Linh Thi Hoai Nguyen

Obstacle avoiding patterns and cohesiveness of fish school

This paper is devoted to studying obstacle avoiding patterns and cohesiveness of fish school. First, we introduce a model of stochastic differential equations (SDEs) for describing the process of fish schools obstacle avoidance. Second, on the basis of the model we find obstacle avoiding patterns. Our observations show that there are clear four obstacle avoiding patterns, namely, Rebound, Pullback, Pass and Reunion, and Separation. Furthermore, the emerging patterns change when parameters change. Finally, we present a scientific definition for fish schools cohesiveness that will be an internal property characterizing the strength of fish schooling. There are then evidences that the school cohesiveness can be measured through obstacle avoiding patterns.

Algebraic connectivity of multi-agent systems with homogeneous substructure

This paper presents a method for finding the algebraic connectivity of multi-agent systems with homogeneous substructure. The systems consist of several homogeneous substructure where only one vertex is connected with main structure. Their algebraic connectivity can be calculated from properties of graphs corresponding to substructure and main structure. Also, it is shown that the algebraic connectivity of an entire system is less than or equals to that of substructure and that of main structure.

Algebraic connectivity of network-of-networks having a graph product structure

In this paper, we present a method for finding the algebraic connectivity of network-of-networks having a graph product structure. The network consists of several homogeneous (identical) subsystems connected with each other according to an interconnection graph. We show that the algebraic connectivity can be calculated from properties of graphs corresponding to the subsystem and the interconnection. Furthermore, we indicate that the algebraic connectivity of the entire system does not exceed those of the subsystem and the interconnection.

Gossip algorithms for clustering problems

This paper presents several algorithms for multi-dimensional data clustering. The main difference of the algorithms introduced in this paper comparing to known ones is that the algorithms are multi-agent based and gossip. Hence, the number of computation in each step is not too large even for large data and the computational burden can be distributed. The basic algorithm is described as follows. Each data object is assigned to an agent in a network and its attributes constitute to a vector which is considered as the initial state of the agent. A common confidence threshold is set for all of the agents. The states of agents in the network will be updated time by time according to an iterative procedure: At each time, (i) two arbitrary agents are chosen randomly, (ii) they exchange their states, and (iii) if the distance between their states does not exceed the confidence threshold, they update their states as the average of the two. Under a certain condition, this algorithm converges almost surely in an equilibrium point such that any two agents either have the same final state or have distinct states which differ more than the confidence threshold from each other. In this way, the given data objects are partitioned into groups such that ones in the same group correspond to the agents with the same final state. Some modified algorithms for improving the performance of clustering and/or getting some prescribed condition are also introduced.