Modularity Values Research Articles

Experimental extraction of nonlocal weak values for demonstrating the failure of a product rule.

We experimentally demonstrate an alternative method for measuring nonlocal weak values in linear optics, avoiding the use of second-order interaction. The method is based on the concept of modular values. The paths of two photons, initialized in hyperentangled states, are adopted as the meter with the polarization acting as the system. The modular values are read out through the reconstructed final states of the meter. The weak value of nonlocal observables is given through its connection to the modular value. Comparing the weak values of local and nonlocal observables, we demonstrate the failure of product rules for an entangled system. Our results significantly simplify the task of measuring nonlocal weak values and will play an important role in the application of weak measurement.

A multi-dimensional decision framework for modular value transfer activity

This paper explores the key dimensions and value-adding elements of a supply chain delivering cockpit modules to an automotive assembly operation in the United Kingdom. The findings demonstrate that supplying on a modular basis is influenced by the initial design decisions of the Original Equipment Manufacturer (OEM), the capabilities of the Module supplier and the ability to offer greater levels of customisation in a high-volume environment. The research articulates the findings through the concept of the ‘Dimensions of Modularity’ which seeks to demonstrate the key decision areas in a modular context and extend the concept of ‘Value Transfer Activity’ within a modular context. Our research provides insights into the specific dynamics of a module supply chain from OEM through to Modular supplier and a supplier of sub-modules. From this research, those involved in developing modular solutions can determine the multi-dimensional issues that need to be addressed to ensure that the supply chain is effectively connected and value transfer implications are accommodated and maximised. By adopting a single supply chain approach to exploring the impact of modular practices this paper provides valuable observations into an area of supply chain and operations management that is becoming increasingly relevant to both academic and practitioner communities.

Information Granulation-Based Community Detection for Social Networks

Online social networks (OSNs) have become so popular that it has changed the Internet to a more collaborative environment. Now, a third of the world's population participates in OSNs, forming communities, and producing and consuming media in different ways. The recent boom of artificial intelligence technologies provides new opportunities to help improve the processing and mining of social data. In this article, an algorithm that can detect communities in the OSNs using the concepts of granular computing in rough sets is proposed. In this information model, a social network as a rough set granular social network (RGSN) is modeled. A new community detection algorithm named granular-based community detection (GBCD) is implemented. This article also defines and uses two measures, namely, a granular community factor and an object community factor. The proposed algorithm is evaluated on four real-world data sets as well as computer-generated data sets. The model is compared with other state-of-the-art community detection algorithms for the values of modularity, normalized mutual information (NMI), Omega index, accuracy, specificity, sensitivity, and F1-measure. The cumulative performance of the GBCD algorithm is found to be 3.99, which outperforms other state-of-the-art community detection algorithms.

Exploring complex adaptive networks in the aftermath of the 2008 Wenchuan earthquake in China

In the decade since the Wenchuan earthquake of 2008, significant earthquakes have occurred in Yushu, Lushan, and Ludian in China. A comparison of the collaborative behaviors of emergency organizations in these four cases reveals some trends or regularities. This study uses complex adaptive network theory to examine three propositions: first, organizational collaborative behaviors are driven by tasks; second, government departments show less initiative in cross-sector cooperation than NGOs and enterprises; and third, the emergency management network has a core-periphery structure. All of these propositions are supported by our social network analysis (SNA), which considers modularity, centrality, cliques, and singular value decomposition (SVD) in a two-mode network. The results support the three propositions given above and suggest that emergency management networks are time-variant systems. In particular, we argue that estrangement between different sectors needs to be overcome to improve these networks.

Repositioning of strongly integrated drugs against achromatopsia (CNGB3)

Achromatopsia (ACHM) is a genetically heterogeneous visual disorder, also known as rod monochromatism, in which human get affected due to cone cells. Mutation in five genes viz. CNGA3, CNGB3, GNAT2, PDE6C, and PDE6H have been reported in ACHM. These genes encode essential constitutes of the cone-specific photo transduction cascade. Present study was focused on CNGB3 gene that accounts 40%-50% mutations of all ACHM cases. A new approach for analyzing drug-drug interactions based on modularity was adopted. This approach depends on the behavioral relationship of drugs against CNGB3 for ACHM, particularly the ADME and toxicity between drugs. Data of 2475 compounds were retrieved, out of which 185 were selected on the basis of Lipinski rule of five. In total, eight clusters were made for which the strongly interacted DDI networks were build based on their modularity values. Strong DDI and minimum toxic values indicates that 5 drugs are effective, but on the basis of docking only 2 drugs indicated no bumps, which shows that they are most appropriate for treating ACHM. Our findings revealed that drug-drug interactions disclose the intervention of drug nature and can also successfully diagnose new indications and more convincing drugs for other diseases as well.

