Mathematics

The COVID-19 pandemic has presented severe challenges in understanding and predicting the spread of infectious diseases, necessitating innovative approaches beyond traditional epidemiological models. This study introduces an advanced method for automated model discovery using the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm, leveraging a dataset from the COVID-19 outbreak in Thuringia, Germany, encompassing over 400,000 patient records and vaccination data. By analysing this dataset, we develop a flexible, data-driven model that captures many aspects of the complex dynamics of the pandemics spread. Our approach incorporates external factors and interventions into the mathematical framework, leading to more accurate modelling of the pandemics behaviour. The fixed coefficient values of the differential equation as globally determined by the SINDy were not found to be accurate for locally modelling the measured data. We therefore refined our technique based on the differential equations as found by SINDy, by investigating three modifications that account for recent local data. In a first approach, we re-optimized the coefficient values using seven days of past data, without changing the globally determined differential equation. In a second approach, we allowed a temporal dependence of the coefficient values fitted using all previous data in combination with regularization. As a last method, we kept the coefficients fixed to the original values but augmented the differential equation with a small neural network, locally optimized to the data of the past week. Our findings reveal the critical role of vaccination and public health measures in the pandemics trajectory. The proposed model offers a robust tool for policymakers and health professionals to mitigate future outbreaks, providing insights into the efficacy of intervention strategies and vaccination campaigns. This study advances the understanding of COVID-19 dynamics and lays the groundwork for future research in epidemic modelling, emphasising the importance of adaptive, data-informed approaches in public health planning.

AO_SCPLOWBSTRACTC_SCPLOWWe study an extension of an environmentally mediated epidemiological model that incorporates direct human-to-human transmission. While the original formulation accounted for environmental exposure, it did not include direct transmission between individuals. Allowing both transmission routes to interact leads to significant qualitative changes in the system dynamics. The analysis reveals multiple dynamical regimes governed by environmental and combined threshold quantities. The stability of the disease-free equilibrium is controlled by an environmental threshold, whereas a combined reproduction number determines the onset of multistability. For certain parameter ranges, endemic equilibria coexist with the disease-free equilibrium, giving rise to backward-type bifurcation behavior and sensitivity to initial conditions. Moreover, the direct transmission rate acts as an organizing parameter by inducing the emergence of an environmental-free equilibrium when exceeding its classical threshold. These results highlight how environmentally coupled transmission mechanisms can generate rich dynamics in low-dimensional models.

Infectious disease surveillance systems in tropical countries show that respiratory disease incidence generally manifests as year-round activity with weak fluctuations and irregular seasonality. Previously, using a ten-year time series of influenza-like illness (ILI) collected from outpatient clinics in Ho Chi Minh City (HCMC), Vietnam, we found a combination of nonannual and annual signals driving these dynamics, but with unknown mechanisms. In this study, we use seven stochastic dynamical models incorporating humidity, temperature, and school term to investigate plausible mechanisms behind these annual and nonannual incidence trends. We use iterated filtering to fit the models and evaluate the models by comparing how well they replicate the combination of annual and nonannual signals. We find that a model including specific humidity, temperature, and school term best fits our observed data from HCMC and partially reproduces the irregular seasonality. The estimated effects from specific humidity and temperature on transmission are nonlinearly negative but weak. School dismissal is associated with decreased transmission, but also with low magnitude. Under these weak external drivers, we hypothesize that stochasticity makes a strong sub-annual cycle more likely to be observed in ILI disease dynamics. Our study shows a possible mechanism for respiratory disease dynamics in the tropics. When the external drivers are weak, the seasonality of respiratory disease dynamics is prone to the influence of stochasticity.

We describe an approach for analyzing biological networks using rows of the Krylov subspace of the adjacency matrix. Specifically, we explore the scenario where the Krylov subspace matrix is computed via power iteration using a non-random and potentially non-uniform initial vector that captures a specific biological state or perturbation. In this case, the rows the Krylov subspace matrix (i.e., Krylov trajectories) carry important functional information about the network nodes in the biological context represented by the initial vector. We demonstrate the utility of this approach for community detection and perturbation analysis using the C. Elegans neural network.

