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DOE OSTI2011

GEOMETRIC AND DYNAMICAL MODELS OF REVERBERATION MAPPING DATA

We present a general method to analyze reverberation (or echo) mapping data that simultaneously provides estimates for the black hole mass and for the geometry and dynamics of the broad-line region (BLR) in active galactic nuclei (AGNs). While previous methods yield a typical scale size of the BLR or a reconstruction of the transfer function, our method directly infers the spatial and velocity distribution of the BLR from the data, from which a transfer function can be easily derived. Previous echo mapping analysis requires an independent estimate of a scaling factor known as the virial coefficient to infer the mass of the black hole, but this is not needed in our more direct approach. We use the formalism of Bayesian probability theory and implement a Markov Chain Monte Carlo algorithm to obtain estimates and uncertainties for the parameters of our BLR models. Fitting of models to the data requires knowledge of the continuum flux at all times, not just the measured times. We use Gaussian Processes to interpolate and extrapolate the continuum light curve data in a fully consistent probabilistic manner, taking the associated errors into account. We illustrate our method using simple models of BLR geometry and dynamics and show that we can recover the parameter values of our test systems with realistic uncertainties that depend upon the variability of the AGN and the quality of the reverberation mapping observing campaign. With a geometry model we can recover the mean radius of the BLR to within {approx}0.1 dex random uncertainty for simulated data with an integrated line flux uncertainty of 1.5%, while with a dynamical model we can recover the black hole mass and the mean radius to within {approx}0.05 dex random uncertainty, for simulated data with a line profile average signal-to-noise ratio of 4 per spectral pixel. These uncertainties do not include modeling errors, which are likely to be present in the analysis of real data, and should therefore be considered as lower limits to the accuracy of the method.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2010

Convexity Conditions and the Legendre-Fenchel Transform for the Product of Finitely Many Positive Definite Quadratic Forms

While the product of finitely many convex functions has been investigated in the field of global optimization, some fundamental issues such as the convexity condition and the Legendre-Fenchel transform for the product function remain unresolved. Focusing on quadratic forms, this paper is aimed at addressing the question: When is the product of finitely many positive definite quadratic forms convex, and what is the Legendre-Fenchel transform for it? First, we show that the convexity of the product is determined intrinsically by the condition number of so-called 'scaled matrices' associated with quadratic forms involved. The main result claims that if the condition number of these scaled matrices are bounded above by an explicit constant (which depends only on the number of quadratic forms involved), then the product function is convex. Second, we prove that the Legendre-Fenchel transform for the product of positive definite quadratic forms can be expressed, and the computation of the transform amounts to finding the solution to a system of equations (or equally, finding a Brouwer's fixed point of a mapping) with a special structure. Thus, a broader question than the open 'Question 11' in Hiriart-Urruty (SIAM Rev. 49, 225-273, 2007) is addressed in this paper.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2010

Nonperturbative QCD Coupling and its $\beta$-function from Light-Front Holography

The light-front holographic mapping of classical gravity in AdS space, modified by a positive-sign dilaton background, leads to a non-perturbative effective coupling $\alpha_s^{AdS}(Q^2)$. It agrees with hadron physics data extracted from different observables, such as the effective charge defined by the Bjorken sum rule, as well as with the predictions of models with built-in confinement and lattice simulations. It also displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale $ \sim 1$ GeV. The resulting $\beta$-function appears to capture the essential characteristics of the full $\beta$-function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD. Commensurate scale relations relate observables to each other without scheme or scale ambiguity. In this paper we extrapolate these relations to the nonperturbative domain, thus extending the range of predictions based on $\alpha_s^{AdS}(Q^2)$.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Peak effect and dynamics of stripe- and pattern-forming systems on a periodic one-dimensional substrate

