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Assessing the similarity of matrices is valuable for analyzing the extent to which data sets exhibit common features in tasks such as data clustering, dimensionality reduction, pattern recognition, group comparison, and graph analysis. Methods proposed for comparing vectors, such as cosine similarity, can be readily generalized to matrices. However, this approach usually neglects the inherent two-dimensional structure of matrices. Here, we propose singular angle similarity (SAS), a measure for evaluating the structural similarity between two arbitrary, real matrices of the same shape based on singular value decomposition. After introducing the measure, we compare SAS with standard measures for matrix comparison and show that only SAS captures the two-dimensional structure of matrices. Further, we characterize the behavior of SAS in the presence of noise and as a function of matrix dimensionality. Finally, we apply SAS to two use cases: square non-symmetric matrices of probabilistic network connectivity, and non-square matrices representing neural brain activity. For synthetic data of network connectivity, SAS matches intuitive expectations and allows for a robust assessment of similarities and differences. For experimental data of brain activity, SAS captures differences in the structure of high-dimensional responses to different stimuli. We conclude that SAS is a suitable measure for quantifying the shared structure of matrices with arbitrary shape., Comment: 12 pages, 6 figures

The mechanisms underlying pathologically synchronized neural oscillations in Parkinson's disease (PD) and generalized epilepsies are jointly explored via a neural field model of the corticothalamic-basal ganglia (CTBG) system. The basal ganglia (BG) are approximated as a single effective population and their roles in modulating oscillatory corticothalamic (CT) dynamics and vice versa are analyzed. Besides normal EEG rhythms, enhanced activity around 4 Hz and 20 Hz exists in the model, consistent with characteristic frequencies in PD. These rhythms result from resonances in loops between the BG and CT populations, analogous to those underlying epileptic oscillations in a previous CT model. Dopamine depletion is argued to weaken the dampening of these resonances in PD, and network connections explain the significant coherence between BG, thalamic, and cortical activity around 4-8 Hz and 20 Hz. Parallels between the afferent and efferent connection sites of the thalamic reticular nucleus (TRN) and BG predict low dopamine to correspond to a reduced likelihood of tonic-clonic (grand mal) seizures, agreeing with experimental findings. Further, the model predicts an increased likelihood of absence (petit mal) seizure resulting from low dopamine levels matching experimental findings. Suppression of absence seizure activity is shown when afferent and efferent BG connections to the CT system are strengthened, consistent with other CTBG modeling studies. The BG are demonstrated to suppress activity of the CTBG system near tonic-clonic seizure states, providing insight into the reported efficacy of current treatments in BG circuits. Sleep states of the TRN are also found to suppress pathological PD activity matching observations. Overall, the findings demonstrate strong parallels between coherent oscillations in generalized epilepsies and PD, and provide insights into possible comorbidities.

Despite its successes, to date Artificial Intelligence (AI) is still characterized by a number of shortcomings with regards to different application domains and goals. These limitations are arguably both conceptual (e.g., related to underlying theoretical models, such as symbolic vs. connectionist), and operational (e.g., related to robustness and ability to generalize). Biologically inspired AI, and more specifically brain-inspired AI, promises to provide further biological aspects beyond those that are already traditionally included in AI, making it possible to assess and possibly overcome some of its present shortcomings. This article examines some conceptual, technical, and ethical issues raised by the development and use of brain-inspired AI. Against this background, the paper asks whether there is anything ethically unique about brain-inspired AI. The aim of the paper is to introduce a method that has a heuristic nature and that can be applied to identify and address the ethical issues arising from brain-inspired AI. The conclusion resulting from the application of this method is that, compared to traditional AI, brain-inspired AI raises new foundational ethical issues and some new practical ethical issues, and exacerbates some of the issues raised by traditional AI., Comment: 30 pages theoretical article resulting from a multidisciplinary collaboration about technical, theoretical and ethical aspects of brain-inspired AI

