Precision Of Parameter Estimates Research Articles

Dynamics of quantum Fisher information and quantum coherence of two interacting atoms under time–fractional analysis

In this paper, we give an exact general solution to the fractional Schrödinger equation of two interacting atoms. It consists of using the Riemann–Liouville fractional integral operator to examine the interaction between two identical atoms under temporal–fractional evolution. The dynamics of quantum Fisher information with respect to changes in the phase parameter and the quantum coherence by means of the l 1 -norm and relative entropy of coherence are discussed. Moreover, the analytical fractional solution allows us to evaluate the relationship between the estimation precision of the phase parameter and the coherence measures for various atom–atom states. Indeed, the obtained results show a good similarity between these measures for certain critical values of the phase parameter. In addition, it is observed that initially, for such coherent-like fractional states, the amount of quantum Fisher information may be sensitive or insensitive to changes in the phase parameter. Therefore, one can conclude that quantum Fisher information can be considered as an indicator of quantum coherence in a composite quantum state.

Pairwise joint modeling of clustered and high-dimensional outcomes with covariate missingness in pediatric pneumonia care.

Multiple outcomes reflecting different aspects of routine care are a common phenomenon in health care research. A common approach of handling such outcomes is multiple univariate analyses, an approach which does not allow for answering research questions pertaining to joint inference. In this study, we sought to study associations among nine pediatric pneumonia care outcomes spanning assessment, diagnosis and treatment domains of care, while circumventing the computational challenge posed by their clustered and high-dimensional nature and incompletely recorded covariates. We analyzed data from a cluster randomized trial conducted in 12 Kenyan hospitals. There were varying degrees of missingness in the covariates of interest, and these were multiply imputed using latent normal joint modeling. We used the pairwise joint modeling strategy to fit a correlated random effects joint model for the nine outcomes. This entailed fitting 36 bivariate generalized linear mixed models and deriving inference for the joint model using pseudo-likelihood theory. We also analyzed the nine outcomes separately before and after multiple imputation. We observed joint effects of patient-, clinician- and hospital-level factors on pneumonia care indicators before and after multiple imputation of missing covariates. In both pairwise joint modeling and separate univariate analysis methods, enhanced audit and feedback improved documentation and adherence to recommended clinical guidelines over time in six and five pneumonia care indicators, respectively. Additionally, multiple imputation improved precision of parameter estimates compared to complete case analysis. The strength and direction of association among pneumonia outcomes varied within and across the three domains of pneumonia care

Super-Heisenberg scaling in Hamiltonian parameter estimation in the long-range Kitaev chain

In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the the estimation of the interaction strength in linear systems with long-range interactions and using the Kitaev chains as a case study, we establish a transition from the Heisenberg to super-Heisenberg scaling in the quantum Fisher information by varying the interaction range. We further show that quantum control can improve the prefactor of the quantum Fisher information. Our results explore the advantage of optimal quantum control and long-range interactions in many-body quantum metrology.

Deep learning approaches for imaging fluorescence correlation spectroscopy parameter estimation with limited data sets

Deep Learning approaches using Convolutional Neural Networks (CNNs) are successfully applied in many disciplines and especially in imaging applications. CNNs provide advantages in terms of data processing time, required data size to reach a particular precision in parameter estimation, as well as the possibility of unsupervised data evaluation. Here we propose two different approaches to estimate diffusion coefficients from Imaging Fluorescence Correlation Spectroscopy (Imaging FCS) experiments and compare their performance with standard non-linear least squares (NLS) fits.

Quantum-enhanced interferometry by entanglement-assisted rejection of environmental noise

Sensing and measurement tasks in severely adverse conditions such as loss, noise, and dephasing can be improved by illumination with quantum states of light. Previous results have shown a modest reduction in the number of measurements necessary to achieve a given precision. Here, we compare three illumination strategies for estimating the relative phase in a noisy, lossy interferometer. When including a common phase fluctuation in the noise processes, we show that using an entangled probe achieves an advantage in parameter estimation precision that scales with the number of entangled modes. This work provides a theoretical foundation for the use of highly multimode entangled states of light for practical measurement tasks in experimentally challenging conditions.

