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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Numerical Analysis of Fixed Point Algorithms in the Presence of Hardware Faults

The exponential growth of computational power of the extreme scale machines over the past few decades has led to a corresponding decrease in reliability and a sharp increase of the frequency of hardware faults. Our research focuses on the mathematical challenges presented by the silent hardware faults. i.e., faults that can perturb the result of computations in an inconspicuous way. Using the approach of selective reliability we present an analytic fault mode that can be used to study the resilience properties of a numerical algorithm. We apply our approach to the classical fixed point iteration and demonstrate that in the presence of hardware faults, the classical method fails to converge in expectation. We preset a modified resilient algorithm that detects and rejects faults resulting in error with large magnitude, while small faults are negated by the natural self-correcting properties of the algorithm. We show that our method is convergent (in first and second statistical moments) even in the presence of silent hardware faults.

algorithmic resilience↗
DOE OSTI2023

Cluster characterization in atom probe tomography: Machine learning using multiple summary functions

In this work, we develop a machine learning-based method to characterize intracluster concentration (ρ c ), background concentration (ρ b ), clustering radius (r̄), and radius dispersity (δ r ) in simulated atom probe tomography data using multiple spatial statistics summary functions to train a Bayesian regularized neural network. Here, we build upon previous work that utilized Ripley’s K-function by incorporating additional features from nearest-neighbor spatial statistics summary functions to better characterize concentration-based metrics. The addition of nearest-neighbor based features allows for highly accurate estimates of ρ c and ρ b , both with 90% of the predictions within 4.0% of the real value; the root-mean-square errors are reduced by 81.5% and 92.8% from predictions using only K-function based features, respectively. Additionally, including these nearest-neighbor based features improves the ability to differentiate between r̄ and δ r .

36 MATERIALS SCIENCE↗
DOE OSTI2020

Stochastic Simulation of Daily Suspended Sediment Concentration Using Multivariate Copulas

Estimation of daily suspended sediment concentration (SSC) is required for water resources and environment management. In this paper, a copula-based stochastic method was proposed for daily SSC simulation. Here, the multivariate copula function, constructed based on a bivariate copula and two bivariate conditional probability distributions, was used to model the temporal and cross dependence structures in daily SSCs. Then, the daily SSCs were generated by sampling from the multivariate conditional distribution. As a result, synthetic long-term SSCs data beyond the limited observation period can be provided for water resources managers, which plays a critical role in accurately estimating frequency and magnitude of extreme SSCs events. The proposed method was under rigorous examination by applying to a case study at Pingshan station in the Jinsha River Basin, China. Results showed that the generated daily SSC sequences not only had a high degree of accuracy in preserving the statistical characteristics of the daily SSC observations, but also captured both the temporal correlation and the cross-correlation between the daily streamflow and daily SSC. Specifically, the average daily relative error values corresponding to mean, standard deviation, skewness, lag-1 temporal correlation, and cross correlation were 0.87%, 4.24%, 7.52%, 0.51% and 2.02%, respectively. The multivariate copula framework proposed here can accurately and efficiently generate long-term daily SSC data for water resources management such as frequency analysis and risk assessment of extreme SSC events.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

A corrected method for Coulomb scattering in arbitrarily weighted particle-in-cell plasma simulations

A physically and statistically accurate method to perform binary, pairwise Coulomb collisions for arbitrarily-weighted macroparticles in particle-in-cell simulations is described. The method is shown to conserve global energy and momentum on average and to produce physically accurate scattering frequencies. This is justified using the statistically expected values of the method and through a series of numerical tests showing that the method is valid independently of macroparticle weight. This novel method is required due to an error in previous work on binary scattering, initially by Nanbu and Yonemura [J. Comp. Phys. 145, 639 (1998)] and applied to subsequent work, that causes inaccuracies in the scattering frequencies for unequally weighted simulations; a problem that occurs both for scattering within the group and between different groups.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Short-lead seasonal precipitation forecast in northeastern Brazil using an ensemble of artificial neural networks

