Reliable Multi-Fractal Characterization of Weighted Complex Networks: Algorithms and Implications

Fractal Similarity of Pain Brain Networks

The conscious perception of pain is the result of dynamic interactions of neural activities from local brain regions to distributed brain networks. Mapping out the networks of functional connections between brain regions that form and disperse when an experimental participant received nociceptive stimulations allow to characterize the pattern of network connections related to the pain experience.Although the pattern of intra- and inter-areal connections across the brain are incredibly complex, they appear also largely scale free, with "fractal" connectivity properties reproducing at short and long-time scales. Our results combining intracranial recordings and functional imaging in humans during pain indicate striking similarities in the activity and topological representation of networks at different orders of temporality, with reproduction of patterns of activation from the millisecond to the multisecond range. The connectivity analyzed using graph theory on fMRI data was organized in four sets of brain regions matching those identified through iEEG (i.e., sensorimotor, default mode, central executive, and amygdalo-hippocampal).Here, we discuss similarities in brain network organization at different scales or "orders," in participants as they feel pain. Description of this fractal-like organization may provide clues about how our brain regions work together to create the perception of pain and how pain becomes chronic when its organization is altered.

GAHLS: an optimized graph analytics based high level synthesis framework

The urgent need for low latency, high-compute and low power on-board intelligence in autonomous systems, cyber-physical systems, robotics, edge computing, evolvable computing, and complex data science calls for determining the optimal amount and type of specialized hardware together with reconfigurability capabilities. With these goals in mind, we propose a novel comprehensive graph analytics based high level synthesis (GAHLS) framework that efficiently analyzes complex high level programs through a combined compiler-based approach and graph theoretic optimization and synthesizes them into message passing domain-specific accelerators. This GAHLS framework first constructs a compiler-assisted dependency graph (CaDG) from low level virtual machine (LLVM) intermediate representation (IR) of high level programs and converts it into a hardware friendly description representation. Next, the GAHLS framework performs a memory design space exploration while account for the identified computational properties from the CaDG and optimizing the system performance for higher bandwidth. The GAHLS framework also performs a robust optimization to identify the CaDG subgraphs with similar computational structures and aggregate them into intelligent processing clusters in order to optimize the usage of underlying hardware resources. Finally, the GAHLS framework synthesizes this compressed specialized CaDG into processing elements while optimizing the system performance and area metrics. Evaluations of the GAHLS framework on several real-life applications (e.g., deep learning, brain machine interfaces) demonstrate that it provides 14.27× performance improvements compared to state-of-the-art approaches such as LegUp 6.2.

A unified approach of detecting phase transition in time-varying complex networks

Deciphering the non-trivial interactions and mechanisms driving the evolution of time-varying complex networks (TVCNs) plays a crucial role in designing optimal control strategies for such networks or enhancing their causal predictive capabilities. In this paper, we advance the science of TVCNs by providing a mathematical framework through which we can gauge how local changes within a complex weighted network affect its global properties. More precisely, we focus on unraveling unknown geometric properties of a network and determine its implications on detecting phase transitions within the dynamics of a TVCN. In this vein, we aim at elaborating a novel and unified approach that can be used to depict the relationship between local interactions in a complex network and its global kinetics. We propose a geometric-inspired framework to characterize the network's state and detect a phase transition between different states, to infer the TVCN's dynamics. A phase of a TVCN is determined by its Forman-Ricci curvature property. Numerical experiments show the usefulness of the proposed curvature formalism to detect the transition between phases within artificially generated networks. Furthermore, we demonstrate the effectiveness of the proposed framework in identifying the phase transition phenomena governing the training and learning processes of artificial neural networks. Moreover, we exploit this approach to investigate the phase transition phenomena in cellular re-programming by interpreting the dynamics of Hi-C matrices as TVCNs and observing singularity trends in the curvature network entropy. Finally, we demonstrate that this curvature formalism can detect a political change. Specifically, our framework can be applied to the US Senate data to detect a political change in the United States of America after the 1994 election, as discussed by political scientists.

Multifractality of Complex Networks Is Also Due to Geometry: A Geometric Sandbox Algorithm

Over the past three decades, describing the reality surrounding us using the language of complex networks has become very useful and therefore popular. One of the most important features, especially of real networks, is their complexity, which often manifests itself in a fractal or even multifractal structure. As a generalization of fractal analysis, the multifractal analysis of complex networks is a useful tool for identifying and quantitatively describing the spatial hierarchy of both theoretical and numerical fractal patterns. Nowadays, there are many methods of multifractal analysis. However, all these methods take into account only the fact of connection between nodes (and eventually the weight of edges) and do not take into account the real positions (coordinates) of nodes in space. However, intuition suggests that the geometry of network nodes' position should have a significant impact on the true fractal structure. Many networks identified in nature (e.g., air connection networks, energy networks, social networks, mountain ridge networks, networks of neurones in the brain, and street networks) have their own often unique and characteristic geometry, which is not taken into account in the identification process of multifractality in commonly used methods. In this paper, we propose a multifractal network analysis method that takes into account both connections between nodes and the location coordinates of nodes (network geometry). We show the results for different geometrical variants of the same network and reveal that this method, contrary to the commonly used method, is sensitive to changes in network geometry. We also carry out tests for synthetic as well as real-world networks.

