Second order optimization may lead to Lévy walks

Sep 8, 2017, 9:50 AM


oral Session 12


Lukasz Kusmierz (RIKEN Brain Science Institute)


Most living organisms perform two different types of search: a directed search (taxis) and a random search. The former is observed when the environment provides cues to guide the motion towards targets, whereas the latter may not involve any memory and information processing and can be modeled by ran- dom walks. There is a large body of experimental results showing that the random walk adopted by many organisms is described well by Lévy walks, which raises questions about the reasons and underlying mech- anisms of such a behavior. Here we show that Lévy walks may emerge from a directed gradient based search, which bridges the gap between the two modes of a search. For a wide range of scenarios our model reproduces the tail index α = 1, in line with previous experimental observations in foraging organisms and predictions based on optimality considerations for sparse targets. Moreover, the model predicts specific relations between features of the search and the curvature of the optimized function, which can be tested experimentally.

Primary authors

Lukasz Kusmierz (RIKEN Brain Science Institute) Taro Toyoizumi (RIKEN Brain Science Institute)

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