Correlations of Cross-Entropy Loss in Machine Learning.

Cross-entropy loss is crucial in training many deep neural networks. In this context, we show a number of novel and strong correlations among various related divergence functions. In particular, we demonstrate that, in some circumstances, (a) cross-entropy is almost perfectly correlated with the little-known triangular divergence, and (b) cross-entropy is strongly correlated with the Euclidean distance over the logits from which the softmax is derived. The consequences of these observations are as follows. First, triangular divergence may be used as a cheaper alternative to cross-entropy. Second, logits can be used as features in a Euclidean space which is strongly synergistic with the classification process. This justifies the use of Euclidean distance over logits as a measure of similarity, in cases where the network is trained using softmax and cross-entropy. We establish these correlations via empirical observation, supported by a mathematical explanation encompassing a number of strongly related divergence functions.

Characterizing Complex Spatiotemporal Patterns from Entropy Measures.

In addition to their importance in statistical thermodynamics, probabilistic entropy measurements are crucial for understanding and analyzing complex systems, with diverse applications in time series and one-dimensional profiles. However, extending these methods to two- and three-dimensional data still requires further development. In this study, we present a new method for classifying spatiotemporal processes based on entropy measurements. To test and validate the method, we selected five classes of similar processes related to the evolution of random patterns: (i) white noise; (ii) red noise; (iii) weak turbulence from reaction to diffusion; (iv) hydrodynamic fully developed turbulence; and (v) plasma turbulence from MHD. Considering seven possible ways to measure entropy from a matrix, we present the method as a parameter space composed of the two best separating measures of the five selected classes. The results highlight better combined performance of Shannon permutation entropy (SHp) and a new approach based on Tsallis Spectral Permutation Entropy (Sqs). Notably, our observations reveal the segregation of reaction terms in this SHp×Sqs space, a result that identifies specific sectors for each class of dynamic process, and it can be used to train machine learning models for the automatic classification of complex spatiotemporal patterns.

NeurostimML: a machine learning model for predicting neurostimulation-induced tissue damage.

Objective. The safe delivery of electrical current to neural tissue depends on many factors, yet previous methods for predicting tissue damage rely on only a few stimulation parameters. Here, we report the development of a machine learning approach that could lead to a more reliable method for predicting electrical stimulation-induced tissue damage by incorporating additional stimulation parameters.Approach. A literature search was conducted to build an initial database of tissue response information after electrical stimulation, categorized as either damaging or non-damaging. Subsequently, we used ordinal encoding and random forest for feature selection, and investigated four machine learning models for classification: Logistic Regression, K-nearest Neighbor, Random Forest, and Multilayer Perceptron. Finally, we compared the results of these models against the accuracy of the Shannon equation.Main Results. We compiled a database with 387 unique stimulation parameter combinations collected from 58 independent studies conducted over a period of 47 years, with 195 (51%) categorized as non-damaging and 190 (49%) categorized as damaging. The features selected for building our model with a Random Forest algorithm were: waveform shape, geometric surface area, pulse width, frequency, pulse amplitude, charge per phase, charge density, current density, duty cycle, daily stimulation duration, daily number of pulses delivered, and daily accumulated charge. The Shannon equation yielded an accuracy of 63.9% using akvalue of 1.79. In contrast, the Random Forest algorithm was able to robustly predict whether a set of stimulation parameters was classified as damaging or non-damaging with an accuracy of 88.3%.Significance. This novel Random Forest model can facilitate more informed decision making in the selection of neuromodulation parameters for both research studies and clinical practice. This study represents the first approach to use machine learning in the prediction of stimulation-induced neural tissue damage, and lays the groundwork for neurostimulation driven by machine learning models.

Examining social vulnerability to multi-hazards in North-Western Himalayas, India.