A New Scatterer Trajectory Association Method for ISAR Image Sequence Utilizing Multiple Hypothesis Tracking Algorithm

Scatterer trajectory association is a critical step of 3-D target reconstruction from the inverse synthetic aperture radar (ISAR) image sequence. To cope with the complex scatterer trajectory association of the noncooperative target, a novel method based on multiple hypothesis tracking (MHT) algorithm is proposed. First, the scatterer trajectory association situation is modeled as a multiple hypothesis tree, in which each branch represents a possible association. Then, to generate the hypothesis in each specific branch, a general trajectory motion model is constructed and the parameters are estimated based on the current trajectory association situation. The parameter estimation precision will increase with the growth of the trajectory length. Besides, to eliminate the influence of inaccurate association initialization and direction selection, a fusion algorithm is proposed to merge the forward and backward associated trajectories. Finally, experimental results based on the simulated data and electromagnetic data verify the effectiveness and robustness of the proposed method.

Maneuvering Target Coherent Integration and Detection in PRI-Staggered Radar Systems

As for a new-style radar, the random pulse repetition interval (PRI) pulse waveform may be transmitted, and then the target Doppler parameter estimation precision and detection ability by using the conventional techniques may be invalid due to the irregular signal sampling. To solve these problems, this letter proposes a simple, yet effective and quasi-optimal coherent integration method with random pulse resampling. The proposed method first reconstructs the nonuniformly sampled signal into a uniform grid in the range frequency domain based on the modified sinc interpolation theory. Then, a matched filtering function related to the target chirp parameter is constructed in order to eliminate the residual coupling between range and azimuth. Finally, a moving target can be well imaged after performing the target motion compensation.

Quantum metrology with one auxiliary particle in a correlated bath and its quantum simulation

In realistic metrology, entangled probes are more sensitive to noise, especially for a correlated environment. The precision of parameter estimation with entangled probes is even lower than that of the unentangled ones in a correlated environment. In this paper, we propose a measurement scheme with only one auxiliary qubit, which can selectively offset the impact of environmental noise under this situation. We analyse the estimation precision of our scheme and find out that it approaches the Heisenberg limit when prepared in a proper auxiliary state. We further discuss employing auxiliary states to improve the precision of measurement in other environment models such as a partially-correlated environment. In order to verify our scheme, we apply a recently-developed quantum algorithm to simulate the quantum dynamics of our proposal and show that it outperform the other proposals with less resources.

Coherence and quantum Fisher information in general single-qubit parameter estimation processes

Quantum metrology is superior to classical metrology in parameter estimation. This is because quantum states have coherence that, however, does not exist in classical states. Previous works were limited to the study of the relationship between quantum Fisher information (QFI) and coherence of the initial probe state only for a specific single-qubit parameter estimation process (e.g., a process described by a single-qubit spin angular momentum operator ${J}_{z}$). Here, we consider a more general case and study the relationship between QFI and coherence of the initial probe state for a single-qubit general parameter estimation process, which is described by a single-qubit spin angular momentum operator ${J}_{\stackrel{P\vec}{n}}$ with a general unit vector $\stackrel{P\vec}{n}$. We find that the QFI is proportional to the square of coherence of the initial probe state, when the single-qubit bases are eigenstates of the spin angular momentum operator ${J}_{\stackrel{P\vec}{n}}$ describing the parametrization process. We also design and conduct a linear optical experiment to support our theory. The experimental results are in good agreement with the theoretical ones. This work provides an important guideline for enhancing the precision of parameter estimation.

Imaging through a scattering medium: the Fisher information and the generalized Abbe limit.

Enhanced-resolution imaging in complex scattering media is revisited from a parameter estimation perspective. A suitably defined Fisher information is shown to offer useful insights into the limiting precision of parameter estimation in a scattering environment and, hence, into the limiting spatial resolution that can be achieved in imaging-through-scattering settings. The Fisher information that defines this resolution limit via the Cramér-Rao lower bound is shown to scale with the number of adaptively controlled space-time modes of the probe field, suggesting a physically intuitive generalization of the Abbe limit to the spatial resolution attainable for complex scattering systems. In a conventional, direct-imaging microscopy setting, this bound is shown to converge to the canonical Abbe limit.

