Detectability limit and uncertainty considerations for laser induced fluorescence spectroscopy in flames

Nuclear-decay data: The statement of uncertainties

Six hundred and thirty references are cited in this review. The information in the review is divided into 12 major areas: books, reviews, and bibliographies; fundamental studies in flames; developments in instrumentation; measurement techniques and procedure; flame emission spectrometry; flame atomic absorption spectrometry; flame molecular absorption spectrometry; electrothermal atomization atomic absorption spectroscopy; hydride generation techniques; graphite furnace atomic emission spectrometry; atomic fluorescence spectrometry; and analytical comparisons. (BLM)

At the annual general meeting of the International Committee for Radionuclide Metrology (ICRM) held last June at the Physikalisch-Technische Bundesanstalt, it was suggested that letters should be sent to the editors of journals that publish nucleardecay data, drawing attention to the need for specific statements of the uncertainties that are associated with such data. Authors frequently fail to state clearly the nature of their estimates of uncertainty, and not all editors insist on such clarity, so that evaluators of nuclear-decay data often f'md that it is necessary to consult with the individual authors to arrive at the weighting factors appropriate to their data. If uncertainties could be dearly characterized in the abstracts or in the text of papers reporthag values of nuclear parameters, there would be a corresponding shortening of the time required for the data to be evaluated and tabulated. There are many methods of stating estimates of conventional random and systematic uncertainties that are acceptable, provided that the methods used are described. Thus random error may be stated as: (i) the estimate of the standard deviation (or the square root of the variance), which is in the same units as the observed data and indicates the order of magnitude of the spread of the data: (ii) the standard error (or the estimated standard deviation of the mean of the distribution); and (ri) the estimated limits for the mean at stated levels of confidence (C1) (e.g. limits at the 99-percent CI define the range within which there is a 99:percent probability of ineluding the mean of a population). Provided that the author states the number of independent measurements made of the given parameter, or the number of degrees of freedom, these statements of random uncertainty are related uniquely to each other. The other component of the overall uncertainty is the estimate of possible systematic error. The significance, or meaning, of the estimate of systematic uncertainties should be dearly stated and also related to the method chosen to state the random uncertainties. Thus an estimate of maximum conceivable systematic uncertainties would logically be combined with a random uncertainty at a 99-percent confidence level. An appropriate fraction of the estimate of maximum conceivable systematic uncertainty would be chose to match smaller random confidence levels. The methods used to combine random and systematic uncertainties should also be stated by authors, and an explicit listing of all components of these uncertainties will allow an evaluator of nuclear data to unravel the statements of uncertainty and to choose

The Period–Luminosity (PL) relation of Cepheid variable stars is a fundamental tool for measuring extragalactic distances and constraining the Hubble constant (H0). Achieving high precision in PL-based distances requires careful consideration of both systematic and statistical uncertainties. We review the main sources of these uncertainties in PL relations, highlighting the increasing impact of random-phase errors in single-epoch observations from limited temporal coverage, such as those obtained with the James Webb Space Telescope (JWST). We discuss mitigation strategies for systematic errors, including photometric calibration offsets, metallicity effects, blending, and parallax biases, and quantify key contributors to statistical errors, such as photometric noise, intrinsic scatter, and phase-sampling limitations. Special attention is given to a recently proposed cross-filter random-phase correction method (Abdollahi et al., 2025), which recovers mean magnitudes from single-epoch data by exploiting correlations between PL residuals in different bands. This technique reduces the dispersion in the infrared PL relation by 28%, equivalent to an order-of-magnitude increase in effective temporal sampling, demonstrating an efficient path to improving Cepheid-based distance measurements and the precision of H0.

Laser induced fluorescence spectroscopy in flames

Many experiments that aim at the direct detection of Dark Matter are able to distinguish a dominant background from the expected feeble signals, based on some measured discrimination parameter. We develop a statistical model for such experiments using the Profile Likelihood ratio as a test statistic in a frequentist approach. We take data from calibrations as control measurements for signal and background, and the method allows the inclusion of data from Monte Carlo simulations. Systematic detector uncertainties, such as uncertainties in the energy scale, as well as astrophysical uncertainties, are included in the model. The statistical model can be used to either set an exclusion limit or to make a discovery claim, and the results are derived with a proper treatment of statistical and systematic uncertainties. We apply the model to the first data release of the XENON100 experiment, which allows to extract additional information from the data, and place stronger limits on the spin-independent elastic WIMP-nucleon scattering cross-section. In particular, we derive a single limit, including all relevant systematic uncertainties, with a minimum of 2.4x10^-44 cm^2 for WIMPs with a mass of 50 GeV/c^2.

