Generalizing Boltzmann Configurational Entropy to Surfaces, Point Patterns and Landscape Mosaics

Several methods have been recently proposed to calculate configurational entropy, based on Boltzmann entropy. Some of these methods appear to be fully thermodynamically consistent in their application to landscape patch mosaics, but none have been shown to be fully generalizable to all kinds of landscape patterns, such as point patterns, surfaces, and patch mosaics. The goal of this paper is to evaluate if the direct application of the Boltzmann relation is fully generalizable to surfaces, point patterns, and landscape mosaics. I simulated surfaces and point patterns with a fractal neutral model to control their degree of aggregation. I used spatial permutation analysis to produce distributions of microstates and fit functions to predict the distributions of microstates and the shape of the entropy function. The results confirmed that the direct application of the Boltzmann relation is generalizable across surfaces, point patterns, and landscape mosaics, providing a useful general approach to calculating landscape entropy.

Some Properties for Adjustable Entropy Function Method and Its Application to Power Systems Dynamic Economic Dispatch with Wind Integrated

With the continuous development of the world economy, the development and utilization of environmentally friendly and renewable energy have become the trend in many countries. In this paper, we study the dynamic economic dispatch with wind integrated. Firstly, we take advantage of the positive and negative spinning reserve to deal with wind power output prediction errors in order to establish a dynamic economic dispatch model of wind integrated. The existence of a min function makes the dynamic economic dispatch model nondifferentiable, which results in the inability to directly use the traditional mathematical methods based on gradient information to solve the model. Inspired by the aggregate function, we can easily transform the nondifferentiable model into a smooth model when parameter p tends to infinity. However, the aggregate function will cause data overflow when p tends to infinity. Then, for solving this problem, we take advantage of the adjustable entropy function method to replace of aggregate function method. In addition, we further discuss the adjustable entropy function method and point out that the solution generated by the adjustable entropy function method can effectively approximate the solution of the original problem without parameter p tending to infinity. Finally, simulation experiments are given, and the simulation results prove the effectiveness and correctness of the adjustable entropy function method.

A Fast Selection Based on Similar Cross-Entropy for Steganalytic Feature

The mutual confrontation between image steganography and steganalysis causes both to iterate continuously, and as a result, the dimensionality of the steganalytic features continues to increase, leading to an increasing spatio-temporal overhead. To this end, this paper proposes a fast steganalytic feature selection method based on a similar cross-entropy. Firstly, the properties of cross-entropy are investigated, through the discussion of different models, and the intra-class similarity criterion and inter-class similarity criterion based on cross-entropy are presented for the first time. Then, referring to the design principles of Fisher’s criterion, the criterion of feature contribution degree is further proposed. Secondly, the variation of the cross-entropy function of a univariate variable is analyzed in principle, thus determining the normalized range and simplifying the subsequent analysis. Then, within the normalized range, the variation of the cross-entropy function of a binary variable is investigated and the setting of important parameters is determined. Thirdly, the concept of similar cross-entropy is further presented by analyzing the changes in the value of the feature contribution measure under different circumstances, and based on this, the criterion for the feature contribution measure is updated to decrease the complexity of the calculation. Remarkably, the contribution measure criterion devised in this paper is a symmetrical structure, which equitably measures the contribution of features in different situations. Fourth, the feature component with the highest contribution is selected as the final selected feature based on the result of the feature metric. Finally, based on the Bossbase 1.01 image base that is a unique standard and recognized base in steganalysis, the feature selection on 8 kinds of low and high-dimensional steganalytic features is carried out. Through extensive experiments, comparison with several classic and state-of-the-art methods, the method designed in this paper attains competitive or even better performance in detection accuracy, calculation cost, storage cost and versatility.

On the Use of Entropy as a Measure of Dependence of Two Events

We define degree of dependence of two events A and B in a probability space by using Boltzmann-Shannon entropy function of an appropriate probability distribution produced by these events and depending on one parameter (the probability of intersection of A and B) varying within a closed interval I. The entropy function attains its global maximum when the events A and B are independent. The important particular case of discrete uniform probability space motivates this definition in the following way. The entropy function has a minimum at the left endpoint of I exactly when one of the events and the complement of the other are connected with the relation of inclusion (maximal negative dependence). It has a minimum at the right endpoint of I exactly when one of these events is included in the other (maximal positive dependence). Moreover, the deviation of the entropy from its maximum is equal to average information that carries one of the binary trials defined by A and B with respect to the other. As a consequence, the degree of dependence of A and B can be expressed in terms of information theory and is invariant with respect to the choice of unit of information. Using this formalism, we describe completely the screening tests and their reliability, measure efficacy of a vaccination, the impact of some events from the financial markets to other events, etc. A link is available for downloading an Excel program which calculates the degree of dependence of two events in a sample space with equally likely outcomes.