The enhancing risk from human action and multi-hazard interaction has substantially complicated the hazard-society relationship. The underlying vulnerabilities are crucial in predicting the probable impact to be caused by multi-hazards. Thus, the evaluation of social vulnerability is decisive in inferring the driving factor and preparing for mitigation strategies. The Himalayan landscape is prone to multiple hazards as well as possesses a multitude of vulnerabilities owing to changing human landscape. Thus, an attempt has been made to inquire into the underlying socioeconomic factors enhancing the susceptibility of the region to multi-hazards. The social vulnerability index (SVIent) has been introduced, consisting of 13 indicators and 33 variables. The variables have been standardized using the maximum and minimum normalization method and the relative importance for each indicator has been determined using Shannon entropy methods to compute SVIent. The findings revealed that female population, population above 60 years old, net irrigated area, migrant population, dilapidated house, nonworkers, bank, and nonworkers seeking jobs were found to be relatively significant contributors to the vulnerability. The western part of the study area was classified as the highly vulnerable category (SVI > 0.40628), attributed to high dependence, and higher share of unemployed workers and high poverty. The SVIent was shown to have positive correlation between unemployment, socioeconomic status, migration, dependency, and household structure significant at two-tailed test. The study's impact can be found in influencing the decision of policymakers and stakeholders in framing the mitigation strategies and policy documents.

Effects of field releases of Neoseiulus barkeri on Megalurothrips usitatus abundance and arthropod diversity.

Megalurothrips usitatus (Bagnall) (Thysanoptera: Thripidae) is an important pest in Vigna unguiculata (L.) Walp. Neoseiulus barkeri (Hughes) (Acari: Phytoseiidae) is widely used for control of pest mites and insects worldwide. We evaluated its effect on M. usitatus when predators (N. barkeri) or insecticides (Spinetoram) were applied in the fields. Neoseiulus barkeri Hughes consumed 80% of M. usitatus prey offered within 6 h, and predation showed Type III functional response with prey density. The maximum consumption of N. barkeri was 27.29 ± 1.02 individuals per d per arena (1.5 cm diameter), while the optimal prey density for the predatory mite was 10.35 ± 0.68 individuals per d per arena (1.5 cm diameter). The developmental duration of N. barkeri fed with M. usitatus was significantly shorter than those fed with the dried fruit mite, Carpoglyphus lactis (L.) (Acari: Astigmata). In field trials, the efficiency of N. barkeri against M. usitatus was not significantly different from that of applications of the insecticide spinetoram. Biodiversity of other insects in treated fields was assessed, and there were 21 insect species in garden plots treated with N. barkeri releases. The total abundance (N), Shannon's diversity index (H), Pielou's evenness index (J) and Simpson's diversity index (D) of the garden plots treated with predatory mites were all significantly higher than that in the garden plots treated with spinetoram, where we found no species of predators or parasitoids and 7 herbivores. Our results show that N. barkeri is a potential means to control M. usitatus while preserving arthropod diversity at the level of treated gardens.

Anatomical Structures at Risk in Percutaneous Distal Bunionette Correction.

Bunionette deformity is an incredibly pervasive issue in our society with almost a quarter of individuals being affected by it. As it is so common, there are numerous techniques and approaches to correct the deformity. Currently, there is a growing trend that favors percutaneous osteotomy of the bunionette. As there are multiple osteotomy sites, there are anatomical considerations that must be made at each one. The purpose of this study was to investigate the anatomic structures at risk during distal osteotomy of bunionette deformity using a Shannon burr. Using 11 fresh cadaver specimens, the fifth metatarsal was accessed through a carefully marked portal. A Shannon burr was employed for the osteotomy. Dissections were performed to assess potential damage to critical structures, including the lateral dorsal cutaneous nerve (LDCN), abductor digiti minimi (ADM), and extensor digitorum longus (EDL). Measurements were taken from the osteotomy site to each structure. The distal osteotomy site was on average greater than 8 mm from the EDL and ADM, whereas it was 1.64 mm from the LDCN. The Shannon burr made contact with and transected the LDCN on 2 occasions. However, previous studies have highlighted potential anatomical variations of the LDCN that arise distally. The study underscored the challenges posed by minimally invasive approaches to treating bunionette deformity and highlighted the need for cautious consideration when using percutaneous methods.Level of Clinical Evidence: 5.

An entropy-based study on the mutational landscape of SARS-CoV-2 in USA: Comparing different variants and revealing co-mutational behavior of proteins.

