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A cumulant functional for static and dynamic correlation

A functional for the cumulant energy is introduced. The functional is composed of a pair-correction and static and dynamic correlation energy components. The pair-correction and static correlation energies are functionals of the natural orbitals and the occupancy transferred between near-degenerate orbital pairs, rather than the orbital occupancies themselves. The dynamic correlation energy is a functional of the statically correlated on-top two-electron density. The on-top density functional used in this study is the well-known Colle-Salvetti functional. Using the cc-pVTZ basis set, the functional effectively models the bond dissociation of H{sub 2}, LiH, and N{sub 2} with equilibrium bond lengths and dissociation energies comparable to those provided by multireference second-order perturbation theory. The performance of the cumulant functional is less impressive for HF and F{sub 2}, mainly due to an underestimation of the dynamic correlation energy by the Colle-Salvetti functional.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Magnetic dipole γ-ray strength functions in the crossover from spherical to deformed neodymium isotopes

We calculate the magnetic dipole $\gamma$-ray strength functions in a chain of even-mass neodymium isotopes $^{144-152}$Nd in the framework of the configuration-interaction (CI) shell model. We infer the strength function by applying the maximum entropy method (MEM) to the exact imaginary-time response function calculated with the shell-model Monte Carlo (SMMC) method. The success of the MEM depends on the choice of a good strength function as a prior distribution. We investigate two choices for the prior strength function: the static path approximation (SPA) and the quasiparticle random-phase approximation (QRPA). We find that the QRPA is a better approximation at low temperatures (i.e., near the ground state), while the SPA is a better choice at finite temperatures. We identify a low-energy enhancement (LEE) in the MEM deexcitation $M1$ strength functions of the even-mass neodymium isotopes and compare with recent experimental results for the total deexcitation $\gamma$-ray strength functions. The LEE is already seen in the SPA strength function but not in the QRPA strength function, indicating the importance of large-amplitude static fluctuations around the mean field in reproducing the LEE. Our method is currently the only one which can reproduce LEE in heavy open-shell nuclei where conventional CI shell model calculations are prohibited. With the onset of deformation as number of neutrons increases along the chain of neodymium isotopes, we observe that some of the LEE strength transfers to a low-energy excitation, which we interpret as a finite-temperature ``scissors'' mode. Here, we also observe a finite-temperature spin-flip mode.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Physically interpretable approximations of many-body spectral functions

The rational function approximation provides a natural and interpretable representation of response functions such as the many-body spectral functions. We apply the vector fitting (VFIT) algorithm to fit a variety of spectral functions calculated from the Holstein model of electron-phonon interactions. We show that the resulting rational functions are highly efficient in their fitting of sharp features in the spectral functions, and could provide a means to infer physically relevant information from a spectral data set. The position of the peaks in the approximated spectral function are determined by the location of poles in the complex plane. Additionally, we developed a variant of VFIT that incorporates regularization to improve the quality of fits. With this procedure, we demonstrate it is possible to achieve accurate spectral function fits that vary smoothly as a function of physical conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Landmark-Warped Emulators for Models with Misaligned Functional Response

Many computer models output functional data, and in some cases, these functional data have similar, but misaligned, shape characteristics. In this paper, we introduce a general approach for building emulators for computer models that output misaligned functional data when key values in the functional response (landmarks) can be easily identified. This approach has two main parts: modeling the aligned (using the landmarks) functional data, and modeling the functions that map the misaligned data to the aligned space (warping functions). As the warping functions are required to be monotonic, we give special attention to modeling monotonic functional response data. We discuss how our approach can be easily applied for a variety of typical emulators, such as Gaussian processes, Bayesian multivariate adaptive regression splines, and Bayesian additive regression trees, and how sensitivity analysis can be performed. We demonstrate our approach by building emulators for two applications: (1) a high-energy-density physics computer model used to simulate inertial confinement fusion ignition experiments, where model outputs are highly misaligned, and (2) a multiphysics continuum hydrocode used to simulate high-velocity impact experiments, where model outputs are only slightly misaligned. In case (1) traditional methods cannot be applied, while in (2) they can be applied, but the proposed method performs significantly better.

