Statistical Spread Research Articles

Estimation of the error of hyperfine parameter distribution in Mössbauer spectroscopy

To obtain reliable information about the structural properties of samples studied by Mossbauer spectroscopy, a technique for estimating the error in the hyperfine parameter distribution in the uniform metric is proposed. The distribution error contains the error caused by the statistical spread of experimental data and the error of the method for solving the ill-posed inverse problem. A criterion of choice of the regularization parameter is proposed.

Effect of the spatial inhomogeneity of a field in a micromaser experiment with the selective measurement of atomic states

It is shown that the theoretical analysis of a micromaser experiment with the selective measurement of atomic states is impossible without consideration of the spatial structure of the field and of the statistical spread of the atomic velocities in the cavity. An approximate theory, ignoring the dynamic effects associated with the mentioned factors, yields not only quantitatively, but also qualitatively different theoretical predictions. The dynamics of the field and the mean number of photons in the trapping states realized in this case differ sig- nificantly from the predictions of the idealized standard theory used at present. Along with the process of estab- lishment of the stationary Fock state of the field, under certain conditions, it appears possible to form the quasi- stationary quantum state of the field with large fluctuations of the number of photons, accompanied by the exit of the field from the cavity ("quasi-dissipation"), and the following stepwise transition into the state of the elec- tromagnetic vacuum. It is shown that, under the conditions of the micromaser experiment, the information about the states of atoms, passed through the cavity, in the case considered, does not allow one to draw an unambig- uous conclusion about the state of the field in the cavity.

A Complex System Model of Glucose Regulatory Metabolism

Consistent with inherent characteristics of a complex system made of a large number of interacting units having deterministic as well as spatiotemporal attributes, a model is developed to represent the human glucose regulatory metabolism within a complex system framework. Essentially, the mass-flow relations pertinent to sugar transport (in the form of glucose), and sugar regulatory hormones (namely, insulin and glucagon) across various participant parts of the body are depicted as nonlinear (logistic) functions; and hence, the temporal growth of blood plasma glucose concentration as well as the rate of change of such concentration levels are derived and expressed in terms of a Bernoulli-Langevin expression, (which functionally depicts the associated nonlinearity whose spatial order is implicitly dictated by the underlying complexity of the processes involved). Simulated results based on theoretical formulations derived are validated with respect to available clinical data due to Cobelli and Mari [1, 2], whose deterministic model of mass-balance relation pertinent to glucose regulatory metabolism is modified and adapted into complex system considerations. The results illustrate the statistical spread with upper and lower bounds associated with the temporal excursions of glucose concentration and its rate of appearance in blood plasma. The outcome of this study, for example, can find applications in refining predictive control algorithms adopted in closed-loop glucose control regimens (via insulin infusion pumping) prescribed to maintain normoglycemia in Type I diabetic patients.

Intrinsic Data Retention in Nanoscaled Phase-Change Memories—Part II: Statistical Analysis and Prediction of Failure Time

The statistical spread of intrinsic data retention times in phase-change memory (PCM) cells is studied. Based on the crystallization and percolation model described in part 1, the crystalline grain size in the amorphous volume after data loss is extracted. From the temperature dependence of grain size, the authors calculate the statistical shape factor for the distribution of failure times, allowing a statistical prediction of data retention in PCM large arrays. The scaling and optimization issues with respect to failure time statistical spread are finally addressed

Collision Risk Posed to the Global Positioning Systemby Disposed Upper Stages

Block IIF satellites in the Global Positioning System will be directly inserted into the constellation by the Evolved Expendable Launch Vehicle. However, the upper stages will not be able to relocate to recommended disposal orbits above the constellation and will remain at least partially in the constellation. The purpose of this study is to determine the collision risk posed to the operational constellation by the disposed upper stages. The analysis includes the effect of the long-term eccentricity growth of the upper-stage disposal orbits. Because eccentricity growth is very sensitive to the initial conditions of the disposal orbit, it is necessary to account for the statistical spread in the initial conditions. This spread is caused by dispersions in launch vehicle and upper-stage maneuvers and by inability to predict the sequence of orbit planes in which disposal will occur. A Monte Carlo procedure was used to quantify this statistical variation. Only one version of the launch vehicle was considered here. Study results include 5-, 50-, and 95-percentile profiles over 200 years of cumulative collision probability and cumulative number of collision avoidance maneuvers that may have to be performed by operational constellation satellites.

