Central Difference Research Articles

NetSim – The framework for complex network generator

Networks are everywhere and their many types, including social networks, the Internet, food webs etc., have been studied for the last few decades. However, in real-world networks, it’s hard to find examples that can be easily comparable, i.e. have the same density or even number of nodes and edges. We propose a flexible and extensible NetSim framework to understand how properties in different types of networks change with varying number of edges and vertices. Our approach enables to simulate three classical network models (random, small-world and scale-free) with easily adjustable model parameters and network size. To be able to compare different networks, for a single experimental setup we kept the number of edges and vertices fixed across the models. To understand how they change depending on the number of nodes and edges we ran over 30,000 simulations and analysed different network characteristics that cannot be derived analytically. Two of the main findings from the analysis are that the average shortest path does not change with the density of the scale-free network but changes for small-world and random networks; the apparent difference in mean betweenness centrality of the scale-free network compared with random and small-world networks.

Efficient time discretization scheme for nonlinear space fractional reaction–diffusion equations

ABSTRACTWe present a novel Exponential Time Differencing (ETD) scheme for nonlinear Riesz space fractional reaction–diffusion equations. This scheme is based on using a real distinct poles (RDP) discretization for the underlying matrix exponentials. Due to these RDP, the algorithm could be easily implemented in parallel to take advantage of multiple processors for increased computational efficiency. The method is established to be second-order convergent; and proven to be robust for problems involving non-smooth/mismatched initial and boundary conditions and steep solution gradients. We examine the stability of the scheme through its amplification factor and plot the boundaries of the stability regions comparative to other second-order ETD schemes. This numerical scheme combined with fractional central differencing is used for simulating some nonlinear space fractional problems. We demonstrate the superiority of our method over competing second-order ETD schemes, BDF2 scheme, and IMEX schemes. Our experiments show that the proposed scheme is computationally more efficient (in terms of cpu time). Furthermore, we investigate the trade-off between using fractional central differencing and matrix transfer technique in discretization of Riesz fractional derivatives.

TOWARD A FUNCTIONAL NEUROMARKER FOR PRECLINICAL AD: EIGENVECTOR CENTRALITY REVEALS PRECLINICAL DIFFERENCES OF FUNCTIONAL INFORMATION FLOW IN THE HIPPOCAMPUS, PRECUNEUS, CEREBELLUM AND INFERIOR PARIETAL LOBULE

