevant manner however, currently presents a challenge. Here we propose signalling entropy, a measure of signalling pathway promiscuity derived from a sample’s genome-wide gene expression profile, as an estimate of the stemness of a tumour sample. By considering over 500 mixtures of diverse cellular expression profiles, we reveal that signalling entropy also associates with intra-tumour heterogeneity. By analysing 3668 breast cancer and 1692 lung adenocarcinoma samples, we further demonstrate that signalling entropy correlates negatively with survival, outperforming leading clinical gene expression based prognostic tools. Signalling entropy is found to be a general prognostic measure, valid in different breast cancer clinical subgroups, as well as within stage I lung adenocarcinoma. We find that its prognostic power is driven by genes involved in cancer stem cells and treatment resistance. In summary, by approximating both stemness and intra-tumour heterogeneity, signalling entropy provides a powerful prognostic measure across different epithelial cancers. PMID:25793737

Intra-tumour signalling entropy determines clinical outcome in breast and lung cancer.

Directory of Open Access Journals (Sweden)

Christopher R S Banerji

2015-03-01

Full Text Available The cancer stem cell hypothesis, that a small population of tumour cells are responsible for tumorigenesis and cancer progression, is becoming widely accepted and recent evidence has suggested a prognostic and predictive role for such cells. Intra-tumour heterogeneity, the diversity of the cancer cell population within the tumour of an individual patient, is related to cancer stem cells and is also considered a potential prognostic indicator in oncology. The measurement of cancer stem cell abundance and intra-tumour heterogeneity in a clinically relevant manner however, currently presents a challenge. Here we propose signalling entropy, a measure of signalling pathway promiscuity derived from a sample's genome-wide gene expression profile, as an estimate of the stemness of a tumour sample. By considering over 500 mixtures of diverse cellular expression profiles, we reveal that signalling entropy also associates with intra-tumour heterogeneity. By analysing 3668 breast cancer and 1692 lung adenocarcinoma samples, we further demonstrate that signalling entropy correlates negatively with survival, outperforming leading clinical gene expression based prognostic tools. Signalling entropy is found to be a general prognostic measure, valid in different breast cancer clinical subgroups, as well as within stage I lung adenocarcinoma. We find that its prognostic power is driven by genes involved in cancer stem cells and treatment resistance. In summary, by approximating both stemness and intra-tumour heterogeneity, signalling entropy provides a powerful prognostic measure across different epithelial cancers.

Refined generalized multiscale entropy analysis for physiological signals

Science.gov (United States)

Liu, Yunxiao; Lin, Youfang; Wang, Jing; Shang, Pengjian

2018-01-01

Multiscale entropy analysis has become a prevalent complexity measurement and been successfully applied in various fields. However, it only takes into account the information of mean values (first moment) in coarse-graining procedure. Then generalized multiscale entropy (MSEn) considering higher moments to coarse-grain a time series was proposed and MSEσ2 has been implemented. However, the MSEσ2 sometimes may yield an imprecise estimation of entropy or undefined entropy, and reduce statistical reliability of sample entropy estimation as scale factor increases. For this purpose, we developed the refined model, RMSEσ2, to improve MSEσ2. Simulations on both white noise and 1 / f noise show that RMSEσ2 provides higher entropy reliability and reduces the occurrence of undefined entropy, especially suitable for short time series. Besides, we discuss the effect on RMSEσ2 analysis from outliers, data loss and other concepts in signal processing. We apply the proposed model to evaluate the complexity of heartbeat interval time series derived from healthy young and elderly subjects, patients with congestive heart failure and patients with atrial fibrillation respectively, compared to several popular complexity metrics. The results demonstrate that RMSEσ2 measured complexity (a) decreases with aging and diseases, and (b) gives significant discrimination between different physiological/pathological states, which may facilitate clinical application.

Rolling Bearing Fault Diagnosis Based on ELCD Permutation Entropy and RVM

Directory of Open Access Journals (Sweden)

Jiang Xingmeng

2016-01-01

Full Text Available Aiming at the nonstationary characteristic of a gear fault vibration signal, a recognition method based on permutation entropy of ensemble local characteristic-scale decomposition (ELCD and relevance vector machine (RVM is proposed. First, the vibration signal was decomposed by ELCD; then a series of intrinsic scale components (ISCs were obtained. Second, according to the kurtosis of ISCs, principal ISCs were selected and then the permutation entropy of principal ISCs was calculated and they were combined into a feature vector. Finally, the feature vectors were input in RVM classifier to train and test and identify the type of rolling bearing faults. Experimental results show that this method can effectively diagnose four kinds of working condition, and the effect is better than local characteristic-scale decomposition (LCD method.

