ABSTRACT
The human brain is a dynamic system that shows frequency-specific features. Neuroimaging studies have shown that both healthy individuals and those with chronic pain disorders experience pain influenced by various processes that fluctuate over time. Primary dysmenorrhea (PDM) is a chronic visceral pain that disrupts the coordinated activity of brain's functional network. However, it remains unclear whether the dynamic interactions across the whole-brain network over time and their associations with neurobehavioral symptoms are dependent on the frequency bands in patients with PDM during the pain-free periovulation phase. In this study, we used an energy landscape analysis to examine the interactions over time across the large-scale network in a sample of 59 patients with PDM and 57 healthy controls (HCs) at different frequency bands. Compared with HCs, patients with PDM exhibit aberrant brain dynamics, with more significant differences in the slow-4 frequency band. Patients with PDM show more indirect neural transition counts due to an unstable intermediate state, whereas neurotypical brain activity frequently transitions between 2 major states. This data-driven approach further revealed that the brains of individuals with PDM have more abnormal brain dynamics than HCs. Our results suggested that unstable brain dynamics were associated with the strength of brain functional segregation and the Pain Catastrophizing Scale score. Our findings provide preliminary evidence that atypical dynamics in the functional network may serve as a potential key feature and biological marker of patients with PDM during the pain-free phase. PERSPECTIVE: We applied energy landscape analysis on brain-imaging data to identify relatively stable and dominant brain activity patterns for patients with PDM. More atypical brain dynamics were found in the slow-4 band and were related to the strength of functional segregation, providing new insights into the dysfunction brain dynamics.
ABSTRACT
Intrinsic neural activities are characterized as endless spontaneous fluctuation over multiple time scales. However, how the intrinsic brain organization changes over time under local perturbation remains an open question. By means of statistical physics, we proposed an approach to capture whole-brain dynamics based on estimating time-varying nonreversibility and k-means clustering of dynamic varying nonreversibility patterns. We first used synthetic fMRI to investigate the effects of window parameters on the temporal variability of varying nonreversibility. Second, using real test-retest fMRI data, we examined the reproducibility, reliability, biological, and physiological correlation of the varying nonreversibility substates. Finally, using repetitive transcranial magnetic stimulation-fMRI data, we investigated the modulation effects of repetitive transcranial magnetic stimulation on varying nonreversibility substate dynamics. The results show that: (i) as window length increased, the varying nonreversibility variance decreased, while the sliding step almost did not alter it; (ii) the global high varying nonreversibility states and low varying nonreversibility states were reproducible across multiple datasets and different window lengths; and (iii) there were increased low varying nonreversibility states and decreased high varying nonreversibility states when the left frontal lobe was stimulated, but not the occipital lobe. Taken together, these results provide a thermodynamic equilibrium perspective of intrinsic brain organization and reorganization under local perturbation.
Subject(s)
Brain Mapping , Brain , Reproducibility of Results , Brain Mapping/methods , Brain/diagnostic imaging , Brain/physiology , Transcranial Magnetic Stimulation/methods , Frontal LobeABSTRACT
Background: The brain in resting state has complex dynamic properties and shows frequency dependent characteristics. The frequency-dependent whole-brain dynamic changes of resting state across the scans have been ignored in Alzheimer's disease (AD). Objective: Coactivation pattern (CAP) analysis can identify different brain states. This paper aimed to investigate the dynamic characteristics of frequency dependent whole-brain CAPs in AD. Methods: We utilized a multiband CAP approach to model the state space and study brain dynamics in both AD and NC. The correlation between the dynamic characteristics and the subjects' clinical index was further analyzed. Results: The results showed similar CAP patterns at different frequency bands, but the occurrence of patterns was different. In addition, CAPs associated with the default mode network (DMN) and the ventral/dorsal visual network (dorsal/ventral VN) were altered significantly between the AD and NC groups. This study also found the correlation between the altered dynamic characteristics of frequency dependent CAPs and the patients' clinical Mini-Mental State Examination assessment scale scores. Conclusion: This study revealed that while similar CAP spatial patterns appear in different frequency bands, their dynamic characteristics in subbands vary. In addition, delineating subbands was more helpful in distinguishing AD from NC in terms of CAP.
