Maximum Entropy Research Articles

Off-policy asymptotic and adaptive maximum entropy deep reinforcement learning

Off-policy asymptotic and adaptive maximum entropy deep reinforcement learning

Design a novel algorithm for enhancing UWB positioning accuracy in GPS denied environments

Accurate indoor positioning is the key to the development of the Internet of Things and intelligent devices. In view of GPS-denied indoor environments, we propose to build the indoor local positioning system by using ultra-wide band (UWB) system. In order to enhance the localization accuracy of UWB system, we propose a novel algorithm which integrates the Maximum Correntropy Criterion (MCC) and unscented Kalman filter (UKF) method to reconstruct the measurement distance by using the maximum entropy principle to reduce the influence of outliers and unknown process noise on the smooth effect. Subsequently, the least square (LS) method is implemented to attain the target node (TN) initial position coordinates, and the Taylor algorithm is then performed to further optimize the localization results of the LS method. Lastly, the experimental investigation is conducted to assess the effectiveness and applicability of the developed method via the UWB system in indoor scenarios. The experimental outcomes demonstrate that the developed MCCUKF-LS method can achieve the lowest root mean square error (RMSE), and enhance the positioning accuracy of the TN compared with the LS, KF-LS, and UKF-LS methods. The overall average RMSE of MCCUKF-LS method is reduced by 45.7% contracted with the LS algorithm. The average error of x-, y- and z-axis orientation for the LS method is reduced from 0.074 m, 0.067 m, 0.098 m to 0.036 m, 0.034 m, 0.044 m, and the achieved accuracy in the orientation of the three axes is increased by 51.4%, 49.3% and 55.1% respectively, which reveals that the designed fusion technique is capable of enhancing the positioning accuracy of the TN effectively, providing a new positioning methodology and reference for indoor positioning in GPS-denied environments.

Quantum radiation reaction: Analytical approximations and obtaining the spectrum from moments

We derive analytical χ≪1 approximations for spin-dependent quantum radiation reaction for locally constant and locally monochromatic fields. We show how to factor out fast spin oscillations and obtain the degree of polarization in the plane orthogonal to the magnetic field from the Frobenius norm of the Mueller matrix. We show that spin effects lead to a transseries in χ, with powers χk, logarithms (lnχ)k, and oscillating terms, cos(…/χ) and sin(…/χ). In our approach we can obtain each moment, ⟨(kP)m⟩, of the light-front longitudinal momentum independently of the other moments and without considering the spectrum. We show how to obtain a low-energy expansion of the spectrum from the moments by treating m as a continuous, complex parameter and performing an inverse Mellin transform. We also show how to obtain the spectrum, without making a low-energy approximation, from a handful of moments using the principle of maximum entropy. Published by the American Physical Society 2024

Predicting the Invasion Risk of the Highly Invasive Acacia mearnsii in Asia under Global Climate Change.

Acacia mearnsii, among the 100 worst invasive weeds worldwide, negatively impacts native biodiversity, agriculture, and natural ecosystems. Global climate change, characterized by rising temperatures and altered precipitation patterns, enhances the risk of A. mearnsii invasion in Asia, making it crucial to identify high-risk areas for effective management. This study performed species distribution modeling using the maximum entropy (MaxEnt) algorithm to predict the potential introduction and spread of A. mearnsii under various climate scenarios based on shared socio-economic pathways (SSP2-4.5 and SSP5-8.5). Currently, only 4.35% of Asia is invaded, with a high invasion risk identified in six countries, including Bhutan, Lebanon, and Taiwan, where more than 75% of their areas are threatened. Under future climate scenarios, 21 countries face invasion risk, among which 14 countries, such as Georgia, Laos, Republic of Korea, and Turkey, are at moderate to very high risk, potentially encompassing up to 87.89% of their territories. Conversely, Northern Asian countries exhibit minimal changes in invasion risk and are considered relatively safe from invasion. These findings underscore that climate change will exacerbate invasion risks across Asia, emphasizing the urgent need for robust management strategies, including stringent quarantine measures and control efforts, to mitigate the threat of A. mearnsii expansion.