Food costs are more significantly impacted by climate change as countries grow. It is well known that climate change has an impact on the productivity of most agricultural goods, but it is unclear how specifically it will affect food costs. The present research explores how the North Atlantic Oscillation (NAO) index, a widely used climate indicator, affects food prices around the world. This is achieved by applying a robust bivariate Hurst exponent (robust bHe). The research creates a color map of this coefficient using a window-sliding technique over various intervals of time, displaying an illustration that changes overtime. Additionally, the NAO index and global food prices are examined for causal connections using variable-lag transfer entropy using a window-sliding technique. The results show that notable rises in a number of international food prices for long as well as short periods are associated with significant increases in the NAO index. Furthermore, the causative function of the NAO index in influencing global food costs is confirmed by variable-lag transfer entropy. Is highly recommended as it directly connects the research to actionable outcomes for policymakers and the overarching goal of sustainability and food security. This study provides the first direct evidence of a robust, long-range cross-correlation and causal link between the North Atlantic Oscillation (NAO) index and key global food prices. It introduces a novel, robust methodological framework to visualize this time-varying relationship, offering a critical tool for policymakers and forecasting models.

Following the suggestion of L. F. Jaffe [1] we propose a mathematical model of fast calcium induced calcium influx waves (CICI Waves). They can propagate at relatively high speeds (up to 1300 micrometers/s). According to [1], they propagate due to a mechanochemical interaction of actomyosin network with the cell membrane. The local stretching of the membrane caused by actin filaments opens mechanically operated ion channels resulting in the influx of calcium to the cell. Moreover, stretching a cells membrane at one point opens nearby stretch activated calcium channels because the mechanical force is relayed by the actin filaments interconnected by myosin bridges. The number of bridges as well as filament density increases with calcium concentration, causing the contraction of the actomyosin network. Thus, the force acting on the membrane from tangled actin filaments is transmitted ahead of the moving front of the calcium concentration. As a result, the ion channels are opened even before the signal of calcium reaches them. This leads to much larger propagation speed of CICI waves in comparison with calcium induced calcium released (CICR) waves, where the wave is sustained by the diffusion of calcium and autocatalytic release of calcium from the internal stores (e.g. endoplasmic reticula).

This study presents a theoretical and mathematical framework for understanding the dynamical behavior of infectious disease spread using a compartmental modeling approach. The proposed model incorporates memory effects to capture temporal dependencies that are not adequately represented by classical formulations. Qualitative analysis is employed to investigate the stability properties of the system and the role of key mechanisms in shaping long term dynamics. Publicly available surveillance information is used only to illustrate the consistency of the model behavior with observed trends. The results highlight the value of memory based modeling structures for describing complex biological processes and provide a general mathematical perspective for studying epidemic dynamics.

Tetanus is a severe disease of the nervous system, transmitted through bacteria in the environment. In the absence of medical attention, case fatality rates are extremely high. Despite progress towards maternal and neonatal tetanus elimination targets, tetanus remains a serious public health problem. Routine infant and maternal vaccination have contributed to considerable reduction in cases and deaths from tetanus globally. However, protective immunity wanes over time. To increase duration of protection, the World Health Organization recommends three diphtheria-tetanus-pertussis-containing vaccine booster doses be given in early childhood, childhood, and adolescence. Evidence to support country-level decision-making about the introduction of these booster doses is critical. We have developed a novel age-structured, deterministic compartmental model of tetanus transmission and vaccination. The model is driven by environmental transmission and incorporates interventions like hygiene and safe birth practices to reduce the magnitude of environmental transmission. It explicitly models vaccination, separating each dose of the primary series, booster doses, and maternal vaccination to capture dose-specific effectiveness and duration of protection. The model captures heterogeneous immunity profiles by dose and age, and the cumulative nature of vaccine-derived protection. The immune dynamics follow the patterns described in literature and can replicate seroprevalence studies, although the exact characterisation of immunity in the literature still has gaps. This model presents a substantial advancement on previously published models and is well positioned to inform tailored vaccination strategies to reduce neonatal and non-neonatal tetanus.

Vaccine-acquired immunity plays an important role in controlling the spread of many infectious diseases; however, vaccine efficacy can diminish over time. This work uses a mathematical model to study the effects of waning vaccination-acquired immunity on infection incidence. With an SEIR-type compartmental model that considers both vaccinated and unvaccinated populations (and their mixing), we present mathematical conditions under which vaccinated individuals drive ongoing growth in infections, i.e., over half of the daily incidence arises from vaccinated individuals. Analysis of a mathematical model of COVID-19 spread in the state of Colorado suggests how and for what duration vaccinated individuals could have sustained such growth. Importantly, our model demonstrates that, despite potential for brief vaccinated-driven periods of growth in infections, which occur among unvaccinated-driven periods of growth in infections, increased vaccination coverage always reduces total cases and total hospitalizations. This work provides insight into how waning immunity in vaccinated populations can contribute to ongoing infection incidence and demonstrates the value of complementary interventions to prevent disease spread in vaccinated populations.