Gradient Dynamics and Entropy Production Maximization

Science.gov (United States)

Janečka, Adam; Pavelka, Michal

2018-01-01

We compare two methods for modeling dissipative processes, namely gradient dynamics and entropy production maximization. Both methods require similar physical inputs-how energy (or entropy) is stored and how it is dissipated. Gradient dynamics describes irreversible evolution by means of dissipation potential and entropy, it automatically satisfies Onsager reciprocal relations as well as their nonlinear generalization (Maxwell-Onsager relations), and it has statistical interpretation. Entropy production maximization is based on knowledge of free energy (or another thermodynamic potential) and entropy production. It also leads to the linear Onsager reciprocal relations and it has proven successful in thermodynamics of complex materials. Both methods are thermodynamically sound as they ensure approach to equilibrium, and we compare them and discuss their advantages and shortcomings. In particular, conditions under which the two approaches coincide and are capable of providing the same constitutive relations are identified. Besides, a commonly used but not often mentioned step in the entropy production maximization is pinpointed and the condition of incompressibility is incorporated into gradient dynamics.

Zero-contingent entropy of quantum states of a Hydrogen atom

International Nuclear Information System (INIS)

Charvot, R.; Majernik, V.

1996-01-01

We calculated the zero-contingent entropy for the position of electron in H-atom as a function of its quantum numbers and compared it with the corresponding value of the Shannon entropy. The values of zero-contingent entropy of quantum states of H-atom correlate well with the corresponding values of Shannon's entropy. This points out that, besides the Shannon entropy, the zero-contingent entropy represents an appropriate, and mathematically rather simple, measure of the spreading out of the wave functions in H-atom. (authors)

Entropy and information

CERN Document Server

Volkenstein, Mikhail V

2009-01-01

The book "Entropy and Information" deals with the thermodynamical concept of entropy and its relationship to information theory. It is successful in explaining the universality of the term "Entropy" not only as a physical phenomenon, but reveals its existence also in other domains. E.g., Volkenstein discusses the "meaning" of entropy in a biological context and shows how entropy is related to artistic activities. Written by the renowned Russian bio-physicist Mikhail V. Volkenstein, this book on "Entropy and Information" surely serves as a timely introduction to understand entropy from a thermodynamic perspective and is definitely an inspiring and thought-provoking book that should be read by every physicist, information-theorist, biologist, and even artist.

Entropy generation of nanofluid flow in a microchannel heat sink

Science.gov (United States)

Manay, Eyuphan; Akyürek, Eda Feyza; Sahin, Bayram

2018-06-01

Present study aims to investigate the effects of the presence of nano sized TiO2 particles in the base fluid on entropy generation rate in a microchannel heat sink. Pure water was chosen as base fluid, and TiO2 particles were suspended into the pure water in five different particle volume fractions of 0.25%, 0.5%, 1.0%, 1.5% and 2.0%. Under laminar, steady state flow and constant heat flux boundary conditions, thermal, frictional, total entropy generation rates and entropy generation number ratios of nanofluids were experimentally analyzed in microchannel flow for different channel heights of 200 μm, 300 μm, 400 μm and 500 μm. It was observed that frictional and total entropy generation rates increased as thermal entropy generation rate were decreasing with an increase in particle volume fraction. In microchannel flows, thermal entropy generation could be neglected due to its too low rate smaller than 1.10e-07 in total entropy generation. Higher channel heights caused higher thermal entropy generation rates, and increasing channel height yielded an increase from 30% to 52% in thermal entropy generation. When channel height decreased, an increase of 66%-98% in frictional entropy generation was obtained. Adding TiO2 nanoparticles into the base fluid caused thermal entropy generation to decrease about 1.8%-32.4%, frictional entropy generation to increase about 3.3%-21.6%.

