Unravelling the multisensory learning advantage: Different patterns of within and across frequency-specific interactions drive uni- and multisensory neuroplasticity

In the field of learning theory and practice, the superior efficacy of multisensory learning over uni-sensory is well-accepted. However, the underlying neural mechanisms at the macro-level of the human brain remain largely unexplored. This study addresses this gap by providing novel empirical evidence and a theoretical framework for understanding the superiority of multisensory learning. Through a cognitive, behavioral, and electroencephalographic assessment of carefully controlled uni-sensory and multisensory training interventions, our study uncovers a fundamental distinction in their neuroplastic patterns. A multilayered network analysis of pre- and post- training EEG data allowed us to model connectivity within and across different frequency bands at the cortical level. Pre-training EEG analysis unveils a complex network of distributed sources communicating through cross-frequency coupling, while comparison of pre- and post-training EEG data demonstrates significant differences in the reorganizational patterns of uni-sensory and multisensory learning. Uni-sensory training primarily modifies cross-frequency coupling between lower and higher frequencies, whereas multisensory training induces changes within the beta band in a more focused network, implying the development of a unified representation of audiovisual stimuli. In combination with behavioural and cognitive findings this suggests that, multisensory learning benefits from an automatic top-down transfer of training, while uni-sensory training relies mainly on limited bottom-up generalization. Our findings offer a compelling theoretical framework for understanding the advantage of multisensory learning.

A generalized eigenvector centrality for multilayer networks with inter-layer constraints on adjacent node importance

We present a novel approach for computing a variant of eigenvector centrality for multilayer networks with inter-layer constraints on node importance. Specifically, we consider a multilayer network defined by multiple edge-weighted, potentially directed, graphs over the same set of nodes with each graph representing one layer of the network and no inter-layer edges. As in the standard eigenvector centrality construction, the importance of each node in a given layer is based on the weighted sum of the importance of adjacent nodes in that same layer. Unlike standard eigenvector centrality, we assume that the adjacency relationship and the importance of adjacent nodes may be based on distinct layers. Importantly, this type of centrality constraint is only partially supported by existing frameworks for multilayer eigenvector centrality that use edges between nodes in different layers to capture inter-layer dependencies. For our model, constrained, layer-specific eigenvector centrality values are defined by a system of independent eigenvalue problems and dependent pseudo-eigenvalue problems, whose solution can be efficiently realized using an interleaved power iteration algorithm. We refer to this model, and the associated algorithm, as the Constrained Multilayer Centrality (CMLC) method. The characteristics of this approach, and of standard techniques based on inter-layer edges, are demonstrated on both a simple multilayer network and on a range of random graph models. An R package implementing the CMLC method along with example vignettes is available at https://hrfrost.host.dartmouth.edu/CMLC/.

The spatial distribution of coupling between tau and neurodegeneration in amyloid-β positive mild cognitive impairment

Synergies between amyloid-β (Aβ), tau, and neurodegeneration persist along the Alzheimer's disease (AD) continuum. This study aimed to evaluate the extent of spatial coupling between tau and neurodegeneration (atrophy) and its relation to Aβ positivity in mild cognitive impairment (MCI). Data from 409 participants were included (95 cognitively normal controls, 158 Aβ positive (Aβ+) MCI, and 156 Aβ negative (Aβ-) MCI). Florbetapir PET, Flortaucipir PET, and structural MRI were used as biomarkers for Aβ, tau and atrophy, respectively. Individual correlation matrices for tau load and atrophy were used to layer a multilayer network, with separate layers for tau and atrophy. A measure of coupling between corresponding regions of interest (ROIs) in the tau and atrophy layers was computed, as a function of Aβ positivity. Fewer than 25% of the ROIs across the brain showed heightened coupling between tau and atrophy in Aβ+ , relative to Aβ- MCI. Coupling strengths in the right rostral middle frontal and right paracentral gyri, in particular, mediated the association between Aβ burden and cognition in this sample.

