An integral equation describing the time evolution of the population activity in a homogeneous pool of spiking neurons of the integrate-and-fire type is discussed. It is analytically shown that transients from a state of incoherent firing can be immediate. The stability of incoherent firing is analyzed in terms of the noise level and transmission delay and a bifurcation diagram is derived. The response of a population of noisy integrate-and-fire neurons to an input current of small amplitude is calculated and characterized by a linear filter L. The stability of perfectly synchronized `locked' solutions is analyzed.

The interconnection of local area networks is increasingly important, but little data are available on the characteristics of the aggregate traffic that LANs will be submitting to the interconnection media. In order to understand the interactions between LANs and the proposed interconnection networks (MANs, WANs, and BISDN networks), it is necessary to study the behavior of this external LAN traffic over many time scales – from milliseconds to hundreds of seconds. We present a high time-resolution hardware monitor for Ethernet LANs that avoids the shortcomings of previous monitoring tools, such as traffic burst clipping and timestamp jitter. Using data recorded by our monitor for several hundred million Ethernet packets, we present an overview of the short-range time correlations in external LAN traffic. Our analysis shows that LAN traffic is extremely bursty across time domains spanning six orders of magnitude. We compare this behavior with simple formal traffic models and employ the data in a trace-driven simulation of the LAN-BISDN interface proposed for the SMDS SM service. Our results suggest that the pronounced short-term traffic correlations, together with the extensive time regime of traffic burstiness, strongly influence the patterns of loss and delay induced by LAN interconnection. 1.

This paper examines the phenomenon of congestion in order to better understand the congestion management techniques that will be needed in high-speed, cell-based networks. The first step of this study is to use high time-resolution local area network (LAN) traffic data to explore the nature of LAN traffic variability. Then, we use the data for a trace-driven simulation of a connectionless service that provides LAN interconnection. The simulation allows us to characterize what congestion might look like in a high-speed, cell-based network. The most

AsTRAcT The statistical analysis oftwo simultaneously observed trainsofneuronal spikes is described, using as a conceptual framework the theory of stochastic point processes. The first statistical question that arises is whether the observed trains are independent; statistical techniques for testing independence are developed around the notion that, under the null hypothesis, the times of spike occurrence in one train represent random instants in time with respect to the other. Ifthe null hypothesis is rejected-if dependence is attributed to the trains-the problem then becomes that of characterizing the nature and source of the observed dependencies. Statistical signs of various classes of dependencies, including direct interaction and shared input, are discussed and illustrated through computer simulations of interacting neurons. The effects ofnonstationarities on the statistical measures for simultaneous spike trains are also discussed. For two-train comparisons of irregularly discharging nerve cells, moderate nonstationarities areshown tohave little effecton the detection of interactions. Combining repetitive stimulation and simultaneous recording of spike trains from two (or more) neurons yields additional clues as to possible modes of interaction among the monitored neurons; the theory presented is illustrated by an application to experimentally obtained data from auditory neurons. Acompanion paper covers the analysis ofsingle spike trains.

Alarge amount of effort is expended every year on finding and patching security holes. The underlying rationale for this activity is that it increases welfare by decreasing the number of vulnerabilities available for discovery and exploitation by bad guys, thus reducing the total cost of intrusions. Given the amount of effort expended, we would expect to see noticeable results in terms of improved software quality. However, our investigation provides a mixed answer: the data does not allow us to exclude the possibility that the rate of vulnerability finding in any given piece of software is constant over long periods of time. Ifthere islittle or no quality improvement, then we have no reason to believe that that the disclosure of vulnerabilities reduces the overall cost of intrusions. 1

Modeling &e reliability of distributed systems requires a good understanding of the reliability of the components'. Careful modeling allows highly fault-tolerant distributed data applications to be constructed at the least cost. Failure and repair

In previous work [24], Fractal Point Processes (FPPs) have been proposed as novel tools for understanding, modeling and analyzing diverse types of self-similar traffic behavior. We apply the FPP models in the context of network traffic modeling and performance analysis. Two qualitatively different fractal data sets (Bellcore Ethernet traces) are characterized by FPP models. Comparison of model-driven and trace-driven queueing simulation results show that the matched models yield close agreement with the traces over a wide range of system parameters. We also show that under suitable conditions, the FPP models yield Gaussian processes. Queueing simulation shows that the FPP models can be computationally efficient alternatives for generating fractional Gaussian noise processes. Finally, we divide fractal traffic into two types, applicationlevel fractal traffic and network-level fractal traffic, and argue that each type has radically different implications for the design and control of fut...

We analyze the effect of noise in integrate-and-fire neurons driven by timedependent input, and compare the diffusion approximation for the membrane potential to escape noise. It is shown that for time-dependent sub-threshold input, diffusive noise can be replaced by escape noise with a hazard function that has a Gaussian dependence upon the distance between the (noise-free) membrane voltage and threshold. The approximation is improved if we add to the hazard function a probability current proportional to the derivative of the voltage. Stochastic resonance in response to periodic input occurs in both noise models and exhibits similar characteristics.

TES (Transform-Expand-Sample) is a versatile methodology for modeling stationary time series with general marginal distributions and a broad range of dependence structures. From the viewpoint of Monte Carlo simulation, TES constitutes a new and flexible input analysis approach whose principal merit is its potential ability to simultaneously capture first-order and second-order statistics of empirical time series. That is, TES is designed to fit an arbitrary empirical marginal distribution (histogram), and to simultaneously approximate the leading empirical autocorrelations. This paper is a tutorial introduction to the theory of TES processes and to the modeling methodology based on it. It employs a didactic approach which relies heavily on visual intuition as a means of conveying key ideas and an aid in building deep understanding of TES. This approach is in line with practical TES modeling which itself is based on visual interaction under software support. The interaction t...

Abstract — A key criterion in the design of high-speed networks is the probability that the buffer content exceeds a given threshold. We consider Ò independent identical traffic sources modelled as point processes, which are fed into a link with speed proportional to Ò. Under fairly general assumptions on the input processes we show that the steady state probability of the buffer content exceeding a threshold � � tends to the corresponding probability assuming Poisson input processes. We verify the assumptions for a large class of long-range dependent sources commonly used to model data traffic. Our results show that with superposition, significant multiplexing gains can be achieved for even smaller buffers than suggested by previous results, which consider Ç Ò buffer size. Moreover, simulations show that for realistic values of the exceedance probability and moderate utilisations, convergence to the Poisson limit takes place at reasonable values of the number of sources superposed. This is particularly relevant for high-speed networks in which the cost of high-speed memory is significant. Keywords—Long-range dependence, overflow probability, Poisson limit, heavy tails, point processes, multiplexing.