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Probability density function of phase difference magnitude, using estimator having gain matched amplifiers
We present a strategy for estimating the error of truncated functional flow equations. While the basic functional renormalization group equation is exact, approximated solutions by means of truncations do not only depend on the choice of the retained information, but also on the precise definition of the truncation. Therefore, results depend on specification parameters that can be used to quantify the error of a given truncation. We demonstrate this for the BCS–BEC crossover in ultracold atoms. Within a simple truncation the precise definition of the frequency dependence of the truncated propagator affects the results, indicating a shortcoming of the choice of a frequency independent cutoff function.
Two types of experiments concerning the estimated magnitude of self-motion during exposure to linear oscillation on a parallel swing are described in this paper. Experiment I examined changes in magnitude estimation as a function of variation of the subject's head orientation, and Experiments II a, II b, and II c assessed changes in magnitude estimation performance following exposure to sustained, 'intense' linear oscillation (fatigue-inducting stimulation). The subjects' performance was summarized employing Stevens' power law R = k x S to the nth, where R is perceived self-motion magnitude, k is a constant, S is amplitude of linear oscillation, and n is an exponent). The results of Experiment I indicated that the exponents, n, for the magnitude estimation functions varied with head orientation and were greatest when the head was oriented 135 deg off the vertical. In Experiments II a-c, the magnitude estimation function exponents were increased following fatigue. Both types of experiments suggest ways in which the vestibular system's contribution to a spatial orientation perceptual system may vary. This variability may be a contributing factor to the development of pilot/astronaut disorientation and may also be implicated in the occurrence of motion sickness.
Computational procedures for improving the reliability of human operator describing functions are described. Special attention is given to the estimation of standard errors associated with mean operator gain and phase shift as computed from an ensemble of experimental trials. This analysis pertains to experiments using sum-of-sines forcing functions. Both open-loop and closed-loop measurement environments are considered.
A function for estimating the effective root-mean-square deviation in coordinates between two proteins has been developed that depends on both the sequence identity and the size of the protein and is optimized for use with molecular replacement in Phaser. A top peak translation-function Z-score of over 8 is found to be a reliable metric of when molecular replacement has succeeded. The estimate of the root-mean-square deviation (r.m.s.d.) in coordinates between the model and the target is an essential parameter for calibrating likelihood functions for molecular replacement (MR). Good estimates of the r.m.s.d. lead to good estimates of the variance term in the likelihood functions, which increases signal to noise and hence success rates in the MR search. Phaser has hitherto used an estimate of the r.m.s.d. that only depends on the sequence identity between the model and target and which was not optimized for the MR likelihood functions. Variance-refinement functionality was added to Phaser to enable determination of the effective r.m.s.d. that optimized the log-likelihood gain (LLG) for a correct MR solution. Variance refinement was subsequently performed on a database of over 21 000 MR problems that sampled a range of sequence identities, protein sizes and protein fold classes. Success was monitored using the translation-function Z-score (TFZ), where a TFZ of 8 or over for the top peak was found to be a reliable indicator that MR had succeeded for these cases with one molecule in the asymmetric unit. Good estimates of the r.m.s.d. are correlated with the sequence identity and the protein size. A new estimate of the r.m.s.d. that uses these two parameters in a function optimized to fit the mean of the refined variance is implemented in Phaser and improves MR outcomes. Perturbing the initial estimate of the r.m.s.d. from the mean of the distribution in steps of standard deviations of the distribution further increases MR success rates.
Four research projects are summarized which include: (1) the generation of random numbers on the IBM 360/44, (2) statistical tests used to check out random number generators, (3) Specht density estimators, and (4) use of estimators of probability density functions in analyzing large amounts of data.
We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide stronger signals on the gradient. In this approach, the value of the quantile function is estimated empirically from samples drawn from the random parameters, and the gradient of the quantile function is estimated via a finite-difference approximation on top of the quantile-function-value estimation. We establish a convergence theory of this approach within the framework of an augmented Lagrangian method for solving general nonlinear constrained optimization problems. The foundation of the convergence analysis is a concentration property of the empirical quantile process, and the analysis is divided based on whether or not the quantile function is differentiable. In contrast to the sampling-and-smoothing approach used in the literature, the method developed in this paper does not involve any smoothing function and hence the quantile-function gradient approximation is easier to implement and there are less accuracy-control parameters to tune. Furthermore, we demonstrate the effectiveness of this approach and compare it with a smoothing method for the quantile-gradient estimation. Numerical investigation shows that the two approaches are competitive for certain problem instances.