97 MATHEMATICS AND COMPUTING↗

Elastic functional principal component regression

We study regression using functional predictors in situations where these functions contains both phase and amplitude variability. In other words, the functions are misaligned due to errors in time measurements, and these errors can significantly degrade both model estimation and prediction performance. The current techniques either ignore the phase variability, or handle it via preprocessing, that is, use an off–the–shelf technique for functional alignment and phase removal. We develop a functional principal component regression model which has a comprehensive approach in handling phase and amplitude variability. The model utilizes a mathematical representation of the data known as the square–root slope function. These functions preserve the L 2 norm under warping and are ideally suited for simultaneous estimation of regression and warping parameters. Furthermore, using both simulated and real–world data sets, we demonstrate our approach and evaluate its prediction performance relative to current models. In addition, we propose an extension to functional logistic and multinomial logistic regression.

97 MATHEMATICS AND COMPUTING↗

Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions

We prove that, within the class of pair potential Hamiltonians, the excess entropy is a universal, temperature-independent functional of the density and pair correlation function. This result extends Henderson’s theorem, which states that the free energy is a temperature dependent functional of the density and pair correlation. The stationarity and concavity of the excess entropy functional are discussed and related to the Gibbs–Bugoliubov inequality and to the free energy. We apply the Kirkwood approximation, which is commonly used for fluids, to both fluids and solids. Approximate excess entropy functionals are developed and compared to results from thermodynamic integration. The pair functional approach gives the absolute entropy and free energy based on simulation output at a single temperature without thermodynamic integration. We argue that a functional of the type, which is strictly applicable to pair potentials, is also suitable for first principles calculation of free energies from Born–Oppenheimer molecular dynamics performed at a single temperature. In conclusion, this advancement has the potential to reduce the evaluation the free energy to a simple modification to any procedure that evaluates the energy and the pair correlation function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Clinical Validation of 4-Dimensional Computed Tomography Ventilation With Pulmonary Function Test Data

Purpose: A new form of functional imaging has been proposed in the form of 4-dimensional computed tomography (4DCT) ventilation. Because 4DCTs are acquired as part of routine care for lung cancer patients, calculating ventilation maps from 4DCTs provides spatial lung function information without added dosimetric or monetary cost to the patient. Before 4DCT-ventilation is implemented it needs to be clinically validated. Pulmonary function tests (PFTs) provide a clinically established way of evaluating lung function. The purpose of our work was to perform a clinical validation by comparing 4DCT-ventilation metrics with PFT data. Methods and Materials: Ninety-eight lung cancer patients with pretreatment 4DCT and PFT data were included in the study. Pulmonary function test metrics used to diagnose obstructive lung disease were recorded: forced expiratory volume in 1 second (FEV1) and FEV1/forced vital capacity. Four-dimensional CT data sets and spatial registration were used to compute 4DCT-ventilation images using a density change–based and a Jacobian-based model. The ventilation maps were reduced to single metrics intended to reflect the degree of ventilation obstruction. Specifically, we computed the coefficient of variation (SD/mean), ventilation V20 (volume of lung ≤20% ventilation), and correlated the ventilation metrics with PFT data. Regression analysis was used to determine whether 4DCT ventilation data could predict for normal versus abnormal lung function using PFT thresholds. Results: Correlation coefficients comparing 4DCT-ventilation with PFT data ranged from 0.63 to 0.72, with the best agreement between FEV1 and coefficient of variation. Four-dimensional CT ventilation metrics were able to significantly delineate between clinically normal versus abnormal PFT results. Conclusions: Validation of 4DCT ventilation with clinically relevant metrics is essential. We demonstrate good global agreement between PFTs and 4DCT-ventilation, indicating that 4DCT-ventilation provides a reliable assessment of lung function. Four-dimensional CT ventilation enables exciting opportunities to assess lung function and create functional avoidance radiation therapy plans. The present work provides supporting evidence for the integration of 4DCT-ventilation into clinical trials.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Functional image-guided stereotactic body radiation therapy planning for patients with hepatocellular carcinoma

