We extend the classic study of the motion of small ellipsoidal particles under shear, focusing on simplifications obtained by considerations of the extreme aspect ratios typical of rheoscopic particles (e.g., Kalliroscope). Specifically, we study conditions under which the long-time behavior of scalene (i.e., triaxial or nonaxisymmetric) ellipsoids are well approximated by a model that is low order in the appropriate aspect ratios. After enumerating and describing the generic long-time motions of such particles in the lowest-order model, we investigate corrections induced by the physically appropriate lowest-order correction to the base model, with special attention to a periodic wobbling motion special to scalene ellipsoids.
We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module, and the inter-module connections are defined by the joint degree-degree distribution of nodes for each pair of modules. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model. The new network ensemble generalizes existing models (e.g., the well-known configuration model and Lancichinetti-Fortunato-Radicchi networks) by allowing a heterogeneous distribution of degree-degree correlations across modules, which is important for the consideration of nonidentical interacting networks.
A method to identify distinct dynamical regimes and transitions between those regimes in a short univariate time series was recently introduced [N. Malik et al., Europhys. Lett. 97, 40009 (2012)], employing the computation of fluctuations in a measure of nonlinear similarity based on local recurrence properties. In this work, we describe the details of the analytical relationships between this newly introduced measure and the well-known concepts of attractor dimensions and Lyapunov exponents. We show that the new measure has linear dependence on the effective dimension of the attractor and it measures the variations in the sum of the Lyapunov spectrum. To illustrate the practical usefulness of the method, we identify various types of dynamical transitions in different nonlinear models. We present testbed examples for the new method's robustness against noise and missing values in the time series. We also use this method to analyze time series of social dynamics, specifically an analysis of the US crime record time series from 1975 to 1993. Using this method, we find that dynamical complexity in robberies was influenced by the unemployment rate until the late 1980s. We have also observed a dynamical transition in homicide and robbery rates in the late 1980s and early 1990s, leading to increase in the dynamical complexity of these rates.
We study the temporal co-variation of network co-evolution via the cross-link structure of networks, for which we take advantage of the formalism of hypergraphs to map cross-link structures back to network nodes. We investigate two sets of temporal network data in detail. In a network of coupled nonlinear oscillators, hyperedges that consist of network edges with temporally co-varying weights uncover the driving co-evolution patterns of edge weight dynamics both within and between oscillator communities. In the human brain, networks that represent temporal changes in brain activity during learning exhibit early co-evolution that then settles down with practice. Subsequent decreases in hyperedge size are consistent with emergence of an autonomous subgraph whose dynamics no longer depends on other parts of the network. Our results on real and synthetic networks give a poignant demonstration of the ability of cross-link structure to uncover unexpected co-evolution attributes in both real and synthetic dynamical systems. This, in turn, illustrates the utility of analyzing cross-links for investigating the structure of temporal networks.
Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little is known in general about mechanistic drivers of structured networks. Here we contrast network properties derived from diffusion spectrum imaging data of the human brain with 13 synthetic network models chosen to probe the roles of physical network embedding and temporal network growth. We characterize both the empirical and synthetic networks using familiar graph metrics, but presented here in a more complete statistical form, as scatter plots and distributions, to reveal the full range of variability of each measure across scales in the network. We focus specifically on the degree distribution, degree assortativity, hierarchy, topological Rentian scaling, and topological fractal scaling--in addition to several summary statistics, including the mean clustering coefficient, the shortest path-length, and the network diameter. The models are investigated in a progressive, branching sequence, aimed at capturing different elements thought to be important in the brain, and range from simple random and regular networks, to models that incorporate specific growth rules and constraints. We find that synthetic models that constrain the network nodes to be physically embedded in anatomical brain regions tend to produce distributions that are most similar to the corresponding measurements for the brain. We also find that network models hardcoded to display one network property (e.g., assortativity) do not in general simultaneously display a second (e.g., hierarchy). This relative independence of network properties suggests that multiple neurobiological mechanisms might be at play in the development of human brain network architecture. Together, the network models that we develop and employ provide a potentially useful starting point for the statistical inference of brain network structure from neuroimaging data.