Graph-based methods for data representation and analysis are well suited for encoding both data points and their interrelationships. This approach integrates data and topology, enabling the representation of interrelated information. In this study, we represent patient cohorts as cohort graphs and discuss their application for real-world patient data. We particularly focus on developing methods to cluster patients with similar symptoms and examine how bias parameters (such as sex and age group) influence interlinking within CGs, thereby improving results for accurate patient stratification and personalized decision-making in a clinical context. In particular we illustrate how by considering sex and age groups we can improve the symptom-clustering of a patient population with lung and gastro-intestinal cancer. Finally, we discuss the essential role of high-performance computing (HPC) in upscaling analytical methods for CGs.

The environments inhabited by flying insects demand a balance between flight efficiency and flight manoeuvrability. In structural oscillators such as the insect indirect flight motor, efficiency (arising from resonance) and manoeuvrability (arising from kinematic modulation) are typically quid pro quo, with modulation incurring penalties to efficiency. Band-type resonance is a phenomenon that offers, in theory, a strategy to lessen these penalties via careful navigation through a band of efficient kinematic states. However, identifying this band is challenging: no methods exist to identify the complete band in realistic motor models, involving elasticity distributed across thorax and wing. Nor are the effects of elasticity distribution on the band known. In this work, we address both open topics. We present a suite of numerical methods for identifying the complete resonance band in general systems. Applying them to models of the insect flight motor with distributed elasticity--thoracic and wing flexion--reveals that distributed elasticity is moderate-risk but high-reward morphological feature. Well-tuned distributions expand the resonance band over fourfold whereas poorly-tuned distributions completely extinguish the resonance band. These results indicate that distributing elasticity across the insect flight motor can have adaptive value, and motivate broader work identifying distributions across species.

Closed-form minimum sample size criteria for developing logistic prediction models, such as the Riley framework implemented in pmsampsize, are widely used but may become optimistic when anticipated discrimination is high. We conducted a Monte Carlo simulation study to compare the formula-based recommended development sample size, nRiley, with an empirical required sample size, nreq, defined by out-of-sample calibration-slope stability under repeated development sampling. Scenarios fixed the candidate parameter dimension at p = 10 and crossed predictor distribution (normal, standardized skewed continuous, binary), signal density (dense versus sparse), prevalence ({phi} [isin] {0.05, 0.10, 0.20}), and target discrimination (AUCtarget [isin] {0.70, 0.75, 0.80, 0.85, 0.90}), with intercept and signal strength calibrated to match targets. We defined nreq as the smallest n such that [E] (bn) [&ge;] 0.90 and Pr(bn < 0.80) [&le;] 0.20, where bn is the truth-based logit-scale calibration slope evaluated on a large fixed validation covariate set. At moderate discrimination, nRiley approximated nreq, but as discrimination increased the formula increasingly underestimated the sample size required for calibration stability, with large deficits at AUCtarget = 0.90. Separation-like behavior (extreme fitted risks and linear predictors) at n = nRiley became common in high-discrimination settings despite nominal convergence, providing a plausible mechanism for formula optimism. These findings support augmenting formula-based planning with targeted simulation stress tests and instability diagnostics when high discrimination is anticipated.

ObjectiveThis study investigates whether incorporating physiological coupling concepts into neural network design can support stable and interpretable feature learning for histopathological image classification under limited data conditions. MethodsA physiologically inspired architecture, termed CardioPulmoNet, is introduced to model interacting feature streams analogous to pulmonary ventilation and cardiac perfusion. Local and global tissue features are integrated through bidirectional multi-head attention, while a homeostatic regularization term encourages balanced information exchange between streams. The model was evaluated on three histopathological datasets involving oral squamous cell carcinoma, oral submucous fibrosis, and heart failure. In addition to end-to-end training, learned representations were assessed using linear support vector machines to examine feature separability. ResultsCardioPulmoNet achieved performance comparable to several pretrained convolutional neural networks across the evaluated datasets. When combined with a linear classifier, improved classification performance and higher area under the receiver operating characteristic curve were observed, suggesting that the learned feature embeddings are well structured for downstream discrimination. ConclusionThese results indicate that physiologically motivated architectural constraints may contribute to stable and discriminative representation learning in computational pathology, particularly when training data are limited. The proposed framework provides a step toward integrating physiological modeling principles into medical image analysis and may support future development of transferable and interpretable learning systems for histopathological diagnosis.

