Related papers: Markov Processes and Brain Network Hubs
We introduce a nonlinear modification of the classical Hawkes process, which allows inhibitory couplings between units without restrictions. The resulting system of interacting point processes provides a useful mathematical model for…
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…
Recurrent networks of binary neurons are a foundational concept in artificial intelligence. While these networks are traditionally assumed to be fully connected, complex dynamics can emerge when the graph structure is varied. One graph…
Graph is a universe data structure that is widely used to organize data in real-world. Various real-word networks like the transportation network, social and academic network can be represented by graphs. Recent years have witnessed the…
The brain is an intricately structured organ responsible for the rich emergent dynamics that support the complex cognitive functions we enjoy as humans. With around $10^{11}$ neurons and $10^{15}$ synapses, understanding how the human brain…
Many complex systems exhibit interactions that depend not only on pairwise connections, but also group structures and memory effects. To capture such effects, we develop a unified tensor framework for modeling higher-order Markov chains…
Markov decision processes (MDPs) in queues and networks have been an interesting topic in many practical areas since the 1960s. This paper provides a detailed overview on this topic and tracks the evolution of many basic results. Also, this…
How perception and reasoning arise from neuronal network activity is poorly understood. This is reflected in the fundamental limitations of connectionist artificial intelligence, typified by deep neural networks trained via gradient-based…
In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following…
In data science, hypergraphs are natural models for data exhibiting multi-way relations, whereas graphs only capture pairwise. Nonetheless, many proposed hypergraph neural networks effectively reduce hypergraphs to undirected graphs via…
Spiking neuronal networks (SNNs) are widely used in computational neuroscience, from biologically realistic modeling of local cortical networks to phenomenological modeling of the whole brain. Despite their prevalence, a systematic…
The problem of finding the optimal set of source nodes in a diffusion network that maximizes the spread of information, influence, and diseases in a limited amount of time depends dramatically on the underlying temporal dynamics of the…
Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the…
We study Markov processes where the "time" parameter is replaced by paths in a directed graph from an initial vertex to a terminal one. Along each directed path the process is Markov and has the same distribution as the one along any other…
A graph generative model defines a distribution over graphs. One type of generative model is constructed by autoregressive neural networks, which sequentially add nodes and edges to generate a graph. However, the likelihood of a graph under…
Neural network models are one of the most successful approaches to machine learning, enjoying an enormous amount of development and research over recent years and finding concrete real-world applications in almost any conceivable area of…
Mathematical modelling of the macroscopic electrical activity of the brain is highly non-trivial and requires a detailed understanding of not only the associated mathematical techniques, but also the underlying physiology and anatomy.…
Graph neural networks (GNNs) have achieved tremendous success on multiple graph-based learning tasks by fusing network structure and node features. Modern GNN models are built upon iterative aggregation of neighbor's/proximity features by…
We consider Markov jump processes on a graph described by a rate matrix that depends on various control parameters. We derive explicit expressions for the static responses of edge currents and steady-state probabilities. We show that they…
Neural networks show a progressive increase in complexity during the time course of evolution. From diffuse nerve nets in Cnidaria to modular, hierarchical systems in macaque and humans, there is a gradual shift from simple processes…