Related papers: A Computational Approach for the inverse problem o…

The Hodgkin and Huxley (H-H) model is a nonlinear system of four equations that describes how action potentials in neurons are initiated and propagated, and represents a major advance in the understanding of nerve cells. However, some of…

We give an approximate solution to the difficult inverse problem of inferring the topology of an unknown network from given time-dependent signals at the nodes. For example, we measure signals from individual neurons in the brain, and infer…

We present a neural network for the solution of the inverse swarm problem of deriving cross sections from swarm transport data. To account for the uncertainty inherent to this somewhat ill-posed inverse problem, we train the neural network…

This paper applies the classical prediction error method (PEM) to the estimation of nonlinear discrete-time models of neuronal systems subject to input-additive noise. While the nonlinear system exhibits excitability, bifurcations, and…

Selfridge, along with Sutherland and Marr provided some of the earliest proposals for how to program computers to recognize shapes. Their emphasis on filtering for contour features, especially the orientation of boundary segments, was…

The traditional view of neural computation in the cerebral cortex holds that sensory neurons are specialized, i.e., selective for certain dimensions of sensory stimuli. This view was challenged by evidence of contextual interactions between…

An inverse procedure is proposed and tested which aims at recovering the a priori unknown functional and structural information from global signals of living brains activity. To this end we consider a Leaky-Integrate and Fire (LIF) model…

In this work, we develop a novel neural network (NN) approach to solve the discrete inverse conductivity problem of recovering the conductivity profile on network edges from the discrete Dirichlet-to-Neumann map on a square lattice. The…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

We introduce and study methods for inferring and learning from correspondences among neurons. The approach enables alignment of data from distinct multiunit studies of nervous systems. We show that the methods for inferring correspondences…

Building on recent work on capsule networks, we propose a new, general-purpose form of "routing by agreement" that activates output capsules in a layer as a function of their net benefit to use and net cost to ignore input capsules from…

We present a simple linear regression based approach for learning the weights and biases of a neural network, as an alternative to standard gradient based backpropagation. The present work is exploratory in nature, and we restrict the…

Neural field equations offer a continuous description of the dynamics of large populations of synaptically coupled neurons. This makes them a convenient tool to describe various neural processes, such as working memory, motion perception,…

The choice of a suitable regularization parameter is an important part of most regularization methods for inverse problems. In the absence of reliable estimates of the noise level, heuristic parameter choice rules can be used to accomplish…

Recent in vitro data show that neurons respond to input variance with varying sensitivities. Here, we demonstrate that Hodgkin-Huxley (HH) neurons can operate in two computational regimes, one that is more sensitive to input variance…

In this paper, the local convergence of Iteratively regularized Landweber iteration method is investigated for solving non-linear inverse problems in Banach spaces. Our analysis mainly relies on the assumption that the inverse mapping…

Neural circuits can be reconstructed from brain images acquired by serial section electron microscopy. Image analysis has been performed by manual labor for half a century, and efforts at automation date back almost as far. Convolutional…

In this work, we use an explainable convolutional neural network (NLS-Net) to solve an inverse problem of the nonlinear Schr\"odinger equation, which is widely used in fiber-optic communications. The landscape and minimizers of the…

We focus on non-stationary Maxwell equations defined on a regular patch of elements as considered in the isogeometric analysis (IGA). We apply the time-integration scheme following the ideas developed by the finite difference community [M.…

We derive and analyse a new variant of the iteratively regularized Landweber iteration, for solving linear and nonlinear ill-posed inverse problems. The method takes into account training data, which are used to estimate the interior of a…