Related papers: The shape of a memorised random walk
To comprehend the multipartite organization of large-scale biological and social systems, we introduce a new information theoretic approach that reveals community structure in weighted and directed networks. The method decomposes a network…
The hippocampus supports spatial navigation by encoding cognitive maps through collective place cell activity. We model the place cell population as non-negative spatial embeddings derived from the spectral decomposition of multi-step…
There are two approaches for simulating memory as well as learning in artificial intelligence; the functionalistic approach and the cognitive approach. The necessary condition to put the second approach into account is to provide a model of…
In this minireview we present the main results regarding the transport properties of stochastic movement with relocations to known positions. To do so, we formulate the problem in a general manner to see several cases extensively studied…
We consider a self-attracting random walk in dimension d=1, in presence of a field of strength s, which biases the walker toward a target site. We focus on the dynamic case (true reinforced random walk), where memory effects are implemented…
The elephant random walk (ERW) is a microscopic, one-dimensional, discrete-time, non-Markovian random walk, which can lead to anomalous diffusion due to memory effects. In this study, I propose a multi-dimensional generalization in which…
We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…
Organisms move through the world by changing their shape, and here we explore the mapping from shape space to movements in the nematode C. elegans as it crawls on a planar agar surface. We characterize the statistics of the trajectories…
Neuronal networks provide living organisms with the ability to process information. They are also characterized by abundant recurrent connections, which give rise to strong feedback that dictates their dynamics and endows them with fading…
Motivated by the psychological literature on the "peak-end rule" for remembered experience, we perform an analysis within a random walk framework of a discrete choice model where agents' future choices depend on the peak memory of their…
This paper proposes a self-supervised objective for learning representations that localize objects under occlusion - a property known as object permanence. A central question is the choice of learning signal in cases of total occlusion.…
When we exercise sequences of actions, their execution becomes more fluent and precise. Here, we consider the possibility that exercised action sequences can also be used to make planning faster and more accurate by focusing expansion of…
We consider random walks in dynamic random environments and propose a criterion which, if satisfied, allows to decompose the random walk trajectory into i.i.d. increments, and ultimately to prove limit theorems. The criterion involves the…
By incorporating feedback loops, that engender amplification and damping so that output is not proportional to input, the biological neural networks become highly nonlinear and thus very likely chaotic in nature. Research in control theory…
A functional approach for the study of the random walks in random sceneries (RWRS) is proposed. Under fairly general assumptions on the random walk and on the random scenery, functional limit theorems are proved. The method allows to study…
Human movements in the real world and in cyberspace affect not only dynamical processes such as epidemic spreading and information diffusion but also social and economical activities such as urban planning and personalized recommendation in…
Memories are stored, retained, and recollected through complex, coupled processes operating on multiple timescales. To understand the computational principles behind these intricate networks of interactions we construct a broad class of…
Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…
This paper discusses two main themes. First, it investigates the formation of a spatiotemporal cognitive map (mental image) of a road network in travelers memory, which entails the travelers global conceptual understanding of congestion or…
Exploration and trapping properties of random walkers that may evanesce at any time as they walk have seen very little treatment in the literature, and yet a finite lifetime is a frequent occurrence, and its effects on a number of random…