All fixations that did not belong to a significant cluster were pooled into

a special cluster, referred to as background state. The background state was crucial for the correct calculation of the transition probabilities to and from significant clusters, i.e., in order to account also for the transitions that are neither within a cluster, nor between two clusters. Further details are described in the next section. The statistical Selleck GSK 3 inhibitor properties of the scanpaths a monkey chose to explore an image were analyzed by a Markov chain (MC) analysis (Markov, 1913). A MC is a sequence of random variables that propagate through a chain of states in accordance with given transition probabilities. These were estimated from the data as normalized frequencies of transitions from a specific state sj to any particular other state sk or to itself. The formerly identified clusters (compare previous section)

Akt inhibitor of fixation points (including the background cluster) defined the states sj. The transition probabilities from any one state to any other state (including the same state) were represented in matrix form. The state of the system at step t with t = 1,…,T − 1, with T being the total number of fixations on an image was derived via P(St + 1 = s|St = si, …, S1 = s1) = P(St + 1 = s|St = si) for all n states si ∈ s1, …,sn, thereby assuming that the scanpaths of the monkeys satisfy the Markov property, i.e., the present state is independent of the past states. For better intuition, we visualized the results of the MC analysis by a transition graph (see example shown for monkey D in Fig. 5), in which the vertices are the states, i.e., the identified fixation

clusters. The graph is composed of oriented edges connecting vertices, weighted with the transition probabilities between the respective states. In addition, each vertex also contains an edge to itself weighted by the probability of staying within the same state in the subsequent step. In the following two cases no edges were drawn between the two vertices: first, whenever the transition ADAMTS5 probability Pjk equals zero; second, for transitions originating in the background state. For better visualization we represented the transition probabilities by the thickness of the edges ( Fig. 5C) (thereby deviating in the graphical display from conventional transition graphs). In order to interpret the transition probabilities derived by the MC analysis we compared them to the transition probabilities obtained assuming homogeneous chance probabilities of the transitions between any two states s  j and s  k, Pexpected(St+1=sk|St=sj)=Pexpected(St+1=sk)=nkT, with nk being the number of fixations in state sk and T the total number of transition steps. As illustrated in Fig.