Modularity of Some Distance Graphs

New bounds on the modularity of distance graphs were obtained and the exact value of modularity was calculated for G(n, 2, 1) graphs.

Векторний спосіб визначення кінематичних параметрів ідеального інерційного модуля у стоповому режимі

The presence of a generalized scheme of the pulse mechanism created by A. I. Leonov does not have a universal mathematical description of parameters by continuous analytical functions, therefore each design is described, for the most part, by complex systems of differential equations, but the lack of clarity in presenting the results makes it difficult to intuitively understand dynamic processes. The objective of the research is the clarity in the study of the kinematic parameters of imbalance of the ideal inertia module during stop mode operation for predicting the dynamic indexes as continuous in time functions. The research method is based on a vector simulation of spherical motion parameters. To do this, a fixed Cartesian coordinate system is introduced so that the plane of the base circle of the initial cone of the jet conical wheel is aligned with the horizontal plane, and the axis of the satellite drive (geometric axis of the carrier) is aligned with the applicate axis. The central axis of the mechanism crossing the diameter of the jet wheel is aligned with the abscissa axis on the complementary branch of which at the initial moment there is the mass center of imbalance. In the stop mode the absolute motion of a point is determined by the result of its rotation around the satellite axis at the speed lying in the plane of the base of the initial cone of the satellite and around the drive axis at a speed which parallel to the plane of the initial cone of the jet wheel. Projections of the absolute velocity and the absolute acceleration of imbalance point on the coordinate axis, in turn, determine the projections of the components of the velocity vector and acceleration vector on the planes of the fixed Cartesian coordinate system, respectively. Determining the arms of these components in the planes of projections relative about the center of the axis makes it possible to further predict the dynamic parameters at certain points of the trajectory (at particular time or another). Analytical calculations of modular values of linear and angular velocities and accelerations, as well as drawing of the appropriate diagrams were performed using the operators of MathCAD software.

Determining the critical thresholds for co-word network based on the theory of percolation transition

PurposeOne of the chief purposes of bibliometric analysis is to reveal the intellectual structure of a knowledge domain. Yet due to the magnitude and the heterogeneous nature of bibliometric networks, some sorts of filtering procedures are often required to make the resulting network interpretable. A co-word analysis of more than 135,000 scholarly publications on Buddhism was conducted to compare the intellectual structure of Buddhist studies in three language communities, Chinese, English and Japanese, over two periods (1957–1986 and 1987–2016). Six co-word similarity networks were created so social network analysis-based community-detection algorithm can be identified to compare major research themes in different languages and eras. The paper aims to discuss this issue.Design/methodology/approachA series of filtering procedures was performed to exclude less discriminatory keywords and spurious relationships of a large, cross-language co-word network in Buddhist studies. Chief among the filtering heuristics was a percolation-transition based method to determine the similarity threshold that involves observing the relative decrease of nodes in the giant component with the increasing similarity threshold.FindingsIt was found that the topical patterns in the Chinese and Japanese scholarship of Buddhism are alike and observably distinct from that of the English scholarship. Furthermore, a far more drastic changes of research themes were observed in the English literature relative to the Chinese and Japanese literature.Originality/valueThe filtering procedures were shown to greatly enhance the modularity values and limited the number of modularity classes; thus, domain expert interpretation is feasible.

Evolutionary Algorithms for Community Detection in Continental-Scale High-Voltage Transmission Grids

Symmetry is a key concept in the study of power systems, not only because the admittance and Jacobian matrices used in power flow analysis are symmetrical, but because some previous studies have shown that in some real-world power grids there are complex symmetries. In order to investigate the topological characteristics of power grids, this paper proposes the use of evolutionary algorithms for community detection using modularity density measures on networks representing supergrids in order to discover densely connected structures. Two evolutionary approaches (generational genetic algorithm, GGA+, and modularity and improved genetic algorithm, MIGA) were applied. The results obtained in two large networks representing supergrids (European grid and North American grid) provide insights on both the structure of the supergrid and the topological differences between different regions. Numerical and graphical results show how these evolutionary approaches clearly outperform to the well-known Louvain modularity method. In particular, the average value of modularity obtained by GGA+ in the European grid was 0.815, while an average of 0.827 was reached in the North American grid. These results outperform those obtained by MIGA and Louvain methods (0.801 and 0.766 in the European grid and 0.813 and 0.798 in the North American grid, respectively).