AD is characterized by complex neuronal changes including compensatory mechanisms in response to atrophy, affected by multiple factors such as age, gender and education. A comprehensive account of the functional changes associated with each progressive stage along the continuum of AD, including the preclinical stage, is required to enhance clinical assessment protocols. Eigenvector centrality is an advanced measure of network information flow that has recently become computable for fMRI data. We investigated significant differences in eigenvector centrality across the entire continuum of AD, from health to dementia, as reflected by the cerebrospinal fluid ratio of phosphorylated tau protein over beta-amyloid peptide 42. Additionally, significant differences of functional connectivity of the identified network hubs were examined comparatively between each pair of consecutive stages across the disease continuum, while controlling for the effects of age, gender and education throughout all analyses (n=96). SyGN normalization was employed, all analyses were data-driven and performed with corrections for multiple comparisons across the whole brain at voxel resolution. During resting-state fMRI, inferior parietal areas show decreasing centrality, whereas the thalamus and cingulate cortex show the opposite effect, across the disease continuum. Complementary analyses suggest that most centrality changes are related to episodic memory decline. Comparisons between consecutive stages of the disease reveal an informative sequence of network-degradation and network-compensation patterns as differences of functional connectivity between the identified network hubs and several prominent brain areas. Importantly, during the preclinical stage, significant alterations in functional connectivity are observed in areas that are typically affected by atrophy many years later (e.g. hippocampus, precuneus, cerebellum, inferior parietal lobule). The identified changes in network centrality and functional connectivity provide a comprehensive account of the incremental changes in neural information flow associated with each progressive stage of AD. These findings suggest specific patterns of functional connectomics for the detection of the preclinical stage and for monitoring clinical progression and therapeutic efficacy in AD. The methodological approach is being further evaluated, using an independent sample, with regards to its potential for diagnostic utility and the development of a neuromarker for the preclinical stage of AD. fMRI results. The first column (a) shows clusters with eigenvector centrality correlating with the p- tau/Aβ42 biomarker index. Significant positive correlations with p-tau/Aβ42 are indicated in medial cingulate (1a), posterior cingulate (2a), thalamus (3a), anterior cingulate (4a); significant negative correlation with p- tau/Aβ42 is indicated in the left inferior parietal lobule (5a). These five clusters were used as seed regions for functional connectivity analyses. The results of the comparison of functional connectivity maps between subject groups are shown separately for the five seed clusters in each row. Columns (b), (c) and (d) show significant differences between subject groups in functional connectivity with the seed cluster of the respective row (red and blue colors depict significant increases and decreases respectively; e.g. cell 1.b shows that during the preclinical stage of AD, the functional connectivity of the medial cingulate decreases with the left hippocampus and increases with the precuneus). Images are shown in neurological convention; variance due to age, gender and education has been accounted by covariates in all analyses; all results are corrected for voxel-wise multiple comparisons (p < 0.05). Conjunction between EC correlations with p-tau/Aβ42 and EC correlations with cognitive measures. The main regression analysis (see Methods section) was repeated twice, replacing p-tau/Aβ42 with score on memory alteration test (M@T; Rami et al., 2007) and score on free recall of selective reminding test (Grober & Buschke, 1987), controlling for age, gender and level of education. Results were corrected for whole-brain multiple comparisons using identical methods to the main analysis. Top row left: significant positive correlations between EC and p-tau/Aβ42; top row middle: significant negative correlations between EC and M@T scores; top row right: green voxels display regions where EC correlated significantly with both p- tau/Aβ42 and M@T scores. Bottom row left: significant negative correlation between EC and p-tau/Aβ42; bottom row middle: significant positive (red) and significant negative (blue) correlations between EC and scores of free recall; bottom row right: green voxels display regions where EC correlated significantly with both p-tau/Aβ42 and free recall scores.

Bidirectional influence between African American mothers' and children's racial centrality from elementary through high school.

For many African Americans, racial identity is an important aspect of their individual identity. We explored developmental change and stability of individual differences in the racial centrality of African American youths and their mothers as well as the relation between maternal and child racial centrality across time. African American youths (N = 380) and mothers completed surveys when youths were in grades 5, 7, 10, and 12. Mean levels of youths' racial centrality did not increase or decrease across the 7 years of the study. The stability of individual differences in youths' racial centrality increased across time, reaching adult levels by high school. Cross-lagged panel analyses showed relations between mothers' and children's racial centrality in middle adolescence but not in early and late adolescence. Results document that the importance of race to the personal identities of African American youths does not show normative developmental change across adolescence, and only minimal change is linked to maternal influence. (PsycINFO Database Record

Mitigation of shock-induced flow separation using magnetohydrodynamic flow control

A numerical investigation is carried out to demonstrate a proof of concept, magnetohydrodynamics-based active flow control, for mitigation of laminar flow separation over a flat plate due to shock wave–boundary layer interaction. The CERANS-MHD code has been used to solve the governing resistive magnetohydrodynamic equations discretized in finite-volume framework. The AUSM-PW+ flux function is used in modelling the advection terms and central differencing is used in modelling the resistive terms. Powell’s source term method is used for divergence cleaning of the magnetic field. The Hartmann number is varied from 0 to 12,000 to effectuate mitigation of flow separation, with the magnetic field applied at the wall and oriented transverse to the flat plate flow direction. Due to the Hartmann effect, flow separation is observed to be suppressed with increase in Hartmann number beyond 6000. However, the overall magnitude of skin friction distribution increases drastically, resulting in large increase in skin friction drag as compared with the non-magnetic case, and is a cause of concern.