Unification theory of classical statistical uncertainty relation and quantum uncertainty relation and its applications

An improved isotopic method for partitioning net ecosystem–atmosphere CO2 exchange

Fitting plasma models to high-quality spectra is a crucial tool for deriving diagnostics about the physical conditions in various astrophysical sources. Despite decades of model development, this prescription often provides an unsatisfying description of observational data. We explore some of the origins of the failure of fits of photoionized plasma models to high-resolution X-ray spectra. In particular, we test whether systematic uncertainties in underlying atomic data can account for data model discrepancies, and whether including model uncertainties during spectral fitting can provide statistically acceptable fits and reasonable parameter estimates. We fit Chandra/HETG spectra of NGC 3783 with the photoionized absorber model warmabs. We use the remaining data model discrepancies to estimate the systematic uncertainties of bound–bound radiative rates for individual transitions quantitatively. We then include these uncertainties into warmabs to return a total model uncertainty. We find residual data model discrepancies which are due to systematic errors that cannot be accounted for solely by a modification of the optical depth of strong absorption lines. Furthermore, statistical uncertainties still dominate the fit statistics. The relevance of model uncertainties in spectral fitting will vary on a case-by-case basis. However, they are likely to have a minor effect on most of the currently existing data sets. We conclude that while the quality of atomic data does have an effect on fitting photoionization models, and so demands further improvement, uncertainties in radiative rates cannot be held solely responsible for statistically unacceptable fits. Other sources of systematic uncertainties are likely to be of comparable importance and require further investigation.

A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are thereby measured in terms of entropies providing a clear operational interpretation in information theory and cryptography. Recently, entropic uncertainty relations have been used to show that the uncertainty can be reduced in the presence of entanglement and to prove security of quantum cryptographic tasks. However, much of this recent progress has been focused on observables with only a finite number of outcomes not including Heisenberg’s original setting of position and momentum observables. Here, we show entropic uncertainty relations for general observables with discrete but infinite or continuous spectrum that take into account the power of an entangled observer. As an illustration, we evaluate the uncertainty relations for position and momentum measurements, which is operationally significant in that it implies security of a quantum key distribution scheme based on homodyne detection of squeezed Gaussian states.

Observations in the mid-eighteenth and early nineteenth centuries by Melvill (1756), Herschel (1823), and Talbot (1826) regarding colors imparted to flames by salts and other materials, studies of the solar spectrum by Wollaston (1802) and Fraunhofer (1817), and studies of spark- and arc-excited spectra by Wheatstone in 1835 and Foucault in 1848, respectively (Schrenk 1975), were the early beginnings of atomic emission and absorption. It is, however, the investigations on emission in about 1860 by Kirchhoff and Bunsen (1860, 1861) that are generally regarded as the foundations of analytical spectrometry. Modern analytical flame emission spectrometry dates to the work reported by Lundegardh (1934) on the determination of a number of metallic elements in biological samples using air-acetylene flame excitation, a prism spectrograph, and photographic recording. It is considered that quantitative (arc/spark) atomic emission spectrochemical analysis originated about 1882 with Hartley using a spark excitation source. Arc and spark emission spectrometry was the method of choice for simultaneous multielement determinations during the three decades (1930–1960) in many fields of analysis notably in metallurgy and geology. Flame emission spectrometry gained rapidly in popularity following the Introduction of commercial instruments in 1937–1945.

This paper is with the permission of Stepan Moskaliuk similar to what he will put in the confer-ence proceedings of the summer teaching school and workshop for Ukrainian PhD physics stu-dents as given in Bratislava, as of summer 2015. With his permission, this paper will be in part reproduced here for this journal. First of all, we restate a proof of a highly localized special case of a metric tensor uncertainty principle first written up by Unruh. Unruh did not use the Roberson-Walker geometry which we do, and it so happens that the dominant metric tensor we will be examining, is variation in δgtt. The metric tensor variations given by δgrr, and are negligible, as compared to the variation δgtt. Afterwards, what is referred to by Barbour as emergent duration of time is from the Heisenberg Uncertainty principle (HUP) applied to δgtt in such a way as to give, in the Planckian space-time regime a nonzero minimum non zero lower ground to a massive graviton, mgraviton. The lower bound to the massive graviton is influenced by δgtt and kinetic energy which is in the Planckian emergent duration of time δt as (E-V) . We find from δgtt version of the Heisenberg Uncertainty Principle (HUP), that the quantum value of the Δt·ΔE Heisenberg Uncertainty Principle (HUP) is likely not recoverable due to δgtt ≠ Ο(1)~gtt ≡ 1. i.e. δgtt≠ Ο(1) . i.e. is consistent with non-curved space, so Δt · ΔE ≥ no longer holds. This even if we take the stress energy tensor approximation Tii= diag (ρ ,-p,-p,-p) where the fluid approximation is used. Our treatment of the inflaton is via Handley et al., where we consider the lower mass limits of the graviton as due to when the inflaton is many times larger than a Potential energy, with a kinetic energy (KE) proportional to ρw ∝ a-3(1-w) ~ g*T4 , with g* initial degrees of freedom, and T initial temperature. Leading to non-zero initial entropy as stated in Appendix A. In addition we also examine a Ricci scalar value at the boundary between Pre Planckian to Planckian regime of space-time, setting the magnitude of k as approaching flat space conditions right after the Planck regime. Furthermore, we have an approximation as to initial entropy production N~Sinitial(graviton)~1037. Finally, this entropy is N, and we get an initial version of the cosmological “constant” as Appendix D which is linked to initial value of a graviton mass. Appendix E is for the Riemannian-Penrose inequality, which is either a nonzero NLED scale factor or quantum bounce as of LQG. Note that, Appendix F gives conditions so that a pre Planckian kinetic energy (inflaton) value greater than Potential energy occurs, which is foundational to the lower bound to Graviton mass. We will in the future add more structure to this calculation so as to confirm via a precise calculation that the lower bound to the graviton mass, is about 10-70 grams. Our lower bound is a dimensional approximation so far. We will make it exact. We conclude in this document with Appendix G, which is comparing our Pre Planckian space-time metric Heisenberg Uncertainty Principle with the generalized uncertainty principle in quantum gravity. Our result is different from the one given by Ali, Khali and Vagenas, in which our energy fluctuation is not proportional to that of processes of energy connected to Black hole physics, and we also allow for the possibility of Pre Planckian time. Whereas their result (and the generalized string theory Heisenberg Uncertainty principle) have a more limited regime of interpolation of final results. We do come up with equivalent bounds to recover δgtt ~ small-value ≠ O(1) and the deviation of fluctuations of energy, but with very specific bounds upon the parameters of Ali, Khali, and Vegenas, but this has to be more fully explored. Finally, we close with a comparison of what this new Metric tensor uncertainty principle presages as far as avoiding the Bicep 2 mistake, and the different theories of gravity, as reviewed in Appendix H.