Structure-based prediction of nucleic acid binding residues by merging deep learning- and template-based approaches

Accurate prediction of nucleic binding residues is essential for the understanding of transcription and translation processes. Integration of feature- and template-based strategies could improve the prediction of these key residues in proteins. Nevertheless, traditional hybrid algorithms have been surpassed by recently developed deep learning-based methods, and the possibility of integrating deep learning- and template-based approaches to improve performance remains to be explored. To address these issues, we developed a novel structure-based integrative algorithm called NABind that can accurately predict DNA- and RNA-binding residues. A deep learning module was built based on the diversified sequence and structural descriptors and edge aggregated graph attention networks, while a template module was constructed by transforming the alignments between the query and its multiple templates into features for supervised learning. Furthermore, the stacking strategy was adopted to integrate the above two modules for improving prediction performance. Finally, a post-processing module dependent on the random walk algorithm was proposed to further correct the integrative predictions. Extensive evaluations indicated that our approach could not only achieve excellent performance on both native and predicted structures but also outperformed existing hybrid algorithms and recent deep learning methods. The NABind server is available at http://liulab.hzau.edu.cn/NABind/.

Hierarchical growth in neural networks structure: Organizing inputs by Order of Hierarchical Complexity

Several studies demonstrate that the structure of the brain increases in hierarchical complexity throughout development. We tested if the structure of artificial neural networks also increases in hierarchical complexity while learning a developing task, called the balance beam problem. Previous simulations of this developmental task do not reflect a necessary premise underlying development: a more complex structure can be built out of less complex ones, while ensuring that the more complex structure does not replace the less complex one. In order to address this necessity, we segregated the input set by subsets of increasing Orders of Hierarchical Complexity. This is a complexity measure that has been extensively shown to underlie the complexity behavior and hypothesized to underlie the complexity of the neural structure of the brain. After segregating the input set, minimal neural network models were trained separately for each input subset, and adjacent complexity models were analyzed sequentially to observe whether there was a structural progression. Results show that three different network structural progressions were found, performing with similar accuracy, pointing towards self-organization. Also, more complex structures could be built out of less complex ones without substituting them, successfully addressing catastrophic forgetting and leveraging performance of previous models in the literature. Furthermore, the model structures trained on the two highest complexity subsets performed better than simulations of the balance beam present in the literature. As a major contribution, this work was successful in addressing hierarchical complexity structural growth in neural networks, and is the first that segregates inputs by Order of Hierarchical Complexity. Since this measure can be applied to all domains of data, the present method can be applied to future simulations, systematizing the simulation of developmental and evolutionary structural growth in neural networks.

Network bypasses sustain complexity

Real-world networks are neither regular nor random, a fact elegantly explained by mechanisms such as the Watts-Strogatz or the Barabási-Albert models, among others. Both mechanisms naturally create shortcuts and hubs, which while enhancing the network's connectivity, also might yield several undesired navigational effects: They tend to be overused during geodesic navigational processes-making the networks fragile-and provide suboptimal routes for diffusive-like navigation. Why, then, networks with complex topologies are ubiquitous? Here, we unveil that these models also entropically generate network bypasses: alternative routes to shortest paths which are topologically longer but easier to navigate. We develop a mathematical theory that elucidates the emergence and consolidation of network bypasses and measure their navigability gain. We apply our theory to a wide range of real-world networks and find that they sustain complexity by different amounts of network bypasses. At the top of this complexity ranking we found the human brain, which points out the importance of these results to understand the plasticity of complex systems.

Sexual dimorphism in the relationship between brain complexity, volume and general intelligence (g): a cross-cohort study

Changes in brain morphology have been reported during development, ageing and in relation to different pathologies. Brain morphology described by the shape complexity of gyri and sulci can be captured and quantified using fractal dimension (FD). This measure of brain structural complexity, as well as brain volume, are associated with intelligence, but less is known about the sexual dimorphism of these relationships. In this paper, sex differences in the relationship between brain structural complexity and general intelligence (g) in two diverse geographic and cultural populations (UK and Indian) are investigated. 3D T1-weighted magnetic resonance imaging (MRI) data and a battery of cognitive tests were acquired from participants belonging to three different cohorts: Mysore Parthenon Cohort (MPC); Aberdeen Children of the 1950s (ACONF) and UK Biobank. We computed MRI derived structural brain complexity and g estimated from a battery of cognitive tests for each group. Brain complexity and volume were both positively corelated with intelligence, with the correlations being significant in women but not always in men. This relationship is seen across populations of differing ages and geographical locations and improves understanding of neurobiological sex-differences.

Novel Texture Feature Descriptors Based on Multi-Fractal Analysis and LBP for Classifying Breast Density in Mammograms

This paper investigates the usefulness of multi-fractal analysis and local binary patterns (LBP) as texture descriptors for classifying mammogram images into different breast density categories. Multi-fractal analysis is also used in the pre-processing step to segment the region of interest (ROI). We use four multi-fractal measures and the LBP method to extract texture features, and to compare their classification performance in experiments. In addition, a feature descriptor combining multi-fractal features and multi-resolution LBP (MLBP) features is proposed and evaluated in this study to improve classification accuracy. An autoencoder network and principal component analysis (PCA) are used for reducing feature redundancy in the classification model. A full field digital mammogram (FFDM) dataset, INBreast, which contains 409 mammogram images, is used in our experiment. BI-RADS density labels given by radiologists are used as the ground truth to evaluate the classification results using the proposed methods. Experimental results show that the proposed feature descriptor based on multi-fractal features and LBP result in higher classification accuracy than using individual texture feature sets.

