A statistical method for analyzing and comparing spatiotemporal cortical activation patterns

Quantifying and Maximizing the Information Flux in Recurrent Neural Networks

Free-running recurrent neural networks (RNNs), especially probabilistic models, generate an ongoing information flux that can be quantified with the mutual information I[x→(t),x→(t+1)] between subsequent system states x→. Although previous studies have shown that I depends on the statistics of the network's connection weights, it is unclear how to maximize I systematically and how to quantify the flux in large systems where computing the mutual information becomes intractable. Here, we address these questions using Boltzmann machines as model systems. We find that in networks with moderately strong connections, the mutual information I is approximately a monotonic transformation of the root-mean-square averaged Pearson correlations between neuron pairs, a quantity that can be efficiently computed even in large systems. Furthermore, evolutionary maximization of I[x→(t),x→(t+1)] reveals a general design principle for the weight matrices enabling the systematic construction of systems with a high spontaneous information flux. Finally, we simultaneously maximize information flux and the mean period length of cyclic attractors in the state-space of these dynamical networks. Our results are potentially useful for the construction of RNNs that serve as short-time memories or pattern generators.

Predictive coding and stochastic resonance as fundamental principles of auditory phantom perception

Mechanistic insight is achieved only when experiments are employed to test formal or computational models. Furthermore, in analogy to lesion studies, phantom perception may serve as a vehicle to understand the fundamental processing principles underlying healthy auditory perception. With a special focus on tinnitus-as the prime example of auditory phantom perception-we review recent work at the intersection of artificial intelligence, psychology and neuroscience. In particular, we discuss why everyone with tinnitus suffers from (at least hidden) hearing loss, but not everyone with hearing loss suffers from tinnitus. We argue that intrinsic neural noise is generated and amplified along the auditory pathway as a compensatory mechanism to restore normal hearing based on adaptive stochastic resonance. The neural noise increase can then be misinterpreted as auditory input and perceived as tinnitus. This mechanism can be formalized in the Bayesian brain framework, where the percept (posterior) assimilates a prior prediction (brain's expectations) and likelihood (bottom-up neural signal). A higher mean and lower variance (i.e. enhanced precision) of the likelihood shifts the posterior, evincing a misinterpretation of sensory evidence, which may be further confounded by plastic changes in the brain that underwrite prior predictions. Hence, two fundamental processing principles provide the most explanatory power for the emergence of auditory phantom perceptions: predictive coding as a top-down and adaptive stochastic resonance as a complementary bottom-up mechanism. We conclude that both principles also play a crucial role in healthy auditory perception. Finally, in the context of neuroscience-inspired artificial intelligence, both processing principles may serve to improve contemporary machine learning techniques.

Towards data-driven biopsychosocial classification of non-specific chronic low back pain: a pilot study

The classification of non-specific chronic low back pain (CLBP) according to multidimensional data could guide clinical management; yet recent systematic reviews show this has not been attempted. This was a prospective cross-sectional study of participants with CLBP (n = 21) and age-, sex- and height-matched pain-free controls (n = 21). Nervous system, lumbar spinal tissue and psychosocial factors were collected. Dimensionality reduction was followed by fuzzy c-means clustering to determine sub-groups. Machine learning models (Support Vector Machine, k-Nearest Neighbour, Naïve Bayes and Random Forest) were used to determine the accuracy of classification to sub-groups. The primary analysis showed that four factors (cognitive function, depressive symptoms, general self-efficacy and anxiety symptoms) and two clusters (normal versus impaired psychosocial profiles) optimally classified participants. The error rates in classification models ranged from 4.2 to 14.2% when only CLBP patients were considered and increased to 24.2 to 37.5% when pain-free controls were added. This data-driven pilot study classified participants with CLBP into sub-groups, primarily based on psychosocial factors. This contributes to the literature as it was the first study to evaluate data-driven machine learning CLBP classification based on nervous system, lumbar spinal tissue and psychosocial factors. Future studies with larger sample sizes should validate these findings.

