Spatial Size Research Articles

Two novel linearized energy-conserving finite element schemes for nonlinear regularized long wave equation

In this paper, two linearized second-order energy-conserving schemes for the nonlinear regularized long wave (RLW) equation are introduced, the unconditional superclose and superconvergence results are presented by using the conforming finite element method (FEM). Initially, through a skillful decomposition of the nonlinear term, two linearized second-order fully discrete schemes are developed. Compared to the previous nonlinear approaches, these schemes significantly reduce the number of iterations and improve computational efficiency; moreover, they conserve energy, and ensure the boundedness of the numerical solution in the H1-norm directly, which represents an advancement over the L∞-norm boundedness reported in prior studies. Secondly, based on the boundedness of the FE solution, the Ritz projection operator and high-precision results of the linear triangular element, the error estimates for superclose and superconvergence are derived without any restrictions on the ratio between time step size Δt and spatial mesh size h. Finally, four numerical examples are provided to confirm the accuracy of the theoretical analysis and the effectiveness of the method.

Searching for the role of membrane lipids in the mechanism of antibacterial effect of hinokitiol

The aim of this work was to investigate the effect of monoterpenoid hinokitiol (β-thujaplicin) on the monolayers and bilayers composed of lipids typical for bacteria membranes and gain insight into the potential role of the lipids in antibacterial activity and selectivity of this compound. To explore this issue, the in vitro studies were performed on different bacterial strains to verify antibacterial potency of hinokitiol. Then, the experiments on E. coli and S. aureus bacteria membrane models (i.e. model multicomponent monolayers and bilayers) were done. Finally, the effect of hinokitiol on one component lipid monolayers was investigated. The lipids used in the experiments included Phosphatidylethanolamines (PEs), Phosphatidylglycerols (PGs) and Cardiolipins differing in the structure of the polar head and/or the hydrophobic chains. This choice allowed the analysis of correlations between the lipid structure and the effect of hinokitiol.In vitro tests confirmed the antimicrobial activity of hinokitiol against most of the strains tested. In addition, the in vitro tests showed that E. coli bacteria were more sensitive to hinokitiol than S. aureus bacteria. Interestingly, the studies on model systems evidenced that hinokitiol molecules are of stronger effect on E.coli film and they are able to insert into these systems even at membrane-related surface pressures. Moreover, the structure of the lipid and its content in the model system correlated with the effect exerted by hinokitiol on the monolayer properties. It was found that hinokitiol differs in the affinity to particular lipids and additionally hinokitiol/lipid interactions may occur according to different mechanisms. Namely, depending on the lipid structure, hinokitiol may incorporate into the lipid film (Cardiolipins and PEs) or interact preferentially with the lipid polar head (PGs) and form hydrogen bonds. The effect of hinokitiol on the lipids was determined by the charge and size of the polar head as well as by the spatial size of the lipid molecule. Moreover, comparing the lipids of the same polar heads, hinokitiol caused stronger expansion of the film formed from the lipid having unsaturated chains. The results obtained may explain the difference in the effect of hinokitiol on particular bacterial strains. In conclusions, it can be suggested that the lipids should be considered as the bacteria membrane structural elements of a possible role in the mechanism of action of hinokitiol.

ENHANCING CNN PERFORMANCE WITH RIGHT-NEIGHBOR DEVIATION (RND) POOLING: A FOCUS ON MULTI-CLASS BRAIN TUMOR CLASSIFICATION IN MRI IMAGES

In recent years, the field of image processing and computer vision has been deeply transformed by the advent of Convolutional Neural Network (CNN). These deep learning models, inspired by biological processes, have demonstrated remarkable success in tasks such as image classification, object detection, and semantic segmentation. A critical component of this success is feature extraction, where the pooling layer within CNN serves as a nonlinear down-sampling technique. This layer reduces the spatial size of the convolved feature map through operations like average or maximum pooling, significantly impacting the model’s performance in complex tasks. This research introduces a novel pooling algorithm, Right-Neighbor Deviation (RND), designed to enhance the performance of CNN. The RND pooling method aims to capture detailed spatial features and hierarchical representations more effectively, thereby improving the accuracy and resilience of deep learning models. A dataset of multi-class brain tumor classification, incorporating MRI images from the BR35H dataset, is utilized to explore the potential benefits of RND pooling compared to traditional methods. The effectiveness of the proposed method is evaluated using performance metrics including accuracy, precision, recall, and F1 score, achieving generalized values of 98.86%, 98.84%, 98.80%, and 98.80%, respectively. The results highlight the potential of RND pooling to significantly advance the state of the art in brain tumor classification using CNNs, potentially leading to improved diagnosis and treatment outcomes.