Adaptive simulations of viscous detonations initiated by a hot jet using a high-order hybrid WENO–CD scheme

In the present work a sixth-order hybrid WENO–Centered Difference (CD) scheme with an adaptive mesh refinement method is employed to investigate gaseous detonation by injecting a hot jet into a hydrogen–oxygen combustible mixture flowing at supersonic speed. Two-dimensional reactive Navier–Stokes (NS) equations with one-step two-species chemistry model are solved numerically. The comparison between viscous and inviscid detonation structures shows that due to the absence of both the physical viscosity in Euler equations and minimization of numerical dissipation in the hybrid WENO–CD scheme, very small-scale vortices can be observed behind the detonation front. The diffusion effect in the NS equations suppresses the small-scale vortices, but it has negligible influence on the large-scale vortices generated by Richtmyer–Meshkov (RM) instability and those along the highly unstable shear layers induced by Kelvin–Helmholtz (KH) instability. When studying the same setup in an expanding channel and beyond the point of detonation initiation, it is found that because of the diffusion effect of detached shear layers, any unburned jet flow is consumed quickly and then additional energy is released periodically. Because of the formation of multiple secondary triple points and subsequent shear layers after the shutdown of the hot jet, a highly turbulent flow is produced behind the detonation front. Rather than the commonly known RM instability, the large-scale vortices involved in the highly unstable shear layers dominate the formation of the turbulent flow and the rapid turbulent mixing between the unburned jet flow and burned product. It is found that the size of unburned jets and vortices due to KH instability is growing for larger expansion angles. The further generated turbulent flow resulting from larger sized vortices, significantly enhances the mixing rate behind the Mach stem, leading to rapid consumption of the unburned reactants. Therefore, detonations propagate faster in channels with larger expansion angle and higher expansion ratio.

Network structure and centralization tendencies in professional football teams from Spanish La Liga and English Premier Leagues

The aim of this study was to analyse the variance of different competitive leagues, score status, and tactical position in the centrality levels of degree prestige, degree centrality and page rank in football players. A total of 20 matches from the Spanish La Liga League (10 matches) and English Premier League (10 matches) were analysed and codified in this study. In this study only the top four teams and their opponents per each competitive league were analysed. A total of 14,738 passes between teammates were recorded and processed. The multivariate MANOVA revealed statistical differences in centrality among tactical positions (λ = 0.958; F (15,1212) = 37.898; p-value = 0.001; = 0.319; Moderate Effect Size). Midfielders had the greatest centrality values, followed by the external and central defenders. The lowest values of centrality were found in goalkeepers and forwards. No statistical differences were found in centrality between different competitive leagues (λ = 0.001; F (3,402) = 0.050; p-value = 0.985; = 0.001; Very Small Effect Size) and score status (λ = 0.003; F (6,806) = 0.175; p-value = 0.983; = 0.001; Very Small Effect Size).

Are women less career centric than men? Structure, culture, and identity investments

Some work/family scholars assume that gender differences in career centrality (i.e. the importance of career to one's identity) are a result of differential job characteristics and family demands; others trace these differences to pre-existing cultural orientations. Using the 2010 Generations of Talent data from 9210 employees working in 11 countries for 7 multinational companies, this study verifies the existence of gender differences in career centrality and explores structural and cultural explanations. Gender disparities in career centrality are modest, indicating that women's and men's identification with careers is more similar than is commonly asserted; the most pronounced (but still relatively small) disparities are observed in Japan and China. A large portion of the gender gap is explained by job characteristics, supporting structural explanations. Family demands contribute to explaining the gap as well, but the findings are unexpected: having minor children is associated with higher career centrality for both women and men. In support of cultural explanations, however, traditional gender beliefs are associated with lower career centrality, especially for women, while two job characteristics (job variety and peer relations) have distinct links to career centrality for women and men. Findings challenge the common assumption that family identities compete against work identities.