Cognitive modelling of concepts in the mental lexicon with multilayer networks: Insights, advancements, and future challenges

The mental lexicon is a complex cognitive system representing information about the words/concepts that one knows. Over decades psychological experiments have shown that conceptual associations across multiple, interactive cognitive levels can greatly influence word acquisition, storage, and processing. How can semantic, phonological, syntactic, and other types of conceptual associations be mapped within a coherent mathematical framework to study how the mental lexicon works? Here we review cognitive multilayer networks as a promising quantitative and interpretative framework for investigating the mental lexicon. Cognitive multilayer networks can map multiple types of information at once, thus capturing how different layers of associations might co-exist within the mental lexicon and influence cognitive processing. This review starts with a gentle introduction to the structure and formalism of multilayer networks. We then discuss quantitative mechanisms of psychological phenomena that could not be observed in single-layer networks and were only unveiled by combining multiple layers of the lexicon: (i) multiplex viability highlights language kernels and facilitative effects of knowledge processing in healthy and clinical populations; (ii) multilayer community detection enables contextual meaning reconstruction depending on psycholinguistic features; (iii) layer analysis can mediate latent interactions of mediation, suppression, and facilitation for lexical access. By outlining novel quantitative perspectives where multilayer networks can shed light on cognitive knowledge representations, including in next-generation brain/mind models, we discuss key limitations and promising directions for cutting-edge future research.

Multilayer network alignment based on topological assessment via embeddings

BACKGROUND

Network graphs allow modelling the real world objects in terms of interactions. In a multilayer network, the interactions are distributed over layers (i.e., intralayer and interlayer edges). Network alignment (NA) is a methodology that allows mapping nodes between two or multiple given networks, by preserving topologically similar regions. For instance, NA can be applied to transfer knowledge from one biological species to another. In this paper, we present DANTEml, a software tool for the Pairwise Global NA (PGNA) of multilayer networks, based on topological assessment. It builds its own similarity matrix by processing the node embeddings computed from two multilayer networks of interest, to evaluate their topological similarities. The proposed solution can be used via a user-friendly command line interface, also having a built-in guided mode (step-by-step) for defining input parameters.

RESULTS

We investigated the performance of DANTEml based on (i) performance evaluation on synthetic multilayer networks, (ii) statistical assessment of the resulting alignments, and (iii) alignment of real multilayer networks. DANTEml over performed a method that does not consider the distribution of nodes and edges over multiple layers by 1193.62%, and a method for temporal NA by 25.88%; we also performed the statistical assessment, which corroborates the significance of its own node mappings. In addition, we tested the proposed solution by using a real multilayer network in presence of several levels of noise, in accordance with the same outcome pursued for the NA on our dataset of synthetic networks. In this case, the improvement is even more evident: +4008.75% and +111.72%, compared to a method that does not consider the distribution of nodes and edges over multiple layers and a method for temporal NA, respectively.

CONCLUSIONS

DANTEml is a software tool for the PGNA of multilayer networks based on topological assessment, that is able to provide effective alignments both on synthetic and real multi layer networks, of which node mappings can be validated statistically. Our experimentation reported a high degree of reliability and effectiveness for the proposed solution.

Overcoming vaccine hesitancy by multiplex social network targeting: an analysis of targeting algorithms and implications

Incorporating social factors into disease prevention and control efforts is an important undertaking of behavioral epidemiology. The interplay between disease transmission and human health behaviors, such as vaccine uptake, results in complex dynamics of biological and social contagions. Maximizing intervention adoptions via network-based targeting algorithms by harnessing the power of social contagion for behavior and attitude changes largely remains a challenge. Here we address this issue by considering a multiplex network setting. Individuals are situated on two layers of networks: the disease transmission network layer and the peer influence network layer. The disease spreads through direct close contacts while vaccine views and uptake behaviors spread interpersonally within a potentially virtual network. The results of our comprehensive simulations show that network-based targeting with pro-vaccine supporters as initial seeds significantly influences vaccine adoption rates and reduces the extent of an epidemic outbreak. Network targeting interventions are much more effective by selecting individuals with a central position in the opinion network as compared to those grouped in a community or connected professionally. Our findings provide insight into network-based interventions to increase vaccine confidence and demand during an ongoing epidemic.

