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The principle of maximum caliber (MaxCal) or maximum path entropy principle, suggested by E. T. Jaynes, [1] can be considered as a generalization of the principle of maximum entropy. It postulates that the most unbiased probability distribution of paths is the one that maximizes their Shannon entropy. This entropy of paths is sometimes called ...
The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden states—called the Viterbi path—that results in a sequence of observed events.
Maximal entropy random walk (MERW) is a popular type of biased random walk on a graph, in which transition probabilities are chosen accordingly to the principle of maximum entropy, which says that the probability distribution which best represents the current state of knowledge is the one with largest entropy.
Any random graph model (at a fixed set of parameter values) results in a probability distribution on graphs, and those that are maximum entropy within the considered class of distributions have the special property of being maximally unbiased null models for network inference [2] (e.g. biological network inference).
The probability of an edge uv between any vertices u and v is some function of the dot product u • v of their respective vectors. The network probability matrix models random graphs through edge probabilities, which represent the probability , that a given edge , exists for a specified time period. This model is extensible to directed and ...
For example, one can consider a square system, and ask for the probability P that there is a path from the top boundary to the bottom boundary. As a function of the occupation probability p, one finds a sigmoidal plot that goes from P=0 at p=0 to P=1 at p=1. The larger the square is compared to the lattice spacing, the sharper the transition ...
A path in G is an alternating path, if its edges are alternately not in M and in M (or in M and not in M). An augmenting path P is an alternating path that starts and ends at two distinct exposed vertices. Note that the number of unmatched edges in an augmenting path is greater by one than the number of matched edges, and hence the total number ...
Hamiltonian path – a path that visits each vertex exactly once. Route inspection problem, search for the shortest path that visits all edges, possibly repeating edges if an Eulerian path does not exist. Veblen's theorem, which states that graphs with even vertex degree can be partitioned into edge-disjoint cycles regardless of their connectivity