Discrete Dynamic Network Research Articles

Robust impulsive synchronization of linear discrete dynamical networks

This paper aims to study robust impulsive synchronization problem for uncertain linear discrete dynamical network. For the discrete dynamical networks with unknown but bounded linear coupling, by introducing the concept of uniformly positive definite matrix functions, some robust impulsive controllers are designed, which ensure that the state of a discrete dynamical network globally asymptotically synchronizes with an arbitrarily assigned state of an isolate node of the network. This paper also investigates the synchronization problem where the network coupling functions are uncertain but bounded nonlinear functions. Finally,two examples are simulated to illustrate our results.

Genetic design of discrete dynamical basis networks that approximate data sequences and functions

This paper extends research in the area of biologically inspired, discrete dynamical basis networks (DDBNs). While similar to locally recurrent globally feedforward (LRGF) networks (Tsoi and Back 1994), DDBNs operate at a lower level of abstraction and were inspired by research in the areas of Control Systems, Artificial Intelligence, and Neurobiology. As described previously, DDBNs can approximate data sequences and consist of networks of simple, bounded mathematical operators (Jones and Olmsted 2003). This paper examines the characteristics of genetically designed DDBNs and compares them with tree-based genetic programs (TBGPs), biological neural networks, and backpropagation neural networks (NNs). Experimental evidence indicates that DDBNs are capable of computing simple logic functions in addition to approximating data sequences.

Discrete dynamics lab: tools for investigating cellular automata and discrete dynamical networks

DDLab is interactive graphics software for creating and visualizing discrete dynamical networks, and studying their behavior in terms of both space‐time patterns and basins of attraction. The networks can range from cellular automata to random Boolean networks. This article provides some general background, and gives the flavor of DDLab with a range of examples. Further details can be found at www.ddlab.comwww.ddlab.com

Parallel Algorithms for Dynamic Shortest Path Problems

The development of intelligent transportation systems (ITS) and the resulting need for the solution of a variety of dynamic traffic network models and management problems require faster‐than‐real‐time computation of shortest path problems in dynamic networks. Recently, a sequential algorithm was developed to compute shortest paths in discrete time dynamic networks from all nodes and all departure times to one destination node. The algorithm is known as algorithm DOT and has an optimal worst‐case running‐time complexity. This implies that no algorithm with a better worst‐case computational complexity can be discovered. Consequently, in order to derive algorithms to solve all‐to‐one shortest path problems in dynamic networks, one would need to explore avenues other than the design of sequential solution algorithms only. The use of commercially‐available high‐performance computing platforms to develop parallel implementations of sequential algorithms is an example of such avenue. This paper reports on the design, implementation, and computational testing of parallel dynamic shortest path algorithms. We develop two shared‐memory and two message‐passing dynamic shortest path algorithm implementations, which are derived from algorithm DOT using the following parallelization strategies: decomposition by destination and decomposition by transportation network topology. The algorithms are coded using two types of parallel computing environments: a message‐passing environment based on the parallel virtual machine (PVM) library and a multi‐threading environment based on the SUN Microsystems Multi‐Threads (MT) library. We also develop a time‐based parallel version of algorithm DOT for the case of minimum time paths in FIFO networks, and a theoretical parallelization of algorithm DOT on an ‘ideal’ theoretical parallel machine. Performances of the implementations are analyzed and evaluated using large transportation networks, and two types of parallel computing platforms: a distributed network of Unix workstations and a SUN shared‐memory machine containing eight processors. Satisfactory speed‐ups in the running time of sequential algorithms are achieved, in particular for shared‐memory machines. Numerical results indicate that shared‐memory computers constitute the most appropriate type of parallel computing platforms for the computation of dynamic shortest paths for real‐time ITS applications.