Maximum Entropy Methods for Quantum State Compatibility Problems

Maximum Entropy Methods for Quantum State Compatibility Problems

Nevanlinna analytic continuation for Migdal–Eliashberg theory

In this work, we present a method to reconstruct real-frequency properties from analytically continued causal Green’s functions within the framework of Migdal–Eliashberg (ME) theory for superconductivity. ME theory involves solving a set of coupled equations self-consistently in imaginary frequency space, but to obtain experimentally measurable properties like the spectral function and quasiparticle density of states, it is necessary to perform an analytic continuation to real frequency space. Traditionally, the ME Green’s function is decomposed into three fundamental complex functions, which are analytically continued independently. However, these functions do not possess the causal properties of Green’s functions, complicating or even preventing the application of standard methods such as Maximum Entropy. Our approach overcomes these challenges, enabling the use of various analytic continuation techniques that were previously impractical. We demonstrate the effectiveness of this method by combining it with Nevanlinna analytic continuation to achieve accurate real-frequency results for ME theory, which are directly comparable to experimental data, with applications highlighted for the superconductors MgB2 and LaBeH8.

Research on planting planning of Glycyrrhiza uralensis in Naiman Banner based on MaxEnt model and remote sensing technology

Benefits of Glycyrrhiza uralensis include removing heat, detoxifying, and moistening the lungs, easing coughs, refueling the spleen, and balancing medications. In addition to providing theoretical guidance for the development of the G. uralensis industry and rural revitalization plan, it is anticipated that this paper will also provide basic data for the formulation of production layout of the G. uralensis industry at the county level, the control of cultivation industry direction, the establishment of high-quality G. uralensis cultivation technology system. The Maximum Entropy (MaxEnt) model was used to simulate the potential distribution of G. uralensis, a Chinese medicine resource, in Naiman Banner. By conducting a field inquiry and a broad assessment of the available Chinese medicine resources, the distribution information was acquired. The random forest technique was used to classify G. uralensis. The phenological cycle and development mode of vegetation, which exhibits diverse temporal traits and aids in identification, were elucidated through long-term series analysis. The random forest classification algorithm based on multiple features showed high accuracy in remote sensing (RS) recognition of G. uralensis. Comparative analysis of the MaxEnt and RS results showed that the planting area of G. uralensis was smaller than that of its potential distribution. The expansion to high-suitability areas planting should be prioritized. Based on the dual analysis of regional and remote sensing, it not only proved the great potential of using geographic information to predict the distribution of G. uralensis, but also verified the great potential of extracting the distribution of G. uralensis from GF-6 images. These results will guide the planting and development of G. uralensis in Naiman Banner and a scientific basis for the development of G. uralensis economy, conducive to optimizing the ecological environment and promoting rural revitalization programs.

Urban Flooding Disaster Risk Assessment Utilizing the MaxEnt Model and Game Theory: A Case Study of Changchun, China

This research employs the maximum entropy (MaxEnt) model alongside game theory, integrated with an extensive framework of natural disaster risk management theory, to conduct a thorough analysis of the indicator factors related to urban flooding. This study conducts an assessment of the risks associated with urban flooding disasters using Changchun city as a case study. The validation outcomes pertaining to urban flooding hotspots reveal that 88.66% of the identified flooding sites are situated within areas classified as high-risk and very high-risk. This finding is considered to be more reliable and justifiable when contrasted with the 77.73% assessment results derived from the MaxEnt model. Utilizing the methodology of exploratory spatial data analysis (ESDA), this study applies both global and local spatial autocorrelation to investigate the disparities in the spatial patterns of flood risk within Changchun. This study concludes that urban flooding occurs primarily in the city center of Changchun and shows a significant agglomeration effect. The region is economically developed, with a high concentration of buildings and a high percentage of impervious surfaces. The Receiver Operating Characteristic (ROC) curve demonstrates that the MaxEnt model achieves an accuracy of 90.3%. On this basis, the contribution of each indicator is analyzed and ranked using the MaxEnt model. The primary determinants affecting urban flooding in Changchun are identified as impervious surfaces, population density, drainage density, maximum daily precipitation, and the Normalized Difference Vegetation Index (NDVI), with respective contributions of 20.6%, 18.1%, 13.1%, 9.6%, and 8.5%. This research offers a scientific basis for solving the urban flooding problem in Changchun city, as well as a theoretical reference for early warnings for urban disaster, and is conducive to the realization of sustainable urban development.

