Sufficient Number Of Measurements Research Articles

Transition role of entangled data in quantum machine learning

Entanglement serves as the resource to empower quantum computing. Recent progress has highlighted its positive impact on learning quantum dynamics, wherein the integration of entanglement into quantum operations or measurements of quantum machine learning (QML) models leads to substantial reductions in training data size, surpassing a specified prediction error threshold. However, an analytical understanding of how the entanglement degree in data affects model performance remains elusive. In this study, we address this knowledge gap by establishing a quantum no-free-lunch (NFL) theorem for learning quantum dynamics using entangled data. Contrary to previous findings, we prove that the impact of entangled data on prediction error exhibits a dual effect, depending on the number of permitted measurements. With a sufficient number of measurements, increasing the entanglement of training data consistently reduces the prediction error or decreases the required size of the training data to achieve the same prediction error. Conversely, when few measurements are allowed, employing highly entangled data could lead to an increased prediction error. The achieved results provide critical guidance for designing advanced QML protocols, especially for those tailored for execution on early-stage quantum computers with limited access to quantum resources.

Quantum algorithm for the radiative-transfer equation

The radiation transfer equation is widely used for simulations, for example, heat transfer in engineering, diffuse optical tomography in healthcare, and radiation hydrodynamics in astrophysics. By combining the lattice Boltzmann method, we propose a quantum algorithm for radiative transfer. This algorithm encompasses all the essential physical processes of radiative transfer: absorption, scattering, and emission. Although a sufficient number of measurements are required to precisely estimate the quantum state, and the initial encoding of the quantum state remains a challenging problem, our quantum algorithm exponentially accelerates radiative-transfer calculations compared to classical algorithms. In order to verify the quantum algorithm, we perform quantum circuit simulation using IBM Qiskit Aer and find good agreement between our numerical result and the exact solution. The algorithm paves the way for applications, such as fault-tolerant quantum computers for plasma engineering, telecommunications, nuclear-fusion technology, healthcare, and astrophysics. Published by the American Physical Society 2024

Influence of milling on representative sample preparation for the analysis of trace elements in waste wood

In Germany, waste wood can be used in various ways. The main ones are recycling in particleboards and energy production if the quality is insufficient for material utilisation. For the decision of usage, it is necessary to determine the wood quality by measuring the concentrations of certain pollutants. If given legal limits are exceeded, energetic utilisation in heat and power plants is recommended.Waste wood is a heterogeneous material. Therefore, special attention has to be given to the sample preparation in order to achieve representative analytical results. This article investigates whether the sample preparation according to ISO 14780 is also useable for a highly heterogeneous material such as waste wood or if a method with better homogenisation is needed. Furthermore, the effect of outliers on the interpretation of measurement results is considered.For this purpose, two milling methods are compared concerning their homogenisation capability. The samples were milled to 4 mm and homogenised. From this total amount, one half was milled directly to 0.25 mm (full milled), while the other half was separated in a sample divider until 100 g of the sample remained (according to ISO 14780), which was milled to 0.25 mm (partial milled).The results show that both milling procedures do not achieve a satisfactory homogenisation of the sample. However, with a sufficient number of measurements, limit value monitoring can still be carried out, as individual outliers are not decisive in whether a limit value is exceeded or not.

Online State Estimation for Time-Varying Systems

The article investigates the problem of estimating the state of a time-varying system with a linear measurement model; in particular, the article considers the case where the number of measurements available can be smaller than the number of states. In lieu of a batch linear least-squares approach—well-suited for static networks, where a sufficient number of measurements could be collected to obtain a full-rank design matrix—the article proposes an online algorithm to estimate the possibly time-varying state by processing measurements as and when available. The design of the algorithm hinges on a generalized least-squares cost augmented with a proximal-point-type regularization. With the solution of the regularized least-squares problem available in closed-form, the online algorithm is written as a linear dynamical system where the state is updated based on the previous estimate and based on the new available measurements. Conditions under which the algorithmic steps are in fact a contractive mapping are shown, and bounds on the estimation error are derived for different noise models. Numerical simulations are provided to corroborate the analytical findings.