A correlational analysis of individual magnitude estimation and production exponents at the same frequency is performed, as is an analysis of individual exponents produced in different sessions by the same procedure across frequency (250, 1000, and 3000 Hz). Taken as a whole, the results show that individual exponent differences do not decrease by counterbalancing magnitude estimation with magnitude production and that individual exponent differences remain stable over time despite changes in stimulus frequency. Further results show that although individual magnitude estimation and production exponents do not necessarily obey the .6 power law, it is possible to predict the slope of an equal-sensation function averaged for a group of listeners from individual magnitude estimation and production data. On the assumption that individual listeners with sensorineural hearing also produce stable and reliable magnitude functions, it is also shown that the slope of the loudness-recruitment function measured by magnitude estimation and production can be predicted for individuals with bilateral losses of long duration. Results obtained in normal and pathological ears thus suggest that individual listeners can produce loudness judgements that reveal, although indirectly, the input-output characteristic of the auditory system.
Purpose: This study aims to determine whether contrast-enhanced (CE)-magnetic resonance imaging (MRI) is comparable to CE-computed tomography (CT) for estimation of split renal function (SRF). For this purpose, two different kidney volumetry methods, the renal cortex volumetry (RCV) and modified ellipsoid volume (MELV), are compared for both acquisition types (CT vs. MRI) with regard to accuracy and reliability, subsequently referred to as RCV{sub CT}/RCV{sub MRI} and MELV{sub CT}/MELV{sub MRI}. Methods: This retrospective study included 29 patients (18 men and 11 women; mean age 62.8 ± 12.4 years) who underwent CE-MRI and CE-CT of the abdomen within a period of 3 months. Two independent readers (R1/R2) performed RCV and MELV in all datasets with corresponding semiautomated software tools. RCV was performed with datasets in the arterial phase and MELV in the venous phase. Statistics were calculated using one-way ANOVA, two-tailed Student’s t test, Pearson´s correlation, and Bland–Altman plots with p ≤ 0.05 being considered statistically significant. Results: In all datasets, SRF was almost identical for both volumetry methods with a mean difference of < 1%. Bland–Altman analysis comparing RCV in CT and MRI showed very good agreement for R1/R2. Interreader agreement was strong for RCV{sub CT} and good for RCV{sub MRI} (r = 0.89; r = 0.69). MELV{sub CT/MRI} interreader agreement was only moderate (r = 0.54; r = 0.50) with a high range of values. Intrareader agreement was excellent for all measurements, except MELV{sub MRI} which showed a high mean bias and range of values (RCV{sub CT}: r = 0.93, RCV{sub MRI}: r = 0.98, MELV{sub CT}: r = 0.89, MELV{sub MRI}: r = 0.54). Conclusion: Renal volumetric estimates of SRF are almost as accurate and reliable with CE-MRI as with CE-CT using RCV method. In distinction, the calculation of SRF using MELV was inferior to RCV with respect to accuracy and reliability. Thus, RCV method is recommended to estimate SRF, primarily using CT datasets. However, RCV with MRI datasets for kidney volumetry allows for comparable accuracy and reliability while sparing patients and healthy donors of unnecessary radiation exposure.
Several approaches to the problem of the calculation of spectral power density of a random function from an estimate of the autocorrelation function were studied. A comparative study was presented of these different methods. The principles on which they are based and the hypothesis implied were pointed out. Some indications on the optimization of the length of the estimated correlation function was given. An example of application of the different methods discussed in this paper was included.
