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Depending on the context the graph can be directed or undirected. A state x v for each vertex v of Y taken from a finite set K. The system state is the n-tuple x = (x 1, x 2, ... , x n), and x[v] is the tuple consisting of the states associated to the vertices in the 1-neighborhood of v in Y (in some fixed order). A vertex function f v for each ...
In spectral clustering and graph-based signal processing, where graph vertices represent data points, the edge weights can be computed, e.g., as inversely proportional to the distances between pairs of data points, leading to all weights being non-negative with larger values informally corresponding to more similar pairs of data points. Using ...
The Watts–Strogatz model is a random graph generation model that produces graphs with small-world properties, including short average path lengths and high clustering. It was proposed by Duncan J. Watts and Steven Strogatz in their article published in 1998 in the Nature scientific journal. [ 1 ]
The function Φ(t,x) is called the evolution function of the dynamical system: it associates to every point x in the set X a unique image, depending on the variable t, called the evolution parameter. X is called phase space or state space , while the variable x represents an initial state of the system.
Further optimizations for the single-target case include bidirectional variants, goal-directed variants such as the A* algorithm (see § Related problems and algorithms), graph pruning to determine which nodes are likely to form the middle segment of shortest paths (reach-based routing), and hierarchical decompositions of the input graph that ...
If function 2 sends data to function 3 and function 5, then the data elements would be placed in the first and third boxes to the right of function 2. If any function sends data back to a previous function, then the associated box to the left of the function would have the data elements placed in it. The squares on either side of the diagonal ...
Any given transfer function which is strictly proper can easily be transferred into state-space by the following approach (this example is for a 4-dimensional, single-input, single-output system): Given a transfer function, expand it to reveal all coefficients in both the numerator and denominator.
In engineering, a transfer function (also known as system function [1] or network function) of a system, sub-system, or component is a mathematical function that models the system's output for each possible input. [2] [3] [4] It is widely used in electronic engineering tools like circuit simulators and control systems.