Double-lined Spectroscopic Binaries in the APOGEE DR16 and DR17 Data

Abstract APOGEE spectra offer ≲1 km s−1 precision in the measurement of stellar radial velocities. This holds even when multiple stars are captured in the same spectrum, as happens most commonly with double-lined spectroscopic binaries (SB2s), although random line-of-sight alignments of unrelated stars can also occur. We develop a code that autonomously identifies SB2s and higher order multiples in the APOGEE spectra, resulting in 7273 candidate SB2s, 813 SB3s, and 19 SB4s. We estimate the mass ratios of binaries, and for a subset of these systems with a sufficient number of measurements we perform a complete orbital fit, confirming that most systems with periods of <10 days have circularized. Overall, we find an SB2 fraction (F SB2) ∼ 3% among main-sequence dwarfs, and that there is not a significant trend in F SB2 with temperature of a star. We are also able to recover a higher F SB2 in sources with lower metallicity, however there are some observational biases. We also examine light curves from TESS to determine which of these spectroscopic binaries are also eclipsing. Such systems, particularly those that are also pre- and post-main sequence, are good candidates for a follow-up analysis to determine their masses and temperatures.

Sparse signal recovery from modulo observations

We consider the problem of reconstructing a signal from under-determined modulo observations (or measurements). This observation model is inspired by a relatively new imaging mechanism called modulo imaging, which can be used to extend the dynamic range of imaging systems; variations of this model have also been studied under the category of phase unwrapping. Signal reconstruction in the under-determined regime with modulo observations is a challenging ill-posed problem, and existing reconstruction methods cannot be used directly. In this paper, we propose a novel approach to solving the signal recovery problem under sparsity constraints for the special case to modulo folding limited to two periods. We show that given a sufficient number of measurements, our algorithm perfectly recovers the underlying signal. We also provide experiments validating our approach on toy signal and image data and demonstrate its promising performance.

Nonlinear observability via Koopman Analysis: Characterizing the role of symmetry

This paper considers the observability of nonlinear systems from a Koopman operator theoretic perspective – and in particular – the effect of symmetry on observability. We first examine an infinite-dimensional linear system (constructed using independent Koopman eigenfunctions) and relate its observability properties to the observability of the original nonlinear system. Next, we derive an analytic relation between symmetry and nonlinear observability; it is shown that symmetry in the nonlinear dynamics is reflected in the symmetry of the corresponding Koopman eigenfunctions, as well as presence of repeated Koopman eigenvalues. We then proceed to show that loss of observability in symmetric nonlinear systems can be traced back to the presence of these repeated eigenvalues. In the case where we have a sufficient number of measurements, the nonlinear system remains unobservable when these functions have symmetries that mirror those of the dynamics. The proposed observability framework provides insights into the minimum number of measurements needed to make an unobservable nonlinear system, observable. The proposed results are then applied to a network of nano-electromechanical oscillators coupled via a symmetric interaction topology.

Optimal Methods for Estimating the JONSWAP Spectrum Peak Enhancement Factor From Measured and Hindcast Wave Data

Abstract The specification of design wave spectra is based on spectral parameters estimated from available wave data. Measured data allow high-resolution estimates to be made, but they suffer from sampling variability and often do not contain a sufficient number of measurements in extreme sea states. Hindcast data can be used to examine spectral features associated with extreme sea states, but they can be limited by resolution and are dependent on how the physics are incorporated in the source terms of the wave model. We examine and compare the effects of estimating JONSWAP spectrum peak enhancement factor from measured and hindcast data for a range of sea states but particularly those with large significant wave heights. In the case of the measured data, we build on earlier work and review effects associated with different methods for processing measured time series data, including the effect of sampling frequency, record length, and smoothing. These are then contrasted with estimates made from typical hindcast data, including the effect of the spectral shape associated with different source terms—in particular the four-wave interaction term. Finally, we provide recommendations on how best to estimate the peak enhancement factor of the JONSWAP spectrum for design purposes.

Limits on Support Recovery With Probabilistic Models: An Information-Theoretic Framework

The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings, such as compressive sensing, subset selection in regression, and group testing. In this paper, we take a unified approach to support recovery problems, considering general probabilistic models relating a sparse data vector to an observation vector. We study the information-theoretic limits of both exact and partial support recovery, taking a novel approach motivated by thresholding techniques in channel coding. We provide general achievability and converse bounds characterizing the trade-off between the error probability and number of measurements, and we specialize these to the linear, 1-bit, and group testing models. In several cases, our bounds not only provide matching scaling laws in the necessary and sufficient number of measurements, but also sharp thresholds with matching constant factors. Our approach has several advantages over previous approaches. For the achievability part, we obtain sharp thresholds under broader scalings of the sparsity level and other parameters (e.g., signal-to-noise ratio) compared with several previous works, and for the converse part, we not only provide conditions under which the error probability fails to vanish, but also conditions under which it tends to one.