Extracting continuous sleep depth from EEG data without machine learning

The human sleep-cycle has been divided into discrete sleep stages that can be recognized in electroencephalographic (EEG) and other bio-signals by trained specialists or machine learning systems. It is however unclear whether these human-defined stages can be re-discovered with unsupervised methods of data analysis, using only a minimal amount of generic pre-processing. Based on EEG data, recorded overnight from sleeping human subjects, we investigate the degree of clustering of the sleep stages using the General Discrimination Value as a quantitative measure of class separability. Virtually no clustering is found in the raw data, even after transforming the EEG signals of each 30-s epoch from the time domain into the more informative frequency domain. However, a Principal Component Analysis (PCA) of these epoch-wise frequency spectra reveals that the sleep stages separate significantly better in the low-dimensional sub-space of certain PCA components. In particular the component C₁(t) can serve as a robust, continuous 'master variable' that encodes the depth of sleep and therefore correlates strongly with the 'hypnogram', a common plot of the discrete sleep stages over time. Moreover, C₁(t) shows persistent trends during extended time periods where the sleep stage is constant, suggesting that sleep may be better understood as a continuum. These intriguing properties of C₁(t) are not only relevant for understanding brain dynamics during sleep, but might also be exploited in low-cost single-channel sleep tracking devices for private and clinical use.

Neural network based formation of cognitive maps of semantic spaces and the putative emergence of abstract concepts

How do we make sense of the input from our sensory organs, and put the perceived information into context of our past experiences? The hippocampal-entorhinal complex plays a major role in the organization of memory and thought. The formation of and navigation in cognitive maps of arbitrary mental spaces via place and grid cells can serve as a representation of memories and experiences and their relations to each other. The multi-scale successor representation is proposed to be the mathematical principle underlying place and grid cell computations. Here, we present a neural network, which learns a cognitive map of a semantic space based on 32 different animal species encoded as feature vectors. The neural network successfully learns the similarities between different animal species, and constructs a cognitive map of 'animal space' based on the principle of successor representations with an accuracy of around 30% which is near to the theoretical maximum regarding the fact that all animal species have more than one possible successor, i.e. nearest neighbor in feature space. Furthermore, a hierarchical structure, i.e. different scales of cognitive maps, can be modeled based on multi-scale successor representations. We find that, in fine-grained cognitive maps, the animal vectors are evenly distributed in feature space. In contrast, in coarse-grained maps, animal vectors are highly clustered according to their biological class, i.e. amphibians, mammals and insects. This could be a putative mechanism enabling the emergence of new, abstract semantic concepts. Finally, even completely new or incomplete input can be represented by interpolation of the representations from the cognitive map with remarkable high accuracy of up to 95%. We conclude that the successor representation can serve as a weighted pointer to past memories and experiences, and may therefore be a crucial building block to include prior knowledge, and to derive context knowledge from novel input. Thus, our model provides a new tool to complement contemporary deep learning approaches on the road towards artificial general intelligence.

Influence of language on perception and concept formation in a brain-constrained deep neural network model

A neurobiologically constrained model of semantic learning in the human brain was used to simulate the acquisition of concrete and abstract concepts, either with or without verbal labels. Concept acquisition and semantic learning were simulated using Hebbian learning mechanisms. We measured the network's category learning performance, defined as the extent to which it successfully (i) grouped partly overlapping perceptual instances into a single (abstract or concrete) conceptual representation, while (ii) still distinguishing representations for distinct concepts. Co-presence of linguistic labels with perceptual instances of a given concept generally improved the network's learning of categories, with a significantly larger beneficial effect for abstract than concrete concepts. These results offer a neurobiological explanation for causal effects of language structure on concept formation and on perceptuo-motor processing of instances of these concepts: supplying a verbal label during concept acquisition improves the cortical mechanisms by which experiences with objects and actions along with the learning of words lead to the formation of neuronal ensembles for specific concepts and meanings. Furthermore, the present results make a novel prediction, namely, that such 'Whorfian' effects should be modulated by the concreteness/abstractness of the semantic categories being acquired, with language labels supporting the learning of abstract concepts more than that of concrete ones. This article is part of the theme issue 'Concepts in interaction: social engagement and inner experiences'.

Neural manifold analysis of brain circuit dynamics in health and disease

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.

