Related papers: On Bootstrap Percolation in Living Neural Networks
A bootstrap percolation process on a graph G is an "infection" process which evolves in rounds. Initially, there is a subset of infected nodes and in each subsequent round every uninfected node which has at least r infected neighbours…
Bootstrap percolation on a graph iteratively enlarges a set of occupied sites by adjoining points with at least $\theta$ occupied neighbors. The initially occupied set is random, given by a uniform product measure, and we say that spanning…
We investigate how the activation function can be used to describe neural firing in an abstract way, and in turn, why it works well in artificial neural networks. We discuss how a spike in a biological neurone belongs to a particular…
An important class of real-world networks have directed edges, and in addition, some rank ordering on the nodes, for instance the "popularity" of users in online social networks. Yet, nearly all research related to explosive percolation has…
The $r$-edge bootstrap percolation on a graph is an activation process of the edges. The process starts with some initially activated edges and then, in each round, any inactive edge whose one of endpoints is incident to at least $r$ active…
Dynamic functional connectivity is an effective measure for the brain's responses to continuous stimuli. We propose an inferential method to detect the dynamic changes of brain networks based on time-varying graphical models. Whereas most…
Cortical neurons whose activity is recorded in behavioral experiments has been classified into several types such as stimulus-related neurons, delay-period neurons, and reward-related neurons. Moreover, the population activity of neurons…
Until recently, artificial neural networks were typically designed with a fixed network structure. Here, I argue that network structure is highly relevant to function, and therefore neural networks should be livewired (Eagleman 2020):…
Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex…
In graph bootstrap percolation, edges of an Erd\H{o}s-R\'enyi random graph ${\mathcal G}_{n,p}$ are initially active. Activation spreads to other edges of the complete graph $K_n$ by an iterative process governed by a fixed graph $H$,…
Cells and tissues exert forces and can actively change shape. This strikingly autonomous behavior is powered by the cytoskeleton, which includes an active gel of actin filaments, crosslinks, and myosin molecular motors. Although individual…
In this paper we address the question of statistical model selection for a class of stochastic models of biological neural nets. Models in this class are systems of interacting chains with memory of variable length. Each chain describes the…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…
Cortical neurons emit seemingly erratic trains of action potentials or "spikes," and neural network dynamics emerge from the coordinated spiking activity within neural circuits. These rich dynamics manifest themselves in a variety of…
The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similar to percolation theory on static networks, this mapping is valid…
How intelligence emerges from living beings has been a fundamental question in neuroscience. However, it remains largely unanswered due to the complex neuronal dynamics and intricate connections between neurons in real neural systems. To…
The dynamics of neural networks is often characterized by collective behavior and quasi-synchronous events, where a large fraction of neurons fire in short time intervals, separated by uncorrelated firing activity. These global temporal…
To gain insight into the neural events responsible for visual perception of static and dynamic optical patterns, we study how neural activation spreads in arrays of inhibition-stabilized neural networks with nearest-neighbor coupling. The…
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad…
Correlations are employed in modern physics to explain microscopic and macroscopic phenomena, like the fractional quantum Hall effect and the Mott insulator state in high temperature superconductors and ultracold atoms. Simultaneously…