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Recent developments in experimental neuroscience make it possible to simultaneously record the activity of thousands of neurons. However, the development of analysis approaches for such large-scale neural recordings have been slower than those applicable to single-cell experiments. One approach that has gained recent popularity is neural manifold learning. This approach takes advantage of the fact that often, even though neural datasets may be very high dimensional, the dynamics of neural activity tends to traverse a much lower-dimensional space. The topological structures formed by these low-dimensional neural subspaces are referred to as "neural manifolds", and may potentially provide insight linking neural circuit dynamics with cognitive function and behavioral performance. In this paper we review a number of linear and non-linear approaches to neural manifold learning, including principal component analysis (PCA), multi-dimensional scaling (MDS), Isomap, locally linear embedding (LLE), Laplacian eigenmaps (LEM), t-SNE, and uniform manifold approximation and projection (UMAP). We outline these methods under a common mathematical nomenclature, and compare their advantages and disadvantages with respect to their use for neural data analysis. We apply them to a number of datasets from published literature, comparing the manifolds that result from their application to hippocampal place cells, motor cortical neurons during a reaching task, and prefrontal cortical neurons during a multi-behavior task. We find that in many circumstances linear algorithms produce similar results to non-linear methods, although in particular cases where the behavioral complexity is greater, non-linear methods tend to find lower-dimensional manifolds, at the possible expense of interpretability. We demonstrate that these methods are applicable to the study of neurological disorders through simulation of a mouse model of Alzheimer's Disease, and speculate that neural manifold analysis may help us to understand the circuit-level consequences of molecular and cellular neuropathology., (© 2022. The Author(s).)

The connectivity of a neuronal network has a major effect on its functionality and role. It is generally believed that the complex network structure of the brain provides a physiological basis for information processing. Therefore, identifying the network's topology has received a lot of attentions in neuroscience and has been the center of many research initiatives such as Human Connectome Project. Nevertheless, direct and invasive approaches that slice and observe the neural tissue have proven to be time consuming, complex and costly. As a result, the inverse methods that utilize firing activity of neurons in order to identify the (functional) connections have gained momentum recently, especially in light of rapid advances in recording technologies; It will soon be possible to simultaneously monitor the activities of tens of thousands of neurons in real time. While there are a number of excellent approaches that aim to identify the functional connections from firing activities, the scalability of the proposed techniques plays a major challenge in applying them on large-scale datasets of recorded firing activities. In exceptional cases where scalability has not been an issue, the theoretical performance guarantees are usually limited to a specific family of neurons or the type of firing activities. In this paper, we formulate the neural network reconstruction as an instance of a graph learning problem, where we observe the behavior of nodes/neurons (i.e., firing activities) and aim to find the links/connections. We develop a scalable learning mechanism and derive the conditions under which the estimated graph for a network of Leaky Integrate and Fire (LIf) neurons matches the true underlying synaptic connections. We then validate the performance of the algorithm using artificially generated data (for benchmarking) and real data recorded from multiple hippocampal areas in rats.

Multiscale modeling by means of co-simulation is a powerful tool to address many vital questions in neuroscience. It can for example be applied in the study of the process of learning and memory formation in the brain. At the same time the co-simulation technique makes it possible to take advantage of interoperability between existing tools and multi-physics models as well as distributed computing. However, the theoretical basis for multiscale modeling is not sufficiently understood. There is, for example, a need of efficient and accurate numerical methods for time integration. When time constants of model components are different by several orders of magnitude, individual dynamics and mathematical definitions of each component all together impose stability, accuracy and efficiency challenges for the time integrator. Following our numerical investigations in Brocke et al. (Frontiers in Computational Neuroscience, 10, 97, 2016), we present a new multirate algorithm that allows us to handle each component of a large system with a step size appropriate to its time scale. We take care of error estimates in a recursive manner allowing individual components to follow their discretization time course while keeping numerical error within acceptable bounds. The method is developed with an ultimate goal of minimizing the communication between the components. Thus it is especially suitable for co-simulations. Our preliminary results support our confidence that the multirate approach can be used in the class of problems we are interested in. We show that the dynamics ofa communication signal as well as an appropriate choice of the discretization order between system components may have a significant impact on the accuracy of the coupled simulation. Although, the ideas presented in the paper have only been tested on a single model, it is likely that they can be applied to other problems without loss of generality. We believe that this work may significantly contribute to the establishment of a firm theoretical basis and to the development of an efficient computational framework for multiscale modeling and simulations.

