Entropy Power Research Articles

Costa’s concavity inequality for dependent variables based on the multivariate Gaussian copula

AbstractAn extension of Shannon’s entropy power inequality when one of the summands is Gaussian was provided by Costa in 1985, known as Costa’s concavity inequality. We consider the additive Gaussian noise channel with a more realistic assumption, i.e. the input and noise components are not independent and their dependence structure follows the well-known multivariate Gaussian copula. Two generalizations for the first- and second-order derivatives of the differential entropy of the output signal for dependent multivariate random variables are derived. It is shown that some previous results in the literature are particular versions of our results. Using these derivatives, concavity of the entropy power, under certain mild conditions, is proved. Finally, special one-dimensional versions of our general results are described which indeed reveal an extension of the one-dimensional case of Costa’s concavity inequality to the dependent case. An illustrative example is also presented.

Spatial Heterogeneity Effects of Green Finance on Absolute and Relative Poverty

In light of the growing emphasis on sustainable development, financial poverty alleviation has become an increasingly important strategy. This study explores whether green finance, a new financial tool aimed at achieving sustainable development, can effectively reduce poverty. Using data from 25 provinces in China between 2004 and 2019, the study builds the China Green Financial Development Index, using the improved entropy power method, and uses a spatial econometric model to analyze the linear and non-linear impact of green finance on absolute and relatively poor poverty. The results demonstrate that green finance has a positive impact on poverty reduction, with a more significant impact on rural poverty reduction than urban poverty reduction. Interestingly, non-linear results reveal that the impact of green finance on rural poverty alleviation has gradually weakened, while the impact on urban poverty alleviation has gradually increased. Moreover, the introduction of technological progress as an intermediary variable has revealed an intermediary effect between green finance and poverty reduction. Overall, this study contributes to our understanding of the link between green finance and poverty and suggests a new approach to poverty alleviation.

Regional differences in the green use level of cultivated land in the Heilongjiang reclamation area

Scientific understanding of the connotation of Green Use of Cultivated Land (GU-CL) is important to promote sustainable use of cultivated land. This study aims to analyze the regional heterogeneity of the Green Use Level of Cultivated Land (GUL-CL) in Heilongjiang Reclamation Area (HRA). Using entropy power method and coupled coordination degree model, statistical analysis was carried out based on the data of the HRA in 2020. The results show that the degree of GUL-CL in the study area is generally well-developed, but internal differences exist. Specifically, the GUL-CL ranges from 0.590 to 38.179, with a mean value of 8.818. Additionally, 29.204% of the total farms are above the higher level, mainly in Jiansanjiang and Baoquanling. In environmental friendliness practices, the high-level areas are concentrated primarily on the Songnen Plain Reclamation Area. Or, the Sanjiang Plain Reclamation Area positively presents significant effects on resource conservation. In the study area, spatial intensification and output efficiency are relatively balanced. The coupling coordination degree of green use of cultivated land (GU-CL) (0.20–0.50) is at a low coupling coordination stage. Consequently, this study can provide practical knowledge for the GU-CL in the black soil region of Northeast China.

A New Approach to Evaluate the Sustainability of Ecological and Economic Systems in Megacity Clusters: A Case Study of the Guangdong–Hong Kong–Macau Bay Area

