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The approximate Kalman filtering algorithm presented in [1] for image sequence processing can introduce unacceptable negative eigenvalues in the information matrix and can have degraded performance in some applications. The improved algorithm presented in this note guarantees a positive definite information matrix, leading to more stable filter performance.
This paper is concerned with the propagation of laser light through a slab of a randomly varying medium. A theoretical analysis is presented which relates the spectrum of the recorded-intensity field some distance downstream of the medium to the spectrum of the index-of-refraction field. For a homogeneous and isotropic random field, the 3-D spectrum of the medium is obtained from the 2-D spectrum of the photograph by dividing each component of the spectrum by the frequency raised to the fourth power. Free-space propagation outside the random medium is accounted for by a scaling factor. Experimental results are presented which support the theoretical analysis. The nonintrusive diagnostic technique presented here is applicable to photographs which contain partially developed caustic networks.
The response of reusable space shuttle insulation panels to random acoustic pressure fields are studied. The basic analytical approach in formulating the governing equations of motion uses a Rayleigh-Ritz technique. The input pressure field is modeled as a stationary Gaussian random process for which the cross-spectral density function is known empirically from experimental measurements. The response calculations are performed in both frequency and time domain.
We present observational evidence for the generation of Langmuir envelope solitons in the source regions of solar type III radio bursts. The solitons appear to be formed by electron beams which excite either the modulational instability or oscillating two-stream instability (OTSI). Millisecond data from the Ulysses Unified Radio and Plasma Wave Experiment (URAP) show that Langmuir waves associated with type III bursts occur as broad intense peaks with time scales ranging from 15 to 90 milliseconds (6 - 27 km). These broad field structures have the properties expected of Langmuir envelope solitons, viz.: the normalized peak energy densities, W(sub L)/n(sub e)T(sub e) approximately 10(exp -5), are well above the modulational instability threshold; the spatial scales, L, which range from 1 - 5 Langmuir wavelengths, show a high degree of inverse correlation with (W(sub L)/n(sub e)T(sub e))(sup 1/2); and the observed widths of these broad peaks agree well with the predicted widths of envelope solitons. We show that the orientation of the Langmuir field structures is random with respect to the ambient magnetic field, indicating that they are probably isotropic structures that have evolved from initially pancake-like solitons. These observations suggest that strong turbulence processes, such as the modulational instability or the OTSI, stabilize the electron beams that produce type III bursts.
The simulation of the diffusion of a continuum field by the random walk (RW) displacement of a set of particles is considered. Elements of the gradients of the diffusive concentration are transported by computational particles. It is demonstrated that, by the use of concentration gradients in the RW process, statistical errors are reduced and each realization of the numerical solution is a representation of the exact solution. The algorithm is grid-free, and the computational elements move to follow the gradients; hence, the algorithm is self-adaptive, and uniform resolution is achieved for all times.
Probabilistic finite element method (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties, and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.
Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.
Low noise amplifier design with field effect transistors, random noise characteristics, and noise measurements on commercial devices
Fluctuations in the solar wind fields tend to not only have velocities and magnetic fields correlated in the sense consistent with Alfven waves traveling from the Sun, but they also have the magnitude of the magnetic field remarkably constant despite their being broadband. This paper provides, for the first time, a method for constructing fields with nearly constant magnetic field, zero divergence, and with any specified power spectrum for the fluctuations of the components of the field. Every wave vector, k, is associated with two polarizations the relative phases of these can be chosen to minimize the variance of the field magnitude while retaining the\random character of the fields. The method is applied to a case with one spatial coordinate that demonstrates good agreement with observed time series and power spectra of the magnetic field in the solar wind, as well as with the distribution of the angles of rapid changes (discontinuities), thus showing a deep connection between two seemingly unrelated issues. It is suggested that using this construction will lead to more realistic simulations of solar wind turbulence and of the propagation of energetic particles.
This paper investigates the equilibrium of a cluster of long, straight, twisted magnetic flux tubes extending in the z-direction in a highly conducting fluid, subject to the boundary condition that the cluster is surrounded by a uniform pressure P. It is shown that there is equilibrium only for axial symmetry, i.e., only for a single twisted flux tube. Any more complicated cluster of twisted tubes is subject to nonequilibrium reconnection of the transverse component of the field. The example provides another perspective on the general absence of equilibrium, and consequent rapid dissipation, of any magnetic field subject to random small-scale internal strains, such as the fields extending outward from the convective zones of stars.
