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We study the signal percolation through heart-like biological system. Starting from an initial distribution of waiting and inactive cells with probabilities $p$ and $(1-p)$ respectively, the signal propagation is observed in terms of active cells. As the signal enters the system from one end, the number of arrival of active sites at the other end is studied and analysis of the system behaviour is made by varying a few important parameters of the system like $p_{switch}$ (switching probability from inactive to waiting) and $p_{act}$ (switching probability from waiting to active). In this connection, the non-regular heart rhythms are discussed. Fraction of paths percolating through the system shows a transition from $0$ to $1$ near $p=p_c$. Some other important quantities like tortuosity and cluster distribution are discussed. Several critical exponents have been obtained and compared the exponents of standard percolation., Comment: 11 pages, 10 figures, 4 tables, revtex4-2

In this work, we study the effect of a moving detector on a discrete time one dimensional Quantum Random Walk where the movement is realized in the form of hopping/shifts. The occupation probability $f(x,t;n,s)$ is estimated as the number of detection $n$ and amount of shift $s$ vary. It is seen that the occupation probability at the initial position $x_D$ of the detector is enhanced when $n$ is small which is a quantum mechanical effect but decreases when $n$ is large. The ratio of occupation probabilities of our walk to that of an Infinite walk shows a scaling behavior of $\frac{x_D^2}{n^2}$. It shows a definite scaling behavior with amount of shifts $s$ also. The limiting behaviors of the walk are observed when $x_D$ is large, $n$ is large and $s$ is large and the walker for these cases approach the Infinite Walk, The Semi Infinite Walk and the Quenched Quantum Walk respectively., Comment: 11 pages, 10 figures, revtex4-2