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Results for “Recurrence relations”

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

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A most misunderstood conditionally-solvable quantum-mechanical model

Highlights: • The Schrödinger equation for some quantum-mechanical models is separable in cylindrical coordinates. • The radial equation exhibits harmonic, linear and Coulomb-like interactions. • The Frobenius method leads to three-term recurrence relations. • Some particular energies are obtained from truncation of the recurrence relation. • Many authors misunderstood these results. In this paper we show that several authors have derived wrong physical conclusions from a gross misunderstanding of the exact eigenvalues and eigenfunctions of a conditionally-solvable quantum-mechanical model. It consists of an eigenvalue equation with seemingly Coulomb, linear and harmonic terms. Here we compare the results derived by those authors with the actual eigenvalues of the models calculated by means of the Ritz variational method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Poincaré constraints on celestial amplitudes

The functional structure of celestial amplitudes as constrained by Poincare symmetry is investigated in 2, 3, and 4-point cases for massless external particles of various spin, as well as massive external scalars. Functional constraints and recurrence relations are found (akin to the findings in [24]) that must be obeyed by the respective permissible correlator structures and function coefficients. In specific three-point cases involving massive scalars the resulting recurrence relations can be solved, e.g., reproducing purely from symmetry a three-point function coefficient known in the literature. Additionally, as a byproduct of the analysis, the three-point function coefficient for gluons in Minkowski signature is obtained from an amplitude map to the celestial sphere.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

On the computation of moments in the Super-Transition-Arrays model for radiative opacity calculations

In the Super-Transition-Array statistical method for the computation of radiative opacity of hot dense matter, the moments of the absorption or emission features involve partition functions with reduced degeneracies, occurring through the calculation of averages of products of subshell populations. Here, in the present work, we discuss several aspects of the computation of such peculiar partition functions, insisting on the precautions that must be taken in order to avoid numerical difficulties. In a previous work, we derived a formula for supershell partition functions, which takes the form of a functional of the distribution of energies within the supershell and allows for fast and accurate computations, truncating the number of terms in the expansion. The latter involves coefficients for which we obtained a recursion relation and an explicit formula. We show that such an expansion can be combined with the recurrence relation for shifted partition functions. We also propose, neglecting the effect of fine structure as a first step, a positive-definite formula for the Super-Transition-Array moments of any order, providing an insight into the asymmetry and sharpness of the latter. The corresponding formulas are free of alternating sums. Several ways to speed up the calculations are also presented.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

The S-matrix of 2D type 0B string theory. Part I. Perturbation theory revisited

We study the perturbative S-matrix of closed strings in the two-dimensional type 0B string theory from the worldsheet perspective, by directly integrating correlation functions of N = 1 Liouville theory. The latter is computed numerically using recurrence relations for super-Virasoro conformal blocks. We show that the tree level 3- and 4-point amplitudes are in agreement with the proposed dual matrix quantum mechanics. The non-perturbative aspects of the duality will be analyzed in a companion paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Analytical integration of the tractions induced by non-singular dislocations on an arbitrary shaped triangular quadratic element

Here, an analytical model is proposed to evaluate the nodal force induced by a segment of dislocation upon an arbitrary shaped triangular element. This calculation is required in hybrid methods that associate dislocation dynamics to boundary or finite element to solve simultaneously the evolution of large ensembles of dislocations with complex boundary conditions. Nodal forces are defined as the triple integration of the unbalanced traction field induced by a straight dislocation upon the surface of the element. Following our previous approach (Queyreau et al 2014 Modelling Simul. Mater. Sci. Eng. 22 035004) on a simpler geometry and in the case of linear isotropic elasticity, triple integrals are solved by sequences of integration by parts that exhibit recurrence relations. The traction field is defined and finite everywhere even at the core of dislocations, thanks to the use of the non-singular stress expression formulated by Cai et al (2006 J. Mech. Phys. Solids 54 561–587). The nodal force expressions can be used when considering both a single convolution or double convolution of the Green's function with the core distribution. A solution is also proposed for the case of a semi-infinite segment through the study of the asymptotic behavior of the analytical expressions. The proposed approach is exact and very computationally efficient. The choice of an arbitrary shaped triangular element and quadratic shape functions allow the consideration of complex geometries and comply with automatic meshing procedures. These analytical expressions could also be employed to estimate dislocation interactions with interfaces.