Fast surface temperature measurement of Teflon propellant-in-pulsed ablative discharges using HgCdTe photovoltaic cells

High-speed mercury cadmium telluride photovoltaic detectors, sensitive to infrared emission, are investigated as a means of measuring surface temperature on a microsecond time frame during pulsed ablative discharges with Teflon™ as the ablated material. Analysis is used to derive a governing equation for detector output voltage for materials with wavelength dependent emissivity. The detector output voltage is experimentally calibrated against thermocouples embedded in heated Teflon. Experimental calibration is performed with Teflon that has been exposed to ∼200 pulsed discharges and non-plasma-exposed Teflon and is compared to theoretical predictions to analyze emissivity differences. The diagnostic capability is evaluated with measurements of surface temperature from the Teflon propellant of electric micropulsed plasma thrusters. During the pulsed current discharge, there is insufficient information to claim that the surface temperature is accurately measured. However, immediately following the discharge, the postpulse cooling curve is measured. The statistical spread of postpulse surface temperature from shot to shot, most likely due to arc constriction and localization, is investigated to determine an operational envelope for postpulse temperature and mass ablation. This information is useful for determining postpulse ablation contributions to mass loss as well as evaluation of theoretical discharge models currently under development.

Threshold-Voltage statistics and conduction regimes in nanocrystal memories

Results of three-dimensional Monte Carlo simulations of nanocrystal (NC) memory cells are presented to investigate the statistical properties of the threshold-voltage shift (/spl Delta/V/sub T/). It is shown that NC-number fluctuations dominate the /spl Delta/V/sub T/ spread in the ON-state cell conduction regime, while percolation effects add a significant contribution to the statistical spread in the subthreshold region. The dependence of the /spl Delta/V/sub T/ statistics on the cell geometry is also investigated, which shows that NC number and position fluctuations can strongly affect the memory performance and must be suitably modeled.

Cranial Defect Regeneration in a Reserved Space

Cranial defects exceeding a certain size do not heal spontaneously and require surgical treatment. The prevention of uncontrolled soft-tissue ingrowth is crucial in the bony healing of such defects. Bone regeneration of full-thickness cranial defects was assessed in 16 adult New Zealand White rabbits. A single epicranially placed cover was compared with a hollow chamber with an additional barrier on the dural side. After 8 weeks, bone regeneration in the defects was assessed radiologically, histologically, and by fluorescence microscopy. The hollow chamber design resulted in almost complete cranial defect healing. In contrast, five out of 16 defects covered with a single epicranial burr-hole cover showed hardly any visible bone. Inside the reserved space, there was twice as much bone coverage as compared with burr-hole covers only. Providing a reserved space for bone regeneration reduces the statistical spread significantly and thus makes the clinical outcome more predictable. Use of a hollow chamber can serve as a useful tool to assess the effect of bone-stimulating factors such as growth factors and bone substitutes. Hollow resorbable implants may offer a new approach in bone regeneration by reducing the need for bone autografting and the associated donor-site morbidity.

Approaching the Resolution Limit of Nanometer-Scale Electron Beam-Induced Deposition

We report the writing of very high resolution tungsten containing dots in regular arrays by electron beam-induced deposition (EBID). The size averaged over 100 dots was 1.0 nm at fwhm. Because of the statistical spread in the dot size, large and small dots are present in the arrays, with the smallest having a diameter of only 0.7 nm at fwhm. To date these are the smallest features fabricated by EBID. We have also fabricated lines with the smallest having a width at fwhm of 1.9 nm and a spacing of 3.2 nm.