This chapter sheds light on the synaptic organization of the brain from the perspective of computational neuroscience. It provides an introductory overview on how to account for empirical data in mathematical models, implement such models in software, and perform simulations reflecting experiments. This path is demonstrated with respect to four key aspects of synaptic signaling: the connectivity of brain networks, synaptic transmission, synaptic plasticity, and the heterogeneity across synapses. Each step and aspect of the modeling and simulation workflow comes with its own challenges and pitfalls, which are highlighted and addressed., Comment: 38 pages, 5 figures, LaTeX; added two figures, clarified and extended formulations, updated format, added references

Sustainable research on computational models of neuronal networks requires published models to be understandable, reproducible, and extendable. Missing details or ambiguities about mathematical concepts and assumptions, algorithmic implementations, or parameterizations hinder progress. Such flaws are unfortunately frequent and one reason is a lack of readily applicable standards and tools for model description. Our work aims to advance complete and concise descriptions of network connectivity but also to guide the implementation of connection routines in simulation software and neuromorphic hardware systems. We first review models made available by the computational neuroscience community in the repositories ModelDB and Open Source Brain, and investigate the corresponding connectivity structures and their descriptions in both manuscript and code. The review comprises the connectivity of networks with diverse levels of neuroanatomical detail and exposes how connectivity is abstracted in existing description languages and simulator interfaces. We find that a substantial proportion of the published descriptions of connectivity is ambiguous. Based on this review, we derive a set of connectivity concepts for deterministically and probabilistically connected networks and also address networks embedded in metric space. Beside these mathematical and textual guidelines, we propose a unified graphical notation for network diagrams to facilitate an intuitive understanding of network properties. Examples of representative network models demonstrate the practical use of the ideas. We hope that the proposed standardizations will contribute to unambiguous descriptions and reproducible implementations of neuronal network connectivity in computational neuroscience.

Being permanently confronted with an uncertain world, brains have faced evolutionary pressure to represent this uncertainty in order to respond appropriately. Often, this requires visiting multiple interpretations of the available information or multiple solutions to an encountered problem. This gives rise to the so-called mixing problem: since all of these "valid" states represent powerful attractors, but between themselves can be very dissimilar, switching between such states can be difficult. We propose that cortical oscillations can be effectively used to overcome this challenge. By acting as an effective temperature, background spiking activity modulates exploration. Rhythmic changes induced by cortical oscillations can then be interpreted as a form of simulated tempering. We provide a rigorous mathematical discussion of this link and study some of its phenomenological implications in computer simulations. This identifies a new computational role of cortical oscillations and connects them to various phenomena in the brain, such as sampling-based probabilistic inference, memory replay, multisensory cue combination, and place cell flickering., Comment: 34 pages, 9 figures

A complex interplay of single-neuron properties and the recurrent network structure shapes the activity of cortical neurons. The single-neuron activity statistics differ in general from the respective population statistics, including spectra and, correspondingly, autocorrelation times. We develop a theory for self-consistent second-order single-neuron statistics in block-structured sparse random networks of spiking neurons. In particular, the theory predicts the neuron-level autocorrelation times, also known as intrinsic timescales, of the neuronal activity. The theory is based on an extension of dynamic mean-field theory from rate networks to spiking networks, which is validated via simulations. It accounts for both static variability, e.g. due to a distributed number of incoming synapses per neuron, and temporal fluctuations of the input. We apply the theory to balanced random networks of generalized linear model neurons, balanced random networks of leaky integrate-and-fire neurons, and a biologically constrained network of leaky integrate-and-fire neurons. For the generalized linear model network with an error function nonlinearity, a novel analytical solution of the colored noise problem allows us to obtain self-consistent firing rate distributions, single-neuron power spectra, and intrinsic timescales. For the leaky integrate-and-fire networks, we derive an approximate analytical solution of the colored noise problem, based on the Stratonovich approximation of the Wiener-Rice series and a novel analytical solution for the free upcrossing statistics. Again closing the system self-consistently, in the fluctuation-driven regime this approximation yields reliable estimates of the mean firing rate and its variance across neurons, the inter-spike interval distribution, the single-neuron power spectra, and intrinsic timescales.