42 ENGINEERING↗
DOE OSTI2025

Greedy emulators for nuclear two-body scattering

Applications of reduced basis method emulators are increasing in low-energy nuclear physics because they enable fast and accurate sampling of high-fidelity calculations, enabling robust uncertainty quantification. Here, in this paper, we develop, implement, and test two model-driven emulators based on the (Petrov-)Galerkin projection using the prototypical test case of two-body scattering with the Minnesota potential and a more realistic local chiral potential. The high-fidelity scattering equations are solved with the matrix Numerov method, a reformulation of the popular Numerov recurrence relation for solving special second-order differential equations as a linear system of coupled equations. A novel error estimator based on reduced-space residuals is applied to an active learning approach (a greedy algorithm) to choosing training samples (“snapshots”) for the emulator and contrasted with a proper orthogonal decomposition (POD) approach. Both approaches allow for computationally efficient offline-online decompositions, but the greedy approach requires many fewer snapshot calculations. These developments set the groundwork for emulating scattering observables based on chiral nucleon-nucleon and three-nucleon interactions and optical models, where computational speed-ups are necessary for Bayesian uncertainty quantification. Our emulators and error estimators are widely applicable to linear systems.

Bayesian methods↗
DOE OSTI2021

Einstein–Rosen waves and the Geroch group

Under the action of the Geroch group, the Minkowski metric can be transformed into any vacuum metric with two commuting Killing vectors. In principle, this reduces the problem of deriving vacuum metrics with two commuting Killing vectors to pure algebra. In this short note, we use these facts to give a purely algebraic derivation of the Einstein-Rosen metric, which describes a cylindrical gravitational wave. Furthermore, our derivation has a straightforward extension to gravitational pulse waves.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Cancer genomics predicts disease relapse and therapeutic response to neoadjuvant chemotherapy of hormone sensitive breast cancers

Several studies provide insight into the landscape of breast cancer genomics with the genomic characterization of tumors offering exceptional opportunities in defining therapies tailored to the patient’s specific need. However, translating genomic data into personalized treatment regimens has been hampered partly due to uncertainties in deviating from guideline based clinical protocols. Here we report a genomic approach to predict favorable outcome to treatment responses thus enabling personalized medicine in the selection of specific treatment regimens. The genomic data were divided into a training set of N = 835 cases and a validation set consisting of 1315 hormone sensitive, 634 triple negative breast cancer (TNBC) and 1365 breast cancer patients with information on neoadjuvant chemotherapy responses. Patients were selected by the following criteria: estrogen receptor (ER) status, lymph node invasion, recurrence free survival. The k-means classification algorithm delineated clusters with low- and high- expression of genes related to recurrence of disease; a multivariate Cox’s proportional hazard model defined recurrence risk for disease. Classifier genes were validated by Immunohistochemistry (IHC) using tissue microarray sections containing both normal and cancerous tissues and by evaluating findings deposited in the human protein atlas repository. Based on the leave-on-out cross validation procedure of 4 independent data sets we identified 51-genes associated with disease relapse and selected 10, i.e. TOP2A, AURKA, CKS2, CCNB2, CDK1 SLC19A1, E2F8, E2F1, PRC1, KIF11 for in depth validation. Expression of the mechanistically linked disease regulated genes significantly correlated with recurrence free survival among ER-positive and triple negative breast cancer patients and was independent of age, tumor size, histological grade and node status. Importantly, the classifier genes predicted pathological complete responses to neoadjuvant chemotherapy (P < 0.001) with high expression of these genes being associated with an improved therapeutic response toward two different anthracycline-taxane regimens; thus, highlighting the prospective for precision medicine. Our study demonstrates the potential of classifier genes to predict risk for disease relapse and treatment response to chemotherapies. The classifier genes enable rational selection of patients who benefit best from a given chemotherapy thus providing the best possible care. The findings encourage independent clinical validation.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

How do North American weather regimes drive wind energy at the sub-seasonal to seasonal timescales?

Abstract There has been an increasing need for forecasting power generation at the subseasonal to seasonal (S2S) timescales to support the operation, management, and planning of the wind-energy system. At the S2S timescales, atmospheric variability is largely related to recurrent and persistent weather patterns, referred to as weather regimes (WRs). In this study, we identify four WRs that influence wind resources over North America using a universal two-stage procedure approach. These WRs are responsible for large-scale wind and power production anomalies over the CONUS at the S2S timescales. The WR-based reconstruction explains up to 40% of the monthly variance of power production over the western United States, and the explanatory power of WRs generally increases with the increase of timescales. The identified relationship between WRs and power production reveals the potential and limitations of the regional WR-based wind resource assessment over different regions of the CONUS across multiple timescales.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Data and code repository for "How do the weather regimes drive wind speed and power production at the sub-seasonal to seasonal timescales over the CONUS?"