Combining geometrical and intensity information to recognize vehicles from super-high density UAV-LiDAR point clouds

The traditional airborne LiDAR point clouds vehicle recognition algorithms only utilize the contained geometric information and are not sufficient to recognize vehicles accurately, especially in complex urban scenes. And their applicability in super-high density UAV-LiDAR point clouds is unknown. Therefore, a 3-D algorithm combining geometric and intensity information from super-high density UAV-LiDAR point clouds is presented. The proposed algorithm firstly converts the original point clouds into a 3D multivalued image which fuses intensity, elevation and density information simultaneously. Thereafter, the potential vehicle voxels are extracted according to the intensity, elevation and density consistency of vehicles. Subsequently, individual vehicles are recognized using the potential vehicle voxel’s spatially connected set with vehicle size constraint. Finally, the quantified attribute information of each individual vehicle, containing the spatial location, type, and size, is determined. The results for recognized vehicles are evaluated using UAV-LiDAR data with different densities and demonstrate an average quality (Kappa coefficient) of 96.58% (96.04%) without being significantly affected by occlusion and the very close vehicle arrangement.

Alternative organization without vertical hierarchies of spatial scale?

Vertical hierarchies of spatial scale—where society in general, and organizations in particular, are differentiated into levels of spatial size—have often been criticized by those encouraging alternatives to capitalist organizing. These vertical scalings are said to promote authoritarianism, a monolithic capitalist economic system, uneven concentrations of social and organizational power and wealth, and ecologically destructive organizational growth. Consequently, so the argument goes, alternative organizing must scale horizontally whereby smaller organizations autonomously associate together into loose networks or federations. The aim of this contribution is to problematize such critiques of vertical hierarchies of scaling for alternative organization. To do so, I combine Management and Organization Studies (MOS) scholarship on scaling alternative organization with two theorizations of the politics of scale in human geography—namely those derived from Neo-Marxist Political Economy and Actor-Network Theories. My argument is that all those looking to understand and encourage the scaling of alternatives to capitalist organizing should engage with and not simply reject vertical scalar hierarchies.

Spatial Size Manipulation of 1D/2D Channels in Covalent Organic Framework Membranes Through Dopamine Chemistry for Ion Separations

AbstractCovalent organic framework (COF) membranes feature with well‐developed 1D in‐plane pores and parallelly arranged 2D interlayer gallery, presenting promising platform for precise separations. However, it remains a formidable challenge to construct and regulate membrane channels at angstrom scale. Herein, pH‐sensitive dopamine is taken advantage to elaborately engineer the spatial size of 1D/2D channels in COF membranes for the separations of alkali metal ions. Acid treatment allows monomolecular dopamine to segment 1D in‐plane pores of COF membrane, achieving ultramicroporous regulation from 1.25 nm to 0.71 nm, which enables high selectivity of 18.7 for K+/Li+ separation. Molecular dynamics simulations reveal the higher dehydration degree, weaker channel‐cation interaction and faster diffusion coefficient of K+ than Li+. For alkaline treatment, dopamine self‐polymerizes to form nanoparticles between COF layers, which enlarges the 2D interlayer channels from 0.33 nm to 0.45 nm in COF membrane, enabling high‐permeance ion/molecule separations. The water permeance increases 86.7% to 404 L m−2 h−1 bar−1, without the sacrifice of membrane sieving ability. Both cation separation and ion/molecule separation performances outperform the current state‐of‐the‐art membranes. This dopamine‐mediated channel engineering strategy may provide the new insights for the design of membrane channels in precise separations.

