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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Quantile-dependent expressivity of serum C-reactive protein concentrations in family sets

“Quantile-dependent expressivity” occurs when the effect size of a genetic variant depends upon whether the phenotype (e.g., C-reactive protein, CRP) is high or low relative to its distribution. We have previously shown that the heritabilities ( h 2 ) of coffee and alcohol consumption, postprandial lipemia, lipoproteins, leptin, adiponectin, adiposity, and pulmonary function are quantile-specific. Whether CRP heritability is quantile-specific is currently unknown. Methods Serum CRP concentrations from 2,036 sibships and 6,144 offspring-parent pairs were analyzed from the Framingham Heart Study. Quantile-specific heritability from full-sib (β FS , h 2 ={(1 + 8r spouse β FS ) 0.5 - 1}/(2r spouse )) and offspring-parent regression slopes (β OP , h 2 = 2β OP /(1 + r spouse )) were estimated robustly by quantile regression with nonparametric significance determined from 1,000 bootstrap samples. Results Quantile-specific h 2 (±SE) increased with increasing percentiles of the offspring’s age- and sex-adjusted CRP distribution when estimated from β OP ( P trend = 0.0004): 0.02 ± 0.01 at the 10th, 0.04 ± 0.01 at the 25th, 0.10 ± 0.02 at the 50th, 0.20 ± 0.05 at the 75th, and 0.33 ± 0.10 at the 90th percentile, and when estimated from β FS ( P trend = 0.0008): 0.03±0.01 at the 10th, 0.06 ± 0.02 at the 25th, 0.14 ± 0.03 at the 50th, 0.24 ± 0.05 at the 75th, and 0.53 ± 0.21 at the 90th percentile. Conclusion Heritability of serum CRP concentration is quantile-specific, which may explain or contribute to the inflated CRP differences between CRP (rs1130864, rs1205, rs1800947, rs2794521, rs3091244), FGB (rs1800787), IL-6 (rs1800795, rs1800796), IL6R (rs8192284), TNF- α (rs1800629) and APOE genotypes following CABG surgery, stroke, TIA, curative esophagectomy, intensive periodontal therapy, or acute exercise; during acute coronary syndrome or Staphylococcus aureus bacteremia; or in patients with chronic rheumatoid arthritis, diabetes, peripheral arterial disease, ankylosing spondylitis, obesity or inflammatory bowel disease or who smoke.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Quantile-Dependent Expressivity of Serum Uric Acid Concentrations

“Quantile-dependent expressivity” occurs when the effect size of a genetic variant depends upon whether the phenotype (e.g., serum uric acid) is high or low relative to its distribution. Analyses were performed to test whether serum uric acid heritability is quantile-specific and whether this could explain some reported gene-environment interactions. Methods. Serum uric acid concentrations were analyzed from 2151 sibships and 12,068 offspring-parent pairs from the Framingham Heart Study. Quantile-specific heritability from offspring-parent regression slopes (β OP , h 2 = 2β OP /(1 + r spouse )) and full-sib regression slopes (β FS ,h 2 = {(1 + 8r spouse β FS ) 0.5 - 1}/(2r spouse ) was robustly estimated by quantile regression with nonparametric significance assigned from 1000 bootstrap samples. Results. Quantile-specific h 2 (±SE) increased with increasing percentiles of the offspring’s sex- and age-adjusted uric acid distribution when estimated from β OP (P trend = 0.001): 0.34 ± 0.03 at the 10th, 0.36 ± 0.03 at the 25th, 0.41 ± 0.03 at the 50th, 0.46 ± 0.04 at the 75th, and 0.49 ± 0.05 at the 90th percentile and when estimated from β FS (P trend = 0.006). This is consistent with the larger genetic effect size of (1) the SLC2A9 rs11722228 polymorphism in gout patients vs. controls, (2) the ABCG2 rs2231142 polymorphism in men vs. women, (3) the SLC2A9 rs13113918 polymorphism in obese patients prior to bariatric surgery vs. two-year postsurgery following 29 kg weight loss, (4) the ABCG2 rs6855911 polymorphism in obese vs. nonobese women, and (5) the LRP2 rs2544390 polymorphism in heavier drinkers vs. abstainers. Quantile-dependent expressivity may also explain the larger genetic effect size of an SLC2A9/PKD2/ABCG2 haplotype for high vs. low intakes of alcohol, chicken, or processed meats. Conclusions. Heritability of serum uric acid concentrations is quantile-specific.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Predicting variations of the least principal stress with depth: Application to unconventional oil and gas reservoirs using a log-based viscoelastic stress relaxation model

