2018/06/30 by Michał Gnacik, Michal Gnacik, Abdulrahman Alsolami +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Neuroscience · Physics and Astronomy · #Diffusion and Search Dynamics #Encoding (memory) #Function (biology) #Neural dynamics and brain function #Random walk #Short-term memory #cond-mat.stat-mech #math.PR #msc:00A69 #msc:60J70 #msc:82B41 #nlin.AO #stochastic dynamics and bifurcation
paper · pdf · doi:10.1088/1742-5468/aad6bd
published in Journal of Statistical Mechanics Theory and Experiment 2018(8), 083207 (Institute of Physics) · In the journal published version, there is a misprint in the statement of Theorem 1 p.6, one should take the limit with $c \to \infty.$
openalex created_date 2018/06/13 · openalex publication_date 2018/08/01 · arxiv created 2018/08/22 · arxiv updated 2018/08/24 · openalex updated_date 2026/08/05
Abstract We view random walks as the paths of foraging animals, perhaps searching for food or avoiding predators while forming a mental map of their surroundings. The formation of such maps requires them to memorise the locations they have visited. We model memory using a kernel, proportional to the number of locations recalled as a function of the time since they were first observed. We give exact analytic expressions relating the elongation of the memorised walk to the structure of the memory kernel, and confirm these by simulation. We find that more slowly decaying memories lead to less elongated mental maps.