Amplitude equations for coupled electrostatic waves in the limit of weak instability

We consider the simplest instabilities involving multiple unstable electrostatic plasma waves corresponding to four-dimensional systems of mode amplitude equations. In each case the coupled amplitude equations are derived up to third order terms. The nonlinear coefficients are singular in the limit in which the linear growth rates vanish together. These singularities are analyzed using techniques developed in previous studies of a single unstable wave. In addition to the singularities familiar from the one mode problem, there are new singularities in coefficients coupling the modes. The new singularities are most severe when the two waves have the same linear phase velocity and satisfy the spatial resonance condition $k_2=2k_1$. As a result the short wave mode saturates at a dramatically smaller amplitude than that predicted for the weak growth rate regime on the basis of single mode theory. In contrast the long wave mode retains the single mode scaling. If these resonance conditions are not satisfied both modes retain their single mode scaling and saturate at comparable amplitudes.Comment: 34 pages (Latex), no figure

Low Cost Quality of Service Multicast Routing in High Speed Networks

Many of the services envisaged for high speed networks, such as B-ISDN/ATM, will support real-time applications with large numbers of users. Examples of these types of application range from those used by closed groups, such as private video meetings or conferences, where all participants must be known to the sender, to applications used by open groups, such as video lectures, where partcipants need not be known by the sender. These types of application will require high volumes of network resources in addition to the real-time delay constraints on data delivery. For these reasons, several multicast routing heuristics have been proposed to support both interactive and distribution multimedia services, in high speed networks. The objective of such heuristics is to minimise the multicast tree cost while maintaining a real-time bound on delay. Previous evaluation work has compared the relative average performance of some of these heuristics and concludes that they are generally efficient, although some perform better for small multicast groups and others perform better for larger groups. Firstly, we present a detailed analysis and evaluation of some of these heuristics which illustrates that in some situations their average performance is reversed; a heuristic that in general produces efficient solutions for small multicasts may sometimes produce a more efficient solution for a particular large multicast, in a specific network. Also, in a limited number of cases using Dijkstra's algorithm produces the best result. We conclude that the efficiency of a heuristic solution depends on the topology of both the network and the multicast, and that it is difficult to predict. Because of this unpredictability we propose the integration of two heuristics with Dijkstra's shortest path tree algorithm to produce a hybrid that consistently generates efficient multicast solutions for all possible multicast groups in any network. These heuristics are based on Dijkstra's algorithm which maintains acceptable time complexity for the hybrid, and they rarely produce inefficient solutions for the same network/multicast. The resulting performance attained is generally good and in the rare worst cases is that of the shortest path tree. The performance of our hybrid is supported by our evaluation results. Secondly, we examine the stability of multicast trees where multicast group membership is dynamic. We conclude that, in general, the more efficient the solution of a heuristic is, the less stable the multicast tree will be as multicast group membership changes. For this reason, while the hybrid solution we propose might be suitable for use with closed user group multicasts, which are likely to be stable, we need a different approach for open user group multicasting, where group membership may be highly volatile. We propose an extension to an existing heuristic that ensures multicast tree stability where multicast group membership is dynamic. Although this extension decreases the efficiency of the heuristics solutions, its performance is significantly better than that of the worst case, a shortest path tree. Finally, we consider how we might apply the hybrid and the extended heuristic in current and future multicast routing protocols for the Internet and for ATM Networks.

A Hybrid Approach to Quality of Service Multicast Routing

Several multicast routing heuristics have been proposed to support multimedia services, both interactive and distribution, in high speed networks such as B-ISDN/ATM. Since such services may have large numbers of members and have real-time constraints, the objective of the heuristics is to minimise the multicast tree cost while maintaining a bound on delay. Previous evaluation work has compared the relative average performance of some of these heuristics and concludes that they are generally efficient, although some perform better for small multicast groups and others perform better for larger groups. We present a detailed analysis and evaluation of some of these heuristics which illustrate that in some situations their average performance is reversed; a heuristic that in general produces efficient solutions for small multicasts may sometimes produce a more efficient solution for a particular large multicast/network combination. Also, in a limited number of cases using Dijkstra's algorithm produces the best result. We conclude that the specific efficiency of a heuristics solution depends on the topology of both the network and the multicast, and that it is difficult to predict. Because of this unpredictability we propose the integration of two heuristics with Dijkstra's shortest path tree algorithm to produce a hybrid that consistently generates efficient multicast solutions for all possible multicast groups in any network. These heuristics are based on Dijkstra's algorithm which maintains acceptable time complexity for the hybrid, and they rarely produce inefficient solutions for the same network/multicast. The resulting performance attained is generally good and in the rare worst cases is that of the shortest path tree. The performance of our proposal is supported by our evaluation results. We conclude by discussing the types of networks for which this method is most appropriate and identifying further work

FUNNet:a novel biologically-inspired routing algorithm based on fungi

Future data communication networks show three emerging trends: increasing size of networks, increasing traffic volumes and dynamic network topologies. Efficient network management solutions are required that are scalable, can cope with large, and increasing, traffic volumes and provide decentralised and adaptive routing strategies that cope with the dynamics of the network topology. Routing strategies are an important aspect of network management as they have a significant influence on the overall network performance. This paper introduces the preliminary studies for FUNNet, a new routing algorithm inspired by the kingdom of Fungi. Fungi form robust, resilient and responsive networks and these networks change topology as a consequence of changes in local conditions. Fungi are capable of expanding in size as they self-regulate and optimise the balance between exploration and exploitation which is dependent on the transport of the internal resource, i.e. ‘traffic’, within the network. FUNNet exploits the biological processes that are responsible for simulating fungal networks in a bio-inspired routing protocol. The initial results are positive and suggest that fungal metaphors can improve network management, although further evaluation of more complex scenarios is required

POPULATION ECOLOGY OF THE NORTHERN SLIMY SALAMANDER (PLETHODON GLUTINOSUS) IN EAST-CENTRAL ILLINOIS

The importance of plethodontid salamanders in forested habitats has been recognized for decades and more recently plethodontids have been touted as a model taxon for monitoring ecosystem integrity and recovery. However, basic demographic data that are crucial to conservation and management plans are currently lacking for many species and regions. The objectives of our study were to characterize the population density, biomass, and capture success of a peripheral population of Plethodon glutinosus to provide a comparison for eastern populations and set a baseline for future monitoring of Midwestern populations. We estimated the population density of P. glutinosus at our site to be 0.41 salamanders/m2, with an estimated biomass of 0.70 g/m2. We did not find any evidence for temperature or precipitation affecting capture success. Our results showed that our density estimate falls within the range of other population ecology studies of Plethodon and sets a baseline for other peripheral Midwestern populations

Modified confidence intervals for the Mahalanobis distance

Reiser (2001) proposes a method of forming confidence interval for a Mahalanobis distance that yields intervals which have exactly the nominal coverage, but sometimes the interval is View the MathML source (0,0). We consider the case where Mahalanobis distance quantifies the difference between an individual and a population mean, and suggest a modification that avoids implausible intervals