ABSTRACT
Repetitive transcranial magnetic stimulation (rTMS) is a noninvasive approach to modulate brain activity and behavior in humans. Still, how individual resting-state brain dynamics after rTMS evolves across different functional configurations is rarely studied. Here, using resting state fMRI data from healthy subjects, we aimed to examine the effects of rTMS to individual large-scale brain dynamics. Using Topological Data Analysis based Mapper approach, we construct the precise dynamic mapping (PDM) for each participant. To reveal the relationship between PDM and canonical functional representation of the resting brain, we annotated the graph using relative activation proportion of a set of large-scale resting-state networks (RSNs) and assigned the single brain volume to corresponding RSN-dominant or a hub state (not any RSN was dominant). Our results show that (i) low-frequency rTMS could induce changed temporal evolution of brain states; (ii) rTMS didn't alter the hub-periphery configurations underlined resting-state brain dynamics; and (iii) the rTMS effects on brain dynamics differ across the left frontal and occipital lobe. In conclusion, low-frequency rTMS significantly alters the individual temporo-spatial dynamics, and our finding further suggested a potential target-dependent alteration of brain dynamics. This work provides a new perspective to comprehend the heterogeneous effect of rTMS.
Subject(s)
Brain , Transcranial Magnetic Stimulation , Humans , Transcranial Magnetic Stimulation/methods , Brain/diagnostic imaging , Magnetic Resonance Imaging/methods , Occipital Lobe , Neural Pathways/diagnostic imaging , Neural Pathways/physiologyABSTRACT
Introduction: Research on the brain activity during resting state has found that brain activation is centered around three networks, including the default mode network (DMN), the salient network (SN), and the central executive network (CEN), and switches between multiple modes. As a common disease in the elderly, Alzheimer's disease (AD) affects the state transitions of functional networks in the resting state. Methods: Energy landscape, as a new method, can intuitively and quickly grasp the statistical distribution of system states and information related to state transition mechanisms. Therefore, this study mainly uses the energy landscape method to study the changes of the triple-network brain dynamics in AD patients in the resting state. Results: AD brain activity patterns are in an abnormal state, and the dynamics of patients with AD tend to be unstable, with an unusually high flexibility in switching between states. Also , the subjects' dynamic features are correlated with clinical index. Discussion: The atypical balance of large-scale brain systems in patients with AD is associated with abnormally active brain dynamics. Our study are helpful for further understanding the intrinsic dynamic characteristics and pathological mechanism of the resting-state brain in AD patients.
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Stroke is the leading cause of disability globally in need of novel and effective methods of rehabilitation. Intermittent theta burst stimulation (iTBS) has been adopted as a Level B recommendation for lower limb spasticity in guidelines on the therapeutic use of repetitive transcranial magnetic stimulation (rTMS). Nonetheless, the methodological differences and deficits of existing work bring about heterogenous results and therefore limit the universal clinical use of rTMS in lower extremity (LE) rehabilitation. The variation of stimulated targets across motor cortex contributes mainly to these heterogeneities. This narrative review includes studies of rTMS on LE motor function rehabilitation in patients after stroke until now. Some analyses of brain imaging and electromagnetic simulation and quantification through computational modeling were also performed. rTMS appears capable of fostering LE motor rehabilitation after stroke, but the actually stimulated targets are considerably bias making it difficult to confirm effectiveness. The main reason for this phenomenon is probably inaccurate targeting of motor cortical leg representation. An underlying updated method is proposed as Individual-Target TMS (IT-TMS) combined with brain imaging. rTMS is a promising validated method for LE function regaining. Future studies should systematically compare the effects of IT-TMS with traditional rTMS using large samples in random clinical trials. This article is categorized under: Neuroscience > Clinical Neuroscience.
