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Understanding cognitive flexibility and task-switching mechanisms in neural systems requires biologically plausible computational models. This tutorial presents a step-by-step approach to constructing a spiking neural network (SNN) that…

The extraordinary computational power of the brain may be related in part to the fact that each of the smaller neural networks that compose it can behave transiently in many different ways, depending on its inputs. Mathematically, input…

Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…

We present a structured neural network architecture that is inspired by linear time-varying dynamical systems. The network is designed to mimic the properties of linear dynamical systems which makes analysis and control simple. The…

Directed information transmission is paramount for many social, physical, and biological systems. For neural systems, scientists have studied this problem under the paradigm of feedforward networks for decades. In most models of feedforward…

We study the dynamics of networks with inhibitory and excitatory leaky-integrate-and-fire neurons with short-term synaptic plasticity in the presence of depressive and facilitating mechanisms. The dynamics is analyzed by a Heterogeneous…

The task of the brain is to look for structure in the external input. We study a network of integrate-and-fire neurons with several types of recurrent connections that learns the structure of its time-varying feedforward input by attempting…

We study a model of spiking neurons, with recurrent connections that result from learning a set of spatio-temporal patterns with a spike-timing dependent plasticity rule and a global inhibition. We investigate the ability of the network to…

Spiking neural networks drawing inspiration from biological constraints of the brain promise an energy-efficient paradigm for artificial intelligence. However, challenges exist in identifying guiding principles to train these networks in a…

A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated…

Bayesian Networks may be appealing for clinical decision-making due to their inclusion of causal knowledge, but their practical adoption remains limited as a result of their inability to deal with unstructured data. While neural networks do…

Networks are ubiquitous throughout science and engineering. A number of methods, including some from our own group, have explored how one goes about computing or predicting the dynamics of networks given information about internal models of…

Computational modeling is becoming a widely used methodology in modern neuroscience. However, as the complexity of the phenomena under study increases, the analysis of the results emerging from the simulations concomitantly becomes more…

Spiking activity of neurons engaged in learning and performing a task show complex spatiotemporal dynamics. While the output of recurrent network models can learn to perform various tasks, the possible range of recurrent dynamics that…

The control of complex networks is of paramount importance in areas as diverse as ecosystem management, emergency response, and cell reprogramming. A fundamental property of networks is that perturbations to one node can affect other nodes,…

Attractor dynamics are a fundamental computational motif in neural circuits, supporting diverse cognitive functions through stable, self-sustaining patterns of neural activity. In these lecture notes, we review four key examples that…

Human brain contains about 10 billion neurons, each of which has about 10~10,000 nerve endings from which neurotransmitters are released in response to incoming spikes, and the released neurotransmitters then bind to receptors located in…

Working Memory is the brain module that holds and manipulates information online. In this work, we design a hybrid model in which a simple feed-forward network is coupled to a balanced random network via a read-write vector called the…

Our understanding of neural computation is founded on the assumption that neurons fire in response to a linear summation of inputs. Yet experiments demonstrate that some neurons are capable of complex functions that require interactions…

Dimensionality reduction, a form of compression, can simplify representations of information to increase efficiency and reveal general patterns. Yet, this simplification also forfeits information, thereby reducing representational capacity.…