Here we examine the ordering, pinning, and dynamics of two-dimensional pattern-forming systems interacting with a periodic one-dimensional substrate. In the absence of the substrate, particles with competing long-range repulsion and short-range attraction form anisotropic crystal, stripe, and bubble states. When the system is tuned across the stripe transition in the presence of a substrate, we find that there is a peak effect in the critical depinning force when the stripes align and become commensurate with the substrate. Under an applied drive, the anisotropic crystal and stripe states can exhibit soliton depinning and plastic flow. When the stripes depin plastically, they dynamically reorder into a moving stripe state that is perpendicular to the substrate trough direction. We also find that when the substrate spacing is smaller than the widths of the bubbles or stripes, the system forms pinned stripe states that are perpendicular to the substrate trough direction. The system exhibits multiple reentrant pinning effects as a function of increasing attraction, with the anisotropic crystal and large bubble states experiencing weak pinning but the stripe and smaller bubble states showing stronger pinning. We map out the different dynamic phases as a function of filling, the strength of the attractive interaction term, the substrate strength, and the drive, and demonstrate that the different phases produce identifiable features in the transport curves and particle orderings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Multi-Sensor Optimal Motion Planning for Radiological Contamination Surveys by Using Prediction-Difference Maps

Distributed and networked mobile sensor platforms using unmanned aerial and/or ground vehicles to survey areas of interest offer a safer and more efficient method for radiological contamination mapping; however, most applications rely on uniformly sweeping of the area in a raster-type motion without utilizing the information available in a dynamic sense. We have developed a fully autonomous optimal motion planning procedure for networks with two or more mobile sensors. The procedure utilizes well-established concepts of Gaussian processes in combination with control laws based on centroidal Voronoi tessellations to achieve optimal next-iteration sensor movements. A new method of informing optimal motion planning is proposed, whereby the absolute difference between the prior and current full-map prediction, referred to as the prediction-difference map, is used as the spatial density function within each Voronoi cell, providing immediate and iterative feedback for dynamic use of available information. The Gaussian process regression model used to estimate the contamination in unvisited locations also provides prediction uncertainties, and can be used as a quantitative metric to assess the confidence in the calculated contamination map; these estimates and prediction uncertainties are unavailable for standard uniform survey routines as they can only produce maps in the vicinity of observed locations. We present through simulation the achievable performance gains from using this new method by directly comparing to a uniform survey method. Results show that using the prediction-difference maps to inform motion planning procedures offers a faster rate of producing an accurate and convergent map relative to a uniform survey route.

47 OTHER INSTRUMENTATION↗
DOE OSTI2016

Quantum learning of classical stochastic processes: The completely positive realization problem

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print http://arxiv.org/abs/1303.3771 (2013)].

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

SDSS-IV MaNGA: Modeling the Spectral Line-spread Function to Subpercent Accuracy

The Sloan Digital Sky Survey IV Mapping Nearby Galaxies at APO (MaNGA) program has been operating from 2014 to 2020, and has now observed a sample of 9269 galaxies in the low redshift universe (z ∼ 0.05) with integral-field spectroscopy. With rest-optical (λλ0.36–1.0 μm) spectral resolution R ∼ 2000 the instrumental spectral line-spread function (LSF) typically has 1σ width of about 70 km s{sup −1}, which poses a challenge for the study of the typically 20–30 km s{sup −1} velocity dispersion of the ionized gas in present-day disk galaxies. In this contribution, we present a major revision of the MaNGA data pipeline architecture, focusing particularly on a variety of factors impacting the effective LSF (e.g., under-sampling, spectral rectification, and data cube construction). Through comparison with external assessments of the MaNGA data provided by substantially higher-resolution R ∼ 10,000 instruments, we demonstrate that the revised MPL-10 pipeline measures the instrumental LSF sufficiently accurately (≤0.6% systematic, 2% random around the wavelength of Hα) that it enables reliable measurements of astrophysical velocity dispersions σ {sub Hα} ∼ 20 km s{sup −1} for spaxels with emission lines detected at signal-to-noise ratio > 50. Velocity dispersions derived from [O II], Hβ, [O III], [N II], and [S II] are consistent with those derived from Hα to within about 2% at σ {sub Hα} > 30 km s{sup −1}. Although the impact of these changes to the estimated LSF will be minimal at velocity dispersions greater than about 100 km s{sup −1}, scientific results from previous data releases that are based on dispersions far below the instrumental resolution should be reevaluated.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

