Random neural networks with synchronized interactions

Large-scale distributed systems, such as natural neuronal and artificial systems, have many local interconnections, but they often also have the ability to propagate information very fast over relatively large distances. Mechanisms that enable such behavior include very long physical signaling paths and possibly saccades of synchronous behavior that may propagate across a network. This letter studies the modeling of such behaviors in neuronal networks and develops a related learning algorithm. This is done in the context of the random neural network (RNN), a probabilistic model with a well-developed mathematical theory, which was inspired by the apparently stochastic spiking behavior of certain natural neuronal systems. Thus, we develop an extension of the RNN to the case when synchronous interactions can occur, leading to synchronous firing by large ensembles of cells. We also present an O(N3) gradient descent learning algorithm for an N-cell recurrent network having both conventional excitatory-inhibitory interactions and synchronous interactions. Finally, the model and its learning algorithm are applied to a resource allocation problem that is NP-hard and requires fast approximate decisions.     

Improved neural heuristics for multicast routing

Future networks must be adequately equipped to handle multipoint communication in a fast and economical manner. Services requiring such support include desktop video conferencing, tele-classrooms, distributed database applications, etc. In networks employing the asynchronous transfer mode (ATM) technology, routing a multicast is achieved by constructing a minimum cost tree that spans the source and all the destinations. When the network is modeled as a weighted, undirected graph, the problem is that of finding a minimal Steiner tree for the graph, given a set of destinations. The problem is known to be NP-complete. Consequently, several heuristics exist which provide approximate solutions to the Steiner problem in networks, We show how the random neural network (RNN) can be used to significantly improve the quality of the Steiner trees delivered by the best available heuristics which are the minimum spanning tree heuristic and the average distance heuristic. We provide an empirical comparison and find that the heuristics which are modified using the neural network yield significantly improved trees     

Stationary deterministic flows in discrete systems 1

We consider a deterministic system whose state space is the n-dimensional first orthant. It may be considered as a network of (deterministic) queues, a Karp-Miller vector addition system, a Petri net, a complex computer system, etc. Weak assumptions are then made concerning the asymptotic or limiting behaviour of the instants at which events are observed across a cut in the system: these instants may be considered as ‘arrival’ or ‘departure’ instants. Thus, like in operational analysis, we deal with deterministic and observable properties and we need no stochastic assumptions or restrictions (such as independence, identical distributions, etc.). We consider however asymptotic or stationary properties, as in conventional queuing analysis. Under our assumptions a set of standard theorems are proved: concerning arrival and departure instant measures, concerning ‘birth and death’ type equations, and concerning Little's formula. Our intention is to set the framework for a new approach to performance modelling of computer systems in a context close to that used in actual measurements, but taking into account infinite time behaviour in order to take advantage of the useful mathematical properties of asymptotic results.     

Probabilistic models of computer systems—Part I (exact results)

Summary This paper is a survey of certain known results concerning networks of queues. The choice of the topics presented has been made with special emphasis on mathematical results which can be applied to the analysis and synthesis of mathematical or simulation models of complex computer systems in which an ensemble of resources is shared among a set of user programs. The subjects covered include the Jackson, and Gordon and Newell theorems; the work-rate theorems of Chang, Lavenberg and Traiger; the Baskett, Chandy, Muntz, Palacios results. We also discuss in a unified manner problems related to Poisson processes in queueing networks. Companion papers (Parts II, III) will present results concerning approximations to queueing networks and some of their applications to computer system performance evaluation.     

An Analytic Evaluation of the Performance of the "Send and Wait" Protocol

In this study, we are concerned with a simple error control protocol, the "send and wait" protocol, which uses the classical technique of positive acknowledgment and time-out periods. We first analyze the influence of the time-out on the packet transmission rate. Then we use a queuing analysis to obtain the ergodicity condition and to compute the buffer queue length probability distribution. Finally we compute buffer overflow when a finite number of packets are allowed to enter the node. This analysis allows us to obtain optimum values of the time-out in order to maximize throughput, or to minimize average transit delay through the node or buffer overflow probabilities.     

Area-based results for mine detection

The cost and the closely related length of time spent in searching for mines or unexploded ordnance (UXO) may well be largely determined by the number of false alarms. False alarms can result in time consuming digging of soil or in additional multisensory tests in the minefield. The authors consider two area-based methods for reducing false alarms. These are: (a) the previously known “declaration” technique and (b) the new δ technique, which they introduce. They first derive expressions and lower bounds for false-alarm probabilities as a function of declaration area and discuss their impact on receiver operation characteristic (ROC) curves. Second, they exploit characteristics of the statistical distribution of sensory energy in the immediate neighborhood of targets and of false alarms from available calibrated data, to propose the δ technique, which significantly improves discrimination between targets and false alarms. The results are abundantly illustrated with statistical data and ROC curves using electromagnetic-induction sensor data made available through DARPA from measurements at various calibrated sites     

Simulation with learning agents

We propose that learning agents (LAs) be incorporated into simulation environments in order to model the adaptive behavior of humans. These LAs adapt to specific circumstances and events during the simulation run. They would select tasks to be accomplished among a given set of tasks as the simulation progresses, or synthesize tasks for themselves based on their observations of the environment and on information they may receive from other agents. We investigate an approach in which agents are assigned goals when the simulation starts and then pursue these goals autonomously and adaptively. During the simulation, agents progressively improve their ability to accomplish their goals effectively and safely. Agents learn from their own observations and from the experience of other agents with whom they exchange information. Each LA starts with a given representation of the simulation environment from which it progressively constructs its own internal representation and uses it to make decisions. The paper describes how learning neural networks can support this approach and shows that goal based learning may be used effectively used in this context. An example simulation is presented in which agents represent manned vehicles; they are assigned the goal of traversing a dangerous metropolitan grid safely and rapidly using goal based reinforcement learning with neural networks and compared to three other algorithms     

Oscillatory corticothalamic response to somatosensory input

We construct a model of the thalamocortical feedback loop using the Random Neural Network model to provide a theoretical explanation for cortical and thalamic damped rapid (circa 60-100 Hz) oscillations which have been observed in lightly anesthesized rats with somatosensory input Nicolelis (1997). Experimental data corroborates the choice of model parameter settings. Model predictions indicate that positive feedback loops and large signaling delays within cortex significantly determine the oscillatory phenomenon and its duration (i.e. its decay), while positive feedback from cortex to thalamus is needed to exhibit oscillations in thalamus.