This study assesses the deterministic and probabilistic forecasting skill of a 1-month-lead ensemble of Artificial Neural Networks (EANN) based on low-frequency climate oscillation indices. The predictand is the February-April (FMA) rainfall in the Brazilian state of Ceará, which is a prominent subject in climate forecasting studies due to its high seasonal predictability. Additionally, the study proposes combining the EANN with dynamical models into a hybrid multi-model ensemble (MME). The forecast verification is carried out through a leave-one-out cross-validation based on 40 years of data. The EANN forecasting skill is compared with traditional statistical models and the dynamical models that compose Ceará’s operational seasonal forecasting system. A spatial comparison showed that the EANN was among the models with the smallest Root Mean Squared Error (RMSE) and Ranked Probability Score (RPS) in most regions. Moreover, the analysis of the area-aggregated reliability showed that the EANN is better calibrated than the individual dynamical models and has better resolution than Multinomial Logistic Regression for above-normal (AN) and below-normal (BN) categories. It is also shown that combining the EANN and dynamical models into a hybrid MME reduces the overconfidence of the extreme categories observed in a dynamically-based MME, improving the reliability of the forecasting system.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Optimization of foreground moment deprojection for semi-blind CMB polarization reconstruction

Abstract Upcoming Cosmic Microwave Background (CMB) experiments, aimed at measuring primordial CMB polarization B-modes, require exquisite control of instrumental systematics and Galactic foreground contamination. Blind minimum-variance techniques, like the Needlet Internal Linear Combination (NILC), have proven effective in reconstructing the CMB polarization signal and mitigating foregrounds and systematics across diverse sky models without suffering from foreground mismodelling errors. Still, residual foreground contamination from NILC may bias the recovered CMB polarization at large angular scales when confronted with the most complex foreground scenarios.By adding constraints to NILC to deproject statistical moments of the Galactic emission, the Constrained Moment ILC (cMILC) method has been demonstrated to further enhance foreground subtraction, albeit with an associated increase in overall noise variance. Faced with this trade-off between foreground bias reduction and overall variance minimization, there is still no recipe on which moments to deproject and which are better suited for blind variance minimization. To address this, we introduce the optimized cMILC (ocMILC) pipeline, which performs full automated optimization of the required number and set of foreground moments to deproject, pivot parameter values, and deprojection coefficients across the sky and angular scales, depending on the actual sky complexity, available frequency coverage, and experiment sensitivity. The optimal number of moments for deprojection, before paying significant noise penalty, is determined through a data diagnosis inspired by the Generalized NILC (GNILC) method.Validated on B-mode simulations of thePICOspace mission concept with four challenging foreground models, ocMILC exhibits lower Galactic foreground contamination compared to NILC and cMILC at all angular scales, with limited noise penalty. This multi-layer optimization enables the ocMILC pipeline to achieve unbiased posteriors of the tensor-to-scalar ratio, regardless of foreground complexity.

Astronomy & Astrophysics↗
DOE OSTI2021

A composite likelihood approach for inference under photometric redshift uncertainty

ABSTRACT Obtaining accurately calibrated redshift distributions of photometric samples is one of the great challenges in photometric surveys like LSST, Euclid, HSC, KiDS, and DES. We present an inference methodology that combines the redshift information from the galaxy photometry with constraints from two-point functions, utilizing cross-correlations with spatially overlapping spectroscopic samples, and illustrate the approach on CosmoDC2 simulations. Our likelihood framework is designed to integrate directly into a typical large-scale structure and weak lensing analysis based on two-point functions. We discuss efficient and accurate inference techniques that allow us to scale the method to the large samples of galaxies to be expected in LSST. We consider statistical challenges like the parametrization of redshift systematics, discuss and evaluate techniques to regularize the sample redshift distributions, and investigate techniques that can help to detect and calibrate sources of systematic error using posterior predictive checks. We evaluate and forecast photometric redshift performance using data from the CosmoDC2 simulations, within which we mimic a DESI-like spectroscopic calibration sample for cross-correlations. Using a combination of spatial cross-correlations and photometry, we show that we can provide calibration of the mean of the sample redshift distribution to an accuracy of at least 0.002(1 + z), consistent with the LSST-Y1 science requirements for weak lensing and large-scale structure probes.

