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We review recent studies demonstrating a nonuniversal (continuously variable) survival exponent for history-dependent random walks, and analyze a new example, the hard movable partial reflector. These processes serve as a simplified models…
Arrays of atoms trapped in optical lattices are appealing as storage media for photons, since motional dephasing of the atoms is eliminated. The regular lattice is also associated with band structure in the dispersion experienced by…
Interleaving learning is a human learning technique where a learner interleaves the studies of multiple topics, which increases long-term retention and improves ability to transfer learned knowledge. Inspired by the interleaving learning…
Randomly crumpled sheets have shape memory. In order to understand the basis of this form of memory, we simulate triangular lattices of springs whose lengths are altered to create a topography with multiple potential energy minima. We then…
Learning and memory relies on synapses changing their strengths in response to neural activity. However there is a substantial gap between the timescales of neural electrical dynamics (1-100 ms) and organism behaviour during learning…
Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…
We consider a minimal model of persistent random searcher with short range memory. We calculate exactly for such searcher the mean first-passage time to a target in a bounded domain and find that it admits a non trivial minimum as function…
Machine learning has typically focused on developing models and algorithms that would ultimately replace humans at tasks where intelligence is required. In this work, rather than replacing humans, we focus on unveiling the potential of…
The ability to learn different tasks sequentially is essential to the development of artificial intelligence. In general, neural networks lack this capability, the major obstacle being catastrophic forgetting. It occurs when the…
The phenomenon of localization usually happens due to the existence of disorder in a medium. Nevertheless, certain quantum systems allow dynamical localization solely due to the nature of internal interactions. We study a discrete time…
1. Spatial memory plays a role in the way animals perceive their environments, resulting in memory-informed movement patterns that are observable to ecologists. Developing mathematical techniques to understand how animals use memory in…
The ensemble properties and time-averaged observables of a memory-induced diffusive-superdiffusive transition are studied. The model consists in a random walker whose transitions in a given direction depend on a weighted linear combination…
We study a one-dimensional sluggish random walk with space-dependent transition probabilities between nearest-neighbour lattice sites. Motivated by trap models of slow dynamics, we consider a model in which the trap depth increases…
We consider a continuous-space and continuous-time diffusion process under resetting with memory. A particle resets to a position chosen from its trajectory in the past according to a memory kernel. Depending on the form of the memory…
Very recently, a fundamental observable has been introduced and analyzed to quantify the exploration of random walks: the time $\tau_k$ required for a random walk to find a site that it never visited previously, when the walk has already…
A catastrophic forgetting problem makes deep neural networks forget the previously learned information, when learning data collected in new environments, such as by different sensors or in different light conditions. This paper presents a…
We show that a quantum walk process can be used to construct and secure quantum memory. More precisely, we show that a localized quantum walk with temporal disorder can be engineered to store the information of a single, unknown qubit on a…
Quadruped locomotion provides a natural setting for understanding when model-free learning can outperform model-based control design, by exploiting data patterns to bypass the difficulty of optimizing over discrete contacts and the…
Several variants of a stochastic local search process for constructing the synaptic weights of an Ising perceptron are studied. In this process, binary patterns are sequentially presented to the Ising perceptron and are then learned as the…
The discrete stochastic dynamics of a random walker in the presence of resetting and memory is analyzed. Resetting and memory effects may compete for certain parameter regime and lead to significant changes in the long time dynamics of the…