Related papers: The shape of a memorised random walk
Recent empirical and modeling research has focused on the semantic fluency task because it is informative about semantic memory. An interesting interplay arises between the richness of representations in semantic memory and the complexity…
We consider a living organism as an observer of the evolution of its environment recording sensory information about the state space X of the environment in real time. Sensory information is sampled and then processed on two levels. On the…
We study a simple model of a forager as a walk that modifies a relaxing substrate. Within it simplicity, this provides an insight on a number of relevant and non-intuitive facts. Even without memory of the good places to feed and no…
We study a family of correlated one-dimensional random walks with a finite memory range M.These walks are extensions of the Taylor's walk as investigated by Goldstein, which has a memory range equal to one. At each step, with a probability…
Elephant random walk, introduced to study the effect of memory on random walks, is a novel type of walk that incorporates the information of one randomly chosen past step to determine the future step. However, memory of a process can be…
The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…
A rational framework is proposed to explain how we accommodate unbounded sensory input within bounded memory. According to this framework, memory is stored as a statistic-like representation that is repeatedly summarized and compressed to…
We consider Reinforced Random Walks where transition probabilities are a function of the proportion of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase transition is observed, similar to…
A random forest is a popular tool for estimating probabilities in machine learning classification tasks. However, the means by which this is accomplished is unprincipled: one simply counts the fraction of trees in a forest that vote for a…
The importance of an element in a visual stimulus is commonly associated with the fixations during a free-viewing task. We argue that fixations are not always correlated with attention or awareness of visual objects. We suggest to filter…
The purpose of this short note is to establish a connection between a one-dimensional random walk in a random sparse environment and the random pinning model. We show that the grand canonical partition function of the pinning model…
As the robot explores the environment, the map grows over time in the simultaneous localization and mapping (SLAM) system, especially for the large scale environment. The ever-growing map prevents long-term mapping. In this paper, we…
Random walk is one of the most classical and well-studied model in probability theory. For two correlated random walks on lattice, every step of the random walks has only two states, moving in the same direction or moving in the opposite…
Semantic memory is the subsystem of human memory that stores knowledge of concepts or meanings, as opposed to life specific experiences. The organization of concepts within semantic memory can be understood as a semantic network, where the…
Human close-range proximity interactions are the key determinant for spreading processes like knowledge diffusion, norm adoption, and infectious disease transmission. These dynamical processes can be modeled with time-respecting paths on…
When studying unconstrained behaviour and allowing mice to leave their cage to navigate a complex labyrinth, the mice exhibit foraging behaviour in the labyrinth searching for rewards, returning to their home cage now and then, e.g. to…
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…
Recent seminal works on human mobility have shown that individuals constantly exploit a small set of repeatedly visited locations. A concurrent literature has emphasized the explorative nature of human behavior, showing that the number of…
In the classical simple random walk the steps are independent, viz., the walker has no memory. In contrast, in the elephant random walk which was introduced by Sch\"utz and Trimper in 2004, the walker remembers the whole past, and the next…
Humans routinely retrace paths in a novel environment both forwards and backwards despite uncertainty in their motion. This paper presents an approach for doing so. Given a demonstration of a path, a first network generates a path…