Vergleich verschiedener Methoden der Leistungsüberprüfung im Lehrfach Allgemeinmedizin

A novel Federal Regulation for Basic Medical Education was issued in Germany, which requires an end of course assessment. General Practice (GP) in Duesseldorf has introduced a written examination. An accompanying study was carried out to understand whether different methods of performance evaluation would show equivalent results intraindividually. Out of the GP class 21 students were randomised to undergo an oral examination on top of the regular written examination. Furthermore their teaching practitioners have appraised these students performance in small group teaching. Finally, the students have been rated following a practical term. At the end the students have been interviewed in a focus group to investigate their preferred method of assessment. The survey of the average grades showed comparable results for the written test, the oral examination and small group teaching while the appraisal at the end of the practical term happened to be significantly higher in grade. The comparison of the individual results, however, showed a statistical spreading in all directions. For example, a poor performance in the written test can come along with excellent results in the oral examination and vice versa. The intra-class correlation across all classes has been as low as 0.1. These results support the conclusion that apparently each method can appropriately evaluate only a very specific part of the complex contents of the GP education and of students' performance. In order to properly examine the performance of GP students a combination of different evaluation methods needs to be applied. As an alternative, different skills can be examined in different practical and theoretical test situations in an OSCE.

Normal distribution of confinement energy from a photoluminescence line shape analysis in oxidized porous silicon

Photoluminescence (PL) spectra of oxidized porous silicon (PS) samples plotted against photon energy scale on x-axis would have pure Gaussian form or asymmetric form, depending on the conditions of preparation. At first a pure Gaussian-shape spectrum plotted against photon energy scale on x-axis is analyzed by statistical method on the assumption that the energy of emitted photon would be considered as a random variable simultaneously affected by two independent factors, namely: the statistical spread of wire width and the fluctuation in barrier height of SiOx/Si structures. Comparison of visual plots and statistic characteristic between three spectra plotted against various variables (confinement energy, logarithmic wire width and wire width) scale on x-axis demonstrates the exact description of the spectrum by Gaussian profile using normal distribution of confinement energy. An expression correlating the PL intensity (the number of emitted photons) to the number of wires and quantum efficiency has been developed. Further this expression has been extended to the case of spectrum having asymmetric form, which corresponds to the emission from both wire and dot nano-structures. Thus, our model permits to calculate the structural and spectroscopic parameters such as proportion of wires and dots, integrated intensity, peak energy position, FWHM and standard deviation.

Quantitative analysis of the microscale of auxetic foams

AbstractThe auxetic foams first produced by Lakes have been modelled in a variety of ways, each model trying to reproduce some observed feature of the microscale of the foams. Such features include bent or broken ribs or inverted angles between ribs. These models can reproduce the Poisson's ratio or Poisson's function of auxetic foam if the model parameters are carefully chosen. However these model parameters may not actually reflect the internal structure of the foams. A big problem is that measurement of parameters such as lengths and angles is not straightforward within a 3‐d sample. In this work a sample of auxetic foam has been imaged by 3‐d X‐ray computed tomography. The resulting image is translated to a form that emphasises the geometrical structure of connected ribs. This connected rib data are suitably analysed to describe both the microstructural construction of auxetic foams and the statistical spread of structure, that is, the heterogeneity of an auxetic foam. From the analysis of the microstructure, observations are made about the requirements for microstructural models and comparisons made to previous existing models. From the statistical data, measures of heterogeneity are made that will help with future modelling that includes the heterogeneous aspect of auxetic foams. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Möglichkeiten der 16-Schicht-CT bei der linksventrikulären Funktionsbestimmung: Beurteilung zweier unterschiedlicher Software-Tools zur quantitativen Funktionsanalyse sowie qualitative Bewertung von Wandbewegungsstörungen im Vergleich zur Magnetresonanztomographie