In this paper we examine how a neuron's dendritic morphology can affect its pattern recognition performance. We use two different algorithms to systematically explore the space of dendritic morphologies: an algorithm that generates all possible dendritic trees with 22 terminal points, and one that creates representative samples of trees with 128 terminal points. Based on these trees, we construct multi-compartmental models. To assess the performance of the resulting neuronal models, we quantify their ability to discriminate learnt and novel input patterns. We find that the dendritic morphology does have a considerable effect on pattern recognition performance and that the neuronal performance is inversely correlated with the mean depth of the dendritic tree. The results also reveal that the asymmetry index of the dendritic tree does not correlate with the performance for the full range of tree morphologies. The performance of neurons with dendritic tapering is best predicted by the mean and variance of the electrotonic distance of their synapses to the soma. All relationships found for passive neuron models also hold, even in more accentuated form, for neurons with active membranes.

This paper compares the ability of different methods to detect and resolve spikes recorded extracellularly with polytrode and high-density microelectrode arrays (MEAs). Detecting spikes on such arrays is more complex than with single electrodes or tetrodes since a single spike from a neuron may cause threshold crossings on several adjacent channels, giving rise to multiple events. These initial events have to be recognized as belonging to a single spike. Combining them is, in essence, a clustering problem. A conflicting need is to be able to resolve spike waveforms that occur close together in space and time. We first evaluated three different detection methods, using simulated data in which spike shape waveforms obtained from real recordings were added to noise with an amplitude and temporal structure similar to that found in real recordings. Performance was assessed by calculating the percentage of correctly identified spikes vs. the false positive rate. Using the best of these detection methods, two different methods for avoiding multiple detections per spike were tested: one based on windowing and the other based on clustering. Using parameters that avoided spatial and temporal duplication, the spatiotemporal resolution of the two methods was next evaluated. The method based on clustering gave slightly better results. Both methods could resolve spikes occurring 1 ms or more apart, regardless of their spatial separation. There was no restriction on the temporal resolution of spike pairs for units more than 200 μm apart.

In this paper we show that the emergence of perceptual units in V1 can be explained in terms of a physical mechanism of simmetry breaking of the mean field neural equation. We consider a mean field neural model which takes into account the functional architecture of the visual cortex modeled as a group of rotations and translations equipped with a degenerate metric. The model generalizes well known results of Bressloff and Cowan which, in absence of input, accounts for hallucination patterns. The main result of our study consists in showing that in presence of a visual input, the stable eigenmodes of the linearized operator represent perceptual units of the visual stimulus. The result is strictly related to dimensionality reduction and clustering problems.

Lyapunov exponents are a basic and powerful tool to characterise the long-term behaviour of dynamical systems. The computation of Lyapunov exponents for continuous time dynamical systems is straightforward whenever they are ruled by vector fields that are sufficiently smooth to admit a variational model. Hybrid neurons do not belong to this wide class of systems since they are intrinsically non-smooth owing to the impact and sometimes switching model used to describe the integrate-and-fire (I&F) mechanism. In this paper we show how a variational model can be defined also for this class of neurons by resorting to saltation matrices. This extension allows the computation of Lyapunov exponent spectrum of hybrid neurons and of networks made up of them through a standard numerical approach even in the case of neurons firing synchronously.

A biologically inspired model of head direction cells is presented and tested on a small mobile robot. Head direction cells (discovered in the brain of rats in 1984) encode the head orientation of their host irrespective of the host's location in the environment. The head direction system thus acts as a biological compass (though not a magnetic one) for its host. Head direction cells are influenced in different ways by idiothetic (host-centred) and allothetic (not host-centred) cues. The model presented here uses the visual, vestibular and kinesthetic inputs that are simulated by robot sensors. Real robot-sensor data has been used in order to train the model's artificial neural network connections. The main contribution of this paper lies in the use of an evolutionary algorithm in order to determine the values of parameters that determine the behaviour of the model. More importantly, the objective function of the evolutionary strategy used takes into consideration quantitative biological observations reported in the literature.

Many research groups have sought to measure phase response curves (PRCs) from real neurons. However, methods of estimating PRCs from noisy spike-response data have yet to be established. In this paper, we propose a Bayesian approach for estimating PRCs. First, we analytically obtain a likelihood function of the PRC from a detailed model of the observation process formulated as Langevin equations. Then we construct a maximum a posteriori (MAP) estimation algorithm based on the analytically obtained likelihood function. The MAP estimation algorithm derived here is equivalent to the spherical spin model. Moreover, we analytically calculate a marginal likelihood corresponding to the free energy of the spherical spin model, which enables us to estimate the hyper-parameters, i.e., the intensity of the Langevin force and the smoothness of the prior.

Most oncological microarray studies focus on molecular distinctions in different cancer entities. Recently, researchers started using microarrays for investigating molecular commonalities of multiple cancer types. This poses novel bioinformatics challenges. In this paper we describe a method that detects common molecular mechanisms in different cancer entities. The method extends previously described concepts by introducing Meta-Analysis Pattern Matches. In an analysis of four prognostic cancer studies, involving breast cancer, leukemia, and mesothelioma, we are able to identify 42 genes that show consistent up- or down-regulation in patients with a poor disease outcome. These genes complement the set of previously published candidates for universal prognostic markers in cancer.