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DOE OSTI2013

USING COLORS TO IMPROVE PHOTOMETRIC METALLICITY ESTIMATES FOR GALAXIES

There is a well known correlation between the mass and metallicity of star-forming galaxies. Because mass is correlated with luminosity, this relation is often exploited, when spectroscopy is not available, to estimate galaxy metallicities based on single band photometry. However, we show that galaxy color is typically more effective than luminosity as a predictor of metallicity. This is a consequence of the correlation between color and the galaxy mass-to-light ratio and the recently discovered correlation between star formation rate (SFR) and residuals from the mass-metallicity relation. Using Sloan Digital Sky Survey spectroscopy of ∼180, 000 nearby galaxies, we derive 'LZC relations', empirical relations between metallicity (in seven common strong line diagnostics), luminosity, and color (in 10 filter pairs and four methods of photometry). We show that these relations allow photometric metallicity estimates, based on luminosity and a single optical color, that are ∼50% more precise than those made based on luminosity alone; galaxy metallicity can be estimated to within ∼0.05-0.1 dex of the spectroscopically derived value depending on the diagnostic used. Including color information in photometric metallicity estimates also reduces systematic biases for populations skewed toward high or low SFR environments, as we illustrate using the host galaxy of the supernova SN 2010ay. This new tool will lend more statistical power to studies of galaxy populations, such as supernova and gamma-ray burst host environments, in ongoing and future wide-field imaging surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

LIKELIHOOD OF THE POWER SPECTRUM IN COSMOLOGICAL PARAMETER ESTIMATION

The likelihood function is a crucial element of parameter estimation. In analyses of galaxy overdensities and weak lensing shear, one often approximates the likelihood of the power spectrum with a Gaussian distribution. The posterior probability derived from such a likelihood deviates considerably from the exact posterior on the largest scales probed by any survey, where the central limit theorem does not apply. We show that various forms of Gaussian likelihoods can have a significant impact on the estimation of the primordial non-Gaussianity parameter f{sub NL} from the galaxy angular power spectrum. The Gaussian plus log-normal likelihood, which has been applied successfully in analyses of the cosmic microwave background, outperforms the Gaussian likelihoods. Nevertheless, even if the exact likelihood of the power spectrum is used, the estimated parameters may be still biased. As such, the likelihoods and estimators need to be thoroughly examined for potential systematic errors.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Estimating stellar radial velocity variability from Kepler and GALEX: Implications for the radial velocity confirmation of exoplanets

We cross match the GALEX and Kepler surveys to create a unique dataset with both ultraviolet (UV) measurements and highly precise photometric variability measurements in the visible light spectrum. As stellar activity is driven by magnetic field modulations, we have used UV emission from the magnetically heated gas in the stellar atmosphere to serve as our proxy for the more well-known stellar activity indicator, R' {sub HK}. The R' {sub HK} approximations were in turn used to estimate the level of astrophysical noise expected in radial velocity (RV) measurements and these were then searched for correlations with photometric variability. We find significant scatter in our attempts to estimate RV noise for magnetically active stars, which we attribute to variations in the phase and strength of the stellar magnetic cycle that drives the activity of these targets. However, for stars we deem to be magnetically quiet, we do find a clear correlation between photometric variability and estimated levels of RV noise (with variability up to ∼10 m s{sup –1}). We conclude that for these quiet stars, we can use photometric measurements as a proxy to estimate the RV noise expected. As a result, the procedure outlined in this paper may help select targets best-suited for RV follow-up necessary for planet confirmation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Imaging redshift estimates for Fermi BL Lac objects

We have obtained WIYN and SOAR i' images of BL Lacertae objects and used these to detect or constrain the flux of the host galaxy. Under common standard candle assumptions, these data provide estimates of, or lower bounds on, the redshift. Our targets are a set of flat-spectrum radio counterparts of high flux Fermi Large Area Telescope sources, with sensitive spectral observations showing them to be continuum-dominated BL Lac objects. In this sample, 5 of 11 BL Lac objects yielded significant host detections, with standard candle redshifts z = 0.13-0.58. Our estimates and lower bounds are generally in agreement with other redshifts estimates, although our z = 0.374 estimate for J0543–5532 implies a significantly sub-luminous host.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

