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Let us note that in general the above sum includes also the waiting probabilities u l l on a given node l before a random walker performs a jump to a neighboring node l′.
The steady-state flux has the following form (5) J = ∑ l ′ w l l ′ p l ′ st, where w l l ′ stands for the transition probabilities per unit time from a set of l′ nodes adjacent to the target node l and occupied by the walker with probabilities p l ′ st.
In formal terms, the stochastic continuous time Markov process realized on a given network of states is described by a system of coupled master equations (1) p ˙ l (t ) = ∑ l ′ w l l ′ p l ′ (t ) − w l ′ l p l (t ) which jointly describe the time variation of the probabilities p l (t) of the hypothetical random walker being in some state l at time t, where the over-dot denotes a time derivative.
Formally, as illustrated in Algorithm 1, we use a vector q(0) = (q i (0))(l + m + n )×1 to represent initial probabilities when a random walker starts a journey, with q i (0) (i = 1,…, l + m + n) being the probability that the walker initially starts from the ith node.
We use a vector q(t ) = (q i (t ))(l + m + n )×1 to represent probabilities that the random walker stays on nodes at step t, with q i (t ) (i = 1,…, l + m + n) being the probability that the walker stays on the ith node.
Total and nitrergic neuronal populations were investigated in jejunum and ileum in four experimental groups: control (C); control l-glutamine-supplemented diet (CG); Walker-256 tumor (TW); and Walker-256 tumor supplemented with l-glutamine (TWG).
MARK L. WALKER Pittsburgh, May 11 , 2000
MARK L. WALKER Pittsburgh, Aug. 11, 2003.
Stilt walker".
"The great walker".
WALKER: Agreed.
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