In this work, we study an effective spin model derived perturbatively from a random transverse-field Ising model on the pyrochlore lattice. The model consists of spin configurations on the pyrochlore lattice, restricted to the spin-ice subspace, with spins interacting with random Ising exchange couplings as well as ring exchanges along the hexagons of the lattice. This model is studied by exact diagonalization up to N=64 site systems. Furthermore, we calculate spin-glass correlation functions and local entanglement entropy S T between spins in a single tetrahedron and the rest of the system. We find that the model undergoes two phase transitions. At weak randomness the model is in a quantum spin-ice phase where S T =ln 6. Increasing randomness, at low transverse fields, first leads to a frozen phase, with long-range spin-glass order and S T =ln 2 corresponding to the Cat states associated with Ising order. Further increase in randomness leads to a random resonating-hexagon phase with a frozen backbone of spins and a broad distribution of entanglement entropies. The implications of these studies for non-Kramers rare-earth pyrochlores are discussed.
The concept of minimum variance is investigated for nonplanar interplanetary Alfvenic fluctuations in which the field direction varies randomly. The theory of the random wandering of a vector of constant length is developed as a representation of the magnetic field, and it is found that the minimum variance tends to coincide with the mean field directions over the correlation time of the fluctuations. The Fokker-Planck limit of the theory is then developed and used to analyze the statistic distribution of field directions with and without a reflecting barrier. Results suggest that the tendency of the Alfvenic fluctuations to have a direction of minimum variance statistically aligned with the mean magnetic field may be purely a consequence of the randomness of the fluctuation and not imply that the fluctuations are necessarily plane waves. Extensive statistical studies of the observed directional variations of the interplanetary magnetic field are necessary to test this hypothesis.
In this paper a scheme is proposed to use a point raingage to compare contemporaneous measurements of rain rate from a single-field-of-view (FOV) estimate based on a satellite remote sensor such as a microwave radiometer. Even in the ideal case the measurements are different because one is at a point and the other is an area average over the field of view. Also the point gage will be located randomly inside the field of view on different overpasses. A space-time spectral formalism is combined with a simple stochastic rain field to find the mean-square deviations between the two systems. It is found that by combining about 60 visits of the satellite to the ground-truth site, the expected error can be reduced to about 10% of the standard deviation of the fluctuations of the systems alone. This seems to be a useful level of tolerance in terms of isolating and evaluating typical biases that might be contaminating retrieval algorithms.
A review is given of selected papers on the theory of cosmic ray (CR) propagation and acceleration. The high isotropy and a comparatively large age of galactic CR are explained by the effective interaction of relativistic particles with random and regular electromagnetic fields in interstellar medium. The kinetic theory of CR propagation in the Galaxy is formulated similarly to the elaborate theory of CR propagation in heliosphere. The substantial difference between these theories is explained by the necessity to take into account in some cases the collective effects due to a rather high density of relativisitc particles. In particular, the kinetic CR stream instability and the hydrodynamic Parker instability is studied. The interaction of relativistic particles with an ensemble of given weak random magnetic fields is calculated by perturbation theory. The theory of CR transfer is considered to be basically completed for this case. The main problem consists in poor information about the structure of the regular and the random galactic magnetic fields. An account is given of CR transfer in a turbulent medium.
The galaxy two-point correlation function, xi, at (z) = 2.6 is determined by comparing the number of Ly-alpha-emitting galaxies in narrowband CCD fields selected for the presence of damped L-alpha absorption to their number in randomly selected control fields. Comparisons between the presented determination of (xi), a density-weighted volume average of xi, and model predictions for (xi) at large redshifts show that models in which the clustering pattern is fixed in proper coordinates are highly unlikely, while better agreement is obtained if the clustering pattern is fixed in comoving coordinates. Therefore, clustering of Ly-alpha-emitting galaxies around damped Ly-alpha systems at large redshifts is strong. It is concluded that the faint blue galaxies are drawn from a parent population different from normal galaxies, the presumed offspring of damped Ly-alpha systems.