Parametric Bayesian Estimation of Differential Entropy and Relative Entropy

OpenAIRE

Gupta; Srivastava

2010-01-01

Given iid samples drawn from a distribution with known parametric form, we propose the minimization of expected Bregman divergence to form Bayesian estimates of differential entropy and relative entropy, and derive such estimators for the uniform, Gaussian, Wishart, and inverse Wishart distributions. Additionally, formulas are given for a log gamma Bregman divergence and the differential entropy and relative entropy for the Wishart and inverse Wishart. The results, as always with Bayesian est...

Using Real-time Event Tracking Sensitivity Analysis to Overcome Sensor Measurement Uncertainties of Geo-Information Management in Drilling Disasters

Science.gov (United States)

Tavakoli, S.; Poslad, S.; Fruhwirth, R.; Winter, M.

2012-04-01

This paper introduces an application of a novel EventTracker platform for instantaneous Sensitivity Analysis (SA) of large scale real-time geo-information. Earth disaster management systems demand high quality information to aid a quick and timely response to their evolving environments. The idea behind the proposed EventTracker platform is the assumption that modern information management systems are able to capture data in real-time and have the technological flexibility to adjust their services to work with specific sources of data/information. However, to assure this adaptation in real time, the online data should be collected, interpreted, and translated into corrective actions in a concise and timely manner. This can hardly be handled by existing sensitivity analysis methods because they rely on historical data and lazy processing algorithms. In event-driven systems, the effect of system inputs on its state is of value, as events could cause this state to change. This 'event triggering' situation underpins the logic of the proposed approach. Event tracking sensitivity analysis method describes the system variables and states as a collection of events. The higher the occurrence of an input variable during the trigger of event, the greater its potential impact will be on the final analysis of the system state. Experiments were designed to compare the proposed event tracking sensitivity analysis with existing Entropy-based sensitivity analysis methods. The results have shown a 10% improvement in a computational efficiency with no compromise for accuracy. It has also shown that the computational time to perform the sensitivity analysis is 0.5% of the time required compared to using the Entropy-based method. The proposed method has been applied to real world data in the context of preventing emerging crises at drilling rigs. One of the major purposes of such rigs is to drill boreholes to explore oil or gas reservoirs with the final scope of recovering the content

Maximum Entropy Fundamentals

Directory of Open Access Journals (Sweden)

F. Topsøe

2001-09-01

Full Text Available Abstract: In its modern formulation, the Maximum Entropy Principle was promoted by E.T. Jaynes, starting in the mid-fifties. The principle dictates that one should look for a distribution, consistent with available information, which maximizes the entropy. However, this principle focuses only on distributions and it appears advantageous to bring information theoretical thinking more prominently into play by also focusing on the "observer" and on coding. This view was brought forward by the second named author in the late seventies and is the view we will follow-up on here. It leads to the consideration of a certain game, the Code Length Game and, via standard game theoretical thinking, to a principle of Game Theoretical Equilibrium. This principle is more basic than the Maximum Entropy Principle in the sense that the search for one type of optimal strategies in the Code Length Game translates directly into the search for distributions with maximum entropy. In the present paper we offer a self-contained and comprehensive treatment of fundamentals of both principles mentioned, based on a study of the Code Length Game. Though new concepts and results are presented, the reading should be instructional and accessible to a rather wide audience, at least if certain mathematical details are left aside at a rst reading. The most frequently studied instance of entropy maximization pertains to the Mean Energy Model which involves a moment constraint related to a given function, here taken to represent "energy". This type of application is very well known from the literature with hundreds of applications pertaining to several different elds and will also here serve as important illustration of the theory. But our approach reaches further, especially regarding the study of continuity properties of the entropy function, and this leads to new results which allow a discussion of models with so-called entropy loss. These results have tempted us to speculate over

A new measure of uncertainty importance based on distributional sensitivity analysis for PSA

International Nuclear Information System (INIS)

Han, Seok Jung; Tak, Nam Il; Chun, Moon Hyun

1996-01-01

The main objective of the present study is to propose a new measure of uncertainty importance based on distributional sensitivity analysis. The new measure is developed to utilize a metric distance obtained from cumulative distribution functions (cdfs). The measure is evaluated for two cases: one is a cdf given by a known analytical distribution and the other given by an empirical distribution generated by a crude Monte Carlo simulation. To study its applicability, the present measure has been applied to two different cases. The results are compared with those of existing three methods. The present approach is a useful measure of uncertainty importance which is based on cdfs. This method is simple and easy to calculate uncertainty importance without any complex process. On the basis of the results obtained in the present work, the present method is recommended to be used as a tool for the analysis of uncertainty importance

Regional Sustainable Development Analysis Based on Information Entropy-Sichuan Province as an Example.