Social network analysis of Twitter interactions: a directed multilayer network approach

Effective employment of social media for any social influence outcome requires a detailed understanding of the target audience. Social media provides a rich repository of self-reported information that provides insight regarding the sentiments and implied priorities of an online population. Using Social Network Analysis, this research models user interactions on Twitter as a weighted, directed network. Topic modeling through Latent Dirichlet Allocation identifies the topics of discussion in Tweets, which this study uses to induce a directed multilayer network wherein users (in one layer) are connected to the conversations and topics (in a second layer) in which they have participated, with inter-layer connections representing user participation in conversations. Analysis of the resulting network identifies both influential users and highly connected groups of individuals, informing an understanding of group dynamics and individual connectivity. The results demonstrate that the generation of a topically-focused social network to represent conversations yields more robust findings regarding influential users, particularly when analysts collect Tweets from a variety of discussions through more general search queries. Within the analysis, PageRank performed best among four measures used to rank individual influence within this problem context. In contrast, the results of applying both the Greedy Modular Algorithm and the Leiden Algorithm to identify communities were mixed; each method yielded valuable insights, but neither technique was uniformly superior. The demonstrated four-step process is readily replicable, and an interested user can automate the process with relatively low effort or expense.

Assessing the Repeatability of Multi-Frequency Multi-Layer Brain Network Topologies Across Alternative Researcher's Choice Paths

There is a growing interest in the neuroscience community on the advantages of multilayer functional brain networks. Researchers usually treated different frequencies separately at distinct functional brain networks. However, there is strong evidence that these networks share complementary information while their interdependencies could reveal novel findings. For this purpose, neuroscientists adopt multilayer networks, which can be described mathematically as an extension of trivial single-layer networks. Multilayer networks have become popular in neuroscience due to their advantage to integrate different sources of information. Here, Ι will focus on the multi-frequency multilayer functional connectivity analysis on resting-state fMRI (rs-fMRI) recordings. However, constructing a multilayer network depends on selecting multiple pre-processing steps that can affect the final network topology. Here, I analyzed the rs-fMRI dataset from a single human performing scanning over a period of 18 months (84 scans in total), and the rs-fMRI dataset containing 25 subjects with 3 repeat scans. I focused on assessing the reproducibility of multi-frequency multilayer topologies exploring the effect of two filtering methods for extracting frequencies from BOLD activity, three connectivity estimators, with or without a topological filtering scheme, and two spatial scales. Finally, I untangled specific combinations of researchers' choices that yield consistently brain networks with repeatable topologies, giving me the chance to recommend best practices over consistent topologies.

Sex differences in multilayer functional network topology over the course of aging in 37543 UK Biobank participants

Aging is a major risk factor for cardiovascular and neurodegenerative disorders, with considerable societal and economic implications. Healthy aging is accompanied by changes in functional connectivity between and within resting-state functional networks, which have been associated with cognitive decline. However, there is no consensus on the impact of sex on these age-related functional trajectories. Here, we show that multilayer measures provide crucial information on the interaction between sex and age on network topology, allowing for better assessment of cognitive, structural, and cardiovascular risk factors that have been shown to differ between men and women, as well as providing additional insights into the genetic influences on changes in functional connectivity that occur during aging. In a large cross-sectional sample of 37,543 individuals from the UK Biobank cohort, we demonstrate that such multilayer measures that capture the relationship between positive and negative connections are more sensitive to sex-related changes in the whole-brain connectivity patterns and their topological architecture throughout aging, when compared to standard connectivity and topological measures. Our findings indicate that multilayer measures contain previously unknown information on the relationship between sex and age, which opens up new avenues for research into functional brain connectivity in aging.

Design principles and mechanistic explanation

In this essay I propose that what design principles in systems biology and systems neuroscience do is to present abstract characterizations of mechanisms, and thereby facilitate mechanistic explanation. To show this, one design principle in systems neuroscience, i.e., the multilayer perceptron, is examined. However, Braillard (2010) contends that design principles provide a sort of non-mechanistic explanation due to two related reasons: they are very general and describe non-causal dependence relationships. In response to this, I argue that, on the one hand, all mechanisms are more or less general (or abstract), and on the other, many (if not all) design principles are causal systems.