Classification at the accuracy limit: facing the problem of data ambiguity

Data classification, the process of analyzing data and organizing it into categories or clusters, is a fundamental computing task of natural and artificial information processing systems. Both supervised classification and unsupervised clustering work best when the input vectors are distributed over the data space in a highly non-uniform way. These tasks become however challenging in weakly structured data sets, where a significant fraction of data points is located in between the regions of high point density. We derive the theoretical limit for classification accuracy that arises from this overlap of data categories. By using a surrogate data generation model with adjustable statistical properties, we show that sufficiently powerful classifiers based on completely different principles, such as perceptrons and Bayesian models, all perform at this universal accuracy limit under ideal training conditions. Remarkably, the accuracy limit is not affected by certain non-linear transformations of the data, even if these transformations are non-reversible and drastically reduce the information content of the input data. We further compare the data embeddings that emerge by supervised and unsupervised training, using the MNIST data set and human EEG recordings during sleep. We find for MNIST that categories are significantly separated not only after supervised training with back-propagation, but also after unsupervised dimensionality reduction. A qualitatively similar cluster enhancement by unsupervised compression is observed for the EEG sleep data, but with a very small overall degree of cluster separation. We conclude that the handwritten letters in MNIST can be considered as 'natural kinds', whereas EEG sleep recordings are a relatively weakly structured data set, so that unsupervised clustering will not necessarily re-cover the human-defined sleep stages.

Systems Medicine Approach for Tinnitus with Comorbid Disorders

Despite the fact that chronic diseases usually occur together with a spectrum of possible comorbidities that may differ strongly between patients, they are classically still viewed as distinct disease entities and, consequently, are often treated with uniform therapies. Unfortunately, such an approach does not take into account that different combinations of symptoms and comorbidities may result from different pathological (e.g., environmental, genetic, dietary, etc.) factors, which require specific and individualised therapeutic strategies. In this opinion paper, we aim to put forward a more differentiated, systems medicine approach to disease and patient treatment. To elaborate on this concept, we focus on the interplay of tinnitus, depression, and chronic pain. In our view, these conditions can be characterised by a variety of phenotypes composed of variable sets of symptoms and biomarkers, rather than distinct disease entities. The knowledge of the interplay of such symptoms and biomarkers will provide the key to a deeper, mechanistic understanding of disease pathologies. This paves the way for prediction and prevention of disease pathways, including more personalised and effective treatment strategies.

Chronic back pain sub-grouped via psychosocial, brain and physical factors using machine learning

Chronic back pain (CBP) is heterogenous and identifying sub-groups could improve clinical decision making. Machine learning can build upon prior sub-grouping approaches by using a data-driven approach to overcome clinician subjectivity, however, only binary classification of pain versus no-pain has been attempted to date. In our cross-sectional study, age- and sex-matched participants with CBP (n = 4156) and pain-free controls (n = 14,927) from the UkBioBank were included. We included variables of body mass index, depression, loneliness/social isolation, grip strength, brain grey matter volumes and functional connectivity. We used fuzzy c-means clustering to derive CBP sub-groups and Support Vector Machine (SVM), Naïve Bayes, k-Nearest Neighbour (kNN) and Random Forest classifiers to determine classification accuracy. We showed that two variables (loneliness/social isolation and depression) and five clusters were optimal for creating sub-groups of CBP individuals. Classification accuracy was greater than 95% for when CBP sub-groups were assessed only, while misclassification in CBP sub-groups increased to 35-53% across classifiers when pain-free controls were added. We showed that individuals with CBP could sub-grouped and accurately classified. Future research should optimise variables by including specific spinal, psychosocial and nervous system measures associated with CBP to create more robust sub-groups that are discernible from pain-free controls.

Objective Recognition of Tinnitus Location Using Electroencephalography Connectivity Features

Purpose: Tinnitus is a common but obscure auditory disease to be studied. This study will determine whether the connectivity features in electroencephalography (EEG) signals can be used as the biomarkers for an efficient and fast diagnosis method for chronic tinnitus.

Methods: In this study, the resting-state EEG signals of tinnitus patients with different tinnitus locations were recorded. Four connectivity features [including the Phase-locking value (PLV), Phase lag index (PLI), Pearson correlation coefficient (PCC), and Transfer entropy (TE)] and two time-frequency domain features in the EEG signals were extracted, and four machine learning algorithms, included two support vector machine models (SVM), a multi-layer perception network (MLP) and a convolutional neural network (CNN), were used based on the selected features to classify different possible tinnitus sources.

Results: Classification accuracy was highest when the SVM algorithm or the MLP algorithm was applied to the PCC feature sets, achieving final average classification accuracies of 99.42 or 99.1%, respectively. And based on the PLV feature, the classification result was also particularly good. And MLP ran the fastest, with an average computing time of only 4.2 s, which was more suitable than other methods when a real-time diagnosis was required.

