Networks of probabilistic events in discrete time

The usual methods of applying Bayesian networks to the modeling of temporal processes, such as Dean and Kanazawa’s dynamic Bayesian networks (DBNs), consist in discretizing time and creating an instance of each random variable for each point in time. We present a new approach called network of probabilistic events in discrete time (NPEDT), for temporal reasoning with uncertainty in domains involving probabilistic events. Under this approach, time is discretized and each value of a variable represents the instant at which a certain event may occur. This is the main difference with respect to DBNs, in which the value of a variable V_i represents the state of a real-world property at time t_i. Therefore, our method is more appropriate for temporal fault diagnosis, because only one variable is necessary for representing the occurrence of a fault and, as a consequence, the networks involved are much simpler than those obtained by using DBNs. In contrast, DBNs are more appropriate for monitoring tasks, since they explicitly represent the state of the system at each moment. We also introduce in this paper several types of temporal noisy gates, which facilitate the acquisition and representation of uncertain temporal knowledge. They constitute a generalization of traditional canonical models of multicausal interactions, such as the noisy OR-gate, which have been usually applied to static domains. We illustrate the approach with the example domain of modeling the evolution of traffic jams produced on the outskirts of a city, after the occurrence of an event that obliges traffic to stop indefinitely.     

A set of measures to quantify the dynamicity of longitudinal social networks

This study proposes a new set of measures for longitudinal social networks (LSNs). A LSN evolves over time through the creation and/or deletion of links among a set of actors (e.g., individuals or organizations). The current literature does feature some methods, such as multiagent simulation models, for studying the dynamics of LSNs. These methods have mainly been utilized to explore evolutionary changes in LSNs from one state to another and to explain the underlying mechanisms for these changes. However, they cannot quantify different aspects of a LSN. For example, these methods are unable to quantify the level of dynamicity shown by an actor in a LSN and its contribution to the overall dynamicity shown by that LSN. This article develops a set of measures for LSNs to overcome this limitation. We illustrate the benefits of these measures by applying them to an exploration of the Enron crisis. These measures successfully identify a significant but previously unobserved change in network structures (both at individual and group levels) during Enron's crisis period. © 2015 Wiley Periodicals, Inc. Complexity 21: 309–320, 2016     

The Role of Metanetworks in Network Evolution

The question of what structures of relations between actors emerge in the evolution of social networks is of fundamental sociological interest. The present research proposes that processes of network evolution can be usefully conceptualized in terms of a network of networks, or “metanetwork,” wherein networks that are one link manipulation away from one another are connected. Moreover, the geography of metanetworks has real effects on the course of network evolution. Specifically, both equilibrium and non-equilibrium networks located in more desirable regions of the metanetwork are found to be more probable. These effects of metanetwork geography are illustrated by two dynamic network models: one in which actors pursue access to unique information through “structural holes,” and the other in which actors pursue access to valid information by minimizing path length. Finally, I discuss future directions for modeling network dynamics in terms of metanetworks.     

A Bayesian record linkage model incorporating relational data

In this article, we introduce a novel Bayesian approach for linking multiple social networks in order to discover the same real world person having different accounts across networks. In particular, we develop a latent model that allows us to jointly characterize the network and linkage structures relying on both relational and profile data. In contrast to other existing approaches in the machine learning literature, our Bayesian implementation naturally provides uncertainty quantification via posterior probabilities for the linkage structure itself or any function of it. Our findings clearly suggest that our methodology can produce accurate point estimates of the linkage structure even in the absence of profile information, and also, in an identity resolution setting, our results confirm that including relational data into the matching process improves the linkage accuracy. We illustrate our methodology using real data from popular social networks such as Twitter , Facebook , and YouTube .     

Joint Modeling of Multiple Network Views

Latent space models (LSM) for network data rely on the basic assumption that each node of the network has an unknown position in a D-dimensional Euclidean latent space: generally the smaller the distance between two nodes in the latent space, the greater their probability of being connected. In this article, we propose a variational inference approach to estimate the intractable posterior of the LSM. In many cases, different network views on the same set of nodes are available. It can therefore be useful to build a model able to jointly summarize the information given by all the network views. For this purpose, we introduce the latent space joint model (LSJM) that merges the information given by multiple network views assuming that the probability of a node being connected with other nodes in each network view is explained by a unique latent variable. This model is demonstrated on the analysis of two datasets: an excerpt of 50 girls from “Teenage Friends and Lifestyle Study” data at three time points and the Saccharomyces cerevisiae genetic and physical protein–protein interactions. Supplementary materials for this article are available online.     

Stochastic actor‐oriented models for network change

A class of models is proposed for longitudinal network data. These models are along the lines of methodological individualism: actors use heuristics to try to achieve their individual goals, subject to constraints. The current network structure is among these constraints. The models are continuous time Markov chain models that can be implemented as simulation models. They incorporate random change in addition to the purposeful change that follows from the actors’ pursuit of their goals, and include parameters that must be estimated from observed data. Statistical methods are proposed for estimating and testing these models. These methods can also be used for parameter estimation for other simulation models. The statistical procedures are based on the method of moments, and use computer simulation to estimate the theoretical moments. The Robbins‐Monro process is used to deal with the stochastic nature of the estimated theoretical moments. An example is given for Newcomb's fraternity data, using a model that expresses reciprocity and balance.     