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Liang, Xuedong; Si, Dongyang; Zhang, Xinli

2017-10-13

According to the implementation of a scientific development perspective, sustainable development needs to consider regional development, economic and social development, and the harmonious development of society and nature, but regional sustainable development is often difficult to quantify. Through an analysis of the structure and functions of a regional system, this paper establishes an evaluation index system, which includes an economic subsystem, an ecological environmental subsystem and a social subsystem, to study regional sustainable development capacity. A sustainable development capacity measure model for Sichuan Province was established by applying the information entropy calculation principle and the Brusselator principle. Each subsystem and entropy change in a calendar year in Sichuan Province were analyzed to evaluate Sichuan Province's sustainable development capacity. It was found that the established model could effectively show actual changes in sustainable development levels through the entropy change reaction system, at the same time this model could clearly demonstrate how those forty-six indicators from the three subsystems impact on the regional sustainable development, which could make up for the lack of sustainable development research.

A New Method of Reliability Evaluation Based on Wavelet Information Entropy for Equipment Condition Identification

International Nuclear Information System (INIS)

He, Z J; Zhang, X L; Chen, X F

2012-01-01

Aiming at reliability evaluation of condition identification of mechanical equipment, it is necessary to analyze condition monitoring information. A new method of reliability evaluation based on wavelet information entropy extracted from vibration signals of mechanical equipment is proposed. The method is quite different from traditional reliability evaluation models that are dependent on probability statistics analysis of large number sample data. The vibration signals of mechanical equipment were analyzed by means of second generation wavelet package (SGWP). We take relative energy in each frequency band of decomposed signal that equals a percentage of the whole signal energy as probability. Normalized information entropy (IE) is obtained based on the relative energy to describe uncertainty of a system instead of probability. The reliability degree is transformed by the normalized wavelet information entropy. A successful application has been achieved to evaluate the assembled quality reliability for a kind of dismountable disk-drum aero-engine. The reliability degree indicates the assembled quality satisfactorily.

Quantifying complexity of financial short-term time series by composite multiscale entropy measure

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Niu, Hongli; Wang, Jun

2015-05-01

It is significant to study the complexity of financial time series since the financial market is a complex evolved dynamic system. Multiscale entropy is a prevailing method used to quantify the complexity of a time series. Due to its less reliability of entropy estimation for short-term time series at large time scales, a modification method, the composite multiscale entropy, is applied to the financial market. To qualify its effectiveness, its applications in the synthetic white noise and 1 / f noise with different data lengths are reproduced first in the present paper. Then it is introduced for the first time to make a reliability test with two Chinese stock indices. After conducting on short-time return series, the CMSE method shows the advantages in reducing deviations of entropy estimation and demonstrates more stable and reliable results when compared with the conventional MSE algorithm. Finally, the composite multiscale entropy of six important stock indices from the world financial markets is investigated, and some useful and interesting empirical results are obtained.

Entropy and wigner functions

Science.gov (United States)

Manfredi; Feix

2000-10-01

The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such a definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive-definite probability distributions which are also admissible Wigner functions.

Entropy and Wigner Functions

OpenAIRE

Manfredi, G.; Feix, M. R.

2002-01-01

The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive definite probability distributions which are also admissible Wigner functions

Path length entropy analysis of diastolic heart sounds.

Science.gov (United States)

Griffel, Benjamin; Zia, Mohammad K; Fridman, Vladamir; Saponieri, Cesare; Semmlow, John L

2013-09-01

Early detection of coronary artery disease (CAD) using the acoustic approach, a noninvasive and cost-effective method, would greatly improve the outcome of CAD patients. To detect CAD, we analyze diastolic sounds for possible CAD murmurs. We observed diastolic sounds to exhibit 1/f structure and developed a new method, path length entropy (PLE) and a scaled version (SPLE), to characterize this structure to improve CAD detection. We compare SPLE results to Hurst exponent, Sample entropy and Multiscale entropy for distinguishing between normal and CAD patients. SPLE achieved a sensitivity-specificity of 80%-81%, the best of the tested methods. However, PLE and SPLE are not sufficient to prove nonlinearity, and evaluation using surrogate data suggests that our cardiovascular sound recordings do not contain significant nonlinear properties. Copyright © 2013 Elsevier Ltd. All rights reserved.

