Techniques and errors in measuring cross- correlation and cross-spectral density functions
Techniques and errors in measuring cross spectral density and cross correlation functions of stationary dynamic pressure data
DYNAMIC PRESSURE↗
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Correlation method for computing sensitivity functions on a high-speed iterative analog computer.
Correlation method for generating sensitivity coefficients of dynamic system on high speed iterative analog computer
CORRELATION FUNCTION↗
A theory and method for correlation analysis of nonstationary signals.
Cross correlation and autocorrelation functions of nonstationary signals based on optimal approximation of ensemble correlation function for one pair of signals
CROSS CORRELATION↗
A Patch Density Recommendation based on Convergence Studies for Vehicle Panel Vibration Response resulting from Excitation by a Diffuse Acoustic Field
Fluid structural interaction problems that estimate panel vibration from an applied pressure field excitation are quite dependent on the spatial correlation of the pressure field. There is a danger of either over estimating a low frequency response or under predicting broad band panel response in the more modally dense bands if the pressure field spatial correlation is not accounted for adequately. Even when the analyst elects to use a fitted function for the spatial correlation an error may be introduced if the choice of patch density is not fine enough to represent the more continuous spatial correlation function throughout the intended frequency range of interest. Both qualitative and quantitative illustrations evaluating the adequacy of different patch density assumptions to approximate the fitted spatial correlation function are provided. The actual response of a typical vehicle panel system is then evaluated in a convergence study where the patch density assumptions are varied over the same finite element model. The convergence study results are presented illustrating the impact resulting from a poor choice of patch density. The fitted correlation function used in this study represents a Diffuse Acoustic Field (DAF) excitation of the panel to produce vibration response.
Smith, Andrew↗
THE ALGEBRA OF PERIODIC SEQUENCES
The set of periodic sequences over a field forms a group-ring algebra in which convolution is the product operation. Decomposition theorems are applied to this ring to aid in finding sequences with an arbitrary, specified autocorrelation function.
Periodic function↗
A Patch Density Recommendation based on Convergence Studies for Vehicle Panel Vibration Response resulting from Excitation by a Diffuse Acoustic Field
Producing fluid structural interaction estimates of panel vibration from an applied pressure field excitation are quite dependent on the spatial correlation of the pressure field. There is a danger of either over estimating a low frequency response or under predicting broad band panel response in the more modally dense bands if the pressure field spatial correlation is not accounted for adequately. It is a useful practice to simulate the spatial correlation of the applied pressure field over a 2d surface using a matrix of small patch area regions on a finite element model (FEM). Use of a fitted function for the spatial correlation between patch centers can result in an error if the choice of patch density is not fine enough to represent the more continuous spatial correlation function throughout the intended frequency range of interest. Several patch density assumptions to approximate the fitted spatial correlation function are first evaluated using both qualitative and quantitative illustrations. The actual response of a typical vehicle panel system FEM is then examined in a convergence study where the patch density assumptions are varied over the same model. The convergence study results illustrate the impacts possible from a poor choice of patch density on the analytical response estimate. The fitted correlation function used in this study represents a diffuse acoustic field (DAF) excitation of the panel to produce vibration response.
Smith, Andrew↗
Life and death of neurons in the aging brain
Neurodegenerative disorders are characterized by extensive neuron death that leads to functional decline, but the neurobiological correlates of functional decline in normal aging are less well defined. For decades, it has been a commonly held notion that widespread neuron death in the neocortex and hippocampus is an inevitable concomitant of brain aging, but recent quantitative studies suggest that neuron death is restricted in normal aging and unlikely to account for age-related impairment of neocortical and hippocampal functions. In this article, the qualitative and quantitative differences between aging and Alzheimer's disease with respect to neuron loss are discussed, and age-related changes in functional and biochemical attributes of hippocampal circuits that might mediate functional decline in the absence of neuron death are explored. When these data are viewed comprehensively, it appears that the primary neurobiological substrates for functional impairment in aging differ in important ways from those in neurodegenerative disorders such as Alzheimer's disease.
