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26
Generalized Stochastic Subdivision
 ACM Transactions on Graphics
, 1987
"... This paper describes the basis for techniques such as stochastic subdivision in the theory of random processes and estimation theory. The popular stochastic subdivision construction is then generalized to provide control of the autocorrelation and spectral properties of the synthesized random functi ..."
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Cited by 37 (2 self)
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This paper describes the basis for techniques such as stochastic subdivision in the theory of random processes and estimation theory. The popular stochastic subdivision construction is then generalized to provide control of the autocorrelation and spectral properties of the synthesized random functions. The generalized construction is suitable for generating a variety of perceptually distinct highquality random functions, including those with nonfractal spectra and directional or oscillatory characteristics. It is argued that a spectral modeling approach provides a more powerful and somewhat more intuitive perceptual characterization of random processes than does the fractal model. Synthetic textures and terrains are presented as a means of visually evaluating the generalized subdivision technique. Categories and Subject Descriptors: I.3.3 [Computer Graphics]: Picture/Image Generation; I.3.7 [Computer Graphics]: Three Dimensional Graphics and Realism <F11.
Secondorder statistics of complex signals
 IEEE Trans. Signal Processing
, 1997
"... Abstract — The secondorder statistical properties of complex signals are usually characterized by the covariance function. However, this is not sufficient for a complete secondorder description, and it is necessary to introduce another moment called the relation function. Its properties, and espec ..."
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Cited by 21 (0 self)
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Abstract — The secondorder statistical properties of complex signals are usually characterized by the covariance function. However, this is not sufficient for a complete secondorder description, and it is necessary to introduce another moment called the relation function. Its properties, and especially the conditions that it must satisfy, are analyzed both for stationary and nonstationary signals. This leads to a new perspective concerning the concept of complex white noise as well as the modeling of any signal as the output of a linear system driven by a white noise. Finally, this is applied to complex autoregressive signals, and it is shown that the classical prediction problem must be reformulated when the relation function is taken into consideration. I.
HAC estimation in a spatial framework
 J. Econom
, 2007
"... We suggest a nonparametric heteroscedasticity and autocorrelation consistent (HAC) estimator of the variancecovariance (VC) matrix for a vector of sample moments within a spatial context. We demonstrate consistency under a set of assumptions that should be satisfied by a wide class of spatial model ..."
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Cited by 19 (2 self)
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We suggest a nonparametric heteroscedasticity and autocorrelation consistent (HAC) estimator of the variancecovariance (VC) matrix for a vector of sample moments within a spatial context. We demonstrate consistency under a set of assumptions that should be satisfied by a wide class of spatial models. We allow for more than one measure of distance, each of which may be measured with error. Monte Carlo results suggest that our estimator is reasonable in finite samples. We then consider a spatial model containing various complexities and demonstrate that our HAC estimator can be applied in the context of that model.
The fading number of singleinput multipleoutput fading channels with memory
 IEEE Transactions on Information Theory
, 2006
"... We derive the fading number of stationary and ergodic (not necessarily Gaussian) singleinput multipleoutput (SIMO) fading channels with memory. This is the second term, after the double logarithmic term, of the high signaltonoise ratio (SNR) expansion of channel capacity. The transmitter and rec ..."
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Cited by 8 (4 self)
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We derive the fading number of stationary and ergodic (not necessarily Gaussian) singleinput multipleoutput (SIMO) fading channels with memory. This is the second term, after the double logarithmic term, of the high signaltonoise ratio (SNR) expansion of channel capacity. The transmitter and receiver are assumed to be cognizant of the probability law governing the fading but not of its realization. It is demonstrated that the fading number is achieved by IID circularly symmetric inputs of squaredmagnitude whose logarithm is uniformly distributed over an SNR dependent interval. The upper limit of the interval is the logarithm of the allowed transmit power, and the lower limit tends to infinity sublogarithmically in the SNR. The converse relies inter alia on a new observation regarding input distributions that escape to infinity. Lower and upper bounds on the fading number for Gaussian fading are also presented. These are related to the mean squarederrors of the onestep predictor and the onegap interpolator of the fading process respectively. The bounds are computed explicitly for stationary mth order autoregressive AR(m) Gaussian fading processes.
The fading number of SIMO fading channels with memory
 In Proc. IEEE Int. Symp. on Inf. Theory and its Appl. (ISITA
, 2004
"... We derive the fading number of a general (not necessarily Gaussian) singleinput multipleoutput (SIMO) fading channel with memory, where the transmitter and receiver—while fully cognizant of the probability law governing the fading process—have no access to the fading realization. It is demonstrate ..."
