Standard Deviation Of Position Research Articles

State Expansion of a Levitated Nanoparticle in a Dark Harmonic Potential.

We spatially expand and subsequently contract the motional thermal state of a levitated nanoparticle using a hybrid trapping scheme. The particle's center-of-mass motion is initialized in a thermal state (temperature 155mK) in an optical trap and then expanded by subsequent evolution in a much softer Paul trap in the absence of optical fields. We demonstrate expansion of the motional state's standard deviation in position by a factor of 24. In our system, state expansion occurs devoid of backaction from photon recoil, making this approach suitable for coherent wave function expansion.

Autonomous Vehicle Control Comparison

Self-driving features rely upon autonomous control of vehicle kinetics, and this manuscript compares several disparate approaches to control predominant kinetics. Classical control using feedback of state position and velocities, open-loop optimal control, real-time optimal control, double-integrator patching filters with and without gain-tuning, and control law inversion patching filters accompanying velocity control are assessed in Simulink, and their performances are compared. Optimal controls are found via Pontryagin’s method of optimization utilizing three necessary conditions: Hamiltonian minimization, adjoint equations, and terminal transversality of the endpoint Lagrangian. It is found that real-time optimal control and control-law patching filter with velocity control incorporating optimization are the two best methods overall as judged in Monte Carlo analysis by means and standard deviations of position and rate errors and cost.

Comparing forecasting approaches for Internet traffic

In this paper, we experiment with several different forecasting approaches for Internet traffic and a scheme for their evaluation. First the existence of properties such as Short or Long Range Dependence and non-linearity is explored in order to take advantage of such information and offer a couple of alternatives as forecasting models. The proposed models include FARIMA with Normal and Student’s t innovations and two different architectures of Artificial Neural Networks, the Multilayer Perceptron and Radial basis function. Next, we construct a model selection scheme based on the White’s Neural Network test for non-linearity or alternatively combine FARIMA and Neural Networks into hybrid forecasting models. The comparison of all suggested approaches is performed using their average position and standard deviation of position when applied to several known datasets of Internet traffic and when the accuracy of forecasts is measured with three different measures. Based on such a data analysis it is shown that hybridization and the selection of a model according to a non-linearity test are more successful as forecasting approaches over all individual models, as well as over other well-known methods such as Holt–Winters, ARIMA/GARCH and FARIMA/GARCH. This result indicates that forecasting approaches which take non-linearity into account lead to better overall forecasts for Internet traffic.

Postural adaptations to a suprapostural memory task among children with and without developmental coordination disorder

The present study investigated the effects of varying the cognitive demands of a memory task (a suprapostural task) while recording postural motion on two groups of children, one diagnosed with developmental coordination disorder (DCD) and an age-matched group of typically developing children. Two groups, each comprising 38 child volunteers (21 males, 17 females) aged 9 to 10 years, participated in the study. Each child performed a digital memory task at two levels of difficulty, low and high. Positional variability (standard deviation of position) of the head and torso were recorded as the biomechanical responses to the variation in task difficulty. Both groups significantly reduced postural motion when engaged in the high-difficulty condition (p<0.05) compared with the low-difficulty condition. Children with DCD exhibited significantly higher levels of postural motion (p<0.05) than the typically developing children. The typically developing children significantly reduced their postural motion in the high-difficulty condition (p<0.05) compared with the low-difficulty condition, whereas children with DCD did not. Our results suggest that the postural responses of children with DCD differ from those of typically developing children while engaging in a memory task with various levels of difficulty.

Quantum limits to center-of-mass measurements

We discuss the issue of measuring the mean position (center-of-mass) of a group of bosonic or fermionic quantum particles, including particle number fluctuations. We introduce a standard quantum limit for these measurements at ultra-low temperatures, and discuss this limit in the context of both photons and ultra-cold atoms. In the case of fermions, we present evidence that the Pauli exclusion principle has a strongly beneficial effect, giving rise to a 1/N scaling in the position standard-deviation -- as opposed to a $1/\sqrt{N}$ scaling for bosons. The difference between the actual mean-position fluctuation and this limit is evidence for quantum wave-packet spreading in the center-of-mass. This macroscopic quantum effect cannot be readily observed for non-interacting particles, due to classical pulse broadening. For this reason, we also study the evolution of photonic and matter-wave solitons, where classical dispersion is suppressed. In the photonic case, we show that the intrinsic quantum diffusion of the mean position can contribute significantly to uncertainties in soliton pulse arrival times. We also discuss ways in which the relatively long lifetimes of attractive bosons in matter-wave solitons may be used to demonstrate quantum interference between massive objects composed of thousands of particles.