(cosmology:) large-scale structure of Universe↗
DOE OSTI2022

A round-robin approach provides a detailed assessment of biomolecular small-angle scattering data reproducibility and yields consensus curves for benchmarking

Through an expansive international effort that involved data collection on 12 small-angle X-ray scattering (SAXS) and four small-angle neutron scattering (SANS) instruments, 171 SAXS and 76 SANS measurements for five proteins (ribonuclease A, lysozyme, xylanase, urate oxidase and xylose isomerase) were acquired. From these data, the solvent-subtracted protein scattering profiles were shown to be reproducible, with the caveat that an additive constant adjustment was required to account for small errors in solvent subtraction. Further, the major features of the obtained consensus SAXS data over the q measurement range 0–1 Å −1 are consistent with theoretical prediction. The inherently lower statistical precision for SANS limited the reliably measured q -range to <0.5 Å −1 , but within the limits of experimental uncertainties the major features of the consensus SANS data were also consistent with prediction for all five proteins measured in H 2 O and in D 2 O. Thus, a foundation set of consensus SAS profiles has been obtained for benchmarking scattering-profile prediction from atomic coordinates. Additionally, two sets of SAXS data measured at different facilities to q > 2.2 Å −1 showed good mutual agreement, affirming that this region has interpretable features for structural modelling. SAS measurements with inline size-exclusion chromatography (SEC) proved to be generally superior for eliminating sample heterogeneity, but with unavoidable sample dilution during column elution, while batch SAS data collected at higher concentrations and for longer times provided superior statistical precision. Careful merging of data measured using inline SEC and batch modes, or low- and high-concentration data from batch measurements, was successful in eliminating small amounts of aggregate or interparticle interference from the scattering while providing improved statistical precision overall for the benchmarking data set.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Tree-Based Ensemble Learning Models for Wall Temperature Predictions in Post-Critical Heat Flux Flow Regimes at Subcooled and Low-Quality Conditions

Accurately predicting post-critical heat flux (CHF) heat transfer is an important but challenging task in water-cooled reactor design and safety analysis. Although numerous heat transfer correlations have been developed to predict post-CHF heat transfer, these correlations are only applicable to relatively narrow ranges of flow conditions due to the complex physical nature of the post-CHF heat transfer regimes. In this paper, a large quantity of experimental data is collected and summarized from the literature for steady-state subcooled and low-quality film boiling regimes with water as the working fluid in vertical tubular test sections. In addition, a low-quality water film boiling (LWFB) database is consolidated with a total of 22,813 experimental data points, which cover a wide flow range of the system pressure from 0.1 to 9.0 MPa, mass flux from 25 to 2750 kg/m 2 s, and inlet subcooling from 1 to 70 °C. Two machine learning (ML) models, based on random forest (RF) and gradient boosted decision tree (GBDT), are trained and validated to predict wall temperatures in post-CHF flow regimes. The trained ML models demonstrate significantly improved accuracies compared to conventional empirical correlations. To further evaluate the performance of these two ML models from a statistical perspective, three criteria are investigated and three metrics are calculated to quantitatively assess the accuracy of these two ML models. For the full LWFB database, the root-mean-square errors between the measured and predicted wall temperatures by the GBDT and RF models are 5.7% and 6.2%, respectively, confirming the accuracy of the two ML models.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

Hierarchical Linear Regression (Rev. 1)

We describe an algorithm for making inferences in a hierarchical linear model. The model allows different slopes and intercepts for different groups, and ties together the different slopes by representing them as samples from a higher level distribution. (The intercepts are treated as statistically independent.) Our model and code permit many options for the variance of this hierarchical distribution for the slopes, including gamma distributions on the precision, t-distributions on the standard error, pooled slopes (all equal), and independent slopes. The algorithm is described in the paper; an implementation of the algorithm in R is available on request.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Inter- and Intrafraction Target Motion in Highly Focused Single Vocal Cord Irradiation of T1a Larynx Cancer Patients