Analysis of conformational exchange processes using methyl-TROSY-based Hahn echo measurements of quadruple-quantum relaxation.

Transverse nuclear spin relaxation is a sensitive probe of chemical exchange on timescales on the order of microseconds to milliseconds. Here we present an experiment for the simultaneous measurement of the relaxation rates of two quadruple-quantum transitions in CH-labelled methyl groups. These coherences are protected against relaxation by intra-methyl dipolar interactions and so have unexpectedly long lifetimes within perdeuterated biomacromolecules. However, these coherences also have an order of magnitude higher sensitivity to chemical exchange broadening than lower order coherences and therefore provide ideal probes of dynamic processes. We show that analysis of the static magnetic field dependence of zero-, double- and quadruple-quantum Hahn echo relaxation rates provides a robust indication of chemical exchange and can determine the signed relative magnitudes of proton and carbon chemical shift differences between ground and excited states. We also demonstrate that this analysis can be combined with established Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion measurements, providing improved precision in parameter estimates, particularly in the determination of H chemical shift differences.

A discussion on the affecting factors of the fitting procedures’ reliability in isothermal titration calorimetry analysis

The standard isothermal titration calorimetry (ITC) curve, characterized as a typical sigmoid is strictly confined by the so-called c value, which is a ratio of titrand concentration to KD. The proper c value with a range from 5 to 500 is commonly recommended as a standard protocol in routine detection process for acquiring the reliable fitting results in 1:1 binding mode. However, if the c value is less than “1” due to the weak binding or low concentration of analyte, fitting precision gets unstable and susceptible to the data noise. Herein, we first got a deep discussion into the reliability of the fitting procedure for 1:1 binding mode by data simulation, then quantized the effect of several affecting factors on the precision of parameters estimation through mathematical analysis. Finally, we proposed the value of 2~4 times KD for final ligand concentration is optimal for the ITC titration in low c system (c < 1). All the theoretical derivations were further verified by a practical experiment of Magnesium-EDTA binding test.

Training data distribution significantly impacts the estimation of tissue microstructure with machine learning

Supervised machine learning (ML) provides a compelling alternative to traditional model fitting for parameter mapping in quantitative MRI. The aim of this work is to demonstrate and quantify the effect of different training data distributions on the accuracy and precision of parameter estimates when supervised ML is used for fitting. We fit a two- and three-compartment biophysical model to diffusion measurements from in-vivo human brain, as well as simulated diffusion data, using both traditional model fitting and supervised ML. For supervised ML, we train several artificial neural networks, as well as random forest regressors, on different distributions of ground truth parameters. We compare the accuracy and precision of parameter estimates obtained from the different estimation approaches using synthetic test data. When the distribution of parameter combinations in the training set matches those observed in healthy human data sets, we observe high precision, but inaccurate estimates for atypical parameter combinations. In contrast, when training data is sampled uniformly from the entire plausible parameter space, estimates tend to be more accurate for atypical parameter combinations but may have lower precision for typical parameter combinations. This work highlights that estimation of model parameters using supervised ML depends strongly on the training-set distribution. We show that high precision obtained using ML may mask strong bias, and visual assessment of the parameter maps is not sufficient for evaluating the quality of the estimates.

Intrinsic Sensitivity Limits for Multiparameter Quantum Metrology.

The quantum Cramér-Rao bound is a cornerstone of modern quantum metrology, as it provides the ultimate precision in parameter estimation. In the multiparameter scenario, this bound becomes a matrix inequality, which can be cast to a scalar form with a properly chosen weight matrix. Multiparameter estimation thus elicits trade-offs in the precision with which each parameter can be estimated. We show that, if the information is encoded in a unitary transformation, we can naturally choose the weight matrix as the metric tensor linked to the geometry of the underlying algebra su(n), with applications in numerous fields. This ensures an intrinsic bound that is independent of the choice of parametrization.