Conclusion: Connectivity features of the resting-state EEG signals could characterize the differentiation of tinnitus location. The connectivity features (PCC and PLV) were more suitable as the biomarkers for the objective diagnosing of tinnitus. And the results were helpful for clinicians in the initial diagnosis of tinnitus.

Sleep as a random walk: a super-statistical analysis of EEG data across sleep stages

In clinical practice, human sleep is classified into stages, each associated with different levels of muscular activity and marked by characteristic patterns in the EEG signals. It is however unclear whether this subdivision into discrete stages with sharply defined boundaries is truly reflecting the dynamics of human sleep. To address this question, we consider one-channel EEG signals as heterogeneous random walks: stochastic processes controlled by hyper-parameters that are themselves time-dependent. We first demonstrate the heterogeneity of the random process by showing that each sleep stage has a characteristic distribution and temporal correlation function of the raw EEG signals. Next, we perform a super-statistical analysis by computing hyper-parameters, such as the standard deviation, kurtosis, and skewness of the raw signal distributions, within subsequent 30-second epochs. It turns out that also the hyper-parameters have characteristic, sleep-stage-dependent distributions, which can be exploited for a simple Bayesian sleep stage detection. Moreover, we find that the hyper-parameters are not piece-wise constant, as the traditional hypnograms would suggest, but show rising or falling trends within and across sleep stages, pointing to an underlying continuous rather than sub-divided process that controls human sleep. Based on the hyper-parameters, we finally perform a pairwise similarity analysis between the different sleep stages, using a quantitative measure for the separability of data clusters in multi-dimensional spaces.

To improve our understand of how EEG activity reflects the dynamics of human sleep, Metzner et al. use human EEG data and superstatistical analysis to demonstrate that each sleep stage has a characteristic distribution and temporal correlation function of raw EEG signals. They also show that the hyper-parameters controlling the EEG signals have characteristic, sleep-stage-dependent distributions, which can be exploited for a simple Bayesian sleep stage detection.

Too Blind to See the Elephant? Why Neuroscientists Ought to Be Interested in Tinnitus

A curative therapy for tinnitus currently does not exist. One may actually exist but cannot currently be causally linked to tinnitus due to the lack of consistency of concepts about the neural correlate of tinnitus. Depending on predictions, these concepts would require either a suppression or enhancement of brain activity or an increase in inhibition or disinhibition. Although procedures with a potential to silence tinnitus may exist, the lack of rationale for their curative success hampers an optimization of therapeutic protocols. We discuss here six candidate contributors to tinnitus that have been suggested by a variety of scientific experts in the field and that were addressed in a virtual panel discussion at the ARO round table in February 2021. In this discussion, several potential tinnitus contributors were considered: (i) inhibitory circuits, (ii) attention, (iii) stress, (iv) unidentified sub-entities, (v) maladaptive information transmission, and (vi) minor cochlear deafferentation. Finally, (vii) some potential therapeutic approaches were discussed. The results of this discussion is reflected here in view of potential blind spots that may still remain and that have been ignored in most tinnitus literature. We strongly suggest to consider the high impact of connecting the controversial findings to unravel the whole complexity of the tinnitus phenomenon; an essential prerequisite for establishing suitable therapeutic approaches.

Pharmacologic treatments in preclinical tinnitus models with special focus on Ginkgo biloba leaf extract EGb 761®

Tinnitus is defined as the perception of sound in the absence of external acoustic stimuli. Frequent comorbidities or associated factors are depression, anxiety, concentration problems, insomnia, resignation, helplessness, headache, bruxism, or social isolation, just to name a few. Although many therapeutic approaches have already been tested with varying success, there still is no cure available for tinnitus. The search for an effective treatment has been hampered by the fact that the mechanisms of tinnitus development are still not fully understood, although several models are available and discussed in this review. Our review will give a brief overview about preclinical models, presenting the heterogeneity of tinnitus sub-types depending on the different inner ear and brain structures involved in tinnitus etiology and pathogenesis. Based on these models we introduce the different target structures and transmitter systems implicated in tinnitus development and provide an extensive overview on preclinical drug-based therapeutic approaches that have been explored in various animal models. As the special extract from Ginkgo biloba leaves EGb 761® has been the most widely tested drug in both non-clinical tinnitus models as well as in clinical trials, a special focus will be given to EGb 761®. The efficacy of terpene lactones, flavone glycosides and proanthocyanidines with their distinct contribution to the overall efficacy profile of the multi-constituent drug EGb 761® will be discussed.

