Random Moments Research Articles

Optimal on-line detection of outside observations

Suppose that a Markov process X1,X2,… appears consecutively. There are two random moments of time θ1 and θ2, independent of (Xn). The distribution of the process (Xn) changes for the first time at instant θ1 and for the second time at instant θ2. Our objective is to find a stopping rule based only upon the former values of (Xn) which maximizes the probability that the moment of stopping is between θ1 and θ2. A sufficient condition is given under which an optimal stopping time is finite. The maximal probability corresponding to the optimal rule is found.

Applied Probability and Stochastic Processes in Engineering and Physical Sciences

Elements of Probability Random Variables and Probability Distribution Moments of Random Variables Moment Generating Function, Characteristic Function and their Application Discrete Random Variables and their Distributions Continuous Random Variables and their Distributions Transformation of Random Variables Extreme Value Statistics Stochastic Processes Spectral Analysis of Random Processes Amplitudes and Periods of Gaussian Random Processes Statistical Analysis of the Time Series Data Wiener-Levy and Markov Processes Linear System and Stochastic Prediction Nonlinear Systems and Stochastic Prediction Non-Guassian Stochastic Processes Counting Stochastic Processes.

Synchronization of spontaneous otoacoustic emissions to a 2f1−f2 distortion product

Synchronization of spontaneous otoacoustic emissions to a cubic distortion frequency fs = 2f1-f2 has been studied. Stimulus, consisting of two primary tones at frequency f1 and f2, could easily be filtered out of the microphone signal. This enabled us to monitor emission phase with respect to synchronization frequency fs, by recording zero-crossing moments of the microphone signal. When primaries were sufficiently loud (typically 30 dB SPL), phase fluctuated around a constant value: The emission was constantly synchronized to fs. Lowering primary levels (to typically 20 dB SPL) resulted in 2 pi-phase jumps at random moments: The emission occasionally slipped out of synchronization, trying to maintain its own natural frequency f0. This behavior can be described as synchronization of an oscillator (frequency f0) to a sinusoidal force (frequency fs) in the presence of noise.

Operator splitting for the random wave moment equations

Much work has been done in recent years on the scattering of waves in random media. Of particular importance are the moment equations, describing the statistical behavior of the wavefield, for most of which exact analytical solutions have not been found. Operator splitting has now been used for the fast and accurate numerical solution of the fourth moment [4] and may also be applied to the higher moments. The purpose of this note is to examine the accuracy of the method in terms of properties of the operators. Operator splitting is particularly suitable in this case: the operators appearing in the equations are easily integrated separately, while their sum is not, especially for strongly scattering media. It turns out that for the most important class of moments, the symmetric ones, the commutator of the operators is small when acting on the solution space, and the method is thus highly accurate. The results here are not precisely quantitative but illustrate the broad behavior of the solution. In Section 2 we give a brief description of the physical setting and moment equations, and the approximate solution used. The accuracy of this solution is examined in Section 3, and some motivation is given for the consideration of the commutativity of the operators.

Changing channels: Early adolescent media choices and shifting investments in family and friends

The decline in TV viewing and increase in music listening associated with the onset of adolescence is examined in terms of the changing social ecology of adolescents' daily lives. Fifth to 9th graders provided self-reports on random moments in their experience over one week. These data suggest that less frequent TV watching by adolescents, as compared to preadolescents, is attributable to a decrease in TV watching done with the family, particularly on weekend mornings and evenings. Adolescents who do watch more TV are those who spend more time with the family overall. In contrast, adolescents who frequently listen to music are those who spend more time with friends. It is argued that the partial shift from television to music during adolescence represents a shift from a medium that reinforces parental values to one that reinforces peer values and speaks to adolescent developmental tasks.

Protein transfer from an aqueous phase into reversed micelles. The effect of protein size and charge distribution.

Proteins are spontaneously transferred from an aqueous solution into reversed micelles, provided the aqueous phase has the proper composition. Besides the composition of the aqueous phase, the composition of the organic phase and the properties of the proteins also play a role. We studied uptake profiles of 19 proteins as a function of pH of the aqueous solution. The organic phase consisted of trioctylmethylammonium chloride and nonylphenol pentaethoxylate (Rewopal HV5) as surfactant, octanol as cosurfactant and isooctane as continuous phase. In all cases, except for rubredoxin, proteins were transferred at pH values above their isoelectric point. The pH where maximal solubilization takes place can be described by the relationship: pHoptimum = isoelectric point +0.11 x 10(-3) Mr -0.97. So, the larger the protein, the more charge is needed to provide the energy required for the adaptation of the micellar size to the protein size. For protein transfer into sodium di-(2-ethylhexyl)sulphosuccinate (AOT) reversed micelles a similar relationship was found. The percentage of protein transferred could be related to the symmetry of charge distribution over the protein. This symmetry was expressed as the % of random electric moments on a protein that is larger than the effective electric moment of the protein (% S) [Barlow, D. J. and Thornton, J. M. (1986) Biopolymers 25, 1717]. The larger the value of % S, the more homogeneously the charges are distributed and the lower the percentage transfer.

