This book contains recent research in mathematical and analytical studies on diatoms. These studies reflect the complex and intricate nature of the problems being analyzed and the need to use mathematics as an aid in finding solutions. Diatoms are important components of marine food webs, the silica and carbon cycles, primary productivity, and carbon sequestration. Their uniqueness as glass-encased unicells and their presence throughout geologic history exemplify the need to better understand such organisms. Explicating the role of diatoms in the biological world is no more urgent than their role as environmental and climate indicators, and as such, is aided by the mathematical studies in this book. This volume contains twelve original research papers as chapters. Macroevolutionary science topics covered are morphological analysis, morphospace analysis, adaptation, food web dynamics, origination-extinction and diversity, biogeography, life cycle dynamics, complexity, symmetry, and evolvability. Mathematics used in the chapters include stochastic and delay differential and partial differential equations, differential geometry, probability theory, ergodic theory, group theory, knot theory, statistical distributions, chaos theory, and combinatorics. Applied sciences used in the chapters include networks, machine learning, robotics, computer vision, image processing, pattern recognition, and dynamical systems. The volume covers a diverse range of mathematical treatments of topics in diatom research.

THE MATHEMATICAL BIOLOGY OF DIATOMS This book contains unique, advanced applications using mathematics, algorithmic techniques, geometric analysis, and other computational methods in diatom research. Historically, diatom research has centered on taxonomy and systematics. While these topics are of the utmost importance, other aspects of this important group of unicells have been increasingly explored in the biological sciences. While mathematical applications are still rare, they are starting take hold and provide an extensive avenue of new diatom research, including applications in multidisciplinary fields. The work contained in this volume is an eclectic mix of analytical studies on diatoms. Mathematical treatment of the various biological disciplines covered in this book range from implicit, but succinct studies to more elaborate detailed computational studies. Topics include growth models, nanostructure, nanoengineering, cell growth, araphid diatoms, valve ontogeny, diatom metabolism, diatom motility, synchronization, diatom kinematics, photonics, biogenic sensors, photochemistry, diatom light response, colony growth, siliceous unicells, algal kinetics, diatom structure, diatom imaging, functional morphology, geometric structure, biomineralization, high-resolution imaging, non-destructive imaging, and 3D structure. This wide-ranging volume provides an introductory as well as an advanced treatment of recent interests in diatom research. The mathematical research in this volume may be applicable to studies of other unicells, biomechanics, biological processes, physio-chemical analyses, or nanoscience.