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The mathematical models used to capture features of complex, biological systems are typically non-linear, meaning that there are no generally valid simple relationships between their outputs and the data that might be used to validate them.…
As metabolomics datasets are becoming larger and more complex, there is an increasing need for model-based data integration and analysis to optimally leverage these data. Dynamical models of metabolism allow for the integration of…
Traffic jams on roadways, echo chambers on social media, crowds of moving pedestrians, and opinion dynamics during elections are all complex social systems. These applications may seem disparate, but some of the questions that they motivate…
Data is a precious resource in today's society, and is generated at an unprecedented and constantly growing pace. The need to store, analyze, and make data promptly available to a multitude of users introduces formidable challenges in…
The abrupt outbreak and transmission of biological diseases has always been a long-time concern of humankind. For long, mathematical modeling has served as a simple and yet efficient tool to investigate, predict, and control spread of…
The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice becomes…
Molecular dynamics simulations hold great promise for providing insight into the microscopic behavior of complex molecular systems. However, their effectiveness is often constrained by long timescales associated with rare events. Enhanced…
Fueled by breakthrough technology developments, the biological, biomedical, and behavioral sciences are now collecting more data than ever before. There is a critical need for time- and cost-efficient strategies to analyze and interpret…
New technologies have enabled the investigation of biology and human health at an unprecedented scale and in multiple dimensions. These dimensions include a myriad of properties describing genome, epigenome, transcriptome, microbiome,…
Social science concerns issues on individuals, relationships, and the whole society. The complexity of research topics in social science makes it the amalgamation of multiple disciplines, such as economics, political science, and sociology,…
Measurement involves the determination of quantitative estimates of physical quantities from experiment, along with estimates of their associated uncertainties. Herewith an experimental system model is the key to extracting information from…
Quantitative social science is not only about regression analysis or, in general, data inference. Computer simulations of social mechanisms have a 60-year long history. They have been used for many different purposes -- to test scenarios,…
Molecular Dynamics (MD) simulation is widely used to analyze the properties of molecules and materials. Most practical applications, such as comparison with experimental measurements, designing drug molecules, or optimizing materials, rely…
This article explores mathematical models for understanding the evolution of contagious diseases. The most widely known set of models are the compartmental ones, which are based on a set of differential equations. But these are not the only…
Despite substantial potential to transform bioscience, medicine, and bioengineering, whole-cell models remain elusive. One of the biggest challenges to whole-cell models is assembling the large and diverse array of data needed to model an…
Formal modelling provides a toolkit for understanding cultural dynamics, from individual decisions to recurring patterns of change. This chapter explains what models are and why they matter. Using a precise, shared language, they aid…
Many mechanical engineering applications call for multiscale computational modeling and simulation. However, solving for complex multiscale systems remains computationally onerous due to the high dimensionality of the solution space.…
The aim of this chapter is to convey the importance and usefulness of mathematical modelling as a tool to achieve a deeper understanding of stem cell biology. We introduce key mathematical concepts (random walk theory, differential…
In the era of big data, analysts usually explore various statistical models or machine learning methods for observed data in order to facilitate scientific discoveries or gain predictive power. Whatever data and fitting procedures are…
Mathematical models are increasingly used in both academia and the pharmaceutical industry to understand how phenotypes emerge from systems of molecular interactions. However, their current construction as monolithic sets of equations…