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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Repopulation of interacting tumor cells during fractionated radiotherapy: Stochastic modeling of the tumor control probability

Purpose: Optimal treatment planning for fractionated external beam radiation therapy requires inputs from radiobiology based on recent thinking about the “five Rs” (repopulation, radiosensitivity, reoxygenation, redistribution, and repair). The need is especially acute for the newer, often individualized, protocols made feasible by progress in image guided radiation therapy and dose conformity. Current stochastic tumor control probability (TCP) models incorporating tumor repopulation effects consider “stem-like cancer cells” (SLCC) to be independent, but the authors here propose that SLCC-SLCC interactions may be significant. The authors present a new stochastic TCP model for repopulating SLCC interacting within microenvironmental niches. Our approach is meant mainly for comparing similar protocols. It aims at practical generalizations of previous mathematical models. Methods: The authors consider protocols with complete sublethal damage repair between fractions. The authors use customized open-source software and recent mathematical approaches from stochastic process theory for calculating the time-dependent SLCC number and thereby estimating SLCC eradication probabilities. As specific numerical examples, the authors consider predicted TCP results for a 2 Gy per fraction, 60 Gy protocol compared to 64 Gy protocols involving early or late boosts in a limited volume to some fractions. Results: In sample calculations with linear quadratic parameters α = 0.3 per Gy, α/β = 10 Gy, boosting is predicted to raise TCP from a dismal 14.5% observed in some older protocols for advanced NSCLC to above 70%. This prediction is robust as regards: (a) the assumed values of parameters other than α and (b) the choice of models for intraniche SLCC-SLCC interactions. However, α = 0.03 per Gy leads to a prediction of almost no improvement when boosting. Conclusions: The predicted efficacy of moderate boosts depends sensitively on α. Presumably, the larger values of α are the ones appropriate for individualized treatment protocols, with the smaller values relevant only to protocols for a heterogeneous patient population. On that assumption, boosting is predicted to be highly effective. Front boosting, apart from practical advantages and a possible advantage as regards iatrogenic second cancers, also probably gives a slightly higher TCP than back boosting. If the total number of SLCC at the start of treatment can be measured even roughly, it will provide a highly sensitive way of discriminating between various models and parameter choices. Updated mathematical methods for calculating repopulation allow credible generalizations of earlier results.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2018

On random fuzzy fractional partial integro-differential equations under Caputo generalized Hukuhara differentiability

This paper is devoted to the study of the solvability of random fuzzy fractional partial integro-differential equations under Caputo generalized Hukuhara differentiability. The notions of random fuzzy variables and fuzzy stochastic processes are developed for multivariable functions. The existence and uniqueness of two types of integral solutions generated from Darboux problem for nonlinear wave equations are proved using the successive approximations method and Gronwall’s inequality for stochastic processes. The continuous dependence on the data, the boundedness, and the stability with probability one of integral solutions are established to confirm the well posedness of our model. Some computational examples are presented to illustrate the theoretical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Host genetic variation drives the differentiation in the ecological role of the native Miscanthus root-associated microbiome

Microbiome recruitment is influenced by plant host, but how host plant impacts the assembly, functions, and interactions of perennial plant root microbiomes is poorly understood. Here we examined prokaryotic and fungal communities between rhizosphere soils and the root endophytic compartment in two native Miscanthus species (Miscanthus sinensis and Miscanthus floridulus) of Taiwan and further explored the roles of host plant on root-associated microbiomes. Our results suggest that host plant genetic variation, edaphic factors, and site had effects on the root endophytic and rhizosphere soil microbial community compositions in both Miscanthus sinensis and Miscanthus floridulus, with a greater effect of plant genetic variation observed for the root endophytic communities. Host plant genetic variation also exerted a stronger effect on core prokaryotic communities than on non-core prokaryotic communities in each microhabitat of two Miscanthus species. From rhizosphere soils to root endophytes, prokaryotic co-occurrence network stability increased, but fungal co-occurrence network stability decreased. Furthermore, we found root endophytic microbial communities in two Miscanthus species were more strongly driven by deterministic processes rather than stochastic processes. Root-enriched prokaryotic OTUs belong to Gammaproteobacteria, Alphaproteobacteria, Betaproteobacteria, Sphingobacteriia, and [Saprospirae] both in two Miscanthus species, while prokaryotic taxa enriched in the rhizosphere soil are widely distributed among different phyla. We provide empirical evidence that host genetic variation plays important roles in root-associated microbiome in Miscanthus. The results of this study have implications for future bioenergy crop management by providing baseline data to inform translational research to harness the plant microbiome to sustainably increase agriculture productivity.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