An emergy analysis is used to assess the sustainability of urban agglomerations’ eco-economic systems, which are generally measured by emergy–value sustainability indicators using a combination of several system indicators. However, this assessment approach is not applicable to economically developed high-density urban agglomerations. The application of the traditional entropy value evaluation method needs to be expanded to further strengthen the sustainability of the complex eco-economic–social relationships in megacity cluster regions. In this study, taking the Guangdong–Hong Kong–Macau Greater Bay Area (GBA) as a case study, we study a new evaluation method for evaluating the sustainable development capacity of cities. This method is based on the entropy power method and is used to construct the evaluation system of all indicators of the social–economic–natural subsystems of the eco-economic system, and it couples the development degree with the coordination degree. (1) This study shows that the new method is applicable for the sustainability assessment of high-density megacity clusters and is more accurate and comprehensive. The sustainability rankings are provided for Zhaoqing, Jiangmen, Huizhou, Guangzhou, Macau, Foshan, Zhongshan, Dongguan, Zhuhai, and Shenzhen. Hong Kong is the most representative, with a high sustainability index, but has the lowest level of coordination and a clear incoherence within the system. (2) The current emergy structure of the GBA city cluster is extremely unreasonable. The GBA city cluster is a resource-consuming city with a common characteristic of a low level of coordinated development. Although urban clusters have some potential in terms of renewable emergy and resources, the recycling rate of waste is low, and the consumption rate of nonrenewable resources is high. The effective use of land resources has become an important factor in the bottlenecking of sustainable development, and all other cities face such problems, except Zhaoqing, Jiangmen, and Huizhou. (3) The GBA city cluster can be divided into three categories according to the new method. Category 1 mainly includes Hong Kong, Shenzhen, Dongguan, and Zhuhai, which have coordinated development degrees ranging between 0.0 and 0.135 and the highest emergy density (ED) values but are extremely dependent on external emergy. They have high levels of emergy use per capita (EUC), high living standards, and high quality of life. The effective use of land resources severely restricts sustainable economic development, resulting in extreme ecological and environmental carrying pressure. Category 2 includes Guangzhou, Macau, Foshan, and Zhongshan, whose coordinated development degrees range from 0.143 to 0.179. The sustainable development capacity of these cities is at the middle level amongst the whole GBA. Their main emergy characteristics are emergy flow and subsystem evaluation indices that are between category 1 and category 3, but each has its own characteristics. The category 3 cities include Zhaoqing, Jiangmen, and Huizhou, whose coordinated development degrees are between 0.192 and 0.369. These cities are characterized by relatively low ED and EUC values, living standards, and quality, but their land resources have certain potential. These cities have a high emergy self-sufficiency rate (ESR) and natural environmental support capacity, but their environmental loading ratio (ELR) is still much higher than the national average. In terms of the economic development and innovation development levels, these cities are ranked as category 1 > category 2 > category 3. In terms of the ecological and environmental conditions and blue–green space protection, these cities are ranked as category 1 < category 2 < category 3. The results of this study can provide cities in the GBA with more scientific and consistent directions for the coordinated development of their ecological–economic–social systems to provide sustainable development decision-making services for megacity cluster systems.

Synergy Degree Evaluation in the Development of Intelligent Construction and Construction Industrialization—A Case Study of Shenyang, China

Abstract In recent years, China’s construction industry has faced looming problems such as sloppy production methods and environmental pollution. Then the initiative of ‘synergistic development of intelligent construction and construction industrialization (ICCI)’ was proposed, which brings new opportunities for the transformation and upgrading and high-quality development of the construction industry. However, the synergy degree in the development of ICCI cannot be measured by the senses. Therefore, this study is devoted to quantitative analysis of the synergy degree in the development of ICCI by establishing a mathematical model. The concept of the synergy degree in the development of ICCI is defined based on synergetics. CiteSpace software is used to determine the five basic elements of talent, technology, information, environment and policy for the synergistic development of ICCI. Based on this, building a mechanism for synergistic development of ICCI with the Driving Force-State-Response (DFSR) model. Establishing an evaluation index system for the synergy degree in the development of ICCI through expert interviews. Then, combining entropy power method and coupling coordination model to empirically analyse the synergy degree in the development of ICCI in Shenyang. The results show that Shenyang is currently at the stage of high-level coupling and high-quality synergy, which is consistent with the actual development. It is also confirmed that the evaluation system of the synergy degree in the development of ICCI is scientific and reasonable. Finally, this study summarizes the suggestions for different levels of the synergy degree in the development of ICCI, which provides a reference for each region to better promote the synergistic development of ICCI.

