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Estimating the parameters of a nonhomogeneous Poisson process with linear rate
 Telecommunication Systems
, 1996
"... Motivated by telecommunication applications, we investigate ways to estimate the parameters of a nonhomogeneous Poisson process with linear rate over a finite interval, based on the number of counts in measurement subintervals. Such a linear arrivalrate function can serve as a component of a piecew ..."
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Cited by 25 (14 self)
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Motivated by telecommunication applications, we investigate ways to estimate the parameters of a nonhomogeneous Poisson process with linear rate over a finite interval, based on the number of counts in measurement subintervals. Such a linear arrivalrate function can serve as a component of a piecewiselinear approximation to a general arrivalrate function. We consider ordinary least squares (OLS), iterative weighted least squares (IWLS) and maximum likelihood (ML), all constrained to yield a nonnegative rate function. We prove that ML coincides with IWLS. As a reference point, we also consider the theoretically optimal weighted least squares (TWLS), which is least squares with weights inversely proportional to the variances (which would not be known with data). Overall, ML performs almost as well as TWLS. We describe computer simulations conducted to evaluate these estimation procedures. None of the procedures differ greatly when the rate function is not near 0 at either end, but when the rate function is near 0 at one end, TWLS and ML are significantly more effective than OLS. The number of measurement subintervals (with fixed total interval) makes surprisingly little difference when the rate function is not near 0 at either end. The variances are higher with only two or three
Extracting Oscillations: Neuronal Coincidence Detection with Noisy Periodic Spike Input
, 1998
"... How does a neuron vary its mean output firing rate if the input changes from random to oscillatory coherent but noisy activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidencedetection properties of an integra ..."
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Cited by 19 (6 self)
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How does a neuron vary its mean output firing rate if the input changes from random to oscillatory coherent but noisy activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidencedetection properties of an integrateandfire neuron. We derive an expression indicating how coincidence detection depends on neuronal parameters. Specifically, we show how coincidence detection depends on the shape of the postsynaptic response function, the number of synapses, and the input statistics, and we demonstrate that there is an optimal threshold. Our considerations can be used to predict from neuronal parameters whether and to what extent a neuron can act as a coincidence detector and thus can convert a temporal code into a rate code.
Simulating Events to Generate Synthetic Data for Pervasive Spaces
"... Abstract—a constant problem in the generation of data for testing pervasive spaces is the lack of real standards in the data generation, and the cost of the pervasive space itself. This hinders the development of the pervasive spaces. If pervasive systems is going to be included into a particular ma ..."
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Abstract—a constant problem in the generation of data for testing pervasive spaces is the lack of real standards in the data generation, and the cost of the pervasive space itself. This hinders the development of the pervasive spaces. If pervasive systems is going to be included into a particular mass production device, for example cars, you should be able to give a percentage of how secure is your system. For example, testing the robustness of the new artificial intelligence layers to increase the capabilities of the pervasive spaces will require large amounts of data portraying different scenarios. Then, it is necessary to design realistic simulations of the pervasive spaces to study the possible advantages and limitations of particular collections of actuators, sensors and systems. A first steep in this direction is trying to simulate chain of events from the sensor output space by the use of pattern recognition models. Specifically, we propose the use of Markov Chains to generate patterns of events due to the fact that they have been used successfully to classify chains of events in machine learning and computer vision. In addition, we propose the use of Poisson spike generators for the randomization of the time stamps for these events. Finally, we use a series of distributions over the ranges of each sensor to obtain a realistic spread on the sensor output values. We believe these strategies will make for a more realistic simulation of the space of sensors in a pervasive space. Index Terms—pervasive spaces, simulation, Markov chains, state machines, spike Poisson generator.
Philippe BAPTISTE
, 2010
"... Analyse des incertitudes dans les flux du trafic aérien Analysis of uncertainties in airtraffic flow par ..."
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Analyse des incertitudes dans les flux du trafic aérien Analysis of uncertainties in airtraffic flow par