To determine global and regional left ventricular (LV) function from retrospectively gated multidetector row computed tomography (CT) by using two different semiautomated analysis tools and to correlate the results with those of magnetic resonance imaging (MRI). Nineteen patients (5 females, 14 males, mean age 69 years) underwent 16-slice spiral-CT (MS-CT) with standard technique without administration of beta-blockers for a decrease in the cardiac rate. Ten series of images were reconstructed at every 10 % of the RR-interval. With commercially available software capable of semiautomated contour detection, end-diastolic and end-systolic LV volumes (EDV and ESV) were determined from short-axis multiplanar CT reformations (MPR). Axial images of the end-systolic and end-diastolic cardiac phase were transformed to 3D volumes (3D) to determine EDV and ESV by using a threshold-supported reconstruction algorithm dependent on the contrast enhancement of the left ventricle. Steady-state free-precession cine MR images were acquired in short-axis orientation on the same day in all but one patient. Regional wall motion was assessed qualitatively in 17 left ventricular segments and classified as normo-, hypo-, a- or dyskinetic. Bland-Altman analysis was performed to calculate limits of agreement and systematic errors between CT and MRI. For MPR/3D, mean end-diastolic (144.4/142.8 mL +/- 67.5/67.1) and end-systolic (66.4/68.7 mL +/- 52.1/49.9) LV volumes as determined with MS-CT correlated well with MRI measurements (147.6 mL +/- 67.6 [ r = 0.98/0.96] and 73.3 mL +/- 55.5 [ r = 0.98/0.98], respectively [ p <.001]). LV stroke volume (77.6/74.1 +/- 19.2/23.4 mL for CT vs. 74.4 mL +/- 18.4 for MRI, r = 0.92/0.74) and LV ejection fraction (58.6/55.9 % +/- 13.5/13.7 for CT vs. 55.6 % +/- 13.5 for MRI, r = 0.95/0.91) also showed good correlation (p <.001). Regional wall motion analysis revealed agreement between CT and MRI in 316/323 (97.8 %) myocardial segments. Semiautomated analysis of 16-detector row CT data sets enables global and regional volumetric and functional analysis. The CT results correlate well with MRI findings for short axis MPR and for 3D volume reconstructions, with a higher statistical spread for the 3D method. The underestimation of end-systolic and end-diastolic volumes with CT may be caused by partial volume averaging due to the lower temporal resolution as compared with MRI.

Monte Carlo Simulation of Residential Electricity Demand for Forecasting Maximum Demand on Distribution Networks

The prevalent engineering practice (PEP) for maximum demand estimation in low-voltage (LV) electricity networks is based on an After Diversity Maximum Demand (ADMD) modified by a diversity factor. This method predicts the maximum likely voltage drop accounting for consumer diversity. However, this approach does not take into account the stochastic nature of the demand and is inconsistent with international power quality standards. We present a Monte Carlo simulation model of consumer demand taking into account the statistical spread of demand in each half hour using data sampled from a gamma distribution. The parameters of the gamma distribution are based on data metered at a number of residential properties fed by one transformer. The simulated demand is corrected for temperature and total consumption. The simulated profiles at the residential properties are aggregated and the simulated maximum demand is compared with actual maximum demand at a given transformer and an entire distribution network showing good agreement in both cases.

