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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Open-closed string duality, branes, and topological recursion

We consider matrix models exhibiting open-closed string duality in two-dimensional string theories with various amounts of supersymmetry. In particular, a relationship between matrix models in the β = 2 Wigner-Dyson class and models in the (1 + 2Γ, 2) Altland-Zirnbauer class relates the perturbative solutions of the two systems’ string equations. Point-like operator insertions in the closed string theory are mapped to the topological expansion of the free energy in the open string theory. We compute correlation functions of macroscopic loop operators and FZZT branes in a general topological gravity background. The relationship between the topological recursion of moduli space volumes and branes is discussed by analyzing the Virasoro conditions in the matrix models.

2D Gravity↗
DOE OSTI2023

Graphically Contracted Function Construction with the Recursive Pairwise Merge Algorithm

A new implementation of a recursive pairwise merge algorithm to construct a GCF from a list of CSF expansion coefficients is presented. The essential new feature is the preallocation of some work arrays used within the intermediate steps of the merge procedure. This results in roughly an order of magnitude improvement in overall efficiency and also approximately eliminates a factor of n, the molecular orbital dimension, from the original implementation. Initial application of this merge procedure to a series of H m molecules shows that the GCF wave functions can be represented well both with delocalized canonical Hartree-Fock orbitals and with localized molecular orbitals. Finally, for a given wave function complexity, as measured by the average facet count, $\bar{\text {f}}$, the delocalized Hartree-Fock orbitals show smaller errors for small $\bar{\text {f}}$ values, while the localized orbitals show smaller errors for larger $\bar{\text {f}}$ values.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A practical extension of the recursive multi-fidelity model for the emulation of hole closure experiments

We report in regimes of high strain rate, the strength of materials often cannot be measured directly in experiments. Instead, the strength is inferred based on an experimental observable, such as a change in shape, that is matched by simulations supported by a known strength model. In hole closure experiments, the rate and degree to which a central hole in a plate of material closes during a dynamic loading event are used to infer material strength parameters. Due to the complexity of the experiment, many computationally expensive, three-dimensional simulations are necessary to train an emulator for calibration or other analyses. These simulations can be run at multiple grid resolutions, where dense grids are slower but more accurate. In an effort to reduce the computational cost, a combination of simulations with different resolutions can be combined to develop an accurate emulator within a limited training time. We explore the novel design and construction of an appropriate functional recursive multi-fidelity emulator of a strength model for tantalum in hole closure experiments that can be applied to arbitrarily large training data. Hence, by formulating a multi-fidelity model to employ low-fidelity simulations, we were able to reduce the error of our emulator by approximately 81% with only an approximately 1.6% increase in computing resource utilization.

36 MATERIALS SCIENCE↗
DOE OSTI2025

On-shell recursion and holomorphic HQET for heavy quark hadronic resonances

We develop a new theoretical framework for the treatment of heavy quark (HQ) resonances within heavy quark effective theory (HQET). This framework uses on-shell recursion techniques to express the resonant amplitude as a product of on-shell subamplitudes, which allows one to employ a form-factor representation of the hadronic matrix elements and to obtain an HQ expansion, but at the price of introducing complex momenta. We construct a generalized “holomorphic HQET” onto which such complex-momentum matrix elements can be matched, and we show that PT symmetry ensures the Isgur-Wise functions (and the perturbative corrections) become holomorphic functions of the complex recoil parameter with real coefficients. They are thus an analytic continuation of the standard HQET description. This framework admits a HQ hadron (strong decay) width expansion. At second order, we show it is compatible with data for the B12∗$$ {B}_{1(2)}^{\left(\ast \right)} $$ and D12∗$$ {D}_{1(2)}^{\left(\ast \right)} $$ HQ doublets. Taking the B¯→D1∗1−→Dπlν$$ \overline{B}\to \left({D}_1^{\ast}\left({1}^{-}\right)\to D\pi \right) l u $$ system as an example, we compute the holomorphic HQET expansion to first order, as well as the complex-momentum on-shell subamplitudes. A toy numerical study of the resulting differential rates demonstrates that this framework generates HQ resonance lineshapes with large tails, resembling those seen in data.

