Network Coherence Research Articles

Robustness of consensus in m-rose networks

The consensus of deterministic networks investigates the relationships between consensus and network topology, which can be measured by network coherence. The m-rose networks are composed of m circles, which share a common node. Recently, scholars have obtained the first-order coherence of 5-rose networks. This paper takes the more general m-rose networks as the research object, firstly, the m-rose networks are introduced. Secondly, the relationships between Laplacian eigenvalues and polynomial coefficients are used to obtain the first-order and second-order coherence of the m-rose networks. Finally, the effects of topology parameters such as the number of petals m and the length of a cycle n on the robustness of network consensus are discussed, and the validity of the conclusion is verified by numerical simulation.

Neural fingerprints of gambling disorder using diffusion tensor imaging

Gambling disorder (GD) is a behavioral addiction associated with personal, social and occupational consequences. Thus, examining GD's clinical relationship with its neural substrates is critical. We compared neural fingerprints using diffusion tensor imaging (DTI) in GD subjects undergoing treatment relative to healthy volunteers (HV). Fifty-three (25 GD, 28 age-matched HV) males were scanned with structural magnetic resonance imaging (MRI) and DTI. We applied probabilistic tractography based on DTI scanning data, preprocessed and analyzed using permutation testing of individual connectivity weights between regions for group comparison. Permutation-based comparisons between group-averaged connectomes highlighted significant structural differences. The GD group demonstrated increased connectivity, and striatal network reorganisation, contrasted by reduced connectivity within and to frontal lobe nodes. Modularity analysis revealed that the GD group had fewer hubs integrating information across the brain. We highlight GD neural changes involved in controlling risk-seeking behaviors. The observed striatal restructuring converges with previous research, and the increased connectivity affects subnetworks highly active in gambling situations, although these findings are not significant when correcting for multiple comparisons. Modularity analysis underlines that, despite connectivity increases, the GD connectome loses hubs, impeding its neuronal network coherence. Together, these results demonstrate the feasibility of using whole-brain computational modeling in assessing GD.

Analysis of the consensus of double-layer chain networks

The multi-layer network topology structures directly affect the robustness of network consensus. The different positions of edges between layers will lead to a great difference in the consensus of double-layer chain networks. Finding the optimal positions of edges for consensus can help to design the network topology structures with optimal robustness. In this paper, we first derive the coherence of double-layer chain networks with one and two connected edges between layers by graph theory. Secondly, the optimal and worst connection edges positions of the two types of networks are simulated. When there is one edge between layers, the optimal edge connection position is found at 1/2 of each chain, and the worst edge connection position is found at the end node of the chain. When there are two edges between layers, the optimal edges connection positions are located at 1/5 and 4/5 of each chain respectively, and the worst edges connection positions are located at the end node of the chain and its neighbor node. Furthermore, we find that the optimal edge connection positions are closely related to the number of single-layer network nodes, and obtain their specific rules.

Loss of neuron network coherence induced by virus-infected astrocytes: a model study

Coherent activations of brain neuron networks underlie many physiological functions associated with various behavioral states. These synchronous fluctuations in the electrical activity of the brain are also referred to as brain rhythms. At the cellular level, rhythmicity can be induced by various mechanisms of intrinsic oscillations in neurons or the network circulation of excitation between synaptically coupled neurons. One specific mechanism concerns the activity of brain astrocytes that accompany neurons and can coherently modulate synaptic contacts of neighboring neurons, synchronizing their activity. Recent studies have shown that coronavirus infection (Covid-19), which enters the central nervous system and infects astrocytes, can cause various metabolic disorders. Specifically, Covid-19 can depress the synthesis of astrocytic glutamate and gamma-aminobutyric acid. It is also known that in the post-Covid state, patients may suffer from symptoms of anxiety and impaired cognitive functions. We propose a mathematical model of a spiking neuron network accompanied by astrocytes capable of generating quasi-synchronous rhythmic bursting discharges. The model predicts that if the release of glutamate is depressed, normal burst rhythmicity will suffer dramatically. Interestingly, in some cases, the failure of network coherence may be intermittent, with intervals of normal rhythmicity, or the synchronization can disappear.

