This paper proposes a scale-free highly clustered echo state network (SHESN). We designed the SHESN to include a naturally evolving state reservoir according to incremental growth rules that account for the following features: (1) short characteristic path length, (2) high clustering coefficient, (3) scale-free distribution, and (4) hierarchical and distributed architecture. This new state reservoir contains a large number of internal neurons that are sparsely interconnected in the form of domains. Each domain comprises one backbone neuron and a number of local neurons around this backbone. Such a natural and efficient recurrent neural system essentially interpolates between the completely regular Elman network and the completely random echo state network (ESN) proposed by Jaeger We investigated the collective characteristics of the proposed complex network model. We also successfully applied it to challenging problems such as the Mackey-Glass (MG) dynamic system and the laser time-series prediction. Compared to the ESN, our experimental results show that the SHESN model has a significantly enhanced echo state property and better performance in approximating highly complex nonlinear dynamics. In a word, this large scale dynamic complex network reflects some natural characteristics of biological neural systems in many aspects such as power law, small-world property, and hierarchical architecture. It should have strong computing power, fast signal propagation speed, and coherent synchronization.

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Collective Behavior of a Small-World Recurrent Neural System With Scale-Free Distribution

The increasing complexity of computer networks calls for the development of new models for their simulation. Cellular automata (CAs) are a well-known and successful model for complex systems. This paper presents a system for modeling and simulation of computer networks based on CAs. More specifically, a 2D NaSch CA computer network model has been developed, and several networks were simulated. Algorithms for connectivity evaluation, system reliability evaluation, and shortest path computation in a computer network have also been implemented. Our system, called Net_CA system, was designed and developed as an interactive tool that offers automated modeling with the assistance of a dynamic and user-friendly graphical environment. The proposed system also produces automatically synthesizable very high speed integrated circuits hardware description language code leading to the parallel hardware implementation of the aformentioned CA algorithms. In terms of circuit design and layout, ease of mask generation, silicon area utilization, and maximization of achievable clock speed, CAs are perhaps the computational structures best suited for a fully parallel very large scale integrated realization. The simulation algorithms developed in the present paper offer high flexibility. Furthermore, connection reliability and other important parameters are inputs to the algorithms, rendering Net_CA a very reliable and fast simulator for wireless networks, ad hoc networks, and generally, for low connection reliability networks.

A CAD System for Modeling and Simulation of Computer Networks Using Cellular Automata

In this paper, we analyze a population model comprising organisms that alternate between nomadic and colonial behaviours by considering stochastic noise. Incorporating stochastic noise into the population dynamics will allow a wide range of environmental fluctuations to be modelled. The theoretical framework is also generalized to include resource depletion by both nomadic and colonial sub-populations, and an ecologically realistic population size-dependent switching scheme is now proposed. We demonstrate the robustness of the present model to stochastic noise, and the use of novel generalized pure time-based switching schemes to achieve consecutive subsidence-recovery cycles and long-term proliferation. Our results are of relevance to many physical and biological systems.

Nomadic-colonial switching with stochastic noise: subsidence-recovery cycles and long-term growth

We present theoretical and numerical results for the performance of a multiprocessor network modeled as a ring and as a toroidal square lattice of nodes with local processors that generate messages for output ports/buffers. The output buffers are assumed to have infinite capacity, and the service time is deterministic. Two models are considered. One assumes that every processor generates messages with rate λ per time slot and per output port/buffer. The other model considers that the generation rate of a node depends on the intensity of the flow of arriving messages. Explicit expressions for the distribution of queue lengths, the average number of messages in the buffers, the average latency, and the critical network load depending on the distance between the source and the destination are obtained. Simulation results show excellent agreement with theoretical predictions based on the assumption of independent queues.

Critical phenomena in discrete-time interconnection networks

In this paper, a new model of evolving networks is proposed based on the dynamical behaviors of nodes in the network. The probability that an existing node in the current network receives a new link from the newly added node is proportional to the defined "activity" of that particular node, which is equivalent to the energy signal of the system from a control theory point of view. This network is found to have the scale-free feature with the degree distribution in a power-law form. This model provides another explanation for the emergence of scale-free networks in many real-world examples.

Evolving Networks Driven by Node Dynamics

Cellular automaton modeling of computer network

Analysis of power spectrum and 1/f type power law in a complex computer network model

Behaviours of networks with different topologies and protocols

The storage ring of the present Hefei Light Source (HLS) consists of four double-bend achromat lattice cells, each with two straight sections. In this paper, a modified double-double bend achromat (DDBA) lattice is proposed for an ultra-low emittance design of HLS, where the circumference of the storage ring and the lengths of all straight sections remain the same. Compared to the typical DDBA lattice, this modified lattice can obtain both lower emittance and lower dispersion in the mid-straight section, thus providing higher brightness of insertion device radiation. The natural emittance of the HLS designed with the modified DDBA lattice is 3.9 nm·rad, about one order of magnitude lower than that of the present HLS.

Zhiliang Ren

Papers

Cellular automaton modeling of computer network

Analysis of power spectrum and 1/f type power law in a complex computer network model

Behaviours of networks with different topologies and protocols

Modified double-double bend achromat lattice for an ultra-low emittance design of the HLS

Spatio-temporal organization of a cellular automaton model for computer network