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POINT PROCESSES GENERATED BY LEVEL CROSSINGS
, 1971
"... This paper consists primarily of a review of available literature (and especially more recent work) concerning the crossings of levels and curves by stochastic processes. Attention is particularly directed towards those properties for which it is most profitable to emphasize the point process nature ..."
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This paper consists primarily of a review of available literature (and especially more recent work) concerning the crossings of levels and curves by stochastic processes. Attention is particularly directed towards those properties for which it is most profitable to emphasize the point process nature of the crossings. Topics considered include the mean and moments of the number of crossings, the distributions of times between them, "crossings" by vector processes and fields, Poisson approximations, and local extremes with particular reference to "cresttrough " times and heights.
Fluctuations of the impulse rate in Limulus eccentric cells
 J. Gen
, 1971
"... ABSTRACT Fluctuations in the discharge of impulses were studied in eccentric cells of the compound eye of the horseshoe crab, Limulus polyphemus. A theory is presented which accounts for the variability in the response of the eccentric cell to light. The main idea of this theory is that the source o ..."
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ABSTRACT Fluctuations in the discharge of impulses were studied in eccentric cells of the compound eye of the horseshoe crab, Limulus polyphemus. A theory is presented which accounts for the variability in the response of the eccentric cell to light. The main idea of this theory is that the source of randomness in the impulse rate is "noise " in the generator potential. Another essential aspect of the theory is that the process which transforms the generator potential "noise" into the impulse rate fluctuations may be treated as a linear filter. These ideas lead directly to Fourier analysis of the fluctuations. Experimental verification of theoretical predictions was obtained by calculation of the variance spectrum of the impulse rate. The variance spectrum of the impulse rate is shown to be the filtered variance spectrum of the generator potential.
GIS and spatial data analysis: converging perspectives
 Papers in Regional Science
, 2004
"... We take as our starting point the state of geographic information systems (GIS) and spatial data analysis 50 years ago when regional science emerged as a new field of enquiry. In the late 1950s and 1960s advances in computing technology were making possible forms of automated cartography that in due ..."
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We take as our starting point the state of geographic information systems (GIS) and spatial data analysis 50 years ago when regional science emerged as a new field of enquiry. In the late 1950s and 1960s advances in computing technology were making possible forms of automated cartography that in due course would lead to the
Conditions for convergence of montecarlo em sequences with an application to diffusion modeling
 Econometrics Journal
, 1999
"... Intractable maximum likelihood problems can sometimes be finessed with a MonteCarlo implementation of the EM algorithm. However, there appears to be little theory governing when MonteCarlo EM (MCEM) sequences converge. Consequently, in some applications, convergence is assumed rather than proved ..."
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Intractable maximum likelihood problems can sometimes be finessed with a MonteCarlo implementation of the EM algorithm. However, there appears to be little theory governing when MonteCarlo EM (MCEM) sequences converge. Consequently, in some applications, convergence is assumed rather than proved. Motivated by this problem in the context of modeling 1 market penetration of new products and services over time, we develop (i) highlevel conditions for rates of almostsure convergence and convergence in distribution of any MCEM sequence and (ii) primitive conditions for almostsure monotonicity and almostsure convergence of an MCEM sequence when MonteCarlo integration is carried out using independent Gibbs runs. We verify the main primitive conditions for the Bass product diffusion model and apply the methodology to data on wireless telecommunication services.
Evolution of the Statistical Properties of Photons Passed through a TravelingWave Laser Amplifier
 IEEE J. Quantum Electron
, 1992
"... We determine the evolution of the photon statistics of a light beam as it passes through a travelingwave laser amplifier, modeled as a birthdeathimmigration (BDI) medium. The relationship between the input and output probability distributions and probability generating functions with given (but p ..."
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We determine the evolution of the photon statistics of a light beam as it passes through a travelingwave laser amplifier, modeled as a birthdeathimmigration (BDI) medium. The relationship between the input and output probability distributions and probability generating functions with given (but possibly varying) birth, death, and immigration rates for arbitrary input statistics is obtained. The case of constant birth, death, and immigration rates is considered in particular detail. The photon statistics at the output of a general BDI travelingwave amplifier are always broader than those at the input, and they can take many forms. Our most general solution can be applied when the input distribution to the amplifier takes the form of a negativebinomial transform. The results are expected to be useful in calculating the performance characteristics of lightwave systems using optical amplifiers in which the object is to detect light with a broad range of statistical properties, including scattered light, spontaneousemission light, and light emitted from a laser. In the latter case the input is Poisson, and the output distribution assumes the form of a noncentralnegativebinomial (Laguerre) distribution which is usually associated with a multimode (phasepreserving) superposition of coherent and chaotic fields.
PROPERTIES OF HIGHREDSHIFT LYMAN ALPHA CLOUDS II. STATISTICAL PROPERTIES OF THE CLOUDS
, 1993
"... Curve of growth analysis, applied to the Lyman series absorption ratios deduced in our previous paper, yields a measurement of the logarithmic slope of distribution of Lyman α clouds in column density N. The observed exponential distribution of the clouds ’ equivalent widths W is then shown to requi ..."