Subject(s)
Stroke Rehabilitation , Stroke , Humans , Stroke Rehabilitation/methods , Transcranial Magnetic Stimulation/methods , Treatment Outcome , Stroke/therapy , Lower ExtremityABSTRACT
Poststroke aphasia is one of the most dramatic functional deficits that results from direct damage of focal brain regions and dysfunction of large-scale brain networks. The reconstruction of language function depends on the hierarchical whole-brain dynamic reorganization. However, investigations into the longitudinal neural changes of large-scale brain networks for poststroke aphasia remain scarce. Here we characterize large-scale brain dynamics in left-frontal-stroke aphasia through energy landscape analysis. Using fMRI during an auditory comprehension task, we find that aphasia patients suffer serious whole-brain dynamics perturbation in the acute and subacute stages after stroke, in which the brains were restricted into two major activity patterns. Following spontaneous recovery process, the brain flexibility improved in the chronic stage. Critically, we demonstrated that the abnormal neural dynamics are correlated with the aberrant brain network coordination. Taken together, the energy landscape analysis exhibited that the acute poststroke aphasia has a constrained, low dimensional brain dynamics, which were replaced by less constrained and high dimensional dynamics at chronic aphasia. Our study provides a new perspective to profoundly understand the pathological mechanisms of poststroke aphasia.
Subject(s)
Aphasia , Connectome , Stroke , Humans , Aphasia/diagnostic imaging , Aphasia/etiology , Aphasia/pathology , Brain , Stroke/complications , Language , Magnetic Resonance ImagingABSTRACT
Primary insomnia (PI) is among the most prevalent sleep-related disorders and has a far-reaching impact on daytime functioning. Repetitive transcranial magnetic stimulation (rTMS) has drawn attention because of its effectiveness and safety. The purpose of the current study was to detect changes in the topological organization of whole-brain functional networks and to determine their associations with the clinical treatment effects of rTMS. Resting-state functional magnetic resonance imaging (rsfMRI) data from 32 patients with PI were collected and compared with findings from 32 age- and gender-matched healthy controls (HCs). The patients were treated with Stanford accelerated intelligent neuromodulation therapy, which is a recently validated neuroscience-informed accelerated intermittent theta-burst stimulation protocol. Graph theoretical analysis was used to construct functional connectivity matrices and to extract the attribute features of small-world networks in insomnia. Scores on the Insomnia Severity Index (ISI), Pittsburgh Sleep Quality Index, Self-Rating Anxiety Scale, Self-Rating Depression Scale, and the associations between these clinical characteristics and functional metrics, were the primary outcomes. At baseline, the patients with PI showed inefficient small-world property and aberrant functional segregation and functional integration compared with the HCs. These properties showed renormalization after individualized rTMS treatment. Furthermore, low functional connectivity between the right insula and left medial frontal gyrus correlated with improvement in ISI scores. We highlight functional network dysfunctions in PI patients and provide evidence into the pathophysiological mechanisms involved and the possible mode of action of rTMS.
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Spatially distinct, self-sustained oscillations in artificial neural networks are fundamental to information encoding, storage, and processing in these systems. Here, we develop a method to induce a large variety of self-sustained oscillatory patterns in artificial neural networks and a controlling strategy to switch between different patterns. The basic principle is that, given a complex network, one can find a set of nodes-the minimum feedback vertex set (mFVS), whose removal or inhibition will result in a tree-like network without any loop structure. Reintroducing a few or even a single mFVS node into the tree-like artificial neural network can recover one or a few of the loops and lead to self-sustained oscillation patterns based on these loops. Reactivating various mFVS nodes or their combinations can then generate a large number of distinct neuronal firing patterns with a broad distribution of the oscillation period. When the system is near a critical state, chaos can arise, providing a natural platform for pattern switching with remarkable flexibility. With mFVS guided control, complex networks of artificial neurons can thus be exploited as potential prototypes for local, analog type of processing paradigms.
