Local Mean Square Research Articles

Characterizing anisotropy and heterogeneity of soil surface microtopography using fractal models

Soil surface roughness and the complementary soil microrelief depression pattern determine water infiltration, overland flow and drainage network development. The characteristic soil surface roughness remains poorly defined, because of difficulties in quantifying soil microrelief by single indices. Moreover, self-affine fractal models have been found to adequately describe soil surface microtopographic features only in a small range of length scales. At least two parameters are required to assess fractal microrelief surfaces, fractal dimension, D, describing how roughness changes with scale, and the so-called crossover length, l, which specifies the variance at a reference scale. This study focuses on isotropy and heterogeneity analysis of soil surface point elevation data sets, measured with different resolutions, by pinmeter and laser scanner, under field and laboratory conditions. Selected examples of elevation data sets illustrate how real surfaces cannot be ideally fractal, even over limited length scales. Values estimated for the fractal parameters, D and l, by two independent methods, semivariogram (SMV) and local root mean square (RMS), presented some bias, although from a practical point of view both methods gave equivalent results. Irrespective of calculation method and after having removed both, slope and primary tillage effects, D SMV and D RMS values were always above 2.5, indicating anti-persistent behavior. The D SMV and D RMS values were highly correlated with each other, although the relationship was not one to one. Differences in l SMV and l RMS were only apparent for plots with very large structural units and random roughness. Fractal characterization of soil anisotropy and heterogeneity by the SMV and the RMS methods, respectively, may be very useful as a way to compare data sets obtained for different treatments or soil surface evolution conditions, when measured with the same resolution. Isotropic/anisotropic features of the soil microrelief were visualized by means of a Hurst rose plot, where D SMV values estimated for different directions were represented. Local spatially variable D RMS values provided a description of the heterogeneity/homogeneity of the soil surface.

Relationship between Local and Global Nonparametric Estimators Measures of Fitting and Smoothing

Following Henderson (1916) who developed a smoothing measure as a function of the weight system of a linear filter, Dagum and Luati (2002a) proposed a set of local statistical measures of bias, variance and mean square error which are intrinsic to the smoother and, thus, independent of the data to which they will be applied on. Theoretical measures of local fitting (LMSE) and smoothing (S) are calculated on the basis of the weight systems of the following nonparametric function estimators, Loess of degree 1 and 2, the cubic smoothing spline, the Gaussian kernel, and the 13-term Henderson filter.Our aim is to evaluate the extent to which these local or weight-based measures of fitting and smoothing can be used to obtain a priori general information on the global (data-based) goodness of fit and smoothness when such filters are applied to real time series. A priori knowledge of a smoother fit and smoothness performances when applied to real data is relevant, among others, for current economic analysis, the main interest of which is the detection of true turning points.For each function estimator, we calculate global measures of fitting (MSE) and smoothing (Q) using two large samples of real and simulated series characterized by different degrees of variability.The results show that the theoretical (weight-based) local smoothing measures are always in agreement with the global empirical ones. Similarly, the local (weight-based) mean square error, analyzed in terms of bias and variance composition, provides sound a priori information on the global goodness of fit given by the symmetric filters of each nonparametric estimator. For the asymmetric filters, the above analysis must be done taking into consideration also the impact of phase shifts which can be inferred from the smoothing measures.

Approximate analysis of some two-degree-of-freedom nonlinear random systems by an extension of Gaussian equivalent linearization

The paper presents the analysis of some two-degree-of-freedom nonlinear systems under random excitation using Local Mean Square Error Criterion which is an extension of Gaussian Equivalent Linearization. The results obtained shows that the new technique can be very efficiently used not only for simple-degree-of-freedom systems as presented in the previous papers, but also for multi-degree-of-freedom ones. The solution accuracy obtained by the proposed technique is much more improved than that using the traditional linearization. The conclusions in the paper point up the significance of this technique.

Economic fluctuations and anomalous diffusion

We quantify the relation between trading activity - measured by the number of transactions N(Deltat)-and the price change G(Deltat) for a given stock, over a time interval [t, t+Deltat]. To this end, we analyze a database documenting every transaction for 1000 U.S. stocks for the two-year period 1994-1995. We find that price movements are equivalent to a complex variant of classic diffusion, where the diffusion constant fluctuates drastically in time. We relate the analog for stock price fluctuations of the diffusion constant-known in economics as the volatility-to two microscopic quantities: (i) the number of transactions N(Deltat) in Deltat, which is the analog of the number of collisions and (ii) the variance W(2)(Deltat) of the price changes for all transactions in Deltat, which is the analog of the local mean square displacement between collisions. Our results are consistent with the interpretation that the power-law tails of P(G(Deltat)) are due to P(W(Deltat)), and the long-range correlations in |G(Deltat)| are due to N(Deltat).