Numerical investigation of a pump-jet with ring rotor using an unstructured mesh technique

In the present study, the hydrodynamic characteristics of a pump-jet were numerically investigated using an incompressible RANS flow solver based on pseudo-compressibility. The focus of the study is the assessment of the flow characteristics and performance, particularly of a ring rotor with the rotor blades interconnected with a circumferential ring at the tip. For this purpose, a vertex-centered finite- volume method on unstructured meshes was used in conjunction with second-order Roe’s FDS to discretize the inviscid fluxes, while the viscous fluxes were computed based on central differencing. For the unsteady time integration, a dual-time stepping method and the Gauss-Seidel iteration were employed. An unstructured overset mesh technique was adopted to treat the relative motion between the rotor and the main body of the pump-jet. For the closure of turbulence, the Spalart-Allmaras one equation model was employed. To validate the flow solver, the calculations were initially made for the High Reynolds number pump (HIREP) configuration at several advancing ratios. Reasonable agreements were obtained between the present results and the experiment in terms of the pressure coefficient on the blade surface, velocity distribution, and integrated blade loadings. To investigate the effect of the ring on the flow characteristics and propulsion performance of the pump-jet, additional calculations were made for the HIREP configuration installed with the circumferential ring at the rotor blade tip, and the results were compared with those of the original HIREP configuration. The addition of the ring at the blade tip helped reduce the tip vortex strength, which might be beneficial in suppressing the formation of water vapor. Furthermore, the cavitation performance on the suction surface of the rotor blades was degraded by the reduced axial velocity because of the passage area reduction after the ring was attached. With the addition of the ring, the blade loadings of the pump-jet, such as the thrust and torque, were reduced even though the efficiency, defined as the ratio of thrust and torque, was maintained.

Sex-based differences in the adaptive value of social behavior contrasted against morphology and environment.

The adaptive nature of sociality has long been a central question in ecology and evolution. However, the relative importance of social behavior for fitness, compared to morphology and environment, remains largely unknown. We assessed the importance of sociality for fitness (lamb production and survival) in a population of mark6d bighorn sheep (Ovis canadensis) over 16 years (n = 1022 sheep-years). We constructed social networks from observations (n = 38,350) of group membership (n = 3150 groups). We then tested whether consistent individual differences in social behavior (centrality) exist and evaluated their relative importance compared to factors known to affect fitness: mass, age, parental effects, and population density. Sheep exhibited consistent individual differences in social centrality. Controlling for maternal carryover effects and age, the positive effect of centrality in a social network on adult female lamb production and survival was equal or greater than the effect of body mass or population density. Social centrality had less effect on male survival and no effect on adult male lamb production or lamb survival. Through its effect on lamb production and survival, sociality in fission-fusion animal societies may ultimately influence population dynamics equally or more than morphological or environmental effects.

Performance of social network sensors during Hurricane Sandy.

Information flow during catastrophic events is a critical aspect of disaster management. Modern communication platforms, in particular online social networks, provide an opportunity to study such flow and derive early-warning sensors, thus improving emergency preparedness and response. Performance of the social networks sensor method, based on topological and behavioral properties derived from the “friendship paradox”, is studied here for over 50 million Twitter messages posted before, during, and after Hurricane Sandy. We find that differences in users’ network centrality effectively translate into moderate awareness advantage (up to 26 hours); and that geo-location of users within or outside of the hurricane-affected area plays a significant role in determining the scale of such an advantage. Emotional response appears to be universal regardless of the position in the network topology, and displays characteristic, easily detectable patterns, opening a possibility to implement a simple “sentiment sensing” technique that can detect and locate disasters.

Work Locus of Control and Workplace Bullying: The Moderating Effect of Work Centrality

This study examined the moderating effect of work centrality on work locus of control and workplace bullying. A total of two hundred and forty-one (241) participants were selected and used as participants in the study. A 10-item Work Centrality Questionnaire (WCQ) designed by Paullay et al., (1994), 16-item Work Locus of Control Scale designed by Paul E. Spector (1988) and the 22-item Workplace Bullying Questionnaire which was designed by Einarsen & Hoel (2001) were used to measure the variables. Result showed that there is a significant effect of work locus of control on workplace bullying and that employee with external locus of control orientation perceived higher workplace bullying than employees with internal locus of control. There is a significant effect of work centrality on workplace bullying, with employees that are high in work centrality reporting lesser experience of workplace bullying. A significant sex difference in work centrality was also observed but there are no significant sex difference in work locus of control and bullying. Finally, we found that work centrality moderate the effect of work locus of control on work place bullying. Implications of our findings are discussed.

