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

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1616
Author(s):  
Samuel A. Cushman
Keyword(s):  
Configurational Entropy ◽  
Direct Application ◽  
Entropy Function ◽  
Landscape Patterns ◽  
Neutral Model ◽  
Boltzmann Entropy ◽  
Point Patterns ◽  
Landscape Mosaics ◽  
Landscape Patch ◽  
Permutation Analysis

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.

scholarly journals belg: A Tool for Calculating Boltzmann Entropy of Landscape Gradients

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 937
Author(s):  
Jakub Nowosad ◽  
Peichao Gao
Keyword(s):  
Missing Values ◽  
Real Data ◽  
R Package ◽  
Landscape Patterns ◽  
Boltzmann Entropy ◽  
The Core ◽  
Landscape Gradients ◽  
Landscape Mosaics ◽  
Basic Functions ◽  
Core Functionality

Entropy is a fundamental concept in thermodynamics that is important in many fields, including image processing, neurobiology, urban planning, and sustainability. As of recently, the application of Boltzmann entropy for landscape patterns was mostly limited to the conceptual discussion. However, in the last several years, a number of methods for calculating Boltzmann entropy for landscape mosaics and gradients were proposed. We developed an R package belg as an open source tool for calculating Boltzmann entropy of landscape gradients. The package contains functions to calculate relative and absolute Boltzmann entropy using the hierarchy-based and the aggregation-based methods. It also supports input raster with missing (NA) values, allowing for calculations on real data. In this study, we explain ideas behind implemented methods, describe the core functionality of the software, and present three examples of its use. The examples show the basic functions in this package, how to adjust Boltzmann entropy values for data with missing values, and how to use the belg package in larger workflows. We expect that the belg package will be a useful tool in the discussion of using entropy for a description of landscape patterns and facilitate a thermodynamic understanding of landscape dynamics.

scholarly journals Landscape Sustainability Evaluation of Ecologically Fragile Areas Based on Boltzmann Entropy

2020 ◽  
Vol 9 (2) ◽  
pp. 77 ◽  
Author(s):  
Jingyi Xu ◽  
Xiaoying Liang ◽  
Hai Chen
Keyword(s):  
Configurational Entropy ◽  
Remote Sensing Data ◽  
Quantitative Relationship ◽  
Field Investigation ◽  
Shaanxi Province ◽  
Landscape Sustainability ◽  
Boltzmann Entropy ◽  
Digital Elevation ◽  
Elevation Model ◽  
Evaluation Matrix

From the perspective of landscape, it is important to evaluate the landscape sustainability of ecologically fragile areas and explore temporal and spatial evolution laws to promote their sustainable development. Presently, most studies on the analysis of landscape Boltzmann entropy (also called configurational entropy) are based on a single landscape, and most of these studies are theoretical discussions. However, there are few case studies on landscape ecology. The main objectives of this paper are to explore a quantitative relationship between Boltzmann entropy and landscape sustainability, to propose a method for evaluating landscape sustainability based on Boltzmann entropy, and to evaluate the sustainability of diverse landscapes in Mizhi County, Shaanxi Province, China. This article uses digital elevation model (DEM) data with a spatial resolution of 30 m in Mizhi County. The remote sensing data on Mizhi County from 2000 were obtained by the Landsat Enhanced Thematic Mapper (ETM) + sensor, and the high-resolution image of Mizhi County from 2015 was obtained by the Gaofen-1 satellite. In this article, the subbasins are taken as the evaluation unit, and the Boltzmann entropy of Mizhi County is calculated based on the experts’ scoring of landscape sustainability in the study area. Through the analysis of landscape sustainability results from 216 subbasins in Mizhi County in 2000 and 2015, the following conclusions are drawn: (1) the evaluation matrix proposed in this paper is effective, and the Boltzmann entropy obtained by this method can directly reflect the level of landscape sustainability; (2) during the research period, the landscape sustainability of Mizhi County showed a good trend overall, especially the three townships of Taozhen, Shadian, and Shigou, which were significantly improved, and these findings were consistent with the field investigation; (3) on the spatial level, the landscape sustainability of mid-eastern Mizhi County is relatively poor compared to that in other regions, but the sustainability is also slowly increasing.

scholarly journals Calculating the Wasserstein Metric-Based Boltzmann Entropy of a Landscape Mosaic

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 381 ◽  
Author(s):  
Hong Zhang ◽  
Zhiwei Wu ◽  
Tian Lan ◽  
Yanyu Chen ◽  
Peichao Gao
Keyword(s):  
Spatial Data ◽  
Software Tool ◽  
Data File ◽  
Landscape Patterns ◽  
Wasserstein Metric ◽  
Boltzmann Entropy ◽  
Landscape Mosaic ◽  
Numerical Work ◽  
Data Set ◽  
User Friendly

Shannon entropy is currently the most popular method for quantifying the disorder or information of a spatial data set such as a landscape pattern and a cartographic map. However, its drawback when applied to spatial data is also well documented; it is incapable of capturing configurational disorder. In addition, it has been recently criticized to be thermodynamically irrelevant. Therefore, Boltzmann entropy was revisited, and methods have been developed for its calculation with landscape patterns. The latest method was developed based on the Wasserstein metric. This method incorporates spatial repetitiveness, leading to a Wasserstein metric-based Boltzmann entropy that is capable of capturing the configurational disorder of a landscape mosaic. However, the numerical work required to calculate this entropy is beyond what can be practically achieved through hand calculation. This study developed a new software tool for conveniently calculating the Wasserstein metric-based Boltzmann entropy. The tool provides a user-friendly human–computer interface and many functions. These functions include multi-format data file import function, calculation function, and data clear or copy function. This study outlines several essential technical implementations of the tool and reports the evaluation of the software tool and a case study. Experimental results demonstrate that the software tool is both efficient and convenient.

Neutral model analysis of landscape patterns from mathematical morphology

2007 ◽  
Vol 22 (7) ◽  
pp. 1033-1043 ◽  
Author(s):  
Kurt H. Riitters ◽  
Peter Vogt ◽  
Pierre Soille ◽  
Jacek Kozak ◽  
Christine Estreguil
Keyword(s):  
Mathematical Morphology ◽  
Model Analysis ◽  
Landscape Patterns ◽  
Neutral Model

Contributions to the mechanisms of mitosis and roles of cytoplasmic microtubules from ultrastructural analyses of fungi

1978 ◽  
Vol 36 (2) ◽  
pp. 266-267
Author(s):  
I. Brent Heath
Keyword(s):  
Nuclear Envelope ◽  
Direct Application ◽  
Ultrastructural Analysis ◽  
General Interest ◽  
Research Results ◽  
Organelle Motility ◽  
Cytoplasmic Microtubules

Detailed ultrastructural analysis of fungal mitotic systems and cytoplasmic microtubules might be expected to contribute to a number of areas of general interest in addition to the direct application to the organisms of study. These areas include possibly fundamental general mechanisms of mitosis; evolution of mitosis; phylogeny of organisms; mechanisms of organelle motility and positioning; characterization of cellular aspects of microtubule properties and polymerization control features. This communication is intended to outline our current research results relating to selected parts of the above questions.Mitosis in the oomycetes Saprolegnia and Thraustotheca has been described previously. These papers described simple kinetochores and showed that the kineto- chores could probably be used as markers for the poorly defined chromosomes. Kineto- chore counts from serially sectioned prophase mitotic nuclei show that kinetochore replication precedes centriole replication to yield a single hemispherical array containing approximately the 4 n number of kinetochore microtubules diverging from the centriole associated "pocket" region of the nuclear envelope (Fig. 1).

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