Background: The "proton radius puzzle" refers to an eight-year old problem that highlights major inconsistencies in the extraction of the charge radius of the proton from muonic Lamb-shift experiments as compared against experiments using elastic electron scattering. For the latter, the determination of the charge radius involves an extrapolation of the experimental form factor to zero momentum transfer.Purpose: To estimate the proton radius by introducing a novel and powerful non-parametric model based on a constrained Gaussian process to model the electric form factor of the proton.Methods: Within a Bayesian paradigm, we develop a model flexible enough to fit the data without any parametric assumptions on the form factor. The Bayesian estimation is guided by imposing only two physical constraints on the form factor: (a) its value at zero momentum transfer (normalization) and (b) its overall shape, assumed to be a monotonically decreasing function of the momentum transfer. Variants of these assumptions are explored to assess the impact of these constraints.Results: So far our results are inconclusive in regard to the proton puzzle, as they depend on both, the assumed constrains and the range of experimental data used to fit the Gaussian process. For example, if only low momentum-transfer data is used, adopting only the normalization constraint provides a value compatible with the smaller muonic result, while imposing only the shape constraint favors the larger electronic value.Conclusions: We have presented a novel technique to estimate the proton radius from electron scattering data based on a non-parametric Gaussian process. We have shown the major impact of the physical constraints imposed on the form factor and of the range of experimental data used to implement the extrapolation. In this regard, we are hopeful that as this technique is refined and with the anticipated new results from the PRad experiment, we will get closer to resolve of the puzzle.
The traditional reliability analysis method based on probabilistic method requires probability distributions of all the uncertain parameters. However, in practical applications, the distributions of some parameters may not be precisely known due to the lack of sufficient sample data. The probabilistic theory cannot directly measure the reliability of structures with epistemic uncertainty, ie, subjective randomness and fuzziness. Hence, a hybrid reliability analysis (HRA) problem will be caused when the aleatory and epistemic uncertainties coexist in a structure. In this paper, by combining the probability theory and the uncertainty theory into a chance theory, a probability‐uncertainty hybrid model is established, and a new quantification method based on the uncertain random variables for the structural reliability is presented in order to simultaneously satisfy the duality of random variables and the subadditivity of uncertain variables; then, a reliability index is explored based on the chance expected value and variance. Besides, the formulas of the chance theory‐based reliability and reliability index are derived to uniformly assess the reliability of structures under the hybrid aleatory and epistemic uncertainties. The numerical experiments illustrate the validity of the proposed method, and the results of the proposed method can provide a more accurate assessment of the structural system under the mixed uncertainties than the ones obtained separately from the probability theory and the uncertainty theory.
A protocol for bioaerosol collection was developed that provides not only accurate predictions of fungal concentration, but also improves species recovery. Random transfer of a subset of 50 of the 400 impaction points from Andersen single-stage bioaerosol sampling plates results in subcultures that are accurate predictors of fungal concentration (CFU/m 3 ), when compared to duplicate untouched Andersen plates. A linear regression model was developed to estimate CFU/m 3 from the colonies counted on the Random-50 plates. The random transfer to five plates (''Random-50'' plates), allows large numbers of fungi to be recovered and identified, including slow-growing fungi that otherwise would be masked by fast-growing fungi.
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