Social networks in primates: smart and tolerant species have more efficient networks.

Network optimality has been described in genes, proteins and human communicative networks. In the latter, optimality leads to the efficient transmission of information with a minimum number of connections. Whilst studies show that differences in centrality exist in animal networks with central individuals having higher fitness, network efficiency has never been studied in animal groups. Here we studied 78 groups of primates (24 species). We found that group size and neocortex ratio were correlated with network efficiency. Centralisation (whether several individuals are central in the group) and modularity (how a group is clustered) had opposing effects on network efficiency, showing that tolerant species have more efficient networks. Such network properties affecting individual fitness could be shaped by natural selection. Our results are in accordance with the social brain and cultural intelligence hypotheses, which suggest that the importance of network efficiency and information flow through social learning relates to cognitive abilities.

Probabilistic diffusion tractography reveals improvement of structural network in musicians.

PurposeMusicians experience a large amount of information transfer and integration of complex sensory, motor, and auditory processes when training and playing musical instruments. Therefore, musicians are a useful model in which to investigate neural adaptations in the brain.MethodsHere, based on diffusion-weighted imaging, probabilistic tractography was used to determine the architecture of white matter anatomical networks in musicians and non-musicians. Furthermore, the features of the white matter networks were analyzed using graph theory.ResultsSmall-world properties of the white matter network were observed in both groups. Compared with non-musicians, the musicians exhibited significantly increased connectivity strength in the left and right supplementary motor areas, the left calcarine fissure and surrounding cortex and the right caudate nucleus, as well as a significantly larger weighted clustering coefficient in the right olfactory cortex, the left medial superior frontal gyrus, the right gyrus rectus, the left lingual gyrus, the left supramarginal gyrus, and the right pallidum. Furthermore, there were differences in the node betweenness centrality in several regions. However, no significant differences in topological properties were observed at a global level.ConclusionsWe illustrated preliminary findings to extend the network level understanding of white matter plasticity in musicians who have had long-term musical training. These structural, network-based findings may indicate that musicians have enhanced information transmission efficiencies in local white matter networks that are related to musical training.

Intragroup contact and anxiety among ethnic minority adolescents: considering ethnic identity and school diversity transitions.

Everyday interactions with same-racial/ethnic others may confer positive benefits for adolescents, but the meaning of these interactions are likely influenced by individual differences and larger structural contexts. This study examined the situation-level association between contact with same-ethnic others and anxiety symptoms among a diverse sample of 306 racial/ethnic minority adolescents (Mage = 14 years; 66% female), based on (1) individual differences in ethnic identity centrality and (2) developmental histories of transitions in diversity between elementary, middle, and high school. The results indicated that at the level of the situation, when adolescents interacted with more same-ethnic others, they reported fewer anxiety symptoms. Further, for adolescents who had experienced a transition in school diversity, the positive benefits of contact with same-ethnic others was only conferred for those who felt that their ethnicity was very important to them. The importance of examining individual differences within larger developmental histories to understand the everyday experiences of ethnic minority adolescents are discussed.

A continuous adjoint approach to design optimization in cavitating flow using a barotropic model

A continuous adjoint method is developed for design optimization in multiphase flow based on a homogeneous multiphase mixture model. The mixture model consists of variable-density mass and momentum equations and uses a barotropic equation of state for the density that depends on only the local static pressure and the vapor pressure of the liquid. In that case, the primary equations are homogeneous, and a conventional hybrid multistage explicit method based on central differencing and second- and fourth-order scalar artificial dissipation can be applied to solve both the primary and adjoint systems. Results are presented for both surface- and volume-based vapor minimization cost functions for a two-dimensional cavitating hydrofoil in which the geometry is parameterized using B-splines. The cost function gradients computed using the adjoint method are shown to compare well with gradients computed using the complex-step method.

