Maximum Information Entropy Research Articles

A Multifactorial Analysis of Ebola Virus Glycoprotein Receptor Binding Domain

An analysis of the receptor-binding domain (RBD) of the ZEBOV-Makona glycoprotein is presented, based upon the following four factors: information entropy (H), protein conformation, thermal imprint (B factor) and predicted epitope activity (Bepipred Score). It was found that the position of maximum information entropy (Hmax) was located within a helical pentapeptide component of a 31-mer peptide in which H=0 at each amino acid except at the amino acid position where H=Hmax. It is proposed that identification of these RBD peptide components and characteristics can help facilitate efficient design of an anti-Ebola vaccine.

Competition between Homophily and Information Entropy Maximization in Social Networks.

In social networks, it is conventionally thought that two individuals with more overlapped friends tend to establish a new friendship, which could be stated as homophily breeding new connections. While the recent hypothesis of maximum information entropy is presented as the possible origin of effective navigation in small-world networks. We find there exists a competition between information entropy maximization and homophily in local structure through both theoretical and experimental analysis. This competition suggests that a newly built relationship between two individuals with more common friends would lead to less information entropy gain for them. We demonstrate that in the evolution of the social network, both of the two assumptions coexist. The rule of maximum information entropy produces weak ties in the network, while the law of homophily makes the network highly clustered locally and the individuals would obtain strong and trust ties. A toy model is also presented to demonstrate the competition and evaluate the roles of different rules in the evolution of real networks. Our findings could shed light on the social network modeling from a new perspective.

Research of uniformity evaluation model based on entropy clustering in the microwave heating processes

This paper proposes a uniformity evaluation method based on Spectral Clustering and Maximum Information Entropy (ECUEM) for clustering the simulation results in the microwave heating system. The proposed method can effectively evaluate the dataset of the electric field E, the magnetic field H, the temperature field T, and analyze the non-uniformity phenomenon in the microwave heating processes. Compared with other clustering algorithms, the ECUEM can get better clustering results for the dataset in simulation of microwave heating. In particular, in the resonant cavity, the experimental results show that the minimum the evaluation results, the better the materials heating uniformity. In addition, when the ECUEM method is used to analyze the experiment of waveguide moving, the best position (0, 11/20⁎do, 3/14⁎ho) of waveguide can be obtained; at the same time, the uniformity or efficiency of materials microwave heating is the best. Moreover, other rules have been obtained in the microwave heating processes. Thus, the proposed method would provide a new method to guide the researchers who are working in the area of dataset clustering in the microwave heating.

Feedstock molecular reconstruction for secondary reactions of fluid catalytic cracking gasoline by maximum information entropy method

A novel methodology of maximum information entropy theory combined with structure oriented lumping (SOL) and Monte Carlo (MC) method was developed to simulate the feedstock for secondary reactions of fluid catalytic cracking (FCC) gasoline at the molecular level. The SOL method was applied to represent the feedstock configuration framework; a molecular library consisting of a large ensemble of computational molecules was created by stochastically assembling structural increments using MC method; then, the maximum information entropy method (MIEM) was introduced to adjust the mole fractions of the structural increments in the molecular library to achieve a closer matching with the actual analytical characteristics. Three samples of catalytic cracking gasoline from the industrial FCC units of China were used to validate and evaluate the proposed method. The simulation results of the feedstock properties, such as the average molecular weight and the weight fractions of main components including paraffin, olefins, naphthenes and aromatics agreed well with the experimental data.

Forecasting Core Business Transformation Risk Using the Optimal Rough Set and the Neural Network

AbstractIn the process of enterprise growth, core business transformation is an eternal theme. Enterprise risk forecasting is always an important concern for stakeholders. Considering the completeness and accuracy of the information in the early‐warning index, this paper presents a new risk‐forecasting method for enterprises to use for core business transformation by using rough set theory and an artificial neural network. First, continuous attribute values are discretized using the fuzzy clustering algorithm based on the maximum discernibility value function and information entropy. Afterwards, the major attributes are reduced by the rough sets. The core business transformation risk rank judgement is extracted to define the connection between network nodes and determine the structure of the neural networks. Finally, the improved back‐propagation (BP) neural network learning and training are used to judge the risk level of the test samples. The experiments are based on 265 listed companies in China, and the results show that the proposed risk‐forecasting model based on rough sets and the neural network provides higher prediction accuracy rates than do other widely developed baselines including logistic regression, neural networks and association rules mining. Copyright © 2015 John Wiley & Sons, Ltd.