On the role of hubs in the coherence of unicyclic and bicyclic networks

In this paper, we aim to study the role of hubs in the network coherence quantified by the Laplacian spectra and choose two families of unicyclic and bicyclic networks with the same network size as our network models. In order to investigate the influence of adding links on the coherence, we construct four types of bicyclic networks with the same average degree. Using the network’s regular structures and matrix theories, we obtain analytical solutions of the coherences regarding the degrees of hub nodes. Based on these exact results for the coherence, the network with one hub displays higher coherence compared to the network with two hubs. We then obtain exact relations for the coherences of the bicyclic networks with the same average degree and show that different adding links and hub’s positions are responsible for distinct performance of the consensus algorithms. Finally, we show that the coherence and average path length behave in a linear way meaning that smaller average path length results in better coherence.

Distinct dorsal and ventral streams for binocular rivalry dominance and suppression revealed by magnetoencephalography.

Binocular rivalry is an example of bistable visual perception extensively examined in neuroimaging. Magnetoencephalography can track brain responses to phasic visual stimulations of predetermined frequency and phase to advance our understanding of perceptual dominance and suppression in binocular rivalry. We used left and right eye stimuli that flickered at two tagging frequencies to track their respective oscillatory cortical evoked responses. We computed time-resolved measures of coherence to track brain responses phase locked with stimulus frequencies and with respect to the participants' indications of alternations of visual rivalry they experienced. We compared the brain maps obtained to those from a non-rivalrous control replay condition that used physically changing stimuli to mimic rivalry. We found stronger coherence within a posterior cortical network of visual areas during rivalry dominance compared with rivalry suppression and replay control. This network extended beyond the primary visual cortex to several retinotopic visual areas. Moreover, network coherence with dominant percepts in primary visual cortex peaked at least 50 ms prior to the suppressed percept nadir, consistent with the escape theory of alternations. Individual alternation rates were correlated with the rate of change in dominant evoked peaks, but not for the slope of response to suppressed percepts. Effective connectivity measures revealed that dominant (respectively, suppressed) percepts were expressed in dorsal (respectively ventral) streams. We thus demonstrate that binocular rivalry dominance and suppression engage distinct mechanisms and brain networks. These findings advance neural models of rivalry and may relate to more general aspects of selection and suppression in natural vision.

Altered electroencephalography resting state network coherence in remitted MDD

Individuals with remitted depression are at greater risk for subsequent depression and therefore may provide a unique opportunity to understand the neurophysiological correlates underlying the risk of depression. Research has identified abnormal resting-state electroencephalography (EEG) power metrics and functional connectivity patterns associated with major depression, however little is known about these neural signatures in individuals with remitted depression. We investigate the spectral dynamics of 64-channel EEG surface power and source-estimated network connectivity during resting states in 37 individuals with depression, 56 with remitted depression, and 49 healthy adults that did not differ on age, education, and cognitive ability across theta, alpha, and beta frequencies. Average reference spectral EEG surface power analyses identified greater left and midfrontal theta in remitted depression compared to healthy adults. Using Network Based Statistics, we also demonstrate within and between network alterations in LORETA transformed EEG source-space coherence across the default mode, fronto-parietal, and salience networks where individuals with remitted depression exhibited enhanced coherence compared to those with depression, and healthy adults. This work builds upon our currently limited understanding of resting EEG connectivity in depression, and helps bridge the gap between aberrant EEG power and brain network connectivity dynamics in this disorder. Further, our unique examination of remitted depression relative to both healthy and depressed adults may be key to identifying brain-based biomarkers for those at high risk for future, or subsequent depression.

Cerebral Activation During Moral Decisions and Salience Network Coherence in Ideation of Suicide

PurposeTo look for structural and/or functional deviations of the salience network in depressive patients that might help to identify individuals with ideation of suicide. Material and methodsIn 2 matched groups of patients with major depression and with and without ideation of suicide and in a healthy control group, structural and functional magnetic resonance imaging was performed during resting state and activation by a moral decision paradigm. Data were evaluated using voxel based morphometry, statistical parametric mapping, independent component analysis and network-based statistics (NBS) and related to the Clinical Analysis Questionnaire score of suicidality. ResultsFunctional connectivity was reduced significantly (p<0.05, NBS corrected) within the salient network during resting state in patients with suicide ideation. Application of a moral paradigm activated nearly identical areas, and both anterior parts of the insulae correlated negatively to the score of suicidality. ConclusionBecause the cerebral areas activated during a moral decision paradigm are nearly identical to the salience network seen in our study and because selected areas within this network, mainly the anterior parts of the insula, correlate negatively to suicidality, a special training using moral tasks or possibly also religious reinforcement might help to reduce suicidality in depressive patients.