Unfolding the multiscale structure of networks with dynamical Ollivier-Ricci curvature

Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes. However, latent space embeddings are limited to specific classes of networks because incompatible metric spaces generally result in information loss. Here, we study arbitrary networks geometrically by defining a dynamic edge curvature measuring the similarity between pairs of dynamical network processes seeded at nearby nodes. We show that the evolution of the curvature distribution exhibits gaps at characteristic timescales indicating bottleneck-edges that limit information spreading. Importantly, curvature gaps are robust to large fluctuations in node degrees, encoding communities until the phase transition of detectability, where spectral and node-clustering methods fail. Using this insight, we derive geometric modularity to find multiscale communities based on deviations from constant network curvature in generative and real-world networks, significantly outperforming most previous methods. Our work suggests using network geometry for studying and controlling the structure of and information spreading on networks.

Biological networks across scales

Many biological systems across scales of size and complexity exhibit a time-varying complex network structure that emerges and self-organizes as a result of interactions with the environment. Network interactions optimize some intrinsic cost functions that are unknown and involve for example energy efficiency, robustness, resilience, and frailty. A wide range of networks exist in biology, from gene regulatory networks important for organismal development, protein interaction networks that govern physiology and metabolism, and neural networks that store and convey information to networks of microbes that form microbiomes within hosts, animal contact networks that underlie social systems, and networks of populations on the landscape connected by migration. Increasing availability of extensive (big) data is amplifying our ability to quantify biological networks. Similarly, theoretical methods that describe network structure and dynamics are being developed. Beyond static networks representing snapshots of biological systems, collections of longitudinal data series can help either at defining and characterizing network dynamics over time or analyzing the dynamics constrained to networked architectures. Moreover, due to interactions with the environment and other biological systems, a biological network may not be fully observable. Also, subnetworks may emerge and disappear as a result of the need for the biological system to cope with for example invaders or new information flows. The confluence of these developments renders tractable the question of how the structure of biological networks predicts and controls network dynamics. In particular, there may be structural features that result in homeostatic networks with specific higher-order statistics (e.g., multifractal spectrum), which maintain stability over time through robustness and/or resilience to perturbation. Alternative, plastic networks may respond to perturbation by (adaptive to catastrophic) shifts in structure. Here, we explore the opportunity for discovering universal laws connecting the structure of biological networks with their function, positioning them on the spectrum of time-evolving network structure, i.e. dynamics of networks, from highly stable to exquisitely sensitive to perturbation. If such general laws exist, they could transform our ability to predict the response of biological systems to perturbations-an increasingly urgent priority in the face of anthropogenic changes to the environment that affect life across the gamut of organizational scales.

Computationally efficient sandbox algorithm for multifractal analysis of large-scale complex networks with tens of millions of nodes

Among various algorithms of multifractal analysis (MFA) for complex networks, the sandbox MFA algorithm behaves with the best computational efficiency. However, the existing sandbox algorithm is still computationally expensive for MFA of large-scale networks with tens of millions of nodes. It is also not clear whether MFA results can be improved by a largely increased size of a theoretical network. To tackle these challenges, a computationally efficient sandbox algorithm (CESA) is presented in this paper for MFA of large-scale networks. Distinct from the existing sandbox algorithm that uses the shortest-path distance matrix to obtain the required information for MFA of networks, our CESA employs the compressed sparse row format of the adjacency matrix and the breadth-first search technique to directly search the neighbor nodes of each layer of center nodes, and then to retrieve the required information. A theoretical analysis reveals that the CESA reduces the time complexity of the existing sandbox algorithm from cubic to quadratic, and also improves the space complexity from quadratic to linear. Then the CESA is demonstrated to be effective, efficient, and feasible through the MFA results of (u,v)-flower model networks from the fifth to the 12th generations. It enables us to study the multifractality of networks of the size of about 11 million nodes with a normal desktop computer. Furthermore, we have also found that increasing the size of (u,v)-flower model network does improve the accuracy of MFA results. Finally, our CESA is applied to a few typical real-world networks of large scale.

Deciphering the laws of social network-transcendent COVID-19 misinformation dynamics and implications for combating misinformation phenomena

The global rise of COVID-19 health risk has triggered the related misinformation infodemic. We present the first analysis of COVID-19 misinformation networks and determine few of its implications. Firstly, we analyze the spread trends of COVID-19 misinformation and discover that the COVID-19 misinformation statistics are well fitted by a log-normal distribution. Secondly, we form misinformation networks by taking individual misinformation as a node and similarity between misinformation nodes as links, and we decipher the laws of COVID-19 misinformation network evolution: (1) We discover that misinformation evolves to optimize the network information transfer over time with the sacrifice of robustness. (2) We demonstrate the co-existence of fit get richer and rich get richer phenomena in misinformation networks. (3) We show that a misinformation network evolution with node deletion mechanism captures well the public attention shift on social media. Lastly, we present a network science inspired deep learning framework to accurately predict which Twitter posts are likely to become central nodes (i.e., high centrality) in a misinformation network from only one sentence without the need to know the whole network topology. With the network analysis and the central node prediction, we propose that if we correctly suppress certain central nodes in the misinformation network, the information transfer of network would be severely impacted.