We present an approach to analysing cell homeostasis using a bond graph modelling approach that ensures that the conservation laws of physics (conservation of mass, charge, and energy, respectively) are satisfied for the interdependent biochemical, electrical, mechanical, and thermal energy storage mechanisms operating within the cell. We apply the bond graph approach to several cell membrane transport mechanisms and then consider how physics constrains intracellular electrolyte homeostasis for enterocytes (the epithelial absorptive cells of the gut). The model includes the electrogenic sodium-potassium ATPase pump (NKA), the glucose transporter (GLUT2), and an inwardly rectifying potassium channel, all in the basolateral membrane, and the electrogenic sodium-driven glucose transporter (SGLT1) in the apical membrane. Glycolysis converts the imported glucose to ATP to drive NKA. For specified levels of sodium, potassium, and glucose in the blood, the model demonstrates how enterocytes absorb sodium and glucose from the gut and transfer glucose to the blood while maintaining the membrane potential and homeostasis of intracellular sodium and potassium. The Gibbs free energy available from the ATP hydrolysis ensures that the cell operates as a sodium battery with a high external to internal ratio of sodium concentration in order to provide the energy for many other cellular transport processes. We show that the 3:2 stoichiometry of Na+/K+ exchange in NKA, coupled with 2:1 Na+/glucose cotransport in SGLT1, a 1:2:2 ratio between glucose consumption and ATP and water production in glycolysis, and K+ and glucose efflux through Kir and GLUT2, respectively, provides a balanced system that maintains homeostasis of intracellular Na+, K+, glucose, ATP and water, and homeostasis of the membrane potential, under varying levels of transport of glucose from the gut to the blood. We also show how the flux expressions for SLC transporters, ATPase pumps and ion channels can all be expressed in a consistent and thermodynamically valid way.

Data scarcity and stylistic heterogeneity pose major challenges for emotion intensity classification. This paper presents a cross-dataset augmentation framework that leverages prompt-conditioned generative models alongside deterministic and heuristic transformations to synthesize target-style examples for improved transfer learning. We introduce a unified taxonomy of augmentation strategies--Heuristic Lexical Perturbation (HLA), Prompt-Conditioned Generative Augmentation (CGA), Sequential Hybrid Pipeline (SHA), Rule-Guided Style Adaptation (DSGA), and Enhanced Hybrid Augmentation (EHA)--and detail an interpretability-oriented prompt engineering approach that conditions LLMs on authentic target exemplars and stylistic features extracted from the target dataset. Augmented datasets were evaluated using multi-dimensional quality metrics (transformation quality, stylistic consistency, BLEU/CHRF, Self-BLEU, uniqueness) and downstream classification via a two-phase BERT-LSTM training with rigorous statistical testing. During source dataset pretraining and subsequent target dataset fine-tuning, CGA achieved the highest single-method gains in F1 and accuracy (F1 = 0.8816; accuracy = 0.8819, 95% CI recalculated). HLA and SHA exhibited improved cross-domain stability, suggesting stronger domain-generalizable features. We observe systematic trade-offs between fluency, lexical diversity, and emotion fidelity: high surface similarity often correlates with classifier performance but does not fully capture affective authenticity. We discuss methodological pitfalls, propose best practices for emotion-aware augmentation, and provide reproducible artifacts (prompts, example transformations, evaluation scripts) to facilitate further research in affective NLP.