Knowledge of layer-to-layer variations of the least principal stress, S hmin , with depth is essential for optimization of multi-stage hydraulic fracturing in unconventional reservoirs. Utilizing a geomechanical model based on viscoelastic stress relaxation in relatively clay rich rocks, we present a new method for predicting continuous S hmin variations with depth. The method utilizes geophysical log data and S hmin measurements from routine diagnostic fracture injection tests (DFITs) at several depths for calibration. We consider a case study in the Wolfcamp formation in the Midland Basin, where both geophysical logs and values of S hmin from DFITs are available. We compute a continuous stress profile as a function of the well logs that fits all of the DFITs well. We utilized several machine learning technologies, such as bootstrap aggregation (or bagging), to improve the generalization of the model and demonstrate that the excellent fit between predicted and observed stress values is not the result of over-fitting the calibration points. The model is then validated by accurately predicting hold-out stress measurements from four wells within the study area and, without recalibration, accurately predicting stress as a function of depth in an offset pad about 6 miles away.

58 GEOSCIENCES↗
DOE OSTI2023

Semidefinite programming algorithm for the quantum mechanical bootstrap

Here, we present a semidefinite programming algorithm to find eigenvalues of Schrödinger operators within the bootstrap approach to quantum mechanics. The bootstrap approach involves two ingredients: a nonlinear set of constraints on the variables (expectation values of operators in an energy eigenstate), plus positivity constraints (unitarity) that need to be satisfied. By fixing the energy we linearize all the constraints and show that the feasibility problem can be presented as an optimization problem for the variables that are not fixed by the constraints and one additional slack variable that measures the failure of positivity. To illustrate the method we are able to obtain high-precision, sharp bounds on eigenenergies for arbitrary confining polynomial potentials in one dimension.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1994

Deep HST imaging of distant weak radio and field galaxies

We present deep Hubble Space Telescope (HST) Wide-Field Camera (WFC) V- and I-band images of three distant weak radio galaxies with z = 0.311-2.390 and seven field galaxies with z = 0.131-0.58. The images were deconvolved with both the Lucy and multiresolution CLEAN methods, which yield a restoring Full Width at Half Maximum (FWHM) of less than or equal to 0.2 sec, (nearly) preserve photons and signal-to-noise ratio at low spatial frequencies, and produce consistent light profiles down to our 2 sigma surface brightness sensitivity limit of V approximately 27.2 and I approximately 25.9 mag/sq arcsec. Multi-component image modeling was used to provide deconvolution-independent estimates of structural parameters for symmetric galaxies. We present 12-band (m(sub 2750) UBVRIgriJHK) photometry for a subset of the galaxies and bootstrap the unknown FOC/48 zero point at 2750 A in three independent ways (yielding m(sub 2750) = 21.34 +/- 0.09 mag for 1.0 e(-)/s). Two radio galaxies with z = 0.311 and 0.528, as well as one field galaxy with z = 0.58, have the colors and spectra of early-type galaxies, and a(exp 1/4)-like light profiles in the HST images. The two at z greater than 0.5 have little or no color gradients in V - I and are likely giant ellipticals, while the z = 0.311 radio galaxy has a dim exponential disk and is likely an S0. Six of the seven field galaxies have light profiles that indicate (small) inner bulges following a(exp 1/4) laws and outer exponential disks, both with little or no color gradients. These are (early-type) spiral galaxies with z = 0.131-0.528. About half have faint companions or bars. One shows lumpy structure, possibly a merger. The compact narrow-line galaxy 53W002 at z = 2.390 has less than or = 30% +/- 10% of its HST V and I flux in the central kiloparsec (due to its weak Active Galactic Nucleus (AGN)). Most of its light (V approximately equal to 23.3) occurs in a symmetric envelope with a regular a(exp 1/4)-like profile of effective radius a approximately equal to 1.1 sec (approximately equal to 12 kpc for H(sub 0) = 50, q(sub 0) = 0.1. Its (HST) V - I color varies at most from approximately 0.3 mag at a approximately equal to 0.2 sec to approximately 1.2 mag at a approximately greater than 0.4 sec, and possibly to approximately greater than 2.2 mag at a approximately greater than 1.2 sec. Together with its I - K color (approximately equal to 2.5 mag for a approximately greater than 1.0 sec-2.0 sec), this is consistent with an aging stellar population approximately 0.3-0.5 Gyr old in the galaxy center (a approx. less than 2 kpc radius), and possibly approximately 0.5-1.0 Gyr old at a approximately greater than 10 kpc radius. While its outer part may thus have started to collapse at z = 2.5-4, its inner part still is aligned with its redshifted Ly(alpha) cloud and its radio axis, possibly caused by star formation associated with the radio jet, or by reflection from its AGN cone.

