Computational Mathematics ePosters

Training recurrent neural networks (RNNs) to perform neuroscience tasks can be challenging. Unlike in machine learning where any architectural modification of an RNN (e.g. GRU or LSTM) is acceptable if it facilitates training, the RNN models trained as models of brain dynamics are subject to plausibility constraints…

In neuroscience, we record neural activity over time. We can try to make sense of this data by studying the (low-dimensional) space the activity is constrained to. To identify these spaces, one typically either treats the rows (neurons / spike trains) or the columns (timepoints / population vectors) of the activity…

Understanding how the brain encodes stimuli is a fundamental problem in computational neuroscience. This has inspired the development of artificial neural networks that learn representations by incorporating brain-like learning abilities. Recent work has focused on learning representations (latents) by capturing…

Navigation is inherently dynamic. It involves learning the environment, as well as positions in and trajectories through it, and then executing a path to reach a target. Spatial navigation skills vary significantly among individuals. But what differentiates a good navigator from a bad one, or an easy-to-navigate path…

Dual-task interference is a widely observed phenomenon where the decision-making becomes less efficient (slower or less accurate) [1]. This inefficiency is proposed to be a potential interference between the two decision-making processes, but the nature and extent of this interference have been debated [2]. For…

Understanding the mechanisms regulating Ca2+ concentrations in the presynapse is crucial for synaptic function. The endoplasmic reticulum (ER) acts as a finite calcium store and can modulate calcium signals involved in presynaptic neurotransmitter release. While computational studies have shed light on the…

We adapt nonlinear optimal control theory (OCT) to control oscillations and network synchrony and apply it to models of neural population dynamics. Conventionally, OCT requires a target trajectory. This requirement may be overly restrictive for oscillatory targets since the exact trajectory shape including amplitude…

A central aim in computational neuroscience is to relate the activity of large populations of neurons to an underlying dynamical system. Models of these neural dynamics should ideally be both interpretable and fit the observed data well. Low-rank recurrent neural networks (RNNs) exhibit such interpretability by having…

Networks composed of Non-Negative Matrix Factorization (NNMF) [1] modules can serve as abstractions of real neural networks. In particular, NNMF networks can be extended easily to perform computations based on stochastic spikes [2,3]. However, due to training via Autograd approaches following exact gradients to train…

In neuroscience, ordinary differential equations (ODEs) are widely used to simulate the dynamics of neural systems, but identifying parameters that explain experimental measurements is challenging. In particular, while these models are differentiable and would allow for gradient-based parameter optimization, the…

A model for NMDA-receptor-mediated synaptic currents generating persistent activity proposed by Wang and Brunel [1–3] has been widely adopted in computational neuroscience, both for spiking-neuron and mean-field models [2, 4]. The model describes NMDA synaptic dynamics by a phenomenological two-dimensional nonlinear…