Patterning by genetic networks

We consider here the morphogenesis (pattern formation) problem for some genetic network models. First, we show that any given spatio‐temporal pattern can be generated by a genetic network involving a sufficiently large number of genes. Moreover, patterning process can be performed by an effective algorithm. We also show that Turing's or Meinhardt's type reaction–diffusion models can be approximated by genetic networks. These results exploit the fundamental fact that the genes form functional units and are organized in blocks. Due to this modular organization, the genes always are capable to construct any new patterns and even any time sequences of new patterns from old patterns. Computer simulations illustrate some analytical results. Copyright © 2005 John Wiley & Sons, Ltd.     

On the complexity of computing the temporal hybridization number for two phylogenies

Phylogenetic networks are now frequently used to explain the evolutionary history of a set of species for which a collection of gene trees, reconstructed from genetic material of different parts of the species’ genomes, reveal inconsistencies. However, in the context of hybridization, the reconstructed networks are often not temporal. If a hybridization network is temporal, then it satisfies the time constraint of instantaneously occurring hybridization events; i.e. all species that are involved in such an event coexist in time. Furthermore, although a collection of phylogenetic trees can often be merged into a hybridization network that is temporal, many algorithms do not necessarily find such a network since their primary optimization objective is to minimize the number of hybridization events. In this paper, we present a characterization for when two rooted binary phylogenetic trees admit a temporal hybridization network. Furthermore, we show that the underlying optimization problem is APX-hard and, therefore, NP-hard. Thus, unless P=NP, it is unlikely that there are efficient algorithms for either computing an exact solution or approximating it within a ratio arbitrarily close to one.     

复杂疾病的分子网络模型研究

复杂疾病是危害人类健康的主要杀手.不同于单基因缺陷性遗传病,复杂疾病的发生发展与多个基因之间、基因与环境之间的相互作用有关,致病机理复杂,其早期诊断及治疗困难是21世纪生物医学研究的重大挑战之一.随着生物知识的不断积累和多层次"组学"数据的井喷式涌现,复杂疾病研究迎来了新的"组学革命",研究模式从以往的只关注某个分子扩展到对分子之间相互形成的生物分子网络的系统分析.作为系统生物学核心概念,生物分子网络系统整合大量生物知识和高通量生物数据,是研究复杂疾病的强有力工具.本文以分子网络为主线,以数学建模为工具来研究复杂疾病,针对复杂疾病关系和复杂疾病的发生发展机制等复杂疾病研究的关键热点问题,分析和集成高通量多层次组学数据,构建并求解生物分子网络的数学模型,在若干复杂疾病相关系统生物学问题中取得有生物学意义的结果.本文提出若干生物网络建模、分析及应用的方法并提供若干应用软件,为从系统层面理解复杂疾病提供重要参考;同时,网络模型在若干实例中的应用得到若干有生物学意义的结论,为揭示复杂疾病机理、推动疾病治疗与预防起到了一定的作用.     

Finite element and finite volume‐element simulation of pseudo‐ECGs and cardiac alternans

In this paper, we are interested in the spatio‐temporal dynamics of the transmembrane potential in paced isotropic and anisotropic cardiac tissues. In particular, we observe a specific precursor of cardiac arrhythmias that is the presence of alternans in the action potential duration. The underlying mathematical model consists of a reaction–diffusion system describing the propagation of the electric potential and the nonlinear interaction with ionic gating variables. Either conforming piecewise continuous finite elements or a finite volume‐element scheme are employed for the spatial discretization of all fields, whereas operator splitting strategies of first and second order are used for the time integration. We also describe an efficient mechanism to compute pseudo‐ECG signals, and we analyze restitution curves and alternans patterns for physiological and pathological cardiac rhythms. Copyright © 2014 John Wiley & Sons, Ltd.     

Network formation and knowledge gains

Incentive-based models for network formation link micro actions to changes in network structure. Sociologists have extended these models on a number of fronts, but there remains a tendency to treat actors as homogenous agents and to disregard social theory. Drawing upon literature on the strategic use of networks for knowledge gains, we specify models exploring the co-evolution of networks and knowledge gains. Our findings suggest that pursuing transitive ties is the most successful strategy, as more reciprocity and cycling result from this pursuit, thus encouraging learning across the network. We also discuss the role of network size, global network structure, and parameter strength in actors’ attainment of knowledge resources.     