COVID-19 emergency has pushed the international scientific community to use every resource to combat the spread of the virus, to understand its biology and predict its possible evolution in terms of new variants. Since the first SARS-CoV-2 virus nucleotide and amino acid sequences were made available, information theory was used to study how viral information content was changing over time and then trace the evolution of its mutational landscape. In this work we analyzed SARS-CoV-2 sequences collected mainly in the USA in a period from March 2020 until December 2022 and computed mutation profiles of viral proteins over time through an entropy-based approach using Shannon Entropy and Hellinger distance. This representation allows an at-a-glance view of the mutational landscape of viral proteins over time and can provide new insights on the evolution of the virus from different points of view. Non-structural proteins typically showed flat mutation profiles, characterized by a very low Average mutation Entropy, while accessory and structural proteins showed mostly non uniform and high mutation profiles, often coupled with the predominance of variants. Interestingly NSP2 protein, whose function is currently still debated, falls in the same branch of NSP14 and NSP10 in the phylogenetic tree of mutations constructed through correlations of mutation profiles, suggesting a co-evolution of those proteins and a possible functional link with each other. To the best of our knowledge this is the first study based on a massive amount of data (n = 107,939,973) that analyzes from an entropy point of view the mutational landscape of SARS-CoV-2 over time and depicts a mutational temporal profile of each protein of the virus.

Revisiting the Characterization of Resting Brain Dynamics with the Permutation Jensen-Shannon Distance.

Taking into account the complexity of the human brain dynamics, the appropriate characterization of any brain state is a challenge not easily met. Actually, even the discrimination of simple behavioral tasks, such as resting with eyes closed or eyes open, represents an intricate problem and many efforts have been and are being made to overcome it. In this work, the aforementioned issue is carefully addressed by performing multiscale analyses of electroencephalogram records with the permutation Jensen-Shannon distance. The influence that linear and nonlinear temporal correlations have on the discrimination is unveiled. Results obtained lead to significant conclusions that help to achieve an improved distinction between these resting brain states.

Impact of Limosilactobacillus fermentum probiotic treatment on gut microbiota composition in sahiwal calves with rotavirus diarrhea: A 16S metagenomic analysis study".

BACKGROUND: Diarrhea poses a major threat to bovine calves leading to mortality and economic losses. Among the causes of calf diarrhea, bovine rotavirus is a major etiological agent and may result in dysbiosis of gut microbiota. The current study was designed to investigate the effect of probiotic Limosilactobacillus fermentum (Accession No.OR504458) on the microbial composition of rotavirus-infected calves using 16S metagenomic analysis technique. Screening of rotavirus infection in calves below one month of age was done through clinical signs and Reverse Transcriptase PCR. The healthy calves (n = 10) were taken as control while the infected calves (n = 10) before treatment was designated as diarrheal group were treated with Probiotic for 5 days. All the calves were screened for the presence of rotavirus infection on each day and fecal scoring was done to assess the fecal consistency. Infected calves after treatment were designated as recovered group. Fecal samples from healthy, recovered and diarrheal (infected calves before sampling) were processed for DNA extraction while four samples from each group were processed for 16S metagenomic analysis using Illumina sequencing technique and analyzed via QIIME 2. RESULTS: The results show that Firmicutes were more abundant in the healthy and recovered group than in the diarrheal group. At the same time Proteobacteria was higher in abundance in the diarrheal group. Order Oscillospirales dominated healthy and recovered calves and Enterobacterials dominated the diarrheal group. Alpha diversity indices show that diversity indices based on richness were higher in the healthy group and lower in the diarrheal group while a mixed pattern of clustering between diarrheal and recovered groups samples in PCA plots based on beta diversity indices was observed. CONCLUSION: It is concluded that probiotic Limosilactobacillus Fermentum N-30 ameliorate the dysbiosis caused by rotavirus diarrhea and may be used to prevent diarrhea in pre-weaned calves after further exploration.

Estimating Transcriptome Diversity and Specialization in Capsicum annuum L.

Chili pepper fruits of the genus Capsicum represent excellent experimental models to study the growth, development, and ripening processes in a non-climacteric species at the physiological, biochemical, and molecular levels. Fruit growth, development, and ripening involve a complex, harmonious, and finely controlled regulation of gene expression. The purpose of this study was to estimate the changes in transcriptome diversity and specialization, as well as gene specificities during fruit development in this crop, and to illustrate the advantages of estimating these parameters. To achieve these aims, we programmed and made publicly available an R package. In this study, we applied these methods to a set of 179 RNA-Seq libraries from a factorial experiment that includes 12 different genotypes at various stages of fruit development. We found that the diversity of the transcriptome decreases linearly from the flower to the mature fruit, while its specialization follows a complex and non-linear behavior during this process. Additionally, by defining sets of genes with different degrees of specialization and applying Gene Ontology enrichment analysis, we identified processes, functions, and components that play a central role in particular fruit development stages. In conclusion, the estimation of diversity, specialization, and specificity summarizes the global properties of the transcriptomes, providing insights that are difficult to achieve by other means.

