A Nexus is a magical barrier used to cut off a space from the outside world, or to act as an alarm by magicians.
In the first example, it is typically impossible for most beings of lesser power to escape the nexus unless it is more powerful than the beings casting the barrier. Creatures that inhibit the power of spirits, who are creatures of fire and air, such as Golems (who are beings of Earth) can blunder their way out of nexus' without apparent effort.
The second example features a similar design, except that that the barrier is not a physical wall intended to prevent transition from within or from without, but to act as an alrm when something passes through it. This type of nexus can create a loud noise when set off, or create a noise in the ears of the casters. This type of nexus can be bypassed by an experienced spirit via one of several methods, one of which can be seen in the example below.
Bartimaeus was able to create a hole within the nexus by forcing one of the holes between these threads to expand while not actually touching them, or allowing the threads to touch each other.