Furthermore analytical- mathematical techniques include the linear programming, mixed integer programming, dynamic programming, gradient based algorithms, simulation modeling, and nature based algorithms.
The second section introduces the mathematical formulation and the third section reviews the numerical solution techniques, including discretisation and optimisation methods for the specific problem formulated.
The algebraic procedures include differencing, ratioing, indexes (like Normalized Difference Vegetation Index – NDVI), while the mathematical analysis techniques include data transformations (like Principal Component Analysis - PCA, Tasselled Cap Transform – TCT, Multivariate Alteration Detector - MAD), Artificial Neural Network (ANN) analysis, fuzzy logic, Bayesian network and others.
The range of applications is large and the mathematical techniques diverse, including dynamical systems, partial differential equations, stochastic dynamics, fluid dynamics, geometry, topology, and algebra.
Therefore, the study of adaptation and evolution of behavior is a particularly complex one, involving a wide range of methodologies and techniques, including mathematical modeling, comparative methods, phenotypic engineering, quantitative genetics, genetic dissection, and artificial selection.
We employ an integrated set of techniques including single cell analysis, mathematical modeling, genomics, structural studies, and in vitro assays.
The data were analyzed using the Mathematical Quality of Instruction instrument and grounded theory techniques including open coding, identification of themes, and the development and description of categories.
René Descartes (1596 1650) employed infinitesimalist techniques, including Cavalieri's method of indivisibles, in his mathematical work.
Experimentally, we combine a wide range of techniques including live imaging, quantitative image and data analysis, mathematical modeling, dynamical systems theory, genetics, molecular cell biology and embryology.
