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In this paper, we present a control synthesis framework for a general class of nonlinear, control-affine systems under spatiotemporal and input constraints. First, we study the problem of fixed-time convergence in the presence of input…

Sparse sequences of neural spikes are posited to underlie aspects of working memory, motor production, and learning. Discovering these sequences in an unsupervised manner is a longstanding problem in statistical neuroscience. Promising…

We study coarse pattern formation in a cellular automaton modelling a spatially-extended stochastic neural network. The model, originally proposed by Gong and Robinson [36], is known to support stationary and travelling bumps of localised…

We propose the Neural Functional Alignment Space (NFAS), a brain-referenced representational framework for characterizing artificial neural networks on equal functional grounds. NFAS departs from conventional alignment approaches that rely…

In neuroscience, functional brain connectivity describes the connectivity between brain regions that share functional properties. Neuroscientists often characterize it by a time series of covariance matrices between functional measurements…

We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…

Filtered shot noise processes have proven to be very effective in modelling the evolution of systems exposed to stochastic shot noise sources, and have been applied to a wide variety of fields ranging from electronics through biology. In…

Mental and cognitive representations are believed to reside on low-dimensional, non-linear manifolds embedded within high-dimensional brain activity. Uncovering these manifolds is key to understanding individual differences in brain…

Neuronal firing activities have attracted a lot of attention since a large population of spatiotemporal patterns in the brain is the basis for adaptive behavior and can also reveal the signs for various neurological disorders including…

The purpose of this paper is to provide a complete description of the eigenvalues of the generator of a neutral multi-type Moran model, and the applications to the study of the speed of convergence to stationarity. The Moran model we…

Large-scale systems with inherent heterogeneity often exhibit complex dynamics that are crucial for their functional properties. However, understanding how such heterogeneity shapes these dynamics remains a significant challenge,…

Using network models consisting of gap junction coupled Wang-Buszaki neurons, we demonstrate that it is possible to obtain not only synchronous activity between neurons but also a variety of constant phase shifts between 0 and \pi. We call…

We introduce a foundational model for brain dynamics that utilizes stochastic optimal control (SOC) and amortized inference. Our method features a continuous-discrete state space model (SSM) that can robustly handle the intricate and noisy…

We consider the feedback design for stabilizing a rigid body system by making and breaking multiple contacts with the environment without prespecifying the timing or the number of occurrence of the contacts. We model such a system as a…

In the cerebral cortex, neurons are subject to a continuous bombardment of synaptic inputs originating from the network's background activity. This leads to ongoing, mostly subthreshold membrane dynamics that depends on the statistics of…

The field of neuroimaging has truly become data rich, and novel analytical methods capable of gleaning meaningful information from large stores of imaging data are in high demand. Those methods that might also be applicable on the level of…

A neuron transforms its input into output spikes, and this transformation is the basic unit of computation in the nervous system. The spiking response of the neuron to a complex, time-varying input can be predicted from the detailed…

When substrate-constrained covariance flow on the Bures--Wasserstein manifold reaches the Williamson boundary, single-mode compression saturates and further admissible covariance evolution is forced into the cross-mode complement. This…

In this paper we report the control and synchronization of chaos in a Memristive Murali-Lakshmanan-Chua circuit. This circuit, introduced by the present authors in 2013, is basically a non-smooth system having two discontinuity boundaries…

A core goal of functional neuroimaging is to study how the environment is processed in the brain. The mainstream paradigm involves concurrently measuring a broad spectrum of brain responses to a small set of environmental features…