Online portal fluoroscopic verification of adaptive radiotherapy for lung cancer

Information gained from 4D planning imaging studies can aid in designing radiotherapy treatments with reduced normal tissue irradiation for patients with thoracic lesions. With this 4D approach, conventional portal verification techniques will not provide sufficient information for treatment verification. We have developed an online portal verification tool for use with 4D-planned radiotherapy. The purpose of this study is to evaluate the efficacy of 4D portal verification for adaptive radiotherapy for lung cancer. Our approach for respiratory compensation is to treat a target located at the mean respiratory position of the primary tumor, and to optimize the dose distribution to best compensate for the random motion determined from pretreatment 4D CT and fluoroscopy. One prerequisite for such a technique is that tumor motion due to respiration is stable both inter- and intrafraction. The mean position and standard deviation provide criteria for determining the stability. Instability can be compensated either in planning by increasing margins or daily by online correction. In either case, the stability must be verified daily by measuring the mean position and standard deviation. To evaluate the clinical feasibility of daily portal verification, digital fluoroscopy was acquired at two orthogonal projections for 5 patients using an Elekta Synergy (Crawley, UK) accelerator equipped with onboard x-ray volumetric imaging (XVI). Our online portal verification tool was used to generate a respiratory curve from each fluoroscopic study by automatically extracting the diaphragm position in relation to the beam isocenter as a function of time. This respiratory trace was used to generate a probability density function of diaphragm position, and the mean and standard deviation of the position were calculated. Fluoroscopy was acquired once weekly for each patient during treatment. The mean and standard deviation for each weekly fluoroscopic study were compared to the simulation study. Patient-specific margin size as a function of probability of a required daily correction was calculated. A dose profile along the cranio-caudal axis from the clinical treatment plan of each patient was convolved with the probability density function from the simulation fluoroscopy to generate a patient-specific deterministic margin. The deterministic margin accounts for motion-induced effects on the dose distribution without considering the possibility of changes to a patient’s respiration over the course of treatment. A stochastic component of the margin was then generated assuming such uncertainty, and the total margin consisted of the sum of the deterministic and stochastic components. Patient-specific margins were generated (table 1) for probabilities of required daily correction of 5%, 10%, 25%, and 45% of total treatments. Deterministic margins ranged from 0.0 to 2.1 mm, while stochastic margins ranged from 1.7 to 4.7 mm. The average stochastic margins for 5%, 10%, 25%, and 45% were 4.6 mm, 4.0 mm, 3.1 mm, and 2.3 mm, respectively. Total margin for 10% correction probability ranged from 3.5 mm to 6.2 mm. Online portal verification for adaptive radiotherapy for lung cancer must include components to verify not only static positioning, but also the dynamic aspects involving tumor motion. For treatment at the mean tumor position, verification of the stability of the mean and standard deviation of the tumor position allows an assessment of the necessity of online correction to be made. For this study, the total population margin due to respiratory motion could be limited to 6.2 mm allowing for setup corrections 10% of the time.

Measures of Steadiness Are influenced by the Frequency Content of the Signals

0077 Fluctuations in limb acceleration during a steady contraction are often not associated with the fluctuations in limb position. Although the two signals often have two major peaks in the frequency range of 0–4 Hz (low frequency) and 8–12 Hz (high frequency), the low-frequency component is more prominent in the position signal. PURPOSE: To determine the influence of the low-frequency component on the association between simulated fluctuations in position and acceleration. METHODS: Position signals (20 s at 1024 Hz) were generated by summing 1,000 sinusoidal waves of varying frequency (< 15 Hz) and phase. The amplitude of each sinusoidal wave was adjusted so that the power of the low-frequency component in the position signal varied, whereas the amplitude of the high-frequency component remained constant. The position signal was double-differentiated to yield the acceleration signal. The low-frequency component was varied from 0.24 to 93.96% of the total power in the frequency spectrum. Fifty pairs of position and acceleration signals were simulated at each level of low-frequency power. Correlation coefficients between the standard deviations of position and acceleration were calculated at each level. RESULTS: The low- and high-frequency power in the acceleration signal ranged from 0.006% to 5.70% and from 86.77% to 79.56% total power, respectively. The correlation coefficients between the standard deviation of position and acceleration was distributed from −0.184 to 0.967. The correlation coefficient was high when the low-frequency component was small and it decreased continuously with an increase in low-frequency power of each signal: up to ∼ 60% in position and ∼ 0.5% in acceleration. For the signals with greater low-frequency power, the correlation coefficient was low (< 0.4) and variable. CONCLUSION: The results suggest that the association between the two measures of steadiness (fluctuations in position and acceleration) depend primarily on small changes in low-frequency power in the signals, particularly the acceleration signal.