An innovative method based on Gaussian cloud distribution and sample information richness for eutrophication assessment of Yangtze's lakes and reservoirs under uncertainty.

The precise assessment of a water body's eutrophication status is essential for making informed decisions in water environment management. However, conventional approaches frequently fail to consider the randomness, fuzziness, and inherent hidden information of water quality indicators. These would result in an unreliable assessment. An enhanced method was proposed for the eutrophication assessment under uncertainty in this study. The multi-dimension gaussian cloud distribution was introduced to capture the randomness and fuzziness. The Shannon entropy based on various sample size and trophic levels was proposed to maximize valuable information hidden in the datasets. Twenty-seven significant lakes and reservoirs located in the Yangtze River Basin were selected to demonstrate the proposed method. The sensitivity and consistency were used to evaluate the accuracy of the proposed method. Results indicate that the proposed method has the capability to effectively assess the eutrophication status of lakes and reservoirs under uncertainty and that it has a better sensitivity since it can identify more than 33-50% trophic levels compared to the traditional methods. Further scenario experiments analysis revealed that the sample information richness, i.e., sample size and the number of trophic levels is of great significance to the accuracy/robustness of the method. Moreover, a sample size of 60 can offer the most favorable balance between accuracy/robustness and the monitoring expenses. These findings are crucial to optimizing the eutrophication assessment.

A geospatial analysis of flood risk zones in Cyprus: insights from statistical and multi-criteria decision analysis methods.

Over the past few decades, flood disasters have emerged as the predominant natural hazard in Cyprus, primarily driven by the escalating influence of climate change in the Mediterranean region. In view of this, the objective of this study is to develop a geospatial flood risk map for the island of Cyprus by considering 14 flood hazard factors and five flood vulnerability factors, utilizing geographic information systems (GIS) and remotely sensed datasets. A comparative assessment was conducted for hazard mapping, employing statistical methods of frequency ratio (FR) and FR Shannon's entropy (FR-SE), and multi-criteria decision analysis method of fuzzy analytic hierarchy process (F-AHP). The main findings indicated that the FR method exhibited the highest predictive capability, establishing it as the most suitable approach for flood hazard mapping. Additionally, vulnerability factors were aggregated using F-AHP to generate the vulnerability map. The resulting flood risk map, which is the product of flood hazard and flood vulnerability, revealed that 9% of the island was located within highly risky regions, while 13.2% was classified as moderate risk zones. Spatial analysis of these high-risk areas indicated their concentration in the primary city districts of the island. Therefore, to mitigate future risks within these cities, an analysis of potential expansion zones was conducted, identifying the best-suited zone exhibiting the lowest risk. The generated flood risk map can serve as a valuable resource for decision-makers on the island, facilitating the integration of flood risk analysis into urban management plans.

Quasi-Equilibrium States and Phase Transitions in Biological Evolution.

We developed a macroscopic description of the evolutionary dynamics by following the temporal dynamics of the total Shannon entropy of sequences, denoted by S, and the average Hamming distance between them, denoted by H. We argue that a biological system can persist in the so-called quasi-equilibrium state for an extended period, characterized by strong correlations between S and H, before undergoing a phase transition to another quasi-equilibrium state. To demonstrate the results, we conducted a statistical analysis of SARS-CoV-2 data from the United Kingdom during the period between March 2020 and December 2023. From a purely theoretical perspective, this allowed us to systematically study various types of phase transitions described by a discontinuous change in the thermodynamic parameters. From a more-practical point of view, the analysis can be used, for example, as an early warning system for pandemics.

(Non)Resonance Bonds in Molecular Dynamics Simulations: A Case Study concerning C60 Fullerenes.

In the case of certain chemical compounds, especially organic ones, electrons can be delocalized between different atoms within the molecule. These resulting bonds, known as resonance bonds, pose a challenge not only in theoretical descriptions of the studied system but also present difficulties in simulating such systems using molecular dynamics methods. In computer simulations of such systems, it is often common practice to use fractional bonds as an averaged value across equivalent structures, known as a resonance hybrid. This paper presents the results of the analysis of five forms of C60 fullerene polymorphs: one with all bonds being resonance, three with all bonds being integer (singles and doubles in different configurations), one with the majority of bonds being integer (singles and doubles), and ten bonds (within two opposite pentagons) valued at one and a half. The analysis involved the Shannon entropy value for bond length distributions and the eigenfrequency of intrinsic vibrations (first vibrational mode), reflecting the stiffness of the entire structure. The maps of the electrostatic potential distribution around the investigated structures are presented and the dipole moment was estimated. Introducing asymmetry in bond redistribution by incorporating mixed bonds (integer and partial), in contrast to variants with equivalent bonds, resulted in a significant change in the examined observables.