A model library containing petabytes of data is proposed by Triada, Ltd., Ann Arbor, Michigan. The library uses the newly patented N-Gram Memory Engine (Neurex), for storage, compression, and retrieval. Neurex splits data into two parts: a hierarchical network of associative memories that store 'information' from data and a permutation operator that preserves sequence. Neurex is expected to offer four advantages in mass storage systems. Neurex representations are dense, fully reversible, hence less expensive to store. Neurex becomes exponentially more stable with increasing data flow; thus its contents and the inverting algorithm may be mass produced for low cost distribution. Only a small permutation operator would be recalled from the library to recover data. Neurex may be enhanced to recall patterns using a partial pattern. Neurex nodes are measures of their pattern. Researchers might use nodes in statistical models to avoid costly sorting and counting procedures. Neurex subsumes a theory of learning and memory that the author believes extends information theory. Its first axiom is a symmetry principle: learning creates memory and memory evidences learning. The theory treats an information store that evolves from a null state to stationarity. A Neurex extracts information data without a priori knowledge; i.e., unlike neural networks, neither feedback nor training is required. The model consists of an energetically conservative field of uniformly distributed events with variable spatial and temporal scale, and an observer walking randomly through this field. A bank of band limited transducers (an 'eye'), each transducer in a bank being tuned to a sub-band, outputs signals upon registering events. Output signals are 'observed' by another transducer bank (a mid-brain), except the band limit of the second bank is narrower than the band limit of the first bank. The banks are arrayed as n 'levels' or 'time domains, td.' The banks are the hierarchical network (a cortex) and transducers are (associative) memories. A model Neurex was built and studied. Data were 50 MB to 10 GB samples of text, data base, and images: black/white, grey scale, and high resolution in several spectral bands. Memories at td, S(m(sub td)), were plotted against outputs of memories at td-1. S(m(sub td)) was Boltzman distributed, and memory frequencies exhibited self-organized criticality (SOC); i.e., 'l/f(sup beta)' after long exposures to data. Whereas output signals from level n may be encoded with B(sub output) = O(-log(2)f(sup beta)) bits, and input data encoded with B(sub input) = O((S(td)/S(td-1))(sup n)), B(sup output)/B(sub input) is much less than 1 always, the Neurex determines a canonical code for data and it is a lossless data compressor. Further tests are underway to confirm these results with more data types and larger samples.
A crystalline solid is considered to consist of a large number of incoherent nonlinear acoustic radiation sources identified with the vibrating particles of the crystalline lattice. Randomization of the field, together with the assumption of a stochastically independent, fluctuating, radiation field at the absolue zero of temperature, leads to an expression of the temperature-dependent radiation field in terms of the zero-point field. The equation is identified with the Planck distribution formula of quantum mechanics in the linear field limit. The thermodynamic state functions are also obtained in terms of the nonlinear acoustic modal energies per unit mass and reduce to the results of the Debye-Einstein stochastic quantum oscillator model in the linear field limit.
Ultrahigh field (UHF) Magnetic Resonance Imaging (MRI) provides a higher signal-to-noise ratio and, thereby, higher spatial resolution. However, UHF MRI introduces challenges such as transmit radiofrequency (RF) field (B+1) inhomogeneities, leading to uneven flip angles and image intensity anomalies. These issues can significantly degrade imaging quality and its medical applications. This study addresses B+1 field homogeneity through a novel deep learning-based strategy. Traditional methods like Magnitude Least Squares (MLS) optimization have been effective but are time-consuming and dependent on the patient’s presence. Recent machine learning approaches, such as RF Shim Prediction by Iteratively Projected Ridge Regression and deep learning frameworks, have shown promise but face limitations like extensive training times and oversimplified architectures. We propose a two-step deep learning strategy. First, we obtain the desired reference RF shimming weights from multi-channel B+1 fields using random-initialized Adaptive Moment Estimation. Then, we employ Residual Networks (ResNets) to train a model that maps B+1 fields to target RF shimming outputs. Our approach does not rely on pre-calculated reference optimizations for the testing process and efficiently learns residual functions. Comparative studies with traditional MLS optimization demonstrate our method’s advantages in terms of speed and accuracy. The proposed strategy achieves a faster and more efficient RF shimming design, significantly improving imaging quality at UHF. This advancement holds potential for broader applications in medical imaging and diagnostics.