Abstract Mathematical oncology integrates mechanistic modeling, experimental biology, clinical medicine, and data science to improve cancer detection, treatment planning, and understanding of tumor dynamics. This work provides a systematic review of the field, tracing its historical development from early population- level growth models and the log-kill hypothesis to contemporary spatial, evolutionary, multiscale, and data-driven approaches, supported by a large-scale bibliometric analysis of the discipline’s emergence and thematic clusters. The review surveys mechanistic descriptions of tumor growth, the tumor microenvironment, clonal evolution, and metastasis, before examining models of treatment response, optimal control of therapy, and evolutionary game theory as frameworks for understanding and counteracting drug resistance. Multiscale modeling approaches for coupling molecular, cellular, and tissue-level processes are discussed alongside data-driven methods, including genomics and bioinformatics, artificial intelligence, and mechanistic learning, which combines knowledge-driven mathematical models with data-driven machine learning. Particular attention is given to digital twins and their prospective clinical validation, and to the practical requirements for translating mathematical models into clinical implementation, including model validation, FAIR data principles, and shared benchmarking infrastructure. The review concludes by outlining future directions for the field, emphasizing that sustained interdisciplinary collaboration across mathematics, biology, data science, and clinical medicine, rather than any single modeling paradigm, will determine the extent to which mathematical oncology translates into improved patient care.
Abstract Mathematical oncology has developed into an increasingly active interdisciplinary field, providing quantitative tools for the study of tumor growth, invasion, metastasis, treatment response, and therapy optimization. Within this field, cellular automata form an important class of models. This overview focuses on cellular automata and their extensions in the context of mathematical oncology. We first introduce the necessary mathematical preliminaries and then present the basic formalism of cellular automata, beginning with deterministic models and elementary cellular automata. We continue with a presentation of biologically motivated extensions, including probabilistic cellular automata, lattice-gas cellular automata, Cellular Potts models, and hybrid cellular automata. Particular attention is given to focusing this survey on the reader with some background in mathematics or computer science, who is interested in first discovering the biological applications of the model. Finally, we review selected works from the recent literature.
Abstract Depression is a common and prognostically important comorbidity of chronic heart failure (CHF). Because datasets from cohort studies in this research area are often small and strongly imbalanced, and a ready-to-apply training and evaluation procedure for binary classification in this setting is still lacking, we provide a rigorous methodological overview and elaborate it into a straightforward protocol: leave-one-out cross-validation (LOOCV) with fixed seeds and default library hyperparameters, and a full panel of confusion matrix metrics, including imbalance-adjusted summaries. As an illustration of the chosen methodology, we reformulated the 9-item Patient Health Questionnaire (PHQ-9) screening as a binary classification task and compared three deliberately chosen standard methods—ridge-regularized logistic regression, decision tree, and RUSBoost—on a public cohort published by Cheng and co-authors in 2023. These methods are evaluated at each learner’s default operating point over the range of PHQ-9 binarization thresholds θ ∈ {1, . . . , 15}. RUSBoost obtained the best results at the standard diagnostic PHQ-9 cut-off θ = 10—sensitivity 0.641, specificity 0.619, accuracy 0.621 and a sensitivity– specificity gap of 0.022. As the only learner with built-in imbalance handling, it also consistently outperforms the two observation-weighted baselines on these metrics across the entire range of thresholds. However, absolute sensitivity and specificity remain below clinically ambitious levels for all three models. We attribute part of this performance ceiling to selection bias introduced during cohort acquisition and eligibility filtering.
Abstract The accurate classification of images into graphics-only, text-only, and mixed-content categories is a critical prerequisite for building efficient, content-aware processing pipelines. This initial triage prevents the unnecessary application of computationally expensive operations, such as Optical Character Recognition (OCR), to irrelevant graphical data. To address this challenge, we introduce the Contextualized Vision Transformer (CVT), a novel architecture designed specifically for this nuanced classification task. The CVT addresses the limitations of standard Vision Transformers (ViTs) through three synergistic components. It employs a Learnable Patch Decomposition (LPD) strategy that efficiently extracts patch embeddings. To model complex spatial arrangements, it introduces an Adaptive Spectral Embedding (ASE) module, which replaces static positional encodings with a dynamic, learnable representation. Crucially, a Contextual Feature Gating (CFG) module enhances feature discriminability by adaptively recalibrating patch-level features, selectively amplifying the salient text or graphic regions. Comprehensive K-fold cross-validation demonstrates the robustness and generalizability of the proposed model. The CVT achieves statistically significant improvements in accuracy, precision, and recall compared to state-of-the-art Vision Transformer baselines. Experimental results highlight the effectiveness of this architecture in providing a fast and accurate solution for the vital task of content triage in large-scale visual processing systems.
Abstract This paper introduces a novel framework for understanding intuitionistic values and fuzzy sets through the automorphism of the unit interval [0, 1]. By generalizing the concepts of classical intuitionistic sets using strong negations generated by these automorphisms, we define the φ -intuitionistic values and explore their arithmetic, establishing a comprehensive set of operations based mainly on additive generators of t-(co)norms and their properties. This approach provides greater flexibility to the modelling with these sets.