Maximum entropy based testing for fuzzy exponential random variable and its applications

Maximum entropy based testing for fuzzy exponential random variable and its applications

Maximum entropy spectral analysis: an application to gravitational waves data analysis

The maximum entropy spectral analysis (MESA) method, developed by Burg, offers a powerful tool for spectral estimation of a time-series. It relies on Jaynes’ maximum entropy principle, allowing the spectrum of a stochastic process to be inferred using the coefficients of an autoregressive process AR(p) of order p. A closed-form recursive solution provides estimates for both the autoregressive coefficients and the order p of the process. We provide a ready-to-use implementation of this algorithm in a Python package called memspectrum, characterized through power spectral density (PSD) analysis on synthetic data with known PSD and comparisons of different criteria for stopping the recursion. Additionally, we compare the performance of our implementation with the ubiquitous Welch algorithm, using synthetic data generated from the GW150914 strain spectrum released by the LIGO-Virgo-Kagra collaboration. Our findings indicate that Burg’s method provides PSD estimates with systematically lower variance and bias. This is particularly manifest in the case of a small (O(5000)) number of data points, making Burg’s method most suitable to work in this regime. Since this is close to the typical length of analysed gravitational waves data, improving the estimate of the PSD in this regime leads to more reliable posterior profiles for the system under study. We conclude our investigation by utilising MESA, and its particularly easy parametrisation where the only free parameter is the order p of the AR process, to marginalise over the interferometers noise PSD in conjunction with inferring the parameters of GW150914

Fluoride Ion Storage and Conduction Mechanism in Fluoride Ion Battery Positive Electrode, Ruddlesden-Popper-Type Layered Perovskite La1.2Sr1.8Mn2O7 Crystal.

Structural characteristics on fluoride ion storage and conduction mechanism in La1.2Sr1.8Mn2O7, and its fluoridated materials, La1.2Sr1.8Mn2O7F and La1.2Sr1.8Mn2O7F2, for an all-solid-state fluoride ion battery positive electrode with a high volumetric capacity surpassing those of lithium-ion ones have been revealed using the Rietveld method and maximum entropy method. In La1.2Sr1.8Mn2O7, once the F- ions are taken into the NaCl slabs in its crystal through the charging process, it forms two stable fluoride compounds, La1.2Sr1.8Mn2O7F and La1.2Sr1.8Mn2O7F2, with the help of the Mn oxidation reaction. In these oxyfluorides, thermal vibrations of the F- ions inserted are much larger, especially in the a-b plane, than along the c axis. When surplus energy, such as an electric field for charging, is applied to these crystals at near room temperature or higher, the anions immediately begin to jump to their neighboring lattice sites, resulting in sufficiently rapid and large ionic conduction. The MEM analyses and density functional theory (DFT) calculations have revealed that the F- ions enable to easily travel along the ⟨110⟩ directions in the NaCl slabs of these crystals. These structural features thus make La1.2Sr1.8Mn2O7 and its fluorides possess both of two features incompatible with each other, ion storage and conduction, indispensable for rechargeable batteries.

On application of the relative entropy concept in reliability assessment of some engineering cable structures

The main research problem studied in this work is an uncertain response and reliability assessment of the spatial cable structures due to the environmental stochasticity as well as material and geometrical imperfections. Some popular cable structures are analyzed for this purpose using the Stochastic Finite Element Method (SFEM) implemented with the use of three different techniques, namely the iterative generalized perturbation method, semi-analytical approach as well as the Monte-Carlo simulation. Uncertainty quantification delivered in this study is based on the series of FEM analyses of both static and dynamic structural problems. They enable the Least Squares Method determination of the structural polynomial responses linking extreme stresses and deformations with several uncorrelated uncertainty sources. Reliability assessment, fundamental in durability and Structural Health Monitoring, is completed using a comparison of the First Order Reliability Method (FORM) with probabilistic distance formulated by Bhattacharyya. Input uncertainties are assumed to be Gaussian according to the Maximum Entropy Principle. They have specific expected values following engineering design demands or the provisions of designing codes, whereas their standard deviations do not exceed the 10% level. The methods presented and the results obtained in this study may serve for further reliability analyses of large-scale civil engineering structures completed with both steel cables and also reinforced concrete plates like suspended bridges, for instance.

Habitat requirements of a critically endangered Ninox hawk‐owl: implications for island‐wide restoration

Small, isolated populations can be especially sensitive to poor habitat conditions due to their limited capacity to adapt or disperse. Management of such populations, with an objective to implement the most effective strategies, is a conservation priority. The Norfolk Island morepork (Ninox novaeseelandiae undulata) is a Critically Endangered hawk‐owl endemic to Norfolk Island with an estimated population of 25 individuals. This species faces compounding threats from habitat degradation and loss, as well as inbreeding depression. It presents an exemplar for the development of habitat management strategies for top‐order predators in small, isolated systems. We paired fine‐scale light detection and ranging‐derived habitat variables with tracking data to quantify habitat suitability and the relative importance of environmental variables. Maximum entropy modeling indicated vegetation patch size and canopy height were important habitat variables, with moreporks more likely to be found in larger patches and canopy heights above 7 m. Morepork presence was not strongly influenced by the type of wooded vegetation; rather, the species appears to be a generalist occupier of forested areas. We demonstrate that suitable habitat during the breeding season is currently constrained, with coverage limited to one‐third (34%) of the island and an estimated carrying capacity of 36 morepork pairs. Restoration of native forest in cleared areas adjacent to existing wooded patches, with a specific goal to increase patch size, was the optimized management strategy to increase in situ carrying capacity. This study has demonstrated how habitat suitability modeling can inform targeted habitat restoration to enhance threatened species recovery.