CMB-PAInT: An inpainting tool for the cosmic microwave background

Abstract The presence of astrophysical emissions in microwave observations forces us to perform component separation to extract the Cosmic Microwave Background (CMB) signal. However, even in the most optimistic cases, there are still strongly contaminated regions, such as the Galactic plane or those with emission from extragalactic point sources, which require the use of a mask. Since many CMB analyses, especially the ones working in harmonic space, need the whole sky map, it is crucial to develop a reliable inpainting algorithm that replaces the values of the excluded pixels by others statistically compatible with the rest of the sky. This is especially important when working withQandUsky maps in order to obtainE- andB-mode maps which are free fromE-to-Bleakage. In this work we study a method based on Gaussian Constrained Realizations (GCR), that can deal with both intensity and polarization. Several tests have been performed to asses the validation of the method, including the study of the one-dimensional probability distribution function (1-PDF),E- andB-mode map reconstruction, and power spectra estimation. We have considered two scenarios for the input simulation: one case with only CMB signal and a second one including also Planck PR4 semi-realistic noise. Even if we are limited to low resolution maps, N side = 64 ifT,QandUare considered, we believe that this is a useful approach to be applied to future missions such as LiteBIRD, where the target are the largest scales.

Astronomy & Astrophysics↗
DOE OSTI2011

The continuity of the output entropy of positive maps

Global and local continuity conditions for the output von Neumann entropy for positive maps between Banach spaces of trace-class operators in separable Hilbert spaces are obtained. Special attention is paid to completely positive maps: infinite dimensional quantum channels and operations. It is shown that as a result of some specific properties of the von Neumann entropy (as a function on the set of density operators) several results on the output entropy of positive maps can be obtained, which cannot be derived from the general properties of entropy type functions. In particular, it is proved that global continuity of the output entropy of a positive map follows from its finiteness. A characterization of positive linear maps preserving continuity of the entropy (in the following sense: continuity of the entropy on an arbitrary subset of input operators implies continuity of the output entropy on this subset) is obtained. A connection between the local continuity properties of two completely positive complementary maps is considered. Bibliography: 21 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Reconstructing the Wave Function of Magnetic Topological Insulators MnBi 2 ⁢Te 4 and MnBi 4 ⁢Te 7 Using Spin-Resolved Photoemission

Despite their importance for exotic quantum effects, the surface electronic structure of magnetic topological insulators MnBi 2 ⁢Te 4 and MnBi 4 ⁢Te 7 remains poorly understood. Using high-efficiency spin- and angle-resolved photoemission spectroscopy, we directly image the spin-polarization and orbital character of the surface states in both compounds and map our observations onto a model wave function to describe the complex spin-orbital texture, which solidifies our understanding of the surface band structure by establishing the single-band nature of the most prominent states. Most importantly, our analysis reveals a new mechanism for reducing the magnetic gap of the topological surface states based on the orbital composition of the wave function.

Han, Xue [SLAC National Accelerator Laboratory (SL↗
DOE OSTI2015

Linear functional minimization for inverse modeling

In this paper, we present a novel inverse modeling strategy to estimate spatially distributed parameters of nonlinear models. The maximum a posteriori (MAP) estimators of these parameters are based on a likelihood functional, which contains spatially discrete measurements of the system parameters and spatiotemporally discrete measurements of the transient system states. The piecewise continuity prior for the parameters is expressed via Total Variation (TV) regularization. The MAP estimator is computed by minimizing a nonquadratic objective equipped with the TV operator. We apply this inversion algorithm to estimate hydraulic conductivity of a synthetic confined aquifer from measurements of conductivity and hydraulic head. The synthetic conductivity field is composed of a low-conductivity heterogeneous intrusion into a high-conductivity heterogeneous medium. Our algorithm accurately reconstructs the location, orientation, and extent of the intrusion from the steady-state data only. Finally, addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Complexions at the iron-magnetite interface