Functional Connectivity Patterns and the Role of 5-HTTLPR Polymorphism on Network Architecture in Female Patients With Anorexia Nervosa.

IntroductionRecent neuroimaging studies suggest that anorexia nervosa (AN) symptoms emerge from failures in the relationships between spatially distributed networks that support different cognitive, emotional, and somatosensory functions. The 5-HTTLPR genotype has been shown to modulate all these abilities in AN, as well as the connectivity patterns between brain regions that support their functioning. This study aims at exploring the presence of any difference in functional connectome properties between AN patients and healthy controls (HC) by means of graph theory tools. The effect of 5-HTTLPR genotype on regional and global network characteristics in AN and HC was also explored.MethodsA sample of 74 subjects (38 HC, 36 AN) underwent a resting state functional magnetic resonance imaging and was genotyped for 5-HTTLPR polymorphism. Comparisons of network properties were made between the AN and HC groups and, within each group, between 5-HTTLPR carriers of low-functioning alleles and carriers of the long–long genotype.ResultsPatients with AN displayed lower network clustering than HC (p = 0.04 at Mann–Whitney U test). Based on both degree and betweenness, a different distribution of network hubs emerged in the two groups. In particular, the anterior part of the anterior cingulate cortex was a hub only in the patient group. A correlation emerged between differences in brain volumes between patients and HC and differences in degree values of basal ganglia, nodes in the insula, and those in the parietal cortex. Carriers of the short allele of the 5-HTTLPR polymorphism were characterized by lower small-world properties (p = 0.027) and modularity (p = 0.031) in the patient group, and a trend toward higher modularity (p = 0.033) and small-world values (p = 0.123) in the HC group.DiscussionPatients with AN showed differences in hubs distribution, providing evidence of the presence of a different functional architectural backbone in this group. Since some correlation emerged between different degree values of nodes and differences in volumes, further longitudinal studies are warranted to better understand the role of malnutrition on brain network architecture. The opposite effects of 5-HTTLPR polymorphism on global network characteristics in the two groups suggest an interaction of the short allele and malnutrition in modulating brain network properties.

Direct Measurement of a Nonlocal Entangled Quantum State.

Entanglement and the wave function description are two of the core concepts that make quantum mechanics such a unique theory. A method to directly measure the wave function, using weak values, was demonstrated by Lundeen etal. [Nature 474, 188 (2011)]. However, it is not applicable to a scenario of two disjoint systems, where nonlocal entanglement can be a crucial element, since that requires obtaining weak values of nonlocal observables. Here, for the first time, we propose a method to directly measure a nonlocal wave function of a bipartite system, using modular values. The method is experimentally implemented for a photon pair in a hyperentangled state, i.e., entangled both in polarization and momentum degrees of freedom.

A spectral method to detect community structure based on the communicability modularity

Community detection in complex networks is a topic of high interest in many fields. In this paper, we propose a new algorithm based on the communicability of vertices, rather than the most weakly connected vertex pairs or a number of edges between communities. Furthermore, the accuracy and efficiency of this algorithm are tested by some representative real-world networks and computer-generated networks(GN networks). The experimental results indicate that the proposed algorithm can accurately and effectively detect the community structure in these networks with higher values of modularity.

Genetic algorithm-based community detection in large-scale social networks

Communities in social networks are the essential feature which may be considered as a potential parameter in modeling the behavior of the social entities. Detection of communities has attracted a lot of attention in research in social network analysis. It is one of the major challenging problems as it involves high complexity in processing complex web structure. In fact, this problem can be considered as a NP-complete problem in large-scale networks, as this problem is somewhat reducible to the clique problem in graph theory. A number of meta-heuristic algorithms have been proposed to explore the hidden communities. Most of these algorithms have considered the modularity of the network as their objective function. But, the aspect of optimizing the value of modularity is associated with a problem known as resolution limit, where the size of the detected communities depends on the number of edges existing in the network. In this paper, a genetic algorithm-based community detection has been proposed where an efficient single objective function based on similarity matrix has been devised. The similarity index between each pair of nodes has been calculated in a distributed manner over multiple computing nodes. Similarity index proposed in this paper is based on the topological structure of the network. The effectiveness of the proposed approach is examined by comparing the performance with other state-of-the-art community detection algorithms applied over some real-world network datasets.

The Explicit Formulae and Evaluations of Ramanujan's Remarkable Product of Theta-functions

On pages 338 and 339 in his first notebook, Ramanujan defined remarkable product of theta-functions $a_{m,n}$ and also recorded eighteen explicit values depending on two parameters $m$ and $n$. All these values have been established by Berndt et al. In this paper, we establish a new general formulae for the explicit evaluations of $a_{3m,3}$ and $a_{m,9}$ by using $P$-$Q$ mixed modular equation and values for certain class invariant of Ramanujan. Using these formulae, we calculate some new explicit values of $a_{3m,3}$ for $m = 2,7,13,17,25,37$ and $a_{m,9}$ for $m = 17,37$.

