Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Paths, Diffusion, and Navigation

Description

This lecture covers the concepts of paths in networks, including walks, trails, and paths. It also delves into the brain's structural connectome, Dijkstra's algorithm for finding shortest paths, global and nodal network efficiency, and network communicability. The importance of following the shortest path in the brain and the challenges of shortest path routing are discussed, along with network navigation and the Milgram experiment. The lecture concludes with a look at navigation in scale-free networks and a reminder about the upcoming midterm.

Official source

Related concepts (20)

Scale-free network

A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction P(k) of nodes in the network having k connections to other nodes goes for large values of k as where is a parameter whose value is typically in the range (wherein the second moment (scale parameter) of is infinite but the first moment is finite), although occasionally it may lie outside these bounds. The name "scale-free" means that some moments of the degree distribution are not defined, so that the network does not have a characteristic scale or "size".

Dijkstra's algorithm

Dijkstra's algorithm (ˈdaɪkstrəz ) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, road networks. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later. The algorithm exists in many variants. Dijkstra's original algorithm found the shortest path between two given nodes, but a more common variant fixes a single node as the "source" node and finds shortest paths from the source to all other nodes in the graph, producing a shortest-path tree.

Complex network

In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real systems. The study of complex networks is a young and active area of scientific research (since 2000) inspired largely by empirical findings of real-world networks such as computer networks, biological networks, technological networks, brain networks, climate networks and social networks.

Social network

A social network is a social structure made up of a set of social actors (such as individuals or organizations), sets of dyadic ties, and other social interactions between actors. The social network perspective provides a set of methods for analyzing the structure of whole social entities as well as a variety of theories explaining the patterns observed in these structures. The study of these structures uses social network analysis to identify local and global patterns, locate influential entities, and examine network dynamics.

Automotive navigation system

An automotive navigation system is part of the automobile controls or a third party add-on used to find direction in an automobile. It typically uses a satellite navigation device to get its position data which is then correlated to a position on a road. When directions are needed routing can be calculated. On the fly traffic information (road closures, congestion) can be used to adjust the route.

Related lectures (31)

Paths, Diffusion, Navigation

Explores paths, diffusion, and navigation in brain networks, including topics like Dijkstra's algorithm and network efficiency.

Node Degree and Strength

Explores brain node connectivity, node degree, strength, random networks, power law distributions, and the complexity of real networks.

GPS Navigation Concept and Limitations

Covers GPS navigation concepts, limitations, aided navigation, and accurate positioning.