There has been an increasing need for forecasting power generation at the sub-seasonal to seasonal (S2S) timescales to support the operation, management, and planning of the wind-energy system. At the S2S timescales, atmospheric variability is largely related to recurrent and persistent weather patterns, referred to as weather regimes (WRs). In the study "How do the weather regimes drive wind speed and power production at the sub-seasonal to seasonal timescales over the CONUS?", we identify four WRs that influence wind resources over North America using a self-organizing map (SOM) algorithm. These WRs are responsible for large-scale wind and power production anomalies over the CONUS at the S2S timescales. The WR-based reconstruction explains up to 50% of the monthly variance of power production over the western United States, and the explanatory power generally increases with the increase of timescales. The identified relationship between WRs and power production reveals the potential and limitations of the regional WR-based wind resource assessment over different regions of the CONUS across multiple timescales. This repository includes all the data and codes we use for analyses in this study. Users may use them to reproduce the results of this study on their end.

17 WIND ENERGY↗
DOE OSTI2021

Understanding Competing Risks

Highlights: • Clinicians and researchers need to be cognizant of competing risks (ie, the occurrence of an event that precludes future development of the outcome of interest). • Censoring is appropriate when a patient being censored at a particular time (eg, owing to loss to follow-up) is deemed to have approximately the same future risk of developing the outcome of interest as patients still being followed, and when the reason for censoring is not related to events of interest. • Censoring is not appropriate in many scenarios; for example, a dead patient can never develop a future cancer recurrence or late effect. • Kaplan-Meier (KM) analysis is commonly used for a time-to-event analysis when the primary outcome (eg, overall survival) has no meaningful competing risk and censoring is appropriate. Cox proportional hazards modeling can be used for multivariable analysis to examine the association between covariates and the primary outcome. • In the presence of competing events, incorrect use of the KM analysis will likely lead to an overestimation of the risk of the outcome of interest and biased estimates from both univariable and multivariable analyses. Therefore, KM usually should not be used to determine local recurrence risk because humanity is always at risk for dying, which is a competing risk. • A competing risk analysis is therefore most appropriate when there are competing events to the primary outcome of interest. The most commonly used multivariable model in these situations is the Fine-Gray model. • Many fundamental questions in radiation oncology—local and regional recurrence, treatment-related toxicity—are best addressed using competing risk methodologies.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2020

SO(3)-invariance of informed-graph-based deep neural network for anisotropic elastoplastic materials

This work examines the frame-invariance (and the lack thereof) exhibited in simulated anisotropic elasto-plastic responses generated from supervised machine learning of classical multi-layer and informed-graph-based neural networks, and proposes different remedies to fix this drawback. The inherent hierarchical relations among physical quantities and state variables in an elasto-plasticity model are first represented as informed, directed graphs, where three variations of the graph are tested. While feed-forward neural networks are used to train path-independent constitutive relations (e.g., elasticity), recurrent neural networks are used to replicate responses that depends on the deformation history, i.e. or path dependent. In dealing with the objectivity deficiency, we use the spectral form to represent tensors and, subsequently, three metrics, the Euclidean distance between the Euler Angles, the distance from the identity matrix, and geodesic on the unit sphere in Lie algebra, can be employed to constitute objective functions for the supervised machine learning. In this, the aim is to minimize the measured distance between the true and the predicted 3D rotation entities. Following this, we conduct numerical experiments on how these metrics, which are theoretically equivalent, may lead to differences in the efficiency of the supervised machine learning as well as the accuracy and robustness of the resultant models. Neural network models trained with tensors represented in component form for a given Cartesian coordinate system are used as a benchmark. Our numerical tests show that, even given the same amount of information and data, the quality of the anisotropic elasto-plasticity model is highly sensitive to the way tensors are represented and measured. The results reveal that using a loss function based on geodesic on the unit sphere in Lie algebra together with an informed, directed graph yield significantly more accurate rotation prediction than the other tested approaches.