Integration of Leaky-Integrate-and-Fire Neurons in Standard Machine Learning Architectures to Generate Hybrid Networks: A Surrogate Gradient Approach

Up to now, modern machine learning (ML) has been based on approximating big data sets with high-dimensional functions, taking advantage of huge computational resources. We show that biologically inspired neuron models such as the leaky-integrate-and-fire (LIF) neuron provide novel and efficient ways of information processing. They can be integrated in machine learning models and are a potential target to improve ML performance. Thus, we have derived simple update rules for LIF units to numerically integrate the differential equations. We apply a surrogate gradient approach to train the LIF units via backpropagation. We demonstrate that tuning the leak term of the LIF neurons can be used to run the neurons in different operating modes, such as simple signal integrators or coincidence detectors. Furthermore, we show that the constant surrogate gradient, in combination with tuning the leak term of the LIF units, can be used to achieve the learning dynamics of more complex surrogate gradients. To prove the validity of our method, we applied it to established image data sets (the Oxford 102 flower data set, MNIST), implemented various network architectures, used several input data encodings and demonstrated that the method is suitable to achieve state-of-the-art classification performance. We provide our method as well as further surrogate gradient methods to train spiking neural networks via backpropagation as an open-source KERAS package to make it available to the neuroscience and machine learning community. To increase the interpretability of the underlying effects and thus make a small step toward opening the black box of machine learning, we provide interactive illustrations, with the possibility of systematically monitoring the effects of parameter changes on the learning characteristics.

Analysis and visualization of sleep stages based on deep neural networks

Automatic sleep stage scoring based on deep neural networks has come into focus of sleep researchers and physicians, as a reliable method able to objectively classify sleep stages would save human resources and simplify clinical routines. Due to novel open-source software libraries for machine learning, in combination with enormous recent progress in hardware development, a paradigm shift in the field of sleep research towards automatic diagnostics might be imminent. We argue that modern machine learning techniques are not just a tool to perform automatic sleep stage classification, but are also a creative approach to find hidden properties of sleep physiology. We have already developed and established algorithms to visualize and cluster EEG data, facilitating first assessments on sleep health in terms of sleep-apnea and consequently reduced daytime vigilance. In the following study, we further analyze cortical activity during sleep by determining the probabilities of momentary sleep stages, represented as hypnodensity graphs and then computing vectorial cross-correlations of different EEG channels. We can show that this measure serves to estimate the period length of sleep cycles and thus can help to find disturbances due to pathological conditions.

Quantifying the separability of data classes in neural networks

We introduce the Generalized Discrimination Value (GDV) that measures, in a non-invasive manner, how well different data classes separate in each given layer of an artificial neural network. It turns out that, at the end of the training period, the GDV in each given layer L attains a highly reproducible value, irrespective of the initialization of the network's connection weights. In the case of multi-layer perceptrons trained with error backpropagation, we find that classification of highly complex data sets requires a temporal reduction of class separability, marked by a characteristic 'energy barrier' in the initial part of the GDV(L) curve. Even more surprisingly, for a given data set, the GDV(L) is running through a fixed 'master curve', independently from the total number of network layers. Finally, due to its invariance with respect to dimensionality, the GDV may serve as a useful tool to compare the internal representational dynamics of artificial neural networks with different architectures for neural architecture search or network compression; or even with brain activity in order to decide between different candidate models of brain function.

GEVI cell-type specific labelling and a manifold learning approach provide evidence for lateral inhibition at the population level in the mouse hippocampal CA1 area