Soluble Model of a Nonequilibrium Steady State: The Van Kampen Objection and Other Lessons.

A simple model of charge transport is provided by a classical particle in a random potential and a dissipative coupling to the environment. The corresponding nonequilibrium steady state (NESS) can be determined analytically when both the disorder and dissipation are weak. We use it to illuminate some foundational issues in nonequilibrium statistical mechanics. We show that at nonlinear level dissipative response sensitively depends on the system-environment coupling, and the range of validity of the linear response theory is set by this coupling. This validates the Van Kampen objection. We also show that the principle of minimum entropy production does not determine the NESS beyond linear order in the electric field, while entropy maximization fails to produce the correct NESS already at linear order.

A data-driven maximum entropy method for probability uncertainty analysis based on the B-spline theory

The probability density function (PDF) is quite important for structural reliability analysis; thus, accurate PDF modeling methods draw increasing attention. This paper proposes a novel metaheuristic data-driven paradigm of the maximum entropy method (MEM) based on the B-spline function theory. Firstly, a B-spline proxy of the MEM PDF is proposed for probability uncertainty analysis. We derive the parameter calculation formulation and calculate the undetermined parameters via the raw data of structural responses. Then, to determine the knots of the B-spline functions, we propose a novel data-driven approach with the aid of a powerful metaheuristic algorithm and the response data information. Different from the traditional MEM, the proposed method is a complete data-driven solution approach and does not involve the statistical moment calculation and the nonlinear equations composed of statistical moments. Combining the advantages of the B-spline theory and the MEM, the proposed method can reconstruct the response PDF with a complex shape, such as the PDF with multiple peaks or heavy tails. For verification, two numerical examples and one engineering example are analyzed, and compared with some classical PDF modeling methods. The results show that the proposed method is superior to the compared methods in terms of computational accuracy, when the same sample data is used.

Maximum entropy-based modeling of community-level hazard responses for civil infrastructures

Perturbed by natural hazards, community-level infrastructure networks operate like many-body systems, with behaviors emerging from coupling individual component dynamics with group correlations and interactions. It follows that we can borrow methods from statistical physics to study the response of infrastructure systems to natural disasters. This study aims to construct a joint probability distribution model to describe the post-hazard state of infrastructure networks and propose an efficient surrogate model of the joint distribution for large-scale systems. Specifically, we present maximum entropy modeling of the regional impact of natural hazards on civil infrastructures. Provided with the current state of knowledge, the principle of maximum entropy yields the “most unbiased“ joint distribution model for the performances of infrastructures. In the general form, the model can handle multivariate performance states and higher-order correlations. In a particular yet typical scenario of binary performance state variables with knowledge of their mean and pairwise correlation, the joint distribution reduces to the Ising model in statistical physics. In this context, we propose using a dichotomized Gaussian model as an efficient surrogate for the maximum entropy model, facilitating the application to large systems. Using the proposed method, we investigate the seismic collective behavior of a large-scale road network (with 8,694 nodes and 26,964 links) in San Francisco, showcasing the non-trivial collective behaviors of infrastructure systems.

Climatic suitability and development potential of facility agriculture at county-level in China

Facility agriculture is a modern cultivation system that utilizes certain facilities and engineering techniques to create a suitable environment for crops growth, which can ensure China's national food security and human nutrition. Both beneficial and limited climatic conditions have influenced the development for facility agriculture. In this study, 12 dominant factors were distilled by using Maximum Entropy model (MaxEnt) to quantify climatic suitability of facility agriculture and its variation in counties across China in 1991–2020. The climatic suitable areas for facility agriculture were mainly distributed in the southern part of Northeast China, North China, central China, southern part of Southwest China, and northern part of East China, especially during 2000–2020. There was a general fluctuating upward trend in the climatic suitability of facility agriculture in traditional advantageous production areas such as Jiangsu, Shandong, Hebei, and Liaoning. Positive trends in the changes of climatic suitability were detected in central and eastern China where rapid development of facility agriculture could be realized through scientific planning and layout. Western provinces such as Gansu, Shaanxi, and Inner Mongolia were highlighted as considerable development potential for facility agriculture, with the perspective of developing energy-saving solar greenhouses in especial. These distribution characteristics and potential changes of climate suitability would help to optimize production layout and achieve green and sustainable development of facility agriculture.