Discrete type dynamic synapses neural network: Speech recognition application

A discrete type of the Dynamic Synapses Neural Network (DSNN) has been developed and applied to speech recognition. In order to speed up the training time of the network, a new discrete time implementation of the original DSNN [J.-S. Liaw and T. W. Berger, 1996] has been introduced based on the impulse invariant transformation. The new architecture of the network was trained with the Genetic Algorithms [H. H. Namarvar et al., 2001] and tested against the continues-type DSNN. The overall speed of the new algorithm with discrete-time difference equation set is about 13 times faster than the same algorithm with the continuous differential equation set. This significant reduction of processing time not only decreases the training time but also makes the system better suited for real-time speech recognition tasks. [Work supported by DARPA.]

Discrete Dynamic Shortest Path Problems in Transportation Applications: Complexity and Algorithms with Optimal Run Time

A solution is provided for what appears to be a 30-year-old problem dealing with the discovery of the most efficient algorithms possible to compute all-to-one shortest paths in discrete dynamic networks. This problem lies at the heart of efficient solution approaches to dynamic network models that arise in dynamic transportation systems, such as intelligent transportation systems (ITS) applications. The all-to-one dynamic shortest paths problem and the one-to-all fastest paths problems are studied. Early results are revisited and new properties are established. The complexity of these problems is established, and solution algorithms optimal for run time are developed. A new and simple solution algorithm is proposed for all-to-one, all departure time intervals, shortest paths problems. It is proved, theoretically, that the new solution algorithm has an optimal run time complexity that equals the complexity of the problem. Computer implementations and experimental evaluations of various solution algorithms support the theoretical findings and demonstrate the efficiency of the proposed solution algorithm. The findings should be of major benefit to research and development activities in the field of dynamic management, in particular real-time management, and to control of large-scale ITSs.

A New Algorithm for Shortest Paths in Discrete Dynamic Networks

Abstract In this paper we study two shortest paths problems in discrete dynamic hetWorks: the one-to-all for one departure time interval, and the all-to-one for all departure time intervals. Early results are revisited. New properties of these problems are established and exploited in developing solution algorithms. A new and simple solution algorithm for the all-to-one fastest paths problem for all departure time intervals is proposed. It is proved, analytically, that the new solution algorithm has an optimal running time complexity that equals the complexity of the problem. Computer implementations and experimental evaluations of four solution algorithms support analytical results and demonstrate the efficiency of the proposed algorithm. We expect our findings to be of major benefit to research and development activities in the field of dynamic management of large-scale transportation systems.

A Discrete Time, Nested Cost Operator Approach to the Dynamic Network User Equilibrium Problem

In this paper we formulate the dynamic network user equilibrium problem as a variational inequality problem in discrete time in terms of unit path cost functions. We then show how arc exit flow functions and nested cost operators can be used to calculate unit path costs given the departure time and route choices of network users. We also demonstrate that, assuming certain regularity conditions hold, a discrete time dynamic network user equilibrium is guaranteed to exist. Finally, a heuristic algorithm and numerical results are presented.

Searching time-table networks

In this paper we present an application of AI search techniques to a class of problems that arise in transportation systems analysis. Rather than adapting the time-space network formulation typically used in Operations Research, we propose a discrete dynamic network to represent a scheduled service network. In a discrete dynamic network, there are finite, discrete, predetermined possibilities for moving from one vertex to another. Visiting a vertex has a cost (possibly zero), which may depend both on how the vertex was reached and how it will be left.We describe the DYNET search algorithm for finding optimal paths in discrete dynamic networks. DYNET has been implemented in a working system (TRAINS) which searches the entire Dutch railway services network. An optimal path in a discrete dynamic network makes us arrive at our destination as early as possible (given our planned earliest departure time), and given this earliest arrival time (eat), will allow us to leave as late as possible, thereby guaranteeing a shortest path relative to the eat. DYNET first conducts a forward search to find the earliest possible arrival time, then a backward search which uses results of the forward search, to find the latest departure to arrive at that eat. Various AI techniques (symmetries, abstraction spaces, distance estimates, etc.) improve the performance of DYNET.