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Mathematical modeling is the process by which a real-world problem is transformed into mathematics to create a model that can then be used to provide details about the actual original problem. Mathematical modeling and finite-element analysis have been widely used to investigate the biomechanics of the spine, and together with in vitro testing and in vivo studies are considered one of the pillars of spine research. Such specific kinetics can not be easily implemented in universal process simulators which are frequently used to search for optimal working conditions. Mathematical modelling and simulation are essential to automatic control. They form the backbone of the methodology for open-loop and closed-loop control systems in analytical design. Mathematical modeling has an important role to play in researching topics that concern our everyday lives. The statistical techniques can show similarities between many observable phenomena when applied to biological experimental data. A mathematical framework is required for quantitative cancer analysis to explain the various characteristics of cancer initiation , progression, chemo-response and chemical resistance. Mathematical models provided insight into tumorigenesis, avascular tumor growth, invasion tumor metabolism, cell migration, angiogenesis, tumor evolution, and stem cells of cancer 

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