Subject(s)
Neural Networks, Computer , Neurons , FeedbackABSTRACT
AIM: This study investigated changes in small-world topology and brain functional connectivity in patients with optic neuritis (ON) by resting-state functional magnetic resonance imaging (rs-fMRI) and based on graph theory. METHODS: A total of 21 patients with ON (8 males and 13 females) and 21 matched healthy control subjects (8 males and 13 females) were enrolled and underwent rs-fMRI. Data were preprocessed and the brain was divided into 116 regions of interest. Small-world network parameters and area under the integral curve (AUC) were calculated from pairwise brain interval correlation coefficients. Differences in brain network parameter AUCs between the 2 groups were evaluated with the independent sample t-test, and changes in brain connection strength between ON patients and control subjects were assessed by network-based statistical analysis. RESULTS: In the sparsity range from 0.08 to 0.48, both groups exhibited small-world attributes. Compared to the control group, global network efficiency, normalized clustering coefficient, and small-world value were higher whereas the clustering coefficient value was lower in ON patients. There were no differences in characteristic path length, local network efficiency, and normalized characteristic path length between groups. In addition, ON patients had lower brain functional connectivity strength among the rolandic operculum, medial superior frontal gyrus, insula, median cingulate and paracingulate gyri, amygdala, superior parietal gyrus, inferior parietal gyrus, supramarginal gyrus, angular gyrus, lenticular nucleus, pallidum, superior temporal gyrus, and cerebellum compared to the control group (P < 0.05). CONCLUSION: Patients with ON show typical "small world" topology that differed from that detected in HC brain networks. The brain network in ON has a small-world attribute but shows reduced and abnormal connectivity compared to normal subjects and likely causes symptoms of cognitive impairment.
Subject(s)
Connectome/methods , Magnetic Resonance Imaging/methods , Optic Neuritis/diagnostic imaging , Case-Control Studies , Female , Gyrus Cinguli/diagnostic imaging , Humans , Insular Cortex/diagnostic imaging , Male , Prefrontal Cortex/diagnostic imaging , RestABSTRACT
Valsa pyri is a fatal canker pathogen that causes significant reduction of crop yield in pear orchards. V. pyri invades the trunk phloem, and is difficult to control by chemical treatment. In this work, it was found for the first time that Bacillus subtilis-produced dipicolinic acid (DPA) exhibits antifungal activity against different canker pathogens, including Alteraria alternata, Botryosphaeria dothidea, Rhizoctonia solani, and V. pyri. Growth inhibition of V. pyri was observed at less than 5 mM concentration (pH = 5.6). DPA showed the highest antifungal activity at acidic pH values and in the presence of bivalent metals, such as zinc(II), cobalt(II), and copper(II). Measurement of mRNA expression levels and scanning electron microscope (SEM) observations revealed that DPA causes V. pyri apoptosis via inhibition of chitin biosynthesis and subsequent cell lysis. Interestingly, DPA showed high stability in the pear bark and was able to cross the pear tree bark into the phloem, protecting the internal phases of the pear trunk. In preventive applications, DPA reduced the canker symptoms of V. pyri on Cuigan pear trees by 90%. Taken together, an efficient strategy for the management of V. pyri-caused canker disease was developed using a novel antifungal agent, DPA, with strong antifungal activity and particular diffusion properties.
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Non-coding RNAs are fundamental to the competing endogenous RNA (CeRNA) hypothesis in oncology. Previous work focused on static CeRNA networks. We construct and analyze CeRNA networks for four sequential stages of lung adenocarcinoma (LUAD) based on multi-omics data of long non-coding RNAs (lncRNAs), microRNAs and mRNAs. We find that the networks possess a two-level bipartite structure: common competing endogenous network (CCEN) composed of an invariant set of microRNAs over all the stages and stage-dependent, unique competing endogenous networks (UCENs). A systematic enrichment analysis of the pathways of the mRNAs in CCEN reveals that they are strongly associated with cancer development. We also find that the microRNA-linked mRNAs from UCENs have a higher enrichment efficiency. A key finding is six microRNAs from CCEN that impact patient survival at all stages, and four microRNAs that affect the survival from a specific stage. The ten microRNAs can then serve as potential biomarkers and prognostic tools for LUAD.