Implications of Onicescu's informational energy in some fundamental physical models

Correlating Shannon's maximum informational entropy variational principle with the constant value of Onicescu's informational energy, the uncertainty relations for canonical systems with SL(2R) invariance are obtained. The constant value of Onicescu's informational energy corresponds, through transitivity manifolds of the SL(2R) group, to the ergodic theorem and, in particular case of a linear oscillator, to a quantification condition. Specifying de Broglie's idea by a periodic field in a complex coordinate, it is proved that the oscillator synchronization group of the same ensemble is still an achievement of the SL(2R) (Barbilian's group). Integrally invoking the invariant functions through the simultaneous action of the two isomorphic SL(2R) groups, the uncertainty relations and Stoler group of synchronization among oscillators from different ensembles (i.e., the second quantification when the annihilation and creation operators refer to a linear oscillator) are obtained. Barbilian's group parameters are interpreted by means of a variational principle as field amplitudes of a stationary vacuum metric.

SL(2, [formula omitted]) Invariance of the Kepler Type Motions and Shannon Informational Entropy. Uncertainty Relations Through the Constant Value of the Onicescu Informational Energy

It is shown that Onicescu's informational energy can be correlated by means of Shannon's maximum informational entropy variational principle with SL(2, ℝ) invariance of the Kepler type motions. For constant value of Onicescu's informational energy, the uncertainty relations are obtained.

A new assessment approach for urban ecosystem health basing on maximum information entropy method

Information entropy is introduced to describe the interactions between diverse agents in urban ecosystems. Basing on maximum information entropy method, a holistic structural parameter and its dynamic equation are derived to reflect urban ecosystem health (UEH). In this way, a new UEH assessment model has been proposed. We then apply the model to assess the UEH of Beijing, Dalian, Shanghai, Wuhan, Xiamen and Guangzhou in China. It is shown that the holistic structural parameter, the radar chart, and the associated correlations from the model can reveal the health features of different cities. According to the calculated ranges of the holistic structural parameter, a new UEH assessment grade standard is suggested and applied to the UEH assessment of some typical cities in China. It is demonstrated that the new model and the new assessment grade standard are precise and readily operational, which can be widely used in other urban ecosystems.

Nonequilibrium-thermodynamics approach to open quantum systems

Open quantum systems are studied from the thermodynamical point of view unifying the principle of maximum informational entropy and the hypothesis of relaxation times hierarchy. The result of the unification is a non-Markovian and local in time master equation that provides a direct connection of dynamical and thermodynamical properties of open quantum systems. The power of the approach is illustrated with the application to the damped harmonic oscillator and the damped driven two-level system resulting in analytical expressions for the non-Markovian and non-equilibrium entropy and inverse temperature.

Computerized optimization of flows and temperature gradient in flow modulated comprehensive two-dimensional gas chromatography

Informational entropy and syentropy percent were used to optimize the flows in the first (1D) and in the second (2D) dimension (1Fm and 2Fm, respectively) as well as the temperature program rate (r) for the flow modulated GC×GC-FID separation of C6–C12 aromatic hydrocarbons in a low boiling petrochemical sample. The separations were performed on a column series consisting of a 25m×0.25mm i.d.×0.2μm df of the polar ionic liquid SLB-IL 100 (1,9-di(3-vinylimidazolium)nonane bis(trifluoromethylsulfonyl)imide) in the first dimension and 5m×0.25mm i.d.×0.25μm df apolar HP-5MS (5% phenyl-95% methylpolysiloxane) in the second dimension. A dependence of a distribution of individual aromatic hydrocarbons in the 2D retention plane on the carrier gas flows (1Fm, and 2Fm,) and temperature gradient (r) was examined in this study. It was found that informational entropy and synentropy percent are advantageous criteria to characterize the distribution of peaks in the 2D retention plane. Maximum informational entropy and synentropy percents correspond to the maximum distribution of C6–C12 aromatic hydrocarbons in the corresponding 2D retention plane gained by the given separation using optimized values of individual carrier gas column volume flows and the temperature rate at the temperature programmed GC×GC separations.