Subgraphs of Interest Social Networks for Diffusion Dynamics Prediction

Finding the building blocks of real-world networks contributes to the understanding of their formation process and related dynamical processes, which is related to prediction and control tasks. We explore different types of social networks, demonstrating high structural variability, and aim to extract and see their minimal building blocks, which are able to reproduce supergraph structural and dynamical properties, so as to be appropriate for diffusion prediction for the whole graph on the base of its small subgraph. For this purpose, we determine topological and functional formal criteria and explore sampling techniques. Using the method that provides the best correspondence to both criteria, we explore the building blocks of interest networks. The best sampling method allows one to extract subgraphs of optimal 30 nodes, which reproduce path lengths, clustering, and degree particularities of an initial graph. The extracted subgraphs are different for the considered interest networks, and provide interesting material for the global dynamics exploration on the mesoscale base.

Stability of Imbalanced Triangles in Gene Regulatory Networks of Cancerous and Normal Cells

Genes communicate with each other through different regulatory effects, which lead to the emergence of complex network structures in cells, and such structures are expected to be different for normal and cancerous cells. To study these differences, we have investigated the Gene Regulatory Network (GRN) of cells as inferred from RNA-sequencing data. The GRN is a signed weighted network corresponding to the inductive or inhibitory interactions. Here we focus on a particular of motifs in the GRN, the triangles, which are imbalanced if the number of negative interactions is odd. By studying the stability of imbalanced triangles in the GRN, we show that the network of cancerous cells has fewer imbalanced triangles compared to normal cells. Moreover, in the normal cells, imbalanced triangles are isolated from the main part of the network, while such motifs are part of the network's giant component in cancerous cells. Our result demonstrates that due to genes' collective behavior the structure of the complex networks is different in cancerous cells from those in normal ones.

Network extraction by routing optimization

Routing optimization is a relevant problem in many contexts. Solving directly this type of optimization problem is often computationally intractable. Recent studies suggest that one can instead turn this problem into one of solving a dynamical system of equations, which can instead be solved efficiently using numerical methods. This results in enabling the acquisition of optimal network topologies from a variety of routing problems. However, the actual extraction of the solution in terms of a final network topology relies on numerical details which can prevent an accurate investigation of their topological properties. In fact, in this context, theoretical results are fully accessible only to an expert audience and ready-to-use implementations for non-experts are rarely available or insufficiently documented. In particular, in this framework, final graph acquisition is a challenging problem in-and-of-itself. Here we introduce a method to extract network topologies from dynamical equations related to routing optimization under various parameters’ settings. Our method is made of three steps: first, it extracts an optimal trajectory by solving a dynamical system, then it pre-extracts a network, and finally, it filters out potential redundancies. Remarkably, we propose a principled model to address the filtering in the last step, and give a quantitative interpretation in terms of a transport-related cost function. This principled filtering can be applied to more general problems such as network extraction from images, thus going beyond the scenarios envisioned in the first step. Overall, this novel algorithm allows practitioners to easily extract optimal network topologies by combining basic tools from numerical methods, optimization and network theory. Thus, we provide an alternative to manual graph extraction which allows a grounded extraction from a large variety of optimal topologies. The analysis of these may open up the possibility to gain new insights into the structure and function of optimal networks. We provide an open source implementation of the code online.

The Modular Organization of Pain Brain Networks: An fMRI Graph Analysis Informed by Intracranial EEG

Intracranial EEG (iEEG) studies have suggested that the conscious perception of pain builds up from successive contributions of brain networks in less than 1 s. However, the functional organization of cortico-subcortical connections at the multisecond time scale, and its accordance with iEEG models, remains unknown. Here, we used graph theory with modular analysis of fMRI data from 60 healthy participants experiencing noxious heat stimuli, of whom 36 also received audio stimulation. Brain connectivity during pain was organized in four modules matching those identified through iEEG, namely: 1) sensorimotor (SM), 2) medial fronto-cingulo-parietal (default mode-like), 3) posterior parietal-latero-frontal (central executive-like), and 4) amygdalo-hippocampal (limbic). Intrinsic overlaps existed between the pain and audio conditions in high-order areas, but also pain-specific higher small-worldness and connectivity within the sensorimotor module. Neocortical modules were interrelated via “connector hubs” in dorsolateral frontal, posterior parietal, and anterior insular cortices, the antero-insular connector being most predominant during pain. These findings provide a mechanistic picture of the brain networks architecture and support fractal-like similarities between the micro-and macrotemporal dynamics associated with pain. The anterior insula appears to play an essential role in information integration, possibly by determining priorities for the processing of information and subsequent entrance into other points of the brain connectome.