Windhorst, R. A.↗
DOE OSTI2024

Improving the five-point bootstrap

We present a new algorithm for the numerical evaluation of five-point conformal blocks in d-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in radial coordinates, derive a set of recursion relations for the unknown coefficients in the ansatz, and evaluate the series using a Padé approximant to accelerate its convergence. We then study the 〈σσϵσσ〉 correlator in the 3d critical Ising model by truncating the operator product expansion (OPE) and only including operators with conformal dimension below a cutoff ∆ ⩽ ∆cutoff. We approximate the contributions of the operators above the cutoff by the corresponding contributions in a suitable disconnected five-point correlator. Using this approach, we compute a number of OPE coefficients with greater accuracy than previous methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Evaluation of DIII-D plasmas for Future Measurements of the Driven Current Density in the DIII-D High Field Side Lower Hybrid Experiment

High field side (HFS) lower hybrid current drive (LHCD) is a promising method for efficiently driving off-axis current in steady state tokamak power plants. The first test of this technology is underway at the DIII-D tokamak. The initial physics goal is to measure the LH-driven current density profile in order to validate the ray-tracing/Fokker-Plank codes GENRAY/CQL3D and gain confidence in their ability to predict LH deposition in future DIII-D experiments and fusion power plants. DIII-D’s motional Stark effect (MSE) diagnostic will be used to constrain the magnetic equilibrium reconstructions. From these reconstructions, the ohmic, bootstrap, and driven non-inductive components of the current density profile can be extracted. Several recent DIII-D plasmas have been identified in which GENRAY/CQL3D predict measurable amounts of current with only 100 kW of coupled power.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Multiparameter Constraints on Empirical Infrasound Period-Yield Relations for Bolides and Implications for Planetary Defense

How effective are methods for estimating bolide energies from infrasound signal period-yield relationships? A single global period–energy relation can obscure significant variability introduced by parameters such as the atmospheric Doppler wind profile and the bolide’s energy deposition profile as a function of altitude. Bolide speed, entry angle, burst altitude, and multiepisode fragmentation may all play a role in defining the detected period of the shockwave. By leveraging bolide light-curve data from the Center for Near Earth Object Studies, we re-examined the period–energy relation as a function of these parameters. Through a bootstrap approach, we show that various event subsets can deviate from widely cited period–energy models and we identify which specific conditions most strongly reshape the period–energy scaling. The results define both the fidelity and reliability of period–energy relations when no additional data beyond the infrasound record is available and improve the outcome when supporting data from bolide trajectories and light curves are included. Ultimately, these findings expand the scope of earlier models, providing a nuanced and robust framework for infrasound-only yield estimation under a range of bolide scenarios.