Multilayer networks with higher-order interaction reveal the impact of collective behavior on epidemic dynamics

The ongoing COVID-19 pandemic has inflicted tremendous economic and societal losses. In the absence of pharmaceutical interventions, the population behavioral response, including situational awareness and adherence to non-pharmaceutical intervention policies, has a significant impact on contagion dynamics. Game-theoretic models have been used to reproduce the concurrent evolution of behavioral responses and disease contagion, and social networks are critical platforms on which behavior imitation between social contacts, even dispersed in distant communities, takes place. Such joint contagion dynamics has not been sufficiently explored, which poses a challenge for policies aimed at containing the infection. In this study, we present a multi-layer network model to study contagion dynamics and behavioral adaptation. It comprises two physical layers that mimic the two solitary communities, and one social layer that encapsulates the social influence of agents from these two communities. Moreover, we adopt high-order interactions in the form of simplicial complexes on the social influence layer to delineate the behavior imitation of individual agents. This model offers a novel platform to articulate the interaction between physically isolated communities and the ensuing coevolution of behavioral change and spreading dynamics. The analytical insights harnessed therefrom provide compelling guidelines on coordinated policy design to enhance the preparedness for future pandemics.

Multilayer Network Analysis of Dynamic Network Reconfiguration in Adults With Posttraumatic Stress Disorder

BACKGROUND

Brain functional network abnormalities are reported in posttraumatic stress disorder (PTSD). Most resting-state functional magnetic resonance imaging studies have assumed that the functional networks remain static during the scans. How these might change dynamically in PTSD remains unclear.

METHODS

Resting-state functional magnetic resonance imaging data were collected from 71 noncomorbid, treatment-naïve patients with PTSD and 70 demographically matched, trauma-exposed non-PTSD control subjects. Network switching rate was used to characterize dynamic changes of individual resting-state functional networks. Results were analyzed by comparing switching rates between the PTSD and trauma-exposed non-PTSD groups, testing for diagnosis × sex interactions, and examining correlations with PTSD symptom severity.

RESULTS

At the global level, the PTSD group showed significantly lower network switching rates than the trauma-exposed non-PTSD group. These were observed mainly in the frontoparietal, default mode, and limbic networks at the subnetwork level and in the frontal and temporal regions at the nodal level. These network switching rate alterations were correlated with PTSD symptom severity. There were no significant effects of sex.

CONCLUSIONS

These disruptions of dynamic functional network stability, reflected by lower network switching rates in the resting state, are a feature of PTSD and suggest that the frontoparietal, default mode, and limbic networks may play a critical role in the underlying neural mechanisms.

Probabilistically Weighted Multilayer Networks disclose the link between default mode network instability and psychosis-like experiences in healthy adults

The brain is a complex system in which the functional interactions among its subunits vary over time. The trajectories of this dynamic variation contribute to inter-individual behavioral differences and psychopathologic phenotypes. Despite many methodological advancements, the study of dynamic brain networks still relies on biased assumptions in the temporal domain. The current paper has two goals. First, we present a novel method to study multilayer networks: by modelling intra-nodal connections in a probabilistic, biologically driven way, we introduce a temporal resolution of the multilayer network based on signal similarity across time series. This new method is tested on synthetic networks by varying the number of modules and the sources of noise in the simulation. Secondly, we implement these probabilistically weighted (PW) multilayer networks to study the association between network dynamics and subclinical, psychosis-relevant personality traits in healthy adults. We show that the PW method for multilayer networks outperforms the standard procedure in modular detection and is less affected by increasing noise levels. Additionally, the PW method highlighted associations between the temporal instability of default mode network connections and psychosis-like experiences in healthy adults. PW multilayer networks allow an unbiased study of dynamic brain functioning and its behavioral correlates.

Sustainable development goals: conceptualization, communication and achievement synergies in a complex network framework

In this work we use a network-based approach to investigate the complex system of interactions among the 17 Sustainable Development Goals (SDGs), that constitute the structure of the United Nations 2030 Agenda for a sustainable future. We construct a three-layer multiplex, in which SDGs represent nodes, and their connections in each layer are determined by similarity definitions based on conceptualization, communication, and achievement, respectively. In each layer of the multiplex, we investigate the presence of nodes with high centrality, corresponding to strategic SDGs. We then compare the networks to establish whether and to which extent similar patterns emerge. Interestingly, we observe a significant relation between the SDG similarity patterns determined by their achievement and their communication and perception, revealed by social network data. The proposed framework represents an instrument to unveil new and nontrivial aspects of sustainability, laying the foundation of a decision support system to define and implement SDG achievement strategies.