Given the difficulty in finding a cure for HIV/AIDS, a promising prevention strategy to reduce HIV transmission is to directly block infection at the portal of entry. The recent Thai RV144 trial offered the first evidence that an antibody-based vaccine may block heterosexual HIV transmission. Unfortunately, the underlying mechanism(s) for protection remain unclear. Here we theoretically examine a hypothesis that builds on our recent laboratory observation: virus-specific antibodies (Ab) can trap individual virions in cervicovaginal mucus (CVM), thereby reducing infection in vivo. Ab are known to have a weak-previously considered inconsequential-binding affinity with the mucin fibers that constitute CVM. However, multiple Ab can bind to the same virion at the same time, which markedly increases the overall Ab-mucin binding avidity, and creates an inheritable virion-mucin affinity. Our model takes into account biologically relevant length and timescales, while incorporating known HIV-Ab affinity and the respective diffusivities of viruses and Ab in semen and CVM. The model predicts that HIV-specific Ab in CVM leads to rapid formation and persistence of an HIV concentration front near the semen/CVM interface, far from the vaginal epithelium. Such an HIV concentration front minimizes the flux of HIV virions reaching target cells, and maximizes their elimination upon drainage of genital secretions. The robustness of the result implies that even exceedingly weak Ab-mucin affinity can markedly reduce the flux of virions reaching target cells. Beyond this specific application, the model developed here is adaptable to other pathogens, mucosal barriers, and geometries, as well as kinetic and diffusional effects, providing a tool for hypothesis testing and producing quantitative insights into the dynamics of immune-mediated protection.
Eliciting broadly neutralizing antibodies (bnAb) in cervicovaginal mucus (CVM) represents a promising "first line of defense" strategy to reduce vaginal HIV transmission. However, it remains unclear what levels of bnAb must be present in CVM to effectively reduce infection. We approached this complex question by modeling the dynamic tally of bnAb coverage on HIV. This analysis introduces a critical, timescale-dependent competition: to protect, bnAb must accumulate at sufficient stoichiometry to neutralize HIV faster than virions penetrate CVM and reach target cells. We developed a model that incorporates concentrations and diffusivities of HIV and bnAb in semen and CVM, kinetic rates for binding (kon) and unbinding (koff) of select bnAb, and physiologically relevant thicknesses of CVM and semen layers. Comprehensive model simulations lead to robust conclusions about neutralization kinetics in CVM. First, due to the limited time virions in semen need to penetrate CVM, substantially greater bnAb concentrations than in vitro estimates must be present in CVM to neutralize HIV. Second, the model predicts that bnAb with more rapid kon, almost independent of koff, should offer greater neutralization potency in vivo. These findings suggest the fastest arriving virions at target cells present the greatest likelihood of infection. It also implies the marked improvements in in vitro neutralization potency of many recently discovered bnAb may not translate to comparable reduction in the bnAb dose needed to confer protection against initial vaginal infections. Our modeling framework offers a valuable tool to gaining quantitative insights into the dynamics of mucosal immunity against HIV and other infectious diseases.
The design of an Agent-Based Model (ABM) is described that integrates Social and Land Use Modules to examine population-environment interactions in a former agricultural frontier in Northeastern Thailand. The ABM is used to assess household income and wealth derived from agricultural production of lowland, rain-fed paddy rice and upland field crops in Nang Rong District as well as remittances returned to the household from family migrants who are engaged in off-farm employment in urban destinations. The ABM is supported by a longitudinal social survey of nearly 10,000 households, a deep satellite image time-series of land use change trajectories, multi-thematic social and ecological data organized within a GIS, and a suite of software modules that integrate data derived from an agricultural cropping system model (DSSAT - Decision Support for Agrotechnology Transfer) and a land suitability model (MAXENT - Maximum Entropy), in addition to multi-dimensional demographic survey data of individuals and households. The primary modules of the ABM are the Initialization Module, Migration Module, Assets Module, Land Suitability Module, Crop Yield Module, Fertilizer Module, and the Land Use Change Decision Module. The architecture of the ABM is described relative to module function and connectivity through uni-directional or bi-directional links. In general, the Social Modules simulate changes in human population and social networks, as well as changes in population migration and household assets, whereas the Land Use Modules simulate changes in land use types, land suitability, and crop yields. We emphasize the description of the Land Use Modules - the algorithms and interactions between the modules are described relative to the project goals of assessing household income and wealth relative to shifts in land use patterns, household demographics, population migration, social networks, and agricultural activities that collectively occur within a marginalized environment that is subjected to a suite of endogenous and exogenous dynamics.
