DNA replication is an essential process in biology and its timing must be robust so that cells can divide properly. Random fluctuations in the formation of replication starting points, called origins, and the subsequent activation of proteins lead to
variations in the replication time. We analyse these stochastic properties of DNA and derive the positions of origins corresponding to the minimum replication time. We show that under some conditions the minimization of replication time leads to the grouping of origins, and relate this to experimental data in a number of species showing origin grouping.
The dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science. Previous studies of escape in chaotic systems have rather focused on the case of unbounded noise, usually assumed to have Gau
ssian distribution. In this paper, we address the problem of escape induced by bounded noise. We show that the dynamics of escape from an attractors basin is equivalent to that of a closed system with an appropriately chosen hole. Using this equivalence, we show that there is a minimum noise amplitude above which escape takes place, and we derive analytical expressions for the scaling of the escape rate with noise amplitude near the escape transition. We verify our analytical predictions through numerical simulations of a two-dimensional map with noise.
A great number of physical processes are described within the context of Hamiltonian scattering. Previous studies have rather been focused on trajectories starting outside invariant structures, since the ones starting inside are expected to stay trap
ped there forever. This is true though only for the deterministic case. We show however that, under finitely small random fluctuations of the field, trajectories starting inside Arnold-Kolmogorov-Moser (KAM) islands escape within finite time. The non-hyperbolic dynamics gains then hyperbolic characteristics due to the effect of the random perturbed field. As a consequence, trajectories which are started inside KAM curves escape with hyperbolic-like time decay distribution, and the fractal dimension of a set of particles that remain in the scattering region approaches that for hyperbolic systems. We show a universal quadratic power law relating the exponential decay to the amplitude of noise. We present a random walk model to relate this distribution to the amplitude of noise, and investigate this phenomena with a numerical study applying random maps.