Purpose: The purpose of this study was to verify clinical target volume–planning target volume (CTV-PTV) margins in single vocal cord irradiation (SVCI) of T1a larynx tumors and characterize inter- and intrafraction target motion. Methods and Materials: For 42 patients, a single vocal cord was irradiated using intensity modulated radiation therapy at a total dose of 58.1 Gy (16 fractions × 3.63 Gy). A daily cone beam computed tomography (CBCT) scan was performed to online correct the setup of the thyroid cartilage after patient positioning with in-room lasers (interfraction motion correction). To monitor intrafraction motion, CBCT scans were also acquired just after patient repositioning and after dose delivery. A mixed online-offline setup correction protocol (“O2 protocol”) was designed to compensate for both inter- and intrafraction motion. Results: Observed interfraction, systematic (Σ), and random (σ) setup errors in left-right (LR), craniocaudal (CC), and anteroposterior (AP) directions were 0.9, 2.0, and 1.1 mm and 1.0, 1.6, and 1.0 mm, respectively. After correction of these errors, the following intrafraction movements derived from the CBCT acquired after dose delivery were: Σ = 0.4, 1.3, and 0.7 mm, and σ = 0.8, 1.4, and 0.8 mm. More than half of the patients showed a systematic non-zero intrafraction shift in target position, (ie, the mean intrafraction displacement over the treatment fractions was statistically significantly different from zero; P<.05). With the applied CTV-PTV margins (for most patients 3, 5, and 3 mm in LR, CC, and AP directions, respectively), the minimum CTV dose, estimated from the target displacements observed in the last CBCT, was at least 94% of the prescribed dose for all patients and more than 98% for most patients (37 of 42). The proposed O2 protocol could effectively reduce the systematic intrafraction errors observed after dose delivery to almost zero (Σ = 0.1, 0.2, 0.2 mm). Conclusions: With adequate image guidance and CTV-PTV margins in LR, CC, and AP directions of 3, 5, and 3 mm, respectively, excellent target coverage in SVCI could be ensured.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2014

SU-C-BRD-03: Analysis of Accelerator Generated Text Logs for Preemptive Maintenance

Purpose: To develop a model to analyze medical accelerator generated parameter and performance data that will provide an early warning of performance degradation and impending component failure. Methods: A robust 6 MV VMAT quality assurance treatment delivery was used to test the constancy of accelerator performance. The generated text log files were decoded and analyzed using statistical process control (SPC) methodology. The text file data is a single snapshot of energy specific and overall systems parameters. A total of 36 system parameters were monitored which include RF generation, electron gun control, energy control, beam uniformity control, DC voltage generation, and cooling systems. The parameters were analyzed using Individual and Moving Range (I/MR) charts. The chart limits were calculated using a hybrid technique that included the use of the standard 3σ limits and the parameter/system specification. Synthetic errors/changes were introduced to determine the initial effectiveness of I/MR charts in detecting relevant changes in operating parameters. The magnitude of the synthetic errors/changes was based on: the value of 1 standard deviation from the mean operating parameter of 483 TB systems, a small fraction (≤ 5%) of the operating range, or a fraction of the minor fault deviation. Results: There were 34 parameters in which synthetic errors were introduced. There were 2 parameters (radial position steering coil, and positive 24V DC) in which the errors did not exceed the limit of the I/MR chart. The I chart limit was exceeded for all of the remaining parameters (94.2%). The MR chart limit was exceeded in 29 of the 32 parameters (85.3%) in which the I chart limit was exceeded. Conclusion: Statistical process control I/MR evaluation of text log file parameters may be effective in providing an early warning of performance degradation or component failure for digital medical accelerator systems. Research is Supported by Varian Medical Systems, Inc.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2016