Network science characteristics of brain-derived neuronal cultures deciphered from quantitative phase imaging data

Understanding the mechanisms by which neurons create or suppress connections to enable communication in brain-derived neuronal cultures can inform how learning, cognition and creative behavior emerge. While prior studies have shown that neuronal cultures possess self-organizing criticality properties, we further demonstrate that in vitro brain-derived neuronal cultures exhibit a self-optimization phenomenon. More precisely, we analyze the multiscale neural growth data obtained from label-free quantitative microscopic imaging experiments and reconstruct the in vitro neuronal culture networks (microscale) and neuronal culture cluster networks (mesoscale). We investigate the structure and evolution of neuronal culture networks and neuronal culture cluster networks by estimating the importance of each network node and their information flow. By analyzing the degree-, closeness-, and betweenness-centrality, the node-to-node degree distribution (informing on neuronal interconnection phenomena), the clustering coefficient/transitivity (assessing the “small-world” properties), and the multifractal spectrum, we demonstrate that murine neurons exhibit self-optimizing behavior over time with topological characteristics distinct from existing complex network models. The time-evolving interconnection among murine neurons optimizes the network information flow, network robustness, and self-organization degree. These findings have complex implications for modeling neuronal cultures and potentially on how to design biological inspired artificial intelligence.

Biomorphic structural batteries for robotics

Batteries with conformal shape and multiple functionalities could provide new degrees of freedom in the design of robotic devices. For example, the ability to provide both load bearing and energy storage can increase the payload and extend the operational range for robots. However, realizing these kinds of structural power devices requires the development of materials with suitable mechanical and ion transport properties. Here, we report biomimetic aramid nanofibers–based composites with cartilage-like nanoscale morphology that display an unusual combination of mechanical and ion transport properties. Ion-conducting membranes from these aramid nanofiber composites enable pliable zinc-air batteries with cyclic performance exceeding 100 hours that can also serve as protective covers in various robots including soft and flexible miniaturized robots. The unique properties of the aramid ion conductors are attributed to the percolating network architecture of nanofibers with high connectivity and strong nanoscale filaments designed using a graph theory of composite architecture when the continuous aramid filaments are denoted as edges and intersections are denoted as nodes. The total capacity of these body-integrated structural batteries is 72 times greater compared with a stand-alone Li-ion battery with the same volume. These materials and their graph theory description enable a new generation of robotic devices, body prosthetics, and flexible and soft robotics with nature-inspired distributed energy storage.

Distinguishing Epileptiform Discharges From Normal Electroencephalograms Using Adaptive Fractal and Network Analysis: A Clinical Perspective

Epilepsy is one of the most common disorders of the brain. Clinically, to corroborate an epileptic seizure-like symptom and to find the seizure localization, electroencephalogram (EEG) data are often visually examined by a clinical doctor to detect the presence of epileptiform discharges. Epileptiform discharges are transient waveforms lasting for several tens to hundreds of milliseconds and are mainly divided into seven types. It is important to develop systematic approaches to accurately distinguish these waveforms from normal control ones. This is a difficult task if one wishes to develop first principle rather than black-box based approaches, since clinically used scalp EEGs usually contain a lot of noise and artifacts. To solve this problem, we analyzed 640 multi-channel EEG segments, each 4s long. Among these segments, 540 are short epileptiform discharges, and 100 are from healthy controls. We have proposed two approaches for distinguishing epileptiform discharges from normal EEGs. The first method is based on Signal Range and EEGs' long range correlation properties characterized by the Hurst parameter H extracted by applying adaptive fractal analysis (AFA), which can also maximally suppress the effects of noise and various kinds of artifacts. Our second method is based on networks constructed from three aspects of the scalp EEG signals, the Signal Range, the energy of the alpha wave component, and EEG's long range correlation properties. The networks are further analyzed using singular value decomposition (SVD). The square of the first singular value from SVD is used to construct features to distinguish epileptiform discharges from normal controls. Using Random Forest Classifier (RF), our approaches can achieve very high accuracy in distinguishing epileptiform discharges from normal control ones, and thus are very promising to be used clinically. The network-based approach is also used to infer the localizations of each type of epileptiform discharges, and it is found that the sub-networks representing the most likely location of each type of epileptiform discharges are different among the seven types of epileptiform discharges.

A Brief Review of Chimera State in Empirical Brain Networks

Understanding the human brain and its functions has always been an interesting and challenging problem. Recently, a significant progress on this problem has been achieved on the aspect of chimera state where a coexistence of synchronized and unsynchronized states can be sustained in identical oscillators. This counterintuitive phenomenon is closely related to the unihemispheric sleep in some marine mammals and birds and has recently gotten a hot attention in neural systems, except the previous studies in non-neural systems such as phase oscillators. This review will briefly summarize the main results of chimera state in neuronal systems and pay special attention to the network of cerebral cortex, aiming to accelerate the study of chimera state in brain networks. Some outlooks are also discussed.

Controlling the Multifractal Generating Measures of Complex Networks

Mathematical modelling of real complex networks aims to characterize their architecture and decipher their underlying principles. Self-repeating patterns and multifractality exist in many real-world complex systems such as brain, genetic, geoscience, and social networks. To better comprehend the multifractal behavior in the real networks, we propose the weighted multifractal graph model to characterize the spatiotemporal complexity and heterogeneity encoded in the interaction weights. We provide analytical tools to verify the multifractal properties of the proposed model. By varying the parameters in the initial unit square, the model can reproduce a diverse range of multifractal spectrums with different degrees of symmetry, locations, support and shapes. We estimate and investigate the weighted multifractal graph model corresponding to two real-world complex systems, namely (i) the chromosome interactions of yeast cells in quiescence and in exponential growth, and (ii) the brain networks of cognitively healthy people and patients exhibiting late mild cognitive impairment leading to Alzheimer disease. The analysis of recovered models show that the proposed random graph model provides a novel way to understand the self-similar structure of complex networks and to discriminate different network structures. Additionally, by mapping real complex networks onto multifractal generating measures, it allows us to develop new network design and control strategies, such as the minimal control of multifractal measures of real systems under different functioning conditions or states.