The Influence of Cerebrospinal Fluid Abnormalities and APOE 4 on PHF-Tau Protein: Evidence From Voxel Analysis and Graph Theory.

Mild cognitive impairment (MCI) is a transitional state between the cognitive changes in normal aging and Alzheimer’s disease (AD), which induces abnormalities in specific brain regions. Previous studies showed that paired helical filaments Tau (PHF-Tau) protein is a potential pathogenic protein which may cause abnormal brain function and structure in MCI and AD patients. However, the understanding of the PHF-Tau protein network in MCI patients is limited. In this study, 225 subjects with PHF-Tau Positron Emission Tomography (PET) images were divided into four groups based on whether they carried Apolipoprotein E ε4 (APOE 4) or abnormal cerebrospinal fluid Total-Tau (CSF T-Tau). They are two important pathogenic factors that might cause cognitive function impairment. The four groups were: individuals harboring CSF T-Tau pathology but no APOE 4 (APOE 4−T+); APOE 4 carriers with normal CSF T-Tau (APOE 4+T−); APOE 4 carriers with abnormal CSF T-Tau (APOE 4+T+); and APOE 4 noncarriers with abnormal CSF T-Tau (APOE 4−T−). We explored the topological organization of PHF-Tau networks in these four groups and calculated five kinds of network properties: clustering coefficient, shortest path length, Q value of modularity, nodal centrality and degree. Our findings showed that compared with APOE 4−T− group, the other three groups showed different alterations in the clustering coefficient, shortest path length, Q value of modularity, nodal centrality and degree. Simultaneously, voxel-level analysis was conducted and the results showed that compared with APOE 4−T− group, the other three groups were found increased PHF-Tau distribution in some brain regions. For APOE 4+T+ group, positive correlation was found between the value of PHF-Tau distribution in altered regions and Functional Assessment Questionnaire (FAQ) score. Our results indicated that the effects of APOE 4 and abnormal CSF T-Tau may induce abnormalities of PHF-Tau protein and APOE 4 has a greater impact on PHF-Tau than abnormal CSF T-Tau. Our results may be particularly helpful in uncovering the pathophysiology underlying the cognitive dysfunction in MCI patients.

Community detection and influential node identification in complex networks using mathematical programming

Integer programming models for community detection in relational networks have diverse applications in different fields. From making our lives easier by improving search engine optimization to saving our lives by aiding in threat detection and disaster management, researches in this niche have added value to human experience and knowledge. Besides the community structure, the influential nodes or members in a complex network are highly effective at diffusing information quickly to others in the community. Prior research dealing with the use of optimization models for clustering networks has independently focused on detecting communities. In this research, we propose a new integer linear programming model to detect community structure in real-life networks and also identify the most influential node within each community. We validate the proposed model by testing it on a well-established community network. Further, the performance of the proposed model is evaluated by comparing it with the existing best performing optimization model as well as three heuristic approaches for community detection. The experimental results indicate that in most cases the proposed integer programming model performs better than the existing optimization model with respect to modularity, Silhouette coefficient and computational time. Besides, our model yields superior Silhouette and competitive modularity values compared to the heuristic approaches in many cases.

A similarity based generalized modularity measure towards effective community discovery in complex networks

Modularity is a widely used goodness metric that effectively measures the strength of the community structures present in a network. However its performance may not be desirable for identifying densely connected communities or clusters of a network. It also often fails to identify communities or clusters that contain very few nodes. Furthermore, modularity is defined based only on the exact node-to-node connectivity of a network while disregarding their neighborhood connectivity. In this paper, we associate the neighborhood connectivity to the modularity function and propose a generalized modularity function based on the node similarity measure which quantifies the quality of a given network partition. Making use of this similarity based modularity function, an effective agglomerative approach for identifying communities is introduced. This agglomerative approach iteratively discovers the final community structure of the network by finding and merging together, at each step, the community pairs which maximize the proposed modularity value. A significant characteristic of the proposed method is that it does not need any prior knowledge about the actual communities of a network. The performance of the proposed method and state-of-the-art algorithms are compared using the value of modularity, normalized mutual information and adjusted variation of information measures on several real world and artificial networks. The empirical results show the effectiveness of the proposed method compared to the state-of-the-art techniques.

