Multitype weakly subcritical branching processes in random environment

A multi-type branching process evolving in a random environment generated by a sequence of independent identically distributed random variables is considered. The asymptotics of the survival probability of the process for a long time is found under the assumption that the matrices of the mean values of direct descendants have a common left eigenvector and the increment X of the associated random walk generated by the logarithms of the Perron roots of these matrices satisfies conditions E X < 0 and E XeX > 0.

Optimizing Pinned Nodes to Maximize the Convergence Rate of Multiagent Systems with Digraph Topologies

This paper investigates how to choose pinned node set to maximize the convergence rate of multiagent systems under digraph topologies in cases of sufficiently small and large pinning strength. In the case of sufficiently small pinning strength, perturbation methods are employed to derive formulas in terms of asymptotics that indicate that the left eigenvector corresponding to eigenvalue zero of the Laplacian measures the importance of node in pinning control multiagent systems if the underlying network has a spanning tree, whereas for the network with no spanning trees, the left eigenvectors of the Laplacian matrix corresponding to eigenvalue zero can be used to select the optimal pinned node set. In the case of sufficiently large pinning strength, by the similar method, a metric based on the smallest real part of eigenvalues of the Laplacian submatrix corresponding to the unpinned nodes is used to measure the stabilizability of the pinned node set. Different algorithms that are applicable for different scenarios are develped. Several numerical simulations are given to verify theoretical results.

First Passage Time Memory Lifetimes for Simple, Multistate Synapses: Beyond the Eigenvector Requirement

Models of associative memory with discrete-strength synapses are palimpsests, learning new memories by forgetting old ones. Memory lifetimes can be defined by the mean first passage time (MFPT) for a perceptron's activation to fall below firing threshold. By imposing the condition that the vector of possible strengths available to a synapse is a left eigenvector of the stochastic matrix governing transitions in strength, we previously derived results for MFPTs and first passage time (FPT) distributions in models with simple, multistate synapses. This condition permits jump moments to be computed via a 1-dimensional Fokker-Planck approach. Here, we study memory lifetimes in the absence of this condition. To do so, we must introduce additional variables, including the perceptron activation, that parameterize synaptic configurations, permitting Markovian dynamics in these variables to be formulated. FPT problems in these variables require solving multidimensional partial differential or integral equations. However, the FPT dynamics can be analytically well approximated by focusing on the slowest eigenmode in this higher-dimensional space. We may also obtain a much better approximation by restricting to the two dominant variables in this space, the restriction making numerical methods tractable. Analytical and numerical methods are in excellent agreement with simulation data, validating our methods. These methods prepare the ground for the study of FPT memory lifetimes with complex rather than simple, multistate synapses.

Utilizing Node Interference Method and Complex Network Centrality Metrics to Explore Requirement Change Propagation

Requirements play very important role in the design process as they specify how stakeholder expectations will be satisfied. Requirements are frequently revised, due to iterative nature of the design process. These changes, if not properly managed, may result in financial and time losses leading to project failure due to possible undesired propagating effect. Current modeling methods for managing requirements do not offer formal reasoning necessary to manage the requirement change and its propagation. Predictive models to assist designers in making well informed decisions prior to change implementation do not exist. Based on the premise that requirement networks can be utilized to study change propagation, this research will allow for investigation of complex network metrics for predicting change throughout the design process. Requirement change prediction ability during the design process may lead to valuable knowledge in designing artifacts more efficiently by minimizing unanticipated changes due to mismanaged requirements. Two research questions (RQs) described are addressed in this paper: RQ 1: Can complex network centrality metrics of a requirement network be utilized to predict requirement change propagation? RQ 2: How does complex network centrality metrics approach perform in comparison to the previously developed Automated Requirement Change Propagation Prediction (ARCPP) tool? Applying the notion of interference, requirement nodes in which change occurs are virtually removed from the network to simulate a change scenario and the changes in values of select metrics of all other nodes are observed. Based on the amount of metric value changes the remaining nodes experience, propagated requirement nodes are predicted. Counting betweenness centrality, left eigenvector centrality, and authority centrality serve as top performing metrics and their performances are comparative to ARCPP tool.

A Distributed Least-Squares Algorithm in Wireless Sensor Networks With Unknown and Limited Communications

In this article, the authors propose a new distributed least-squares algorithm to address the sensor fusion problem in using wireless sensor networks (WSN) to monitor the behaviors of large-scale multiagent systems. Under a mild assumption on network observability, that is, each sensor can take the measurements of a limited number of agents but the complete multiagent systems are covered under the union of all sensors in the network, the proposed algorithm achieves the estimation consensus if local information exchange can be performed among sensors. The proposed distributed least-squares algorithm can handle the directed communication network by explicitly estimating the left eigenvector corresponding to the largest eigenvalue of the sensing/communication matrix. The convergence of the proposed algorithm is analyzed, and simulation results are provided to further illustrate its effectiveness.