Choice of Metric Divergence in Genome Sequence Comparison.

The paper introduces a novel probability descriptor for genome sequence comparison, employing a generalized form of Jensen-Shannon divergence. This divergence metric stems from a one-parameter family, comprising fractions up to a maximum value of half. Utilizing this metric as a distance measure, a distance matrix is computed for the new probability descriptor, shaping Phylogenetic trees via the neighbor-joining method. Initial exploration involves setting the parameter at half for various species. Assessing the impact of parameter variation, trees drawn at different parameter values (half, one-fourth, one-eighth). However, measurement scales decrease with parameter value increments, with higher similarity accuracy corresponding to lower scale values. Ultimately, the highest accuracy aligns with the maximum parameter value of half. Comparative analyses against previous methods, evaluating via Symmetric Distance (SD) values and rationalized perception, consistently favor the present approach's results. Notably, outcomes at the maximum parameter value exhibit the most accuracy, validating the method's efficacy against earlier approaches.

COVID-19 detection in lung CT slices using Brownian-butterfly-algorithm optimized lightweight deep features.

Several deep-learning assisted disease assessment schemes (DAS) have been proposed to enhance accurate detection of COVID-19, a critical medical emergency, through the analysis of clinical data. Lung imaging, particularly from CT scans, plays a pivotal role in identifying and assessing the severity of COVID-19 infections. Existing automated methods leveraging deep learning contribute significantly to reducing the diagnostic burden associated with this process. This research aims in developing a simple DAS for COVID-19 detection using the pre-trained lightweight deep learning methods (LDMs) applied to lung CT slices. The use of LDMs contributes to a less complex yet highly accurate detection system. The key stages of the developed DAS include image collection and initial processing using Shannon's thresholding, deep-feature mining supported by LDMs, feature optimization utilizing the Brownian Butterfly Algorithm (BBA), and binary classification through three-fold cross-validation. The performance evaluation of the proposed scheme involves assessing individual, fused, and ensemble features. The investigation reveals that the developed DAS achieves a detection accuracy of 93.80% with individual features, 96% accuracy with fused features, and an impressive 99.10% accuracy with ensemble features. These outcomes affirm the effectiveness of the proposed scheme in significantly enhancing COVID-19 detection accuracy in the chosen lung CT database.

Mathematical constraints on a family of biodiversity measures via connections with Rényi entropy.

The Hill numbers are statistics for biodiversity measurement in ecological studies, closely related to the Rényi and Shannon entropies from information theory. Recent developments in the mathematics of diversity in the setting of population genetics have produced mathematical constraints that characterize how standard measures depend on the highest-frequency class in a discrete probability distribution. Here, we apply these constraints to diversity statistics in ecology, focusing on the Hill numbers and the Rényi and Shannon entropies. The mathematical bounds can shift perspectives on the diversities of communities, in that when upper and lower bounds on Hill numbers are evaluated in a classic butterfly example, Hill numbers that are initially larger in one community switch positions-so that associated normalized Hill numbers are instead smaller than those of the other community. The new bounds hence add to the tools available for interpreting a commonly used family of statistics for ecological data.

Exploring the fidelity of satellite precipitation products in capturing flood risks: A novel framework incorporating hazard and vulnerability dimensions over a sensitive coastal multi-hazard catchment.