Dynamic reconfiguration of human brain networks across altered states of consciousness

Consciousness is supported by rich neuronal dynamics to orchestrate behaviors and conscious processing can be disrupted by general anesthetics. Previous studies suggested that dynamic reconfiguration of large-scale functional network is critical for learning and higher-order cognitive function. During altered states of consciousness, how brain functional networks are dynamically changed and reconfigured at the whole-brain level is still unclear. To fill this gap, using multilayer network approach and functional magnetic resonance imaging (fMRI) data of 21 healthy subjects, we investigated the dynamic network reconfiguration in three different states of consciousness: wakefulness, dexmedetomidine-induced sedation, and recovery. Applying time-varying community detection algorithm, we constructed multilayer modularity networks to track and quantify dynamic interactions among brain areas that span time and space. We compared four high-level network features (i.e., switching, promiscuity, integration, and recruitment) derived from multilayer modularity across the three conditions. We found that sedation state is primarily characterized by increased switching rates as well as decreased integration, representing a whole-brain pattern with higher modular dynamics and more fragmented communication; such alteration can be mostly reversed after the recovery of consciousness. Thus, our work can provide additional insights to understand the modular network reconfiguration across different states of consciousness and may provide some clinical implications for disorders of consciousness.

Observations and conversations: how communities learn about infection risk can impact the success of non-pharmaceutical interventions against epidemics

BACKGROUND

Individual behavioural decisions are responses to a person's perceived social norms that could be shaped by both their physical and social environment. In the context of the COVID-19 pandemic, these environments correspond to epidemiological risk from contacts and the social construction of risk by communication within networks of friends. Understanding the circumstances under which the influence of these different social networks can promote the acceptance of non-pharmaceutical interventions and consequently the adoption of protective behaviours is critical for guiding useful, practical public health messaging.

METHODS

We explore how information from both physical contact and social communication layers of a multiplex network can contribute to flattening the epidemic curve in a community. Connections in the physical contact layer represent opportunities for transmission, while connections in the communication layer represent social interactions through which individuals may gain information, e.g. messaging friends.

RESULTS

We show that maintaining focus on awareness of risk among each individual's physical contacts promotes the greatest reduction in disease spread, but only when an individual is aware of the symptoms of a non-trivial proportion of their physical contacts (~ ≥ 20%). Information from the social communication layer without was less useful when these connections matched less well with physical contacts and contributed little in combination with accurate information from physical contacts.

CONCLUSIONS

We conclude that maintaining social focus on local outbreak status will allow individuals to structure their perceived social norms appropriately and respond more rapidly when risk increases. Finding ways to relay accurate local information from trusted community leaders could improve mitigation even where more intrusive/costly strategies, such as contact-tracing, are not possible.

Network Analysis of Microarray Data

DNA microarrays are widely used to investigate gene expression. Even though the classical analysis of microarray data is based on the study of differentially expressed genes, it is well known that genes do not act individually. Network analysis can be applied to study association patterns of the genes in a biological system. Moreover, it finds wide application in differential coexpression analysis between different systems. Network based coexpression studies have for example been used in (complex) disease gene prioritization, disease subtyping, and patient stratification.In this chapter we provide an overview of the methods and tools used to create networks from microarray data and describe multiple methods on how to analyze a single network or a group of networks. The described methods range from topological metrics, functional group identification to data integration strategies, topological pathway analysis as well as graphical models.

Intracranial brain stimulation modulates fMRI-based network switching

The extent to which functional MRI (fMRI) reflects direct neuronal changes remains unknown. Using 160 simultaneous electrical stimulation (es-fMRI) and intracranial brain stimulation recordings acquired in 26 individuals with epilepsy (with varying electrode locations), we tested whether brain networks dynamically change during intracranial brain stimulation, aiming to establish whether switching between brain networks is reduced after intracranial brain stimulation. As the brain spontaneously switches between a repertoire of intrinsic functional network configurations and the rate of switching is likely increased in epilepsy, we hypothesised that intracranial stimulation would reduce the brain's switching rate, thus potentially normalising aberrant brain network dynamics. To test this hypothesis, we quantified the rate that brain regions changed networks over time in response to brain stimulation, using network switching applied to multilayer modularity analysis of time-resolved es-fMRI connectivity. Network switching and synchrony was decreased after the first brain stimulation, followed by a more consistent pattern of network switching over time. This change was commonly observed in cortical networks and adjacent to the electrode targets. Our results suggest that neuronal perturbation is likely to modulate large-scale brain networks, and multilayer network modelling may be used to inform the clinical efficacy of brain stimulation in epilepsy.