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Curve of growth analysis, applied to the Lyman series absorption ratios deduced in our previous paper, yields a measurement of the logarithmic slope of distribution of Lyman α clouds in column density N. The observed exponential distribution of the clouds ’ equivalent widths W is then shown to require a broad distribution of velocity parameters b, extending up to 80 km s −1. We show how the exponential itself emerges in a natural way. An absolute normalization for the differential distribution of cloud numbers in z, N, and b is obtained. By detailed analysis of absorption fluctuations along the line of sight (including correlations among neighboring spectral frequency bins) we are able to put upper limits on the cloudcloud correlation function ξ on several megaparsec length scales. We show that observed b values, if thermal, are incompatible, in several different ways, with the hypothesis of equilibrium heating and ionization by a background UV flux. Either a significant component of b is due to bulk motion (which we argue against on several grounds), or else the clouds are out of equilibrium, and hotter than is implied by their ionization state, a situation which could be indicative of recent adiabatic collapse. Subject headings: cosmology: observations – quasars – intergalactic medium – 2 – 1.
Measurements of SecondOrder Properties of Point Processes
"... Abstract—The secondorder statistical properties of point processes (PPs) are described by the coincidence function which can be measured by a coincidence device, but such measurements are long and complicated. We propose another method of measurement, and we analyze its performances. The starting p ..."
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Abstract—The secondorder statistical properties of point processes (PPs) are described by the coincidence function which can be measured by a coincidence device, but such measurements are long and complicated. We propose another method of measurement, and we analyze its performances. The starting point is that the coincidence function can be deduced from the probability density functions of the life times (the distances between points) of the process. The idea is to transform the PP into a positive signal whose values are these distances. From an appropriate processing of this signal, we deduce the coincidence function. For the validation of the method, we use PPs for which the coincidence function is known. The agreement between theory and experiment is, in general, excellent. Finally, the method is applied to measure the coincidence functions of some PPs for which no theoretical result is available. Index Terms—Point processes (PPs), signal processing, signal representation, statistical measurements. I.
GoodnessofFit Test for Long Range Dependent Processes
"... In this paper, we make use of the information measure introduced by Mokkadem (1997) for building a goodnessoffit test for longrange dependent processes. Our test statistic is in the frequency domain and writes as a non linear functional of the normalized periodogram. We establish the asymptotic d ..."
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In this paper, we make use of the information measure introduced by Mokkadem (1997) for building a goodnessoffit test for longrange dependent processes. Our test statistic is in the frequency domain and writes as a non linear functional of the normalized periodogram. We establish the asymptotic distribution of our statistic under the null hypothesis. Under specific alternative hypotheses, we prove that the power converges to one. The performance of our test procedure is illustrated from different simulated series. In particular, we compare its size and its power with test of Chen and Deo.
A SetBased Methodology for White Noise Modeling
, 1994
"... This paper provides a new framework for analyzing white noise disturbances in linear systems: rather than the usual stochastic approach, noise signals are described as elements in sets and their effect is analyzed from a worstcase perspective. The paper studies how these sets must be chosen in orde ..."
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This paper provides a new framework for analyzing white noise disturbances in linear systems: rather than the usual stochastic approach, noise signals are described as elements in sets and their effect is analyzed from a worstcase perspective. The paper studies how these sets must be chosen in order to have adequate properties for system response in the worstcase, statistics consistent with the stochastic point of view, and simple descriptions that allow for tractable worstcase analysis. The methodology is demonstrated by considering its implications in two problems: rejection of white noise signals in the presence of system uncertainty, and worstcase system identification. 1 Introduction A general feature of mathematical models in engineering science is the presence of modeling errors, which arise due to poorly understood or highly unpredictable phenomena, or from simplifications deliberately introduced for the sake of model tractability. Essentially two approaches are available ...
Memoirs on highway traffic flow theory in the 1950s
 Oper. Res
"... There has been a revival of interest in traffic flow theory in the late 1990s, mostly because vehicle detectors have been installed at many highway locations throughout the world to record the passing of vehicles. The purpose of these detectors is to monitor congestion and provide information for ..."
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There has been a revival of interest in traffic flow theory in the late 1990s, mostly because vehicle detectors have been installed at many highway locations throughout the world to record the passing of vehicles. The purpose of these detectors is to monitor congestion and provide information for possible control or to advise motorists of possible alternative routing. To understand the consequences of some strategy, however, one must have some theories or models of how traffic will respond to various actions. Students who review the literature on traffic flow theory in an attempt to develop such models observe that most of the references on this subject are dated in the 1950s and 1960s. There is very little useful literature in the 1970s, 1980s, or early 1990s. Students wonder how this started, who were these people who wrote the early papers, and why did the subject die in the 1970s? There are not many people left who were involved in the early developments of traffic flow theory, so it is difficult to research the history of it. Many of these people were involved for only a short time and then moved on to other things. Most of them had grown up during the Depression era and had lived through World War II. Any one of them could have told stories about what the world was like then and what motivated them, but perhaps the stories would be rather similar. The 1950s was a time to try to put civilization back together and to create a society people could live with. I can tell the story only from my own perspective and from my encounters with others. It is appropriate that traffic flow theory be included as part of the anniversary celebration of Operations Research, because many of the early papers on traffic flow theory were published in this publication, and the national meetings of ORSA were one of the main forums for exchange of ideas. A special issue of Operations Research devoted to transportation was published in 1964, and the journal