Planetary science↗
DOE OSTI2023

Scalable Bayesian optimization with randomized prior networks

Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment. Bayesian Optimization (BO) techniques are known to be effective in tackling global optimization problems using a relatively small number objective function evaluations, but their performance suffers when dealing with high-dimensional outputs. To overcome the major challenge of dimensionality, here we propose a deep learning framework for BO and sequential decision making based on bootstrapped ensembles of neural architectures with randomized priors. Using appropriate architecture choices, we show that the proposed framework can approximate functional relationships between design variables and quantities of interest, even in cases where the latter take values in high-dimensional vector spaces or even infinite-dimensional function spaces. In the context of BO, we augmented the proposed probabilistic surrogates with re-parameterized Monte Carlo approximations of multiple-point (parallel) acquisition functions, as well as methodological extensions for accommodating black-box constraints and multi-fidelity information sources. We test the proposed framework against state-of-the-art methods for BO and demonstrate superior performance across several challenging tasks with high-dimensional outputs, including a constrained multi-fidelity optimization task involving shape optimization of rotor blades in turbo-machinery.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A Tutorial on Bayesian analysis of linear shock compression data

Gas gun and other shock compression experiments often produce shock wave velocity measurements that are linearly associated with particle velocity. Traditionally, this empirical relationship is quantified with a single Hugoniot curve that is estimated using least squares regression. However, for downstream modeling and simulation tasks, it is often more useful to have multiple Hugoniot curves in the pressure–volume plane that are consistent with the data. We employ Bayesian uncertainty quantification methods as a framework for propagating measurement uncertainty through to model parameters and predictions. Specifically, this Tutorial shows how to sample multiple Hugoniot curves in the pressure–volume plane that are consistent with the shock wave-particle velocity measurements in a two-step Bayesian approach. First, we obtain an analytical expression for the posterior distribution of the linear model parameters using Bayesian linear regression. Second, we propagate samples from the posterior distribution through the Rankine–Hugoniot equations to yield Hugoniot curves in the pressure–volume plane. The procedure is demonstrated with publicly available data on argon, copper, and nickel, and compared against bootstrapping and linear regression. The Bayesian procedure is shown to be interpretable, computationally inexpensive, and less sensitive than an alternative bootstrapping approach to the removal of the point in the copper dataset that has the largest particle velocity. As a Tutorial on Bayesian methodology for the shock compression community, we provide several derivations and explanations that make this paper self-contained, and make all code and data available at github.com/llnl/BALSCD.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Machine-Learning Assisted Identification of Battery Life Models

Predictive battery life models are commonly utilized to extrapolate degradation trends observed during accelerated aging tests for simulation of degradation in real-world applications. Thus, fitting accelerated aging data as accurately as possible and with low uncertainty is crucial for making believable projections of battery lifetime, but it is challenging to identify algebraic expressions that accurately fit multivariate degradation trends. A review of models published in literature reveal some common expressions for fitting calendar aging data, which is only dependent on temperature and state-of-charge, but no consistency across many models for fitting cycle aging data, indicating the need for a statistically rigorous data driven approach for developing empirical models. This talk will describe a machine-learning assisted method for identification of predictive battery life models utilizing bilevel optimization and symbolic regression. Bilevel optimization with cross-validation is used to statistically determine cell- and stress-dependent model parameters, while symbolic regression identifies both linear and multiplicative candidate expressions to predict stress-dependent degradation rates by selecting low-order subsets of features from a generated feature library. Because model expressions are identified empirically, it is crucial to ensure resulting models behave according to physical expectations, so the stability of models for interpolation or extrapolation is interrogated qualitatively through simulation and quantitatively through cross-validation and uncertainty quantification via bootstrap resampling. This model identification approach substantially improves upon models identified purely using expert judgement in terms of both accuracy and uncertainty. Model simulation and validation is then conducted by deriving a state-equation form of the predictive model, enabling simulation of battery aging under dynamic stresses. This enables validation of the predictive battery model on lab-based tests with varying conditions or on drive-cycle or application-cycle testing protocols. Parameter uncertainty can be carried forward into model simulation, giving lifetime estimates and confidence windows for cell- or system-level lifetime. The financial impact of battery model uncertainty can be estimated by incorporating uncertainty into a technoeconomic model.

battery↗
DOE OSTI2021

Privacy-Preserving Knowledge Transfer with Bootstrap Aggregation of Teacher Ensembles