Energy-efficient data collection in wireless sensor networks with time constraints

We consider the problem of retrieving a reliable estimate of an attribute from a wireless sensor network within a fixed time window and with minimum energy consumption for the sensors. The sensors are located in the plane according to some random spatial process. They perform energy harvesting and follow an asleep/awake cycle. A sink, at a random location in the plane, requests measurements from the awake sensors in order to retrieve an estimate of an attribute. The sink has to collect a sufficient number of measurements within a fixed time window. Moreover, the sink aims to minimize the energy that the sensors use to transmit their measurements. We determine a closed-form expression for the expected energy consumption of the sensors when measurements are retrieved according to a Greedy schedule. We also provide an upper bound on the maximum expected distance over which a sensor transmits under this Greedy schedule. Furthermore, we formulate a Markov Decision Process (MDP) to determine a sensor transmission schedule with general time constraints. We also develop a heuristic that schedules the sensors for transmission. We compare numerically the performance of the MDP schedule with the heuristic and with an offline, optimal schedule, where the asleep/awake state of the sensors is assumed to be known ahead of time. We show that the energy consumption under the MDP schedule converges to the energy of the offline schedule as the size of the time window for measurement collection increases. We also show that the heuristic performs close to the MDP schedule in terms of energy consumption.

Underground structure defect detection and reconstruction using crosshole GPR and Bayesian waveform inversion

Abstract Crosshole ground-penetrating radar (GPR) is a widely used measurement technique to help inspect the structural integrity of man-made underground structures, yet the resulting waveform and travel-time data can be difficult, complex and challenging to interpret. Here, we introduce the elements of a Bayesian inversion method for analyzing crosshole GPR data to guide detection of defects (weakness zones) in underground concrete structures. This framework uses as main building blocks the two-dimensional finite-difference time-domain (FDTD) simulator, the discrete cosine transform (DCT) method, and the DREAM (ZS) algorithm to reconstruct the relative permittivity field of an underground concrete structure from full-waveform GPR inversion. The FDTD simulator solves numerically Maxwell's equations in the time and space domain of the crosshole GPR experiment and simulates iteratively the electromagnetic (EM) waveforms. The DCT algorithm transforms the Cartesian parameterization to the frequency domain and reduces drastically the dimensionality of the parameter space by retaining only the low-frequency DCT-coefficients. Markov chain Monte Carlo (MCMC) simulation with the DREAM (ZS) algorithm is used to estimate the posterior distribution of the DCT-coefficients. The usefulness and applicability of the FDTD-DCT-DREAM (ZS) framework is demonstrated on a synthetic test example involving a unit square concrete structure with a small defect. Our results demonstrate that the proposed method successfully detects and locates defects in concrete structures. The inversion results appear rather insensitive to the noise level of the measured GPR waveforms, and the amount of data used (number of receiving antenna positions), as long as a sufficient number of measurements is available. The more DCT-coefficients that are used to characterize the concrete structure, the more accurate the results, yet the larger the posterior uncertainty of the reconstructed permittivity fields.

Guided ultrasound calibration: where, how, and how many calibration fiducials.

Many image-guided interventions rely on tracked ultrasound where the transducer is augmented with a tracking device. The relationship between the ultrasound image coordinate system and the tracking sensor must be determined accurately via probe calibration. We introduce a novel calibration framework guided by the prediction of target registration error (TRE): Between successive measurements of the calibration phantom, our framework guides the user in choosing the pose of the calibration phantom by optimizing TRE. We introduced an oriented line calibration phantom and modeled the ultrasound calibration process as a point-to-line registration problem. We then derived a spatial stiffness model of point-to-line registration for estimating TRE magnitude at any target. Assuming isotropic, identical localization error, we used the model to estimate TRE for each pixel using the current calibration estimate. We then searched through the calibration tool space to find the pose for the next fiducial which maximally minimized TRE. Both simulation and experimental results suggested that TRE decreases monotonically, reaching an asymptote when a sufficient number of measurements (typically around 12) are made. Independent point reconstruction accuracy assessment showed sub-millimeter accuracy of the calibration framework. We have introduced the first TRE-guided ultrasound calibration framework. Using a hollow straw as an oriented line phantom, we virtually constructed a rigid lines phantom and modeled the calibration process as a point-to-line registration. Highly accurate calibration was achieved with minimal measurements by using a spatial stiffness model of TRE to strategically choose the pose of the calibration phantom between successive measurements.