A comprehensive method of estimating electric fields from vector magnetic field and Doppler measurements

Photospheric electric fields, estimated from sequences of vector magnetic field and Doppler measurements, can be used to estimate the flux of magnetic energy (the Poynting flux) into the corona and as time-dependent boundary conditions for dynamic models of the coronal magnetic field. We have modified and extended an existing method to estimate photospheric electric fields that combines a poloidal-toroidal decomposition (PTD) of the evolving magnetic field vector with Doppler and horizontal plasma velocities. Our current, more comprehensive method, which we dub the 'PTD-Doppler-FLCT Ideal' (PDFI) technique, can now incorporate Doppler velocities from non-normal viewing angles. It uses the FISHPACK software package to solve several two-dimensional Poisson equations, a faster and more robust approach than our previous implementations. Here, we describe systematic, quantitative tests of the accuracy and robustness of the PDFI technique using synthetic data from anelastic MHD (ANMHD) simulations, which have been used in similar tests in the past. We find that the PDFI method has less than 1% error in the total Poynting flux and a 10% error in the helicity flux rate at a normal viewing angle (θ = 0) and less than 25% and 10% errors, respectively, at large viewing angles (θ < 60°). We compare our results with other inversion methods at zero viewing angle and find that our method's estimates of the fluxes of magnetic energy and helicity are comparable to or more accurate than other methods. We also discuss the limitations of the PDFI method and its uncertainties.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

BLACK HOLE MASS ESTIMATES AND RAPID GROWTH OF SUPERMASSIVE BLACK HOLES IN LUMINOUS z ∼ 3.5 QUASARS

We present new near-infrared (IR) observations of the Hβ λ4861 and Mg II λ2798 lines for 32 luminous quasars with 3.2 < z < 3.9 using the Palomar Hale 200 inch telescope and the Large Binocular Telescope. We find that the Mg II FWHM is well correlated with the Hβ FWHM, confirming itself as a good substitute for the Hβ FWHM in the black hole mass estimates. The continuum luminosity at 5100 Å well correlates with the continuum luminosity at 3000 Å and the broad emission line luminosities (Hβ and Mg II). With simultaneous near-IR spectroscopy of the Hβ and Mg II lines to exclude the influences of flux variability, we are able to evaluate the reliability of estimating black hole masses based on the Mg II line for high redshift quasars. With the reliable Hβ line based black hole mass and Eddington ratio estimates, we find that the z ∼ 3.5 quasars in our sample have black hole masses 1.90 × 10{sup 9} M {sub ☉} ≲ M {sub BH} ≲ 1.37 × 10{sup 10} M {sub ☉}, with a median of ∼5.14 × 10{sup 9} M {sub ☉} and are accreting at Eddington ratios between 0.30 and 3.05, with a median of ∼1.12. Assuming a duty cycle of 1 and a seed black hole mass of 10{sup 4} M {sub ☉}, we show that the z ∼ 3.5 quasars in this sample can grow to their estimated black hole masses within the age of the universe at their redshifts.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A COMPARATIVE STUDY OF DENSITY FIELD ESTIMATION FOR GALAXIES: NEW INSIGHTS INTO THE EVOLUTION OF GALAXIES WITH ENVIRONMENT IN COSMOS OUT TO z ∼ 3