Measurement reliability for individual differences in multilayer network dynamics: Cautions and considerations

Multilayer network models have been proposed as an effective means of capturing the dynamic configuration of distributed neural circuits and quantitatively describing how communities vary over time. Beyond general insights into brain function, a growing number of studies have begun to employ these methods for the study of individua differences. However, test–retest reliabilities for multilayer network measures have yet to be fully quantified or optimized, potentially limiting their utility for individual difference studies. Here, we systematically evaluated the impact of multilayer community detection algorithms, selection of network parameters, scan duration, and task condition on test–retest reliabilities of multilayer network measures (i.e., flexibility, integration, and recruitment). A key finding was that the default method used for community detection by the popular generalized Louvain algorithm can generate erroneous results. Although available, an updated algorithm addressing this issue is yet to be broadly adopted in the neuroimaging literature. Beyond the algorithm, the present work identified parameter selection as a key determinant of test–retest reliability; however, optimization of these parameters and expected reliabilities appeared to be dataset-specific. Once parameters were optimized, consistent with findings from the static functional connectivity literature, scan duration was a much stronger determinant of reliability than scan condition. When the parameters were optimized and scan duration was sufficient, both passive (i.e., resting state, Inscapes, and movie) and active (i.e., flanker) tasks were reliable, although reliability in the movie watching condition was significantly higher than in the other three tasks. The minimal data requirement for achieving reliable measures for the movie watching condition was 20 min, and 30 min for the other three tasks. Our results caution the field against the use of default parameters without optimization based on the specific datasets to be employed – a process likely to be limited for most due to the lack of test–retest samples to enable parameter optimization.

A heat diffusion multilayer network approach for the identification of functional biomarkers in rumen methane emissions

A better understanding of rumen microbial interactions is crucial for the study of rumen metabolism and methane emissions. Metagenomics-based methods can explore the relationship between microbial genes and metabolites to clarify the effect of microbial function on the host phenotype. This study investigated the rumen microbial mechanisms of methane metabolism in cattle by combining metagenomic data and network-based methods. Based on the relative abundance of 1461 rumen microbial genes and the main volatile fatty acids (VFAs), a multilayer heterogeneous network was constructed, and the functional modules associated with metabolite-microbial genes were obtained by heat diffusion algorithm. The PLS model by integrating data from VFAs and microbial genes explained 72.98% variation of methane emissions. Compared with single-layer networks, more previously reported biomarkers of methane prediction can be captured by the multilayer network. More biomarkers with the rank of top 20 topological centralities were from the PLS models of diffusion subsets. The heat diffusion algorithm is different from the strategy used by the microbial metabolic system to understand methane phenotype. It inferred 24 novel biomarkers that were preferentially affected by changes in specific VFAs. Results showed that the heat diffusion multilayer network approach improved the understanding of the microbial patterns of VFAs affecting methane emissions which represented by the functional microbial genes.

A multiplex centrality metric for complex social networks: sex, social status, and family structure predict multiplex centrality in rhesus macaques

Members of a society interact using a variety of social behaviors, giving rise to a multi-faceted and complex social life. For the study of animal behavior, quantifying this complexity is critical for understanding the impact of social life on animals' health and fitness. Multilayer network approaches, where each interaction type represents a different layer of the social network, have the potential to better capture this complexity than single layer approaches. Calculating individuals' centrality within a multilayer social network can reveal keystone individuals and more fully characterize social roles. However, existing measures of multilayer centrality do not account for differences in the dynamics and functionality across interaction layers. Here we validate a new method for quantifying multiplex centrality called consensus ranking by applying this method to multiple social groups of a well-studied nonhuman primate, the rhesus macaque. Consensus ranking can suitably handle the complexities of animal social life, such as networks with different properties (sparse vs. dense) and biological meanings (competitive vs. affiliative interactions). We examined whether individuals' attributes or socio-demographic factors (sex, age, dominance rank and certainty, matriline size, rearing history) were associated with multiplex centrality. Social networks were constructed for five interaction layers (i.e., aggression, status signaling, conflict policing, grooming and huddling) for seven social groups. Consensus ranks were calculated across these five layers and analyzed with respect to individual attributes and socio-demographic factors. Generalized linear mixed models showed that consensus ranking detected known social patterns in rhesus macaques, showing that multiplex centrality was greater in high-ranking males with high certainty of rank and females from the largest families. In addition, consensus ranks also showed that females from very small families and mother-reared (compared to nursery-reared) individuals were more central, showing that consideration of multiple social domains revealed individuals whose social centrality and importance might otherwise have been missed.