42 ENGINEERING↗
DOE OSTI2026

Response of soil nutrient pools and microbiomes to recurrent wildfire disturbance and varying burn severities in a mixed conifer forest

Wildfire is a pervasive disturbance in mixed-conifer forests, yet the relative influence of fire recurrence versus burn severity on soil biogeochemistry and microbial communities remains poorly quantified. We examined a natural gradient of fire history (0–3 prior fires) and burn severity (low–high) spanning 50 yr in a mixed-conifer ecosystem to assess how repeated fire shapes soil carbon (C) and nitrogen (N) pools, their isotopic signatures, mineral and particulate fractions, microbial community composition, carbon-use, CO₂ fluxes, and vegetation cover. Successive fires produced progressively higher bare-ground percentages and lower tree cover, which were tightly linked to declines in microbial diversity and reductions bulk %C, and %N. δ 13 C increased with fire frequency, indicating preferential loss of labile C through combustion or enhanced microbial oxidation, thereby explaining the observed net soil-C decline. Conversely, δ 15 N decreased and pH increased as tree density declined, reflecting altered N cycling and reduced acidification in post-fire soils. Fire recurrence, more than severity, corresponded with a marked shift in the bacterial community: for example, Xanthobacteraceae—key N-fixers and C-cyclers—diminished, while N-fixing Bacillaceae increased, underscoring the tightly coupled nature of soil nutrient dynamics and microbiome composition after repeated burns. Our results demonstrate that fire recurrence appears to be a stronger driver of post-fire soil ecosystem responses in this mixed-conifer forest, influencing both abiotic nutrient pools and the functional potential of the soil microbiome. These findings provide a more enhanced assessment and understanding to date of the biogeochemical consequences of repeated wildfire disturbance that can be used to inform management strategies aimed at preserving soil health in fire-prone landscapes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Development and validation of a next-generation sequencing-based multigene assay to predict the prognosis of estrogen receptor-positive, HER2-negative breast cancer

Purpose: Multigene assays provide useful prognostic information regarding hormone receptor (HR)-positive breast cancer. Next-generation sequencing (NGS)-based platforms have numerous advantages including reproducibility and adaptability in local laboratories. Here we aimed to develop and validate an NGS-based multigene assay to predict the distant recurrence risk. Experimental Design: In total, 179 genes including 30 reference genes highly correlated with the 21-gene recurrence score (RS) algorithm were selected from public databases. Targeted RNA-sequencing was performed using 250 and 93 archived breast cancer samples with a known RS in the training and verification sets, respectively, to develop the algorithm and NGS–Prognostic Score (NGS-PS). The assay was validated in 413 independent samples with long-term follow-up data on distant metastasis. Results: In the verification set, the NGS-PS and 21-gene RS displayed 91.4% concurrence (85/93 samples). In the validation cohort of 413 samples, area under the receiver operating characteristic curve plotted using NGS-PS values classified for distant recurrence was 0.76. The best NGS-PS cut-off value predicting distant metastasis was 20. Furthermore, 269 and 144 patients were classified as low- and high-risk patients in accordance with the cut-off. Five- and 10-year estimates of distant metastasis–free survival (DMFS) for low- versus high-risk groups were 97.0% versus 77.8% and 93.2% versus 64.4%, respectively. The age-related HR for distant recurrence without chemotherapy was 9.73 (95% CI, 3.59–26.40) and 3.19 (95% CI, 1.40–7.29) for patients aged ≤50 and >50 years, respectively. Conclusions: The newly developed and validated NGS-based multigene assay can predict the distant recurrence risk in ER-positive, HER2-negative breast cancer.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Evaluation of overtime phenotypic variation of yeasts in chronic vulvovaginal candidosis cases

Abstract Chronic vulvovaginal candidosis results either from reinfection or from the ability of Candida spp. to persist in the vulva and/or vagina. Persistence is usually associated with increased antifungal (mainly azoles) resistance rates, which can explain treatment failure, and/or increased expression of virulence factors by Candida spp. The aim of this study was to assess the mechanisms leading to Candida spp persistence, by studying sequential isolates from women with chronic vulvovaginal candidosis, focusing on strains genotypes, azole resistance, and ability to form biofilms along the period of clinical evaluation. The strains were identified at species level by automated analysis of biochemical profiles and molecular typing evaluated by polymorphic DNA analysis. The capacity to form biofilm was assessed with a microtiter plate assay. Fluconazole susceptibility was determined by the microdilution broth assay at both pH 7 (following the recommended guideline) and pH 4.5 (as representative of vaginal pH). We studied samples from 17 clinically recurrent cases. In 53% of the chronic cases there were two or more isolates that had a phylogenetic relationship while the remaining (47%) were caused by different species. In those cases where related strains were involved in recurrence, we verified an increase in MIC at pH 7 and also an increased capacity to form biofilms over time. Significant correlation between these two parameters was observed only in cases caused by C. glabrata, evidencing the importance of these two factors to enhance persistence in the vaginal mucosa for this particular species.