It is well-known that a galaxy’s environment has a fundamental influence in shaping its properties. We study the environmental effects on galaxy evolution, with an emphasis on the environment defined as the local number density of galaxies. The density field is estimated with different estimators (weighted adaptive kernel smoothing, 10th and 5th nearest neighbors, Voronoi and Delaunay tessellation) for a K{sub s} < 24 sample of ∼190,000 galaxies in the COSMOS field at 0.1 < z < 3.1. The performance of each estimator is evaluated with extensive simulations. We show that overall there is a good agreement between the estimated density fields using different methods over ∼2 dex in overdensity values. However, our simulations show that adaptive kernel and Voronoi tessellation outperform other methods. Using the Voronoi tessellation method, we assign surface densities to a mass complete sample of quiescent and star-forming galaxies out to z ∼ 3. We show that at a fixed stellar mass, the median color of quiescent galaxies does not depend on their host environment out to z ∼ 3. We find that the number and stellar mass density of massive (>10{sup 11} M{sub ⊙}) star-forming galaxies have not significantly changed since z ∼ 3, regardless of their environment. However, for massive quiescent systems at lower redshifts (z ≲ 1.3), we find a significant evolution in the number and stellar mass densities in denser environments compared to lower density regions. Our results suggest that the relation between stellar mass and local density is more fundamental than the color–density relation and that environment plays a significant role in quenching star-formation activity in galaxies at z ≲ 1.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Improved estimates of the Milky Way’s stellar mass and star formation rate from hierarchical Bayesian meta-analysis

We present improved estimates of several global properties of the Milky Way, including its current star formation rate (SFR), the stellar mass contained in its disk and bulge+bar components, as well as its total stellar mass. We do so by combining previous measurements from the literature using a hierarchical Bayesian (HB) statistical method that allows us to account for the possibility that any value may be incorrect or have underestimated errors. We show that this method is robust to a wide variety of assumptions about the nature of problems in individual measurements or error estimates. Ultimately, our analysis yields an SFR for the Galaxy of M-dot {sub ⋆}=1.65±0.19 M{sub ⊙} yr{sup −1}, assuming a Kroupa initial mass function (IMF). By combining HB methods with Monte Carlo simulations that incorporate the latest estimates of the Galactocentric radius of the Sun, R{sub 0}, the exponential scale length of the disk, L{sub d}, and the local surface density of stellar mass, Σ{sub ⋆}(R{sub 0}), we show that the mass of the Galactic bulge+bar is M{sub ⋆}{sup B}=0.91±0.07×10{sup 10} M{sub ⊙}, the disk mass is M{sub ⋆}{sup D}=5.17±1.11×10{sup 10} M{sub ⊙}, and their combination yields a total stellar mass of M{sub ⋆}=6.08±1.14×10{sup 10} M{sub ⊙} (assuming a Kroupa IMF and an exponential disk profile). This analysis is based upon a new compilation of literature bulge mass estimates, normalized to common assumptions about the stellar IMF and Galactic disk properties, presented herein. We additionally find a bulge-to-total mass ratio for the Milky Way of B/T=0.150{sub −0.019}{sup +0.028} and a specific SFR of M-dot {sub ⋆}/M{sub ⋆}=2.71±0.59×10{sup −11} yr{sup −1}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2011

Estimating the tensor-to-scalar ratio and the effect of residual foreground contamination

We consider future balloon-borne and ground-based suborbital experiments designed to search for inflationary gravitational waves, and investigate the impact of residual foregrounds that remain in the estimated cosmic microwave background maps. This is achieved by propagating foreground modelling uncertainties from the component separation, under the assumption of a spatially uniform foreground frequency scaling, through to the power spectrum estimates, and up to measurement of the tensor to scalar ratio in the parameter estimation step. We characterize the error covariance due to subtracted foregrounds, and find it to be subdominant compared to instrumental noise and sample variance in our simulated data analysis. We model the unsubtracted residual foreground contribution using a two-parameter power law and show that marginalization over these foreground parameters is effective in accounting for a bias due to excess foreground power at low l. We conclude that, at least in the suborbital experimental setups we have simulated, foreground errors may be modeled and propagated up to parameter estimation with only a slight degradation of the target sensitivity of these experiments derived neglecting the presence of the foregrounds.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Removing the ISW-lensing bias from the local-form primordial non-Gaussianity estimation