Revisiting the Velocity Dispersion-Size Relation in Molecular Cloud Structures

Abstract Structures in molecular ISM are observed to follow a power-law relation between the velocity dispersion and spatial size, known as Larson's first relation, which is often attributed to the turbulent nature of molecular ISM and imprints the dynamics of molecular cloud structures.
Using the 13CO(J=1-0) data from the Milky Way Imaging Scroll Painting survey, we built a sample with 360 structures having relatively accurate distances obtained from either the reddened background stars with Gaia parallaxes or associated maser parallaxes, spanning from 0.4 to ~15 kpc.
Using this sample and about 0.3 million pixels, we analyzed the correlations between velocity dispersion, surface/column density, and spatial scales. 
Our structure-wise results show power-law indices smaller than 0.5 in both the σv-Reff and σv-ReffΣ relations. 
In the pixel-wise results, the σv pix is statistically scaling with the beam physical size (Rs ≡ ΘD/2) in form of σv pix∝ Rs 0.43± 0.03.
Meanwhile, σv pix in the inner Galaxy is statistically larger than the outer side.
We also analyzed correlations between σv pix and the H2 column density N(H2), finding that σv pix stops increasing with N(H2) after >1022 cm-2. 
The structures with and without high-column-density (>1022 cm-2) pixels show different σv pix ∝ N(H2)ξ relations, where the mean (std) ξ values are 0.38(0.14) and 0.62(0.27), respectively.

Unconditionally superconvergence error analysis of an energy-stable finite element method for Schrödinger equation with cubic nonlinearity

In this paper, the unconditionally superconvergence analysis is studied for the cubic Schrödinger equation with an energy-stable finite element method. A different approach is proposed to obtain the unconditionally superclose error estimate in H1-norm firstly without using the time splitting technique required in the previous literature. The key to the analysis is to use a priori boundedness of the numerical solution in energy norm and control the nonlinear terms rigorously by two cases, i.e., τ≤h2 and τ≥h2, where τ denotes the temporal size and h is the spatial size. Subsequently, the global superconvergence error estimate in H1-norm is derived by an effective interpolation post-processing approach. Finally, some numerical experiments are carried out to confirm the theoretical findings.

Quantifying the topology of magnetic skyrmions in three dimensions.

Magnetic skyrmions have so far been treated as two-dimensional spin structures characterized by a topological winding number. However, in real systems with the finite thickness of the device material being larger than the magnetic exchange length, the skyrmion spin texture extends into the third dimension and cannot be assumed as homogeneous. Using soft x-ray laminography, we reconstruct with about 20-nanometer spatial (voxel) size the full three-dimensional spin texture of a skyrmion in an 800-nanometer-diameter and 95-nanometer-thin disk patterned into a 30× [iridium/cobalt/platinum] multilayered film. A quantitative analysis finds that the evolution of the radial profile of the topological skyrmion number is nonuniform across the thickness of the disk. Estimates of the micromagnetic energy densities suggest that the changes in topological profile are related to nonuniform competing energetic interactions. Our results provide a foundation for nanoscale metrology for spintronics devices using topology as a design parameter.

Spatial distribution of poultry farms using point pattern modelling: A method to address livestock environmental impacts and disease transmission risks.

The distribution of farm locations and sizes is paramount to characterize patterns of disease spread. With some regions undergoing rapid intensification of livestock production, resulting in increased clustering of farms in peri-urban areas, measuring changes in the spatial distribution of farms is crucial to design effective interventions. However, those data are not available in many countries, their generation being resource-intensive. Here, we develop a farm distribution model (FDM), which allows the prediction of locations and sizes of poultry farms in countries with scarce data. The model combines (i) a Log-Gaussian Cox process model to simulate the farm distribution as a spatial Poisson point process, and (ii) a random forest model to simulate farm sizes (i.e. the number of animals per farm). Spatial predictors were used to calibrate the FDM on intensive broiler and layer farm distributions in Bangladesh, Gujarat (Indian state) and Thailand. The FDM yielded realistic farm distributions in terms of spatial clustering, farm locations and sizes, while providing insights on the factors influencing these distributions. Finally, we illustrate the relevance of modelling realistic farm distributions in the context of epidemic spread by simulating pathogen transmission on an array of spatial distributions of farms. We found that farm distributions generated from the FDM yielded spreading patterns consistent with simulations using observed data, while random point patterns underestimated the probability of large outbreaks. Indeed, spatial clustering increases vulnerability to epidemics, highlighting the need to account for it in epidemiological modelling studies. As the FDM maintains a realistic distribution of farm location and sizes, its use to inform mathematical models of disease transmission is particularly relevant for regions where these data are not available.

Single-Beam Acoustic Tweezers for Cell Biology: Molecular to In Vivo Level.