Neutron diffraction study of the crystallographic and magnetic structures of the BaFe 12− xMn xO 19 m-type hexagonal ferrites

The cationic distributions, ionic valencies and magnetic structures of the magnetoplumbite-like BaFe 12- x Mn x O 19 hexagonal ferrites have been studied from powder diffraction data in the paramagnetic and ferrimagnetic phases. The paramagnetic diagrams show that the Mn cations enter all the sublattices of the M-type structure except the pseudo-tetrahedral one within the R-block. It is also concluded that, in the spinel block, the tetrahedral site is occupied by Fe 3+ and Mn 2+ ions whereas in the remaining octahedral sites are located Fe 3+, Mn 3+, Mn 4+ cations in a selective way and with a hierarchy of preferences. From the magnetic diagrams it is concluded that even if the long range magnetic ordering has a collinear ferrimagnetic character, the 12k and 2a octahedral sublattices present a random moment canting which decreases further the saturation magnetization.

Microbehavioral approaches to monitoring human experience.

Microbehavioral approaches to social science research minimize the complexities of general activity reporting by limiting questions to elementary activity experience in the context of daily life. Time diaries and sampling studies of activity at random moments during the day are two examples of this approach.

Moment method in the theory of cascade-process fluctuations

A method for calculating the fluctuations and correlations in cascade processes is outlined, on the basis of deriving random cascade curves from their spatial (longitudinal) moment. The method reduces the problem of calculating cascade fluctuations in a homogeneous medium to calculating the covariational matrix of random moments, depending only on the energy variable. The set of elements of this matrix allows the fluctuations and core correlations of any track characteristics of the cascade to be calculated. The method is intended for calculations of high-energy cascades, when the influence of fluctuations of high-order longitudinal moments (n ≧ 5) may be neglected.

Approximate reconstruction of randomly sampled signals

We study the use of polynomial interpolation to approximate a function specified by samples taken at random moments satisfying a Poisson distribution with uniform mean sampling rate. Two different selection schemes are considered to determine which samples should be used in the construction of the polynomials, and detailed error estimates are derived for each case. The results are compared with the classical interpolation methods of convolution with a smoothing window. It is concluded that only low order polynomials are useful for interpolation in the presence of noise, but that they are comparable or superior to nonadaptive convolution in most cases, as well as computationally more efficient. Some simulation experiments are presented to support the theoretical estimates.

Generalized random forcing in random-walk turbulent dispersion models

The Kramers–Moyal expansion is used to derive an infinite hierarchy of Eulerian moment conservation equations from a random-walk model with non-Gaussian random forcing, thus generalizing the Langevin-equation–Fokker–Planck analysis of van Dop et al. [H. van Dop, F. T. M. Nieuwstadt, and J. C. R. Hunt, Phys. Fluids 28, 1639 (1985)]. By imposing the condition that an initially well-mixed state should remain so, equations for random forcing moments of arbitrary order are derived in terms of the Eulerian velocity moments of the turbulence. This procedure makes explicit the equivalence of the different procedures used by van Dop et al. and Thomson [D. J. Thomson, Q. J. R. Meteorol. Soc. 110, 1107 (1984)] to derive the first few forcing moments and extends their results. It is then shown that the random forcing approximation implies an infinite hierarchy of Eulerian closure assumptions, the first few of which were derived by van Dop et al. The analysis is extended to a class of rescaled random-walk equations, and it is shown that the version developed by Wilson et al. [J. D. Wilson, B. J. Legg, and D. J. Thomson, Boundary-Layer Meteorol. 27, 163 (1983)] is unique in that it alone is realizable for inhomogeneous Gaussian turbulence and then has Gaussian random forcing.

Restoration of coherence effects in high-power excitation of an intramolecular quasicontinuum

Three theoretical models were advanced for the dynamics of molecular multiphoton excitation: (i) The zero-order optically active mode connected by intramolecular random anharmonic couplings to a background manifold. (ii) Molecular eigenstates coupled by random radiative transition dipole moments. (iii) The kinetic master equation approach. It is demonstrated that in the Markoffian limit, as long as the intramolecular vibrational relaxation width is small relative to the Rabi frequency, these three approaches are equivalent. In the case of high-field excitation, coherent quantum effects are exhibited even in a randomly coupled system. Resurrection of the quantum oscillations and coherent pumping can be exhibited in intense field excitation on the time scale of intramolecular vibrational relaxation.

