## 2 Bioinspired Networking: A Brief Overview
### Artificial Immune System  
The artificial immune systems (AIS) mimics the property of the biological immune system. Several studies reports on the application of artificial immune systems and its application in computer science and engineering [11, 23, 24, 25, 26]. The role of the natural immune system is to protect the body from infections by continuously scanning for invading pathogens, e.g., exogenous proteins and by adapting with a proper response.  
In nature, two immune responses are identified. The primary one is to launch a response to invading pathogens by provides an immediate, but non-specific, innate response. The secondary immune response  
Figure 1: The firefly inspired time synchronization mechanism. (a) A node fires a pulse when its internal time \(t\) equals a multiple \(n\) of the oscillation period \(T\). (b) An adjacent node responds to a neighbor’s pulse by incrementing its internal phase such that \(\theta(nT+\Delta t_{n})=\theta(nT)+\epsilon\).  
remembers past encounters and, hence, it represents the immunologic memory. If pathogens successfully evade the innate response, the adaptive immune system is activated by the innate response. This secondary immune response allows a faster response the second time around showing a very specific response by using lymphocytes, which are white blood cells (T-cells and B-cells). The function of T-cells and B-cells is to recognize specific non-self antigens. B-cells respond to pathogens by producing large quantities of antibodies, which then neutralize foreign objects. In response to pathogens some T-cells produce cytokines that direct the immune response while other T-cells produce toxic granules that cause the death of pathogen infected cells.  
AIS based algorithms typically exploit the immune systems characteristics of self-learning and memorization. The immune system is, in its simplest form, a cascade of detection and adaptation, culminating in a system that is remarkably effective. A simplified computational model based on the immune system has been given by [PERSON], Packard and [PERSON] [10]. It models the set of \(N\) antibody concentrations \(x_{i}\) and antigens concentrations \(y_{i}\) in the organism by a set of coupled first order differential equations and uses a matrix of matching specificities \(m_{ij}\) of binary classification to map parts of the antigen (the epitope) to the part of an antibody (the paratope) which recognizes an antigen. The rate at which the antibody concentration changes is given by  
\[\frac{dx_{i}}{dt}=c\left(\sum_{j=1}^{N}m_{ji}x_{i}x_{j}-k_{1}\sum_{j=1}^{N}m_{ ij}x_{i}x_{j}+\sum_{j=1}^{N}m_{ji}x_{i}y_{j}\right)-k_{2}x_{i}\enspace, \tag{5}\]  
where \(k_{1}\) and \(k_{2}\) are constants. The first term in the equation represents the stimulation of the paratope of an antibody of type \(i\) by the epitope of an antibody of type \(j\). The second term represents the suppression of antibody of type \(i\) when its epitope is recognized by the paratope of type \(j\). The constant \(k_{1}\) represents the possible inequality between stimulation and suppression, whereas \(k_{2}\) determines the rate at which cell dies. To model the full immune response we must also introduce equations to model the time-variations of antigen concentrations \(y_{j}\), caused by antigens generation and eliminated. To our knowledge no consistent model for antigen concentrations in AIS is found in the literature.