Significance tests for R2 of out-of-sample prediction using polygenic scores.

The coefficient of determination (R2) is a well-established measure to indicate the predictive ability of polygenic scores (PGSs). However, the sampling variance of R2 is rarely considered so that 95% confidence intervals (CI) are not usually reported. Moreover, when comparisons are made between PGSs based on different discovery samples, the sampling covariance of R2 is required to test the difference between them. Here, we show how to estimate the variance and covariance of R2 values to assess the 95% CI and p value of the R2 difference. We apply this approach to real data calculating PGSs in 28,880 European participants derived from UK Biobank (UKBB) and Biobank Japan (BBJ) GWAS summary statistics for cholesterol and BMI. We quantify the significantly higher predictive ability of UKBB PGSs compared to BBJ PGSs (p value 7.6e-31 for cholesterol and 1.4e-50 for BMI). A joint model of UKBB and BBJ PGSs significantly improves the predictive ability, compared to a model of UKBB PGS only (p value 3.5e-05 for cholesterol and 1.3e-28 for BMI). We also show that the predictive ability of regulatory SNPs is significantly enriched over non-regulatory SNPs for cholesterol (p value 8.9e-26 for UKBB and 3.8e-17 for BBJ). We suggest that the proposed approach (available in R package r2redux) should be used to test the statistical significance of difference between pairs of PGSs, which may help to draw a correct conclusion about the comparative predictive ability of PGSs.

Decoding Cortical Chronotopy - Comparing the Influence of Different Cortical Organizational Schemes.

The brain's diverse intrinsic timescales enable us to perceive stimuli with varying temporal persistency. This study aimed to uncover the cortical organizational schemes underlying these variations, revealing the neural architecture for processing a wide range of sensory experiences. We collected resting-state fMRI, task-fMRI, and diffusion-weighted imaging data from 47 individuals. Based on this data, we extracted six organizational schemes: (1) the structural Rich Club (RC) architecture, shown to synchronize the connectome; (2) the structural Diverse Club architecture, as an alternative to the RC based on the network's module structure; (3) the functional uni-to-multimodal gradient, reflected in a wide range of structural and functional features; and (4) the spatial posterior/lateral-to-anterior/medial gradient, established for hierarchical levels of cognitive control. Also, we explored the effects of (5) structural graph theoretical measures of centrality and (6) cytoarchitectural differences. Using Bayesian model comparison, we contrasted the impact of these organizational schemes on (1) intrinsic resting-state timescales and (2) inter-subject correlation (ISC) from a task involving hierarchically nested digit sequences. As expected, resting-state timescales were slower in structural network hubs, hierarchically higher areas defined by the functional and spatial gradients, and thicker cortical regions. ISC analysis demonstrated hints for the engagement of higher cortical areas with more temporally persistent stimuli. Finally, the model comparison identified the uni-to-multimodal gradient as the best organizational scheme for explaining the chronotopy in both task and rest. Future research should explore the microarchitectural features that shape this gradient, elucidating how our brain adapts and evolves across different modes of processing.

Insights into the occurrence, distribution and dissipation of widespread agrochemicals in celery agrosystems for joint risk assessment.

Elucidating exposure risks associated with the most widely used agrochemicals and their metabolites in celery agrosystems are vital for food safety and human health. The occurrence, distribution, dissipation and metabolism of imidacloprid (IMI), acetamiprid (ACE), thiamethoxam (THM) and difenoconazole (DIF) in celery tissues reflected by initial depositions, uptake characteristics, half-lives, concentration variations. DIF exhibited unacceptable ecological risk to soil organisms under multi-risk evaluation models, including toxicity exposure ratio, risk quotient, and BITSSD model. The joint dietary risks of target pesticides were 37.273-647.454% and 0.400-2522.016% based on deterministic and probabilistic models, with non-carcinogenic risks of 30.207-85.522% and 1.229-2524.662%, respectively. Children aged 1-6 years suffered the highest exposure, with the leaves posing higher risk than other tissues. Long-term exposure risks should be continuously assessed for ecological sustainability and human health, given the widespread usage and cumulative effects of target pesticides, especially for rural children.

Nonlinear compartmental modeling to monitor ovarian follicle population dynamics on the whole lifespan.

