Discovering causes and effects of a given node in Bayesian networks

Causal relationships among variables can be depicted by a causal network of these variables. We propose a local structure learning approach for discovering the direct causes and the direct effects of a given target variable. In the approach, we first find the variable set of parents, children, and maybe some descendants (PCD) of the target variable, but generally we cannot distinguish the parents from the children in the PCD of the target variable. Next, to distinguish the causes from the effects of the target variable, we find the PCD of each variable in the PCD of the target variable, and we repeat the process of finding PCDs along the paths starting from the target variable. Without constructing a whole network over all variables, we find only a local structure around the target variable. Theoretically, we show the correctness of the proposed approach under the assumptions of faithfulness, causal sufficiency, and that conditional independencies are correctly checked.     

Exploring the dynamics of business survey data using Markov models

Computational Management Science - Business tendency surveys are widely used for monitoring economic activity. They provide timely feedback on the current business conditions and outlook. We...     

Cooperative dynamics in neuronal networks

There exist rich cooperative behaviors and their transitions in biological neuronal systems as some key biological factors are changed. Among all of cooperative behaviors of neuronal systems, the existing experiments have shown that the spatiotemporal pattern and synchronization dynamics are very crucial, which are closely related to normal function and dysfunction of neuronal systems. Based on different neuron models, the recent works have been made to explore the mechanisms of pattern formation and synchronization transition. This paper mainly overviews the recent studies of the cooperative dynamics including the pattern formation and synchronization transition in biological neuronal networks. Firstly, we review complicated spatiotemporal pattern dynamics of neuronal networks. Secondly, the interesting synchronization transition is reviewed. Finally, conclusion is given and we put forward some outlooks of research on the cooperative behaviors in real neuronal networks.     

Learning dynamics in second order networks

A model of a second order neural network incorporating a weight adjusting learning component and time delays in processing and transmission is formulated. Delay-independent sufficient conditions are derived for the existence of an asymptotically and exponentially stable equilibrium state. The learning dynamics is modelled with an unsupervised Hebbian-type learning algorithm together with a forgetting term. If there is nothing for the network to learn or if there are no second order synaptic interactions, then our analysis will correspond to one of the standard model of neural networks.     

Complex dynamics of epidemic models on adaptive networks

There has been a substantial amount of well mixing epidemic models devoted to characterizing the observed complex phenomena (such as bistability, hysteresis, oscillations, etc.) during the transmission of many infectious diseases. A comprehensive explanation of these phenomena by epidemic models on complex networks is still lacking. In this paper we study epidemic dynamics in an adaptive network proposed by Gross et al., where the susceptibles are able to avoid contact with the infectious by rewiring their network connections. Such rewiring of the local connections changes the topology of the network, and inevitably has a profound effect on the transmission of the disease, which in turn influences the rewiring process. We rigorously prove that the adaptive epidemic model investigated in this paper exhibits degenerate Hopf bifurcation, homoclinic bifurcation and Bogdanov–Takens bifurcation. Our study shows that adaptive behaviors during an epidemic may induce complex dynamics of disease transmission, including bistability, transient and sustained oscillations, which contrast sharply to the dynamics of classical network models. Our results yield deeper insights into the interplay between topology of networks and the dynamics of disease transmission on networks.     

Neural networks and reaction-diffusion systems with prescribed dynamics

Reaction-diffusion systems and neural networks are considered. We prove that they can produce any structurally stable inertial dynamics.     