SOLAR CYCLE VARIABILITY AND SURFACE DIFFERENTIAL ROTATION FROM Ca II K-LINE TIME SERIES DATA

Analysis of over 36 yr of time series data from the NSO/AFRL/Sac Peak K-line monitoring program elucidates 5 components of the variation of the 7 measured chromospheric parameters: (a) the solar cycle (period {approx} 11 yr), (b) quasi-periodic variations (periods {approx} 100 days), (c) a broadband stochastic process (wide range of periods), (d) rotational modulation, and (e) random observational errors, independent of (a)-(d). Correlation and power spectrum analyses elucidate periodic and aperiodic variation of these parameters. Time-frequency analysis illuminates periodic and quasi-periodic signals, details of frequency modulation due to differential rotation, and in particular elucidates the rather complex harmonic structure (a) and (b) at timescales in the range {approx}0.1-10 yr. These results using only full-disk data suggest that similar analyses will be useful for detecting and characterizing differential rotation in stars from stellar light curves such as those being produced by NASA's Kepler observatory. Component (c) consists of variations over a range of timescales, in the manner of a 1/f random process with a power-law slope index that varies in a systematic way. A time-dependent Wilson-Bappu effect appears to be present in the solar cycle variations (a), but not in the more rapid variations of the stochastic process (c). Component (d) characterizes differential rotation of the active regions. Component (e) is of course not characteristic of solar variability, but the fact that the observational errors are quite small greatly facilitates the analysis of the other components. The data analyzed in this paper can be found at the National Solar Observatory Web site http://nsosp.nso.edu/cak{sub m}on/, or by file transfer protocol at ftp://ftp.nso.edu/idl/cak.parameters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Two-Dimensional Anisotropic Random Walks: Fixed Versus Random Column Configurations for Transport Phenomena

We consider random walks on the square lattice of the plane along the lines of Heyde (J Stat Phys 27:721–730, 1982, Stochastic processes, Springer, New York, 1993) and den Hollander (J Stat Phys 75:891–918, 1994), whose studies have in part been inspired by the so-called transport phenomena of statistical physics. Two-dimensional anisotropic random walks with anisotropic density conditions á la Heyde (J Stat Phys 27:721–730, 1982, Stochastic processes, Springer, New York, 1993) yield fixed column configurations and nearest-neighbour random walks in a random environment on the square lattice of the plane as in den Hollander (J Stat Phys 75:891–918, 1994) result in random column configurations. In both cases we conclude simultaneous weak Donsker and strong Strassen type invariance principles in terms of appropriately constructed anisotropic Brownian motions on the plane, with self-contained proofs in both cases. The style of presentation throughout will be that of a semi-expository survey of related results in a historical context.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

High performance techniques for micro channel plate computations in photo multipliers

Monte Carlo - MC methods, requiring heavy computations of large data volume, can be used to predict the amplitude distribution and variance of outputted electron charge in Micro Channel Plates - MCPs, which are fed with primary emitted electrons in their inputs. The concept of parallel and serial combination of separate stages of such stochastic processes, which can be applied in MCP systems and simulated using MC computations, has recently proposed and shown interesting theorems and results. Separating the electron multiplication procedures, occurring in the channels of MCP systems, into sub-procedures, which are similar in nature and occur either in parallel or in consecutive manners, is equivalent to splitting the relevant stochastic system calculations into smaller ones, which can be performed concurrently and/or sequentially. In this way, calculations similar in nature, can be executed only once, thus, eliminating a great percentage of heavy computations. However, when designing and implementing the calculation inferences of the derived theorems using High Performance Computation - HPC techniques, the overall computation cost can further and significantly be reduced. In this paper, the hardware mappings of the relevant theorem inferences onto parallel computing architectures, resulting in circuits of computing blocks for calculation purposes of MCP system stochastic processes, are investigated. Each of the designed and implemented computing circuits corresponds to a theorem inference or to a combination of inferences. The parallelism of the proposed circuits consists of both the concurrent functioning of all the system blocks and of the simultaneous operation of each block, which is processing pieces of data, for many parts of the whole circuit in which it belongs. All the circuits are designed and tested using Altera Quartus II environment and can be implemented as chips, which can be incorporated in computing devices to assist Monte Carlo computations for the estimation of different MCP electron multiplication system performances.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1975