Acoustic tweezers have attracted attention in various fields of cell biology, including in vitro single-cell and intercellular mechanics. Compared with other tweezing technologies such as optical and magnetic tweezers, acoustic tweezers possess stronger forces and are safer for use in biological systems. However, due to the limited spatial resolution or limited size of target objects, acoustic tweezers have primarily been used to manipulate cells in vitro. To extend the advantages of acoustic tweezers to other levels (e.g., molecular and in vivo levels), researchers have recently developed various types of acoustic tweezers such as single-beam acoustic tweezers (SBATs), surface acoustic wave (SAW) tweezers, and acoustic-streaming tweezers. Among these, SBATs utilize a single-focused beam, making the transducer and system simple, noninvasive, and capable of producing strong forces compared with other types of tweezers. Depending on the acoustic beam pattern, SBATs can be classified into Rayleigh regime, Mie regime, and acoustic vortex with different trapping dynamics and application levels. In this review, we provide an overview of the principles and configuration of each type of SBAT, their applications ranging from molecular to in vivo studies, and their limitations and prospects. Thus, this review demonstrates the significance and potential of SBAT technology in biophysics and biomedical engineering.

History of Ambo Ambaa Lafaa of Western Shewa Zone of Oromia Regional State: The Heartland of Hero and Heroism

History is indispensable to understanding ourselves and the world around us. This study attempts to construct the history of Ambo Ambaa lafaa of western shewa zone of Oromia regional state. Its foundation, gradual change, economic activity, politico-administration and religion in different leaders. Further the study recognizes the problem which affects the development of Ambo town. In this study, the researcher utilized primary, secondary and pamphlet sources as well as oral information through interview in order to gather the data. The collected data was organized and analyzed using qualitative research methods. The study is based on historical and Ethnographic approach. The historical foundation of Ambo was not directly concern for the cause of military garrisons like many other Ethiopia Towns, its growth and internal character came to be closely connected with the mineral water, God Bridge and commercial activities. Ambo is town found in west shewa zone of oromia regional state. Ambo was known by pride of their nation in different era of various ruler of Ethiopia. They struggles for their right and know their responsibility simultaneously. Ambo known by patriots, hero and brave those who stand for the freedom of country in any controversy and pleasure time. The society of town needs peace, stability, truth, justice, equality, brotherly hood and fraternity with diverse nation and nationalities in the empire, because Oromo are founders of gada system that did for equality of human beings. Ambo town was established in late of 19<sup>th</sup> century. At the beginning the spatial size of Ambo town is small, it is around 1320 hectares and became expand to 8578 hectares after it makes gradual expansion to the neighboring farm land. As the result Ambo is very comfortable for different investment activities because of comfortable climate condition and stability (safety) in area, there is also different attraction site including Wanchi lake, Dandi Lake (it had number eight shape/symbol), Guder fall, obse fall, old palace of emperor Haile sillase and other different natural, cultural and ritual sites

Simulation modelling demonstrates differential performance of connectivity methods in their ability to predict genetic diversity in complex landscapes

ContextThere have been few evaluations of how well different connectivity modelling methods are able to predict the spatial genetic structure and genetic diversity of populations residing in complex landscapes. Given the wide application of connectivity modelling tools in applied conservation planning, it is crucial to broadly evaluate how these models perform across resistance, movement, and population structure conditions in predicting genetic diversity patterns. Such evaluations are critical to provide rigorous, biologically based guidance for conservation and management applications. ObjectivesOur goal was to investigate how the predictions of three connectivity models were related to spatial patterns of genetic diversity complex landscapes, considering factors such as population structure, resistance, genetic drift, genetic disequilibrium, and organism movement abilities. MethodsWe evaluated the performance of several connectivity methods across seven a priori landscape resistance surfaces to provide a broad assessment of their performance. We used CDPOP, an individual-based, spatially explicit population and genetic simulation model, to simulate genetic diversity across these resistance surfaces. This provided a pool of genetic diversity patterns that were the response factor in our simulation experiment. We then simulated landscape connectivity with several popular connectivity methods, including resistant kernels, Circuitscape, and Pathwalker, and evaluated how well they were able to predict spatial patterns of genetic diversity. ResultsResistant kernel outperformed other connectivity methods in predicting landscape patterns of genetic diversity. The strongest relationships occurred when the population process has created spatial structure but has not yet led to significant genetic diversity loss due to drift. The time lag disequilibrium was relatively short. Long simulation times resulted in severe reduction in prediction ability due to drift. ConclusionsResistant kernel predictions were much more strongly related to spatial patterns of genetic diversity than were predictions produced by Circuitscape and Pathwalker, across a large combination of population structures. Strong relationships exist between functional connectivity and genetic diversity, with clearer and stronger associations seen in spatial patterns of allelic richness compared to heterozygosity or spatial effective population size. Our results confirm the strong relationship between genetic diversity and population connectivity, and suggest that computationally efficient incidence function algorithms, such as resistant kernel methods, are well suited to predicting functional connectivity.