The aim of the current planning study is to evaluate the ability of gadoxetate disodium-enhanced magnetic resonance imaging (EOB-MRI)–guided stereotactic body radiation therapy (SBRT) planning by using intensity-modulated radiation therapy (IMRT) techniques in sparing the functional liver tissues during SBRT for hepatocellular carcinoma. In this study, 20 patients with hepatocellular carcinoma were enrolled. Functional liver tissues were defined according to quantitative liver-spleen contrast ratios ≥ 1.5 on a hepatobiliary phase scan. Functional images were fused with the planning computed tomography (CT) images; the following 2 SBRT plans were designed using a “step-and-shoot” static IMRT technique for each patient: (1) an anatomical SBRT plan optimization based on the total liver; and (2) a functional SBRT plan based on the functional liver. The total prescribed dose was 48 gray (Gy) in 4 fractions. Dosimetric parameters, including dose to 95% of the planning target volume (PTV D{sub 95%}), percentages of total and functional liver volumes, which received doses from 5 to 30 Gy (V5 to V30 and fV5 to fV30), and mean doses to total and functional liver (MLD and fMLD, respectively) of the 2 plans were compared. Compared with anatomical plans, functional image-guided SBRT plans reduced MLD (mean: plan A, 5.5 Gy; and plan F, 5.1 Gy; p < 0.0001) and fMLD (mean: plan A, 5.4 Gy; and plan F, 4.9 Gy; p < 0.0001), as well as V5 to V30 and fV5 to fV30. No differences were noted in PTV coverage and nonhepatic organs at risk (OARs) doses. In conclusion, EOB-MRI–guided SBRT planning using the IMRT technique may preserve functional liver tissues in patients with hepatocellular carcinoma (HCC).

61 RADIATION PROTECTION AND DOSIMETRY↗

Comparative Density Functional Theory Study of Magnetic Exchange Couplings in Dinuclear Transition-Metal Complexes

Multicenter transition-metal complexes (MCTMs) with magnetically interacting ions have been proposed as components for information-processing devices and storage units. For any practical application of MCTMs as magnetic units, it is crucial to characterize their magnetic behavior, and in particular, the isotropic magnetic exchange coupling, J, between its magnetic centers. Due to the large size of typical MCTMs, density functional theory is the only practical electronic structure method for evaluating the J coupling. Here, we assess the accuracy of different density functional approximations for predicting the magnetic couplings of eight dinuclear transition-metal complexes, including five dimanganese, two dicopper, and one divanadium with known reliable experimental J couplings spanning from ferromagnetic to strong antiferromagnetic. The density functionals considered include global hybrid functionals which mix semilocal density functional approximations and exact exchange with a fixed admixing parameter, six local hybrid functionals where the admixing parameters are extended to be spatially dependent, the SCAN and r 2 SCAN meta-generalized gradient approximations (GGAs), and two widely used GGAs. We found that global hybrids tested in this work have a tendency to over-correct the error in magnetic coupling parameters from the Perdew–Burke–Ernzerhof (PBE) GGA as seen for manganese complexes. The performance of local hybrid density functionals shows no improvement in terms of bias and is scattered without a clear trend, suggesting that more efforts are needed for the extension from global to local hybrid density functionals for this particular property. The SCAN and r 2 SCAN meta-GGAs are found to perform as well as benchmark global hybrids on most tested complexes. We further analyze the charge density redistribution of meta-GGAs as well as global and local hybrid density functionals with respect to that of PBE, in connection to the self-interaction error or delocalization error.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Perspectives on van der Waals Density Functionals: The Case of TiS 2