Searching for a more valid form of parental rating scales of preschoolers’ intellectual giftedness – development and validation of the Preschooler’s Ability Rating Scale (PARS)

Objectives. The aim of this study was to develop a new parental rating scale for identification of intellectually gifted preschoolers (4 to 6 years of age). This new scale, the Preschooler’s Ability Rating Scale (PARS), consists of two parts – PARS-PRE, which follows the principle of precocity and inquires about the age at which giftedness-relevant behavior appeared for the first time; and PARS-CUR, which focuses on the current level of abilities.Participants and setting. In total, 263 Czech mothers and 90 children participated in the main study.Hypotheses. PARS will have a two-dimensional structure corresponding to its two parts. Both parts will significantly correlate with scores on the Woodcock-Johnson: International edition II (WJ IE II COG).Statistical analysis. 1. Item analysis; 2. Exploratory factor analysis; 3. Correlational analyses with WJ IE II COG; 4. ROC analysis to evaluate the specificity and sensitivity.Results. Factor analysis suggests a three-factor structure – two of the factors correspond to the scale’s original parts, and the third factor reflects early reading and counting (4 items from the precocity part). The diagnostic accuracy of the first two factors is similarly low (rPRE = .33, rCUR = .25), but substantially higher for the early reading/counting factor (rLIT = .52). Additionally, parental ratings are, in general, based more on children’s verbal abilities than their nonverbal abilities. Given the low criterial validity, the authors do not recommend utilizing the PARS scale in a practical setting, however, the conclusions are useful for further development of similarly-minded scales.Study limitations. Only 90 children were administered the WJ IE II COG – the small sample size affects the precision of parameter estimates. The parentsʼ sample consists only of mothers.

Computational Intelligence Technologies for Occupancy Estimation and Comfort Control in Buildings

This paper focuses on the development of a multi agent control system (MACS), combined with a stochastic based approach for occupancy estimation. The control framework aims to maintain the comfort levels of a building in high levels and reduce the overall energy consumption. Three independent agents, each dedicated to the thermal comfort, the visual comfort, and the indoor air quality, are deployed. A stochastic model describing the CO2 concentration has been studied, focused on the occupancy estimation problem. A probabilistic approach, as well as an evolutionary algorithm, are used to provide insights on the stochastic model. Moreover, in order to induce uncertainty, parameters are treated in a fuzzy modelling framework and the results on the occupancy estimation are investigated. In the control framework, to cope with the continuous state-action space, the three agents utilise Fuzzy Q-learning. Simulation results highlight the precision of parameter and occupancy estimation, as well as the high capabilities of the control framework, when taking into account the occupancy state, as energy consumption is reduced by 55.9%, while the overall comfort index is kept in high levels, with values close to one.

Linking of Rasch-Scaled Tests: Consequences of Limited Item Pools and Model Misfit

In the context of item response theory (IRT), linking the scales of two measurement points is a prerequisite to examine a change in competence over time. In educational large-scale assessments, non-identical test forms sharing a number of anchor-items are frequently scaled and linked using two− or three-parametric item response models. However, if item pools are limited and/or sample sizes are small to medium, the sparser Rasch model is a suitable alternative regarding the precision of parameter estimation. As the Rasch model implies stricter assumptions about the response process, a violation of these assumptions may manifest as model misfit in form of item discrimination parameters empirically deviating from their fixed value of one. The present simulation study investigated the performance of four IRT linking methods—fixed parameter calibration, mean/mean linking, weighted mean/mean linking, and concurrent calibration—applied to Rasch-scaled data with a small item pool. Moreover, the number of anchor items required in the absence/presence of moderate model misfit was investigated in small to medium sample sizes. Effects on the link outcome were operationalized as bias, relative bias, and root mean square error of the estimated sample mean and variance of the latent variable. In the light of this limited context, concurrent calibration had substantial convergence issues, while the other methods resulted in an overall satisfying and similar parameter recovery—even in the presence of moderate model misfit. Our findings suggest that in case of model misfit, the share of anchor items should exceed 20% as is currently proposed in the literature. Future studies should further investigate the effects of anchor item composition regarding unbalanced model misfit.