Complexity-based decoding of brain-skin relation in response to olfactory stimuli

BACKGROUND AND OBJECTIVE

Human body is covered with skin in different parts. In fact, skin reacts to different changes around human. For instance, when the surrounding temperature changes, human skin will react differently. It is known that the activity of skin is regulated by human brain. In this research, for the first time we investigate the relation between the activities of human skin and brain by mathematical analysis of Galvanic Skin Response (GSR) and Electroencephalography (EEG) signals.

METHOD

For this purpose, we employ fractal theory and analyze the variations of fractal dimension of GSR and EEG signals when subjects are exposed to different olfactory stimuli in the form of pleasant odors.

RESULTS

Based on the obtained results, the complexity of GSR signal changes with the complexity of EEG signal in case of different stimuli, where by increasing the molecular complexity of olfactory stimuli, the complexity of EEG and GSR signals increases. The results of statistical analysis showed the significant effect of stimulation on variations of complexity of GSR signal. In addition, based on effect size analysis, fourth odor with greatest molecular complexity had the greatest effect on variations of complexity of EEG and GSR signals.

CONCLUSION

Therefore, it can be said that human skin reaction changes with the variations in the activity of human brain. The result of analysis in this research can be further used to make a model between the activities of human skin and brain that will enable us to predict skin reaction to different stimuli.

Pharmacogenomic network analysis of the gene-drug interaction landscape underlying drug disposition

In recent decades the identification of pharmacogenomic gene-drug associations has evolved tremendously. Despite this progress, a major fraction of the heritable inter-individual variability remains elusive. Higher-dimensional phenomena, such as gene-gene-drug interactions, in which variability in multiple genes synergizes to precipitate an observable phenotype have been suggested to account at least for part of this missing heritability. However, the identification of such intricate relationships remains difficult partly because of analytical challenges associated with the complexity explosion of the problem. To facilitate the identification of such combinatorial pharmacogenetic associations, we here propose a network analysis strategy. Specifically, we analyzed the landscape of drug metabolizing enzymes and transporters for 100 top selling drugs as well as all compounds with pharmacogenetic germline labels or dosing guidelines. Based on this data, we calculated the posterior probabilities that gene i is involved in metabolism, transport or toxicity of a given drug under the condition that another gene j is involved for all pharmacogene pairs (i, j). Interestingly, these analyses revealed significant patterns between individual genes and across pharmacogene families that provide insights into metabolic interactions. To visualize the gene-drug interaction landscape, we use multidimensional scaling to collapse this similarity matrix into a two-dimensional network. We suggest that Euclidian distance between nodes can inform about the likelihood of epistatic interactions and thus might provide a useful tool to reduce the search space and facilitate the identification of combinatorial pharmacogenomic associations.

Exoskeleton Hand Control by Fractional Order Models

This paper deals with the fractional order control for the complex systems, hand exoskeleton and sensors, that monitor and control the human behavior. The control laws based on physical significance variables, for fractional order models, with delays or without delays, are proposed and discussed. Lyapunov techniques and the methods that derive from Yakubovici-Kalman-Popov lemma are used and the frequency criterions that ensure asymptotic stability of the closed loop system are inferred. An observer control is proposed for the complex models, exoskeleton and sensors. The asymptotic stability of the system, exoskeleton hand-observer, is studied for sector control laws. Numerical simulations for an intelligent haptic robot-glove are presented. Several examples regarding these models, with delays or without delays, by using sector control laws or an observer control, are analyzed. The experimental platform is presented.

Evaluation of the 3D fractal dimension as a marker of structural brain complexity in multiple-acquisition MRI

Fractal analysis represents a promising new approach to structural neuroimaging data, yet systematic evaluation of the fractal dimension (FD) as a marker of structural brain complexity is scarce. Here we present in-depth methodological assessment of FD estimation in structural brain MRI. On the computational side, we show that spatial scale optimization can significantly improve FD estimation accuracy, as suggested by simulation studies with known FD values. For empirical evaluation, we analyzed two recent open-access neuroimaging data sets (MASSIVE and Midnight Scan Club), stratified by fundamental image characteristics including registration, sequence weighting, spatial resolution, segmentation procedures, tissue type, and image complexity. Deviation analyses showed high repeated-acquisition stability of the FD estimates across both data sets, with differential deviation susceptibility according to image characteristics. While less frequently studied in the literature, FD estimation in T2-weighted images yielded robust outcomes. Importantly, we observed a significant impact of image registration on absolute FD estimates. Applying different registration schemes, we found that unbalanced registration induced (a) repeated-measurement deviation clusters around the registration target, (b) strong bidirectional correlations among image analysis groups, and (c) spurious associations between the FD and an index of structural similarity, and these effects were strongly attenuated by reregistration in both data sets. Indeed, differences in FD between scans did not simply track differences in structure per se, suggesting that structural complexity and structural similarity represent distinct aspects of structural brain MRI. In conclusion, scale optimization can improve FD estimation accuracy, and empirical FD estimates are reliable yet sensitive to image characteristics.