Rate-Exponent Region for a Class of Distributed Hypothesis Testing Against Conditional Independence Problems

We study a class of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -encoder hypothesis testing against conditional independence problems. Under the criterion that stipulates minimization of the Type II error subject to a (constant) upper bound <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula> on the Type I error, we characterize the set of encoding rates and exponent for both discrete memoryless and memoryless vector Gaussian settings. For the DM setting, we provide a converse proof and show that it is achieved using the Quantize-Bin-Test scheme of Rahman and Wagner. For the memoryless vector Gaussian setting, we develop a tight outer bound by means of a technique that relies on the de Bruijn identity and the properties of Fisher information. In particular, the result shows that for memoryless vector Gaussian sources the rate-exponent region is exhausted using the Quantize-Bin-Test scheme with Gaussian test channels; and there is no loss in performance caused by restricting the sensors’ encoders not to employ time sharing. Furthermore, we also study a variant of the problem in which the source, not necessarily Gaussian, has finite differential entropy and the sensors’ observations noises under the null hypothesis are Gaussian. For this model, our main result is an upper bound on the exponent-rate function. The bound is shown to mirror a corresponding explicit lower bound, except that the lower bound involves the source power (variance) whereas the upper bound has the source entropy power. Part of the utility of the established bound is for investigating asymptotic exponent/rates and losses incurred by distributed detection as function of the number of sensors.

Research on the Theoretical Framework, Spatio-temporal Laws, and Driving Mechanism of Beautiful Human Settlements—A Case Study of the 14 Prefecture-Level Cities in Liaoning Province

The existing research on Beautiful China focuses on the major strategic research that is horizontal and comprehensive, and it is urgent to conduct a vertical and in-depth study from the important focus of human settlements. This paper proposes the theoretical framework of “five-sphere integrated plan”, “three-state entirety”, and “binary fusion” of beautiful human settlements, and integrates the entropy power method, kernel density estimation method, geographic probe, and spatial analysis to study the spatio-temporal Laws and the driving mechanism of beautiful human settlements in Liaoning Province. The results show that: (1) In terms of time course, from 2009 to 2018, the beautiful human settlement in Liaoning showed a fluctuating upward trend, and there were more obvious stage divergence characteristics and discrete characteristics; over time, they clustered from low level to high level. (2) In terms of spatial pattern, beautiful human settlements in general showed regional heterogeneous characteristics. The construction in western Liaoning is relatively stable, while northern Liaoning has changed greatly. There is an obvious inverted “U” spatial structure in the province, and it was both higher in the north and south and lower in the east and west, specifically decreasing from southeast to northwest. The distribution pattern is a “dicaryon” dominated by Shenyang and Dalian, and a “triad” trend of core area, development area, and starting area. (3) System properties, such as environmental, support, and social systems show fluctuating upward trends, while systems such as population show downward trends with different discrete characteristics. (4) Driving mechanisms, social systems, and support systems are the main driving systems, and it is also driven by a combination of urban economic strength, population quantity and quality, infra-structure development such as housing, and emerging technology development. The purpose of studying the beautiful human settlements is to promote the integration and development of the sciences of human settlements and other cross disciplines and to clarify the focus of Liaoning local government on building a Beautiful China.

Explicit Performance Limit for Joint Range and Direction of Arrival Estimation in Phased-Array Radar Sensors

For radar sensors in vehicle safety systems, it is of importance to establish a fundamental performance limit for the estimation accuracy of targets. Bayesian bounds, such as the ZivZakai bound (ZZB), can provide an accurate prediction for the performance limit under all signal-to-noise ratio (SNR) conditions. However, Bayesian bounds for the joint estimation of multiple parameters in radar systems have not been sufficiently studied and the explicit expression is still unavailable. In this paper, we employ the thought of Shannon's information theory to propose a tight bound with closed-form expression for joint range and direction of arrival (DOA) estimation in phased-array radar. Based on the joint <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> probability density function, we define range-DOA entropy error (RDEE) as the entropy power of range and DOA. With normalized <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> entropies in low and high SNRs, the closed-form approximation for the theoretical RDEE is derived. The explicit theoretical RDEE is comprehensive and captures the effect of the SNR, the number of elements, and the ratio of the signal bandwidth to the carrier frequency. The explicit theoretical RDEE is compared with the Cramér-Rao bound and the ZZB by a numerical simulation and the result shows that the theoretical RDEE can provide a more accurate performance prediction for the joint range-DOA estimation in phased-array radar.