A Study on the Design of an Integrated Pipe Surveying System for the Deformation Analysis of Landfill Sites

In the course of a research program on the monitoring of structures which takes place at the Technical University, Braunschweig, we have set ourselves the goal to survey the pipe systems of landfill sites. The intended standard deviation of position is three centimeters on one hundred meters. Here, the process of choosing and planning the adaptation of a system apt to fulfil this task is summarized. We compared three systems: the deflectometer, the Swedish Maxibor system and an inertial measurement system comprising three Honeywell GG 1320 laser gyros and three Q-Flex QA 2000–30 accelerometers, which finally made the race.

A method for obtaining the error of a peak position due to counting statistics

A method is described to determine the standard deviation of a peak position due to counting statistics. In this method, the statistical noise for a peak is first simulated based on the model of Poisson distribution and then imposed on the peak. The peak position is then determined by a profile fitting routine. By repeated application of these processes on a given peak, one obtains a number of slightly different peak positions and hence their corresponding standard deviation. This method can be applied to a peak described by any analytical function or a set of any number of digitized points. Investigation of the precision of peak positions was carried out by applying this method on various analytical peaks located at low, medium, and high 2θ angles. The results showed that the standard deviation of a peak position decreases with increasing P/B and P/σ, where P is the net peak count above the background B and σ=(P + B)½ is the estimated standard deviation for noise. It increases with increasing peak width and Δ2θ, the step size used to digitize the peak profiles. It decreases as the 2θ range of simulation and fitting increases up to 2θ=3 FWHMs (full width at half maximum) and remains at a constant value thereafter. The standard deviation of the position of a real peak obtained by ten repeated measurements is 0.0034°; the corresponding result obtained by the current method is 0.0035°. This peak is best fitted by a Pearson-VII function and the standard deviation obtained by this method is 0.013° when only the head portion with intensity ≥85% maximum net intensity is simulated and fitted. The corresponding result obtained by the traditional method of parabola fitting is 0.0055°. Therefore, the precision of a peak position also depends on the peak shape.

Validating and improving elevation data of a satellite-image map of Filchner,Ronne Ice Shelf, Antarctica, with Results from ERS-1

A satellite-image map with surface-elevation contours of Filchner Ronne Ice Shelf has been published previously as a topographic map. The image map was constructed from a mosaic of 69 Landsat Multispectral Scanner (MSS) images and NOAA AVHRR data. The standard deviation in position in the central part of the mosaic is ±125m. Topographic-glaciologic features were taken from Landsat scenes and represent the best coastline of this region. Surface elevations have been calculated from airborne and ground measurements of either ice thickness (by assuming hydrostatic equilibrium) or barometric pressure. Accuracies vary from ±2 to ±7 m, Oversnow trigonometric levelling in the northeastern part of the ice shelf, tied to sea level at the ice front, has given accuracies of ± 1m. Accuracies reduce to about ±20 m in the grounded ice areas,ERS-I radar-altimeter data over the ice shelf have been processed to give ellipsoidal heights elevation above the ellipsoid), Geoidal reductions have been used to convert these to orthometric heights (elevation above sea level). No tidal corrections have been applied. The overall accuracy of the radar-altimeter-derived elevations is estimated to be better than ±5m. There are noticeable differences from the topographic map in the central part where the radar data indicate a lower surface. However, the maps agree to within the stated error figures.