The van der Waals interaction is of foundational importance for a wide variety of physical systems. In particular, van der Waals forces lie at the heart of potential device technologies that may be realized from the functional organization of layered two-dimensional (2D) nanomaterials. Furthermore, for intermediate to large-scale applications modeling, van der Waals density functionals have become the de facto choice for first-principles calculations. In particular, the vdW-DF family of functionals have provided a systematic approach to this theoretically challenging problem. While much progress has been made, there remains room for improvement in the microscopic description of vdW forces from these density functionals. In this work, we compute benchmark results for the binding energy and the electronic density response to binding in TiS2 via accurate diffusion quantum Monte Carlo calculations. We compare these benchmark data to results obtained from local, semilocal, and van der Waals functionals. In particular, we gauge the quality of the original vdW-DF/vdW-DF2 functionals, as well as updated variants such as vdW-DF-C09, vdW-DF-optB88, vdW-DF-optB86b, and vdW-DF2-B86R. We find a close relationship between the accuracy of predicted interlayer separation distances and binding energies for TiS 2 , with the vdW-DF-optB88 functional performing very well in terms of both quantities. In general, the more recently developed functionals are systematic improvements over older ones. However, when considering the response of the electron density to binding, we find that local-density approximation (LDA) and PBEsol generally outperform the vdW-DF functionals in describing the interlayer charge accumulation with vdW-DF-C09 variants performing the best overall.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Predicting taxonomic and functional structure of microbial communities in acid mine drainage

Predicting the dynamics of community composition and functional attributes responding to environmental changes is an essential goal in community ecology but remains a major challenge, particularly in microbial ecology. Here, by targeting a model system with low species richness, we explore the spatial distribution of taxonomic and functional structure of 40 acid mine drainage (AMD) microbial communities across Southeast China profiled by 16S ribosomal RNA pyrosequencing and a comprehensive microarray (GeoChip). Similar environmentally dependent patterns of dominant microbial lineages and key functional genes were observed regardless of the large-scale geographical isolation. Functional and phylogenetic β-diversities were significantly correlated, whereas functional metabolic potentials were strongly influenced by environmental conditions and community taxonomic structure. Using advanced modeling approaches based on artificial neural networks, we successfully predicted the taxonomic and functional dynamics with significantly higher prediction accuracies of metabolic potentials (average Bray-Curtis similarity 87.8) as compared with relative microbial abundances (similarity 66.8), implying that natural AMD microbial assemblages may be better predicted at the functional genes level rather than at taxonomic level. Furthermore, relative metabolic potentials of genes involved in many key ecological functions (for example, nitrogen and phosphate utilization, metals resistance and stress response) were extrapolated to increase under more acidic and metal-rich conditions, indicating a critical strategy of stress adaptation in these extraordinary communities. Collectively, our findings indicate that natural selection rather than geographic distance has a more crucial role in shaping the taxonomic and functional patterns of AMD microbial community that readily predicted by modeling methods and suggest that the model-based approach is essential to better understand natural acidophilic microbial communities.

59 BASIC BIOLOGICAL SCIENCES↗

The evolution of the galaxy rest-frame ultraviolet luminosity function over the first two billion years