In this work, we introduce a compartmental model of ovarian follicle development all along lifespan, based on ordinary differential equations. The model predicts the changes in the follicle numbers in different maturation stages with aging. Ovarian follicles may either move forward to the next compartment (unidirectional migration) or degenerate and disappear (death). The migration from the first follicle compartment corresponds to the activation of quiescent follicles, which is responsible for the progressive exhaustion of the follicle reserve (ovarian aging) until cessation of reproductive activity. The model consists of a data-driven layer embedded into a more comprehensive, knowledge-driven layer encompassing the earliest events in follicle development. The data-driven layer is designed according to the most densely sampled experimental dataset available on follicle numbers in the mouse. Its salient feature is the nonlinear formulation of the activation rate, whose formulation includes a feedback term from growing follicles. The knowledge-based, coating layer accounts for cutting-edge studies on the initiation of follicle development around birth. Its salient feature is the co-existence of two follicle subpopulations of different embryonic origins. We then setup a complete estimation strategy, including the study of structural identifiability, the elaboration of a relevant optimization criterion combining different sources of data (the initial dataset on follicle numbers, together with data in conditions of perturbed activation, and data discriminating the subpopulations) with appropriate error models, and a model selection step. We finally illustrate the model potential for experimental design (suggestion of targeted new data acquisition) and in silico experiments.

Cross-model validation of public health microsimulation models; comparing two models on estimated effects of a weight management intervention.

BACKGROUND: Health economic modelling indicates that referral to a behavioural weight management programme is cost saving and generates QALY gains compared with a brief intervention. The aim of this study was to conduct a cross-model validation comparing outcomes from this cost-effectiveness analysis to those of a comparator model, to understand how differences in model structure contribute to outcomes. METHODS: The outcomes produced by two models, the School for Public Health Research diabetes prevention (SPHR) and Health Checks (HC) models, were compared for three weight-management programme strategies; Weight Watchers (WW) for 12 weeks, WW for 52 weeks, and a brief intervention, and a simulated no intervention scenario. Model inputs were standardised, and iterative adjustments were made to each model to identify drivers of differences in key outcomes. RESULTS: The total QALYs estimated by the HC model were higher in all treatment groups than those estimated by the SPHR model, and there was a large difference in incremental QALYs between the models. SPHR simulated greater QALY gains for 12-week WW and 52-week WW relative to the Brief Intervention. Comparisons across socioeconomic groups found a stronger socioeconomic gradient in the SPHR model. Removing the impact of treatment on HbA1c from the SPHR model, running both models only with the conditions that the models have in common and, to a lesser extent, changing the data used to estimate risk factor trajectories, resulted in more consistent model outcomes. CONCLUSIONS: The key driver of difference between the models was the inclusion of extra evidence-based detail in SPHR on the impacts of treatments on HbA1c. The conclusions were less sensitive to the dataset used to inform the risk factor trajectories. These findings strengthen the original cost-effectiveness analyses of the weight management interventions and provide an increased understanding of what is structurally important in the models.

Evaluation of machine learning models for cytochrome P450 3A4, 2D6, and 2C9 inhibition.

Cytochrome P450 (CYP) enzymes are involved in the metabolism of approximately 75% of marketed drugs. Inhibition of the major drug-metabolizing P450s could alter drug metabolism and lead to undesirable drug-drug interactions. Therefore, it is of great significance to explore the inhibition of P450s in drug discovery. Currently, machine learning including deep learning algorithms has been widely used for constructing in silico models for the prediction of P450 inhibition. These models exhibited varying predictive performance depending on the use of machine learning algorithms and molecular representations. This leads to the difficulty in the selection of appropriate models for practical use. In this study, we systematically evaluated the conventional machine learning and deep learning models for three major P450 enzymes, CYP3A4, CYP2D6, and CYP2C9 from several perspectives, such as algorithms, molecular representation, and data partitioning strategies. Our results showed that the XGBoost and CatBoost algorithms coupled with the combined fingerprint/physicochemical descriptor features exhibited the best performance with Area Under Curve (AUC)  of 0.92, while the deep learning models were generally inferior to the conventional machine learning models (average AUC reached 0.89) on the same test sets. We also found that data volume and sampling strategy had a minor effect on model performance. We anticipate that these results are helpful for the selection of molecular representations and machine learning/deep learning algorithms in the P450 model construction and the future model development of P450 inhibition.

Genomic analysis of feed efficiency traits in beef cattle using random regression models.