The Integrated Sachs-Wolfe (ISW) effect produces a secondary temperature aniso\-tropy of the cosmic microwave background (CMB), as CMB photons travel through time-varying potentials along the line-of-sight. The main contribution comes from redshifts z∼<2, where dark energy leads to a decay of potentials. As the same photons are gravitationally lensed by these decaying potentials, there exists a high degree of correlation between the ISW effect and CMB lensing, leading to a non-zero three-point correlation (bispectrum) of the observed temperature anisotropy. This ISW-lensing bispectrum, whose shape resembles that of the so-called ''local-form'' primordial bispectrum parametrized by f{sub NL}, is known to be the largest contamination of f{sub NL}. In order to avoid a spurious detection of primordial non-Gaussianity, we need to remove the ISW-lensing bias. In this work, we investigate three debiasing methods: (I) subtraction of an expected, ensemble average of the ISW-lensing bispectrum; (II) subtraction of a measured ISW-lensing bispectrum; and (III) direct subtraction of an estimated ISW signal from an observed temperature map. One may use an estimation of the ISW map from external non-CMB data or that from the CMB data themselves. As the methods II and III are based on fewer assumptions about the nature of dark energy, they are preferred over the method I. While the methods I and II yield unbiased estimates of f{sub NL} with comparable error bars, the method III yields a biased result when the underlying primordial f{sub NL} is non-zero and the ISW map is estimated from a lensing potential reconstructed from the observed temperature map. One of the sources of the bias is a lensing reconstruction noise bias which is independent of f{sub NL} and can be calculated precisely, but other f{sub NL}-dependent terms are difficult to compute reliably. We thus conclude that the method II is the best, model-independent way to remove the ISW-lensing bias of f{sub NL}, enabling us to test the physics of inflation with smaller systematic errors.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Searching for primordial non-Gaussianity in Planck CMB maps using a combined estimator

The extensive search for deviations from Gaussianity in cosmic microwave background radiation (CMB) data is very important due to the information about the very early moments of the universe encoded there. Recent analyses from Planck CMB data do not exclude the presence of non-Gaussianity of small amplitude, although they are consistent with the Gaussian hypothesis. The use of different techniques is essential to provide information about types and amplitudes of non-Gaussianities in the CMB data. In particular, we find interesting to construct an estimator based upon the combination of two powerful statistical tools that appears to be sensitive enough to detect tiny deviations from Gaussianity in CMB maps. This estimator combines the Minkowski functionals with a Neural Network, maximizing a tool widely used to study non-Gaussian signals with a reinforcement of another tool designed to identify patterns in a data set. We test our estimator by analyzing simulated CMB maps contaminated with different amounts of local primordial non-Gaussianity quantified by the dimensionless parameter f{sub NL}. We apply it to these sets of CMB maps and find ∼> 98% of chance of positive detection, even for small intensity local non-Gaussianity like f{sub NL} = 38±18, the current limit from Planck data for large angular scales. Additionally, we test the suitability to distinguish between primary and secondary non-Gaussianities: first we train the Neural Network with two sets, one of nearly Gaussian CMB maps (|f{sub NL}| ≤ 10) but contaminated with realistic inhomogeneous Planck noise (i.e., secondary non-Gaussianity) and the other of non-Gaussian CMB maps, that is, maps endowed with weak primordial non-Gaussianity (28 ≤ f{sub NL} ≤ 48); after that we test an ensemble composed of CMB maps either with one of these non-Gaussian contaminations, and find out that our method successfully classifies ∼ 95% of the tested maps as being CMB maps containing primordial or secondary non-Gaussianity. Furthermore, we analyze the foreground-cleaned Planck maps obtaining constraints for non-Gaussianity at large-angles that are in good agreement with recent constraints. Finally, we also test the robustness of our estimator including cut-sky masks and realistic noise maps measured by Planck, obtaining successful results as well.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

An optimally weighted estimator of the linear power spectrum disentangling the growth of density perturbations across galaxy surveys

Measuring the clustering of galaxies from surveys allows us to estimate the power spectrum of matter density fluctuations, thus constraining cosmological models. This requires careful modelling of observational effects to avoid misinterpretation of data. In particular, signals coming from different distances encode information from different epochs. This is known as ''light-cone effect'' and is going to have a higher impact as upcoming galaxy surveys probe larger redshift ranges. Generalising the method by Feldman, Kaiser and Peacock (1994) [1], I define a minimum-variance estimator of the linear power spectrum at a fixed time, properly taking into account the light-cone effect. An analytic expression for the estimator is provided, and that is consistent with the findings of previous works in the literature. I test the method within the context of the Halofit model, assuming Planck 2014 cosmological parameters [2]. I show that the estimator presented recovers the fiducial linear power spectrum at present time within 5% accuracy up to k ∼ 0.80 h Mpc{sup −1} and within 10% up to k ∼ 0.94 h Mpc{sup −1}, well into the non-linear regime of the growth of density perturbations. As such, the method could be useful in the analysis of the data from future large-scale surveys, like Euclid.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Light in the dark forest. Part I. An efficient optimal estimator for 3D Lyman-alpha forest power spectrum