Review, Tutorial↗
Time-Distance Helioseismology
Time-distance helioseismology is a method of ambient noise imaging using the solar oscillations. The basic realization that led to time-distance helioseismology was that the temporal cross correlation of the signals at two 'surface' (or photospheric) locations should show a feature at the time lag corresponding to the subsurface travel time between the locations. The temporal cross correlation, as a function of the location separation, is the Fourier transform of the spatio-temporal power spectrum of the solar oscillations, a commonly used function in helioseismology. It is therefore likely the characteristic ridge structure of the correlation function had been seen before without appreciation of its significance. Travel times are measured from the cross correlations. The times are sensitive to a number of important subsurface solar phenomena. These include sound speed variations, flows, and magnetic fields. There has been much interesting progress in the 17 years since the first paper on this subject (Duvall et al., Nature, 1993, 362, 430-432). This progress will be reviewed in this paper.
Duvall, Thomas L., Jr.↗
Short-term X-ray variability of the globular cluster source 4U 1820 - 30 (NGC 6624)
Analytical techniques for improved identification of the temporal and spectral variability properties of globular cluster and galactic bulge X-ray sources are described in terms of their application to a large set of observations of the source 4U 1820 - 30 in the globular cluster NGC 6624. The autocorrelation function, cross-correlations, time skewness function, erratic periodicities, and pulse trains are examined. The results are discussed in terms of current models with particular emphasis on recent accretion disk models. It is concluded that the analyzed observations provide the first evidence for shot-noise variability in a globular cluster X-ray source.
Stella, L.↗
Self‐Consistent Convolutional Density Functional Approximations: Application to Adsorption at Metal Surfaces
The exchange-correlation (XC) functional in density functional theory is used to approximate multi-electron interactions. A plethora of different functionals are available, but nearly all are based on the hierarchy of inputs commonly referred to as “Jacob's ladder.” This paper introduces an approach to construct XC functionals with inputs from convolutions of arbitrary kernels with the electron density, providing a route to move beyond Jacob's ladder. We derive the variational derivative of these functionals, showing consistency with the generalized gradient approximation (GGA), and provide equations for variational derivatives based on multipole features from convolutional kernels. A proof-of-concept functional, PBEq, which generalizes the PBEα framework with mathematical equation being a spatially-resolved function of the monopole of the electron density, is presented and implemented. It allows a single functional to use different GGAs at different spatial points in a system, while obeying PBE constraints. Analysis of the results underlines the importance of error cancellation and the XC potential in data-driven functional design. After testing on small molecules, bulk metals, and surface catalysts, the results indicate that this approach is a promising route to simultaneously optimize multiple properties of interest.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Correlation method for computing sensitivity functions on a high-speed iterative analog computer
Digital correlation for computing sensitivity coefficients on iterative analog computer
Ogrady, E. P.↗
Sensory integration for neuroprostheses: from functional benefits to neural correlates
In the field of sensory neuroprostheses, one ultimate goal is for individuals to perceive artificial somatosensory information and use the prosthesis with high complexity that resembles an intact system. To this end, research has shown that stimulation elicited somatosensory information improves prosthesis perception and task performance. While studies strive to achieve sensory integration, a crucial phenomenon that entails naturalistic interaction with the environment, this topic has not been commensurately reviewed. Therefore, here we present a perspective for understanding sensory integration in neuroprostheses. First, we review the engineering aspects and functional outcomes in sensory neuroprosthesis studies. In this context, we summarize studies that have suggested sensory integration. We focus on how they have used stimulation-elicited percepts to maximize and improve the reliability of somatosensory information. Next, we review studies that have suggested multisensory integration. These works have demonstrated that congruent and simultaneous multisensory inputs provided cognitive benefits such that an individual experiences a greater sense of authority over prosthesis movements (i.e., agency) and perceives the prosthesis as part of their own (i.e., ownership). Thereafter, we present the theoretical and neuroscience framework of sensory integration. We investigate how behavioral models and neural recordings have been applied in the context of sensory integration. Sensory integration models developed from intact-limb individuals have led the way to sensory neuroprosthesis studies to demonstrate multisensory integration. Neural recordings have been used to show how multisensory inputs are processed across cortical areas. Lastly, we discuss some ongoing research and challenges in achieving and understanding sensory integration in sensory neuroprostheses. Here, resolving these challenges would help to develop future strategies to improve the sensory feedback of a neuroprosthetic system.