Arginine–vasopressin-expressing neurons in the murine suprachiasmatic nucleus exhibit a circadian rhythm in network coherence in vivo

The suprachiasmatic nucleus (SCN) is composed of functionally distinct subpopulations of GABAergic neurons which form a neural network responsible for synchronizing most physiological and behavioral circadian rhythms in mammals. To date, little is known regarding which aspects of SCN rhythmicity are generated by individual SCN neurons, and which aspects result from neuronal interaction within a network. Here, we utilize invivo miniaturized microscopy to measure fluorescent GCaMP-reported calcium dynamics in arginine vasopressin (AVP)-expressing neurons in the intact SCN of awake, behaving mice. We report that SCN AVP neurons exhibit periodic, slow calcium waves which we demonstrate, using invivo electrical recordings, likely reflect burst firing. Further, we observe substantial heterogeneity of function in that AVP neurons exhibit unstable rhythms, and relatively weak rhythmicity at the population level. Network analysis reveals that correlated cellular behavior, or coherence, among neuron pairs also exhibited stochastic rhythms with about 33% of pairs rhythmic at any time. Unlike single-cell variables, coherence exhibited a strong rhythm at the population level with time of maximal coherence among AVP neuronal pairs at CT/ZT 6 and 9, coinciding with the timing of maximal neuronal activity for the SCN as a whole. These results demonstrate robust circadian variation in the coordination between stochastically rhythmic neurons and that interactions between AVP neurons in the SCN may be more influential than single-cell activity in the regulation of circadian rhythms. Furthermore, they demonstrate that cells in this circuit, like those in many other circuits, exhibit profound heterogenicity of function over time and space.

HyperDNE: Enhanced hypergraph neural network for dynamic network embedding

Representation learning provides an attractive opportunity to model the evolution of dynamic networks. However, the existing methods have two limitations: (1) most graph neural network-based methods fail to utilize the high-order proximity of nodes that captures the important properties of a network topology; (2) evolutionary dynamics-based methods are much fine-grained in modeling time information but neglect the coherence of dynamic networks, which leads to the model being susceptible to subtle noise. In this paper, we propose an enhanced hypergraph neural network framework for dynamic network embedding (HyperDNE) to tackle these issues. Specifically, we innovatively design a sequential hypergraph with dual-stream output to explore the group properties of nodes and edges, and a line graph neural network is added as an auxiliary enhancement scheme to further aggregate social influence from the degree of social convergence. Then, we compute the final embedding through attentions along the node and hyperedge levels to fuse multi-level variations in the network structure. The experimental results on six real networks demonstrate significant gains for HyperDNE over several state-of-the-art network embedding baselines. The dataset and source code of HyperDNE are publicly available at https://github.com/qhgz2013/HyperDNE.

On the Consensus Performance of Multi-Layered MASs with Various Graph Parameters-From the Perspective of Cardinalities of Vertex Sets.

This work studies the first-order coherence of noisy multi-agent networks with multi-layered structures. The coherence, which is a sort of performance index of networks, can be seen as a sort of measurement for a system's robustness. Graph operations are applied to design the novel multi-layered networks, and a graph spectrum approach, along with analysis methods, is applied to derive the mathematical expression of the coherence, and the corresponding asymptotic results on the performance index have been obtained. In addition, the coherence of these non-isomorphic multi-layered networks with three different graph parameters are compared and analyzed. We find that, when the cardinalities of the vertex sets of corresponding counterpart layers are the same, the multi-layered topology class with a balanced, complete, multi-partite structure has the best robustness of all the considered networks, if the sufficient conditions for the node-related parameters hold. Finally, simulations are given to verify the asymptotic results.

Functional Coherence in Intrinsic Frontal Executive Networks Predicts Cognitive Impairments in Alcohol Use Disorder.

Growing evidence highlights the potential of innovative rehabilitative interventions such as cognitive remediation and neuromodulation, aimed at reducing relapses in Alcohol Use Disorder (AUD). Enhancing their effectiveness requires a thorough description of the neural correlates of cognitive alterations in AUD. Past related attempts, however, were limited by the focus on selected neuro-cognitive variables. We aimed to fill this gap by combining, in 22 AUD patients and 18 controls, an extensive neuro-cognitive evaluation and metrics of intrinsic connectivity as highlighted by resting-state brain activity. We addressed an inherent property of intrinsic activity such as intra-network coherence, the temporal correlation of the slow synchronous fluctuations within resting-state networks, representing an early biomarker of alterations in the functional brain architecture underlying cognitive functioning. AUD patients displayed executive impairments involving working-memory, attention and visuomotor speed, reflecting abnormal coherence of activity and grey matter atrophy within default mode, in addition to the attentional and the executive networks. The stronger relationship between fronto-lateral coherent activity and executive performance in patients than controls highlighted possible compensatory mechanisms counterbalancing the decreased functionality of networks driving the switch from automatic to controlled behavior. These results provide novel insights into AUD patients' cognitive impairments, their neural bases, and possible targets of rehabilitative interventions.

