Small Measurement Errors Research Articles

Adaptive Density Estimation From Data With Small Measurement Errors

In this paper, we study the problem of density estimation from data that contains small measurement errors. The only assumption on these errors is that the maximal measurement error is bounded by some real number converging to zero for sample size tending to infinity. In particular, we do not assume that the measurement errors are independent with expectation zero. We estimate the density by a standard kernel density estimate applied to data with measurement errors and derive a data-driven method to choose its bandwidth. We derive an adaptation result for this estimate and analyze the expected L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> error of our density estimate depending on the smoothness of the density and the size of the maximal measurement error. The results are applied in a density estimation problem in a simulation model, where we show under suitable assumptions that the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> error of our newly proposed estimate converges to zero much faster than the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> error of the standard kernel density estimate if both are based on the same number of observations in the simulation model. The performance of the method in case of finite sample size is analyzed using simulated data.

Combining point and regular lattice data in geostatistical interpolation

This work studies how to include both point and areal measurements when estimating gaussian fields by kriging. To achieve this objective, three geostatistical approaches are considered for the areal distributed data: (a) regionalized measurements that are geographically referenced by their centroid as if they were point measurements, (b) regionalized measurements that are explicitly accounted by formally computing all the needed covariances (i.e. area-to-area, area-to-point and point-to-point covariances, respectively) and (c) regionalized measurements that are used as an external drift variable. Results indicate that the measurement error corresponding to the areal data plays a key role to decide when the spatial support of the areal measurements is relevant. For small measurement errors, it is necessary to explicitly consider the spatial support of the areal measurements to avoid large estimation variances. For large measurement errors, the difference between defining areal measurements by using their actual spatial support and defining areal measurements by referencing them by their centroids (i.e. gravity centre) is small. In this situation, it is possible to use the areal measurements as an external drift instead of merging both types of information (i.e. point and areal data) as measurements for kriging. In this case, the cross-validation analysis shows a larger coefficient of determination, similar average kriging variance and smaller mean square error than the obtained in the case of merging point and areal measurements for kriging.

The graded cycling test combined with the talk test is reliable for patients with ischemic heart disease

PURPOSE: To assess relative reliability and measurement error of the Graded Cycling Test (GCT) with the Talk Test (TT) for patients with cardiac disease. METHODS: Patients (N = 64; women, n = 30) with ischemic heart disease performed the GCT with the TT twice in 1 day. Every minute the patient recited a text passage of 30 words. The question Are you still able to speak comfortably? was then answered: Yes (TT+), Not sure (TT+/-), or No (TT-). Two physiotherapists (PTs) rated when the speaking ability was affected by ventilation. Relative reliability: intraclass correlation coefficient (ICC)2.1 and absolute reliability: standard error of measurement with 95% CI (SEM95) and smallest real difference (SRD) were calculated. RESULTS: Intraclass correlation coefficient values of 0.90, 0.91, and 0.90 were observed for TT+, TT+/-, and TT-, respectively. Physiotherapist ICCs ranged between 0.81 and 0.88. SEM95 ranged between 17.2 and 18.3 watts (W), with corresponding SRD values between 24.4 and 25.9 W for the patient ratings. The PT ratings ranged between 15.8 and 21.4 W (SEM95) and between 22.3 and 30.3 W (SRD). CONCLUSIONS: The TT, combined with the GCT, was well tolerated by patients with cardiac disease in clinical settings with small measurement error and an excellent relative reliability. These results apply to both patient-rated and PT-rated TT.

Correction of wall adhesion effects in batch settling of strong colloidal gels

The batch settling test is widely used to estimate the compressive rheology of strongly flocculated colloidal suspensions, in particular the compressive yield strength and hydraulic permeability. Recently it has been discovered (Lester et al., 2014) that wall adhesion effects in these tests may be significantly greater than previously appreciated, which can introduce unbounded errors in the estimation of these rheological functions. Whilst a methodology to solve the underlying static problem and correct for wall adhesion effects has been developed, this method is quite complex and unwieldy, involving solution of a 2D visco-elastic constitutive model for strong colloidal gels. In this paper we develop a highly simplified 1D visco-plastic approximation to the visco-elastic model which admits analytic expressions for the equilibrium solids concentration profile and bed height. These expressions facilitate robust estimation of the compressive yield and wall adhesion strength via nonlinear regression of experimental data in the presence of small measurement errors.

Volumetric blood flow measurement using Doppler ultrasound: concerns about the technique.