Stochastic model for fatigue crack size and cost effective design decisions

This paper describes a methodology for making cost effective fatigue design decisions. The methodology is based on a probabilistic model for the stochastic process of fatigue crack growth with time. The development of a particular model for the stochastic process is also discussed in the paper. The model is based on the assumption of continuous time and discrete space of crack lengths. Statistical decision theory and the developed probabilistic model are used to develop the procedure for making fatigue design decisions on the basis of minimum expected cost or risk function and reliability bounds. Selections of initial flaw size distribution, NDT, repair threshold crack lengths, and inspection intervals are discussed.

Hanagud, S.↗
DOE OSTI2013

A stochastic diffusion process for Lochner's generalized Dirichlet distribution

The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N stochastic variables with Lochner’s generalized Dirichlet distribution as its asymptotic solution. Individual samples of a discrete ensemble, obtained from the system of stochastic differential equations, equivalent to the Fokker-Planck equation developed here, satisfy a unit-sum constraint at all times and ensure a bounded sample space, similarly to the process developed in for the Dirichlet distribution. Consequently, the generalized Dirichlet diffusion process may be used to represent realizations of a fluctuating ensemble of N variables subject to a conservation principle. Compared to the Dirichlet distribution and process, the additional parameters of the generalized Dirichlet distribution allow a more general class of physical processes to be modeled with a more general covariance matrix.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Computational Mechanics for Heterogeneous Materials

The subject of this work is the development of models for the numerical simulation of matter, momentum, and energy balance in heterogeneous materials. These are materials that consist of multiple phases or species or that are structured on some (perhaps many) scale(s). By computational mechanics we mean to refer generally to the standard type of modeling that is done at the level of macroscopic balance laws (mass, momentum, energy). We will refer to the flow or flux of these quantities in a generalized sense as transport. At issue here are the forms of the governing equations in these complex materials which are potentially strongly inhomogeneous below some correlation length scale and are yet homogeneous on larger length scales. The question then becomes one of how to model this behavior and what are the proper multi-scale equations to capture the transport mechanisms across scales. To address this we look to the area of generalized stochastic process that underlie the transport processes in homogeneous materials. The archetypal example being the relationship between a random walk or Brownian motion stochastic processes and the associated Fokker-Planck or diffusion equation. Here we are interested in how this classical setting changes when inhomogeneities or correlations in structure are introduced into the problem. Aspects of non-classical behavior need to be addressed, such as non-Fickian behavior of the mean-squared-displacement (MSD) and non-Gaussian behavior of the underlying probability distribution of jumps. We present an experimental technique and apparatus built to investigate some of these issues. We also discuss diffusive processes in inhomogeneous systems, and the role of the chemical potential in diffusion of hard spheres is considered. Also, the relevance to liquid metal solutions is considered. Finally we present an example of how inhomogeneities in material microstructure introduce fluctuations at the meso-scale for a thermal conduction problem. These fluctuations due to random microstructures also provide a means of characterizing the aleatory uncertainty in material properties at the mesoscale.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Model Agnostic Bayesian Framework for Online Anomaly/Event Detection in PMU Data

Phasor measurement units (PMU) are integral to the modernization and automation plan of the electric power industry. A PMU data signature contains system-level events (e.g., faults, generation/load change, etc.) and any measurement/device-related errors. Therefore, the reliable and resilient operation of power systems is equivalent to the quality of the PMU data and the situation awareness provided by its data signature. Despite recent progress, current state-of-the-art methods are not fool-proof and have certain limitations tracing an error/abnormality to sensor sub-components and grid systems. This is because of technical challenges imposed by the scarcity of the labeled information, loss of data quality, and non-stationarity of data. In this paper, we consider the online PMU data stream as an output of a stochastic process and pose the anomaly/event detection as a changepoint detection problem dealing with detecting parameter changes in the underlying stochastic processes. The proposed model-agnostic framework relies on: (a) feature extraction utilizing the minimum volume enclosing ellipsoids (MVEE) method from raw PMU observations and (b) a Bayesian framework of changepoint detection. The validity of the proposed methodology is discussed through numerical experiments on real-world utility-scale PMU data.