We present a robust measurement and analysis of the rest-frame ultraviolet (UV) luminosity functions at z = 4–8. We use deep Hubble Space Telescope imaging over the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey/GOODS fields, the Hubble Ultra Deep Field, and the Hubble Frontier Field deep parallel observations near the Abell 2744 and MACS J0416.1-2403 clusters. The combination of these surveys provides an effective volume of 0.6–1.2 × 10{sup 6} Mpc{sup 3} over this epoch, allowing us to perform a robust search for faint (M{sub UV}=−18) and bright (M{sub UV}<−21) high-redshift galaxies. We select candidate galaxies using a well-tested photometric redshift technique with careful screening of contaminants, finding a sample of 7446 candidate galaxies at 3.5 < z < 8.5, with >1000 galaxies at z ≈ 6–8. We measure both a stepwise luminosity function for candidate galaxies in our redshift samples, and a Schechter function, using a Markov Chain Monte Carlo analysis to measure robust uncertainties. At the faint end, our UV luminosity functions agree with previous studies, yet we find a higher abundance of UV-bright candidate galaxies at z ⩾ 6. Our best-fit value of the characteristic magnitude M{sub UV}{sup ∗} is consistent with −21 at z ⩾ 5, which is different than that inferred based on previous trends at lower redshift, and brighter at ∼2σ significance than previous measures at z = 6 and 7. At z = 8, a single power law provides an equally good fit to the UV luminosity function, while at z = 6 and 7 an exponential cutoff at the bright end is moderately preferred. We compare our luminosity functions to semi-analytical models, and find that the lack of evolution in M{sub UV}{sup ∗} is consistent with models where the impact of dust attenuation on the bright end of the luminosity function decreases at higher redshift, although a decreasing impact of feedback may also be possible. We measure the evolution of the cosmic star-formation rate (SFR) density by integrating our observed luminosity functions to M{sub UV}=−17, correcting for dust attenuation, and find that the SFR density declines proportionally to (1 +z){sup −4.3±0.5} at z > 4, which is consistent with observations at z ⩾ 9. Our observed luminosity functions are consistent with a reionization history that starts at z ≳ 10, completes at z > 6, and reaches a midpoint (x{sub H II} = 0.5) at 6.7 < z < 9.4. Finally, using a constant cumulative number density selection and an empirically derived rising star-formation history, our observations predict that the abundance of bright z = 9 galaxies is likely higher than previous constraints, although consistent with recent estimates of bright z ∼ 10 galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

NEW INSIGHTS ON THE GALACTIC BULGE INITIAL MASS FUNCTION

We have derived the Galactic bulge initial mass function (IMF) of the Sagittarius Window Eclipsing Extrasolar Planet Search field in the mass range 0.15 < M/M{sub ⊙} 1.0, using deep photometry collected with the Advanced Camera for Surveys on the Hubble Space Telescope. Observations at several epochs, spread over 9 years, allowed us to separate the disk and bulge stars down to very faint magnitudes, F814W ≈ 26 mag, with a proper-motion accuracy better than 0.5 mas yr{sup −1} (20 km s{sup −1}). This allowed us to determine the IMF of the pure bulge component uncontaminated by disk stars for this low-reddening field in the Sagittarius window. In deriving the mass function, we took into account the presence of unresolved binaries, errors in photometry, distance modulus and reddening, as well as the metallicity dispersion and the uncertainties caused by adopting different theoretical color–temperature relations. We found that the Galactic bulge IMF can be fitted with two power laws with a break at M∼ 0.56 M{sub ⊙}, the slope being steeper (α=−2.41±0.50) for the higher masses, and shallower (α=−1.25±0.20) for the lower masses. In the high-mass range, our derived mass function agrees well with the mass function derived for other regions of the bulge. In the low-mass range however, our mass function is slightly shallower, which suggests that separating the disk and bulge components is particularly important in the low-mass range. The slope of the bulge mass function is also similar to the slope of the mass function derived for the disk in the high-mass regime, but the bulge mass function is slightly steeper in the low-mass regime. We used our new mass function to derive stellar mass-to-light values for the Galactic bulge and we obtained 2.1 < M/L{sub F814W} < 2.4 and 3.1 < M/L{sub F606W} < 3.6 according to different assumptions on the slope of the IMF for masses larger than 1M{sub ⊙}.