Feed efficiency plays a major role in the overall profitability and sustainability of the beef cattle industry, as it is directly related to the reduction of the animal demand for input and methane emissions. Traditionally, the average daily feed intake and weight gain are used to calculate feed efficiency traits. However, feed efficiency traits can be analysed longitudinally using random regression models (RRMs), which allow fitting random genetic and environmental effects over time by considering the covariance pattern between the daily records. Therefore, the objectives of this study were to: (1) propose genomic evaluations for dry matter intake (DMI), body weight gain (BWG), residual feed intake (RFI) and residual weight gain (RWG) data collected during an 84-day feedlot test period via RRMs; (2) compare the goodness-of-fit of RRM using Legendre polynomials (LP) and B-spline functions; (3) evaluate the genetic parameters behaviour for feed efficiency traits and their implication for new selection strategies. The datasets were provided by the EMBRAPA-GENEPLUS beef cattle breeding program and included 2920 records for DMI, 2696 records for BWG and 4675 genotyped animals. Genetic parameters and genomic breeding values (GEBVs) were estimated by RRMs under ssGBLUP for Nellore cattle using orthogonal LPs and B-spline. Models were compared based on the deviance information criterion (DIC). The ranking of the average GEBV of each test week and the overall GEBV average were compared by the percentage of individuals in common and the Spearman correlation coefficient (top 1%, 5%, 10% and 100%). The highest goodness-of-fit was obtained with linear B-Spline function considering heterogeneous residual variance. The heritability estimates across the test period for DMI, BWG, RFI and RWG ranged from 0.06 to 0.21, 0.11 to 0.30, 0.03 to 0.26 and 0.07 to 0.27, respectively. DMI and RFI presented within-trait genetic correlations ranging from low to high magnitude across different performance test-day. In contrast, BWG and RWG presented negative genetic correlations between the first 3 weeks and the other days of performance tests. DMI and RFI presented a high-ranking similarity between the GEBV average of week eight and the overall GEBV average, with Spearman correlations and percentages of individuals selected in common ranging from 0.95 to 1.00 and 93 to 100, respectively. Week 11 presented the highest Spearman correlations (ranging from 0.94 to 0.98) and percentages of individuals selected in common (ranging from 85 to 94) of BWG and RWG with the average GEBV of the entire period of the test. In conclusion, the RRM using linear B-splines is a feasible alternative for the genomic evaluation of feed efficiency. Heritability estimates of DMI, RFI, BWG and RWG indicate enough additive genetic variance to achieve a moderate response to selection. A new selection strategy can be adopted by reducing the performance test to 56 days for DMI and RFI selection and 77 days for BWG and RWG selection.

Utilising raw psycho-physiological data and functional data analysis for estimating mental workload in human drivers.

Recent studies have focused on accurately estimating mental workload using machine learning algorithms and extracting features from physiological measures. However, feature extraction leads to the loss of valuable information and often results in binary classifications that lack specificity in the identification of optimum mental workload. This study investigates the feasibility of using raw physiological data (EEG, facial EMG, ECG, EDA, pupillometry) combined with Functional Data Analysis (FDA) to estimate the mental workload of human drivers. A driving scenario with five tasks was employed, and subjective ratings were collected. Results demonstrate that the FDA applied nine different combinations of raw physiological signals achieving a maximum 90% accuracy, outperforming extracted features by 73%. This study shows that the mental workload of human drivers can be accurately estimated without utilising burdensome feature extraction. The approach proposed in this study offers promise for mental workload assessment in real-world applications.

This study aimed to estimate the mental workload of human drivers using physiological signals and Functional Data Analysis (FDA). By comparing models using raw data and extracted features, the results show that the FDA with raw data achieved a high accuracy of 90%, outperforming the model with extracted features (73%).

Opinion Models, Election Data, and Political Theory.

A unifying setup for opinion models originating in statistical physics and stochastic opinion dynamics are developed and used to analyze election data. The results are interpreted in the light of political theory. We investigate the connection between Potts (Curie-Weiss) models and stochastic opinion models in the view of the Boltzmann distribution and stochastic Glauber dynamics. We particularly find that the q-voter model can be considered as a natural extension of the Zealot model, which is adapted by Lagrangian parameters. We also discuss weak and strong effects (also called extensive and nonextensive) continuum limits for the models. The results are used to compare the Curie-Weiss model, two q-voter models (weak and strong effects), and a reinforcement model (weak effects) in explaining electoral outcomes in four western democracies (United States, Great Britain, France, and Germany). We find that particularly the weak effects models are able to fit the data (Kolmogorov-Smirnov test) where the weak effects reinforcement model performs best (AIC). Additionally, we show how the institutional structure shapes the process of opinion formation. By focusing on the dynamics of opinion formation preceding the act of voting, the models discussed in this paper give insights both into the empirical explanation of elections as such, as well as important aspects of the theory of democracy. Therefore, this paper shows the usefulness of an interdisciplinary approach in studying real world political outcomes by using mathematical models.