Synthesizing distinct phases and controlling crystalline defects are key concepts in materials design. These approaches are often decoupled, with the former grounded in equilibrium thermodynamics and the latter in nonequilibrium kinetics. By unifying them through defect phase diagrams, we can apply phase equilibrium models to thermodynamically evaluate defects—including dislocations, grain boundaries, and phase boundaries—establishing a theoretical framework linking material imperfections to properties. Using scanning transmission electron microscopy (STEM) with differential phase contrast (DPC) imaging, we achieve the simultaneous imaging of heavy Fe and light O atoms, precisely mapping the atomic structure and chemical composition at the iron-magnetite (Fe/Fe 3 O 4 ) interface. We identify a well-ordered two-layer interface-stabilized phase state (referred to as complexion) at the Fe[001]/Fe 3 O 4 [001] interface. Using density-functional theory (DFT), we explain the observed complexion and map out various interface-stabilized phases as a function of the O chemical potential. The formation of complexions increases interface adhesion by 20% and alters charge transfer between adjacent materials, impacting transport properties. Our findings highlight the potential of tunable defect-stabilized phase states as a degree of freedom in materials design, enabling optimized corrosion protection, catalysis, and redox-driven phase transitions, with applications in materials sustainability, efficient energy conversion, and green steel production.

36 MATERIALS SCIENCE↗
DOE OSTI2013

PRIMORDIAL GRAVITATIONAL WAVE DETECTABILITY WITH DEEP SMALL-SKY COSMIC MICROWAVE BACKGROUND EXPERIMENTS

We use the Bayesian estimation on direct T - Q - U cosmic microwave background (CMB) polarization maps to forecast errors on the tensor-to-scalar power ratio r, and hence on primordial gravitational waves, as a function of sky coverage f{sub sky}. This map-based likelihood filters the information in the pixel-pixel space into the optimal combinations needed for r detection for cut skies, providing enhanced information over a first-step linear separation into a combination of E, B, and mixed modes, and ignoring the latter. With current computational power and for typical resolutions appropriate for r detection, the large matrix inversions required are accurate and fast. Our simulations explore two classes of experiments, with differing bolometric detector numbers, sensitivities, and observational strategies. One is motivated by a long duration balloon experiment like Spider, with pixel noise {proportional_to}{radical}(f{sub sky}) for a specified observing period. This analysis also applies to ground-based array experiments. We find that, in the absence of systematic effects and foregrounds, an experiment with Spider-like noise concentrating on f{sub sky} {approx} 0.02-0.2 could place a 2{sigma}{sub r} Almost-Equal-To 0.014 boundary ({approx}95% confidence level), which rises to 0.02 with an l-dependent foreground residual left over from an assumed efficient component separation. We contrast this with a Planck-like fixed instrumental noise as f{sub sky} varies, which gives a Galaxy-masked (f{sub sky} = 0.75) 2{sigma}{sub r} Almost-Equal-To 0.015, rising to Almost-Equal-To 0.05 with the foreground residuals. Using as the figure of merit the (marginalized) one-dimensional Shannon entropy of r, taken relative to the first 2003 WMAP CMB-only constraint, gives -2.7 bits from the 2012 WMAP9+ACT+SPT+LSS data, and forecasts of -6 bits from Spider (+ Planck); this compares with up to -11 bits for CMBPol, COrE, and PIXIE post-Planck satellites and -13 bits for a perfectly noiseless cosmic variance limited experiment. We thus confirm the wisdom of the current strategy for r detection of deeply probed patches covering the f{sub sky} minimum-error trough with balloon and ground experiments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Kelvin probe force microscopy for high-resolution imaging of hydrogen in steel alloys [Poster]

Kelvin probe force microscopy (KPFM) was used to image and co-locate the presence of hydrogen in stainless steel (SS) with microstructure. Various SS samples were investigated, including forged, welded, LENS® fabricated, and pinch welded materials. KPFM images the local work function of a surface as a function of spatial position using atomic force microscopy. KPFM is capable of delivering high spatial (~10 nm) and potential (~5mV) resolution maps characterizing the microstrucure and the locally varying work function of surfaces. Hydrogen segregated at the surface of SS increases the local work function by either reducing tensile strain or by reducing the chemical potential of surface species. In a process known as hydrogen embrittlement, hydrogen segregates to and becomes trapped at extended defects (e.g. dislocations, boundaries, pores) which leads to the initiation of cracking and can result in structural failure. Hydrogen storage necessitates a proper understanding of the mechanisms of hydrogen embrittlement in SS. Developing advanced characterization techniques for hydrogen embrittlement is critical to identify long term solutions for materials exposed to hydrogen. Current techniques of observing hydrogen embrittlement involve mechanical testing, and optical microscopy with low resolution. Advance microstructural imaging techniques capable of resolving features down to the nanometer scale are needed. KPFM provides high resolution imaging for the characterization and development of SS components for hydrogen storage.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Latent map Gaussian processes for mixed variable metamodeling