Linearization of randomly excited nonlinear systems by using local mean square error criterion

The paper presents the analysis of three non-linear systems under random excitation by using Local Mean Square Error Criterion which is an extension of Gaussian Equivalent Linearization proposed by Caughey. The obtained results shows that the new technique allows to get much more accurate solutions than .that using Caughey Criterion. The paper leads out some new conclusions which have not been found yet by the previous researches. The new conclusions more clarify the significance of this technique.

Statistical modeling of RMS-delay spread under multipath fading conditions in local areas

Two statistical models for the parameter of local root mean square (RMS) delay spread taking into account multipath fading characteristics of the received paths' amplitudes are presented. The models have been developed under the assumption that only two "paths" exist in the radio channel. A rather specialized definition for the term "path" is used, which is explained in the introduction. The aim is the description of RMS delay spread when the transceiver moves in a local area and experiences multipath fading. For this reason, the amplitudes of the two paths have been assumed to follow both the Rayleigh distribution at the first model and the Rayleigh and Rice distributions, respectively, at the second model. The time difference between the arrival of the two paths has been assumed to follow the uniform distribution for both models. In order to examine the validity of the models, measurements have been conducted and experimental results have been compared with the theoretical ones. Moreover, measurements from the literature have been obtained for additional confirmation of the models.

Surface analysis of human plasma fibronectin adsorbed to commercially pure titanium materials.

Protein binding on metallic implant surfaces, such as titanium, is governed by the physico-chemical nature of the metallic surface. Human plasma fibronectin (HPF) is an important matrix glycoprotein that mediates cell and protein attachment to each other or to the extracellular matrix present during wound healing. The objective of this study was to investigate the adsorption of HPF onto polished commercially pure titanium (cpTi) by using atomic force microscopy (AFM) and electron spectroscopy for chemical analysis (ESCA) and to measure the resultant surface contact angle before and after HPF binding. Two types of cpTi disks, one highly polished in our laboratory (HSS) and one commercially prepared (31), were reacted with HPF solutions of varying concentrations (1 microg/mL-10 ng/mL). ESCA survey spectra of samples coated with 1 microg/mL of fibronectin showed an increase in organic nitrogen and carbon compared with uncoated controls. Contact angle measurements of HSS and 31 cpTi disks showed no significant difference in average contact angle (36.3 degrees +/- 3.5 and 39.1 degrees +/- 3.1) despite differences in local root mean square (RMS) surface roughness (4.45 +/- 0.46 nm and 22.37 +/- 4.17 nm) as measured by AFM. Images obtained by AFM showed that 31 specimens were more irregular, with large parallel polishing grooves. Adsorbed HPF appeared in a globular form with an average length of 16.5 +/- 1.0 nm, a height of 2.5 +/- 0.5 nm, and a width of 9.6 +/- 1.2 nm. Fibronectin coating on both HSS and 31 cpTi specimens resulted in a significant increase in hydrophobicity compared to uncoated specimens. These results indicate the significance of HPF on cpTi and may explain how cpTi implants function in situ.

Adaptive motion-compensated filtering of noisy image sequences

The authors propose a novel adaptive spatiotemporal filter, called the adaptive weighted averaging (AWA) filter, for effective noise suppression in image sequences without introducing visually disturbing blurring artifacts. Filtering is performed by computing the weighted average of image values within a spatiotemporal support along the estimated motion trajectory at each pixel. The weights are determined by optimizing a well defined mathematical criterion, which provides an implicit mechanism for deemphasizing the contribution of the outlier pixels within the spatiotemporal filter support to avoid blurring. The AWA filter is therefore particularly well suited for filtering sequences that contain segments with abruptly changing scene content due to, for example, rapid zooming and changes in the view of the camera. The performance of the proposed AWA filter is compared with that of the spatiotemporal, local linear minimum mean square error (LMMSE) filtering. The results demonstrate that the proposed AWA filter-outperforms the LMMSE filter, especially in the cases of low signal-to-noise ratios and abruptly varying scene content. >

Reformulation of Stokes's theory for higher than second‐degree reference field and modification of integration kernels

An argument is put forward in favor of using a model gravity field of a degree and order higher than 2 as a reference in gravity field studies. Stokes's approach to the evaluation of the geoid from gravity anomalies is then generalized to be applicable to a higher than second‐order reference spheroid. The effects of truncating Stokes's integration and of modifying the integration kernels are investigated in the context of the generalized approach. Several different modification schemes, starting with a Molodenskij‐like modification and ending with the least squares modification, are studied. Particular attention is devoted to looking at both global and local biases and mean square errors of the individual schemes.