Faria-Gonçalves, Paula↗
DOE OSTI2022

Prognostic Implications of MRI-Detected EMVI and Tumor Deposits and Their Response to Neoadjuvant Therapy in cT3 and cT4 Rectal Cancer

Magnetic resonance imaging–detected extramural venous invasion (mrEMVI) and tumor deposits (TDs) are risk factors for the development of local recurrence and distant metastases (DMs) in rectal cancer. However, little is known about their response to neoadjuvant treatment and its relation to oncologic outcomes. This study evaluated the incidence and features of mrEMVI and TDs before and after neoadjuvant treatment in relation to the development of local recurrence and DMs.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2024

Quantile regression-enriched event modeling framework for dropout analysis in high-temperature superconductor manufacturing

High-temperature superconductor (HTS) tapes have shown promising characteristics of high critical current, which are prerequisites for applications in high-field magnets. Due to the unstable growth conditions in the HTS manufacturing process, however, the frequent occurrences of dropouts in the critical current impede the consistent performance of HTS tapes. To manufacture HTS tapes with large scale, high yield, and uniform performance, it is essential to develop novel data analysis approaches for modeling the dropouts and identifying the related important process parameters. Conventional methods for modeling recurrent events, such as the point process, require the extraction of events from quality measurements. As the critical current is a continuous process, it may not comprehensively represent the drop patterns by transforming the time-series measurements into a set of events. Here, to solve this issue, we develop a novel quantile regression-enriched event modeling (QREM) framework that integrates the non-homogeneous Poisson process for modeling the occurrence of dropouts and the quantile regression for capturing the drop patterns. By incorporating the feature selection and regularization, the proposed framework identifies a set of significant process parameters that can potentially cause the dropouts of HTS tapes. The proposed method is tested on real HTS tapes produced using an advanced manufacturing process, successfully identifying important parameters that influence dropout events including the substrate temperature and voltage. The results demonstrate that the proposed QREM method outperforms the standard point process in predicting the occurrence of dropouts.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Overcoming persistent challenges in putting environmental flow policy into practice: a systematic review and bibliometric analysis

The implementation of environmental flows (e-flows) aims to reduce the negative impacts of hydrological alteration on freshwater ecosystems. Despite the growing attention to the importance of e-flows since the 1970s, actual implementation has lagged. Therefore, we explore the limitations in e-flows implementation, their systemic reasons, and solutions. We conducted a systematic review and a bibliometric analysis to identify peer-reviewed articles published on the topic of e-flows implementation research in the last two decades, resulting in 68 research and review papers. Co-occurrence of terms, and geographic and temporal trends were analyzed to identify the gaps in environmental water management and propose recommendations to address limitations on e-flows implementation. We identify the underlying causes and potential solutions to such challenges in environmental water management. The limitations to e-flow implementation identified were categorized into 21 classes. The most recognized limitation was the competing priorities of human uses of water (n = 29). Many secondary limitations, generally co-occurring in co-causation, were identified as limiting factors, especially for implementing more nuanced and sophisticated e-flows. The lack of adequate hydrological data (n = 24) and ecological data (n = 28) were among the most mentioned, and ultimately lead to difficulties in starting or continuing monitoring/adaptive management (n = 28) efforts. The lack of resource/capacity (n = 21), experimentation (n = 19), regulatory enforcement (n = 17), and differing authorities involved (n = 18) were also recurrent problems, driven by the deficiencies in the relative importance given to e-flows when facing other human priorities. In order to provide a clearer path for successful e-flow implementation, system mapping can be used as a starting point and general-purpose resource for understanding the sociohydrological problems, interactions, and inherited complexity of river systems. Secondly, we recommend a system analysis approach to address competing demands, especially with the use of coupled water-energy modeling tools to support decision-making when hydropower generation is involved. Such approaches can better assess the complex interactions among the hydrologic, ecological, socioeconomic, and engineering dimensions of water resource systems and their effective management. Lastly, given the complexities in environmental water allocation, implementation requires both scientific rigor and proven utility. Consequently, and where possible, we recommend a move from simplistic flow allocations to a more holistic approach informed by hydroecological principles. To ease conflicts between competing water demands, water managers can realize more 'pop per drop' by supporting key components of a flow regime that include functional attributes and processes that enhance biogeochemical cycling, structural habitat formation, and ecosystem maintenance.

54 ENVIRONMENTAL SCIENCES↗