Background based Gaussian mixture model lesion segmentation in PET

Purpose: Quantitative {sup 18}F-fluorodeoxyglucose positron emission tomography is limited by the uncertainty in lesion delineation due to poor SNR, low resolution, and partial volume effects, subsequently impacting oncological assessment, treatment planning, and follow-up. The present work develops and validates a segmentation algorithm based on statistical clustering. The introduction of constraints based on background features and contiguity priors is expected to improve robustness vs clinical image characteristics such as lesion dimension, noise, and contrast level. Methods: An eight-class Gaussian mixture model (GMM) clustering algorithm was modified by constraining the mean and variance parameters of four background classes according to the previous analysis of a lesion-free background volume of interest (background modeling). Hence, expectation maximization operated only on the four classes dedicated to lesion detection. To favor the segmentation of connected objects, a further variant was introduced by inserting priors relevant to the classification of neighbors. The algorithm was applied to simulated datasets and acquired phantom data. Feasibility and robustness toward initialization were assessed on a clinical dataset manually contoured by two expert clinicians. Comparisons were performed with respect to a standard eight-class GMM algorithm and to four different state-of-the-art methods in terms of volume error (VE), Dice index, classification error (CE), and Hausdorff distance (HD). Results: The proposed GMM segmentation with background modeling outperformed standard GMM and all the other tested methods. Medians of accuracy indexes were VE <3%, Dice >0.88, CE <0.25, and HD <1.2 in simulations; VE <23%, Dice >0.74, CE <0.43, and HD <1.77 in phantom data. Robustness toward image statistic changes (±15%) was shown by the low index changes: <26% for VE, <17% for Dice, and <15% for CE. Finally, robustness toward the user-dependent volume initialization was demonstrated. The inclusion of the spatial prior improved segmentation accuracy only for lesions surrounded by heterogeneous background: in the relevant simulation subset, the median VE significantly decreased from 13% to 7%. Results on clinical data were found in accordance with simulations, with absolute VE <7%, Dice >0.85, CE <0.30, and HD <0.81. Conclusions: The sole introduction of constraints based on background modeling outperformed standard GMM and the other tested algorithms. Insertion of a spatial prior improved the accuracy for realistic cases of objects in heterogeneous backgrounds. Moreover, robustness against initialization supports the applicability in a clinical setting. In conclusion, application-driven constraints can generally improve the capabilities of GMM and statistical clustering algorithms.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Systematic and statistical uncertainties of the hilbert-transform based high-precision FID frequency extraction method

Pulsed nuclear magnetic resonance (NMR) is widely used in high-precision magnetic field measurements. The absolute value of the magnetic field is determined from the precession frequency of nuclear magnetic moments. The Hilbert transform is widely used to extract the phase function from the observed free induction decay (FID) signal and then its frequency. In this paper, a detailed implementation of a Hilbert-transform based FID frequency extraction method is described. How artifacts and noise level in the FID signal affect the extracted phase function are derived analytically. A method of mitigating the artifacts in the extracted phase function of an FID is discussed. Correlations between noises of the phase function samples are studied for different noise spectra. We discovered that the error covariance matrix for the extracted phase function is nearly singular and improper for constructing the $\chi^2$ used in the fitting routine. A down-sampling method for fixing the singular covariance matrix has been developed, so that the minimum $\chi^2$-fit yields properly the statistical uncertainty of the extracted frequency. Other practical methods of obtaining the statistical uncertainty are also discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

Neutrino Interactions

The neutrino group of the University of Tennessee, Knoxville was involved from 05/01/2013 to 04/30/2015 in the neutrino physics research funded by DOE-HEP grant DE-SC0009861. Contributions were made to the Double Chooz nuclear reactor experiment in France where second detector was commissioned during this period and final series of measurements has been started. Although Double Chooz was smaller experimental effort than competitive Daya Bay and RENO experiments, its several advantages make it valuable for understanding of systematic errors in measurements of neutrino oscillations. Double Chooz was the first experiment among competing three that produced initial result for neutrino angle θ 13 measurement, giving other experiments the chance to improve measured value statistically. Graduate student Ben Rybolt defended his PhD thesis on the results of Double Chooz experiment in 2015. UT group has fulfilled all the construction and analysis commitments to Double Chooz experiment, and has withdrawn from the collaboration by the end of the mentioned period to start another experiment. Larger effort of UT neutrino group during this period was devoted to the participation in another DOE-HEP project - NOvA experiment. The 14,000-ton "FAR" neutrino detector was commissioned in northern Minnesota in 2014 together with 300-ton "NEAR" detector located at Fermilab. Following that, the physics measurement program has started when Fermilab accelerator complex produced the high-intensity neutrino beam propagating through Earth to detector in MInnessota. UT group contributed to NOvA detector construction and developments in several aspects. Our Research Associate Athanasios Hatzikoutelis was managing (Level 3 manager) the construction of the Detector Control System. This work was successfully accomplished in time with the commissioning of the detectors. Group was involved in the development of the on-line software and study of the signatures of the cosmic ray backgrounds. Flumerfelt and another graduate student Philip Mason were also studying the non-linearity properties of the NOvA liquid scintillator - information that will be essential at the final stages of NOvA data analysis. Philip Mason also studied the response of the FAR NOvA detector in correlation with solar flares. Flumerfelt and Mason successfully defended their PhD in 2015. Also, undergraduate student Cameron Blake Erickson has defended his undergraduate thesis on the NOvA liquid scintillator studies with Compton gamma spectrometer at UT.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