Gauging Functional Brain Activity: From Distinguishability to Accessibility

Standard neuroimaging techniques provide non-invasive access not only to human brain anatomy but also to its physiology. The activity recorded with these techniques is generally called functional imaging, but what is observed per se is an instance of dynamics, from which functional brain activity should be extracted. Distinguishing between bare dynamics and genuine function is a highly non-trivial task, but a crucially important one when comparing experimental observations and interpreting their significance. Here we illustrate how neuroimaging's ability to extract genuine functional brain activity is bounded by functional representations' structure. To do so, we first provide a simple definition of functional brain activity from a system-level brain imaging perspective. We then review how the properties of the space on which brain activity is represented induce relations on observed imaging data which allow determining the extent to which two observations are functionally distinguishable and quantifying how far apart they are. It is also proposed that genuine functional distances would require defining accessibility, i.e., how a given observed condition can be accessed from another given one, under the dynamics of some neurophysiological process. We show how these properties result from the structure defined on dynamical data and dynamics-to-function projections, and consider some implications that the way and extent to which these are defined have for the interpretation of experimental data from standard system-level brain recording techniques.

Reconstructing missing complex networks against adversarial interventions

Interactions within complex network components define their operational modes, collective behaviors and global functionality. Understanding the role of these interactions is limited by either sensing methodologies or intentional adversarial efforts that sabotage the network structure. To overcome the partial observability and infer with good fidelity the unobserved network structures (latent subnetworks that are not random samples of the full network), we propose a general causal inference framework for reconstructing network structures under unknown adversarial interventions. We explore its applicability in both biological and social systems to recover the latent structures of human protein complex interactions and brain connectomes, as well as to infer the camouflaged social network structure in a simulated removal process. The demonstrated effectiveness establishes its good potential for capturing hidden information in much broader research domains.

The impact of fasting on resting state brain networks in mice

Fasting is known to influence learning and memory in mice and alter the neural networks that subserve these cognitive functions. We used high-resolution functional MRI to study the impact of fasting on resting-state functional connectivity in mice following 12 h of fasting. The cortex and subcortex were parcellated into 52 subregions and functional connectivity was measured between each pair of subregions in groups of fasted and non-fasted mice. Functional connectivity was globally increased in the fasted group compared to the non-fasted group, with the most significant increases evident between the hippocampus (bilateral), retrosplenial cortex (left), visual cortex (left) and auditory cortex (left). Functional brain networks in the non-fasted group comprised five segregated modules of strongly interconnected subregions, whereas the fasted group comprised only three modules. The amplitude of low frequency fluctuations (ALFF) was decreased in the ventromedial hypothalamus in the fasted group. Correlation in gamma oscillations derived from local field potentials was increased between the left visual and retrosplenial cortices in the fasted group and the power of gamma oscillations was reduced in the ventromedial hypothalamus. These results indicate that fasting induces profound changes in functional connectivity, most likely resulting from altered coupling of neuronal gamma oscillations.

The cingulum as a marker of individual differences in neurocognitive development

The canonical approach to exploring brain-behaviour relationships is to group individuals according to a phenotype of interest, and then explore the neural correlates of this grouping. A limitation of this approach is that multiple aetiological pathways could result in a similar phenotype, so the role of any one brain mechanism may be substantially underestimated. Building on advances in network analysis, we used a data-driven community-clustering algorithm to identify robust subgroups based on white-matter microstructure in childhood and adolescence (total N = 313, mean age: 11.24 years). The algorithm indicated the presence of two equal-size groups that show a critical difference in fractional anisotropy (FA) of the left and right cingulum. Applying the brain-based grouping in independent samples, we find that these different 'brain types' had profoundly different cognitive abilities with higher performance in the higher FA group. Further, a connectomics analysis indicated reduced structural connectivity in the low FA subgroup that was strongly related to reduced functional activation of the default mode network. These results provide a proof-of-concept that bottom-up brain-based groupings can be identified that relate to cognitive performance. This provides a first demonstration of a complimentary approach for investigating individual differences in brain structure and function, particularly for neurodevelopmental disorders where researchers are often faced with phenotypes that are difficult to define at the cognitive or behavioural level.