There is a need to transfer knowledge among institutions and organizations to save effort in annotation and labeling or in enhancing task performance. However, knowledge transfer is difficult because of restrictions that are in place to ensure data security and privacy. Institutions are not allowed to exchange data or perform any activity that may expose personal information. With the leverage of a differential privacy algorithm in a high-performance computing environment, we propose a new training protocol, Bootstrap Aggregation of Teacher Ensembles (BATE), which is applicable to various types of machine learning models. The BATE algorithm is based on and provides enhancements to the PATE algorithm, maintaining competitive task performance scores on complex datasets with underrepresented class labels.We conducted a proof-of-the-concept study of the information extraction from cancer pathology report data from four cancer registries and performed comparisons between four scenarios: no collaboration, no privacy-preserving collaboration, the PATE algorithm, and the proposed BATE algorithm. The results showed that the BATE algorithm maintained competitive macro-averaged F1 scores, demonstrating that the suggested algorithm is an effective yet privacy-preserving method for machine learning and deep learning solutions.

Yoon, Hong-Jun↗
DOE OSTI2020

A measurement of the Hubble constant from Type II supernovae

ABSTRACT Progressive increases in the precision of the Hubble-constant measurement via Cepheid-calibrated Type Ia supernovae (SNe Ia) have shown a discrepancy of ∼4.4σ with the current value inferred from Planck satellite measurements of the cosmic microwave background radiation and the standard $\Lambda $cold dark matter (ΛCDM) cosmological model. This disagreement does not appear to be due to known systematic errors and may therefore be hinting at new fundamental physics. Although all of the current techniques have their own merits, further improvement in constraining the Hubble constant requires the development of as many independent methods as possible. In this work, we use SNe II as standardisable candles to obtain an independent measurement of the Hubble constant. Using seven SNe II with host-galaxy distances measured from Cepheid variables or the tip of the red giant branch, we derive H$_0= 75.8^{+5.2}_{-4.9}$ km s−1 Mpc−1 (statistical errors only). Our value favours that obtained from the conventional distance ladder (Cepheids + SNe Ia) and exhibits a difference of 8.4 km s−1 Mpc−1 from the Planck + ΛCDM value. Adding an estimate of the systematic errors (2.8 km s−1 Mpc−1) changes the ∼1.7σ discrepancy with Planck +ΛCDM to ∼1.4σ. Including the systematic errors and performing a bootstrap simulation, we confirm that the local H0 value exceeds the value from the early Universe with a confidence level of 95 per cent. As in this work, we only exchange SNe II for SNe Ia to measure extragalactic distances, we demonstrate that there is no evidence that SNe Ia are the source of the H0 tension.

de Jaeger, T.↗
NASA NTRS1982

Evaluation of the CEAS trend and monthly weather data models for soybean yields in Iowa, Illinois, and Indiana

The CEAS models evaluated use historic trend and meteorological and agroclimatic variables to forecast soybean yields in Iowa, Illinois, and Indiana. Indicators of yield reliability and current measures of modeled yield reliability were obtained from bootstrap tests on the end of season models. Indicators of yield reliability show that the state models are consistently better than the crop reporting district (CRD) models. One CRD model is especially poor. At the state level, the bias of each model is less than one half quintal/hectare. The standard deviation is between one and two quintals/hectare. The models are adequate in terms of coverage and are to a certain extent consistent with scientific knowledge. Timely yield estimates can be made during the growing season using truncated models. The models are easy to understand and use and are not costly to operate. Other than the specification of values used to determine evapotranspiration, the models are objective. Because the method of variable selection used in the model development is adequately documented, no evaluation can be made of the objectivity and cost of redevelopment of the model.