Subject(s)
Adenocarcinoma of Lung/genetics , Gene Expression Profiling/methods , Gene Regulatory Networks/genetics , Biomarkers, Tumor/genetics , Computational Biology/methods , Databases, Genetic , Disease Progression , Gene Expression Regulation, Neoplastic/genetics , Humans , Kaplan-Meier Estimate , Lung Neoplasms/genetics , MicroRNAs/genetics , Prognosis , RNA, Long Noncoding/genetics , RNA, Messenger/genetics , Transcriptome/geneticsABSTRACT
Primary human hepatocytes (PHHs) are the 'gold standard' for investigating hepatitis B virus (HBV) infection and antiviral drugs. However, poor availability, variation between batches and ethical issues regarding PHHs limit their applications. The discovery of human sodium taurocholate cotransporting polypeptide (hNTCP) as a functional HBV receptor has enabled the development of a surrogate model to supplement the use of PHHs. In the present study, the evolutionary distance of seven species was assessed based on singlecopy homologous genes. Based on the evolutionary distance and availability, PHHs and primary rabbit hepatocytes (PRHs) were isolated and infected with hNTCPrecombinant lentivirus, and susceptibility to HBV infection in the two cell types was tested and compared. In addition, HBV infection efficiency of hNTCPexpressing PPHs with pooled HBVpositive serum and purified particles was determined. The potential use of HBVinfected hNTCPexpressing PPHs for drug screening was assessed. The results demonstrated that pigs and rabbits are closer to humans in the divergence tree compared with mice and rats, indicating that pigs and rabbits were more likely to facilitate the HBV postentry lifecycle. Following hNTCP complementation and HBV infection, PPHs and Huh7D human hepatocellular carcinoma cells, but not PRHs, exhibited increased hepatitis B surface antigen and hepatitis B eantigen secretion, covalently closed circular DNA formation and infectious particle secretion. hNTCPexpressing PPHs were susceptible to infection with HBV particles purified from pooled HBVpositive sera, but were poisoned by raw HBVpositive sera. The use of HBVinfected hNTCPexpressing PPHs for viral entry inhibitor screening was revealed to be applicable and reproducible. In conclusion, hNTCPexpressing PPHs may be valuable tool for investigating HBV infection and antiviral drugs.
Subject(s)
Antiviral Agents/pharmacology , Hepatitis B virus/drug effects , Hepatitis B/drug therapy , Hepatocytes/virology , Organic Anion Transporters, Sodium-Dependent/genetics , Symporters/genetics , Animals , Cells, Cultured , Gene Expression , Hepatitis B/genetics , Hepatocytes/drug effects , Hepatocytes/metabolism , Humans , Mice , Microbial Sensitivity Tests/methods , Rabbits , Rats , Species Specificity , SwineABSTRACT
The main point of this paper is to provide an affirmative answer through exploiting reinforcement learning (RL) in artificial intelligence (AI) for eliminating herding without any external control in complex resource allocation systems. In particular, we demonstrate that when agents are empowered with RL (e.g., the popular Q-learning algorithm in AI) in that they get familiar with the unknown game environment gradually and attempt to deliver the optimal actions to maximize the payoff, herding can effectively be eliminated. Furthermore, computations reveal the striking phenomenon that, regardless of the initial state, the system evolves persistently and relentlessly toward the optimal state in which all resources are used efficiently. However, the evolution process is not without interruptions: there are large fluctuations that occur but only intermittently in time. The statistical distribution of the time between two successive fluctuating events is found to depend on the parity of the evolution, i.e., whether the number of time steps in between is odd or even. We develop a physical analysis and derive mean-field equations to gain an understanding of these phenomena. Since AI is becoming increasingly widespread, we expect our RL empowered minority game system to have broad applications.
