Related papers: From Neuron to Neural Networks dynamics

We present a neural network approach for closed-loop deep brain stimulation (DBS). We cast the problem of finding an optimal neurostimulation strategy as a control problem. In this setting, control policies aim to optimize therapeutic…

Predicting how the brain can be driven to specific states by means of internal or external control requires a fundamental understanding of the relationship between neural connectivity and activity. Network control theory is a powerful tool…

The links between optimal control of dynamical systems and neural networks have proved beneficial both from a theoretical and from a practical point of view. Several researchers have exploited these links to investigate the stability of…

Mounting evidence in neuroscience suggests the possibility of neuronal representations that individual neurons serve as the substrates of different mental representations in a point-to-point way. Combined with associationism, it can…

We study two population models describing the dynamics of interacting neurons, initially proposed by Pakdaman, Perthame, and Salort (2010, 2014). In the first model, the structuring variable $s$ represents the time elapsed since its last…

The brain is formed by cortical regions that are associated with different cognitive functions. Neurons within the same region are more likely to connect than neurons in distinct regions, making the brain network to have characteristics of…

Diversity conveys advantages in nature, yet homogeneous neurons typically comprise the layers of artificial neural networks. Here we construct neural networks from neurons that learn their own activation functions, quickly diversify, and…

We propose the use of recurrent neural networks for classifying phases of matter based on the dynamics of experimentally accessible observables. We demonstrate this approach by training recurrent networks on the magnetization traces of two…

Graph neural networks (GNNs) have demonstrated significant promise in modelling relational data and have been widely applied in various fields of interest. The key mechanism behind GNNs is the so-called message passing where information is…

The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the…

The first part of the thesis is devoted to factorizations of linear and nonlinear differential equations leading to solutions of the kink type. The second part contains a study of the synchronization of the chaotic dynamics of two…

The need for more transparency of the decision-making processes in artificial neural networks steadily increases driven by their applications in safety critical and ethically challenging domains such as autonomous driving or medical…

We consider the effects of correlations between the in- and out-degrees of individual neurons on the dynamics of a network of neurons. By using theta neurons, we can derive a set of coupled differential equations for the expected dynamics…

A single axon can generate branches connecting with plenty synaptic targets. Process of branching is very important for making connections in central nervous system. The interstitial branching along primary axon shaft occurs during nervous…

Cross-correlations in the activity in neural networks are commonly used to characterize their dynamical states and their anatomical and functional organizations. Yet, how these latter network features affect the spatiotemporal structure of…

The quintessential property of neuronal systems is their intensive patterns of selective synaptic connections. The current work describes a physics-based approach to neuronal shape modeling and synthesis and its consideration for the…

Neuromorphic computing exploits the dynamical analogy between many physical systems and neuron biophysics. Superconductor systems, in particular, are excellent candidates for neuromorphic devices due to their capacity to operate in great…

We present an interacting branching model of neural network dynamics, incorporating key biological features such as inhibition with several types of inhibitory interactions. We establish a hierarchy of analytical mean-field approximations…

Research showed that, the information transmitted in biological neurons is encoded in the instants of successive action potentials or their firing rate. In addition to that, in-vivo operation of the neuron makes measurement difficult and…

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…