60 APPLIED LIFE SCIENCES↗
Superluminal matter waves
The Dirac equation has resided among the greatest successes of modern physics since its emergence as the first quantum mechanical theory fully compatible with special relativity. This compatibility ensures that the expectation value of the velocity is less than the vacuum speed of light. Here, we show that the Dirac equation admits free-particle solutions where the peak amplitude of the wave function can travel at any velocity, including those exceeding the vacuum speed of light, despite having a subluminal velocity expectation value. The solutions are constructed by superposing basis functions with correlations in momentum space. These arbitrary velocity wave functions feature a near-constant profile and may impact quantum mechanical processes that are sensitive to the local value of the probability density as opposed to expectation values.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Note on binaural masking-level differences as a function of the interaural correlation of the masking noise.
Model for interpreting data, describing binaural masked threshold dependence on proportion of noise in masking signals
CROSS CORRELATION↗
Further investigations of random numbers
Random numbers generated by linear recurrence modulo 2 and correlation and distribution functions
CORRELATION FUNCTION↗
Detection of monaural signals as a function of interaural noise correlation and signal frequency.
Interaural correlation effects for masking noise in ear detection of monaural signals
Whitmore, J. K.↗
Fine structure of transient waves in a random medium: The correlation and spectral density functions
This is essentially a progress report on a theoretical investigation of the propagation of transient waves in a random medium. The emphasis in this study is on applications to sonic-boom propagation, particularly as regards the effect of atmospheric turbulence on the sonic-boom waveform. The analysis is general, however, and is applicable to other types of waves besides sonic-boom waves. The phenomenon of primary concern in this investigation is the fine structure of the wave. A figure is used to illustrate what is meant by finestructure.
Wenzel, Alan R.↗
Long-term modulation of galactic cosmic radiation and its model for space exploration
As the human exploration of space has received new attention in the United States, studies find that exposure to space radiation could adversely impact the mission design. Galactic Cosmic Radiation (GCR), with its very wide range of charges and energies, is particularly important for a mission to Mars, because it imposes a stiff mass penalty for spacecraft shielding. Dose equivalent versus shielding thickness calculations, show a rapid initial drop on exposure with thickness, but an asymptotic behavior at a higher shielding thickness. Uncertainties in the radiobiology are largely unknown. For a fixed radiation risk, this leads to large uncertainties in shielding thickness for small uncertainties in estimated dose. In this paper we investigate the application of steady-state, spherically-symmetric diffusion-convection theory of solar modulation to individual measurements of differential energy spectra from 1954 to 1989 in order to estimate the diffusion coefficient, kappa(r,t), as a function of time. We have correlated the diffusion coefficient to the Climax neutron monitor rates and show that, if the diffusion coefficient can be separated into independent functions of space and time: kappa(r,t)=K(t) k(sub 0) beta Pk(sub 1) (r), where beta is the particle velocity and P the rigidity, then (i) The time dependent quantity 1/K(t), which is proportional to the deceleration potential, phi(r,t), is linearly related to the Climax neutron monitor counting rate. (ii) The coefficients obtained from hydrogen or helium intensity measurements are the same. (iii) There are different correlation functions for odd and even solar cycles. (iv) The correlation function for the Climax neutron monitor counting rate for given time, t, can be used to estimate mean deceleration parameter phi(t) to within +/- 15% with 90% confidence. We have shown that k(r,t) determined from hydrogen and/or helium data, can be used to fit the oxygen and iron differential energy spectra with a root mean square error of about +/- 10%, and essentially independent of the particle charge or energy. We have also examined the ion chamber and C-14 measurements which allow the analysis to be extended from the year 1906 to 1990. Using this model we have defined reference GCR spectra at solar minimum and solar maximum. These can be used for space exploration studies and provide a quantitative estimate of the error in dose due to changes in GCR intensities.
Badhwan, G. D.↗