79 ASTRONOMY AND ASTROPHYSICS↗

Proton structure functions at small x

Proton structure functions are measured in electron-proton collision through inelastic scattering of virtual photons with virtuality Q on protons; x denotes the momentum fraction carried by the struck parton. Proton structure functions are currently described with excellent accuracy in terms of scale dependent parton distribution functions, defined in terms of collinear factorization and DGLAP evolution in Q. With decreasing x however, parton densities increase and are ultimately expected to saturate. In this regime DGLAP evolution will finally break down and non-linear evolution equations w.r.t x are expected to take over. In the first part of the talk we present recent result on an implementation of physical DGLAP evolution. Unlike the conventional description in terms of parton distribution functions, the former describes directly the Q dependence of the measured structure functions. It is therefore physical insensitive to factorization scheme and scale ambiguities. It therefore provides a more stringent test of DGLAP evolution and eases the manifestation of (non-linear) small x effects. It however requires a precise measurement of both structure functions F 2 and F L , which will be only possible at future facilities, such as an Electron Ion Collider. In the second part we present a recent analysis of the small x region of the combined HERA data on the structure function F 2 . We demonstrate that (linear) next-to-leading order BFKL evolution describes the effective Pomeron intercept, determined from the combined HERA data, once a resummation of collinear enhanced terms is included and the renormalization scale is fixed using the BLM optimal scale setting procedure. We also provide a detailed description of the Q and x dependence of the full structure functions F 2 in the small x region, as measured at HERA. As a result, predictions for the structure function F L are found to be in agreement with the existing HERA data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Minimally entangled state preparation of localized wave functions on quantum computers

Initializing a single site of a lattice scalar field theory into an arbitrary state with support throughout the quantum register requires $O(2^{nQ})$ entangling gates on a quantum computer with $n_Q$ qubits per site. It is conceivable that instead initializing to functions that are good approximations to states may have utility in reducing the number of required entangling gates. In the case of a single site of a noninteracting scalar field theory, initializing to a symmetric exponential wave function requires $n_Q – 1$ entangling gates, the minimal number necessary to create an entangled state of all $n_Q$ qubits. This is compared with the $2^{nQ – 1} + n_Q – 3 + δ_{nQ, 1}$ required for a symmetric Gaussian wave function. In this work, we explore the initialization of one-site $(n_Q = 4)$, two-site $(n_Q = 3)$, and three-site ( n Q = 3 ) noninteracting scalar field theories with symmetric exponential wave functions using IBM's quantum simulators and quantum devices (Poughkeepsie and Tokyo). With the digitizations attainable with $n_Q = 3,4$, these tensor-product wave functions are found to have large overlap with a Gaussian wave function and provide a suitable low-noise initialization for improvement and Somma inflation. Further, in performing these simulations, we have employed a workflow that interleaves calibrations to mitigate systematic errors in production. The calibrations allow tolerance cuts on gate performance including the fidelity of the symmetrizing Hadamard gate, both in vacuum $(|\textbf{0}\gg^{\bigotimes nQ})$ and in medium ($n_Q –1$ qubits initialized to an exponential function). The results obtained in this work are relevant to systems beyond scalar field theories, such as the deuteron radial wave function, two- and three-dimensional Cartesian-space wave functions, and nonrelativistic multinucleon systems built on a localized eigenbasis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Scaling within the spectral function approach

Scaling features of the nuclear electromagnetic response functions unveil aspects of nuclear dynamics that are crucial for interpreting neutrino-and electron-scattering data. In the large momentum-transfer regime, the nucleon-density response function defines a universal scaling function, which is independent of the nature of the probe. In this work, we analyze the nucleon-density response function of 12 C, neglecting collective excitations. We employ particle and hole spectral functions obtained within two distinct many-body methods, both widely used to describe electroweak reactions in nuclei. We show that the two approaches provide compatible nucleon-density scaling functions that for large momentum transfers satisfy first-kind scaling. Both methods yield scaling functions characterized by an asymmetric shape, although less pronounced than that of experimental scaling functions. Finally, this asymmetry, only mildly affected by final state interactions, is mostly due to nucleon-nucleon correlations, encoded in the continuum component of the hole spectral function.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Should regional ventilation function be considered during radiation treatment planning to prevent radiation-induced complications?