The highly anisotropic nature of the Lyman-alpha (Lyα) forest data introduces a complex survey window function that complicates the measurement of the three-dimensional power spectrum ( P 3D ). In this paper, we present the first fully optimal estimator for P 3D , which exactly deconvolves the survey window function and marginalizes contaminated modes that distort the power spectrum. Our approach adapts optimal estimator techniques developed for the 2D cosmic microwave background data to the 3D case. To achieve computational feasibility, we employ the conjugate gradient method and implement the P 3 M formalism to handle large-scale and small-scale operations separately and efficiently. We validate our estimator using Monte Carlo mocks and Gaussian simulations, demonstrating its accuracy and computational efficiency. We confirm that mode marginalization eliminates distortions arising from quasar continuum errors and delivers robust power spectrum estimation, though it also inflates errors at large scales. This first implementation works in the flat-sky case; we discuss the remaining steps needed to generalize it to the curved-sky case. This formalism offers a foundation for the Lyα forest P 3D measurements and a new path toward cosmological constraints from the Lyα forest data.

Lyman alpha forest↗
DOE OSTI2020

Subsea permafrost carbon stocks and climate change sensitivity estimated by expert assessment

The continental shelves of the Arctic Ocean and surrounding seas contain large stocks of organic matter (OM) and methane (CH4), representing a potential ecosystem feedback to climate change not included in international climate agreements. We performed a structured expert assessment with 25 permafrost researchers to combine quantitative estimates of the stocks and sensitivity of organic carbon in the subsea permafrost domain (i.e. unglaciated portions of the continental shelves exposed during the last glacial period). Experts estimated that the subsea permafrost domain contains ~560 gigatons carbon (GtC; 170–740, 90% confidence interval) in OM and 45 GtC (10–110) in CH 4 . Current fluxes of CH 4 and carbon dioxide (CO 2 ) to the water column were estimated at 18 (2–34) and 38 (13–110) megatons C yr –1 , respectively. Under Representative Concentration Pathway (RCP) RCP8.5, the subsea permafrost domain could release 43 Gt CO 2 – equivalent (CO 2 e) by 2100 (14–110) and 190 Gt CO 2 e by 2300 (45–590), with ~30% fewer emissions under RCP2.6. The range of uncertainty demonstrates a serious knowledge gap but provides initial estimates of the magnitude and timing of the subsea permafrost climate feedback.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2012

THE IMPORTANCE OF BROAD EMISSION LINE WIDTHS IN SINGLE-EPOCH BLACK HOLE MASS ESTIMATES

Estimates of the mass of super-massive black holes (BHs) in distant active galactic nuclei (AGNs) can be obtained efficiently only through single-epoch (SE) spectra, using a combination of their broad emission line widths and continuum luminosities. Yet the reliability and accuracy of the method and the resulting mass estimates, M{sub BH}, remain uncertain. A recent study by Croom using a sample of Sloan Digital Sky Survey, 2dF QSO Redshift Survey, and 2dF-SDSS LRG and QSO Survey quasars suggests that line widths contribute little information about the BH mass in these SE estimates and can be replaced by a constant value without significant loss of accuracy. In this Letter, we use a sample of nearby reverberation-mapped AGNs to show that this conclusion is not universally applicable. We use the bulge luminosity (L{sub Bulge}) of these local objects to test how well the known M{sub BH}-L{sub Bulge} correlation is recovered when using randomly assigned line widths instead of the measured ones to estimate M{sub BH}. We find that line widths provide significant information about M{sub BH}, and that for this sample, the line width information is just as significant as that provided by the continuum luminosities. We discuss the effects of observational biases upon the analysis of Croom and suggest that the results can probably be explained as a bias of flux-limited, shallow quasar samples.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Flood Estimation under Snowmelt and Rain-on-Snow Processes in Alaska: A Military Installation Perspective