Diffusion dynamics in small-world networks with heterogeneous consumers

Diffusions of new products and technologies through social networks can be formalized as spreading of infectious diseases. However, while epidemiological models describe infection in terms of transmissibility, we propose a diffusion model that explicitly includes consumer decision-making affected by social influences and word-of-mouth processes. In our agent-based model consumers’ probability of adoption depends on the external marketing effort and on the internal influence that each consumer perceives in his/her personal networks. Maintaining a given marketing effort and assuming its effect on the probability of adoption as linear, we can study how social processes affect diffusion dynamics and how the speed of the diffusion depends on the network structure and on consumer heterogeneity. First, we show that the speed of diffusion changes with the degree of randomness in the network. In markets with high social influence and in which consumers have a sufficiently large local network, the speed is low in regular networks, it increases in small-world networks and, contrarily to what epidemic models suggest, it becomes very low again in random networks. Second, we show that heterogeneity helps the diffusion. Ceteris paribus and varying the degree of heterogeneity in the population of agents simulation results show that the more heterogeneous the population, the faster the speed of the diffusion. These results can contribute to the development of marketing strategies for the launch and the dissemination of new products and technologies, especially in turbulent and fashionable markets. This paper won the best student paper award at the North American Association for Computational Social and Organizational Science (NAACSOS) Conference 2005, University of Notre Dame, South Bend, Indiana, USA. Preceding versions of this paper have been presented to the Conference of the North American Association for Computational Social and Organizational Science (NAACSOS), 2005, University of Notre Dame, South Bend, USA and to the Conference of the European Social Simulation Association (ESSA), 2005, Koblenz, Germany. Sebastiano Alessio Delre received his Master Degree in Communication Science at the University of Salerno. After one year collaboration at the Institute of Science and Technologies of Cognition (ISTC, Rome, Italy), now he is a PhD student at the faculty of economics, University of Groningen, the Netherlands. His work focus on how different network structures affect market dynamics. His current application domain concerns Agent-Based Simulation Models for social and economic phenomena like innovation diffusion, fashions and turbulent market. Wander Jager is an associate professor of marketing at the University of Groningen. He studied social psychology and obtained his PhD in the behavioral and social sciences, based on a dissertation about the computer modeling of consumer behaviors in situations of common resource use. His present research is about consumer decision making, innovation diffusion, market dynamics, crowd behavior, stock-market dynamics and opinion dynamics. In his work he combines methods of computer simulation and empirical surveys. He is involved in the management committee of the European Social Simulation Association (ESSA). Marco Janssen is an assistant professor in the School of Human Evolution and Social Change and in the Department of Computer Science and Engineering at Arizona State University. He got his degrees in Operations Research and Applied Mathematics. During the last 15 years, he uses computational tools to study social phenomena, especially human-environmental interactions. His present research focuses on diffusion dynamics, institutional innovation and robustness of social-ecological systems. He combined computational studies with laboratory and field experiments, case study analysis and archeological data. He is an associate editor-in-chief of the journal Ecology and Society.     

Information dynamics algorithm for detecting communities in networks

The problem of community detection is relevant in many scientific disciplines, from social science to statistical physics. Given the impact of community detection in many areas, such as psychology and social sciences, we have addressed the issue of modifying existing well performing algorithms by incorporating elements of the domain application fields, i.e. domain-inspired. We have focused on a psychology and social network-inspired approach which may be useful for further strengthening the link between social network studies and mathematics of community detection. Here we introduce a community-detection algorithm derived from the van Dongen’s Markov Cluster algorithm (MCL) method [4] by considering networks’ nodes as agents capable to take decisions. In this framework we have introduced a memory factor to mimic a typical human behavior such as the oblivion effect. The method is based on information diffusion and it includes a non-linear processing phase. We test our method on two classical community benchmark and on computer generated networks with known community structure. Our approach has three important features: the capacity of detecting overlapping communities, the capability of identifying communities from an individual point of view and the fine tuning the community detectability with respect to prior knowledge of the data. Finally we discuss how to use a Shannon entropy measure for parameter estimation in complex networks.     

Asymptotical stability for complex dynamical networks via link dynamics

From the perspective of large-scale system, a complex dynamical network can be regarded as the interconnected system with the node subsystem and link subsystem, which implies that the node subsystem and the link subsystem are the two main bodies of dynamical behaviors of network. Therefore, the whole stability of network is influenced by not only the dynamics of node subsystem but also the dynamics of link subsystem. According to the above view, the wholly asymptotical stability (WAS) is defined in this paper for the complex dynamical network with the model of differential equations. The WAS is used to describe the node subsystem achieves asymptotical stability when link subsystem achieves also the asymptotic stability in Lyapunov sense. For the WAS of the complex dynamical network, the corresponding criteria are derived by checking whether certain matrices are Hurwitz. The analysis results show that even if the isolated nodes are not asymptotically stable in Lyapunov sense, employing the dynamics of link can also force the node subsystem to achieve the asymptotical stability. Finally, the simulation examples show the validity of methods in this paper.     

Leader-following consensus for networks with single- and double-integrator dynamics

In the paper, consensus protocols for networks of dynamic agents with single- and double-integrator dynamics are proposed. We provide necessary and sufficient conditions for leader-following consensus problem of the presented models. In order to examine the studied cases in a general way the time scale calculus is employed to get the results. The method used in the proofs is based on spectral characterization of stability for time invariant linear systems on time scales. All the results are enriched in illustrative examples and numerical simulations.     

Equation-Free multiscale computational analysis of individual-based epidemic dynamics on networks

The surveillance, analysis and ultimately the efficient long-term prediction and control of epidemic dynamics appear to be some of the major challenges nowadays. Detailed individual-based mathematical models on complex networks play an important role towards this aim. In this work, it is shown how one can exploit the Equation-Free approach and optimization methods such as Simulated Annealing to bridge detailed individual-based epidemic models with coarse-grained, system-level analysis within a pair-wise representation perspective. The proposed computational methodology provides a systematic approach for analyzing the parametric behavior of complex/multiscale epidemic simulators much more efficiently than simply simulating forward in time. It is shown how steady state and (if required) time-dependent computations, stability computations, as well as continuation and numerical bifurcation analysis can be performed in a straightforward manner. The approach is illustrated through a simple individual-based SIRS epidemic model deploying on a random regular connected graph. Using the individual-based simulator as a black box coarse-grained timestepper and with the aid of Simulated Annealing I compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level.