Purpose: To investigate the incorporation of pretherapy regional ventilation function in predicting radiation fibrosis (RF) in stage III nonsmall cell lung cancer (NSCLC) patients treated with concurrent thoracic chemoradiotherapy. Methods: Thirty-seven patients with stage III NSCLC were retrospectively studied. Patients received one cycle of cisplatin–gemcitabine, followed by two to three cycles of cisplatin–etoposide concurrently with involved-field thoracic radiotherapy (46–66 Gy; 2 Gy/fraction). Pretherapy regional ventilation images of the lung were derived from 4D computed tomography via a density change–based algorithm with mass correction. In addition to the conventional dose–volume metrics (V{sub 20}, V{sub 30}, V{sub 40}, and mean lung dose), dose–function metrics (fV{sub 20}, fV{sub 30}, fV{sub 40}, and functional mean lung dose) were generated by combining regional ventilation and radiation dose. A new class of metrics was derived and referred to as dose–subvolume metrics (sV{sub 20}, sV{sub 30}, sV{sub 40}, and subvolume mean lung dose); these were defined as the conventional dose–volume metrics computed on the functional lung. Area under the receiver operating characteristic curve (AUC) values and logistic regression analyses were used to evaluate these metrics in predicting hallmark characteristics of RF (lung consolidation, volume loss, and airway dilation). Results: AUC values for the dose–volume metrics in predicting lung consolidation, volume loss, and airway dilation were 0.65–0.69, 0.57–0.70, and 0.69–0.76, respectively. The respective ranges for dose–function metrics were 0.63–0.66, 0.61–0.71, and 0.72–0.80 and for dose–subvolume metrics were 0.50–0.65, 0.65–0.75, and 0.73–0.85. Using an AUC value = 0.70 as cutoff value suggested that at least one of each type of metrics (dose–volume, dose–function, dose–subvolume) was predictive for volume loss and airway dilation, whereas lung consolidation cannot be accurately predicted by any of the metrics. Logistic regression analyses showed that dose–function and dose–subvolume metrics were significant (P values ≤ 0.02) in predicting volume airway dilation. Likelihood ratio test showed that when combining dose–function and/or dose–subvolume metrics with dose–volume metrics, the achieved improvements of prediction accuracy on volume loss and airway dilation were significant (P values ≤ 0.04). Conclusions: The authors’ results demonstrated that the inclusion of regional ventilation function improved accuracy in predicting RF. In particular, dose–subvolume metrics provided a promising method for preventing radiation-induced pulmonary complications.

60 APPLIED LIFE SCIENCES↗

THE LOCAL [C ii] 158 μ m EMISSION LINE LUMINOSITY FUNCTION

We present, for the first time, the local [C ii] 158 μ m emission line luminosity function measured using a sample of more than 500 galaxies from the Revised Bright Galaxy Sample. [C ii] luminosities are measured from the Herschel PACS observations of the Luminous Infrared Galaxies (LIRGs) in the Great Observatories All-sky LIRG Survey and estimated for the rest of the sample based on the far-infrared (far-IR) luminosity and color. The sample covers 91.3% of the sky and is complete at S{sub 60μm} > 5.24 Jy. We calculate the completeness as a function of [C ii] line luminosity and distance, based on the far-IR color and flux densities. The [C ii] luminosity function is constrained in the range ∼10{sup 7–9} L{sub ⊙} from both the 1/ V{sub max} and a maximum likelihood methods. The shape of our derived [C ii] emission line luminosity function agrees well with the IR luminosity function. For the CO(1-0) and [C ii] luminosity functions to agree, we propose a varying ratio of [C ii]/CO(1-0) as a function of CO luminosity, with larger ratios for fainter CO luminosities. Limited [C ii] high-redshift observations as well as estimates based on the IR and UV luminosity functions are suggestive of an evolution in the [C ii] luminosity function similar to the evolution trend of the cosmic star formation rate density. Deep surveys using the Atacama Large Millimeter Array with full capability will be able to confirm this prediction.

79 ASTRONOMY AND ASTROPHYSICS↗