Volumetric blood flow measurement using Doppler ultrasound: concerns about the technique.

Measurement errors should always be incorporated in phylogenetic comparative analysis

Summary The evolution of continuous traits is the central component of comparative analyses in phylogenetics, and the comparison of alternative models of trait evolution has greatly improved our understanding of the mechanisms driving phenotypic differentiation. Several factors influence the comparison of models, and we explore the effects of random errors in trait measurement on the accuracy of model selection. We simulate trait data under a Brownian motion model (BM) and introduce different magnitudes of random measurement error. We then evaluate the resulting statistical support for this model against two alternative models: Ornstein–Uhlenbeck (OU) and accelerating/decelerating rates (ACDC). Our analyses show that even small measurement errors (10%) consistently bias model selection towards erroneous rejection of BM in favour of more parameter‐rich models (most frequently the OU model). Fortunately, methods that explicitly incorporate measurement errors in phylogenetic analyses considerably improve the accuracy of model selection. Our results call for caution in interpreting the results of model selection in comparative analyses, especially when complex models garner only modest additional support. Importantly, as measurement errors occur in most trait data sets, we suggest that estimation of measurement errors should always be performed during comparative analysis to reduce chances of misidentification of evolutionary processes.

An Inline RF Power Sensor Based on Fixed Capacitive Coupling for GaAs MMIC Applications

This letter proposes an inline RF power sensor based on fixed capacitive coupling for GaAs MMIC applications. In the design, a certain percentage of the input power coupled by a beam and sensed in a thermopile sensor, where the beam is not required to release to obtain a fixed capacitance for high-power levels and increase the dynamic range. This sensor offers the compatible capability with the GaAs MMIC technology. Measured reflection and insertion losses are <;-24.2 and 0.73 dB at X-band, respectively. Experiments demonstrate that this inline sensor exhibits good linearity of the output response from 1 to 200 mW, and results in the average sensitivity of ~29.5 μV/mW at 10 GHz. The sensitivity increases with the increase of the X-band frequency, with small measurement errors.

The influence of an object surface on measuring geometric dimensions in digital optical microscopy

The paper presents experimental findings on measuring metrological parameters of LOMO projections obtained with an atomic force microscope. The research has proved that gauge-producing technologies that consist in mechanical mirror cutting result in flood coating. The floods obscure the position of the marker point in the program of the coordinates that outline object dimensions. We have determined that, with equal deviations from the focus, the biggest measurement error is observed while using a LOMO gauge on the projection. The experiment has proved that, under the same conditions of the experiment, a gauge on LOMO transmission (photolithography technology) and a 2D Bruker projection gauge, which is produced by means of electronic lithography, cause much smaller measurement errors. This should be taken into account while choosing a microscope focus gauge.

Quantifying forearm and wrist joint power during unconstrained movements in healthy individuals.

BackgroundWrist movement-related injuries account for a large number of repetitive motion injuries. Remarkably little, if any, empirical data exist to quantify the impact of neuromuscular disorders affecting the wrist or to validate the effectiveness of rehabilitation training programs on wrist functions. The aim of this project was to develop a biomechanical model for quantifying wrist and forearm kinetics during unconstrained movements, to assess its reliability and to determine its sensitivity.MethodsTwenty healthy subjects with no history of upper arm and wrist pain volunteered for the experiment. To evaluate the reliability of the data, we quantified their forearm and wrist kinetics on two different days (minimum and maximum number of days between experimental sessions were 1 and 4 days respectively). To measure forearm and wrist kinetics, an apparatus was built to offer rotational inertia during forearm and wrist movements. An inertial measurement unit was located near the top of the device measuring its angular position along the frontal and sagittal planes. We used a mathematical model to infer forearm and wrist torque. Thereafter, we calculated the product of torque and angular velocity to determine forearm and wrist power.ResultsResults revealed that for 75% of the power and torque measurements the ICC was greater than 0.75 (range: 0.77 – 0.83). Torque and power measurements for adduction movements, however, were less reliable (i.e., ICC of 0.60 and 0.47, respectively) across testing sessions. The biomechanical model was robust to small measurement errors, and the power peaks between the first and second testing session were not different indicating that there was no systematic bias (i.e., motor performance improvement) between testing sessions.ConclusionsThe biomechanical model can be used to assess the effectiveness of rehabilitation programs, document the progression of athletes or conduct research-oriented testing of maximum forearm and wrist kinetic capacities. Nonetheless, caution should be taken when assessing forearm and wrist power adduction movements. Future studies should aim at defining a set of normative values, for various age groups, for forearm and wrist joint torque and power in healthy individuals.Electronic supplementary materialThe online version of this article (doi:10.1186/1743-0003-11-157) contains supplementary material, which is available to authorized users.