The CA1 area in the mammalian hippocampus is essential for spatial learning. Pyramidal cells are the hippocampus output neurons and their activities are regulated by inhibition exerted by a diversified population of interneurons. Lateral inhibition has been suggested as the mechanism enabling the reconfiguration of pyramidal cell assembly activity observed during spatial learning tasks in rodents. However, lateral inhibition in the CA1 lacks the overwhelming evidence reported in other hippocampal areas such as the CA3 and the dentate gyrus. The use of genetically encoded voltage indicators and fast optical recordings permits the construction of cell-type specific response maps of neuronal activity. Here, we labelled mouse CA1 pyramidal neurons with the genetically encoded voltage indicator ArcLight and optically recorded their response to Schaffer Collaterals stimulation in vitro. By undertaking a manifold learning approach, we report a hyperpolarization-dominated area focused in the perisomatic region of pyramidal cells receiving late excitatory synaptic input. Functional network organization metrics revealed that information transfer was higher in this area. The localized hyperpolarization disappeared when GABA_A receptors were pharmacologically blocked. This is the first report where the spatiotemporal pattern of lateral inhibition is visualized in the CA1 by expressing a genetically encoded voltage indicator selectively in principal neurons. Our analysis suggests a fundamental role of lateral inhibition in CA1 information processing.

Will We Ever Have Conscious Machines?

The question of whether artificial beings or machines could become self-aware or conscious has been a philosophical question for centuries. The main problem is that self-awareness cannot be observed from an outside perspective and the distinction of being really self-aware or merely a clever imitation cannot be answered without access to knowledge about the mechanism's inner workings. We investigate common machine learning approaches with respect to their potential ability to become self-aware. We realize that many important algorithmic steps toward machines with a core consciousness have already been taken.

EEG Biomarkers Related With the Functional State of Stroke Patients

Introduction

Recent studies explored promising new quantitative methods to analyze electroencephalography (EEG) signals. This paper analyzes the correlation of two EEG parameters, Brain Symmetry Index (BSI) and Laterality Coefficient (LC), with established functional scales for the stroke assessment.

Methods

Thirty-two healthy subjects and thirty-six stroke patients with upper extremity hemiparesis were recruited for this study. The stroke patients where subdivided in three groups according to the stroke location: Cortical, Subcortical, and Cortical + Subcortical. The participants performed assessment visits to record the EEG in the resting state and perform functional tests using rehabilitation scales. Then, stroke patients performed 25 sessions using a motor-imagery based Brain Computer Interface system (BCI). BSI was calculated with the EEG data in resting state and LC was calculated with the Event-Related Synchronization maps.

Results

The results of this study demonstrated significant differences in the BSI between the healthy group and Subcortical group (P = 0.001), and also between the healthy and Cortical+Subcortical group (P = 0.019). No significant differences were found between the healthy group and the Cortical group (P = 0.505). Furthermore, the BSI analysis in the healthy group based on gender showed statistical differences (P = 0.027). In the stroke group, the correlation between the BSI and the functional state of the upper extremity assessed by Fugl-Meyer Assessment (FMA) was also significant, ρ = −0.430 and P = 0.046. The correlation between the BSI and the FMA-Lower extremity was not significant (ρ = −0.063, P = 0.852). Similarly, the LC calculated in the alpha band has significative correlation with FMA of upper extremity (ρ = −0.623 and P < 0.001) and FMA of lower extremity (ρ = −0.509 and P = 0.026). Other important significant correlations between LC and functional scales were observed. In addition, the patients showed an improvement in the FMA-upper extremity after the BCI therapy (ΔFMA = 1 median [IQR: 0–8], P = 0.002).

Conclusion

The quantitative EEG tools used here may help support our understanding of stroke and how the brain changes during rehabilitation therapy. These tools can help identify changes in EEG biomarkers and parameters during therapy that might lead to improved therapy methods and functional prognoses.

Analysis of Structure and Dynamics in Three-Neuron Motifs

Recurrent neural networks can produce ongoing state-to-state transitions without any driving inputs, and the dynamical properties of these transitions are determined by the neuronal connection strengths. Due to non-linearity, it is not clear how strongly the system dynamics is affected by discrete local changes in the connection structure, such as the removal, addition, or sign-switching of individual connections. Moreover, there are no suitable metrics to quantify structural and dynamical differences between two given networks with arbitrarily indexed neurons. In this work, we present such permutation-invariant metrics and apply them to motifs of three binary neurons with discrete ternary connection strengths, an important class of building blocks in biological networks. Using multidimensional scaling, we then study the similarity relations between all 3,411 topologically distinct motifs with regard to structure and dynamics, revealing a strong clustering and various symmetries. As expected, the structural and dynamical distance between pairs of motifs show a significant positive correlation. Strikingly, however, the key parameter controlling motif dynamics turns out to be the ratio of excitatory to inhibitory connections.