Complexities involved in flood risks over global coastal multi-hazard catchments are a severe concern for vulnerable communities, infrastructure, and the environment. Data scarcity in these regions often hinders our holistic understanding of flood risks, especially when socio-economic and physical vulnerabilities are involved. The extent to which Satellite Precipitation Products (SPPs), which are looked upon as alternatives to ground-based observations, can influence flood risk dynamics remains unexplored. In an attempt to answer the most riveted questions in flood management literature, this study, for the first time, explores the suitability of two competent SPPs, i.e., CHIRPS v2.0 and PERSIANN-CDR, in multi-hazard flood risk mapping. The proposed framework is demonstrated over the sensitive flood-prone deltaic stretches of the Lower Mahanadi River Basin (India). A computationally efficient MIKE+ 1D2D hydrodynamic model is developed to account for the wave propagation of concurrent flood drivers and generate high-resolution flood hazard maps for three disastrous historical flood events (July 2019, September 2020, and August 2022). To understand the hidden characteristics of vulnerability, a comprehensive set of 24 physical and socio-economic indicators is considered in a Shannon-entropy and TOPSIS framework. The variations in flood risk from both SPPs at the finest administrative scale are represented using the novel concept of Bivariate Choropleth, which portrays the marginal and compound contributions of hazard and vulnerability. A superlative performance of CHIRPS v2.0 over PERSIANN-CDR was observed in capturing hydro-climatological behaviors. CHIRPS v2.0-derived flood hazards were found analogous to the SAR-derived maps for all the three events. >70 % of villages display large disparities in flood risk, thereby affirming the role of appropriate SPPs towards efficient flood management. The observations from the study add vital information to the existing flood management policies, especially over resource-constrained regions in low and middle-income nations.

Shannon entropy of performance metrics to choose the best novel hybrid algorithm to predict groundwater level (case study: Tabriz plain, Iran).

Predicting groundwater level (GWL) fluctuations, which act as a reserve water reservoir, particularly in arid and semi-arid climates, is vital in water resources management and planning. Within the scope of current research, a novel hybrid algorithm is proposed for estimating GWL values in the Tabriz plain of Iran by combining the artificial neural network (ANN) algorithm with newly developed nature-inspired Coot and Honey Badger metaheuristic optimization algorithms. Various combinations of meteorological data such as temperature, evaporation, and precipitation, previous GWL values, and the month and year values of the data were used to evaluate the algorithm's success. Furthermore, the Shannon entropy of model performance was assessed according to 44 different statistical indicators, classified into two classes: accuracy and error. Hence, based on the high value of Shannon entropy, the best statistical indicator was selected. The results of the best model and the best scenario were analyzed. Results indicated that value of Shannon entropy is higher for the accuracy class than error class. Also, for accuracy and error class, respectively, Akaike information criterion (AIC) and residual sum of squares (RSS) indexes with the highest entropy value which is equal to 12.72 and 7.3 are the best indicators of both classes, and Legate-McCabe efficiency (LME) and normalized root mean square error-mean (NRMSE-Mean) indexes with the lowest entropy value which is equal to 3.7 and - 8.3 are the worst indicators of both classes. According to the evaluation best indicator results in the testing phase, the AIC indicator value for HBA-ANN, COOT-ANN, and the standalone ANN models is equal to - 344, - 332.8, and - 175.8, respectively. Furthermore, it was revealed that the proposed metaheuristic algorithms significantly improve the performance of the standalone ANN model and offer satisfactory GWL prediction results. Finally, it was concluded that the Honey Badger optimization algorithm showed superior results than the Coot optimization algorithm in GWL prediction.

The influence of resolution on the predictive power of spatial heterogeneity measures as biomarkers of liver fibrosis.

Spatial heterogeneity of cells in liver biopsies can be used as biomarker for disease severity of patients. This heterogeneity can be quantified by non-parametric statistics of point pattern data, which make use of an aggregation of the point locations. The method and scale of aggregation are usually chosen ad hoc, despite values of the aforementioned statistics being heavily dependent on them. Moreover, in the context of measuring heterogeneity, increasing spatial resolution will not endlessly provide more accuracy. The question then becomes how changes in resolution influence heterogeneity indicators, and subsequently how they influence their predictive abilities. In this paper, cell level data of liver biopsy tissue taken from chronic Hepatitis B patients is used to analyze this issue. Firstly, Morisita-Horn indices, Shannon indices and Getis-Ord statistics were evaluated as heterogeneity indicators of different types of cells, using multiple resolutions. Secondly, the effect of resolution on the predictive performance of the indices in an ordinal regression model was investigated, as well as their importance in the model. A simulation study was subsequently performed to validate the aforementioned methods. In general, for specific heterogeneity indicators, a downward trend in predictive performance could be observed. While for local measures of heterogeneity a smaller grid-size is outperforming, global measures have a better performance with medium-sized grids. In addition, the use of both local and global measures of heterogeneity is recommended to improve the predictive performance.