Topology design for leader-follower coherence in noisy asymmetric networks

In this paper, we aim to study the effect of the leader’s positions in leader-follower coherence quantified by the spectrum in noisy asymmetric networks with a set of hub nodes. In order to compare the impact of leader selection in different ways on the studied coherence, we choose a family of ring-trees networks to conveniently assign the leaders and hubs. Based on the regular network topology and matrix theories, we obtain analytical solutions for the leader-follower coherence regarding network parameters and the number of leaders. Using these expressions, we then obtain exact relations among the coherences and show that the leader’s positions and network parameters have a profound impact on the coherence. More specifically, the network with one hub displays better coherence than the networks with two hubs. In addition, two adjacent and nonadjacent hubs lead to distinct performance of leader-follower consensus dynamics that depends on network parameters and assigned leaders in the ring or the tree network.

Quantum Coherence in Loopless Superconductive Networks.

Measurements indicating that planar networks of superconductive islands connected by Josephson junctions display long-range quantum coherence are reported. The networks consist of superconducting islands connected by Josephson junctions and have a tree-like topological structure containing no loops. Enhancements of superconductive gaps over specific branches of the networks and sharp increases in pair currents are the main signatures of the coherent states. In order to unambiguously attribute the observed effects to branches being embedded in the networks, comparisons with geometrically equivalent-but isolated-counterparts are reported. Tuning the Josephson coupling energy by an external magnetic field generates increases in the Josephson currents, along the above-mentioned specific branches, which follow a functional dependence typical of phase transitions. Results are presented for double comb and star geometry networks, and in both cases, the observed effects provide positive quantitative evidence of the predictions of existing theoretical models.

Early remission in multiple sclerosis is linked to altered coherence of the Cerebellar Network

BackgroundThe development of permanent disability in multiple sclerosis (MS) is highly variable among patients, and the exact mechanisms that contribute to this disability remain unknown.MethodsFollowing the idea that the brain has intrinsic network organization, we investigated changes of functional networks in MS patients to identify possible links between network reorganization and remission from clinical episodes in MS. Eighteen relapsing–remitting MS patients (RRMS) in their first clinical manifestation underwent resting-state functional MRI and again during remission. We used ten template networks, identified from independent component analysis, to compare changes in network coherence for each patient compared to those of 44 healthy controls from the Human Connectome Project test–retest dataset (two-sample t-test of pre-post differences). Combining a binomial test with Monte Carlo procedures, we tested four models of how functional coherence might change between the first clinical episode and remission: a network can change its coherence (a) with itself (“one-with-self”), (b) with another network (“one-with-other”), or (c) with a set of other networks (“one-with-many”), or (d) multiple networks can change their coherence with respect to one common network (“many-with-one”).ResultsWe found evidence supporting two of these hypotheses: coherence decreased between the Executive Control Network and several other networks (“one-with-many” hypothesis), and a set of networks altered their coherence with the Cerebellar Network (“many-with-one” hypothesis).ConclusionGiven the unexpected commonality of the Cerebellar Network’s altered coherence with other networks (a finding present in more than 70% of the patients, despite their clinical heterogeneity), we conclude that remission in MS may result from learning processes mediated by the Cerebellar Network.

Methodology for restarting hospital activities after a pandemic: COVID-19 experience

In addition to the health responsibility of hospitals in managing this COVID-19 crisis, hospital managers must also ensure the financial viability of healthcare structures. This is why, at the dawn of a lockdown exit, managers must anticipate the identification of recovery scenarios. This point refers in particular to the selection and scale of progression of hospital activities, and also to the impacts this will have on staff and patients in the short and medium term. Unfortunately, there is a serious lack of literature on the subject.The aim of this document is therefore to propose a methodology for resuming the medical, economic and social activities of a healthcare network or hospital.In our approach, we identify 6 stages following the COVID-19 peak: assessment of the situation, Act 2, development of scenarios-criteria-conditions, restarting, continuous improvement, and transversal activities.The entirety of our developed methodology is supported by a pragmatic approach with, in particular, the creation of specific tools for each stage of the process. This strategy and these tools have been created with the operational players and adapted to meet the specific features of each hospital while respecting the coherence of the healthcare network's decisions.We are convinced that this approach can be exported on a larger scale to inspire other healthcare networks and other hospitals that have also found themselves without the weapons to prepare for the resumption of hospital activities.