Design of Automatic Test Platform for the Gyroscope Group Based on Pertinence Matrix

Aiming the problem of the armored vehicle's gun control system that there are many kinds of internal devices, complex fault reasons ,but no all-around and online fault diagnosis and state inspection mean, The automatic test platform for the gyroscope group with performance test and fault diagnosis for component and circuit is designed .The platform based on dependency matrix and optimal criterion of the maximum failure feature information entropy optimize test points ,choose optimal test points design. Performance test module is created and provides test result information for fault dictionary in fault diagnosis module. Automatic test platform is able to locate the circuit component failure.The platform is tested by actual vehicle experiment, and the results prove the reliability and validity of the platform.

The maximum entropy principle applied to a dynamical system proposed by Lorenz

Lorenz has proposed a dynamical system in two versions (I and II) that have both proved very useful as benchmark systems in geophysical fluid dynamics. In version I of the system, used in predictability and data-assimilation studies, the system’s state vector is a periodic array of large-scale variables that represents an atmospheric field on a latitude circle. The system is driven by a constant forcing, is linearly damped and has a simple form of advection that causes the system to behave chaotically if the forcing is large enough. The present paper sets out to obtain the statistical properties of version I of Lorenz’ system by applying the principle of maximum entropy. The principle of maximum entropy asserts that the system’s probability density function should have maximal information entropy, constrained by information on the system’s dynamics such as its average energy. Assuming that the system is in a statistically stationary state, the entropy is maximized using the system’s average energy and zero averages of the first and higher order time-derivatives of the energy as constraints. It will be shown that the combination of the energy and its first order time-derivative leads to a rather accurate description of the marginal probability density function of individual variables. If the average second order time-derivative of the energy is used as well, also the correlations between the variables are reproduced. By leaving out the constraint on the average energy – so that no information is used other than statistical stationarity – it is shown that the principle of maximum entropy still yields acceptable results for moderate values of the forcing.

A new mode reduction strategy for the generalized Kuramoto-Sivashinsky equation

Consider the generalized Kuramoto–Sivashinsky (gKS) equation. It is a model prototype for a wide variety of physical systems, from flame-front propagation, and more general front propagation in reaction–diffusion systems, to interface motion of viscous film flows. Our aim is to develop a systematic and rigorous low-dimensional representation of the gKS equation. For this purpose, we approximate it by a renormalization group equation which is qualitatively characterized by rigorous error bounds. This formulation allows for a new stochastic mode reduction guaranteeing optimality in the sense of maximal information entropy. Herewith, noise is systematically added to the reduced gKS equation and gives a rigorous and analytical explanation for its origin. These new results would allow one to reliably perform low-dimensional numerical computations by accounting for the neglected degrees of freedom in a systematic way. Moreover, the presented reduction strategy might also be useful in other applications where classical mode reduction approaches fail or are too complicated to be implemented.

Improved thresholding based on negative selection algorithm (NSA)

Thresholding is a tool of image segmentation which groups the pixels in a logical way. In this paper, a novel algorithm based on negative selection algorithm a model of artificial immune system is proposed for image thresholding. The proposed algorithm is applied on the thresholded images of lathe tool produced using maximum information entropy (MIE) and global thresholding based technique resulting in an improved image. To verify the algorithm and results, it has also been applied on some of the inbuilt MATLAB (MATrix LABoratory) images. Histogram is employed to analyze the results. Further, the results of improved algorithm are compared with the results of MIE and the global thresholding methods to check the effectiveness of the proposed method. The experimental results confirm the potential of the developed algorithm.

The Application of CRI Method in Fuzzy Reasoning

The paper discuss the application of CRI method in the fuzzy reasoning in the following three aspects: (1) the influence of different implication operators on the classification result; (2) the influence of different shape of triangles on the classification result when fuzzying the example as a triangle; (3) the influence of different compound algorithms on the classification result. The paper presents the maximum information entropy methods to calculate the classification result for a given rule and compares the CRI method with the similarity-based method in the fuzzy classification problems. The experiments show that choosing proper parameters can make the classification accuracy obtained by CRI method prior to the accuracy obtained by similarity-based method. Thereby proves the validity of CRI method in the classification problems.