ABSTRACT
We analyze five big data sets from a variety of online social networking (OSN) systems and find that the growth dynamics of meme popularity exhibit characteristically different behaviors. For example, there is linear growth associated with online recommendation and sharing platforms, a plateaued (or an "S"-shape) type of growth behavior in a web service devoted to helping users to collect bookmarks, and an exponential increase on the largest and most popular microblogging website in China. Does a universal mechanism with a common set of dynamical rules exist, which can explain these empirically observed, distinct growth behaviors? We provide an affirmative answer in this paper. In particular, inspired by biomimicry to take advantage of cell population growth dynamics in microbial ecology, we construct a base growth model for meme popularity in OSNs. We then take into account human factors by incorporating a general model of human interest dynamics into the base model. The final hybrid model contains a small number of free parameters that can be estimated purely from data. We demonstrate that our model is universal in the sense that, with a few parameters estimated from data, it can successfully predict the distinct meme growth dynamics. Our study represents a successful effort to exploit principles in biology to understand online social behaviors by incorporating the traditional microbial growth model into meme popularity. Our model can be used to gain insights into critical issues such as classification, robustness, optimization, and control of OSN systems.
Subject(s)
Internet , Models, Theoretical , Social Behavior , Social Media , Social Networking , HumansABSTRACT
Chimera states in spatiotemporal dynamical systems have been investigated in physical, chemical, and biological systems, and have been shown to be robust against random perturbations. How do chimera states achieve their robustness? We uncover a self-adaptation behavior by which, upon a spatially localized perturbation, the coherent component of the chimera state spontaneously drifts to an optimal location as far away from the perturbation as possible, exposing only its incoherent component to the perturbation to minimize the disturbance. A systematic numerical analysis of the evolution of the spatiotemporal pattern of the chimera state towards the optimal stable state reveals an exponential relaxation process independent of the spatial location of the perturbation, implying that its effects can be modeled as restoring and damping forces in a mechanical system and enabling the articulation of a phenomenological model. Not only is the model able to reproduce the numerical results, it can also predict the trajectory of drifting. Our finding is striking as it reveals that, inherently, chimera states possess a kind of "intelligence" in achieving robustness through self-adaptation. The behavior can be exploited for the controlled generation of chimera states with their coherent component placed in any desired spatial region of the system.
ABSTRACT
Radiotherapy plays a vital role in cancer treatment, for which accurate prognosis is important for guiding sequential treatment and improving the curative effect for patients. An issue of great significance in radiotherapy is to assess tumor radiosensitivity for devising the optimal treatment strategy. Previous studies focused on gene expression in cells closely associated with radiosensitivity, but factors such as the response of a cancer patient to irradiation and the patient survival time are largely ignored. For clinical cancer treatment, a specific pre-treatment indicator taking into account cancer cell type and patient radiosensitivity is of great value but it has been missing. Here, we propose an effective indicator for radiosensitivity: radiosensitive gene group centrality (RSGGC), which characterizes the importance of the group of genes that are radiosensitive in the whole gene correlation network. We demonstrate, using both clinical patient data and experimental cancer cell lines, which RSGGC can provide a quantitative estimate of the effect of radiotherapy, with factors such as the patient survival time and the survived fraction of cancer cell lines under radiotherapy fully taken into account. Our main finding is that, for patients with a higher RSGGC score before radiotherapy, cancer treatment tends to be more effective. The RSGGC can have significant applications in clinical prognosis, serving as a key measure to classifying radiosensitive and radioresistant patients.