Predicting Pattern Formation in Multilayer Networks

We investigate how the structure of interactions between coupled oscillators influences the formation of asynchronous patterns in a multilayer network by formulating a simple, general multilayer oscillator model. We demonstrate the analysis of this model in three-oscillator systems, illustrating the role of interactions among oscillators in sustaining differences in both the phase and amplitude of oscillations leading to the formation of asynchronous patterns. Finally, we demonstrate the generalizability of our model's predictions through comparison with a more realistic multilayer model. Overall, our model provides a useful approach for predicting the types of asynchronous patterns that multilayer networks of coupled oscillators which cannot be achieved by the existing methods which focus on characterizing the synchronous state.

Effect of Inter-layer Coupling on Multilayer Network Centrality Measures

The study of networks has been evolving because of its applications in diverse fields. Many complex systems involve multiple types of interactions and such systems are better modeled as multilayer networks.The question "which are the most (or least) important nodes in a given network?", has gained substantial attention in the network science community. The importance of a node is known as centrality and there are multiple ways to define it. Extending the centrality measure to multilayer networks is challenging since the relative contribution of intra-layer edges vs. that of inter-layer edges to multilayer centrality is not straight-forward. With the growing applications of multilayer networks, several attempts have been made to define centrality in multilayer networks in recent years. There are different ways of tuning the inter-layer couplings which may lead to different classes of centrality measures. In this article, we provide an overview of the recent works related to centrality in multilayer networks with a focus on key use cases and implications of the type of inter-layer coupling on centrality and subsequent uses of the different centrality measures. We discuss the effect of three popular interlayer coupling methods viz. diagonal coupling between adjacent layers, diagonal coupling and cross coupling. We hope the colloquial tone of this article would make it a pleasant read for understanding the theoretical as well as experimental aspects of the work.

Control of multilayer biological networks and applied to target identification of complex diseases

BACKGROUND

Networks have been widely used to model the structures of various biological systems. The ultimate aim of research on biological networks is to steer biological system structures to desired states by manipulating signals. Despite great advances in the linear control of single-layer networks, it has been observed that many complex biological systems have a multilayer networked structure and extremely complicated nonlinear processes.

RESULT

In this study, we propose a general framework for controlling nonlinear dynamical systems with multilayer networked structures by formulating the problem as a minimum union optimization problem. In particular, we offer a novel approach for identifying the minimal driver nodes that can steer a multilayered nonlinear dynamical system toward any desired dynamical attractor. Three disease-related biology multilayer networks are used to demonstrate the effectiveness of our approaches. Moreover, in the set of minimum driver nodes identified by the algorithm we proposed, we confirmed that some nodes can act as drug targets in the biological experiments. Other nodes have not been reported as drug targets; however, they are also involved in important biological processes from existing literature.

CONCLUSIONS

The proposed method could be a promising tool for determining higher drug target enrichment or more meaningful steering nodes for studying complex diseases.

Frequency-based brain networks: From a multiplex framework to a full multilayer description

We explore how to study dynamical interactions between brain regions by using functional multilayer networks whose layers represent different frequency bands at which a brain operates. Specifically, we investigate the consequences of considering the brain as (i) a multilayer network, in which all brain regions can interact with each other at different frequency bands; and as (ii) a multiplex network, in which interactions between different frequency bands are allowed only within each brain region and not between them. We study the second-smallest eigenvalue λ 2 of the combinatorial supra-Laplacian matrix of both the multiplex and multilayer networks, as λ 2 has been used previously as an indicator of network synchronizability and as a biomarker for several brain diseases. We show that the heterogeneity of interlayer edge weights and, especially, the fraction of missing edges crucially modify the value of λ 2, and we illustrate our results with both synthetic network models and real data obtained from resting-state magnetoencephalography. Our work highlights the differences between using a multiplex approach and a full multilayer approach when studying frequency-based multilayer brain networks.

