### Mathematical Modeling

A mathematical model uses mathematical language to describe a system. Mathematical models are used not only in the natural sciences and engineering disciplines (such as physics, biology, earth science, meteorology, and electrical engineering) but also in the social sciences (such as economics, psychology, sociology and political science); physicists, engineers, computer scientists, and economists use mathematical models most extensively.

Eykhoff (1974) defined a *mathematical model* as 'a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form'.

Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures.

### Biostatistics

Biostatistics is the application of statistics to a wide range of topics in biology. The science of biostatistics encompasses the design of biological experiments, especially in medicine and agriculture; the collection, summarization, and analysis of data from those experiments; and the interpretation of, and inference from, the results.

### Bioinformatics

Bioinformatics is the application of information technology to the field of molecular biology. The term *Bioinformatics* was coined by Paulien Hogeweg in 1978 for the study of informatic processes in biotic systems. *Bioinformatics* nowadays entails the creation and advancement of databases, algorithms, computational and statistical techniques, and theory to solve formal and practical problems arising from the management and analysis of biological data. Over the past few decades rapid developments in genomic and other molecular research technologies combined developments in information technologies have combined to produce a tremendous amount of information related to molecular biology. It is the name given to these mathematical and computing approaches used to glean understanding of biological processes. Common activities in Bioinformatics include mapping and analyzing DNA and protein sequences, aligning different DNA and protein sequences to compare them and creating and viewing 3-D models of protein structures. Bioinformatics is that branch of life science,which deals with the study of application of information technology to the field of molecular biology.

The primary goal of bioinformatics is to increase our understanding of biological processes. What sets it apart from other approaches, however, is its focus on developing and applying computationally intensive techniques (e.g., data mining, and machine learning algorithms) to achieve this goal. Major research efforts in the field include sequence alignment, gene finding, genome assembly, protein structure alignment, protein structure prediction, prediction of gene expression and protein-protein interactions, and the modeling of evolution.

### Bioengineering

Bioengineering (also known as Biological Engineering) is the application of engineering principles to address challenges in the fields of biology and medicine. As a study, it encompasses biomedical engineering and it is related to biotechnology.

Bioengineering applies engineering principles to the full spectrum of living systems. This is achieved by utilising existing methodologies in such fields as molecular biology, biochemistry, microbiology, pharmacology, cytology, immunology and neuroscience and applies them to the design of medical devices, diagnostic equipment, biocompatible materials, and other important medical needs.

Bioengineering is not limited to the medical field. Bioengineers have the ability to exploit new opportunities and solve problems within the domain of complex systems. They have a great understanding of living systems as complex systems which can be applied to many fields including entrepreneurship.

Much as other engineering disciplines also address human health (e.g., prosthetics in mechanical engineering), bioengineers can apply their expertise to other applications of engineering and biotechnology, including genetic modification of plants and microorganisms, bioprocess engineering, and biocatalysis. However, the Main Fields of Bioengineering may be categorised as:

- Biomedical Engineering; Biomedical technology; Biomedical Diagnosis, Biomedical Therapy, Biomechanics, Biomaterials.
- Genetic Engineering; Cell Engineering, Tissue Culture Engineering.

### Neural Networks

An artificial neural network (ANN), usually called "neural network" (NN), is a mathematical model or computational model that tries to simulate the structure and/or functional aspects of biological neural networks. It consists of an interconnected group of artificial neurons and processes information using a connectionist approach to computation. In most cases an ANN is an adaptive system that changes its structure based on external or internal information that flows through the network during the learning phase. In more practical terms neural networks are non-linear statistical data modeling tools. They can be used to model complex relationships between inputs and outputs or to find patterns in data.

### Optimization Theory

In mathematics, optimization, or mathematical programming, refers to choosing the best element from some set of available alternatives.

In the simplest case, this means solving problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set. This (a scalar real valued objective function) is actually a small subset of this field which comprises a large area of applied mathematics. More generally, it means finding "best available" values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains.