اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدEfficient search by optimized intermittent random walks
247
0
0.0
(
0
)
تأليف
Gleb Oshanin
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We study the kinetics for the search of an immobile target by randomly moving searchers that detect it only upon encounter. The searchers perform intermittent random walks on a one-dimensional lattice. Each searcher can step on a nearest neighbor site with probability alpha, or go off lattice with probability 1 - alpha to move in a random direction until it lands back on the lattice at a fixed distance L away from the departure point. Considering alpha and L as optimization parameters, we seek to enhance the chances of successful detection by minimizing the probability P_N that the target remains undetected up to the maximal search time N. We show that even in this simple model a number of very efficient search strategies can lead to a decrease of P_N by orders of magnitude upon appropriate choices of alpha and L. We demonstrate that, in general, such optimal intermittent strategies are much more efficient than Brownian searches and are as efficient as search algorithms based on random walks with heavy-tailed Cauchy jump-length distributions. In addition, such intermittent strategies appear to be more advantageous than Levy-based ones in that they lead to more thorough exploration of visited regions in space and thus lend themselves to parallelization of the search processes.
قيم البحث
اقرأ أيضاً
This review examines intermittent target search strategies, which combine phases of slow motion, allowing the searcher to detect the target, and phases of fast motion during which targets cannot be detected. We first show that intermittent search str
ategies are actually widely observed at various scales. At the macroscopic scale, this is for example the case of animals looking for food ; at the microscopic scale, intermittent transport patterns are involved in reaction pathway of DNA binding proteins as well as in intracellular transport. Second, we introduce generic stochastic models, which show that intermittent strategies are efficient strategies, which enable to minimize the search time. This suggests that the intrinsic efficiency of intermittent search strategies could justify their frequent observation in nature. Last, beyond these modeling aspects, we propose that intermittent strategies could be used also in a broader context to design and accelerate search processes.
We study Markovian continuous-time random walk models for Levy flights and we show an example in which the convergence to stable densities is not guaranteed when jumps follow a bi-modal power-law distribution that is equal to zero in zero. The signif
icance of this result is two-fold: i) with regard to the probabilistic derivation of the fractional diffusion equation and also ii) with regard to the concept of site fidelity in the framework of Levy-like motion for wild animals.
The time of the first occurrence of a threshold crossing event in a stochastic process, known as the first passage time, is of interest in many areas of sciences and engineering. Conventionally, there is an implicit assumption that the notional senso
r monitoring the threshold crossing event is always active. In many realistic scenarios, the sensor monitoring the stochastic process works intermittently. Then, the relevant quantity of interest is the $textit{first detection time}$, which denotes the time when the sensor detects the threshold crossing event for the first time. In this work, a birth-death process monitored by a random intermittent sensor is studied, for which the first detection time distribution is obtained. In general, it is shown that the first detection time is related to, and is obtainable from, the first passage time distribution. Our analytical results display an excellent agreement with simulations. Further, this framework is demonstrated in several applications -- the SIS compartmental and logistic models, and birth-death processes with resetting. Finally, we solve the practically relevant problem of inferring the first passage time distribution from the first detection time.
Chase-escape percolation is a variation of the standard epidemic spread models. In this model, each site can be in one of three states: unoccupied, occupied by a single prey, or occupied by a single predator. Prey particles spread to neighboring empt
y sites at rate $p$, and predator particles spread only to neighboring sites occupied by prey particles at rate $1$, killing the prey particle that existed at that site. It was found that the prey can survive with non-zero probability, if $p>p_c$ with $p_c<1$. Using Monte Carlo simulations on the square lattice, we estimate the value of $p_c = 0.49451 pm 0.00001$, and the critical exponents are consistent with the undirected percolation universality class. We define a discrete-time parallel-update version of the model, which brings out the relation between chase-escape and undirected bond percolation. For all $p < p_c$ in $D$-dimensions, the number of predators in the absorbing configuration has a stretched-exponential distribution in contrast to the exponential distribution in the standard percolation theory. We also study the problem starting from the line initial condition with predator particles on all lattice points of the line $y=0$ and prey particles on the line $y=1$. In this case, for $p_c<p < 1$, the center of mass of the fluctuating prey and predator fronts travel at the same speed. This speed is strictly smaller than the speed of an Eden front with the same value of $p$, but with no predators. At $p=1$, the fronts undergo a depinning transition. The fluctuations of the front follow Kardar-Parisi-Zhang scaling both above and below this depinning transition.
We introduce a heterogeneous continuous time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environmen
ts, weighted graphs or networks. We derive the exact form of the propagator and investigate the effects of spatio-temporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. In particular, we show how the distribution of first passage times changes due to local and global heterogeneities of the medium. The HCTRW formalism offers a unified mathematical language to address various diffusion-reaction problems, with numerous applications in material sciences, physics, chemistry, biology, and social sciences.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