Fractal and Multifractal Properties of Electrographic Recordings of Human Brain Activity: Toward Its Use as a Signal Feature for Machine Learning in Clinical Applications

The quantification of brain dynamics is essential to its understanding. However, the brain is a system operating on multiple time scales, and characterization of dynamics across time scales remains a challenge. One framework to study such dynamics is that of fractal geometry; and currently there exist several methods for the study of brain dynamics using fractal geometry. We aim to highlight some of the practical challenges of applying fractal geometry to brain dynamics—and as a putative feature for machine learning applications, and propose solutions to enable its wider use in neuroscience. Using intracranially recorded electroencephalogram (EEG) and simulated data, we compared monofractal and multifractal methods with regards to their sensitivity to signal variance. We found that both monofractal and multifractal properties correlate closely with signal variance, thus not being a useful feature of the signal. However, after applying an epoch-wise standardization procedure to the signal, we found that multifractal measures could offer non-redundant information compared to signal variance, power (in different frequency bands) and other established EEG signal measures. We also compared different multifractal estimation methods to each other in terms of reliability, and we found that the Chhabra-Jensen algorithm performed best. Finally, we investigated the impact of sampling frequency and epoch length on the estimation of multifractal properties. Using epileptic seizures as an example event in the EEG, we show that there may be an optimal time scale (i.e., combination of sampling frequency and epoch length) for detecting temporal changes in multifractal properties around seizures. The practical issues we highlighted and our suggested solutions should help in developing robust methods for the application of fractal geometry in EEG signals. Our analyses and observations also aid the theoretical understanding of the multifractal properties of the brain and might provide grounds for new discoveries in the study of brain signals. These could be crucial for the understanding of neurological function and for the developments of new treatments.

Differential Age-Related Changes in Structural Covariance Networks of Human Anterior and Posterior Hippocampus

The hippocampus plays an important role in memory function relying on information interaction between distributed brain areas. The hippocampus can be divided into the anterior and posterior sections with different structure and function along its long axis. The aim of this study is to investigate the effects of normal aging on the structural covariance of the anterior hippocampus (aHPC) and the posterior hippocampus (pHPC). In this study, 240 healthy subjects aged 18-89 years were selected and subdivided into young (18-23 years), middle-aged (30-58 years), and older (61-89 years) groups. The aHPC and pHPC was divided based on the location of uncal apex in the MNI space. Then, the structural covariance networks were constructed by examining their covariance in gray matter volumes with other brain regions. Finally, the influence of age on the structural covariance of these hippocampal sections was explored. We found that the aHPC and pHPC had different structural covariance patterns, but both of them were associated with the medial temporal lobe and insula. Moreover, both increased and decreased covariances were found with the aHPC but only increased covariance was found with the pHPC with age (p < 0.05, family-wise error corrected). These decreased connections occurred within the default mode network, while the increased connectivity mainly occurred in other memory systems that differ from the hippocampus. This study reveals different age-related influence on the structural networks of the aHPC and pHPC, providing an essential insight into the mechanisms of the hippocampus in normal aging.

Fractal features of soil particle size distributions and their potential as an indicator of Robinia pseudoacacia invasion1

To study the fractal dimensions of the soil particle size distributions (PSDs) within different plantations (of Pinus densiflora, Quercus acutissima, Robinia pseudoacacia, and Larix kaempferi) and evaluate PSDs as an indicator of the likelihood of Robinia pseudoacacia invasion, the soil porosity of 0–20 cm soil layers was measured at different plantations in the Yaoxiang Forest Farm, Shandong Province, China. The results showed that the fractal dimension (D_m) values varied from 2.59 to 2.70 among the different plantations and were significantly negatively correlated to sand content and positively correlated to silt content and clay content. Significant negative correlations were observed between D_m and both soil organic matter (SOM) (P < 0.05) and available phosphorus (P < 0.01). The multifractal entropy dimension (D₁) and entropy dimension/capacity dimension (D₁/D₀) parameters were not significantly correlated with SOM, although significant correlations were found between SOM and each of D₀, Δα, and Δf(α). Compared with the other plantations, the Robinia pseudoacacia plantation had higher nutrient contents, higher D₀ and D₁ values and lower D_m values. Based on principal component analysis (PCA) ordination, we concluded that Robinia pseudoacacia and Pinus densiflora shared a similar habitat and that Robinia pseudoacacia is more likely to invade Pinus densiflora plantations for soil.

The dorsal striatum and the dynamics of the consensus connectomes in the frontal lobe of the human brain

In the applications of the graph theory, it is unusual that one considers numerous, pairwise different graphs on the very same set of vertices. In the case of human braingraphs or connectomes, however, this is the standard situation: the nodes correspond to anatomically identified cerebral regions, and two vertices are connected by an edge if a diffusion MRI-based workflow identifies a fiber of axons, running between the two regions, corresponding to the two vertices. Therefore, if we examine the braingraphs of n subjects, then we have n graphs on the very same, anatomically identified vertex set. It is a natural idea to describe the k-frequently appearing edges in these graphs: the edges that are present between the same two vertices in at least k out of the n graphs. Based on the NIH-funded large Human Connectome Project's public data release, we have reported the construction of the Budapest Reference Connectome Server http://www.connectome.pitgroup.org that generates and visualizes these k-frequently appearing edges. We call the graphs of the k-frequently appearing edges "k-consensus connectomes" since an edge could be included only if it is present in at least k graphs out of n. Considering the whole human brain, we have reported a surprising property of these consensus connectomes earlier. In the present work we are focusing on the frontal lobe of the brain, and we report here a similarly surprising dynamical property of the consensus connectomes when k is gradually changed from k = n to k = 1: the connections between the nodes of the frontal lobe are seemingly emanating from those nodes that were connected to sub-cortical structures of the dorsal striatum: the caudate nucleus, and the putamen. We hypothesize that this dynamic behavior copies the axonal fiber development of the frontal lobe. An animation of the phenomenon is presented at https://youtu.be/wBciB2eW6_8.