As a person learns a new skill, distinct synapses, brain regions, and circuits are engaged and change over time. In this paper, we develop methods to examine patterns of correlated activity across a large set of brain regions. Our goal is to identify properties that enable robust learning of a motor skill. We measure brain activity during motor sequencing and characterize network properties based on coherent activity between brain regions. Using recently developed algorithms to detect time-evolving communities, we find that the complex reconfiguration patterns of the brains putative functional modules that control learning can be described parsimoniously by the combined presence of a relatively stiff temporal core that is composed primarily of sensorimotor and visual regions whose connectivity changes little in time and a flexible temporal periphery that is composed primarily of multimodal association regions whose connectivity changes frequently. The separation between temporal core and periphery changes over the course of training and, importantly, is a good predictor of individual differences in learning success. The core of dynamically stiff regions exhibits dense connectivity, which is consistent with notions of core-periphery organization established previously in social networks. Our results demonstrate that core-periphery organization provides an insightful way to understand how putative functional modules are linked. This, in turn, enables the prediction of fundamental human capacities, including the production of complex goal-directed behavior.
We describe techniques for the robust detection of community structure in some classes of time-dependent networks. Specifically, we consider the use of statistical null models for facilitating the principled identification of structural modules in semi-decomposable systems. Null models play an important role both in the optimization of quality functions such as modularity and in the subsequent assessment of the statistical validity of identified community structure. We examine the sensitivity of such methods to model parameters and show how comparisons to null models can help identify system scales. By considering a large number of optimizations, we quantify the variance of network diagnostics over optimizations ("optimization variance") and over randomizations of network structure ("randomization variance"). Because the modularity quality function typically has a large number of nearly degenerate local optima for networks constructed using real data, we develop a method to construct representative partitions that uses a null model to correct for statistical noise in sets of partitions. To illustrate our results, we employ ensembles of time-dependent networks extracted from both nonlinear oscillators and empirical neuroscience data.
Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes--flexibility and selection--must operate over multiple temporal scales as performance of a skill changes from being slow and challenging to being fast and automatic. Such selective adaptability is naturally provided by modular structure, which plays a critical role in evolution, development, and optimal network function. Using functional connectivity measurements of brain activity acquired from initial training through mastery of a simple motor skill, we investigate the role of modularity in human learning by identifying dynamic changes of modular organization spanning multiple temporal scales. Our results indicate that flexibility, which we measure by the allegiance of nodes to modules, in one experimental session predicts the relative amount of learning in a future session. We also develop a general statistical framework for the identification of modular architectures in evolving systems, which is broadly applicable to disciplines where network adaptability is crucial to the understanding of system performance.
We demonstrate that a tree-based theory for various dynamical processes operating on static, undirected networks yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance ? is sufficiently small--that is, as long as it is close to the value of ? in a random network with negligible clustering and the same degree-degree correlations. We support this hypothesis numerically using both real-world networks from various domains and several classes of synthetic clustered networks. We present analytical calculations that further support our claim that tree-based theories can be accurate for clustered networks, provided that the networks are "sufficiently small" worlds.
Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly connected groups of nodes known as communities. We developed a generalized framework of network quality functions that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices. This framework allows studies of community structure in a general setting encompassing networks that evolve over time, have multiple types of links (multiplexity), and have multiple scales.
We formulate a spectral graph-partitioning algorithm that uses the two leading eigenvectors of the matrix corresponding to a selected quality function to split a network into three communities in a single step. In so doing, we extend the recursive bipartitioning methods developed by Newman [M. E. J. Newman, Proc. Natl. Acad. Sci. U.S.A. 103, 8577 (2006); Phys. Rev. E 74, 036104 (2006)] to allow one to consider the best available two-way and three-way divisions at each recursive step. We illustrate the method using simple "bucket brigade" examples and then apply the algorithm to examine the community structures of the coauthorship graph of network scientists and of U. S. Congressional networks inferred from roll call voting similarities.
