Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal non-Markovian search strategies with n-step memory   Stochastic search processes are ubiquitous in nature and are expected to
become more efficient when equipped with a memory, where the searcher has been
before. A natural realization of a search process with long-lasting memory is a
migrating cell that is repelled from the diffusive chemotactic signal that it
secrets on its way, denoted as auto-chemotactic searcher. To analyze the
efficiency of this class of non-Markovian search processes we present a general
formalism that allows to compute the mean first passage time (MFPT) for a given
set of conditional transition probabilities for non-Markovian random walks on a
lattice. We show that the optimal choice of the $n$-step transition
probabilities decreases the MFPT systematically and substantially with an
increasing number of steps. It turns out that the optimal search strategies can
be reduced to simple cycles defined by a small parameter set and that
mirror-asymmetric walks are more efficient. For the auto-chemotactic searcher
we show that an optimal coupling between the searcher and the chemical reduces
the MFPT to 1/3 of the one for a Markovian random walk.

0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org