The role of symmetry in neural networks and their Laplacian spectra

Human and animal nervous systems constitute complexly wired networks that form the infrastructure for neural processing and integration of information. The organization of these neural networks can be analyzed using the so-called Laplacian spectrum, providing a mathematical tool to produce systems-level network fingerprints. In this article, we examine a characteristic central peak in the spectrum of neural networks, including anatomical brain network maps of the mouse, cat and macaque, as well as anatomical and functional network maps of human brain connectivity. We link the occurrence of this central peak to the level of symmetry in neural networks, an intriguing aspect of network organization resulting from network elements that exhibit similar wiring patterns. Specifically, we propose a measure to capture the global level of symmetry of a network and show that, for both empirical networks and network models, the height of the main peak in the Laplacian spectrum is strongly related to node symmetry in the underlying network. Moreover, examination of spectra of duplication-based model networks shows that neural spectra are best approximated using a trade-off between duplication and diversification. Taken together, our results facilitate a better understanding of neural network spectra and the importance of symmetry in neural networks

Fluctuations between high- and low-modularity topology in time-resolved functional connectivity

Modularity is an important topological attribute for functional brain networks. Recent studies have reported that modularity of functional networks varies not only across individuals being related to demographics and cognitive performance, but also within individuals co-occurring with fluctuations in network properties of functional connectivity, estimated over short time intervals. However, characteristics of these time-resolved functional networks during periods of high and low modularity have remained largely unexplored. In this study we investigate spatiotemporal properties of time-resolved networks in the high and low modularity periods during rest, with a particular focus on their spatial connectivity patterns, temporal homogeneity and test-retest reliability. We show that spatial connectivity patterns of time-resolved networks in the high and low modularity periods are represented by increased and decreased dissociation of the default mode network module from task-positive network modules, respectively. We also find that the instances of time-resolved functional connectivity sampled from within the high (low) modularity period are relatively homogeneous (heterogeneous) over time, indicating that during the low modularity period the default mode network interacts with other networks in a variable manner. We confirmed that the occurrence of the high and low modularity periods varies across individuals with moderate inter-session test-retest reliability and that it is correlated with previously-reported individual differences in the modularity of functional connectivity estimated over longer timescales. Our findings illustrate how time-resolved functional networks are spatiotemporally organized during periods of high and low modularity, allowing one to trace individual differences in long-timescale modularity to the variable occurrence of network configurations at shorter timescales.Comment: Reorganized the paper; to appear in NeuroImage; arXiv abstract shortened to fit within character limit

Generative models of the human connectome

The human connectome represents a network map of the brain's wiring diagram and the pattern into which its connections are organized is thought to play an important role in cognitive function. The generative rules that shape the topology of the human connectome remain incompletely understood. Earlier work in model organisms has suggested that wiring rules based on geometric relationships (distance) can account for many but likely not all topological features. Here we systematically explore a family of generative models of the human connectome that yield synthetic networks designed according to different wiring rules combining geometric and a broad range of topological factors. We find that a combination of geometric constraints with a homophilic attachment mechanism can create synthetic networks that closely match many topological characteristics of individual human connectomes, including features that were not included in the optimization of the generative model itself. We use these models to investigate a lifespan dataset and show that, with age, the model parameters undergo progressive changes, suggesting a rebalancing of the generative factors underlying the connectome across the lifespan.Comment: 38 pages, 5 figures + 19 supplemental figures, 1 tabl

Early human brain development:insights into macroscale connectome wiring

BACKGROUND: Early brain development is closely dictated by distinct neurobiological principles. Here, we aimed to map early trajectories of structural brain wiring in the neonatal brain. METHODS: We investigated structural connectome development in 44 newborns, including 23 preterm infants and 21 full-term neonates scanned between 29 and 45 postmenstrual weeks. Diffusion-weighted imaging data were combined with cortical segmentations derived from T2 data to construct neonatal connectome maps. RESULTS: Projection fibers interconnecting primary cortices and deep gray matter structures were noted to mature faster than connections between higher-order association cortices (fractional anisotropy (FA) F = 58.9, p < 0.001, radial diffusivity (RD) F = 28.8, p < 0.001). Neonatal FA-values resembled adult FA-values more than RD, while RD approximated the adult brain faster (F = 358.4, p < 0.001). Maturational trajectories of RD in neonatal white matter pathways revealed substantial overlap with what is known about the sequence of subcortical white matter myelination from histopathological mappings as recorded by early neuroanatomists (mean RD 68 regions r = 0.45, p = 0.008). CONCLUSION: Employing postnatal neuroimaging we reveal that early maturational trajectories of white matter pathways display discriminative developmental features of the neonatal brain network. These findings provide valuable insight into the early stages of structural connectome development

