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On inverse problems for several coupled PDE systems arising in mathematical biology
In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by...
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Oscillations in Biology
Experiments in molecular biology are generally performed in a static state; analytes are frozen in time and displayed as if there had been no changes...
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A celebration of Fred Brauer’s legacy in mathematical biology
Fred Brauer (1932–2021), one of the pioneers of mathematical population biology, shaped generations of researchers through his lines of research, his...
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Mathematical Biology: Looking Back and Going Forward
Mathematical biology has grown over the past 50 years from a niche subject, pursued by a small number of visionary pioneers, to a core sub-discipline...
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Teaching Dynamics to Biology Undergraduates: the UCLA Experience
There is a growing realization that traditional “Calculus for Life Sciences” courses do not show their applicability to the Life Sciences and...
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The Use and Abuse of Probability in Evolutionary Biology
Darwin’s publication of The Origin of Species in 1859 situated biology firmly within the “probabilistic revolution” in the history of science. One...
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Modeling in Biology
This chapter presents the most fundamental concepts of mathematical modeling. There is an initial section that introduces parameters, followed by a...
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Systems Biology Modeling, Analysis, and Simulation
This book discusses the mathematical simulation of biological systems, with a focus on the modeling of gene expression, gene regulatory networks and...
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The Use and Abuse of Probability in Evolutionary Biology
Darwin’s publication of The Origin of Species in 1859 situated biology firmly within the “probabilistic revolution” in the history of science. One...
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From Computational Logic to Computational Biology Essays Dedicated to Alfredo Ferro to Celebrate His Scientific Career
Alfredo Ferro’s impact on information technology has traversed diverse domains, encompassing Computational Logic, Data Mining, Bioinformatics, and...
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Discrete Linear Systems
In Chap. 4 , we considered the dynamics of single quantities changing in either discrete or...
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On the Stability of Stationary States in Diffusion Models in Biology and Humanities
AbstractWe consider an initial-boundary value problem for the system of partial differential equations describing processes of growth and spread of...
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Fast and precise inference on diffusivity in interacting particle systems
Particle systems made up of interacting agents is a popular model used in a vast array of applications, not the least in biology where the agents can...
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Multiphase Models for Moving Boundary Problems in Biology
We address the modelling of tissue deformation using mixture theory. The governing equations consist of mass and momentum balances for two phases,...
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Learning theory for inferring interaction kernels in second-order interacting agent systems
Modeling the complex interactions of systems of particles or agents is a fundamental problem across the sciences, from physics and biology, to...
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Dynamical Systems and Fitness Maximization in Evolutionary Biology
Five years after Charles Darwin put forward his theory of Natural Selection, Herbert Spencer coined the phrase “survival of the fittest.” Survival of...
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Dynamical Systems and Fitness Maximization in Evolutionary Biology
Five years after Charles Darwin put forward his theory of Natural Selection, Herbert Spencer coined the phrase “survival of the fittest.” Survival of...
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Continuous Dynamical Systems
DynamicsDynamics is a time-evolutionary process. It may be deterministic or stochastic. Long-term predictions of some systems often become...
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Data-Driven Modeling of Partially Observed Biological Systems
We present a numerical approach for modeling unknown dynamical systems using partially observed data, with a focus on biological systems with...