Validating and improving elevation data of a satellite-image map of Filchner,Ronne Ice Shelf, Antarctica, with Results from ERS-1

A satellite-image map with surface-elevation contours of Filchner Ronne Ice Shelf has been published previously as a topographic map. The image map was constructed from a mosaic of 69 Landsat Multispectral Scanner (MSS) images and NOAA AVHRR data. The standard deviation in position in the central part of the mosaic is ±125m. Topographic-glaciologic features were taken from Landsat scenes and represent the best coastline of this region. Surface elevations have been calculated from airborne and ground measurements of either ice thickness (by assuming hydrostatic equilibrium) or barometric pressure. Accuracies vary from ±2 to ±7 m, Oversnow trigonometric levelling in the northeastern part of the ice shelf, tied to sea level at the ice front, has given accuracies of ± 1m. Accuracies reduce to about ±20 m in the grounded ice areas, ERS-I radar-altimeter data over the ice shelf have been processed to give ellipsoidal heights elevation above the ellipsoid), Geoidal reductions have been used to convert these to orthometric heights (elevation above sea level). No tidal corrections have been applied. The overall accuracy of the radar-altimeter-derived elevations is estimated to be better than ±5m. There are noticeable differences from the topographic map in the central part where the radar data indicate a lower surface. However, the maps agree to within the stated error figures.

Changes in the Variability of Movement Trajectories With Practice

We studied variability in movement phase plane trajectories (velocity-position relation) during movement. Human subjects performed 10 degrees and 30 degrees elbow flexion and extension movements in a visual step tracking paradigm. The area of ellipses with radii equal to one standard deviation in position and velocity was taken as a measure of trajectory variability. Trajectory variability was determined at 10-ms intervals throughout movements. Trajectory variability in both the acceleration and deceleration phases of movement decreased with practice. The average trajectory variability during deceleration was greater than that during acceleration even after extended practice (1000 trials). During practice, subjects usually increased movement speed while maintaining end-position accuracy. Trajectory variability was also related to movement speed when equal amounts of practice were given. Short duration (fast) movements had greater trajectory variability than long duration movements. Thus there is a tradeoff between movement speed and trajectory variability similar to the classical speed-accuracy tradeoff. Trajectory variability increased rapidly during the acceleratory phase of movement. The rate of increase was positively related to both movement amplitude and speed. Thus, the forces producing limb acceleration were variable and this variability was more marked in faster and larger movements. In contrast, trajectory variability increased more slowly or actually decreased during the deceleratory phase of movements. Forces involved in limb deceleration thus appeared to compensate to a greater or lesser degree for the variability in accelerative forces. The experiments indicate that the entire trajectory of simple limb movements is controlled by the central nervous system. Variations in accelerative forces may be compensated for by associated variations in decelerative forces. The linkage between accelerative and decelerative forces is progressively refined with practice resulting in decreased variability of the movement trajectory.

Arrival and departure time in quantum mechanics

The arrival time at a point in the case of the one-dimensional motion of a classical particle is only predictable if initially the position and velocity are both known precisely. It is shown that such an arrival time can be defined in a probabilistic sense when only the initial means and standard deviations of position and velocity are known. The arrival time so defined depends on the subjective concept of confidence limit. It is further shown that arrival time in the latter sense goes over to quantum mechanics. A lower bound on the transit time is derived for this situation by use of the Mandelstam-Tamm inequality.

Error analysis in the biophysical applications of a flatbed autodensitometer

The positional, electronic, and density accuracy of the Syntex AD-1 flatbed autodensitometer is discussed. The standard deviation of optical density measurements due to electronic noise is ± 0.001 optical density units at an optical density of 0, rising to ± 0.04 at an optical density of 2. No deviation from linearity in optical density measurements could be measured. During scanning, the standard deviation in position is less than 1.5 μm. Film grain noise for various films is compared and the effect of signal averaging on this noise is studied. This scanner is compared with other scanners available for accuracy of data collection from precession films.

Control Densification by Analytic Photogrammetry

Numerical methods in photogrammetry began to receive wide-spread attention in the early fifties with the development of the large digital computers. The Worldwide Satellite Triangulation Program of the sixties proved that, with care and deliberate production controls, first-order geodetic accuracies could be obtained for precision photogrammetric cameras and numerical data reduction. Research is presently underway at the National Ocean Survey to develop equipment, flight configuration, and reduction techniques that will provide internal photogrammetric pointing precision of at least one part in 250,000 of the flight altitude for conventional mapping. The projected goals of the system are to produce ground coordinates with a standard deviation in position of —2.5 cm over an area of 48 km with peripheral horizontal geodetic control spaced at 16 km.