Short-horizon epidemic forecasting is difficult when surveillance series are highly nonstationary and affected by structural change and evolving reporting conditions. This study evaluates statistical models for global daily COVID-19 incidence using a rolling-origin benchmark designed to approximate real-time forecasting under such conditions. Using global incidence data from 22 January to 27 July 2020, we compare naive, seasonal naive, drift, ARIMA(log1p), ETS(log1p), and Prophet(log1p) forecasts at horizons h [isin] {1, 3, 7, 14} days. Structural phases are identified retrospectively on a variance-stabilized scale and used only to stratify forecast errors. Forecast ranking is strongly horizon-dependent. In the full-sample benchmark, drift performs best at the 1-, 7-, and 14-day horizons, while seasonal naive performs best at 3 days. Among the transformed statistical models, ARIMA(log1p) is competitive at short horizons, whereas ETS(log1p) becomes stronger at 7 and 14 days. Diebold-Mariano tests confirm that several of these differences are statistically meaningful, particularly in favor of drift at short and long horizons and in favor of ETS(log1p) over ARIMA(log1p) at longer horizons. Prophet(log1p) is not competitive in point forecasting and achieves high nominal interval coverage mainly through very wide prediction intervals. Robustness analyses show that the main ranking patterns are broadly stable to alternative segmentation settings, training-window policies, coverage-stabilized subsamples, and alternative target construction based on cumulative confirmed counts. Overall, the results show that simple baselines remain difficult to outperform in epidemic surveillance data and that horizon-specific rolling evaluation is essential for credible forecast comparison under structural change. Author summaryForecasting infectious disease incidence is difficult when case data change rapidly over time and when reporting systems are still evolving. In this study, I examined how several common statistical forecasting models perform on global daily COVID-19 incidence during the early pandemic. Rather than asking which model is best overall, I focused on whether model ranking changes across forecast horizons and whether those conclusions remain stable under different evaluation choices. I compared simple baselines, including naive, seasonal naive, and drift forecasts, with ARIMA, exponential smoothing, and Prophet models using a rolling-origin benchmark that mimics real-time forecasting. I found that forecast ranking depends strongly on the horizon: drift performed best at 1, 7, and 14 days, while seasonal naive performed best at 3 days. Among the transformed statistical models, ARIMA was more competitive at shorter horizons, whereas exponential smoothing was stronger at longer horizons. I also found that these conclusions remained broadly stable under alternative segmentation settings, training windows, coverage-stabilized subsamples, and target definitions. These results show that simple baselines can remain highly competitive in epidemic surveillance data and that horizon-specific evaluation is essential for fair forecast comparison under structural change.

Background: Atrial fibrillation (AFib) is the most common sustained arrhythmia in the world, imposing a heavy clinical and economic burden on global healthcare systems. Early detection of AFib can reduce mortality and morbidity, while helping to alleviate the growing economic burden of cardiovascular diseases. With the increasing availability of digital health technologies, computational solutions have great potential to support the timely diagnosis of cardiac abnormalities. Objectives: With the increasing availability of electrocardiogram (ECG) data from clinical and wearable devices, manual interpretation has become impractical due to its time-consuming and subjective nature. Existing automated approaches often rely on single classifiers or fixed ensembles that primarily optimize predictive accuracy while neglecting model diversity, which leads to limited robustness and generalization across heterogeneous datasets. Therefore, this study aims to develop a robust and diversity-aware framework for automatic AFib detection that simultaneously improves classification performance and model generalizability. To this end, we propose MOE-ECG, a multi-objective ensemble selection and fusion framework that explicitly optimizes both predictive performance and inter-model diversity for reliable AFib detection from ECG recordings. Methods: The proposed multi-objective ensemble (MOE) framework uses ensemble selection as a bi-objective optimization problem and employs multi-objective particle swarm optimization to identify complementary classifiers from a heterogeneous model pool. Unlike conventional ensembles, it explicitly optimizes both predictive performance and diversity and integrates Dempster-Shafer theory for uncertainty-aware decision fusion. After filtering the ECG signals to remove baseline wander and noise, they were segmented into windows of 20, 60, and 120 heartbeats with 50% overlap. The proposed approach was evaluated over five independent runs to assess its stability and generalization. Fifteen statistical and nonlinear features were obtained from the RR-intervals of the pre-processed ECG signals, of which eight features were selected with correlation analysis to capture subtle information from the ECG data. We trained and evaluated the performance of the proposed model in three open source databases, namely, the MIT-BIH Atrial Fibrillation Database, Saitama Heart Database Atrial Fibrillation, and Long-Term AF Database. Results: The proposed approach achieved the best overall performance on 60-beat segments, with an average accuracy of 89.85%, precision of 91.14%, recall of 94.19%, an F1-score of 92.64%, and area under the curve (AUC) of around 0.95. Statistical analysis using Holm-adjusted Wilcoxon tests confirmed significant improvements (p<0.05) compared to both the best individual classifier and the unoptimized average ensemble of all classifiers. These findings show that the proposed selection and evaluation methodology, rather than group aggregation alone, is the key driver of performance improvements. Conclusion: The results obtained demonstrate that the MOE-ECG model offers a robust, accurate, and reliable solution for the detection of AFib from short ECG segments. The empirical findings, in general, confirm that multi-objective ensemble fusion enhances diagnostic performance and offers robust predictions that will open up possibilities for real-time AFib detection in clinical and tele-health settings.