Chimera states in neuronal networks: A review

Neuronal networks, similar to many other complex systems, self-organize into fascinating emergent states that are not only visually compelling, but also vital for the proper functioning of the brain. Synchronous spatiotemporal patterns, for example, play an important role in neuronal communication and plasticity, and in various cognitive processes. Recent research has shown that the coexistence of coherent and incoherent states, known as chimera states or simply chimeras, is particularly important and characteristic for neuronal systems. Chimeras have also been linked to the Parkinson's disease, epileptic seizures, and even to schizophrenia. The emergence of this unique collective behavior is due to diverse factors that characterize neuronal dynamics and the functioning of the brain in general, including neural bumps and unihemispheric slow-wave sleep in some aquatic mammals. Since their discovery, chimera states have attracted ample attention of researchers that work at the interface of physics and life sciences. We here review contemporary research dedicated to chimeras in neuronal networks, focusing on the relevance of different synaptic connections, and on the effects of different network structures and coupling setups. We also cover the emergence of different types of chimera states, we highlight their relevance in other related physical and biological systems, and we outline promising research directions for the future, including possibilities for experimental verification.

Asymmetric disease dynamics in multihost interconnected networks

Epidemic spread in single-host systems strongly depends on the population's transmission network. However, little is known regarding the spread of epidemics across networks representing populations of multiple hosts. We explored cross-species transmission in a multilayer network where layers represent populations of two distinct hosts, and disease can spread across intralayer (within-host) and interlayer (between-host) edges. We developed an analytic framework for the SIR epidemic model to examine the effect of (i) source of infection and (ii) between-host asymmetry in infection probabilities, on disease risk. We measured risk as outbreak probability and outbreak size in a focal host, represented by one network layer. Numeric simulations were used to validate the analytic formulations. We found that outbreak probability is determined by a complex interaction between source of infection and between-host infection probabilities, whereas outbreak size is mainly affected by the non-focal host to focal host infection probability. Hence, inter-specific asymmetry in infection probabilities shapes disease dynamics in multihost networks. These results highlight the importance of considering multiple measures of disease risk and advance our understanding of disease spread in multihost systems. The study provides a flexible way to model disease dynamics in multiple hosts while considering contact heterogeneity within and between species. We strongly encourage empirical studies that include information on both cross-species infection rates and network structure of multiple hosts. Such studies are necessary to corroborate our theoretical results and to improve our understanding of multihost epidemiology.

EIGENVECTOR-BASED CENTRALITY MEASURES FOR TEMPORAL NETWORKS. MULTISCALE MODELING & SIMULATION : A SIAM INTERDISCIPLINARY JOURNAL 2017;15:537-574. [PMID: 29046619 PMCID: PMC5643020 DOI: 10.1137/16m1066142]

Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvector-based centrality. We consider a temporal network with N nodes as a sequence of T layers that describe the network during different time windows, and we couple centrality matrices for the layers into a supra-centrality matrix of size NT × NT whose dominant eigenvector gives the centrality of each node i at each time t. We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node i and the time layer t. We also introduce the concepts of marginal and conditional centralities, which facilitate the study of centrality trajectories over time. We find that the strength of coupling between layers is important for determining multiscale properties of centrality, such as localization phenomena and the time scale of centrality changes. In the strong-coupling regime, we derive expressions for time-averaged centralities, which are given by the zeroth-order terms of a singular perturbation expansion. We also study first-order terms to obtain first-order-mover scores, which concisely describe the magnitude of nodes' centrality changes over time. As examples, we apply our method to three empirical temporal networks: the United States Ph.D. exchange in mathematics, costarring relationships among top-billed actors during the Golden Age of Hollywood, and citations of decisions from the United States Supreme Court.

Integrating Multidimensional Data Sources to Identify Genes Regulating Complex Phenotypes

Phenotypes collected with a view to quantitative trait locus mapping can be augmented with compatible whole-transcriptome expression data and information from several other sources. These different data sources can be assembled into multidimensional network models which allow the identification of key genes potentially driving the phenotype of interest. The following chapter describes this approach using an example workflow. Several alternatives and potential limitations are discussed to aid the researcher when applying these techniques to their own work.