Accurate flood estimation in snow-dominated and high-latitude regions remains challenging due to complex interactions among rainfall, snowmelt, and rain-on-snow (ROS) processes, which are not captured in conventional precipitation-based intensity-duration-frequency (PREC-IDF) curves. This study evaluates the Next-Generation IDF (NG-IDF) framework, an extension of PREC-IDF that incorporates total water available for runoff (precipitation minus changes in snow water equivalent), in two contrasting Alaskan watersheds of Department of Defense (DoD) significance: the Little Chena River Basin (LCRB) in interior Alaska, a tributary of the Chena River that flows through Fort Wainwright and near Eielson Air Force Base, and the Upper Ship Creek Basin (USCB), which drains Joint Base Elmendorf-Richardson near Anchorage. Using long-term SNOTEL observations and event-based rainfall-runoff modeling, NG-IDF and PREC-IDF flood estimates were compared against observation-based flood frequency analyses. Results show that NG-IDF consistently reduces flood-estimation bias by 15–20% relative to PREC-IDF, particularly for snowmelt- and ROS-dominated events. In the interior LCRB, permafrost conditions can substantially amplify flood responses during snowmelt events, an effect not explicitly represented in standard design tools. These findings demonstrate that NG-IDF provides a more physically consistent and transferable framework for flood estimation in cold regions, with potential relevance to mission-critical DoD installation resilience. Projected increases in ROS frequency and permafrost degradation across Alaska further emphasize the need to integrate physics-based hydrologic models that explicitly represent snow and permafrost processes to enhance design resilience and operational readiness for military and other critical infrastructure.

Yan, Hongxiang (ORCID:000000022387403X)↗
DOE OSTI2023

A robust estimator of mutual information for deep learning interpretability

Abstract We develop the use of mutual information (MI), a well-established metric in information theory, to interpret the inner workings of deep learning (DL) models. To accurately estimate MI from a finite number of samples, we present GMM-MI (pronounced ‘Jimmie’), an algorithm based on Gaussian mixture models that can be applied to both discrete and continuous settings. GMM-MI is computationally efficient, robust to the choice of hyperparameters and provides the uncertainty on the MI estimate due to the finite sample size. We extensively validate GMM-MI on toy data for which the ground truth MI is known, comparing its performance against established MI estimators. We then demonstrate the use of our MI estimator in the context of representation learning, working with synthetic data and physical datasets describing highly non-linear processes. We train DL models to encode high-dimensional data within a meaningful compressed (latent) representation, and use GMM-MI to quantify both the level of disentanglement between the latent variables, and their association with relevant physical quantities, thus unlocking the interpretability of the latent representation. We make GMM-MI publicly available in this GitHub repository.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Optimal adjustment sets for causal query estimation in partially observed biomolecular networks

Abstract Causal query estimation in biomolecular networks commonly selects a ‘valid adjustment set’, i.e. a subset of network variables that eliminates the bias of the estimator. A same query may have multiple valid adjustment sets, each with a different variance. When networks are partially observed, current methods use graph-based criteria to find an adjustment set that minimizes asymptotic variance. Unfortunately, many models that share the same graph topology, and therefore same functional dependencies, may differ in the processes that generate the observational data. In these cases, the topology-based criteria fail to distinguish the variances of the adjustment sets. This deficiency can lead to sub-optimal adjustment sets, and to miss-characterization of the effect of the intervention. We propose an approach for deriving ‘optimal adjustment sets’ that takes into account the nature of the data, bias and finite-sample variance of the estimator, and cost. It empirically learns the data generating processes from historical experimental data, and characterizes the properties of the estimators by simulation. We demonstrate the utility of the proposed approach in four biomolecular Case studies with different topologies and different data generation processes. The implementation and reproducible Case studies are at https://github.com/srtaheri/OptimalAdjustmentSet.

59 BASIC BIOLOGICAL SCIENCES↗