Rich club organization and cognitive performance in healthy older participants

The human brain is a complex network that has been noted to contain a group of densely interconnected hub regions. With a putative 'rich club' of hubs hypothesized to play a central role in global integrative brain functioning, we assessed whether hub and rich club organizations are associated with cognitive performance in healthy participants and whether the rich club might be differentially involved in cognitive functions with a heavier dependence on global integration. A group of 30 relatively older participants (range = 39-79 years of age) underwent extensive neuropsychological testing, combined with diffusion-weighted magnetic resonance imaging to reconstruct individual structural brain networks. Rich club connectivity was found to be associated with general cognitive performance. More specifically, assessing the relationship between the rich club and performance in two specific cognitive domains, we found rich club connectivity to be differentially associated with attention/executive functions-known to rely on the integration of distributed brain areas-rather than with visuospatial/visuoperceptual functions, which have a more constrained neuroanatomical substrate. Our findings thus provide first empirical evidence of a relevant role played by the rich club in cognitive processes

Whole-Brain Structural Connectivity in Dyskinetic Cerebral Palsy and Its Association With Motor and Cognitive Function

Dyskinetic cerebral palsy (CP) has long been associated with basal ganglia and thalamus lesions. Recent evidence further points at white matter (WM) damage. This study aims to identify altered WM pathways in dyskinetic CP from a standardized, connectome-based approach, and to assess structure-function relationship in WM pathways for clinical outcomes. Individual connectome maps of 25 subjects with dyskinetic CP and 24 healthy controls were obtained combining a structural parcellation scheme with whole-brain deterministic tractography. Graph theoretical metrics and the network-based statistic were applied to compare groups and to correlate WM state with motor and cognitive performance. Results showed a widespread reduction of WM volume in CP subjects compared to controls and a more localized decrease in degree (number of links per node) and fractional anisotropy (FA), comprising parieto-occipital regions and the hippocampus. However, supramarginal gyrus showed a significantly higher degree. At the network level, CP subjects showed a bilateral pathway with reduced FA, comprising sensorimotor, intraparietal and fronto-parietal connections. Gross and fine motor functions correlated with FA in a pathway comprising the sensorimotor system, but gross motor also correlated with prefrontal, temporal and occipital connections. Intelligence correlated with FA in a network with fronto-striatal and parieto-frontal connections, and visuoperception was related to right occipital connections. These findings demonstrate a disruption in structural brain connectivity in dyskinetic CP, revealing general involvement of posterior brain regions with relative preservation of prefrontal areas. We identified pathways in which WM integrity is related to clinical features, including but not limited to the sensorimotor system

Genome-wide association study of frontotemporal dementia identifies a <i>C9ORF72</i> haplotype with a median of 12-G4C2 repeats that predisposes to pathological repeat expansions

Genetic factors play a major role in frontotemporal dementia (FTD). The majority of FTD cannot be genetically explained yet and it is likely that there are still FTD risk loci to be discovered. Common variants have been identified with genome-wide association studies (GWAS), but these studies have not systematically searched for rare variants. To identify rare and new common variant FTD risk loci and provide more insight into the heritability of C9ORF72-related FTD, we performed a GWAS consisting of 354 FTD patients (including and excluding N = 28 pathological repeat carriers) and 4209 control subjects. The Haplotype Reference Consortium was used as reference panel, allowing for the imputation of rare genetic variants. Two rare genetic variants nearby C9ORF72 were strongly associated with FTD in the discovery (rs147211831: OR = 4.8, P = 9.2 × 10−9, rs117204439: OR = 4.9, P = 6.0 × 10−9) and replication analysis (P &lt; 1.1 × 10−3). These variants also significantly associated with amyotrophic lateral sclerosis in a publicly available dataset. Using haplotype analyses in 1200 individuals, we showed that these variants tag a sub-haplotype of the founder haplotype of the repeat expansion that was previously found to be present in virtually all pathological C9ORF72 G4C2 repeat lengths. This new risk haplotype was 10 times more likely to contain a C9ORF72 pathological repeat length compared to founder haplotypes without one of the two risk variants (~22% versus ~2%; P = 7.70 × 10−58). In haplotypes without a pathologic expansion, the founder risk haplotype had a higher number of repeats (median = 12 repeats) compared to the founder haplotype without the risk variants (median = 8 repeats) (P = 2.05 × 10−260). In conclusion, the identified risk haplotype, which is carried by ~4% of all individuals, is a major risk factor for pathological repeat lengths of C9ORF72 G4C2. These findings strongly indicate that longer C9ORF72 repeats are unstable and more likely to convert to germline pathological C9ORF72 repeat expansions.</p