French, V.↗
DOE OSTI2021

Machine learning elastic constants of multi-component alloys

The present manuscript explores application of machine learning methods for determining elastic constants and other derived mechanical properties of multi-component alloys. Here, a number of machine learning models, including linear regression, neural network and random forest based models, are trained and tested on a dataset of binary alloys generated using density functional theory (DFT) calculations and spanning over a large number of elemental species in the periodic table. Starting with a wide range of simple and easily accessible compositionally-averaged elemental features, a correlation-based feature selection strategy was used to systematically down-select a set of most relevant features towards the prediction of the elasticity tensor components. The true predictive performance and the associated uncertainties of the models were established by testing on unseen data and bootstrapping, respectively. A single and pair-wise feature partial dependence analysis was performed to visualize the average property trends in the multi-dimensional feature space in order to further understand the achieved predictive performance. The utility of the trained model is further demonstrated by obtaining sufficiently accurate yet highly efficient approximations for bulk modulus, Young’s modulus, shear modulus and Poisson’s ratio for alloys beyond the binary space (i.e., two-component alloys) on which the model was originally trained. More importantly, we test and validate the predictive performance of the developed model directly against the experimentally measured elastic constants of technologically relevant multi-component alloys (such as, Ni- and Ti-based alloys). Finally, utility of such a data-enabled route is demonstrated by predicting the possible range of various elastic properties for vast composition space available within the five component Ni-Cr-Fe-Mo-W alloy system in a high-throughput manner.

36 MATERIALS SCIENCE↗
DOE OSTI2023

On extended supersymmetry of 4d Galileons and 3-brane effective actions

We use on-shell amplitude methods to systematically analyze the possibility of extended supersymmetry for 4d Galileon models, expanding on previous $\mathcal{N}$ = 1 results. Assuming spins ≤1, we prove that there exists no $\mathcal{N}$ = 4 supersymmetric extension of 4d Galileons with a single vector multiplet. Thus the Galileons cannot be part of the effective action of a single flat maximally supersymmetric D3-brane, and that explains why such terms do not appear in the α'-expansion of the abelian open superstring amplitude. For $\mathcal{N}$ = 2 Galileons, we show that the complex scalar Z = $\phi$ + $iχ$ of the vector supermultiplet cannot have $\phi$ and $χ$ both enjoy enhanced shift symmetry; instead, $χ$ can at best be an R-axion with constant shift symmetry. Using the soft bootstrap, we demonstrate that the quartic DBI-Galileon is incompatible with $\mathcal{N}$ = 2 supersymmetry. A similar analysis performed at 7-point shows that a 2-parameter family of $\mathcal{N}$ = 2 supersymmetric quintic Galileons coupled with DBI passes the soft bootstrap. Finally, we show how supersymmetric couplings between Galileons and gravitons arise in generalizations of our constructions, and we conclude with a discussion of Galileons and DBI-Galileons in the context of UV-completability vs. the Swampland.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2014

Verification of a New NOAA/NSIDC Passive Microwave Sea-Ice Concentration Climate Record

A new satellite-based passive microwave sea-ice concentration product developed for the National Oceanic and Atmospheric Administration (NOAA)Climate Data Record (CDR) programme is evaluated via comparison with other passive microwave-derived estimates. The new product leverages two well-established concentration algorithms, known as the NASA Team and Bootstrap, both developed at and produced by the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC). The sea ice estimates compare well with similar GSFC products while also fulfilling all NOAA CDR initial operation capability (IOC) requirements, including (1) self describing file format, (2) ISO 19115-2 compliant collection-level metadata,(3) Climate and Forecast (CF) compliant file-level metadata, (4) grid-cell level metadata (data quality fields), (5) fully automated and reproducible processing and (6) open online access to full documentation with version control, including source code and an algorithm theoretical basic document. The primary limitations of the GSFC products are lack of metadata and use of untracked manual corrections to the output fields. Smaller differences occur from minor variations in processing methods by the National Snow and Ice Data Center (for the CDR fields) and NASA (for the GSFC fields). The CDR concentrations do have some differences from the constituent GSFC concentrations, but trends and variability are not substantially different.

Passive Microwave↗
DOE OSTI2021

Missing-Data Nonparametric Coherency Estimation

Chave recently proposed an estimator for multitaper spectral density where the time series contains missing values. In this article we generalize this technique to a multitaper estimator of coherence and phase and show that one can also obtain bootstrapped confidence intervals. Additionally, we give two examples. The first is a toy example in which the true coherence is known. In the second example we show that the multitaper missing-data coherence estimator computed on real data with a single gap comprising 11% of the data outperforms the Daniell-smoothed coherence estimator where there are no gaps. The case where the two time series have different missing indices is also discussed.

42 ENGINEERING↗