Step function with more than two values for computing variance of energy distribution for flat and nonflat spectra
We consider spaces of entire functions with systems of weighted estimates. The case of twoterm weight sequences consisting of radial and nonradial components is studied. Under some assumptions on the weight sequence, we obtain a complete description of generators in these spaces. We apply this result to the problem of normal solvability of systems of convolution equations in the Roumieu spaces of ultradifferentiable functions and, as a particular case, in Gevrey classes.
Exponential estimates and saddle point property for neutral functional differential equations
Prolate spheroidal wave functions for solution of Fredholm equation for bandlimited signal detection
A new estimator for three-center two-particle Coulomb integrals is presented. Our estimator is exact for some classes of integrals and is much more efficient than the standard Schwartz counterpart due to the proper account of distance decay. Although it is not a rigorous upper bound, the maximum degree of underestimation can be controlled by two adjustable parameters. We also give numerical evidence of the excellent tightness of the estimator. The use of the estimator will lead to increased efficiency in reduced-scaling one- and many-body electronic structure theories.
Functional connectomes (FCs) containing pairwise estimations of functional couplings between pairs of brain regions are commonly represented by correlation matrices. As symmetric positive definite matrices, FCs can be transformed via tangent space projections, resulting into tangent-FCs. Tangent-FCs have led to more accurate models predicting brain conditions or aging. Motivated by the fact that tangent-FCs seem to be better biomarkers than FCs, we hypothesized that tangent-FCs have also a higher fingerprint. We explored the effects of six factors: fMRI condition, scan length, parcellation granularity, reference matrix, main-diagonal regularization, and distance metric. Our results showed that identification rates are systematically higher when using tangent-FCs across the “fingerprint gradient” (here including test-retest, monozygotic and dizygotic twins). Highest identification rates were achieved when minimally (0.01) regularizing FCs while performing tangent space projection using Riemann reference matrix and using correlation distance to compare the resulting tangent-FCs. Such configuration was validated in a second dataset (resting-state).
Several mathematical relationships between air sample filter mass loading and the correlated analytical self-absorption factor were developed using data from other published research in this meta-study. Gross-alpha and -beta applications are addressed for this research. As filter media becomes loaded with particulate matter, there is potential for measurement losses due to self-absorption by mass loading. Components contributing to absorption include particulate dust, radioactive particulates, and filter material. Standards indicate a correction factor should be used when the penetration of radioactive material into the collection media or self-absorption of radiation by the material collected would reduce the detection rate by more than 5%. Previously, losses due to self-absorption have been reported up to 100% over a range up to ~10 mg∙cm -2 mass loading. These absorption losses then can be used to determine a correction factor for sample results. For low mass loadings (e.g., ≤0.1 mg∙cm -2 ) corrections factors in the 0.85 - 1 range have been recommended and used, while at higher mass loadings nearer to 10 mg∙cm -2 correction factors closer to 0 (representing near 100% losses) are used. Based on data from published studies, the different methods for relating percent loss due to self-absorption to mass loading include linear, exponential, quadratic, and trinomial derived functions. Where applicable, both forced zero and non-forced zero results were evaluated. From the derived functions evaluated, the trinomial function provided the best fit. Once the sample filter mass loading is known, the trinomial function can be applied to estimate losses and the corresponding self-absorption factor. When applied to routine operating conditions for radiological facility stacks monitored at the Pacific Northwest National Laboratory for an average sample filter mass loading of 0.09 ± 0.12 (2σ) mg∙cm -2 (excluding negative values and outliers) and a range from 0 - 0.24 mg∙cm -2 , the estimated trinomial function nominal self-absorption losses are less than 5% at 0.09 mg∙cm -2 and less than 10% at 0.24 mg∙cm -2 . The trinomial function is one method that may be used to adjust the activity results of an air sample when the sample-specific mass loading is determined. The application of no correction factor when the ANSI/HPS N13.1-2021 guidance of a 5% threshold for loss is not reached with typical stack sample mass loadings may be reasonable in high-efficiency particulate air filtered systems. For simplicity, it would be conservative in assigning the self-absorption correction factor at the 5% threshold (i.e., 0.95) for general uses but in cases of heavy mass loading to calculate the factor.
We describe a method based on the total deviation approach whereby we improve the confidence of the estimation of the Hadamard deviation that is used primarily in GPS operations.