Gaussian processes (GPs) are ubiquitously used in sciences and engineering as metamodels. Standard GPs, however, can only handle numerical or quantitative variables. Here we introduce latent map Gaussian processes (LMGPs) that inherit the attractive properties of GPs and are also applicable to mixed data which have both quantitative and qualitative inputs. The core idea behind LMGPs is to learn a continuous, low-dimensional latent space or manifold which encodes all qualitative inputs. To learn this manifold, we first assign a unique prior vector representation to each combination of qualitative inputs. We then use a low-rank linear map to project these priors on a manifold that characterizes the posterior representations. As the posteriors are quantitative, they can be directly used in any standard correlation function such as the Gaussian or Matern. Hence, the optimal map and the corresponding manifold, along with other hyperparameters of the correlation function, can be systematically learned via maximum likelihood estimation. Through a wide range of analytic and real-world examples, we demonstrate the advantages of LMGPs over state-of-the-art methods in terms of accuracy and versatility. In particular, we show that LMGPs can handle variable-length inputs, have an explainable neural network interpretation, and provide insights into how qualitative inputs affect the response or interact with each other. We also employ LMGPs in Bayesian optimization and illustrate that they can discover optimal compound compositions more efficiently than conventional methods that convert compositions to qualitative variables via manual featurization.

42 ENGINEERING↗
DOE OSTI2012

CONNECTING THE DOTS: ANALYZING SYNTHETIC OBSERVATIONS OF STAR-FORMING CLUMPS IN MOLECULAR CLOUDS

In this paper, we investigate the extent to which observations of molecular clouds can correctly identify and measure star-forming clumps. We produced a synthetic column density map and a synthetic spectral-line data cube from the simulated collapse of a 5000 M{sub Sun} molecular cloud. By correlating the clumps found in the simulation to those found in the synthetic observations, clump masses derived from spectral-line data cubes were found to be quite close to the true physical properties of the clumps. We also find that the 'observed' clump mass function (CMF) derived from the column density map is shifted by a factor of {approx}3 higher than the true CMF, due to projection of low-density material along the line of sight. Alves et al. first proposed that a shift of a CMF to higher masses by a factor of three can be attributed to a star formation efficiency of 30%. Our results indicate that this finding may instead be due to an overestimate of clump masses determined from column density observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

SU-E-J-89: Motion Effects On Organ Dose in Respiratory Gated Stereotactic Body Radiation Therapy

Purpose: Existing reports on gated radiation therapy focus mainly on optimizing dose delivery to the target structure. This work investigates the motion effects on radiation dose delivered to organs at risk (OAR) in respiratory gated stereotactic body radiation therapy (SBRT). A new algorithmic tool of dose analysis is developed to evaluate the optimality of gating phase for dose sparing on OARs while ensuring adequate target coverage. Methods: Eight patients with pancreatic cancer were treated on a phase I prospective study employing 4DCT-based SBRT. For each patient, 4DCT scans are acquired and sorted into 10 respiratory phases (inhale-exhale- inhale). Treatment planning is performed on the average CT image. The average CT is spatially registered to other phases. The resultant displacement field is then applied on the plan dose map to estimate the actual dose map for each phase. Dose values of each voxel are fitted to a sinusoidal function. Fitting parameters of dose variation, mean delivered dose and optimal gating phase for each voxel over respiration cycle are mapped on the dose volume. Results: The sinusoidal function accurately models the dose change during respiratory motion (mean fitting error 4.6%). In the eight patients, mean dose variation is 3.3 Gy on OARs with maximum of 13.7 Gy. Two patients have about 100cm{sup 3} volumes covered by more than 5 Gy deviation. The mean delivered dose maps are similar to plan dose with slight deformation. The optimal gating phase highly varies across the patient, with phase 5 or 6 on about 60% of the volume, and phase 0 on most of the rest. Conclusion: A new algorithmic tool is developed to conveniently quantify dose deviation on OARs from plan dose during the respiratory cycle. The proposed software facilitates the treatment planning process by providing the optimal respiratory gating phase for dose sparing on each OAR.

60 APPLIED LIFE SCIENCES↗