Simulating multi-scale optimization and variable selection in species distribution modeling

Species distribution modeling (SDM) is a fundamental tool in theoretical and applied ecology. However, relatively little is known about the performance of different approaches for scale optimization, model selection, and algorithmic prediction in the context of nonlinear, multiscale and interactive relationships between environmental variables and species occurrence. Modelers often struggle to optimize a tradeoff between ecological relevance, model robustness, complexity, and overfitting. In this paper, we investigated several methods designed to optimize spatial scale and variable selection in SDMs, in each case evaluating model fitness, parsimony and predictive performance. We used a simulation approach to produce a large pool of alternative underlying habitat relationships that reflect a broad range of realistic habitat associations. We also compared several different modeling algorithms, including logistic regression with a generalized linear model (GLM), Lasso and Elastic-Net Regularized GLMs (GLMNet), and random forest (RF), as well as alternative variable and scale selection methods. We found that GLM methods employing all-subsets dredge routines for variable selection were consistently the best predictors based on all criteria of our model performance assessment and across all attributes of the simulated underlying relationship, including nonlinearity and interaction. We had expected machine learning approaches, such as random forest, to perform better in these more complex forms of species-environment relationships. GLM using dredge variable selection was also the method that included the fewest spurious covariates and included the most correct predictors as a proportion of all predictors. We found that univariate scaling was the most robust method of variable and scale selection, along with Minimal Redundancy Maximal Relevancy (MRMR) which performed equivalently. The simulation experiment presented here provides a robust assessment of simulated multi-species distribution model performance, complexity and fidelity. By simulating a large range of potential habitat relationships with varying spatial scale, effect sizes, linearity, and interactions, we comprehensively evaluated model performance across gradients of complexity of the underlying relationships and violations of classical statistical assumptions. This study provides a valuable assessment and a broader example of the power and utility of controlled simulation experiments in habitat relationships and other ecological spatial predictive modeling.

Lightweight omni-dimensional dynamic convolution with spatial-spectral self-attention network for hyperspectral image classification

ABSTRACT Omni-dimensional dynamic convolution can adjust spatial sizes, the amount of input/output channels, and kernel size based on the characteristics of the input, thus improving the capacity to extract characteristics through convolution, resulting in increased computation and model complexity. As a result, it is challenging to deploy these models on resource-limited airborne high-spectral testing systems. This paper proposes a lightweight omni-dimensional dynamic convolution network as a possible solution to this issue. In this network, the LS2CM module is used for spatial-spectral information extraction, and the pyramidal residual network is the basic architecture for extracting features from shallow to deep layers, and lightweight omni-dimensional dynamic convolution is adopted in the convolution module. Overcoming the pyramidal structure can only extract local information, we proposed a new simple spatial-spectral self-attention mechanism to extract global information from hyperspectral. Besides, the Huber function as an activation function. The IP, WHU-Hi-LongKou, SA, and PU datasets were used to verify the accuracy of the suggested network model. The results show that the proposed lightweight network maintains an appropriate equilibrium among model complexity as well as accuracy.

General synthetic iterative scheme for rarefied gas mixture flows

The numerical simulation of rarefied gas mixtures with disparate mass and concentration is a huge research challenge. Based on our recent kinetic modeling for monatomic gas mixture flows, this problem is tackled by the general synthetic iterative scheme (GSIS), where the mesoscopic kinetic and macroscopic synthetic equations are alternately solved by the finite-volume discrete velocity method. Three important features of GSIS are highlighted. First, the synthetic equations are precisely derived from the kinetic equation, naturally reducing to the Navier-Stokes equations in the continuum flow regime; in other flow regimes, the kinetic equation provides high-order closure of the constitutive relations to capture the rarefaction effects. Second, these synthetic equations, which can be solved quickly, help to adjust the kinetic system to relax rapidly toward the steady state. Furthermore, in such a two-way coupling, the constraint on the spatial cell size is relieved. Third, the linear Fourier stability analysis demonstrates that the error decay rate in GSIS is smaller than 0.5 for various combinations of mass, concentration and viscosity ratios, such that the error can be reduced by three orders of magnitude after 10 iterations. The efficiency and accuracy of GSIS are demonstrated through several challenging cases covering a wide range of mass ratio, species concentration, and flow speed.