Research on Fire Alarm System Based on Entropy Power Method and Topsis Superiority and Inferiority Solution Distance Method

According to the statistics of China Fire and Rescue Bureau, in 2021, 748,000 fires were reported to the national fire and rescue teams, with 1,987 deaths, 2,225 injuries and direct property losses of 6.75 billion yuan. The loss of these innocent lives and the loss of a large amount of property make us think while deploring: is there a more effective, scientific and accurate way to prevent the great harm caused by the occurrence of fire. The fire alarm system studied in this paper can be used to reduce the hazards. Firstly, the number of real fires is given 430 times by using three indicators of fire occurrence: address, machine number and loop. After selecting the high-frequency parts in the loop, machine number and component type respectively and finding their corresponding false alarm rate and failure rate, the evaluation weights are obtained using the entropy weight method. A comprehensive evaluation model based on the entropy weight method is established to score each major component. Two most reliable components of the fire alarm system are obtained: the intelligent photoelectric probe and the manual alarm button. Next, the normalized management level of each fire brigade needs to be analyzed. First, the five important parameters of normalized average coverage rate, normalized component reliability, normalized component failure rate, normalized jurisdictional fire frequency (times/hour), and normalized false alarm rate are derived for each fire brigade. The comprehensive score index of each brigade was derived and ranked by the Topsis superiority and inferiority solution distance method, and it was concluded that M brigade, L brigade, and F brigade were the three jurisdictions with the lowest comprehensive management level.

A Mutual Information Inequality and Some Applications

In this paper we derive an inequality relating linear combinations of mutual information between subsets of mutually independent random variables and an auxiliary random variable. One choice of a family of auxiliary variables leads to a new proof of a Stam-type inequality regarding the Fisher Information of sums of independent random variables. Another choice of a family of auxiliary random variables leads to new results as well as new proofs of results relating to strong data processing constants and maximal correlation between sums of independent random variables. Other results obtained include convexity of Kullback–Leibler divergence over a parameterized path along pairs of binomial and Poisson distributions, as well as a new duality-based argument relating the Stam-type inequality and entropy power inequality.

Study on the risk level assessment of light pollution based on entropy power method

Study on the risk level assessment of light pollution based on entropy power method

Can sustained development of education lead to employment - an empirical study based on TVP-VAR model

This paper explores the time-varying nature of the continuous development of education and employment from 1993-2021, completes the measurement of education integrated scale and education integrated talent indicators using the entropy power method, constructs a TVP-VAR model, and completes the investigation of the dynamic relationship between changes in education development and changes in employment growth using equally spaced impulse responses and time-point impulse responses. It is found that: there are different degrees of positive and negative impact fluctuations of the change in increase in education expenditure, the change in increase in education integrated scale and the change in increase in the number of education integrated talents on the change in employment growth, and overall the change in increase in education expenditure, the change in increase in education integrated scale and the change in the number of education integrated talents positively affect the change in employment growth under medium-term shocks. Based on the results of the study, this paper puts forward relevant suggestions for further promoting the positive impact of continuous development of education on employment growth.

Research on safety evaluation of assembly building construction by integrating entropy power method and network analysis model

Unlike the traditional construction mode of rough operation, assembly building construction implements the concept of green development in terms of energy consumption and environmental adaptability. Although assembly construction can effectively reduce construction energy consumption and improve the environmental resilience of building construction work, there is an urgent need for an effective safety assessment model for construction development due to the imperfect operation system and harsh construction environment in the construction industry. Therefore, the study analyzes the relationship of construction safety factors by using Analytic Network Process (ANP) to filter safety evaluation indexes according to the importance ranking. At the same time, the objective weights of safety indicators were determined by the entropy weight method, and the subjective weights determined by the ANP method were combined to construct the safety evaluation model for the construction of assembled buildings. The experiment shows that the maximum similarity between the comprehensive evaluation results of the model in the simulation of safety evaluation of high-rise residential construction and the actual evaluation criteria is 0.772. The experiment proves the reliability of the evaluation of the model, which reduces the safety loopholes and operation hazards for the construction of assembled buildings.