Subject(s)
Gene Regulatory Networks/radiation effects , Models, Biological , Neoplasms/radiotherapy , Radiation Tolerance/genetics , Cell Death/radiation effects , Cell Line, Tumor , Female , Humans , Male , Neoplasms/diagnosis , Neoplasms/mortality , PrognosisABSTRACT
Alzheimer's disease (AD) is a worldwide progressive neurodegenerative disorder in the elderly. Previous research has indicated that Alzheimer's disease impairs white matter (WM) tracts. Anatomical and neuroimaging studies have indicated that WM tracts are associated with cognitive function. Whether the abnormal WM integrity in AD is associated with cognitive impairments and the clinical symptoms is still not clear. To this end, we investigated the relationship between the impairments in WM tracts and the decline of cognitive ability in AD. Diffusion tensor imaging (DTI) data were collected from 38 AD patients and 30 normal, cognitively healthy volunteers. The tract-based spatial statistics (TBSS) approach was used to compare the fractional anisotropy (FA) and mean diffusivity (MD) values between the two groups. WM tracts (cingulum, superior longitudinal fasciculus (SLF), uncinate fasciculus (UF), and inferior longitudinal fasciculus (ILF)) associated with cognition function were extracted for region of interest (ROI)-based analysis. Significantly decreased FA values and increased MD values of the cognition-related WM tracts were observed in the AD group compared with the normal cognition (NC) group. In addition, we further demonstrated that the decreased FA values and increased MD values of the cognition-related WM tracts were significantly correlated with MMSE scores. These results indicated that abnormal changes in WM integrity are observed following AD. Finally, we used support vector machine (SVM) with a repeated, stratified 10-fold cross-validated classifier to evaluate the ability of FA and MD values to discriminate disease. The accuracy of the SVM using cognition-related WM as classified features was higher than that using non-cognition-related tracts. Most importantly, our results showed the relationship between abnormal WM tracts and cognitive ability in AD. These findings further suggested that AD-related impairments in cognition-related WM tracts may influence the cognitive ability of AD patients.
Subject(s)
Alzheimer Disease/diagnostic imaging , Cognition/physiology , White Matter/metabolism , Aged , Alzheimer Disease/complications , Anisotropy , Brain/physiopathology , Cognitive Dysfunction , Diffusion Magnetic Resonance Imaging/methods , Diffusion Tensor Imaging/methods , Female , Humans , Male , Middle Aged , Neuropsychological Tests , White Matter/diagnostic imagingABSTRACT
Clique percolation has attracted much attention due to its significance in understanding topological overlap among communities and dynamical instability of structured systems. Rich critical behavior has been observed in clique percolation on Erdos-Rényi (ER) random graphs, but few works have discussed clique percolation on finite dimensional systems. In this paper, we have defined a series of characteristic events, i.e., the historically largest size jumps of the clusters, in the percolating process of adding bonds and developed a new finite-size scaling scheme based on the interval of the characteristic events. Through the finite-size scaling analysis, we have found, interestingly, that, in contrast to the clique percolation on an ER graph where the critical exponents are parameter dependent, the two-dimensional (2D) clique percolation simply shares the same critical exponents with traditional site or bond percolation, independent of the clique percolation parameters. This has been corroborated by bridging two special types of clique percolation to site percolation on 2D lattices. Mechanisms for the difference of the critical behaviors between clique percolation on ER graphs and on 2D lattices are also discussed.
ABSTRACT
Complex networked systems ranging from ecosystems and the climate to economic, social, and infrastructure systems can exhibit a tipping point (a "point of no return") at which a total collapse of the system occurs. To understand the dynamical mechanism of a tipping point and to predict its occurrence as a system parameter varies are of uttermost importance, tasks that are hindered by the often extremely high dimensionality of the underlying system. Using complex mutualistic networks in ecology as a prototype class of systems, we carry out a dimension reduction process to arrive at an effective 2D system with the two dynamical variables corresponding to the average pollinator and plant abundances. We show, using 59 empirical mutualistic networks extracted from real data, that our 2D model can accurately predict the occurrence of a tipping point, even in the presence of stochastic disturbances. We also find that, because of the lack of sufficient randomness in the structure of the real networks, weighted averaging is necessary in the dimension reduction process. Our reduced model can serve as a paradigm for understanding and predicting the tipping point dynamics in real world mutualistic networks for safeguarding pollinators, and the general principle can be extended to a broad range of disciplines to address the issues of resilience and sustainability.