An assessment method for unstable vibration in multispan tube bundles

The flow external to the tubes in a heat exchanger tube bundle may cause large amplitude tube vibration. The most severe mechanism is a fluidelastic instability which can damage tubes in a matter of weeks or months. This mechanism has been the subject of many laboratory experiments and theoretical research over the past 30 years, and consequently, there is a body of data ready to be passed on to those involved in the design of heat exchangers. However, this data is not in a readily usable form because laboratory conditions are very different to those found in a typical heat exchanger where fluid properties vary considerably with location. In order to deal with these variations, an assessment equation is derived which takes into account the changing flow conditions along the length of a heat exchanger, the geometry of the tube support system and the dissipation of energy by the vibrating tubes. The assessment equation uses fluidelastic force coefficients. Unfortunately, there has only been a very limited attempt to measure these coefficients directly. Therefore, a method is developed which shows how these coefficients can be deduced from available measured data. This requires the existing data correlations for fluidelastic instability to be viewed in a fresh and more general manner. The heart of the assessment method is a modal analysis of the tubes. This modal analysis is undertaken in two stages and covers both the fluid forces that cause interactions between neighbouring tubes and the variations in tube amplitude controlled by the tube supports. The assessment equation makes the energy dissipation, expressed by a damping factor, the subject of the assessment equation. This is useful because damping data has a wide statistical spread, which introduces considerable uncertainty, and it is necessary to introduce a probabilistic approach when managing the technical risks of fluidelastic vibration.

Estimation of parameters of dose–volume models and their confidence limits

Predictions of the normal-tissue complication probability (NTCP) for the ranking of treatment plans are based on fits of dose–volume models to clinical and/or experimental data. In the literature several different fit methods are used. In this work frequently used methods and techniques to fit NTCP models to dose response data for establishing dose–volume effects, are discussed. The techniques are tested for their usability with dose–volume data and NTCP models. Different methods to estimate the confidence intervals of the model parameters are part of this study. From a critical-volume (CV) model with biologically realistic parameters a primary dataset was generated, serving as the reference for this study and describable by the NTCP model. The CV model was fitted to this dataset. From the resulting parameters and the CV model, 1000 secondary datasets were generated by Monte Carlo simulation. All secondary datasets were fitted to obtain 1000 parameter sets of the CV model. Thus the ‘real’ spread in fit results due to statistical spreading in the data is obtained and has been compared with estimates of the confidence intervals obtained by different methods applied to the primary dataset. The confidence limits of the parameters of one dataset were estimated using the methods, employing the covariance matrix, the jackknife method and directly from the likelihood landscape. These results were compared with the spread of the parameters, obtained from the secondary parameter sets. For the estimation of confidence intervals on NTCP predictions, three methods were tested. Firstly, propagation of errors using the covariance matrix was used. Secondly, the meaning of the width of a bundle of curves that resulted from parameters that were within the one standard deviation region in the likelihood space was investigated. Thirdly, many parameter sets and their likelihood were used to create a likelihood-weighted probability distribution of the NTCP. It is concluded that for the type of dose response data used here, only a full likelihood analysis will produce reliable results. The often-used approximations, such as the usage of the covariance matrix, produce inconsistent confidence limits on both the parameter sets and the resulting NTCP values.

An international round-robin experiment to evaluate the consistency of nanoindentation hardness measurements of thin films

We conducted an international round-robin experiment to determine the consistency of nanoindentation hardness measurements of thin films among six different laboratories, using three different samples. These samples were chosen to present a challenge of indenting at small loads (μN range). They were: 250-nm-thick TiN x , 700-nm-thick TiC, and 500-nm-thick TiB 2/TiC multilayer coatings (each layer being 3-nm thick), prepared at Northwestern University using magnetron sputtering on silicon (0 0 1) substrates. Each research team was free to use whatever nanoindentor and analysis methods at its disposal. This round-robin experiment demonstrates that for the hardness range of interest (15–35 GPa) and using well-documented procedures and analysis methods, the reported results from all laboratories are essentially the same, allowing for a statistical spread of approximately ±14%. For consistent hardness measurements, four precautions must be observed: (i) proper tip-area function calibration, (ii) using sharp indenters, (iii) performing nanoindentation measurements with minimal thermal drift and with drift correction, (iv) using smooth samples, and (v) measuring the full hardness–maximum penetration curve.