Measurement of Geometric Parameters for Cutting Tools Based on MATLAB

In this paper, the MATLAB image processing technology has been adopted to obtain the contour of a turning tool with arc blade by binarization of the image, median filter as well as detection of the edge. Then curve-fitting method have been used to fit the contour of straight edge and arc-edge respectively. Finally, the nose angle of the cutter and the arc radius of the turning tool have been obtained by the analysis of fitting results of slope for straight edge and curvature radius for arc-edge. It is shown that the measurement of geometric parameters for cutting tools based on MATLAB not only has small measurement errors and high measurement efficiency, but also can be widely used to obtain tiny geometry parameters for tools with high precision.

The impact of mismeasurement in performance benchmarking: A Monte Carlo comparison of SFA and DEA with different multi-period budgeting strategies

Performance-based budgeting has received increasing attention from public and for-profit organizations in an effort to achieve a fair and balanced allocation of funds among their individual producers or operating units for overall system optimization. Although existing frontier estimation models can be used to measure and rank the performance of each producer, few studies have addressed how the mismeasurement by frontier estimation models affects the budget allocation and system performance. There is therefore a need for analysis of the accuracy of performance assessments in performance-based budgeting. This paper reports the results of a Monte Carlo analysis in which measurement errors are introduced and the system throughput in various experimental scenarios is compared. Each scenario assumes a different multi-period budgeting strategy and production frontier estimation model; the frontier estimation models considered are stochastic frontier analysis (SFA) and data envelopment analysis (DEA). The main results are as follows: (1) the selection of a proper budgeting strategy and benchmark model can lead to substantial improvement in the system throughput; (2) a “peanut butter” strategy outperforms a discriminative strategy in the presence of relatively high measurement errors, but a discriminative strategy is preferred for small measurement errors; (3) frontier estimation models outperform models with randomly-generated ranks even in cases with relatively high measurement errors; (4) SFA outperforms DEA for small measurement errors, but DEA becomes increasingly favorable relative to SFA as the measurement errors increase.

The graded cycling test combined with the talk test is reliable for patients with ischemic heart disease.

To assess relative reliability and measurement error of the Graded Cycling Test (GCT) with the Talk Test (TT) for patients with cardiac disease. Patients (N = 64; women, n = 30) with ischemic heart disease performed the GCT with the TT twice in 1 day. Every minute the patient recited a text passage of 30 words. The question "Are you still able to speak comfortably?" was then answered: "Yes" (TT+), "Not sure" (TT±), or "No" (TT-). Two physiotherapists (PTs) rated when the speaking ability was affected by ventilation. Relative reliability: intraclass correlation coefficient (ICC)2.1 and absolute reliability: standard error of measurement with 95% CI (SEM95) and smallest real difference (SRD) were calculated. Intraclass correlation coefficient values of 0.90, 0.91, and 0.90 were observed for TT+, TT±, and TT-, respectively. Physiotherapist ICCs ranged between 0.81 and 0.88. SEM95 ranged between 17.2 and 18.3 watts (W), with corresponding SRD values between 24.4 and 25.9 W for the patient ratings. The PT ratings ranged between 15.8 and 21.4 W (SEM95) and between 22.3 and 30.3 W (SRD). The TT, combined with the GCT, was well tolerated by patients with cardiac disease in clinical settings with small measurement error and an excellent relative reliability. These results apply to both patient-rated and PT-rated TT.

Photonic Multiple Frequency Measurement Using a Frequency Shifting Recirculating Delay Line Structure

A new photonic frequency measurement structure that can realise multiple-frequency measurement, while simultaneously achieving a high resolution and a wide measurement range is presented. It is based on successively frequency shifting the modulation sideband of an optical signal until it falls close to the reference carrier frequency, and then combining it with an unshifted carrier and detecting it through a narrowband filter. Experimental results demonstrate a multiple-frequency detection capability over a range of 0.1-20 GHz, which can readily be extended to 100 GHz, together with a high measurement resolution of 250 MHz and small measurement error.