Estimation the measurement uncertainty of physico-chemical properties of coals according to ISO 17025

One of the important elements for addressing the requirements of international Standard ISO/IEC 17025:2006, specifically set forth in paragraph 5.4.6.2, is to assess the uncertainty of testing and/or calibration. For determination the coal technical analysis uncertainty (moisture, ash, volatiles and combustible substances, c-fix, total sulfur, gross calorific value and net calorific value), the certified reference materials (CRM) benzoic acid (Ref.: 33 045 and Ref.: C723, Id. No.: 32 430 00) and coal tags GBW 11107k were used. Potential laboratory reference material (RM) was also used for comparison the measurement results and uncertainty in order that, after sufficient number of measurements and statistical analysis, could be used as a laboratory RM. The results showed that both CRM and selected potential laboratory RM could be successfully applied to determine the uncertainty of technical coal analysis, what is significantly cheaper for laboratory work, and in accordance with Standard ISO 17025.

Estimation of low back moments from video analysis: A validation study

This study aimed to develop, compare and validate two versions of a video analysis method for assessment of low back moments during occupational lifting tasks since for epidemiological studies and ergonomic practice relatively cheap and easily applicable methods to assess low back loads are needed. Ten healthy subjects participated in a protocol comprising 12 lifting conditions. Low back moments were assessed using two variants of a video analysis method and a lab-based reference method. Repeated measures ANOVAs showed no overall differences in peak moments between the two versions of the video analysis method and the reference method. However, two conditions showed a minor overestimation of one of the video analysis method moments. Standard deviations were considerable suggesting that errors in the video analysis were random. Furthermore, there was a small underestimation of dynamic components and overestimation of the static components of the moments. Intraclass correlations coefficients for peak moments showed high correspondence (>0.85) of the video analyses with the reference method. It is concluded that, when a sufficient number of measurements can be taken, the video analysis method for assessment of low back loads during lifting tasks provides valid estimates of low back moments in ergonomic practice and epidemiological studies for lifts up to a moderate level of asymmetry.

A multiple projection approach for constrained system identification

This paper deals with the constrained system identification problem of linear discrete time dynamical systems. It is assumed that the parameters of the system are constrained due to physical limitations. Using a multiple projection approach, a minimum variance estimator and its associated recursive version are developed to estimate the constrained parameters of the system. The most important feature of the developed technique is that it gives estimates of the system parameters once the first set of measurements is received. Therefore, there is no need to wait till sufficient number of measurements are collected to start the algorithm. The simulation results of illustrative examples are presented to show the effectiveness of the proposed estimation scheme.

Estimating spatial correlation structures based on CPT data

Spatial correlation structures are usually used while modelling inherent uncertainty associated with soil properties. To retrieve this information a sufficient number of measurements and equal intervals between measurements or samples are always required. However, in practice, it is not usual to conduct site investigation in that way subject to a limited budget. Therefore, it is of interest to understand the possible bias created by using samples with unequal intervals. This research focuses on estimating the vertical spatial correlation structures of cone penetration tests (CPT) data conducted at a liquefaction site in Taiwan. The appropriate fitting range used in calibrating the correlation model is also discussed. The results show that cone tip resistance has larger correlation distances than that of sleeve friction. The estimated correlation distances of the CPT profiles are similar while using an equal sampling interval within a certain fitting range (denoted as the critical interval of measurements in this research). The results indicate that the effect of using different curve-fitting ranges is relatively insignificant for correlation distances of sleeve friction, whereas the correlation distances of cone tip resistance are more sensitive to different curve-fitting ranges. Moreover, the mean values of correlation distances are more constant for the equal sampling interval cases than for the unequal interval cases.

Broadband ambient noise surface wave tomography across the United States

This study presents surface wave dispersion maps across the contiguous United States determined using seismic ambient noise. Two years of ambient noise data are used from March 2003 through February 2005 observed at 203 broadband seismic stations in the US, southern Canada, and northern Mexico. Cross‐correlations are computed between all station‐pairs to produce empirical Green functions. At most azimuths across the US, coherent Rayleigh wave signals exist in the empirical Green functions implying that ambient noise in the frequency band of this study (5–100 s period) is sufficiently isotropically distributed in azimuth to yield largely unbiased dispersion measurements. Rayleigh and Love wave group and phase velocity curves are measured together with associated uncertainties determined from the temporal variability of the measurements. A sufficient number of measurements (>2000) is obtained between 8 and 25 s period for Love waves and 8 and 70 s period for Rayleigh waves to produce tomographic dispersion maps. Both phase and group velocity maps are presented in these period bands. Resolution is estimated to be better than 100 km across much of the US from 8–40 s period for Rayleigh waves and 8–20 s period for Love waves, which is unprecedented in a study at this spatial scale. At longer and shorter periods, resolution degrades as the number of coherent signals diminishes. The dispersion maps agree well with each other and with known geological and tectonic features and, in addition, provide new information about structures in the crust and uppermost mantle beneath much of the US.