Consensus-Related Performance of Triplex MASs Based on Partial Complete Graph Structure.

This article mainly studies first-order coherence related to the robustness of the triplex MASs consensus models with partial complete graph structures; the performance index is studied through algebraic graph theory. The topologies of the novel triplex networks are generated by graph operations and the approach of graph spectra is applied to calculate the first-order network coherence. The coherence asymptotic behaviours of the three cases of the partial complete structures are analysed and compared. We find that under the condition that the number of nodes in partial complete substructures n tends to infinity, the coherence asymptotic behaviour of the two sorts of non-isomorphic three-layered networks will be increased by , which is irrelevant to the peripheral vertices number p; when p tends to infinity, adding star copies to the original triplex topologies will reverse the original size relationship of the coherence under consideration of the triplex networks. Finally, the coherence of the three-layered networks with the same sorts of parameters, but non-isomorphic graphs, are simulated to verify the results.

Performance Analysis of Consensus Algorithms Over Prism Networks Using Laplacian Spectra

Prism networks belong to generalized petersen graph topologies with planar and polyhedral properties. These networks are extensively used to study the complex networks in the context of computer science, biological networks, brain networks, and social networks. In this letter, the performance analysis of consensus algorithms over prism networks is investigated in terms of convergence time, network coherence, and communication delay. Specifically, in this letter, we first derive the explicit expressions for eigenvalues of Laplacian matrix over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> -dimensional prism networks using spectral graph theory. Subsequently, the study of consensus metrics such as convergence time, maximum communication time delay, first order network coherence, and second order network coherence is performed. Our results indicate that the effect of noise and communication time-delay on the consensus dynamics in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> -dimensional prism networks is minimal. The obtained results illustrate that the scale-free topology of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> -dimensional prism networks along with loopy structure is responsible for strong robustness with respect to consensus dynamics in prism networks.

Aromatic patterns: Tryptophan aromaticity as a catalyst for the emergence of life and rise of consciousness.

Sunlight held the key to the origin of life on Earth. The earliest life forms, cyanobacteria, captured the sunlight to generate energy through photosynthesis. Life on Earth evolved in accordance with the circadian rhythms tied to sensitivity to sunlight patterns. A unique feature of cyanobacterial photosynthetic proteins and circadian rhythms' molecules, and later of nearly all photon-sensing molecules throughout evolution, is that the aromatic amino acid tryptophan (Trp) resides at the center of light-harvesting active sites. In this perspective, I review the literature and integrate evidence from different scientific fields to explore the role Trp plays in photon-sensing capabilities of living organisms through its resonance delocalization of π-electrons. The observations presented here are the product of apparently unrelated phenomena throughout evolution, but nevertheless share consistent patterns of photon-sensing by Trp-containing and Trp-derived molecules. I posit the unique capacity to transfer electrons during photosynthesis in the earliest life forms is conferred to Trp due to its aromaticity. I propose this ability evolved to assume more complex functions, serving as a host for mechanisms underlying mental aptitudes - a concept which provides a theoretical basis for defining the neural correlates of consciousness. The argument made here is that Trp aromaticity may have allowed for the inception of the mechanistic building blocks used to fabricate complexity in higher forms of life. More specifically, Trp aromatic non-locality may have acted as a catalyst for the emergence of consciousness by instigating long-range synchronization and stabilizing the large-scale coherence of neural networks, which mediate functional brain activity. The concepts proposed in this perspective provide a conceptual foundation that invites further interdisciplinary dialogue aimed at examining and defining the role of aromaticity (beyond Trp) in the emergence of life and consciousness.

Consensus analysis of the weighted corona networks

The consensus of complex networks has attracted the attention of many scholars. The graph operation is a common method to construct complex networks, which is helpful in studying the consensus of complex networks. Based on the corona networks G1◦G2, this study gives different weights to the edges of G1◦G2 to obtain the weighted corona networks G̃1◦G̃2 and studies the consensus of G̃1◦G̃2. The consensus of the networks can be measured by coherence. First, the Laplacian polynomial of G̃1◦G̃2 is derived by using the properties of an orthogonal matrix. Second, the relationship between the first-order coherence of G̃1◦G̃2 and G1 is deduced by using the relevant properties of the determinant and the conclusion of polynomial coefficients and the principal minors of the matrix. Third, the join operation is introduced to further simplify the analytical formula of network coherence. Finally, a specific network example is used to verify the validity of the conclusion.