Stress testing network reconstruction via graphical causal model

An resilience optimal evaluation of financial portfolios implies having plausible hypotheses about the multiple interconnections between the macroeconomic variables and the risk parameters. In this article, we propose a graphical model for the reconstruction of the causal structure that links the multiple macroeconomic variables and the assessed risk parameters, it is this structure that we call stress testing network. In this model, the relationships between the macroeconomic variables and the risk parameter define a “relational graph” among their time‐series, where related time‐series are connected by an edge. Our proposal is based on the temporal causal models, but unlike, we incorporate specific conditions in the structure which correspond to intrinsic characteristics this type of networks. Using the proposed model and given the high‐dimensional nature of the problem, we used regularization methods to efficiently detect causality in the time‐series and reconstruct the underlying causal structure. In addition, we illustrate the use of model in credit risk data of a portfolio. Finally, we discuss its uses and practical benefits in stress testing.     

内生网络环境下2-步邻域内的局部策略互动及其仿真

考察内生网络环境下局中人与2-步邻域内的邻居进行的局部协同对策,较为完整地给出了均衡网络的结构特性,以及费用参数和互动半径对于均衡结构的影响. 基于 NetLogo仿真系统,编制了局部互动仿真模拟实验程序. 仿真结果显示,网络生成的动态进程对于网络均衡结果存在很大影响. 结果对于解决社会和经济领域中的互动问题可提供策略性指导.     

Individual decision‐making in dynamic collective systems

One of the most popular individual choice models is the multinomial logit model (MLM). The basic hypothesis of the MLM is that an individual chooses an alternative among a set of alternatives available to him by comparing the utilities of all the choices. The MLM is, however, limited in its usefulness because it doesn't account for the effects of the time factor and the social interactions between individuals. This work describes a dynamic extension of the MLM that allows for such interactions. The new model is formulated as an interactive continuous‐time Markov process, and is approximated, for a large population, by a deterministic system. Some possible consequences of the interaction phenomena are discussed with a special binary choice model.     

Computational Statistical Methods for Social Network Models

We review the broad range of recent statistical work in social network models, with emphasis on computational aspects of these methods. Particular focus is applied to exponential-family random graph models (ERGM) and latent variable models for data on complete networks observed at a single time point, though we also briefly review many methods for incompletely observed networks and networks observed at multiple time points. Although we mention far more modeling techniques than we can possibly cover in depth, we provide numerous citations to current literature. We illustrate several of the methods on a small, well-known network dataset, Sampson's monks, providing code where possible so that these analyses may be duplicated.     

Finding Optimal Targets for Change Agents: A Computer Simulation of Innovation Diffusion

We introduce a diffusion of innovation model based on a network threshold approach. Realistic network and threshold data were gathered regarding the diffusion of new software tools within part of a large organization. Novel model features are a second threshold for innovation rejection and a memory that allows actors to take trends into account. Computer simulations produce expected outcomes, such as the S-shaped diffusion curve, but also diffusion breakdown and oscillations. We define and compute the quality of change agent targets in terms of the impact targeted actors have on the diffusion process. Our simulations reveal considerable variance in the quality of actors as change agent targets. Certain actors can be singled out as especially important to the diffusion process. Small changes in the distribution of thresholds and changes in some parameters, such as the sensitivity for trends, lead to significant changes in the target quality measure. To illustrate these interdependencies we outline how the impact of an actor targeted by a change agent spreads through the network. We thus can explain why a good change agent target does not necessarily need to be an opinion leader. Simulations comparing the effectiveness of randomly selected targets versus a group of good change agent targets indicate that the selection of good targets can accelerate innovation diffusion.     

Structural cohesion and embeddedness in two-mode networks

The detection of structural cohesion is a key utility of social network analysis, but little work has been done to refine the detection of structural cohesion in two-mode networks. Most work on cohesion in two-mode networks either: (1) attempts to detect cohesion in such networks using one-mode projections (which can be problematic for reasons we discuss); or (2) focuses on restrictive substructures like bi-cliques to identify cohesive subgroups. We propose a new strategy for two-mode networks that follows the general reasoning of approaches to detecting structural cohesion in one-mode networks. Our approach identifies the number of actors from one node set that may be removed before disconnecting actors in the opposite set. We also develop a definition of embeddedness that draws on Moody and White’s hierarchical nesting approach.     

Multiresolution Network Models

Many existing statistical and machine learning tools for social network analysis focus on a single level of analysis. Methods designed for clustering optimize a global partition of the graph, whereas projection-based approaches (e.g., the latent space model in the statistics literature) represent in rich detail the roles of individuals. Many pertinent questions in sociology and economics, however, span multiple scales of analysis. Further, many questions involve comparisons across disconnected graphs that will, inevitably be of different sizes, either due to missing data or the inherent heterogeneity in real-world networks. We propose a class of network models that represent network structure on multiple scales and facilitate comparison across graphs with different numbers of individuals. These models differentially invest modeling effort within subgraphs of high density, often termed communities, while maintaining a parsimonious structure between said subgraphs. We show that our model class is projective, highlighting an ongoing discussion in the social network modeling literature on the dependence of inference paradigms on the size of the observed graph. We illustrate the utility of our method using data on household relations from Karnataka, India. Supplementary material for this article is available online.