SU‐FF‐J‐39: Comparison of Patient Positioning Corrections For Prostate IMRT Patients Using Competing Image Guided Radiation Therapy Technologies

We compared prostate position corrections using ultrasound and megavoltage CT image guided systems following initial patient positioning with lasers. Internal prostate movements between the two patient cohorts were assumed to be equivalent given a sufficient number of measurements, so we hypothesize the image guided shifts should average out to the same magnitude. Therapists adjusted patient positions with physician supervision based on daily imaging prior to each treatment. A total of 17 prostate patients were studied. Ten patients (Group I) were scanned in 3‐D mode using an ultrasound system. Contours (prostate/bladder/rectum) from the treatment planning system were transposed on the image set to register the ultrasound image. Therapists shift the contours to match the ultrasound image set and then adjust the patient by these same shifts. The number of shifts recorded from Group I was 432. Group II patients (seven subjects yielding 315 recorded shifts) were treated using Tomotherapy. Patients were scanned over the prostate region and the megavoltage CT image was registered with the treatment planning CT and contours. Shifts were produced for each axes and in roll. The patient table is adjusted to match the registration shifts. Roll corrections were minor and deemed insignificant for this study. The average prostate size from Group I was 104.9cc with a standard deviation of 42.1cc while Group II was 104.2cc and 54.8cc. A panel of four was formed to evaluate the quality of images to check possible operator bias due to image quality. Group I showed an average shift magnitude of 6.1mm with a standard deviation of 3.4mm. The average shift from Group II was 10.6mm with a standard deviation of 6.1mm. Tomotherapy imaging averaged 43% larger shifts compared to ultrasound. Possible explanations for this difference include operator laxity in initial tomotherapy positioning while depending on imaging and auto‐adjustment to compensate.

Mensural discrimination of Myotis (Chiroptera, Vespertilionidae) in the southeastern United States

Discriminant functions were constructed using external and cranial measurements to distinguish the six species of Myotis that occur in the southeastern United States. Twenty-three morphological characters were measured from 161 specimens of Myotis. Differences among species for morphological characters were examined using analysis of variance and discriminant analysis. A bootstrap procedure was used to validate the final discriminant model using all six species. Differences were observed among species for all 23 characters measured in univariate tests, but the range of values for most species overlapped the range of other species. Bootstrap analyses indicated that our discriminant functions constructed using both external and cranial measures allowed correct identification of 99.4% of specimens examined. Discriminant models constructed using only cranial characters permitted correct identification of 96.9% of specimens examined. Univariate analyses were not reliable because variation within species prevented unambiguous identification of any species based on a single character. However, Myotis species in the southeastern United States can be distinguished with a high level of accuracy using multivariate techniques when a sufficient number of measurements are used.

Detection of masked hypertension by home blood pressure measurement: is the number of measurements an important issue?

Office blood pressure (OBP) and home blood pressure (HBP) enable the identification of patients with masked hypertension. Masked hypertension is defined by normal OBP and high HBP and is known as a pejorative cardiovascular risk factor. The objective was to evaluate in the SHEAF study the influence of the number of office or home blood pressure measurements on the classification of patients as masked hypertensives. Patients with OBP <140/90 mmHg (mean of six values: three measurements at two separate visits, V1 and V2) and HBP >135/85 mmHg (mean of all valid measurements performed over a 4-day period) were the masked hypertensive reference group. The consistency of the classification was evaluated by using five definitions of HBP values (mean of the 3, 6, 9, 12 and 15 first measurements) and two definitions of OBP values (mean of three measurements at V1 and mean of three measurements at V2). Among the 4939 treated hypertensives included in the SHEAF study, 463 (9.4%) were classified as masked hypertensives (reference group). By decreasing the number of office or home measurements, the prevalence of masked hypertension ranged from 8.9-12.1%. The sensitivity of the classification ranged from 94-69% therefore 6-31% of the masked hypertensives were not detected. The specificity ranged from 98-94% therefore 1-6% of patients were wrongly classified as masked hypertensives. A limited number of home and office BP measurements allowed the detection of masked hypertension with a high specificity and a low sensitivity. A sufficient number of measurements (three measurements at two visits for OBP and three measurements in the morning and in the evening over 2 days for HBP) are required to diagnose masked hypertension.