Manzari, Claudio Andrea↗
DOE OSTI2019

Recursion relation for general 3d blocks

We derive closed-form expressions for all ingredients of the Zamolodchikov-like recursion relation for general spinning conformal blocks in 3-dimensional conformal field theory. This result opens a path to efficient automatic generation of conformal block tables, which has immediate applications in numerical conformal bootstrap program. Our derivation is based on an understanding of null states and conformally-invariant differential operators in momentum space, combined with a careful choice of the relevant tensor structures bases. This derivation generalizes straightforwardly to higher spacetime dimensions d, provided the relevant Clebsch-Gordan coefficients of Spin (d) are known.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Optimized recursion relation for the computation of partition functions in the superconfiguration approach

Partition functions of a canonical ensemble of non-interacting bound electrons are a key ingredient of the super-transition-array approach to the computation of radiative opacity. A few years ago, we published a robust and stable recursion relation for the calculation of such partition functions. In this work, we propose an optimization of the latter method and explain how to implement it in practice. The formalism relies on the evaluation of elementary symmetric polynomials, which opens the way to further improvements.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

New Breast Cancer Recursive Partitioning Analysis Prognostic Index in Patients With Newly Diagnosed Brain Metastases

Purpose: The aim of the study was to present a new breast cancer recursive partitioning analysis (RPA) prognostic index for patients with newly diagnosed brain metastases as a guide in clinical decision making. Methods and Materials: A prospectively collected group of 441 consecutive patients with breast cancer and brain metastases treated between the years 2003 and 2009 was assessed. Prognostic factors significant for univariate analysis were included into RPA. Results: Three prognostic classes of a new breast cancer RPA prognostic index were selected. The median survival of patients within prognostic Classes I, II, and III was 29, 9, and 2.4 months, respectively (p < 0.0001). Class I included patients with one or two brain metastases, without extracranial disease or with controlled extracranial disease, and with Karnofsky performance status (KPS) of 100. Class III included patients with multiple brain metastases with KPS of {<=}60. Class II included all other cases. Conclusions: The breast cancer RPA prognostic index is an easy and valuable tool for use in clinical practice. It can select patients who require aggressive treatment and those in whom whole-brain radiotherapy or symptomatic therapy is the most reasonable option. An individual approach is required for patients from prognostic Class II.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2012

Recursive Partitioning Analysis Index Is Predictive for Overall Survival in Patients Undergoing Spine Stereotactic Body Radiation Therapy for Spinal Metastases

Purpose: To generate a prognostic index using recursive partitioning analysis (RPA) for patients undergoing spine stereotactic body radiation therapy (sSBRT) for spinal metastases (sMet). Methods and Materials: From an institutional review board-approved database, 174 patients were treated for sMet with sSBRT between February 2006 and August 2009. Median dose was 14 Gy (range, 8-24 Gy), typically in a single fraction (range, 1-5). Kaplan-Meier analysis was performed to detect any correlation between survival and histology. Histologies were divided into favorable (breast and prostate), radioresistant (renal cell, melanoma and sarcoma), and other (all other histologies). RPA was performed to identify any association of the following variables with overall survival (OS) following sSBRT: histology, gender, age, Karnofsky performance status (KPS), control of primary, extraosseous metastases, time from primary diagnosis (TPD), dose of sSBRT ({<=}14 Gy vs. >14 Gy), extent of spine disease (epidural only, bone and epidural, bone only), upfront or salvage treatment, presence of paraspinal extension, and previous surgery. Results: Median follow-up was 8.9 months. Median OS time from sSBRT was 10.7 months. Median OS intervals for favorable histologies were 14 months, 11.2 months for radioresistant histologies, and 7.3 months for other histologies (p = 0.02). RPA analysis resulted in three classes (p < 0.0001). Class 1 was defined as TPD of >30 months and KPS of >70; Class 2 was TPD of >30 months and KPS of {<=}70 or a TPD of {<=}30 months and age <70 years old; Class 3 was TPD of {<=}30 months and age {>=}70 years old. Median OS was 21.1 months for Class 1 (n = 59), 8.7 months for Class 2 (n = 104), and 2.4 months for Class 3 (n = 11). Conclusion: sSBRT patients treated for sMet have a wide variability in OS. We developed an RPA classification system that is predictive of OS. While many patients are treated for palliation of pain or to avoid symptomatic progression, this index may be used to predict which patients may benefit most from sSBRT.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2012

Subclassification of Recursive Partitioning Analysis Class II Patients With Brain Metastases Treated Radiosurgically