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Cited by 5 (3 self)
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We derive the fading number of a general (not necessarily Gaussian) singleinput multipleoutput (SIMO) fading channel with memory, where the transmitter and receiver—while fully cognizant of the probability law governing the fading process—have no access to the fading realization. It is demonstrated that the fading number is achieved by IID circularlysymmetric inputs of log squaredmagnitude that is uniformly distributed over a signaltonoise (SNR) dependent interval. The upper limit of the interval is the logarithm of the allowed transmit power, and the lower limit tends to infinity sublogarithmically in the SNR. Among the new ingredients in the proof is a new theorem regarding input distributions that escape to infinity. Upper and lower bounds on the fading number for SIMO Gaussian fading are also presented. Those are computed explicitly for stationary mth order autoregressive AR(m) Gaussian fading processes.
Optimal prediction for the KuramotoSivashinsky equation
, 2003
"... Abstract. We examine the problem of predicting the evolution of solutions of the KuramotoSivashinsky equation when initial data are missing. We use the optimal prediction method to construct equations for the reduced system. The resulting equations for the resolved components of the solution are ra ..."
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Cited by 3 (2 self)
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Abstract. We examine the problem of predicting the evolution of solutions of the KuramotoSivashinsky equation when initial data are missing. We use the optimal prediction method to construct equations for the reduced system. The resulting equations for the resolved components of the solution are random integrodifferential equations. The accuracy of the predictions depends on the type of projection used in the integral term of the optimal prediction equations and on the choice of resolved components. The novel features of our work include the first application of the optimal prediction formalism to a nonlinear, nonHamiltonian equation and the use of a noninvariant measure constructed through inference from empirical data.
unknown title
"... A brief account of my life and work This account is not as short as I wanted to make it due to my long life while my life and my work cannot be separated. I belong to a generation which was too young for active duty in the First World War and too old for the Second. To give the story some structure ..."
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A brief account of my life and work This account is not as short as I wanted to make it due to my long life while my life and my work cannot be separated. I belong to a generation which was too young for active duty in the First World War and too old for the Second. To give the story some structure I divide it into significant periods, 1. Romania 1903–1922. I was born on April 21, 1903, in Galatz, Romania, as the youngest of four children. My father, trained as an accountant, inherited the lumber business of my grandfather Isaac Segal, on my mother’s side, but my father was not a good business man. The fortunes of the family improved in 1910 when we moved to Jassy, Romania, where my father eventually became SubDirector (Vice President) of the newly founded “Banca Moldova”. The building of the Banca Moldova, at present a main Post Office of Jassy, was new in 1910, and our family occupied onehalf of its second floor. We four children enjoyed the cultural interests of our parents, especially of mother’s who wrote and spoke French fluently. My father was an AustroHungarian subject and Consul in Jassy of the Dual Monarchy. This caused difficulties during the First World War after
EFFICIENT OPTICAL COMMUNICATION IN A TURBULENT ATMOSPHERE
"... laboratory in which faculty members and graduate students from numerous academic departments conduct research. The research reported in this document was made possible in ..."
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laboratory in which faculty members and graduate students from numerous academic departments conduct research. The research reported in this document was made possible in
Stochastic Methods in Applied Mathematics and Physics
, 2002
"... A sequence which converges is a Cauchy sequence, although the converse is not necessarily true. If the converse is true for all Cauchy sequences in a given inner product space, then the space is called complete. We shall assume that all of the spaces we work with from now on are complete. A few mor ..."
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A sequence which converges is a Cauchy sequence, although the converse is not necessarily true. If the converse is true for all Cauchy sequences in a given inner product space, then the space is called complete. We shall assume that all of the spaces we work with from now on are complete. A few more de nitions from real analysis: De nition 3. An open ball centered at x with radius r > 0 is the set B r (x) = fu : ku xk < rg De nition 4. A set S is closed if x 2 S whenever there exists a sequence fu n g 2 S such that fu n g ! x. De nition 5. A set S is open if, for all x 2 S, there exists an open ball B r (x) such that B r (x) S. An example of a closed set is the closed interval [0; 1] R. An example of an open set is the open interval (0; 1) R. The complement of an open set is closed, and the complement of a closed set is open. Given a set S and some point b outside of S, we want to determine under what conditions there is a point b 2 S closest to b, i.e., such that