Current and future habitat suitability modelling of Bambusa teres outside forest areas in Nepal under climate change scenarios

Bambusa teres Buch.-Ham. ex Munro (syn. Bambusa nutans subsp. capulata Stapleton) is a fast-growing perennial bamboo that has ecological, economic, cultural and climate change mitigation benefits. However, information on its current and future potential distribution outside forest areas across Nepal and the key factors affecting its growth and distribution are little known. We used a total of 298 occurrence points obtained from the National Bamboo Resource Assessment and 23 environmental variables to project the distribution of B. teres throughout its potential range in Nepal. Maximum entropy model (MaxEnt) was utilized for this study. We assessed the performance of the model using a receiver operating characteristic curve and evaluated the relative importance of predictor variables through a Jackknife procedure. The model achieved a high level of performance with an area under the curve value of 0.928. Precipitation of the coldest quarter (bio_19), temperature seasonality (bio_4) and precipitation seasonality (bio_15) were the significant contributing variables for the distribution of B. teres. The most suitable habitat for B. teres, with a suitability index >0.6, covered 9264.6 km2, with large sections in Eastern and Central Nepal. However, under future climate change scenarios, the area of suitable habitat for the species is projected to increase across Nepal. This study serves as a baseline for assessing potential climate change impacts on B. teres and will enable the development of adaptive measures to protect and establish various bamboo populations outside forest areas in Nepal and globally.

Impacts of climate change and human activities on three Glires pests of the Qinghai-Tibet Plateau.

The range of Glires is influenced by human activities and climate change. However, the extent to which human activities and environmental changes have contributed to this relationship remains unclear. We examined alterations in the distribution changes and driving factors of the Himalayan marmot, plateau pika, and plateau zokor on the Qinghai-Tibet Plateau (QTP) using the maximum entropy (MaxEnt) model and a geographical detector (Geodetector). The MaxEnt model showed that the contribution rates of the human footprint index (HFI) to the distribution patterns of the three types of Glires were 46.70%, 58.70%, and 59.50%, respectively. The Geodetector results showed that the distribution pattern of the Himalayan marmot on the QTP was influenced by altitude and the normalized difference vegetation index (NDVI). The distribution patterns for plateau pikas and plateau zokors were driven by HFI and NDVI. Climate has played a substantial role in shaping suitable habitats for these three Glires on the QTP. Their suitable area is expected to decrease over the next 30-50 years, along with their niche breadth and overlap. Future suitable habitats for the three Glires tended to shift toward higher latitudes on the QTP. These findings underscore the impacts of environmental and human factors on the distribution of the three Glires on the QTP. They have enhanced our understanding of the intricate relationships between Glires niches and environments. This can aid in identifying necessary interventions for developing effective early warning systems and prevention strategies to mitigate Glires infestations and plague epidemics on the QTP. © 2024 Society of Chemical Industry.

Modeling of ecological niches of Barbary Partridge (Alectoris barbara) under conditions of bioclimatic variability in the Fes-Meknes region (Morocco)

Abstract The Barbary Partridge (Alectoris barbara) is a bird species belonging to the Phasianidae family and is endemic to North Africa, including Morocco. Effective conservation of this species requires a thorough understanding and accurate assessment of the environmental factors that influence reproductive parameters. In this study, we used the species distribution models (SDM) to study the geographical distribution of the Barbary Partridge in Morocco. These models are tools that allow us to study the effects of climate change on the spatial distribution of species, they are based on the Maxent (maximum entropy) algorithm. These models are based on environmental and biological data and can predict the probability of a species’ occurrence in a given geographic area. They can also predict how climatic and environmental conditions will change over time and how these changes will affect the species’ distribution. The results obtained revealed that the environmental factors that have a significant influence on the distribution area of Barbary Partridge under Moroccan conditions are: annual precipitation (Bio12) with a contribution rate of 23.3%; precipitation of the driest quarter (Bio17) at 19.9%; altitude at 9.9%; minimum temperature of the coldest month (Bio 6) at 7.6%; precipitation of the driest month (Bio14) at 7.2%; and mean temperature of the wettest quarter (Bio8) at 4.4%. This information can be used to assist in long-term conservation planning by identifying areas that may become more or less suitable for the species.