Space-time analysis of informational properties of GPS time series recorded at the Campi Flegrei caldera (Italy)

In this work the time dynamics of GPS time series recorded at the Campi Flegrei caldera from 2000 to 2019 was investigated by using the Fisher Information Measure (FIM) and the Shannon entropy power (SEP), two informational methods that allow the detection of changes in the dynamical behavior of a complex system, like the volcanic one, quantifying respectively the order/organization and the disorder/uncertainty. By jointly analyzing the FIM and the SEP through the Fisher-Shannon Information Plane (FSIP) it was shown that the SEP discriminates quite well the vertical displacement time series, while the FIM discriminates better the horizontal ones, which are featured by a more complex behavior. Globally, the most striking change in the SEP is found in 2012, while at local scale abrupt loss of order (indicated by low values of FIM) well correlate with the occurrence of seismic swarms. A further informational quantity, the complexity C (given by the product between SEP and FIM), has been revealed to be sensitive to the baseline deformation level increases and to the small-amplitude modulation of deformation signals within the caldera.

Unifying the Brascamp-Lieb Inequality and the Entropy Power Inequality

The entropy power inequality (EPI) and the Brascamp-Lieb inequality (BLI) are fundamental inequalities concerning the differential entropies of linear transformations of random vectors. The EPI provides lower bounds for the differential entropy of linear transformations of random vectors with independent components. The BLI, on the other hand, provides upper bounds on the differential entropy of a random vector in terms of the differential entropies of some of its linear transformations. In this paper, we define a family of entropy functionals, which we show are subadditive. We then establish that Gaussians are extremal for these functionals by adapting a proof technique from Geng and Nair (2014). As a consequence, we obtain a new entropy inequality that generalizes both the BLI and EPI. By considering a variety of independence relations among the components of the random vectors appearing in these functionals, we also obtain families of inequalities that lie between the EPI and the BLI.

The Concavity of Generalized Entropy Powers

In this note we introduce a new family of entropy powers which are related to generalized entropies, called Sharma-Mittal entropies, and we prove their concavity along diffusion processes generated by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L^{2}$ </tex-math></inline-formula> -Wasserstein gradient flows of corresponding entropy functionals. This result extends the result of Savaré and Toscani (2014) on the concavity of Rényi entropy powers and reveals a connection to Rényi entropy power inequalities by Bobkov and Marsiglietti (2017).

Oblique Projection-Based Covariance Matrix Reconstruction and Steering Vector Estimation for Robust Adaptive Beamforming

Adaptive beamforming can efficiently contract interference and noise. Due to high sensitivity of the beamformer to model mismatch, the capability of interference reduction will critically degrade when the signal model mismatch occurs, particularly when the sampling sequence contains the desired signal. For the purpose of enhancing the robustness of beamformers to signal model mismatch, we propose a new robust adaptive beamforming (RAB) method. Firstly, the precise steering vector (SV) associating with the desired signal is estimated by employing the minimum norm of subspace projection (MNSP) approach. Secondly, the nominal interference SVs are estimated via the maximum entropy power spectrum. Subsequently, the corrected interference SVs and powers are obtained by oblique projection. Finally, the interference-plus-noise covariance matrix (INCM) is reconstructed, and the proposed RAB is obtained. Multiple simulations are carried out and demonstrate the robustness of the proposed RAB method.

Has the Yangtze river economic belt strategy promoted the construction of ecological civilization in the upper reaches of the Yangtze river?

