Related papers: Geometric analysis enables biological insight from…
Understanding structure-property relations is essential to optimally design materials for specific applications. Two-scale simulations are often employed to analyze the effect of the microstructure on a component's macroscopic properties.…
Practical identifiability is a critical concern in data-driven modeling of mathematical systems. In this paper, we propose a novel framework for practical identifiability analysis to evaluate parameter identifiability in mathematical models…
The bifactor model and its extensions are multidimensional latent variable models, under which each item measures up to one subdimension on top of the primary dimension(s). Despite their wide applications to educational and psychological…
Geometric, topological and graph theory modeling and analysis of biomolecules are of essential importance in the conceptualization of molecular structure, function, dynamics, and transport. On the one hand, geometric modeling provides…
Comparing mathematical models offers a means to evaluate competing scientific theories. However, exact methods of model calibration are not applicable to many probabilistic models which simulate high-dimensional spatio-temporal data.…
In recent years, disease mapping studies have become a routine application within geographical epidemiology and are typically analysed within a Bayesian hierarchical model formulation. A variety of model formulations for the latent level…
The speed and the versatility of today's computers open up new opportunities to simulate complex biological systems. Here we review a computational approach recently proposed by us to model large tumor cell populations and spheroids, and we…
During the last decades, medical observations and multiscale data concerning tumor growth are mounting. At the same time, contemporary imaging techniques well established in clinical practice, provide a variety of information on real-time,…
Mammographic screening is an effective method for detecting breast cancer, facilitating early diagnosis. However, the current need to manually inspect images places a heavy burden on healthcare systems, spurring a desire for automated…
Cancer diagnosis, prognosis, and therapeutic response predictions are based on morphological information from histology slides and molecular profiles from genomic data. However, most deep learning-based objective outcome prediction and…
Researchers develop models to explain the unknowns. These models typically involve parameters that capture tangible quantities, the estimation of which is desired. Parameter identifiability investigates the recoverability of the unknown…
Cancer research has shifted from a purely gene-centric view to a more holistic understanding that recognizes the critical role of the tumour microenvironment, where mechanics and metabolism are key drivers of disease progression. However,…
Experience in the physical sciences suggests that the only realistic means of understanding complex systems is through the use of mathematical models. Typically, this has come to mean the identification of quantitative models expressed as…
Identifiability of discrete statistical models with latent variables is known to be challenging to study, yet crucial to a model's interpretability and reliability. This work presents a general algebraic technique to investigate…
In this study, we propose a method for extracting the hidden algebraic structures of model parameters that are uniquely determined by observed time-series data and unidentifiable state-space models, explicitly and exhaustively. State-space…
Machine learning (ML) and deep learning models are extensively used for parameter optimization and regression problems. However, not all inverse problems in ML are ``identifiable,'' indicating that model parameters may not be uniquely…
Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of…
Phylogenetic mixture models are statistical models of character evolution allowing for heterogeneity. Each of the classes in some unknown partition of the characters may evolve by different processes, or even along different trees. The…
Mathematical oncology provides unique and invaluable insights into tumour growth on both the microscopic and macroscopic levels. This review presents state-of-the-art modelling techniques and focuses on their role in understanding…
Recent advances in cancer research largely rely on new developments in microscopic or molecular profiling techniques offering high level of detail with respect to either spatial or molecular features, but usually not both. Here, we present…