Maximum entropy reconstruction of the configurational density of states from microcanonical simulations

International Nuclear Information System (INIS)

Davis, Sergio

2013-01-01

In this work we develop a method for inferring the underlying configurational density of states of a molecular system by combining information from several microcanonical molecular dynamics or Monte Carlo simulations at different energies. This method is based on Jaynes' Maximum Entropy formalism (MaxEnt) for Bayesian statistical inference under known expectation values. We present results of its application to measure thermodynamic entropy and free energy differences in embedded-atom models of metals.

Quantum dynamical entropy revisited

International Nuclear Information System (INIS)

Hudetz, T.

1996-10-01

We define a new quantum dynamical entropy, which is a 'hybrid' of the closely related, physically oriented entropy introduced by Alicki and Fannes in 1994, and of the mathematically well-developed, single-argument entropy introduced by Connes, Narnhofer and Thirring in 1987. We show that this new quantum dynamical entropy has many properties similar to the ones of the Alicki-Fannes entropy, and also inherits some additional properties from the CNT entropy. In particular, the 'hybrid' entropy interpolates between the two different ways in which both the AF and the CNT entropy of the shift automorphism on the quantum spin chain agree with the usual quantum entropy density, resulting in even better agreement. Also, the new quantum dynamical entropy generalizes the classical dynamical entropy of Kolmogorov and Sinai in the same way as does the AF entropy. Finally, we estimate the 'hybrid' entropy both for the Powers-Price shift systems and for the noncommutative Arnold map on the irrational rotation C * -algebra, leaving some interesting open problems. (author)

ECG contamination of EEG signals: effect on entropy.

Science.gov (United States)

Chakrabarti, Dhritiman; Bansal, Sonia

2016-02-01

Entropy™ is a proprietary algorithm which uses spectral entropy analysis of electroencephalographic (EEG) signals to produce indices which are used as a measure of depth of hypnosis. We describe a report of electrocardiographic (ECG) contamination of EEG signals leading to fluctuating erroneous Entropy values. An explanation is provided for mechanism behind this observation by describing the spread of ECG signals in head and neck and its influence on EEG/Entropy by correlating the observation with the published Entropy algorithm. While the Entropy algorithm has been well conceived, there are still instances in which it can produce erroneous values. Such erroneous values and their cause may be identified by close scrutiny of the EEG waveform if Entropy values seem out of sync with that expected at given anaesthetic levels.

Entropy in the Tangled Nature Model of evolution

DEFF Research Database (Denmark)

Roach, Ty N.F.; Nulton, James; Sibani, Paolo

2017-01-01

Applications of entropy principles to evolution and ecology are of tantamount importance given the central role spatiotemporal structuring plays in both evolution and ecological succession. We obtain here a qualitative interpretation of the role of entropy in evolving ecological systems. Our...... interpretation is supported by mathematical arguments using simulation data generated by the Tangled Nature Model (TNM), a stochastic model of evolving ecologies. We define two types of configurational entropy and study their empirical time dependence obtained from the data. Both entropy measures increase...... logarithmically with time, while the entropy per individual decreases in time, in parallel with the growth of emergent structures visible from other aspects of the simulation. We discuss the biological relevance of these entropies to describe niche space and functional space of ecosystems, as well as their use...

Entropy resistance minimization: An alternative method for heat exchanger analyses

International Nuclear Information System (INIS)

Cheng, XueTao

2013-01-01

In this paper, the concept of entropy resistance is proposed based on the entropy generation analyses of heat transfer processes. It is shown that smaller entropy resistance leads to larger heat transfer rate with fixed thermodynamic force difference and smaller thermodynamic force difference with fixed heat transfer rate, respectively. For the discussed two-stream heat exchangers in which the heat transfer rates are not given and the three-stream heat exchanger with prescribed heat capacity flow rates and inlet temperatures of the streams, smaller entropy resistance leads to larger heat transfer rate. For the two-stream heat exchangers with fixed heat transfer rate, smaller entropy resistance leads to larger effectiveness. Furthermore, it is shown that smaller values of the concepts of entropy generation numbers and modified entropy generation number do not always correspond to better performance of the discussed heat exchangers. - Highlights: • The concept of entropy resistance is defined for heat exchangers. • The concepts based on entropy generation are used to analyze heat exchangers. • Smaller entropy resistance leads to better performance of heat exchangers. • The applicability of entropy generation minimization is conditional

Interim heterogeneity changes measured using entropy texture features on T2-weighted MRI at 3.0 T are associated with pathological response to neoadjuvant chemotherapy in primary breast cancer.