Multi-electrode arrays covering several square millimeters of neural tissue provide simultaneous access to population signals such as extracellular potentials and spiking activity of one hundred or more individual neurons. The interpretation of the recorded data calls for multiscale computational models with corresponding spatial dimensions and signal predictions. Multi-layer spiking neuron network models of local cortical circuits covering about 1 mm$^2$ have been developed, integrating experimentally obtained neuron-type-specific connectivity data and reproducing features of observed in-vivo spiking statistics. Local field potentials (LFPs) can be computed from the simulated spiking activity. We here extend a local network and LFP model to an area of 4x4 mm$^2$, preserving the neuron density and introducing distance-dependent connection probabilities and conduction delays. We find that the upscaling procedure preserves the overall spiking statistics of the original model and reproduces asynchronous irregular spiking across populations and weak pairwise spike-train correlations in agreement with experimental recordings from sensory cortex. Also compatible with experimental observations, the correlation of LFP signals is strong and decays over a distance of several hundred micrometers. Enhanced spatial coherence in the low-gamma band around 50 Hz may explain the recent report of an apparent band-pass filter effect in the spatial reach of the LFP., Comment: 31 pages, 10 figures, 7 tables

We present a multi-scale spiking network model of all vision-related areas of macaque cortex that represents each area by a full-scale microcircuit with area-specific architecture. The layer- and population-resolved network connectivity integrates axonal tracing data from the CoCoMac database with recent quantitative tracing data, and is systematically refined using dynamical constraints. Simulations reveal a stable asynchronous irregular ground state with heterogeneous activity across areas, layers, and populations. Elicited by large-scale interactions, the model reproduces longer intrinsic time scales in higher compared to early visual areas. Activity propagates down the visual hierarchy, similar to experimental results associated with visual imagery. Cortico-cortical interaction patterns agree well with fMRI resting-state functional connectivity. The model bridges the gap between local and large-scale accounts of cortex, and clarifies how the detailed connectivity of cortex shapes its dynamics on multiple scales.

Due to rapid advances in multielectrode recording technology, the local field potential (LFP) has again become a popular measure of neuronal activity in both basic research and clinical applications. Proper understanding of the LFP requires detailed mathematical modeling incorporating the anatomical and electrophysiological features of neurons near the recording electrode, as well as synaptic inputs from the entire network. Here we propose a hybrid modeling scheme combining the efficiency of commonly used simplified point-neuron network models with the biophysical principles underlying LFP generation by real neurons. The scheme can be used with an arbitrary number of point-neuron network populations. The LFP predictions rely on populations of network-equivalent, anatomically reconstructed multicompartment neuron models with layer-specific synaptic connectivity. The present scheme allows for a full separation of the network dynamics simulation and LFP generation. For illustration, we apply the scheme to a full-scale cortical network model for a $\sim$1 mm$^2$ patch of primary visual cortex and predict laminar LFPs for different network states, assess the relative LFP contribution from different laminar populations, and investigate the role of synaptic input correlations and neuron density on the LFP. The generic nature of the hybrid scheme and its publicly available implementation in \texttt{hybridLFPy} form the basis for LFP predictions from other point-neuron network models, as well as extensions of the current application to larger circuitry and additional biological detail.

The continuous integration of experimental data into coherent models of the brain is an increasing challenge of modern neuroscience. Such models provide a bridge between structure and activity, and identify the mechanisms giving rise to experimental observations. Nevertheless, structurally realistic network models of spiking neurons are necessarily underconstrained even if experimental data on brain connectivity are incorporated to the best of our knowledge. Guided by physiological observations, any model must therefore explore the parameter ranges within the uncertainty of the data. Based on simulation results alone, however, the mechanisms underlying stable and physiologically realistic activity often remain obscure. We here employ a mean-field reduction of the dynamics, which allows us to include activity constraints into the process of model construction. We shape the phase space of a multi-scale network model of the vision-related areas of macaque cortex by systematically refining its connectivity. Fundamental constraints on the activity, i.e., prohibiting quiescence and requiring global stability, prove sufficient to obtain realistic layer- and area-specific activity. Only small adaptations of the structure are required, showing that the network operates close to an instability. The procedure identifies components of the network critical to its collective dynamics and creates hypotheses for structural data and future experiments. The method can be applied to networks involving any neuron model with a known gain function., Comment: J. Schuecker and M. Schmidt contributed equally to this work