Observing cognitive processes in time through functional MRI model comparison.

The temporal specificity of functional magnetic resonance imaging (fMRI) is limited by a sluggish and locally variable hemodynamic response trailing the neural activity by seconds. Here, we demonstrate for an attention capture paradigm that it is, never the less, possible to extract information about the relative timing of regional brain activity during cognitive processes on the scale of 100 ms by comparing alternative signal models representing early versus late activation. We demonstrate that model selection is not driven by confounding regional differences in hemodynamic delay. We show, including replication, that the activity in the dorsal anterior insula is an early signal predictive of behavioral performance, while amygdala and ventral anterior insula signals are not. This specific finding provides new insights into how the brain assigns salience to stimuli and emphasizes the role of the dorsal anterior insula in this context. The general analytic approach, named "Cognitive Timing through Model Comparison" (CTMC), offers an exciting and novel method to identify functional brain subunits and their causal interactions.

Ion transport properties in the pH-dependent bipolar nanochannels.

In recent years, researchers have made significant strides in understanding the ion transport characteristics of nanochannels, resulting in the development of various materials, modifications, and shapes of nano ion channel membranes. The aim is to create a nanochannel membrane with optimal ion transport properties and high stability by adjusting factors, such as channel size, surface charge, and wettability. However, during the nanochannel film fabrication process, controlling the geometric structures of nanochannels can be challenging. Therefore, exploring the stability of nanochannel performance under different geometric structures has become an essential aspect of nanochannel design. This article focuses on the study of cylindrical nanochannel structures, which are categorized based on the different methods for generating bipolar surface charges on the channel's inner surface, either through pH gradient effects or different material types. Through these two approaches, the study designed and analyzed the stability of ion transport characteristics in two nanochannel models under varying geometric structures. Our findings indicate that nanochannels with bipolar properties generated through pH gradients demonstrate more stable ion selection, whereas nanochannels with bipolar properties generated through different materials show stronger stability in ion rectification. This conclusion provides a theoretical foundation for future nanochannel designs.

Cost-Effectiveness of Respiratory Syncytial Virus Preventive Interventions in Children: A Model Comparison Study.

OBJECTIVES: Model-based cost-effectiveness analyses on maternal vaccine (MV) and monoclonal antibody (mAb) interventions against respiratory syncytial virus (RSV) use context-specific data and produce varied results. Through model comparison, we aim to characterize RSV cost-effectiveness models and examine drivers for their outputs. METHODS: We compared 3 static and 2 dynamic models using a common input parameter set for a hypothetical birth cohort of 100 000 infants. Year-round and seasonal programs were evaluated for MV and mAb interventions, using available evidence during the study period (eg, phase III MV and phase IIb mAb efficacy). RESULTS: Three static models estimated comparable medically attended (MA) cases averted versus no intervention (MV, 1019-1073; mAb, 5075-5487), with the year-round MV directly saving ∼€1 million medical and €0.3 million nonmedical costs, while gaining 4 to 5 discounted quality-adjusted life years (QALYs) annually in <1-year-olds, and mAb resulting in €4 million medical and €1.5 million nonmedical cost savings, and 21 to 25 discounted QALYs gained. In contrast, both dynamic models estimated fewer MA cases averted (MV, 402-752; mAb, 3362-4622); one showed an age shift of RSV cases, whereas the other one reported many non-MA symptomatic cases averted, especially by MV (2014). These differences can be explained by model types, assumptions on non-MA burden, and interventions' effectiveness over time. CONCLUSIONS: Our static and dynamic models produced overall similar hospitalization and death estimates, but also important differences, especially in non-MA cases averted. Despite the small QALY decrement per non-MA case, their larger number makes them influential for the costs per QALY gained of RSV interventions.

A quantitative assessment of the consistency of projections from five mathematical models of the HIV epidemic in South Africa: a model comparison study.