Purpose: Although the recursive partitioning analysis (RPA) class is generally used for predicting survival periods of patients with brain metastases (METs), the majority of such patients are Class II and clinical factors vary quite widely within this category. This prompted us to divide RPA Class II patients into three subclasses. Methods and Materials: This was a two-institution, institutional review board-approved, retrospective cohort study using two databases: the Mito series (2,000 consecutive patients, comprising 787 women and 1,213 men; mean age, 65 years [range, 19-96 years]) and the Chiba series (1,753 patients, comprising 673 female and 1,080 male patients; mean age, 65 years [range, 7-94 years]). Both patient series underwent Gamma Knife radiosurgery alone, without whole-brain radiotherapy, for brain METs during the same 10-year period, July 1998 through June 2008. The Cox proportional hazard model with a step-wise selection procedure was used for multivariate analysis. Results: In the Mito series, four factors were identified as favoring longer survival: Karnofsky Performance Status (90% to 100% vs. 70% to 80%), tumor numbers (solitary vs. multiple), primary tumor status (controlled vs. not controlled), and non-brain METs (no vs. yes). This new index is the sum of scores (0 and 1) of these four factors: RPA Class II-a, score of 0 or 1; RPA Class II-b, score of 2; and RPA Class II-c, score of 3 or 4. Next, using the Chiba series, we tested whether our index is valid for a different patient group. This new system showed highly statistically significant differences among subclasses in both the Mito series and the Chiba series (p < 0.001 for all subclasses). In addition, this new index was confirmed to be applicable to Class II patients with four major primary tumor sites, that is, lung, breast, alimentary tract, and urogenital organs. Conclusions: Our new grading system should be considered when designing future clinical trials involving brain MET patients.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2012

Recursive Partitioning Analysis for New Classification of Patients With Esophageal Cancer Treated by Chemoradiotherapy

Background: The 7th edition of the American Joint Committee on Cancer staging system does not include lymph node size in the guidelines for staging patients with esophageal cancer. The objectives of this study were to determine the prognostic impact of the maximum metastatic lymph node diameter (ND) on survival and to develop and validate a new staging system for patients with esophageal squamous cell cancer who were treated with definitive chemoradiotherapy (CRT). Methods: Information on 402 patients with esophageal cancer undergoing CRT at two institutions was reviewed. Univariate and multivariate analyses of data from one institution were used to assess the impact of clinical factors on survival, and recursive partitioning analysis was performed to develop the new staging classification. To assess its clinical utility, the new classification was validated using data from the second institution. Results: By multivariate analysis, gender, T, N, and ND stages were independently and significantly associated with survival (p < 0.05). The resulting new staging classification was based on the T and ND. The four new stages led to good separation of survival curves in both the developmental and validation datasets (p < 0.05). Conclusions: Our results showed that lymph node size is a strong independent prognostic factor and that the new staging system, which incorporated lymph node size, provided good prognostic power, and discriminated effectively for patients with esophageal cancer undergoing CRT.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2017

Moderate deviations-based importance sampling for stochastic recursive equations

Subsolutions to the Hamilton–Jacobi–Bellman equation associated with a moderate deviations approximation are used to design importance sampling changes of measure for stochastic recursive equations. Analogous to what has been done for large deviations subsolution-based importance sampling, these schemes are shown to be asymptotically optimal under the moderate deviations scaling. Here, we present various implementations and numerical results to contrast their performance, and also discuss the circumstances under which a moderate deviation scaling might be appropriate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Recursive Factorization of the Inverse Overlap Matrix in Linear Scaling Quantum Molecular Dynamics Simulations

We present a reduced complexity algorithm to compute the inverse overlap factors required to solve the generalized eigenvalue problem in a quantum-based molecular dynamics (MD) simulation. Our method is based on the recursive iterative re nement of an initial guess Z of the inverse overlap matrix S. The initial guess of Z is obtained beforehand either by using an approximate divide and conquer technique or dynamically, propagated within an extended Lagrangian dynamics from previous MD time steps. With this formulation, we achieve long-term stability and energy conservation even under incomplete approximate iterative re nement of Z. Linear scaling performance is obtained using numerically thresholded sparse matrix algebra based on the ELLPACK-R sparse matrix data format, which also enables e cient shared memory parallelization. As we show in this article using selfconsistent density functional based tight-binding MD, our approach is faster than conventional methods based on the direct diagonalization of the overlap matrix S for systems as small as a few hundred atoms, substantially accelerating quantum-based simulations even for molecular structures of intermediate size. For a 4,158 atom water-solvated polyalanine system we nd an average speedup factor of 122 for the computation of Z in each MD step.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Deep material network via a quilting strategy: visualization for explainability and recursive training for improved accuracy