Science.gov (United States)

Henderson, Shelley; Purdie, Colin; Michie, Caroline; Evans, Andrew; Lerski, Richard; Johnston, Marilyn; Vinnicombe, Sarah; Thompson, Alastair M

2017-11-01

To investigate whether interim changes in hetereogeneity (measured using entropy features) on MRI were associated with pathological residual cancer burden (RCB) at final surgery in patients receiving neoadjuvant chemotherapy (NAC) for primary breast cancer. This was a retrospective study of 88 consenting women (age: 30-79 years). Scanning was performed on a 3.0 T MRI scanner prior to NAC (baseline) and after 2-3 cycles of treatment (interim). Entropy was derived from the grey-level co-occurrence matrix, on slice-matched baseline/interim T2-weighted images. Response, assessed using RCB score on surgically resected specimens, was compared statistically with entropy/heterogeneity changes and ROC analysis performed. Association of pCR within each tumour immunophenotype was evaluated. Mean entropy percent differences between examinations, by response category, were: pCR: 32.8%, RCB-I: 10.5%, RCB-II: 9.7% and RCB-III: 3.0%. Association of ultimate pCR with coarse entropy changes between baseline/interim MRI across all lesions yielded 85.2% accuracy (area under ROC curve: 0.845). Excellent sensitivity/specificity was obtained for pCR prediction within each immunophenotype: ER+: 100%/100%; HER2+: 83.3%/95.7%, TNBC: 87.5%/80.0%. Lesion T2 heterogeneity changes are associated with response to NAC using RCB scores, particularly for pCR, and can be useful across all immunophenotypes with good diagnostic accuracy. • Texture analysis provides a means of measuring lesion heterogeneity on MRI images. • Heterogeneity changes between baseline/interim MRI can be linked with ultimate pathological response. • Heterogeneity changes give good diagnostic accuracy of pCR response across all immunophenotypes. • Percentage reduction in heterogeneity is associated with pCR with good accuracy and NPV.

Entropy of balance - some recent results

Directory of Open Access Journals (Sweden)

Laxåback Gerd

2010-07-01

Full Text Available Abstract Background Entropy when applied to biological signals is expected to reflect the state of the biological system. However the physiological interpretation of the entropy is not always straightforward. When should high entropy be interpreted as a healthy sign, and when as marker of deteriorating health? We address this question for the particular case of human standing balance and the Center of Pressure data. Methods We have measured and analyzed balance data of 136 participants (young, n = 45; elderly, n = 91 comprising in all 1085 trials, and calculated the Sample Entropy (SampEn for medio-lateral (M/L and anterior-posterior (A/P Center of Pressure (COP together with the Hurst self-similariy (ss exponent α using Detrended Fluctuation Analysis (DFA. The COP was measured with a force plate in eight 30 seconds trials with eyes closed, eyes open, foam, self-perturbation and nudge conditions. Results 1 There is a significant difference in SampEn for the A/P-direction between the elderly and the younger groups Old > young. 2 For the elderly we have in general A/P > M/L. 3 For the younger group there was no significant A/P-M/L difference with the exception for the nudge trials where we had the reverse situation, A/P Eyes Open. 5 In case of the Hurst ss-exponent we have for the elderly, M/L > A/P. Conclusions These results seem to be require some modifications of the more or less established attention-constraint interpretation of entropy. This holds that higher entropy correlates with a more automatic and a less constrained mode of balance control, and that a higher entropy reflects, in this sense, a more efficient balancing.

Generalized phase retrieval algorithm based on information measures

OpenAIRE

Shioya, Hiroyuki; Gohara, Kazutoshi

2006-01-01

An iterative phase retrieval algorithm based on the maximum entropy method (MEM) is presented. Introducing a new generalized information measure, we derive a novel class of algorithms which includes the conventionally used error reduction algorithm and a MEM-type iterative algorithm which is presented for the first time. These different phase retrieval methods are unified on the basis of the framework of information measures used in information theory.