Intra- and Inter-Modular Connectivity Alterations in the Brain Structural Network of Spinocerebellar Ataxia Type 3.

In addition to cerebellar degeneration symptoms, patients with spinocerebellar ataxia type 3 (SCA3) exhibit extensive involvements with damage in the prefrontal cortex. A network model has been proposed for investigating the structural organization and functional mechanisms of clinical brain disorders. For neural degenerative diseases, a cortical feature-based structural connectivity network can locate cortical atrophied regions and indicate how their connectivity and functions may change. The brain network of SCA3 has been minimally explored. In this study, we investigated this network by enrolling 48 patients with SCA3 and 48 healthy subjects. A novel three-dimensional fractal dimension-based network was proposed to detect differences in network parameters between the groups. Copula correlations and modular analysis were then employed to categorize and construct the structural networks. Patients with SCA3 exhibited significant lateralized atrophy in the left supratentorial regions and significantly lower modularity values. Their cerebellar regions were dissociated from higher-level brain networks, and demonstrated decreased intra-modular connectivity in all lobes, but increased inter-modular connectivity in the frontal and parietal lobes. Our results suggest that the brain networks of patients with SCA3 may be reorganized in these regions, with the introduction of certain compensatory mechanisms in the cerebral cortex to minimize their cognitive impairment syndrome.

Evaluating the structure of commensalistic epiphyte–phorophyte networks: a comparative perspective of biotic interactions

Epiphytic vascular plants comprise an essential part of the tropical flora and are a key component for ecosystem functioning. Some recent studies have used a network approach to investigate the interaction of epiphytes with host phorophytes at the community level. However, knowledge on commensalistic epiphyte–phorophyte network structure still lags behind with regard to other biotic interaction networks. Our goal was to provide a more complete overall perspective on commensalistic epiphyte–phorophyte interaction and its placement with respect to other better studied mutualistic interactions. We hypothesized that the intensity of the fitness effect of the different types of biotic interactions would determine the degree of specialization of the interacting organisms. Thus, commensalistic epiphyte–phorophyte interactions would have lower specialization than mutualistic interactions. We compiled and analysed the structural properties (nestedness, network specialization and modularity) of 12 commensalistic epiphyte–phorophyte networks and compared them with the same metrics to 11 ant–myrmecophyte, 86 pollination and 13 seed dispersal mutualistic networks. Epiphyte–phorophyte networks were nested and modular with regard to the corresponding null models and had greater nestedness than mutualistic networks, whereas specialization and modularity were significantly lower. Commensalistic epiphyte–phorophyte networks of interactions are both nested and modular, and hence, are structured in a similar way to most other types of networks that involve co-evolutionary interactions. Nevertheless, the nature and intensity of the ecological processes involved in the generation of these patterns is likely to differ. The lower values of modularity in commensalistic epiphyte–phorophyte networks are probably due to the low levels of specialization and the lack of co-evolutionary processes between the interacting partners.

Altered topology of large-scale structural brain networks in chronic stroke.

Beyond disruption of neuronal pathways, focal stroke lesions induce structural disintegration of distant, yet connected brain regions via retrograde neuronal degeneration. Stroke lesions alter functional brain connectivity and topology in large-scale brain networks. These changes are associated with the degree of clinical impairment and recovery. In contrast, changes of large scale, structural brain networks after stroke are less well reported. We therefore aimed to analyse the impact of focal lesions on the structural connectome after stroke based on data from diffusion-weighted imaging and probabilistic fibre tracking. In total, 17 patients (mean age 64.5 ± 8.4 years) with upper limb motor deficits in the chronic stage after stroke and 21 healthy participants (mean age 64.9 ± 10.3 years) were included. Clinical deficits were evaluated by grip strength and the upper extremity Fugl-Meyer assessment. We calculated global and local graph theoretical measures to characterize topological changes in the structural connectome. Results from our analysis demonstrated significant alterations of network topology in both ipsi- and contralesional, primarily unaffected, hemispheres after stroke. Global efficiency was significantly lower in stroke connectomes as an indicator of overall reduced capacity for information transfer between distant brain areas. Furthermore, topology of structural connectomes was shifted toward a higher degree of segregation as indicated by significantly higher values of global clustering and modularity. On a level of local network parameters, these effects were most pronounced in a subnetwork of cortico-subcortical brain regions involved in motor control. Structural changes were not significantly associated with clinical measures. We propose that the observed network changes in our patients are best explained by the disruption of inter- and intrahemispheric, long white matter fibre tracts connecting distant brain regions. Our results add novel insights on topological changes of structural large-scale brain networks in the ipsi- and contralesional hemisphere after stroke.