The Vicsek model is a mathematical model used to simulate the collective behavior of self-propelled particles, such as birds or fish in a flock, or cells in a tissue. In the model, each particle updates its velocity based on the average velocity of its neighbors within a certain distance, and then moves in the updated direction. The model is important for studying living systems because it can help scientists understand the emergence of coordinated behavior in groups of individuals, such as flocks of birds or schools of fish, without the need for a leader or central control. The model can also help explain how cells in a tissue can coordinate their behavior to form patterns, such as in developmental processes.

Force-directed graph drawing is an algorithm for visualizing complex network structures, such as social networks, transportation networks, or biological networks. The algorithm uses a physical metaphor, where nodes in the network are treated as particles and edges as springs, and simulates the forces acting on the particles using physical principles such as Hooke's law. The goal of the algorithm is to minimize the energy of the system, which results in a layout that is easy to read and interpret.

Force-directed graph drawing is useful in network science because it can help researchers to uncover hidden patterns and relationships in large and complex networks. For example, it can be used to identify groups of highly connected nodes (called "communities" or "clusters") within a network, to reveal the structure of network hierarchies, or to identify key players or influential nodes. Additionally, force-directed graph drawing can be used to visualize relationships between nodes in a way that is easy to interpret by non-experts.

The Active Elastic Model is a minimal model for self-propelled agents that interact through attraction, repulsion, and alignment using elastic interactions. It has a simple mechanical realization and can be applied to real-world systems such as active cell membranes and robotic or animal groups. The agents are connected to their neighbors by linear springs located a certain distance R in front of their centers of rotation. Depending on the value of R, the elastic interactions mainly produce attraction-repulsion or alignment forces.

The Active Elastic Model is a minimal model for self-propelled agents that interact through attraction, repulsion, and alignment using elastic interactions. It has a simple mechanical realization and can be applied to real-world systems such as active cell membranes and robotic or animal groups. The agents are connected to their neighbors by linear springs located a certain distance R in front of their centers of rotation. Depending on the value of R, the elastic interactions mainly produce attraction-repulsion or alignment forces.