Related papers: The shape of a memorised random walk
We consider learning on graphs, guided by kernels that encode similarity between vertices. Our focus is on random walk kernels, the analogues of squared exponential kernels in Euclidean spaces. We show that on large, locally treelike,…
The statistical study of human memory requires large-scale experiments, involving many stimuli conditions and test subjects. While this approach has proven to be quite fruitful for meaningless material such as random lists of words,…
Modular structure is ubiquitous among real-world networks from related proteins to social groups. Here we analyze the modular organization of brain networks at a large-scale (voxel level) extracted from functional magnetic resonance imaging…
Branching processes are widely used to model the viral epidemic evolution. For more adequate investigation of viral epidemic modelling, we suggest to apply branching processes with transport of particles usually called branching random…
In the mammalian brain, many neuronal ensembles are involved in representing spatial structure of the environment. In particular, there exist cells that encode the animal's location and cells that encode head direction. A number of studies…
We consider random walks on $\Z^d$ among nearest-neighbor random conductances which are i.i.d., positive, bounded uniformly from above but whose support extends all the way to zero. Our focus is on the detailed properties of the paths of…
We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. Based on…
We study how memory impacts passages at the origin for a so-called elephant random walk in the diffusive regime. We observe that the number of zeros always grows asymptotically like the square root of the time, despite the fact that,…
This paper highlights the significance of including memory structures in neural networks when the latter are used to learn perception-action loops for autonomous robot navigation. Traditional navigation approaches rely on global maps of the…
Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random…
Memories in neural system are shaped through the interplay of neural and learning dynamics under external inputs. By introducing a simple local learning rule to a neural network, we found that the memory capacity is drastically increased by…
A quantitative understanding of cities' demographic dynamics is becoming a potentially useful tool for planning sustainable growth. The concomitant theory should reveal details of the cities' past and also of its interaction with nearby…
In the paper the memory effect in the system consisting from a trajectory of process and an environment is considered. The environment is presented by scalar potential and noise. The evolution of system is interpreted as process of the…
In this paper we study some properties of random walks perturbed at extrema, which are generalizations of the walks considered e.g., in Davis (1999). This process can also be viewed as a version of {\em excited random walk}, studied…
The Martin boundary associated with the simple random walk on an example of partially oriented lattice is shown to be trivial by computing fine estimates of the Green kernel.
The movement of organisms is subject to a multitude of influences of widely varying character: from the bio-mechanics of the individual, over the interaction with the complex environment many animals live in, to evolutionary pressure and…
Aging refers to the property of two-time correlation functions to decay very slowly on (at least) two time scales. This phenomenon has gained recent attention due to experimental observations of the history dependent relaxation behavior in…
Reinforcement Learning faces an important challenge in partial observable environments that has long-term dependencies. In order to learn in an ambiguous environment, an agent has to keep previous perceptions in a memory. Earlier memory…
Sequential activation of neurons is a common feature of network activity during a variety of behaviors, including working memory and decision making. Previous network models for sequences and memory emphasized specialized architectures in…
In a landscape composed of N randomly distributed sites in Euclidean space, a walker (``tourist'') goes to the nearest one that has not been visited in the last \tau steps. This procedure leads to trajectories composed of a transient part…