Distributions of elastic moduli in mechanically percolating composites

Power-law percolation models contain very little mechanics other than the theoretical or simulated value of a percolation threshold, the volume fraction where a connected microstructure forms. For mechanical percolation these theoretical values do not correspond well to experimental results and so the models are commonly used empirically; results are correlative rather than predictive. In recent work, the effective elastic properties of a model polymer nanocomposite were approximated using a computational micromechanics model within a Monte Carlo framework. Significantly, the statistical averages resulting from these simulations displayed distinct percolation-like behavior. Of equal interest is the distribution of properties that resulted from the randomly simulated microstructures. This strongly suggests that mechanical percolation in nanocomposites is the result of a combination of microstructural mechanisms. Analysis aimed at determining which microstructure produces what response is a challenging task if microstructure is the random variable. In this work, the effective composite properties are considered as the random variable; probability distribution functions (PDFs) of the properties at discrete volume fractions are developed using the Principle of Maximum Informational Entropy. The evolution of these PDFs with increasing volume fraction helps visualize and track the significant property changes that result from microstructural randomness.

A Vision Detection Algorithm for LIGA Part Assembly

This paper proposes a vision detection algorithm to acquire LIGA part’s edges based on an in-house multi-DOF manipulator for LIGA part assembly. Feature recognition based on maximum information entropy is proposed to solve the problem that high precision edge recognition under backlight source. In order to further improve vision recognition accuracy, edge feature recognition algorithm based on symmetrical edge is proposed to recognize the center line of the symmetrical parts when the quality of the image is poor.

SELECTION AND ASSESSMENT OF PHENOMENOLOGICAL MODELS OF TUMOR GROWTH

We address general approaches to the rational selection and validation of mathematical and computational models of tumor growth using methods of Bayesian inference. The model classes are derived from a general diffuse-interface, continuum mixture theory and focus on mass conservation of mixtures with up to four species. Synthetic data are generated using higher-order base models. We discuss general approaches to model calibration, validation, plausibility, and selection based on Bayesian-based methods, information theory, and maximum information entropy. We also address computational issues and provide numerical experiments based on Markov chain Monte Carlo algorithms and high performance computing implementations.

Taxon Categories and the Universal Species-Area Relationship

A theory of macroecology based on the maximum information entropy (MaxEnt) inference procedure predicts that the log-log slope of the species-area relationship (SAR) at any spatial scale is a specified function of the ratio of abundance, N(A), to species richness, S(A), at that scale. The theory thus predicts, in generally good agreement with observation, that all SARs collapse onto a specified universal curve when local slope, z(A), is plotted against N(A)/S(A). A recent publication, however, argues that if it is assumed that patterns in macroecology are independent of the taxonomic choices that define assemblages of species, then this principle of "taxon invariance" precludes the MaxEnt-predicted universality of the SAR. By distinguishing two dimensions of the notion of taxon invariance, we show that while the MaxEnt-based theory predicts universality regardless of the taxonomic choices that define an assemblage of species, the biological characteristics of assemblages should under MaxEnt, and do in reality, influence the realism of the predictions.

PRIOR AND POSTERIOR ROBUST STOCHASTIC PREDICTIONS FOR DYNAMICAL SYSTEMS USING PROBABILITY LOGIC

An overview is given of a powerful unifying probabilistic framework for treating modeling uncertainty, along with input uncertainty, when using dynamic models to predict the response of a system during its design or operation. This framework uses probability as a multivalued conditional logic for quantitative plausible reasoning in the presence of uncertainty due to incomplete information. The fundamental probability models that represent the system’s uncertain behavior are specified by the choice of a stochastic system model class: a set of input–output probability models for the system and a prior probability distribution over this set that quantifies the relative plausibility of each model. A model class can be constructed from a parametrized deterministic system model by stochastic embedding which utilizes Jaynes’ principle of maximum information entropy. Robust predictive analyses use the entire model class with the probabilistic predictions of each model being weighted by its prior probability, or if response data are available, by its posterior probability from Bayes’ theorem for the model class. Additional robustness to modeling uncertainty comes from combining the robust predictions of each model class in a set of competing candidates weighted by the prior or posterior probability of the model class, the latter being computed from Bayes’ theorem. This higher-level application of Bayes’ theorem automatically applies a quantitative Ockham razor that penalizes the data-fit of more complex model classes that extract more information from the data. Robust predictive analyses involve integrals over high-dimensional spaces that usually must be evaluated numerically by Laplace’s method of asymptotic approximation or by Markov chain Monte Carlo methods. These computational tools are demonstrated in an illustrative example involving the vertical dynamic response of a car being driven along a rough road.