Related papers: Open Problems in Mathematical Biology
Development of several alternative mathematical models for the biological system in question and discrimination between such models using experimental data is the best way to robust conclusions. Models which challenge existing theories are…
Statistical mechanics is one of the most powerful and elegant tools in the quantitative sciences. One key virtue of statistical mechanics is that it is designed to examine large systems with many interacting degrees of freedom, providing a…
Mathematical modelling has a long history in the context of collective cell migration, with applications throughout development, disease and regenerative medicine. The aim of modelling in this context is to provide a framework in which to…
Increasingly sophisticated experiments, coupled with large-scale computational models, have the potential to systematically test biological hypotheses to drive our understanding of multicellular systems. In this short review, we explore key…
The role of mathematics in a complex system such as the Internet has yet to be deeply explored. In this paper, we summarize some of the important and pressing problems in cyber security from the viewpoint of open science environments. We…
Biological systems are generally complicated and/or complex. In the former approach, one sets up a model with a large number of parameters to describe the system in detail. The latter approach focuses on understanding the universal aspects…
The grand challenges in biology today are being shaped by powerful high-throughput technologies that have revealed the genomes of many organisms, global expression patterns of genes and detailed information about variation within…
The applicability of computational models to the biological world is an active topic of debate. We argue that a useful path forward results from abandoning hard boundaries between categories and adopting an observer-dependent, pragmatic…
Understanding the mechanisms of interactions within cells, tissues, and organisms is crucial to driving developments across biology and medicine. Mathematical modeling is an essential tool for simulating biological systems and revealing…
Mathematical models are increasingly a part of microbiological research. Here, we share our perspective on how modeling advances the discipline by: (i) enforcing logical consistency, (ii) enabling quantitative prediction, (iii) extracting…
The molecular biology revolution of the last seventy five years has transformed our view of living systems. Scientific explanations of biological phenomena are now synonymous with the identification of the genes, proteins, and signaling…
At its core, the physics paradigm adopts a reductionist approach, aiming to understand fundamental phenomena by decomposing them into simpler, elementary processes. While this strategy has been tremendously successful in physics, it has…
Modeling and simulation are recognized as important aspects of the scientific method for more than 70 years but its adoption in biology has been slow. Debates on its representativeness, usefulness, and whether the effort spent on such…
Systems biology models are useful models of complex biological systems that may require a large amount of experimental data to fit each model's parameters or to approximate a likelihood function. These models range from a few to thousands…
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.…
Many open problems in biology, as in the physical sciences, display nonlinear and 'chaotic' dynamics, which, to the extent possible, cannot be reasonably understood. Moreover, mathematical models which aim to predict/estimate unknown…
Integrative biological simulations have a varied and controversial history in the biological sciences. From computational models of organelles, cells, and simple organisms, to physiological models of tissues, organ systems, and ecosystems,…
Theoretical physics is the search for simple and universal mathematical descriptions of the natural world. In contrast, much of modern biology is an exploration of the complexity and diversity of life. For many, this contrast is prima facie…
This dissertation contributes to mathematical and algorithmic problems that arise in the analysis of network and biological data.
Many of life's most fascinating phenomena emerge from interactions among many elements--many amino acids determine the structure of a single protein, many genes determine the fate of a cell, many neurons are involved in shaping our thoughts…