[Analysis of the Muscle Fatigue Based on Band Spectrum Entropy of Multi-channel Surface Electromyography].

Science.gov (United States)

Liu, Jian; Zou, Renling; Zhang, Dongheng; Xu, Xiulin; Hu, Xiufang

2016-06-01

Exercise-induced muscle fatigue is a phenomenon that the maximum voluntary contraction force or power output of muscle is temporarily reduced due to muscular movement.If the fatigue is not treated properly,it will bring about a severe injury to the human body.With multi-channel collection of lower limb surface electromyography signals,this article analyzes the muscle fatigue by adoption of band spectrum entropy method which combined electromyographic signal spectral analysis and nonlinear dynamics.The experimental result indicated that with the increase of muscle fatigue,muscle signal spectrum began to move to low frequency,the energy concentrated,the system complexity came down,and the band spectrum entropy which reflected the complexity was also reduced.By monitoring the entropy,we can measure the degree of muscle fatigue,and provide an indicator to judge fatigue degree for the sports training and clinical rehabilitation training.

The effect of orthostatic stress on multiscale entropy of heart rate and blood pressure

International Nuclear Information System (INIS)

Turianikova, Zuzana; Javorka, Kamil; Calkovska, Andrea; Javorka, Michal; Baumert, Mathias

2011-01-01

Cardiovascular control acts over multiple time scales, which introduces a significant amount of complexity to heart rate and blood pressure time series. Multiscale entropy (MSE) analysis has been developed to quantify the complexity of a time series over multiple time scales. In previous studies, MSE analyses identified impaired cardiovascular control and increased cardiovascular risk in various pathological conditions. Despite the increasing acceptance of the MSE technique in clinical research, information underpinning the involvement of the autonomic nervous system in the MSE of heart rate and blood pressure is lacking. The objective of this study is to investigate the effect of orthostatic challenge on the MSE of heart rate and blood pressure variability (HRV, BPV) and the correlation between MSE (complexity measures) and traditional linear (time and frequency domain) measures. MSE analysis of HRV and BPV was performed in 28 healthy young subjects on 1000 consecutive heart beats in the supine and standing positions. Sample entropy values were assessed on scales of 1–10. We found that MSE of heart rate and blood pressure signals is sensitive to changes in autonomic balance caused by postural change from the supine to the standing position. The effect of orthostatic challenge on heart rate and blood pressure complexity depended on the time scale under investigation. Entropy values did not correlate with the mean values of heart rate and blood pressure and showed only weak correlations with linear HRV and BPV measures. In conclusion, the MSE analysis of heart rate and blood pressure provides a sensitive tool to detect changes in autonomic balance as induced by postural change

On quantum Rényi entropies: A new generalization and some properties

International Nuclear Information System (INIS)

Müller-Lennert, Martin; Dupuis, Frédéric; Szehr, Oleg; Fehr, Serge; Tomamichel, Marco

2013-01-01

The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in information theory and beyond. Various generalizations of Rényi entropies to the quantum setting have been proposed, most prominently Petz's quasi-entropies and Renner's conditional min-, max-, and collision entropy. However, these quantum extensions are incompatible and thus unsatisfactory. We propose a new quantum generalization of the family of Rényi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropy as special cases, thus encompassing most quantum entropies in use today. We show several natural properties for this definition, including data-processing inequalities, a duality relation, and an entropic uncertainty relation

Microscopic entropy and nonlocality

International Nuclear Information System (INIS)

Karpov, E.; Ordonets, G.; Petroskij, T.; Prigozhin, I.

2003-01-01

We have obtained a microscopic expression for entropy in terms of H function based on nonunitary Λ transformation which leads from the time evolution as a unitary group to a Markovian dynamics and unifies the reversible and irreversible aspects of quantum mechanics. This requires a new representation outside the Hilbert space. In terms of H, we show the entropy production and the entropy flow during the emission and absorption of radiation by an atom. Analyzing the time inversion experiment, we emphasize the importance of pre- and postcollisional correlations, which break the symmetry between incoming and outgoing waves. We consider the angle dependence of the H function in a three-dimensional situation. A model including virtual transitions is discussed in a subsequent paper

Entropy in bimolecular simulations: A comprehensive review of atomic fluctuations-based methods.