A Mixed Methods Approach to Network Data Collection.

There is a growing interest in examining network processes with a mix of qualitative and quantitative network data. Research has consistently shown that free recall name generators entail recall bias and result in missing data that affects the quality of social network data. This study describes a mixed methods approach for collecting social network data, combining a free recall name generator in the context of an online survey with network relations data coded from transcripts of semi-structured qualitative interviews. The combined network provides substantially more information about the network space, both quantitatively and qualitatively. While network density was relatively stable across networks generated from different data collection methodologies, there were noticeable differences in centrality and component structure across networks. The approach presented here involved limited participant burden and generated more complete data than either technique alone could provide. We make suggestions for further development of this method.

A time-considered multicast routing scheme based on social differences in delay-tolerant networks

In delay-tolerant networks (DTNs), multicast is widely used in many group communication scenarios as it can make full use of network resources and provide high data delivery ratio. As node behaviours demonstrate social characteristics in DTNs, in this paper, a multicast routing scheme based on social difference (SDMR) is proposed. SDMR considers the social differences between nodes, including both the similarity and the centrality differences. SDMR chooses the nodes with greater social differences to forward data, which can expand the data transmission range and increase the data delivery ratio to multicast destinations efficiently. Considering the critical role of the recent contact history, we further propose a time-considered multicast routing scheme based on social difference (SDMRT), which can improve the transmission efficiency further. Through extensive trace-driven simulation with the Infocom06 trace data, it shows that SDMR cannot only ensure high data delivery ratio and low delay, but also reduce the transmission cost greatly compared to other existing protocols. Moreover, SDMRT can further reduce the transmission cost of SDMR without comprising data delivery ratio and delay.

A Meta-Analysis on Women’s Social Network Position: Does Education Help?

We meta-analytically review studies on gender difference in people’s occupancy of central positions in organizational social networks. Drawing upon the human capital perspective of network formation, we examine the potential disadvantages (or advantage) for women to have less (or more) central positions than men and the moderating role of education in reducing such gender differences. Results based on 111 independent samples (N = 17,972) reveal that women have higher in-degree and closeness centrality in organizational expressive networks, and higher out-degree and closeness centrality in organizational instrumental networks. Further, gender differences in brokerage position and eigenvector centrality in both expressive and instrumental networks were moderated by women’s education (as compared to men’s as a group), such that women’s disadvantages of occupying central networks positions were mitigated by their better education. Our study sheds important light on gender stratification in informal structures...

Childhood Maltreatment: Altered Network Centrality of Cingulate, Precuneus, Temporal Pole and Insula

Childhood abuse is a major risk factor for psychopathology. Previous studies have identified brain differences in maltreated individuals but have not focused on potential differences in network architecture. High-resolution T1-weighted magnetic resonance imaging scans were obtained from 265 unmedicated, right-handed 18- to 25-year-olds who were classified as maltreated (n = 142, 55 men/87 women) or nonmaltreated (n = 123, 46 men/77 women) based on extensive interviews. Cortical thickness was assessed in 112 cortical regions (nodes) and interregional partial correlations across subjects were calculated to derive the lowest equivalent cost single-cluster group networks. Permutation tests were used to ascertain whether maltreatment was associated with significant alterations in key centrality measures of these regions and membership in the highly interconnected "rich club." Marked differences in centrality (connectedness, "importance") were observed in a handful of cortical regions. Left anterior cingulate had the second highest number of connections (degree centrality) and was a component of the "rich club" in the control network but ranked low in connectedness (106th of 112 nodes) in the network derived from maltreated-subjects (p < .01). Conversely, right precuneus and right anterior insula ranked first and 15th in degree centrality in the maltreated network versus 90th (p = .01) and 105th (p < .03) in the control network. Maltreatment was associated with decreased centrality in regions involved in emotional regulation and ability to accurately attribute thoughts or intentions to others and with enhanced centrality in regions involved in internal emotional perception, self-referential thinking, and self-awareness. This may provide a potential mechanism for how maltreatment increases risk for psychopathology.