Current commands for high-efficiency torque control of DC shunt motor

The current commands for a high-efficiency torque control of a DC shunt motor are described. In the proposed control method, the effect of a magnetic saturation and an armature reaction are taken into account by representing the coefficients of an electromotive force and a torque as a function of the field current, the armature current and the revolving speed. The current commands at which the loss of the motor drive system becomes a minimum are calculated as an optimal problem. The proposed control technique of a motor is implemented on the microprocessor-based control system. The effect of the consideration of the magnetic saturation and the armature reaction on the produced torque and the minimisation of the loss are discussed analytically and experimentally </p

Analysis of shared heritability in common disorders of the brain

ience, this issue p. eaap8757 Structured Abstract INTRODUCTION Brain disorders may exhibit shared symptoms and substantial epidemiological comorbidity, inciting debate about their etiologic overlap. However, detailed study of phenotypes with different ages of onset, severity, and presentation poses a considerable challenge. Recently developed heritability methods allow us to accurately measure correlation of genome-wide common variant risk between two phenotypes from pools of different individuals and assess how connected they, or at least their genetic risks, are on the genomic level. We used genome-wide association data for 265,218 patients and 784,643 control participants, as well as 17 phenotypes from a total of 1,191,588 individuals, to quantify the degree of overlap for genetic risk factors of 25 common brain disorders. RATIONALE Over the past century, the classification of brain disorders has evolved to reflect the medical and scientific communities' assessments of the presumed root causes of clinical phenomena such as behavioral change, loss of motor function, or alterations of consciousness. Directly observable phenomena (such as the presence of emboli, protein tangles, or unusual electrical activity patterns) generally define and separate neurological disorders from psychiatric disorders. Understanding the genetic underpinnings and categorical distinctions for brain disorders and related phenotypes may inform the search for their biological mechanisms. RESULTS Common variant risk for psychiatric disorders was shown to correlate significantly, especially among attention deficit hyperactivity disorder (ADHD), bipolar disorder, major depressive disorder (MDD), and schizophrenia. By contrast, neurological disorders appear more distinct from one another and from the psychiatric disorders, except for migraine, which was significantly correlated to ADHD, MDD, and Tourette syndrome. We demonstrate that, in the general population, the personality trait neuroticism is significantly correlated with almost every psychiatric disorder and migraine. We also identify significant genetic sharing between disorders and early life cognitive measures (e.g., years of education and college attainment) in the general population, demonstrating positive correlation with several psychiatric disorders (e.g., anorexia nervosa and bipolar disorder) and negative correlation with several neurological phenotypes (e.g., Alzheimer's disease and ischemic stroke), even though the latter are considered to result from specific processes that occur later in life. Extensive simulations were also performed to inform how statistical power, diagnostic misclassification, and phenotypic heterogeneity influence genetic correlations. CONCLUSION The high degree of genetic correlation among many of the psychiatric disorders adds further evidence that their current clinical boundaries do not reflect distinct underlying pathogenic processes, at least on the genetic level. This suggests a deeply interconnected nature for psychiatric disorders, in contrast to neurological disorders, and underscores the need to refine psychiatric diagnostics. Genetically informed analyses may provide important "scaffolding" to support such restructuring of psychiatric nosology, which likely requires incorporating many levels of information. By contrast, we find limited evidence for widespread common genetic risk sharing among neurological disorders or across neurological and psychiatric disorders. We show that both psychiatric and neurological disorders have robust correlations with cognitive and personality measures. Further study is needed to evaluate whether overlapping genetic contributions to psychiatric pathology may influence treatment choices. Ultimately, such developments may pave the way toward reduced heterogeneity and improved diagnosis and treatment of psychiatric disorders