Soliton solutions of derivative nonlinear Schrödinger equations: Conservative schemes and numerical simulation

In this paper, we numerically study soliton solutions of derivative nonlinear Schrödinger equations based on several conservative finite difference methods. All schemes own second-order accuracy with the convergence order O(τ2+h2) in the discrete L∞-norm, where h denotes the spatial step size and τ denotes the temporal step size. We show that difference schemes preserve some discrete counterparts of continuous conservation laws, and all these schemes are solvable. Extensive numerical examples with soliton solutions are carried out to verify the theoretical results. These results manifest that our schemes have potential application to soliton propagation in optical fibers.

Coarse-to-Fine Structure and Semantic Learning for Single-Sample SAR Image Generation

Synthetic Aperture Radar (SAR) enables the acquisition of high-resolution imagery even under severe meteorological and illumination conditions. Its utility is evident across a spectrum of applications, particularly in automatic target recognition (ATR). Since SAR samples are often scarce in practical ATR applications, there is an urgent need to develop sample-efficient augmentation techniques to augment the SAR images. However, most of the existing generative approaches require an excessive amount of training samples for effective modeling of the SAR imaging characteristics. Additionally, they show limitations in augmenting the interesting target samples while maintaining image recognizability. In this study, we introduce an innovative single-sample image generation approach tailored to SAR data augmentation. To closely approximate the target distribution across both the spatial layout and local texture, a multi-level Generative Adversarial Network (GAN) architecture is constructed. It comprises three distinct GANs that independently model the structural, semantic, and texture patterns. Furthermore, we introduce multiple constraints including prior-regularized noise sampling and perceptual loss optimization to enhance the fidelity and stability of the generation process. Comparative evaluations against the state-of-the-art generative methods demonstrate the superior performance of the proposed method in terms of generation diversity, recognizability, and stability. In particular, its advantages over the baseline method are up to 0.2 and 0.22 in the SIFID and SSIM, respectively. It also exhibits stronger robustness in the generation of images across varying spatial sizes.

High-order approximation of Caputo–Prabhakar derivative with applications to linear and nonlinear fractional diffusion models

Abstract In this study, we devise a high-order numerical scheme to approximate the Caputo–Prabhakar derivative of order α ∈ (0, 1), using an rth-order time stepping Lagrange interpolation polynomial, where 3 ≤ r ∈ N $3\le r\in \mathbb{N}$ . The devised scheme is a generalization of the existing schemes developed earlier. Further, we adopt the discussed scheme for solving a linear time fractional advection–diffusion equation and a nonlinear time fractional reaction–diffusion equation with Dirichlet type boundary conditions. We show that the discussed method is unconditionally stable, uniquely solvable and convergent with convergence order O(τ r+1−α , h 2), where τ and h are the temporal and spatial step sizes, respectively. Without loss of generality, applicability of the discussed method is established by illustrative examples for r = 4, 5.

Plant size inequality: How to analyse competing spatial dissimilarity Indices?

Worldwide biodiversity loss is perceived as a major threat and is likely to be enforced by ongoing climate change. Continued monitoring of biodiversity can assist in compensating for decreasing biodiversity by goal-oriented conservation management. Plant size diversity, also termed size inequality and size hierarchy, has often been neglected in studies of biodiversity, but plays a crucial role in many ecosystems, e.g. in forests. Several competing diversity indices and other characteristics of spatial plant size inequality have been proposed but to date no protocols or guidelines exist for evaluating their relative merits. In our study, we proposed a broad framework for such an analysis. In order to put this framework to a test, we revisited the dissimilarity coefficient, a somewhat ignored but promising spatial size inequality index published at the end of the 1990s, identified its nearest index competitors and analysed their performances in different mathematical-statistical contexts. We learned that the dissimilarity coefficient is more sensitive in statistical significance tests relating to three very different summary characteristics than its closest competitor, the size differentiation index. In addition the dissimilarity coefficient has a more solid foundation than the differentiation index, since it is based on the well-known coefficient of variation. The dissimilarity coefficient can be recommended in a wide range of plant diversity applications. The principle of the dissimilarity coefficient can also be used to define an effective mark correlation function. We recommend our evaluation framework for use in similar analyses of competing diversity characteristics.