Inverse modeling of a solar collector involving Fourier and non-Fourier heat conduction

This article applies the golden section search method (GSSM), simplex search method (SSM) and differential evolution (DE) for predicting the unknown Fourier number (Fo), Vernotte number (Ve) and non-dimensional solar heat flux (S∗) in a flat-plate solar collector when subjected to a given temperature requirement. The required temperature field is calculated using an analytical forward method by considering Fourier and non-Fourier heat conduction, and using this, the inverse problem is solved to predict the Fo, Ve and S∗ which are assumed to be the unknown parameters. The study reveals that the temperature field is highly sensitive to the Fo, thus even a small error in the temperature measurement can result in an unrealistic estimation of heating time of the collector. The present study is proposed to be useful in determining the time, the time lag and solar heat flux for controlled heating of an absorber plate within a stipulated time, which will be required to attain a prescribed/desired temperature distribution. Additionally, the study also shows that subjected to different time levels, the same temperature distribution is possible through different absorber plate materials. It has been observed from the present study that apart from SSM and DE, GSSM fails to estimate the unknown parameters at large value of Ve and small value of Fo, due to the associated fluctuation in the measured temperature field. The present study further discusses the computational performance of direct search method (e.g. GSSM and SSM) with that of the evolutionary method (DE) in terms of the maximum number of iteration and CPU time required to achieve the desired objective.

A Procedure to Determine the Optimal Sensor Positions for Locating AE Sources in Rock Samples

Within a research work aimed to better understand frost weathering mechanisms of rocks, laboratory tests have been designed to specifically assess a theoretical model of crack propagation due to ice segregation process in water-saturated and thermally microcracked cubic samples of Arolla gneiss. As the formation and growth of microcracks during freezing tests on rock material is accompanied by a sudden release of stored elastic energy, the propagation of elastic waves can be detected, at the laboratory scale, by acoustic emission (AE) sensors. The AE receiver array geometry is a sensitive factor influencing source location errors, for it can greatly amplify the effect of small measurement errors. Despite the large literature on the AE source location, little attention, to our knowledge, has been paid to the description of the experimental design phase. As a consequence, the criteria for sensor positioning are often not declared and not related to location accuracy. In the present paper, a tool for the identification of the optimal sensor position on a cubic shape rock specimen is presented. The optimal receiver configuration is chosen by studying the condition numbers of each of the kernel matrices, used for inverting the arrival time and finding the source location, and obtained for properly selected combinations between sensors and sources positions.

Design of quasi-static piezoelectric plate based transducers by using topology optimization

Sensors and actuators based on piezoelectric plates have shown relevance in the field of smart structures. Recently, modern design techniques such as the topology optimization method have been applied to design laminated piezoelectric transducers, and design requirements such as maximizing static displacements (actuator design) and output voltages (sensor design) have been employed. However, it may be desirable to keep the transducer working range before its first resonance frequency. In this case, the (displacement or voltage) amplitude is expected to be constant with excitation frequency, which may not be the case when only static design requirements are employed. Thus, considering sensor design, if the amplitude is constant, an undetected change in the excitation frequency would cause a small measurement error. Regarding actuators, on the other hand, if the first resonance frequency is small, oscillations in the response to a step excitation (which is usually applied in quasi-static applications, i.e. applications in which the transducer operates under the first resonance frequency) could be high, ultimately causing overshoot, for instance. Thus, in this work, the topology optimization method has been applied to design piezoelectric transducers considering quasi-static operation, by distributing piezoelectric material over a metallic plate and by selecting the material polarization sign, in order to fulfil quasi-static design requirements. This is achieved by maximizing an objective function that depends on both displacements (for actuators) or output voltages (for sensors), and first resonance frequencies. The applied methodology, which encompasses the optimization problem formulation and numerical implementation, is presented. The achieved computational results, corresponding to the design of different types of transducers, clearly show the potential of the proposed methodology to increase the quasi-static working frequency range.

Universal Properties of Łukasiewicz Consequence

Boolean logic deals with {0, 1}-observables and yes–no events, as many-valued logic does for continuous ones. Since every measurement has an error, continuity ensures that small measurement errors on elementary observables have small effects on compound observables. Continuity is irrelevant for {0, 1}-observables. Functional completeness no longer holds when n-ary connectives are understood as [0, 1]-valued maps defined on [0, 1] n . So one must envisage suitable selection criteria for [0, 1]-connectives. Łukasiewicz implication has a well known characterization as the only continuous connective $${\Rightarrow}$$ satisfying the following conditions: (i) $${x\Rightarrow(y\Rightarrow z)= y\Rightarrow(x\Rightarrow z)}$$ and (ii) $${x\Rightarrow y=1\, \, {\rm iff} x\leq y}$$ . Then syntactic consequence can be defined purely algorithmically using the Łukasiewicz axioms and Modus Ponens. As discussed in this paper, to recover a strongly complete semantics one may use differential valuations.