The critical temperature dependence of birefringence near the normal-incommensurate phase transition in Rb2ZnBr4

Anomalous (non-classical) temperature behaviour of birefringence at the second-order normal-incommensurate phase transition in Rb2ZnBr4 crystals is studied experimentally. An attempt is undertaken to discuss it using the existing theoretical approach. A critical review of some theoretical results concerning the temperature dependence of the local mean square of an order parameter is given both for the region of small corrections to the results of the Landau theory and for the scaling region. It is shown that, in the region of 'small corrections' (at mod tau mod approximately=10-1), qualitative agreement of the experiment with the results of fluctuation theory can be recognised. Near the critical point, at mod tau mod <10-3, the deviation from the critical behaviour of the XY model is found; the nature of this deviation is not clear.

Multiple time scaling of the response of a Duffing oscillator to narrow-band random excitation

The response of a Duffing oscillator to narrow-band random excitation is considered. Two approaches, multiple time scaling and stochastic averaging, are used. Both lead to the same set of three state equations for the slowly varying local mean square response or envelope (and two other variables). The stationary solution of these equations is similar to results previously obtained by using statistical linearization. The stationary and nonstationary (from the three state equations) results compare, favourably with digital simulations. Random jumps are shown to occur if the excitation bandwidth is sufficiently small.

Time-dependent power spectral density of earthquake ground motion

This paper investigates the stationarity of earthquake accelerograms and shows that the strong motion segments constitute a locally stationary random process. For such a process, a time-dependent power spectral density may be formulated as the product of: (a) a mean-square acceleration; (b) a time scale factor describing the variation of the local mean square acceleration; and (c) a normalized power spectral density describing the frequency structure of the motion. A segmental time averaging procedure is proposed for obtaining a time scale factor, an envelope function, and a normalized power spectral density from the strong motion segment of accelerograms. The procedure is used to compute smooth normalized power spectral densities from a total of 367 horizontal and vertical components of accelerograms recorded on alluvium, rock, and alluvium underlain by rock.

A method for compression — Reconstruction of ECG signals

A new method of data compression — reconstruction for ECG signals is presented. The method gives the ability (a) to control the final accuracy of the reconstructed signal before the transmission (or storage) of samples and (b) to control the compression ratio (CR) in order to obtain an optimum use of the channel capacity. The main advantage of the method was found to be the very strong improvement of the local re-construction during the active periods. Indeed, we can obtain CR values between 3 and 10 with local root mean square error (r.m.s.e.) improvement, compared to the total r.m.s.e. value, by 85% during the active period.

Rigorous bounds in structural phase transitions

Exact inequalities for the local mean-square of displacement as well as its fluctuation are derived for a quantum anharmonic phonon model. Rigorous bounds for the transition temperature, the melting temperature and the kinetic energy are then obtained.

Mean-Value Characteristic-Impedance Method of Predicting Vibration and Sound Radiation

The mean-value characteristic-impedance method predicts the mean line through the frequency-response curve and the sound pressure of a vibrator in terms of its mode mass and the average frequency difference between successive resonances with a few slide-rule computations, regardless of the complexity of the vibrator. This mean line can easily be supplemented with the curves that represent the height of the resonant peaks and the depth of the antiresonant mimima. If the vibrator is excited by white noise, the amplitude of the vibration becomes proportional to the local mean square root of the energy density. The radiation resistance above the coincidence frequency is ρc. The sound radiation below the coincidence frequency consists of a force component and an edge component both of which can be predicted. The theory makes it possible to compute, for example, the sound pressure that is generated by a spring-mounted motor in a cage inside a housing, taking into account all the resonances of cage, housing, and mounting. In applications of this theory to praccal situations, the results agreed with experimental results within a few decibels. [This research was performed for the Ordnance Research Laboratory and the Physics Department at The Pennsylvania State University under contract with the Office of Naval Research.]