Initiation of microwave-induced electrical breakdown of high-pressure gases

Measurements of microwave-induced electrical breakdown at 2.45 GHz in Ar, Kr, and Xe have been made in a tunable microwave cavity. The influence of UV illumination on gas breakdown at pressures up to 300 torr, and data on fiber initiator-induced breakdown above atmospheric pressure are presented. A marked decrease in the statistical spread in breakdown was observed with UV illumination, but the maximum pressures at which breakdown occurred with available microwave power, with and without UV illumination, were the same. To initiate breakdown in gases above 1 atm, a conducting fiber was used to enhance the applied macroscopic electric field at the fiber tip. Using 8-/spl mu/m diameter SiC fibers coated with 0.2-/spl mu/m-thick Pt, breakdown was obtained with pulses as short as 0.25 ms in the pressure range 1-3 atm for Ar, Kr, and Xe. The required microwave electric field at 2280 torr with one fiber was less than that at 200 torr without a fiber. The increase of the breakdown field with pressure was much slower than linear. The effect of fiber length, diameter, orientation, and conductivity, and of the number of fibers, on the required breakdown electric field, and fiber initiation in Cl/sub 2/ mixture gases, were also investigated.

The silica heat flow interpretation technique: application to continental Australia

The silica heat flow interpretation technique [Swanberg, C.A. and Morgan, P., J. Geophys. Res. 117 (1979) 227–241; J. Geophys. Res. 85 (1980) 7206–7214] has been applied and tested in mainland Australia, using a database of approximately 41 000 Australian groundwater analyses. The silica geotemperature of the groundwaters was obtained by substituting the dissolved silica content of a groundwater into the quartz geothermometer equation of Truesdell [(1976) Proceedings of the Second United Nations Symposium on the Development and Use of Geothermal Resources. San Francisco, CA, USA, 20–29 May, 1975, Vol. 1]. The average silica geotemperature value for 1×1° (latitude×longitude) grid cells has been calculated and the results plotted against published traditional heat flow values for those grid cells [Cull, J.P. (1982) BMR J. Aust. Geol. Geophys. 7, 11–21], to form silica heat flow estimation models. Data exclusion criteria, based upon data quantity and statistical spread have been applied to both the groundwater data and the traditional heat flow data. This was done in order to exclude areas that were poorly categorized in terms of data quality and quantity. For the remaining data, a significant linear relationship between the groundwater geotemperature estimates and traditional heat flow measurements has been identified for four of the models with a t-test on the correlation coefficient. Estimates of regional heat flow were then made by applying the calibration models in areas with no traditional heat flow measurements but adequate groundwater data. A silica heat flow map has been constructed using one of the models and the differences between it and the traditional heat flow map evaluated. Good correlations exist between the silica heat flow map and the traditional heat flow map, except for the northwest Yilgarn, of WA, Australia, where silica heat flow data give significantly higher values than traditional data. The silica heat flow map identifies areas of high heat flow associated with some large-scale geological features such as the granite belt in southeastern Australia. The calibration models result in some silica heat flow estimates exceeding natural likely values. This suggests that the calibrations need further refining for Australian conditions.

Bias properties of logarithmic and asinh magnitudes at very low flux levels

The observation of flux sources near the limit of detection requires a careful evaluation of possible biases in magnitude determination. Both the traditional logarithmic magnitudes and the recently proposed inverse hyperbolic sine (asinh) magnitudes are considered. Formulae are derived for three different biasing mechanisms: the statistical spread of the observed flux values arising from e.g. measurement error; the dependence of these errors on the true flux; and the dependence of the observing probability on the true flux. As an example of the results, it is noted that biases at large signal-to-noise ratios R, at which the two types of magnitude are similar, are of the order of — (p+1)/R2, where the exponent p parametrizes a power-law dependence of the probability of observation on the true flux.