BACKGROUND: Mathematical models are increasingly used to inform HIV policy and planning. Comparing estimates obtained using different mathematical models can test the robustness of estimates and highlight research gaps. As part of a larger project aiming to determine the optimal allocation of funding for HIV services, in this study we compare projections from five mathematical models of the HIV epidemic in South Africa: EMOD-HIV, Goals, HIV-Synthesis, Optima, and Thembisa. METHODS: The five modelling groups produced estimates of the total population, HIV incidence, HIV prevalence, proportion of people living with HIV who are diagnosed, ART coverage, proportion of those on ART who are virally suppressed, AIDS-related deaths, total deaths, and the proportion of adult males who are circumcised. Estimates were made under a "status quo" scenario for the period 1990 to 2040. For each output variable we assessed the consistency of model estimates by calculating the coefficient of variation and examining the trend over time. RESULTS: For most outputs there was significant inter-model variability between 1990 and 2005, when limited data was available for calibration, good consistency from 2005 to 2025, and increasing variability towards the end of the projection period. Estimates of HIV incidence, deaths in people living with HIV, and total deaths displayed the largest long-term variability, with standard deviations between 35 and 65% of the cross-model means. Despite this variability, all models predicted a gradual decline in HIV incidence in the long-term. Projections related to the UNAIDS 95-95-95 targets were more consistent, with the coefficients of variation below 0.1 for all groups except children. CONCLUSIONS: While models produced consistent estimates for several outputs, there are areas of variability that should be investigated. This is important if projections are to be used in subsequent cost-effectiveness studies.

Comparison and multi-model inference of excess risks models for radiation-related solid cancer.

In assessments of detrimental health risks from exposures to ionising radiation, many forms of risk to dose-response models are available in the literature. The usual practice is to base risk assessment on one specific model and ignore model uncertainty. The analysis illustrated here considers model uncertainty for the outcome all solid cancer incidence, when modelled as a function of colon organ dose, using the most recent publicly available data from the Life Span Study on atomic bomb survivors of Japan. Seven recent publications reporting all solid cancer risk models currently deemed plausible by the scientific community have been included in a model averaging procedure so that the main conclusions do not depend on just one type of model. The models have been estimated with different baselines and presented for males and females at various attained ages and ages at exposure, to obtain specially computed model-averaged Excess Relative Risks (ERR) and Excess Absolute Risks (EAR). Monte Carlo simulated estimation of uncertainty on excess risks was accounted for by applying realisations including correlations in the risk model parameters. Three models were found to weight the model-averaged risks most strongly depending on the baseline and information criteria used for the weighting. Fitting all excess risk models with the same baseline, one model dominates for both information criteria considered in this study. Based on the analysis presented here, it is generally recommended to take model uncertainty into account in future risk analyses.

Bayesian inference of chromatin structure ensembles from population-averaged contact data.

Mounting experimental evidence suggests a role for the spatial organization of chromatin in crucial processes of the cell nucleus such as transcription regulation. Chromosome conformation capture techniques allow us to characterize chromatin structure by mapping contacts between chromosomal loci on a genome-wide scale. The most widespread modality is to measure contact frequencies averaged over a population of cells. Single-cell variants exist, but suffer from low contact numbers and have not yet gained the same resolution as population methods. While intriguing biological insights have already been garnered from ensemble-averaged data, information about three-dimensional (3D) genome organization in the underlying individual cells remains largely obscured because the contact maps show only an average over a huge population of cells. Moreover, computational methods for structure modeling of chromatin have mostly focused on fitting a single consensus structure, thereby ignoring any cell-to-cell variability in the model itself. Here, we propose a fully Bayesian method to infer ensembles of chromatin structures and to determine the optimal number of states in a principled, objective way. We illustrate our approach on simulated data and compute multistate models of chromatin from chromosome conformation capture carbon copy (5C) data. Comparison with independent data suggests that the inferred ensembles represent the underlying sample population faithfully. Harnessing the rich information contained in multistate models, we investigate cell-to-cell variability of chromatin organization into topologically associating domains, thus highlighting the ability of our approach to deliver insights into chromatin organization of great biological relevance.

New Frontiers in Prevention Research Models: Commentary on the Special Issue.

Models considered in the current special issue represent valuable additions to the statistical toolbox of prevention researchers for many types of research questions and designs. Their appropriate use, however, depends on critical evaluation relative to previously existing techniques. This evaluation includes (a.) model choice involving "right-sizing" of the model relative to the amount and quality of data at hand, (b.) examination of the external validity of identified associations relative to observed or latent subgroups, (c.) confirmation of the reasonableness of the functional form assumed by the model, and (d.) identification of influential or outlying observations which unduly affect model fit or parameter estimates. Models in this issue allow for testing of new types of hypotheses in prevention research, and can constitute counterarguments to existing statistical practice. These models may, however, in turn be the object of critical examination of counterarguments a reasonable skeptic may offer.

