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We consider a ring network of quadratic integrate-and-fire neurons with nonlocal synaptic and gap junction coupling. The corresponding neural field model supports solutions such as standing and travelling waves, and also lurching waves. We…
Wireless networks are inherently graph-structured, which can be utilized in graph representation learning to solve complex wireless network optimization problems. In graph representation learning, feature vectors for each entity in the…
The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work…
Mathematical modeling has broad applications in neuroscience whether modeling the dynamics of a single synapse or an entire network of neurons. In Part I, we model vesicle replenishment and release at the photoreceptor synapse to better…
The application of graph theory to model the complex structure and function of the brain has shed new light on its organization and function, prompting the emergence of network neuroscience. Despite the tremendous progress that has been…
A neural network system in an animal brain contains many modules and generates adaptive behavior by integrating the outputs from the modules. The mathematical modeling of such large systems to elucidate the mechanism of rapidly finding…
Graph neural networks have emerged as a powerful tool for learning spatiotemporal interactions. However, conventional approaches often rely on predefined graphs, which may obscure the precise relationships being modeled. Additionally,…
Finding optimal paths in connected graphs requires determining the smallest total cost for traveling along the graph's edges. This problem can be solved by several classical algorithms where, usually, costs are predefined for all edges.…
The central nervous system is composed of many individual units -- from cells to areas -- that are connected with one another in a complex pattern of functional interactions that supports perception, action, and cognition. One natural and…
The neural mechanism of memory has a very close relation with the problem of representation in artificial intelligence. In this paper a computational model was proposed to simulate the network of neurons in brain and how they process…
Grid cells in the entorhinal cortex, together with head direction, place, speed and border cells, are major contributors to the organization of spatial representations in the brain. In this work we introduce a novel theoretical and…
Autonomous navigation is a key skill for assistive and service robots. To be successful, robots have to minimise the disruption caused to humans while moving. This implies predicting how people will move and complying with social…
When the navigational environment is known, it can be represented as a graph where landmarks are nodes, the robot behaviors that move from node to node are edges, and the route is a set of behavioral instructions. The route path from source…
Identifying unusual brain activity is a crucial task in neuroscience research, as it aids in the early detection of brain disorders. It is common to represent brain networks as graphs, and researchers have developed various graph-based…
Spatial navigation in mammals is based on building a mental representation of their environment---a cognitive map. However, both the nature of this cognitive map and its underpinning in neural structures and activity remains vague. A key…
With the fast and unstoppable evolution of robotics and artificial intelligence, effective autonomous navigation in real-world scenarios has become one of the most pressing challenges in the literature. However, demanding requirements, such…
The irreducible complexity of natural phenomena has led Graph Neural Networks to be employed as a standard model to perform representation learning tasks on graph-structured data. While their capacity to capture local and global patterns is…
The hippocampal formation is thought to learn spatial maps of environments, and in many models this learning process consists of forming a sensory association for each location in the environment. This is inefficient, akin to learning a…
The human brain can be considered to be a graphical structure comprising of tens of billions of biological neurons connected by synapses. It has the remarkable ability to automatically re-route information flow through alternate paths in…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…