The study of networks has become a substantial interdisciplinary endeavor that encompasses myriad disciplines in the natural, social, and information sciences. Here we introduce a framework for constructing taxonomies of networks based on their structural similarities. These networks can arise from any of numerous sources: They can be empirical or synthetic, they can arise from multiple realizations of a single process (either empirical or synthetic), they can represent entirely different systems in different disciplines, etc. Because mesoscopic properties of networks are hypothesized to be important for network function, we base our comparisons on summaries of network community structures. Although we use a specific method for uncovering network communities, much of the introduced framework is independent of that choice. After introducing the framework, we apply it to construct a taxonomy for 746 networks and demonstrate that our approach usefully identifies similar networks. We also construct taxonomies within individual categories of networks, and we thereby expose nontrivial structure. For example, we create taxonomies for similarity networks constructed from both political voting data and financial data. We also construct network taxonomies to compare the social structures of 100 Facebook networks and the growth structures produced by different types of fungi.
Motor chunking facilitates movement production by combining motor elements into integrated units of behavior. Previous research suggests that chunking involves two processes: concatenation, aimed at the formation of motor-motor associations between elements or sets of elements, and segmentation, aimed at the parsing of multiple contiguous elements into shorter action sets. We used fMRI to measure the trial-wise recruitment of brain regions associated with these chunking processes as healthy subjects performed a cued-sequence production task. A dynamic network analysis identified chunking structure for a set of motor sequences acquired during fMRI and collected over 3 days of training. Activity in the bilateral sensorimotor putamen positively correlated with chunk concatenation, whereas a left-hemisphere frontoparietal network was correlated with chunk segmentation. Across subjects, there was an aggregate increase in chunk strength (concatenation) with training, suggesting that subcortical circuits play a direct role in the creation of fluid transitions across chunks.
Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for real-world networks with clustering and modular structure. In this paper, we compare mean-field predictions to numerical simulation results for dynamical processes running on 21 real-world networks and demonstrate that the accuracy of such theory depends not only on the mean degree of the networks but also on the mean first-neighbor degree. We show that mean-field theory can give (unexpectedly) accurate results for certain dynamics on disassortative real-world networks even when the mean degree is as low as 4.
We consider a simplified model of a social network in which individuals have one of two opinions (called 0 and 1) and their opinions and the network connections coevolve. Edges are picked at random. If the two connected individuals hold different opinions then, with probability 1 - ?, one imitates the opinion of the other; otherwise (i.e., with probability ?), the link between them is broken and one of them makes a new connection to an individual chosen at random (i) from those with the same opinion or (ii) from the network as a whole. The evolution of the system stops when there are no longer any discordant edges connecting individuals with different opinions. Letting ? be the fraction of voters holding the minority opinion after the evolution stops, we are interested in how ? depends on ? and the initial fraction u of voters with opinion 1. In case (i), there is a critical value ?(c) which does not depend on u, with ? ? u for ? > ?(c) and ? ? 0 for ? < ?(c). In case (ii), the transition point ?(c)(u) depends on the initial density u. For ? > ?(c)(u), ? ? u, but for ? < ?(c)(u), we have ?(?,u) = ?(?,1/2). Using simulations and approximate calculations, we explain why these two nearly identical models have such dramatically different phase transitions.
Related JoVE Video
Journal of Visualized Experiments
What is Visualize?
JoVE Visualize is a tool created to match the last 5 years of PubMed publications to methods in JoVE's video library.
How does it work?
We use abstracts found on PubMed and match them to JoVE videos to create a list of 10 to 30 related methods videos.
Video X seems to be unrelated to Abstract Y...
In developing our video relationships, we compare around 5 million PubMed articles to our library of over 4,500 methods videos. In some cases the language used in the PubMed abstracts makes matching that content to a JoVE video difficult. In other cases, there happens not to be any content in our video library that is relevant to the topic of a given abstract. In these cases, our algorithms are trying their best to display videos with relevant content, which can sometimes result in matched videos with only a slight relation.