Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side. Theoretical biology focuses more on the development of theoretical principles for biology while mathematical biology focuses on the use of mathematical tools to study biological systems, even though the two terms are sometimes interchanged.
Mathematical biology aims at the mathematical representation and modeling of biological processes, using techniques and tools of applied mathematics. It can be useful in both theoretical and practical research. Describing systems in a quantitative manner means their behavior can be better simulated, and hence properties can be predicted that might not be evident to the experimenter. This requires precise mathematical models.
Because of the complexity of the living systems, theoretical biology employs several fields of mathematics, and has contributed to the development of new techniques.
Mathematics has been used in biology as early as the 13th century, when Fibonacci used the famous Fibonacci series to describe a growing population of rabbits. In the 18th century, Daniel Bernoulli applied mathematics to describe the effect of smallpox on the human population. Thomas Malthus' 1789 essay on the growth of the human population was based on the concept of exponential growth. Pierre François Verhulst formulated the logistic growth model in 1836.
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This course provides exposure to research in biophysics and physical biology, with emphasis on the nature of scientific breakthroughs, and using critical reading of scientific literature. Each week, w
Closely interfacing with bioengineering and medicine, this course provides foundational concepts in applying small-molecule chemical toolsets to probe the functions of living systems at the mechanisti
The course introduces and develops the key concepts from systems biology and systems engineering in the context of complex biological networks. The lectures elaborate on techniques and methods to mode
The course provides a comprehensive overview of digital signal processing theory, covering discrete time, Fourier analysis, filter design, sampling, interpolation and quantization; it also includes a
Adaptive signal processing, A/D and D/A. This module provides the basic
tools for adaptive filtering and a solid mathematical framework for sampling and
quantization
'Charles Robert Darwin' (ˈdɑrwɪn ; 12 February 1809 – 19 April 1882) was an English naturalist, geologist, and biologist, widely known for his contributions to evolutionary biology. His proposition that all species of life have descended from a common ancestor is now generally accepted and considered a fundamental concept in science. In a joint publication with Alfred Russel Wallace, he introduced his scientific theory that this branching pattern of evolution resulted from a process he called natural selection, in which the struggle for existence has a similar effect to the artificial selection involved in selective breeding.
In biology and other experimental sciences, an in silico experiment is one performed on computer or via computer simulation. The phrase is pseudo-Latin for 'in silicon' (correct in silicio), referring to silicon in computer chips. It was coined in 1987 as an allusion to the Latin phrases in vivo, in vitro, and in situ, which are commonly used in biology (especially systems biology). The latter phrases refer, respectively, to experiments done in living organisms, outside living organisms, and where they are found in nature.
"The Chemical Basis of Morphogenesis" is an article that the English mathematician Alan Turing wrote in 1952. It describes how patterns in nature, such as stripes and spirals, can arise naturally from a homogeneous, uniform state. The theory, which can be called a reaction–diffusion theory of morphogenesis, has become a basic model in theoretical biology. Such patterns have come to be known as Turing patterns. For example, it has been postulated that the protein VEGFC can form Turing patterns to govern the formation of lymphatic vessels in the zebrafish embryo.
Explores the science of articulation and the relationship between space and mental imagery.
Introduces students to the physics course structure, emphasizing the importance of attending exercises and using mathematical tools for motion description.
Covers the concept of replicas for the random field Ising model, discussing various mathematical formulations and assumptions.
vanishing viscosity, networks. This work has received funding from the Alexander von Humboldt-Professorship program, the Transregio 154 Project "Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks" of the DFG, the grant PI ...
Accessing the thermal transport properties of glasses is a major issue for the design of production strategies of glass industry, as well as for the plethora of applications and devices where glasses are employed. From the computational standpoint, the che ...
In this article, we propose a dynamical system to avoid obstacles which are star shaped and simultaneously converge to a goal. The convergence is almost-global in a domain and the stationary points are identified explicitly. Our approach is based on the id ...