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Bump attractors are wandering localised patterns observed in in vivo experiments of spatially-extended neurobiological networks. They are important for the brain's navigational system and specific memory tasks. A bump attractor is…
Self-sustained, elevated neuronal activity persisting on time scales of ten seconds or longer is thought to be vital for aspects of working memory, including brain representations of real space. Continuous-attractor neural networks, one of…
This paper investigates the conditions for the formation of local bumps in the activity of binary attractor neural networks with spatially dependent connectivity. We show that these formations are observed when asymmetry between the…
Persistent activity in neuronal populations has been shown to represent the spatial position of remembered stimuli. Networks that support bump attractors are often used to model such persistent activity. Such models usually exhibit…
A bump attractor network is a model that implements a competitive neuronal process emerging from a spike pattern related to an input source. Since the bump network could behave in many ways, this paper explores some critical limits of the…
Maintaining stable internal representations of continuous variables is fundamental for effective robotic control. Continuous attractor networks provide a biologically inspired mechanism for encoding such variables, yet neuromorphic…
Bump hunting deals with finding in sample spaces meaningful data subsets known as bumps. These have traditionally been conceived as modal or concave regions in the graph of the underlying density function. We define an abstract bump…
Continuous attractors have been used to understand recent neuroscience experiments where persistent activity patterns encode internal representations of external attributes like head direction or spatial location. However, the conditions…
We investigate the dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of their neuronal interactions, CANNs can hold a continuous family of stationary states. We systematically explore how their…
We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of…
Identification of attractors, that is, stable states and sustained oscillations, is an important step in the analysis of Boolean models and exploration of potential variants. We describe an approach to the search for asynchronous cyclic…
Attractor models are simplified models used to describe the dynamics of firing rate profiles of a pool of neurons. The firing rate profile, or the neuronal activity, is thought to carry information. Continuous attractor neural networks…
Recurrent neural networks are powerful tools for understanding and modeling computation and representation by populations of neurons. Continuous-variable or "rate" model networks have been analyzed and applied extensively for these…
We introduce a novel model for updating perceptual beliefs about the environment by extending the concept of Allostasis to the control of internal representations. Allostasis is a fundamental regulatory mechanism observed in animal…
We investigated the dynamical behaviors of bimodular continuous attractor neural networks, each processing a modality of sensory input and interacting with each other. We found that when bumps coexist in both modules, the position of each…
Understanding how the dynamics of a neural network is shaped by the network structure, and consequently how the network structure facilitates the functions implemented by the neural system, is at the core of using mathematical models to…
Information coding by precise timing of spikes can be faster and more energy-efficient than traditional rate coding. However, spike-timing codes are often brittle, which has limited their use in theoretical neuroscience and computing…
In this review, we describe the singular success of attractor neural network models in describing how the brain maintains persistent activity states for working memory, error-corrects, and integrates noisy cues. We consider the mechanisms…
We present a theoretical study aiming at model fitting for sensory neurons. Conventional neural network training approaches are not applicable to this problem due to lack of continuous data. Although the stimulus can be considered as a…
A fundamental problem in neuroscience is understanding how working memory -- the ability to store information at intermediate timescales, like 10s of seconds -- is implemented in realistic neuronal networks. The most likely candidate…