As a regional development strategy based on the world’s third largest river basin unit, the Yangtze river economic belt strategy plays a vital role in building ecological civilization with the core concept of “ecological priority and green development”. To study the impact of the Yangtze River Economic Belt strategy on the construction of ecological civilization in the upper reaches of the Yangtze River. This paper uses the entropy power method to measure the level of ecological civilization construction in 37 prefecture-level cities in the upper reaches of the Yangtze River. It examines the impact of the Yangtze River Economic Belt Strategy on the construction of ecological civilization in the upper reaches of the Yangtze River based on the DID method. The study results show that 1) the level of ecological civilization construction in the Yangtze River’s upper reaches has continuously improved from 2003 to 2020. 2) The implementation of the Yangtze River Economic Belt Strategy has a significant positive impact on the construction of ecological civilization in the upper reaches of the Yangtze River. 3) The Yangtze River Economic Belt Strategy can promote the construction of ecological civilization in the upper reaches of the Yangtze River by improving the level of science and technology innovation. 4) The implementation of the Yangtze River Economic Belt Strategy does not significantly impact the level of ecological civilization construction in the regions participating in the Belt and Road Initiative, so it is necessary to pay attention to the synergy between different policies. This study will help to raise the awareness of developing countries on economic development and ecological protection in the river basin, and provide a reference for policymakers.

Oil Spill Detection by CP SAR Based on the Power Entropy Decomposition

In recent years, marine oil spills have adversely affected the marine economy and ecosystem, and the detection of marine oil slicks has attracted great attention. Combining different polarimetric features for better oil spill detection is a topic that needs to be studied in depth. Previous studies have shown that the compact polarimetric (CP) synthetic aperture radar (SAR) can be effectively applied to the detection of sea surface oil spill due to its own ability, which is conducive to the extraction of sea surface oil slick. In this paper, we apply the power–entropy (PE) decomposition theory, which decomposes the total scattered power according to the entropy contribution of each cell in the response, to CP SAR data for oil spill detection. The purpose of this study is to enhance the oil slick and the separability of the sea. As a result, an oil spill detection method based on the low-entropy radiation amplitude parameter lesa is proposed. We compare lesa with the other five popular polarimetric features and validate by quantitative evaluation that lesa is superior to other types of polarization feature parameters under different band data. Moreover, the random forest classification is performed on the feature map and achieves the visualization results of oil spill detection. The experimental results show that the lesa can combine the information of the two polarimetric characteristic parameters of entropy and total scattering power, and can clearly indicate the oil slick information under different scenarios.

Research on the Multi-attribute Evaluation Model for the Investment Results of County-level Highways in New Urbanization

County-level highway, as a transport carrier to expand the external economic exchanges of rural areas, plays an important role as a hub in the rural road network system, and it is an important infrastructure for the country to promote the construction of new urbanization. In order to ensure the sustainable development of county-level highway, according to the relevant policies in China, the research on the investment effect evaluation of county-level highway projects has been regarded as a focus in the “14th Five-Year Plan”. Therefore, evaluating the investment benefits of the in-service county-level highways by identifying key evaluation factors has become an important research topic for new urbanization development. Since there is a lack of a comprehensive and reasonable evaluation index system. Therefore, this paper has taken the policy applicability and maximization of comprehensive benefits as the research goal, and started from five criteria, including new urbanization development ability, road network construction ability, economic benefits, social benefits and environmental benefits. Later, 14 second-level factors including industrial development ability, coverage of road network structure and national economic evaluation conclusion, etc., as well as a total of 58 third-level factors including the growth rate of the number of townships service industries and service industries, the increase of highway transport tools and regional urbanization growth rate, etc. were screened and constructed as the investment effect evaluation system. Subsequently, according to the characteristics of gray fuzzy of county-level highway indexes, this paper established a hybrid model applicable to the multi-attribute investment effect evaluation of new urbanization county-level highway, which used the game combination weighting method (GCWM), to combine the entropy power method and hierarchical analysis method to assign weights and reasonably calculate the comprehensive weights of indexes, and on this basis, it combined grey Euclid relational analysis method (GERAM) and the attribute theory to rank the correlation degrees of evaluation objects and further classify the investment effect level of the project. Finally, the hybrid model was applied to the county-level highway under the new urbanization construction demonstration counties to derive the optimal solution, as well as the optimization paths and measures for other auxiliary solutions. The results of this study provide an effective theoretical basis for the evaluation of the investment yield of rural transportation infrastructure with the support of policies, and provide a reliable practical method for the developing countries to achieve the maximum comprehensive benefits of the county-level highway investment programs with limited funds.