Infectious diseases and chronic diseases are two major fields in epidemiology that have traditionally been studied separately because of their distinct etiologies and modeling methods. Infectious disease data are typically collected at an aggregated level and analyzed using compartmental models, most commonly the susceptible (S), infectious (I), and recovered (R) (SIR) model, whereas chronic disease data are usually collected at the individual level and analyzed using multi-state survival models. Previous studies have pointed out the link between compartmental models and survival analysis by reconstructing the aggregated infection disease data into individual-level data. However, these studies have largely focused on the two-state transition from S to I state, and few studies have simultaneously modeled the three-state process, S, I, and R. In this paper, we propose to use a discrete-time multi-state framework to model the three-state progression of infectious disease. We first introduce and compare the underlying methodological foundations for modeling infectious disease and chronic disease dynamics, then show the link between compartment models and multi-state models, and finally present how infectious disease can be modeled using the multi-state framework under the two scenarios: 1) all S, I, and R states are observed, and 2) only the I state is observed, with the R state treated as latent. In the application, we applied the multi-state approach to estimate the dynamics of influenza using the data in a British boarding school in 1978, where only the infected cases were observed over time. The estimated recovery rate was 0.42 and the corresponding contact rate was0.91 (95% CI: 0.84, 0.98). The basic reproductive number was 2.17 (95% CI: 2.00, 2.33), which declined to approximately 1 by day 6, and continued to decrease thereafter. Overall, we propose a unified multi-state approach for modeling infectious and chronic disease progression, which may provide evidence to inform timely and effective infectious disease prevention.

PurposeDeep learning models are increasingly being used in medical diagnostics, but their vulnerability to adversarial perturbations raises concerns about their reliability in clinical applications. Capsule networks (CapsNets) are a promising architecture for medical imaging tasks, given their ability to model spatial relationships and train with smaller amounts of data. Although previous studies have focused on adversarial training approaches to improve robustness, exploring alternative architectures is an underexplored direction for combating poor adversarial stability. Prior work has suggested that CapsNets may exhibit improved robustness to adversarial perturbations compared to convolutional neural networks (CNNs), but performance on adversarial images has not been studied systematically in clinical environments. We evaluated the robustness of CapsNets compared to CNNs and vision transformers (ViTs) across multiple medical image classification tasks. MethodsWe trained two CNNs (ResNet-18 and ResNet-50), one ViT (MedViT), and two CapsNets (DR-CapsNet and BP-CapsNet) on four distinct medical imaging datasets (PneumoniaMNIST, BreastMNIST, NoduleMNIST3D, and BloodMNIST) and one natural image dataset (MNIST). Models were evaluated on adversarial examples generated by projected gradient descent and fast gradient sign method across a range of perturbation bounds. Interpretability experiments, including latent space and Gradient-weighted Class Activation Mapping (Grad-CAM) analyses, were conducted to better understand model stability on adversarial inputs. ResultsCapsNets demonstrated superior robustness under adversarial perturbations compared to CNNs and ViTs across all medical imaging datasets and the natural image dataset. Latent space and Grad-CAM visualizations revealed that CapsNets maintained more consistent embedding representations and attention maps after adversarial perturbations compared to CNNs and ViTs, suggesting that advantages in CapsNet robustness are supported, at least in part, by more stable feature encodings. Bayes-Pearson routing further improved robustness over standard dynamic routing in CapsNets without compromising baseline performance, suggesting a potential architectural improvement. ConclusionCapsNets exhibit intrinsic advantages in adversarial robustness over CNN- and ViT-based models on medical imaging tasks, suggesting they are a reliable alternative for medical image classification. These findings support the use of CapsNets in clinical applications where model reliability is critical.

Genes with similar expression profiles often exhibit similar functional properties. An "integrated similarity score" (ISS) is developed by combining different expression similarity measures through weights, obtained using biological information, for improving gene similarity. The expression similarity measures are converted to the common framework of positive predictive value using functional annotation. A fitness function, called "fitness function using functional annotation of genes" (FFFAG), is also developed by minimizing the difference between functional similarity value and the ISS. The FFFAG is used to determine the weight combination of different similarity measures in ISS. In addition, an existing similarity measure, called TMJ (integrated similarity measure by multiplying Triangle and Jaccard similarity), is also modified to incorporate biological knowledge involving functional annotation. The results demonstrate that ISS is superior to individual similarity measure to find similar gene pairs. Further, the ISS predicts the functional categories of 40 unclassified yeast genes at p-value cutoff of 10-10 from 12 clusters. The associated code is accessible at http://www.isical.ac.in/[~]shubhra/ISS.html.