Random regression models to estimate genetic parameters for milk yield, fat, and protein contents in Tunisian Holsteins.

This study aimed to find the parsimonious random regression model (RRM) to evaluate the genetic potential for milk yield (MY), fat content (FC), and protein content (PC) in Tunisian Holstein cows. For this purpose, 551,139; 331,654; and 302,396 test day records for MY, FC, and PC were analysed using various RRMs with different Legendre polynomials (LP) orders on additive genetic (AG) and permanent environmental (PE) effects, and different types of residual variances (RV). The statistical analysis was performed in a Bayesian framework with Gibbs sampling, and the model performances were assessed, mainly, on the predictive ability criteria. The study found that the optimal model for evaluating these traits was an RRM with a third LP order and nine classes of heterogeneous RV. In addition, the study found that heritability estimates for MY, FC, and PC ranged from 0.11 to 0.22, 0.11 to 0.17, and 0.12 to 0.18, respectively, indicating that genetic improvement should be accompanied by improvements in the production environment. The study also suggested that new selection rules could be used to modify lactation curves by exploiting the canonical transformation of the random coefficient covariance (RC) matrix or by using the combination of slopes of individual lactation curves and expected daily breeding values.

The quest for simplicity in human learning: Identifying the constraints on attention.

For better or worse, humans live a resource-constrained existence; only a fraction of physical sensations ever reach conscious awareness, and we store a shockingly small subset of these experiences in memory for later use. Here, we examined the effects of attention constraints on learning. Among models that frame selective attention as an optimization problem, attention orients toward information that will reduce errors. Using this framing as a basis, we developed a suite of models with a range of constraints on the attention available during each learning event. We fit these models to both choice and eye-fixation data from four benchmark category-learning data sets, and choice data from another dynamic categorization data set. We found consistent evidence for computations we refer to as "simplicity", where attention is deployed to as few dimensions of information as possible during learning, and "competition", where dimensions compete for selective attention via lateral inhibition.

Infant temperament, early-childhood parenting, and early-adolescent development: Testing alternative models of Parenting × Temperament interaction.

Here we evaluate whether infant difficult temperament (6 months) functions as a vulnerability or more general plasticity factor when investigating effects of early-childhood parenting (8-42 months) on both positive and negative early-adolescent socioemotional development (age 8-11 years). Using data from the Avon Longitudinal Study of Parents and Children (ALSPAC, N = 14,541) and a re-parameterized model-testing approach to distinguish alternative person × environment conceptual models, results indicated that temperament × parenting interacted in predicting externalizing (i.e., hyperactivity, conduct problems), but not other behavior (i.e., emotional symptoms, peer problems), in a (weak) differential susceptibility manner. While more and less supportive parenting predicted, respectively, fewer and more behavior problems, it did so more strongly for children who were more difficult as infants.

A group theoretic approach to model comparison with simplicial representations.

The complexity of biological systems, and the increasingly large amount of associated experimental data, necessitates that we develop mathematical models to further our understanding of these systems. Because biological systems are generally not well understood, most mathematical models of these systems are based on experimental data, resulting in a seemingly heterogeneous collection of models that ostensibly represent the same system. To understand the system we therefore need to understand how the different models are related to each other, with a view to obtaining a unified mathematical description. This goal is complicated by the fact that a number of distinct mathematical formalisms may be employed to represent the same system, making direct comparison of the models very difficult. A methodology for comparing mathematical models based on their underlying conceptual structure is therefore required. In previous work we developed an appropriate framework for model comparison where we represent models, specifically the conceptual structure of the models, as labelled simplicial complexes and compare them with the two general methodologies of comparison by distance and comparison by equivalence. In this article we continue the development of our model comparison methodology in two directions. First, we present a rigorous and automatable methodology for the core process of comparison by equivalence, namely determining the vertices in a simplicial representation, corresponding to model components, that are conceptually related and the identification of these vertices via simplicial operations. Our methodology is based on considerations of vertex symmetry in the simplicial representation, for which we develop the required mathematical theory of group actions on simplicial complexes. This methodology greatly simplifies and expedites the process of determining model equivalence. Second, we provide an alternative mathematical framework for our model-comparison methodology by representing models as groups, which allows for the direct application of group-theoretic techniques within our model-comparison methodology.