A MAXIMUM LIKELIHOOD APPROACH TO ESTIMATING CORRELATION FUNCTIONS

We define a Maximum Likelihood (ML for short) estimator for the correlation function, {\xi}, that uses the same pair counting observables (D, R, DD, DR, RR) as the standard Landy and Szalay (1993, LS for short) estimator. The ML estimator outperforms the LS estimator in that it results in smaller measurement errors at any fixed random point density. Put another way, the ML estimator can reach the same precision as the LS estimator with a significantly smaller random point catalog. Moreover, these gains are achieved without significantly increasing the computational requirements for estimating {\xi}. We quantify the relative improvement of the ML estimator over the LS estimator, and discuss the regimes under which these improvements are most significant. We present a short guide on how to implement the ML estimator, and emphasize that the code alterations required to switch from a LS to a ML estimator are minimal.

Validation of the urogenital distress inventory (UDI-6) and incontinence impact questionnaire (IIQ-7) in a Dutch population

The Urogenital Distress Inventory (UDI-6) and Incontinence Impact Questionnaire (IIQ-7) assess symptom distress and the impact on daily life of urinary incontinence. The UDI-6 has not been validated before in males. Our aim was to validate the UDI-6 and IIQ-7 in Dutch men and women. The translation to Dutch followed standardized procedures. We validated the IIQ-7 with and without an additional gender-neutral item (IIQ-SF). Adults with urinary incontinence for at least 3 months, completed the measures at inclusion; 1-week after inclusion to evaluate the test-retest reproducibility; and 6 months after inclusion with the addition of the RAND-36 health transition item to assess responsiveness and interpretability. To assess the discriminate ability, a reference population was enrolled. To assess construct validity, the urodynamic diagnosis was used. Questionnaire data of 160 patients were analyzed. Patients reported more symptoms and bother than the reference population (P < 0.001). The internal consistency was good in the IIQ-SF baseline scores (Cronbach's alphas 0.86-0.92), though moderate in the UDI-6 (Cronbach's alphas 0.44-0.66). Both measures showed good reproducibility at the test-retest (Intraclass Correlations Coefficients 0.75-0.85). Construct was adequate with 75% confirmed hypotheses of urodynamic data with measure scores. The measures were responsive after treatment with smaller measurement errors than the minimal important change. No floor or ceiling effects were observed in baseline data. The Dutch UDI-6 and IIQ-7 are reliable, valid, and responsive instruments for assessing symptom distress of urinary incontinence and its impact on daily life in both men and women.

A conceptual framework for geographic knowledge engineering

In many applications, the management of geographic knowledge is very important especially not only for urban and environmental planning, but also for any application in territorial intelligence. However there are several practical problems hindering the efficiency, some of them being technical and other being more conceptual. The goal of this paper is to present a tentative conceptual framework for managing practical geographic knowledge taking account of accuracy, rotundity of earth, the mobility of objects, multiple-representation, multi-scale, existence of sliver polygons, differences in classifying real features (ontologies), the many-to-many relationship of place names (gazetteers) and the necessity of interoperability. In other words, this framework must be robust against scaling, generalization and small measurement errors. Therefore, geographic objects must be distinguished into several classes of objects with different properties, namely geodetic objects, administrative objects, manmade objects and natural objects. Regarding spatial relations, in addition to conventional topological and projective relations, other relations including tessellations and ribbon topology relations are presented in order to help model geographic objects by integrating more practical semantics. Any conceptual framework is based on principles which are overall guidelines and rules; moreover, principles allow at making predictions and drawing implications and are finally the basic building blocks of theoretical models. But before identifying the principles, one needs some preliminary considerations named prolegomena. In our case, principles will be essentially rules for transforming geographic knowledge whereas prolegomena will be assertions regarding more the foundations of geographic science. Based on those considerations, 12 principles are given, preceded by 12 prolegomena. For instance, some principles deal with the transformation of spatial relationships based on visual acuity and granularity of interest, with the influence of neighboring information and cross-boundary interoperability. New categories of geographic knowledge types are presented, spatial facts, cluster of areas, flows of persons, goods, etc., topological constraints and co-location rules. To represent knowledge chunks, three styles are presented, based respectively on descriptive logics, XML and visual languages. To conclude this paper, after having defined contexts of interpretation, an example of visual language to manage geographic knowledge is proposed.