High-precision timing of millisecond pulsars (MSPs) over years to decades is a promising technique for direct detection of gravitational waves at nanohertz frequencies. Time-variable, multi-path scattering in the interstellar medium is a significant source of noise for this detector, particularly as timing precision approaches 10 ns or better for MSPs in the pulsar timing array. For many MSPs, the scattering delay above 1 GHz is at the limit of detectability; therefore, we study it at lower frequencies. Using the LOw-Frequency ARray (LOFAR) radio telescope, we have analyzed short (5-20 minutes) observations of 3 MSPs in order to estimate the scattering delay at 110-190 MHz, where the number of scintles is large and, hence, the statistical uncertainty in the scattering delay is small. We used cyclic spectroscopy, still relatively novel in radio astronomy, on baseband-sampled data to achieve unprecedented frequency resolution while retaining adequate pulse-phase resolution. We detected scintillation structure in the spectra of the MSPs PSR B1257+12, PSR J1810+1744, and PSR J2317+1439 with diffractive bandwidths of 6 ± 3, 2.0 ± 0.3, and ~7 kHz, respectively, where the estimate for PSR J2317+1439 is reliable to about a factor of two. For the brightest of the three pulsars, PSR J1810+1744, we found that the diffractive bandwidth has a power-law behavior Δνdvpropνα, where ν is the observing frequency and α = 4.5 ± 0.5, consistent with a Kolmogorov inhomogeneity spectrum. We conclude that this technique holds promise for monitoring the scattering delay of MSPs with LOFAR and other high-sensitivity, low-frequency arrays like the low-frequency component of the Square Kilometre Array.

The growth of structure in the Universe is tightly correlated with the cosmological parameters. Galaxy clusters as tracers of the large scale structure are the ideal objects to witness this evolution. The X-ray bright, hot gas in the potential well of a galaxy cluster enables systematic X-ray studies of samples of galaxy clusters to constrain cosmological parameters. HIFLUGCS consists of the 64 X-ray brightest clusters in the Universe, building up a local sample of galaxy clusters. Here we utilize this sample to determine, for the first time, individual hydrostatic mass estimates for all the clusters of the sample and, by making use of the completeness of the sample, we quantify constraints on the two interesting cosmological parameters, OmegaM and sigma8. In paper I we describe the data analysis procedure and compared the individual mass estimates with other references. Now we apply the total hydrostatic and gas mass estimates from the X-ray analysis to a Bayesian cosmological likelihood analysis and leave several parameters free to be constrained. We find OmegaM = 0.30+-0.01 and sigma8 = 0.79+-0.03 (statistical uncertainties, 68% credibility level) using our default analysis strategy combining both, a mass function analysis and the gas mass fraction results. The main sources of biases that we also correct here are (1) the influence of galaxy groups, (2) the hydrostatic mass bias, (3) the extrapolation of the total mass, (4) the theoretical halo mass function and (5) other physical effects. We find that galaxy groups introduce a strong bias, since their number density seems to be over predicted by the halo mass function. On the other hand, baryonic effects as incorporated by recent hydrodynamical simulations do not result in a significant change in the constraints. The total systematic uncertainties (20%) clearly dominate the statistical uncertainties on cosmological parameters.

A number of statistical analysis techniques are described which meet demands arising in collider experiments in problems of processing the sampled data distributions by including systematic and statistical uncertainties of measurements.