Principles of the Construction of Complex Algorithms for Information Processing and Control in Systems with Stochastic Exchange Structure

The automatic stochastic system with jumps of the structure in random time moments is considered. The problem of the determination of an optimal control for the systems with stochastic exchange structure is formulated. The structure of the control algorithm based on some stochastic principle of the maximum is obtained. At the same time the theorem of separation is generalized. In order to develop an algorithm for the optimal information processing of such a system there is a theory based on the mixed discrete-continuous Markovian processes. The generalized stochastic equation for a posteriori probability density function with the observation of the phase coordinates and the process structure is obtained.

Recognition of Nonstationary Random Processes

Abstract The problem of recognition of nonstationary random processes whose statistical properties change step-wise at random time moments is considered. Methods of the problem solution are described realised by means of computing technique.

Determination of Sufficient Sample Size for Linear Estimation Problems

Abstract The problem of determining sufficient sample size during recursive estimation of the parameters of single-input single-output dynamic systems is considered in this paper. Mainly, the problem mentioned reduces to that of determining a random moment of ceasing of recursive estimator calculation when the given accuracy of the estimates is achieved. For this purpose a successive procedure is proposed here, which can also determine whether the estimator is efficient or not. Applicability of the procedure is supported by simulation tests and by experimental identification of the processes in a hydraulic pipeline.

Linear System Analysis Method When Regime Change Process is Semi-Markov One

Abstract The linear dynamic system the operational regime of which (dynamics, actions) changes abruptly at random moments of time is considered. This paper provides an analysis of such system in the case that the regime change process is represented by semi-Markov process with discrete state space. The Laplace transform of the expectation of the vector system state is derived explicity. Some particular cases are considered in a practical way. An application of the results for determining second moments of state variables under constant actions or central white noise actions, moments of accumulated time of system staying in specified state subset is illustrated.

Daily well-being of older adults with friends and family.

Family members are the major source of physical and emotional support for older adults, yet researchers suggest that friendships have a stronger bearing on subjective well-being. In this research we sought an explanation for this inconsistency in older adults' immediate experiences with friends. Retired adults provided self-reports on their subjective states at random moments during a typical week. Analyses of these reports confirmed the prediction that older adults have more favorable experiences with their friends than with family members. The difference is partly attributable to the greater frequency of active leisure activities with friends, but is also due to unique qualities of interactions with friends that facilitate transcendence of mundane daily realities. We propose that friends provide an immediate situation of openness, reciprocity, and positive feedback that engenders enjoyment and subjectively meaningful exchanges.

Computer-automated sensitivity analysis in reliability-based plastic design

The evaluation of the total probability of a plastic collapse failure P f for a highly redundant structure of random interdependent plastic moments acted on by random interdependent loads is a difficult and computationally very costly process. The evaluation of reasonable bounds to this probability requires the use of second moment algebra involving many statistical parameters. A computer program which selects the best strategy for minimizing the interval between the upper and lower bounds of P f is now in its final stage of development at the University of Colorado. For the purpose of investigating the relative importance of various uncertainties involved in the computational process on the resulting bounds of P f . sensitivity analysisis used. Numerical examples are provided to illustrate response sensitivities for both mode and system reliability of an ideal-plastic portal frame.

Orthogonal jumps of the wavefunction in white-noise potentials

The master equation of the quantum noise theory is derived by means of Feynman's path integral method. We propose an equivalent stochastic process where the wavefunction satisfies a nonlinear Schrödinger equation except for random moments at which it shows orthogonal jumps.

Measurement of erythrocyte orientation in flow by spin labeling II--phenomenological models for erythrocyte orientation rate.

We present two phenomenological models describing the flowing erythrocyte orientation rate. The first concerns the onset of a stable orientation in a very dilute erythrocyte suspension. It is based on a simple formula for erythrocyte elongation as a function of shear stress, and we assume that beyond a threshold of elongation, erythrocytes take on a stable orientation, while below this threshold, they have a flipping motion. We extend this model to high hematocrit values assuming that the effect of red cell collisions imposes a random moment to each erythrocyte, shifting it from its stable orientation. We obtain an approximate expression for erythrocyte orientation rate as a function of shear rate and then we compare these results to our experimental data in part III of this series.