Identifying Predictive Factors for Incident Reports in Patients Receiving Radiation Therapy

Purpose: To describe radiation therapy cases during which voluntary incident reporting occurred; and identify patient- or treatment-specific factors that place patients at higher risk for incidents. Methods and Materials: We used our institution's incident learning system to build a database of patients with incident reports filed between January 2011 and December 2013. Patient- and treatment-specific data were reviewed for all patients with reported incidents, which were classified by step in the process and root cause. A control group of patients without events was generated for comparison. Summary statistics, likelihood ratios, and mixed-effect logistic regression models were used for group comparisons. Results: The incident and control groups comprised 794 and 499 patients, respectively. Common root causes included documentation errors (26.5%), communication (22.5%), technical treatment planning (37.5%), and technical treatment delivery (13.5%). Incidents were more frequently reported in minors (age <18 years) than in adult patients (37.7% vs 0.4%, P<.001). Patients with head and neck (16% vs 8%, P<.001) and breast (20% vs 15%, P=.03) primaries more frequently had incidents, whereas brain (18% vs 24%, P=.008) primaries were less frequent. Larger tumors (17% vs 10% had T4 lesions, P=.02), and cases on protocol (9% vs 5%, P=.005) or with intensity modulated radiation therapy/image guided intensity modulated radiation therapy (52% vs 43%, P=.001) were more likely to have incidents. Conclusions: We found several treatment- and patient-specific variables associated with incidents. These factors should be considered by treatment teams at the time of peer review to identify patients at higher risk. Larger datasets are required to recommend changes in care process standards, to minimize safety risks.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2022

Regression of exchangeable relational arrays

Relational arrays represent measures of association between pairs of actors, often in varied contexts or over time. Trade flows between countries, financial transactions between individuals, contact frequencies between school children in classrooms and dynamic protein-protein interactions are all examples of relational arrays. Elements of a relational array are often modelled as a linear function of observable covariates. Uncertainty estimates for regression coefficient estimators, and ideally the coefficient estimators themselves, must account for dependence between elements of the array, e.g., relations involving the same actor. Existing estimators of standard errors that recognize such relational dependence rely on estimating extremely complex, heterogeneous structure across actors. This paper develops a new class of parsimonious coefficient and standard error estimators for regressions of relational arrays. Here we leverage an exchangeability assumption to derive standard error estimators that pool information across actors, and are substantially more accurate than existing estimators in a variety of settings. This exchangeability assumption is pervasive in network and array models in the statistics literature, but not previously considered when adjusting for dependence in a regression setting with relational data. We demonstrate improvements in inference theoretically, via a simulation study, and by analysis of a dataset involving international trade.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Forecasting constraints on the mean free path of ionizing photons at z ≥ 5.4 from the Lyman-α forest flux autocorrelation function

ABSTRACT Fluctuations in Lyman-α (Ly α) forest transmission towards high-z quasars are partially sourced from spatial fluctuations in the ultraviolet background, the level of which are set by the mean free path of ionizing photons (λmfp). The autocorrelation function of Ly α forest flux characterizes the strength and scale of transmission fluctuations and, as we show, is thus sensitive to λmfp. Recent measurements at z ∼ 6 suggest a rapid evolution of λmfp at z > 5.0 which would leave a signature in the evolution of the autocorrelation function. For this forecast, we model mock Ly α forest data with properties similar to the XQR-30 extended data set at 5.4 ≤ z ≤ 6.0. At each z, we investigate 100 mock data sets and an ideal case where mock data matches model values of the autocorrelation function. For ideal data with λmfp = 9.0 cMpc at z = 6.0, we recover $\lambda _{\text{mfp}}=12^{+6}_{-3}$ cMpc. This precision is comparable to direct measurements of λmfp from the stacking of quasar spectra beyond the Lyman limit. Hypothetical high-resolution data leads to a $\sim 40~{{\ \rm per\ cent}}$ reduction in the error bars over all z. The distribution of mock values of the autocorrelation function in this work is highly non-Gaussian for high-z, which should caution work with other statistics of the high-z Ly α forest against making this assumption. We use a rigorous statistical method to pass an inference test, however future work on non-Gaussian methods will enable higher precision measurements.

Astronomy & Astrophysics↗