Recent developments integrating micromechanics and neural networks offer promising paths for rapid predictions of the response of heterogeneous materials with similar accuracy as direct numerical simulations. The deep material network is one such approaches, featuring a multi-layer network and micromechanics building blocks trained on anisotropic linear elastic properties. Once trained, the network acts as a reduced-order model, which can extrapolate the material’s behavior to more general constitutive laws, including nonlinear behaviors, without the need to be retrained. However, current training methods initialize network parameters randomly, incurring inevitable training and calibration errors. Here, we introduce a way to visualize the network parameters as an analogous unit cell and use this visualization to “quilt” patches of shallower networks to initialize deeper networks for a recursive training strategy. The result is an improvement in the accuracy and calibration performance of the network and an intuitive visual representation of the network for better explainability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Recursive polarization of nuclear spins in diamond at arbitrary magnetic fields

We introduce an alternate route to dynamically polarize the nuclear spin host of nitrogen-vacancy (NV) centers in diamond. Our approach articulates optical, microwave, and radio-frequency pulses to recursively transfer spin polarization from the NV electronic spin. Using two complementary variants of the same underlying principle, we demonstrate nitrogen nuclear spin initialization approaching 80% at room temperature both in ensemble and single NV centers. Unlike existing schemes, our approach does not rely on level anti-crossings and is thus applicable at arbitrary magnetic fields. This versatility should prove useful in applications ranging from nanoscale metrology to sensitivity-enhanced NMR.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Majorant recursions to determine eigenstate bounds of a symmetric exponential quantum anharmonic oscillator

The determination of the energy states is highly studied issue in the quantum mechanics. Based on expectation values dynamics, energy states can be observed. But conditions and calculations vary depending on the created system. In this work, a symmetric exponential anharmonic oscillator is considered and development of a recursive approximation method is studied to find its ground energy state. The use of majorant values facilitates the approximate calculation of expectation values.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm

A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose–Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh–Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born–Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick’s theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn–Luttinger-type nonconvergence.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

Target tracking via recursive Bayesian state estimation in radar networks

Modern cognitive radar networks incorporating intelligent and cognitive support-modules can actively adjust the radar-target geometry and optimally select a subset of radars to track the target of interest. Based on the theories of dynamic graphical models (DGM) and recursive Bayesian state estimation (RBSE), we propose a framework for single target tracking in mobile and cooperative radar networks, jointly considering path planning and radar selection. We formulate the tracking procedure as two iterative steps: (i) solving a combinatorial problem based on the expected cross-entropy measure to select the optimal subset of radars and their locations, and (ii) tracking the target using RBSE technique. We simulate the proposed framework using an illustrative example in 2-D space and demonstrate the tracking performance.

Xiang, Yijian↗
DOE OSTI2023

Evaluating Recursive Blind Forecast Against API and Baseline: A Puerto Rican Case Study on Solar Irradiance for Normal and Extreme Weather

This paper leverages ongoing work in a community microgrid in Adjuntas, Puerto Rico to forecast global horizontal irradiance (GHI) and compare performance in normal and extreme weather. Given a positive correlation of 0.98 between GHI and PV power, forecasting GHI can be an effective, indirect forecast of photovoltaic (PV) power, especially in microgrids where the end-users, owners, operators, or other stakeholders are reluctant to share data for training or validation due to privacy and security concerns. A recursive one-shot (termed as "blind") forecast is, hence, formulated, wherein a gradient-boosted regression tree (GBR) is built to forecast GHI for a 7-day horizon in normal weather, and a 2-day horizon in extreme weather. To demonstrate its resilience, the architecture is trained on normal and hurricane weather GHI from 2002-2022. It is generalized on February 9-16, 2023, and on the landfall of Hurricane Nicole (Nov 4-5, 2022), respectively. Forecasts from GBR are compared against that from a satellite-based API resource and three baselines: persistence, averaging, and exponential smoothing. Results show GBR and persistence outperform sophisticated API in both types of weather for this case study.

Sundararajan, Aditya↗