Does relativistic motion always degrade quantum Fisher information?

We investigate the ultimate estimation precision, characterized by the quantum Fisher information, of a two-level atom as a detector which is coupled to massless scalar field in the Minkowski vacuum. It has been shown that for an inertial detector moving with a constant velocity, its quantum Fisher information is completely unaffected by the velocity, however, it still decays over time due to the decoherence caused by the interaction between the atom and the field. In addition, for a uniformly accelerated detector ($w=0$) moving along spatially straight line, the accelerated motion will reduce the quantum Fisher information in the estimation of state parameters. However, when the detector trajectory is generated by a combination of the linear accelerated motion and a component of the four-velocity $w=dy/d\tau$, we find quite unlike the previous results that, for the non-relativistic case $(w\ll1)$, the acceleration could degrade the quantum Fisher information, while the four-velocity component will suppress the degradation of the quantum Fisher information, and thus could enhance the precision of parameters estimation. Furthermore, in the case for ultra-relativistic velocities $(w\rightarrow\infty)$, although the detector still interacts with the environment, it behaves as if it were a closed system as a consequence of relativity correction associated to the velocity, and the quantum Fisher information in this case can be shield from the effect of the external environment, and thus from the relativistic motion.

Exploring group size for statistical analysis of real-time signalling experiments.

Classical pharmacological bioassays generally use observed effects from a concentration series, at a single equilibrium time point to construct a concentration-effect curve, representing one experiment. However, if the full kinetic profile of the effect data for each concentration was evaluated simultaneously, then the analysis would be more powerful. In this work, we explore if more precise parameters can be achieved by using the full kinetic method. We used a simulation estimation study to explore the influence of kinetic analysis on the precision of the Emax model parameter estimates (Emax and C50 ). We compared a full kinetic approach in which all effect versus time data from a theoretical real-time signalling experiment were analysed simultaneously with a 'reference' approach. The theoretical real-time signalling experiment was based on a previously published CB2 receptor-binding experiment. The reference method with a group size (n) of 5 provided highly precise parameter estimates (coefficient of variation [CV] 3.4% for Emax and 0.72% for C50 ). A full kinetic method provided more precise estimates than the reference with equal or smaller group sizes. Note that group size 'n' here refers to the number of technical replicates rather than the number of biological replicates. A full kinetic method can yield more precise parameter estimates than the equilibrium method. Such an approach may be more useful for researchers.

Predictors associated with the variation of CD4 cell count and body mass index (BMI) for HIV positive adults under ART

The rate of prevalence of HIV among adults has been increasing in Sub-Sahara African countries over the last decade. The objective of this study was to identify the most significant variables associated with the variation of CD4 cell count and body mass index (BMI) of HIV positive adults who initiated HAART at Felege Hiwot Teaching and Specialized Hospital, North-West Ethiopia. This study also aimed to compare the precision of parameter estimates conducted by separate and joint models.A cohort longitudinal study of 792 HIV-infected patients was performed. A joint model was employed to identify predictor variables. A random of 792 samples was taken among patients using individual charts in the hospital.Among the main effects, Socio-demographic variables (Level of education, level of disclosure of the disease to persons living together and Marital status), individuals factors(age, weight and gender), economic factors (ownership of cell phone, level of income), clinical factors (baseline CD4 cell count) retention (food and medication adherence, follow-up time/visit) significantly affected the variables of interests. Similarly, the interaction effects of follow-up times/visits * cell phone ownership, follow-up times/visits * gender, age * gender of patients significantly affected both response variables in current investigation. Socio-demographic, individual and Clinical variables had significant effect on CD4 cell count and BMI in HAART medication program. Follow-up time/visit in the HAART program had also direct and significant effect on the variables of interest. The patients should be advised to disclose the disease to get support from communities around them.