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Register a new userUnraveling the structure of treelike networks from first-passage times of lazy random walkers
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We study the problem of random search in finite networks with a tree topology, where it is expected that the distribution of the first-passage time F(t) decays exponentially. We show that the slope of the exponential tail is independent of the initial conditions of entering the tree in general, and scales exponentially or as a power law with the extent of the tree L, depending on the tendency p to jump toward the target node. It is unfeasible to uniquely determine L and p from measuring the tail slope or the mean first-passage time (MFPT) of an ordinary diffusion along the tree. To unravel the structure, we consider lazy random walkers that take steps with probability m when jumping on the nodes and return with probability q from the leaves. By deriving an exact analytical expression for the MFPT of the intermittent random walk, we verify that the structural information of the tree can be uniquely extracted by measuring the MFPT for two randomly chosen types of tracer particles with distinct experimental parameters m and q. We also address the applicability of our approach in the presence of disorder in the structure of the tree or statistical uncertainty in the experimental parameters.
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We present a general framework, applicable to a broad class of random walks on complex networks, which provides a rigorous lower bound for the mean first-passage time of a random walker to a target site averaged over its starting position, the so-called global mean first-passage time (GMFPT). This bound is simply expressed in terms of the equilibrium distribution at the target, and implies a minimal scaling of the GMFPT with the network size. We show that this minimal scaling, which can be arbitrarily slow for a proper choice of highly connected target, is realized under the simple condition that the random walk is transient at the target site, and independently of the small-world, scale free or fractal properties of the network. Last, we put forward that the GMFPT to a specific target is not a representative property of the network, since the target averaged GMFPT satisfies much more restrictive bounds, which forbid any sublinear scaling with the network size.
We investigate the voltage-driven transport of hybridized DNA through membrane channels. As membrane channels are typically too narrow to accommodate hybridized DNA, the dehybridization of the DNA is the critical rate limiting step in the transport process. Using a two-dimensional stochastic model, we show that the dehybridization process proceeds by two distinct mechanisms; thermal denaturation in the limit of low driving voltage, and direct stripping in the high to moderate voltage regime. Additionally, we investigate the effects of introducing non-homologous defects into the DNA strand.
We consider the first-passage problem for $N$ identical independent particles that are initially released uniformly in a finite domain $Omega$ and then diffuse toward a reactive area $Gamma$, which can be part of the outer boundary of $Omega$ or a reaction centre in the interior of $Omega$. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the $N$ particles reacts with $Gamma$. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fastest first-passage time with the particle number $N$, namely, a much stronger dependence ($1/N$ and $1/N^2$ for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.
An efficient searcher needs to balance properly the tradeoff between the exploration of new spatial areas and the exploitation of nearby resources, an idea which is at the core of scale-free Levy search strategies. Here we study multi-scale random walks as an approximation to the scale- free case and derive the exact expressions for their mean-first passage times in a one-dimensional finite domain. This allows us to provide a complete analytical description of the dynamics driving the asymmetric regime, in which both nearby and faraway targets are available to the searcher. For this regime, we prove that the combination of only two movement scales can be enough to outperform both balistic and Levy strategies. This two-scale strategy involves an optimal discrimination between the nearby and faraway targets, which is only possible by adjusting the range of values of the two movement scales to the typical distances between encounters. So, this optimization necessarily requires some prior information (albeit crude) about targets distances or distributions. Furthermore, we found that the incorporation of additional (three, four, ...) movement scales and its adjustment to target distances does not improve further the search efficiency. This allows us to claim that optimal random search strategies in the asymmetric regime actually arise through the informed combination of only two walk scales (related to the exploitative and the explorative scale, respectively), expanding on the well-known result that optimal strategies in strictly uninformed scenarios are achieved through Levy paths (or, equivalently, through a hierarchical combination of multiple scales).
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