Hossain, Ramij Raja↗
NASA NTRS2014

Chromospheric Variability: Analysis of 36 years of Time Series from the National Solar Observatory/Sacramento Peak Ca II K-line Monitoring Program

Analysis of more than 36 years of time series of seven parameters measured in the NSO/AFRL/Sac Peak K-line monitoring program elucidates five elucidates five components of the variation: (1) the solar cycle (period approx. 11 years), (2) quasi-periodic variations (periods approx 100 days), (3) a broad band stochastic process (wide range of periods), (4) rotational modulation, and (5) random observational errors. Correlation and power spectrum analyses elucidate periodic and aperiodic variation of the chromospheric parameters. Time-frequency analysis illuminates periodic and quasi periodic signals, details of frequency modulation due to differential rotation, and in particular elucidates the rather complex harmonic structure (1) and (2) at time scales in the range approx 0.1 - 10 years. These results using only full-disk data further suggest that similar analyses will be useful at detecting and characterizing differential rotation in stars from stellar light-curves such as those being produced by NASA's Kepler observatory. Component (3) consists of variations over a range of timescales, in the manner of a 1/f random noise process. A timedependent Wilson-Bappu effect appears to be present in the solar cycle variations (1), but not in the stochastic process (3). Component (4) characterizes differential rotation of the active regions, and (5) is of course not characteristic of solar variability, but the fact that the observational errors are quite small greatly facilitates the analysis of the other components. The recent data suggest that the current cycle is starting late and may be relatively weak. The data analyzed in this paper can be found at the National Solar Observatory web site http://nsosp.nso.edu/cak_mon/, or by file transfer protocol at ftp://ftp.nso.edu/idl/cak.parameters.

Solar physics↗
DOE OSTI2022

Microbial and Environmental Processes Shape the Link between Organic Matter Functional Traits and Composition

Dissolved organic matter (DOM) is a large and complex mixture of molecules that fuels biogeochemical reaction in virtually all ecosystems on Earth. However, the relative importance of deterministic and stochastic processes in structuring DOM composition remains poorly characterized. Here we develop a framework for partitioning molecular composition based on key molecular traits, including lability vs. recalcitrance and activity vs. inactivity. Within this framework, we examine the ecological processes governing the assembly of DOM fractions by deploying aquatic microcosms on mountainsides that span gradients of temperature and nutrient loading in subtropical and subarctic ecosystems. Across study regions, deterministic and stochastic processes primarily structure active and inactive fractions, respectively. However, recalcitrant molecules are more deterministically assembled than labile molecules in the inactive fraction. Deterministic processes leading to variable selection generally exhibit more variation across the energy supply gradient for inactive fractions, and their importance increases with energy supply for recalcitrant molecules in both active and inactive fractions. Together, our results indicate that active and inactive fractions of DOM assemblages are structured by contrasting ecological processes, and their recalcitrant components are sensitive to global change. In conclusion, our framework opens new avenues to understand the assembly and turnover of DOM in a changing world, which can be used to predict carbon cycling at local to global scales.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Temperature drives local contributions to beta diversity in mountain streams: stochastic and deterministic processes

Community variation (i.e. beta diversity) in geographical coenoclines is of substantial interest in ecology, yet the elevational patterns in beta diversity are still understudied, and no general conclusions have been reached. Here, we explored local contributions to beta diversity (LCBD) of stream bacteria, diatoms and macroinvertebrates on mountainsides. Across all taxa, we revealed a general U-shaped LCBD-elevation relationships (LCBDer), suggesting higher uniqueness of community composition at the two ends of the elevational gradients. This pattern was confirmed by coenocline simulations based on observed communities, and supported by the dominance of species replacement in total beta diversity. Across mountains and taxonomic groups, temperature was the main environmental factor underlying elevational patterns in LCBD and its metric relatives, which were also mediated by local environmental variables. The observed magnitudes of U-shaped LCBDer across mountains and taxonomic groups were specifically related to the heterogeneity of stream morphology, and the mean annual temperature on each mountain. U-shaped LCBDer were strengthened by the occurrence of generalist species with large elevational ranges, while rare species had a lesser effect on the patterns. Raup-Crick beta diversity indicated that both stochastic and deterministic processes drove the community assembly, and the latter one was positively related to the magnitudes of LCBDer. Our synthesis across mountains and taxonomic groups clearly shows that there are consistent elevational patterns in LCBD among taxonomic groups, and that these patterns are explained by similar ecological mechanisms, producing a more complete picture in understanding and bridging the spatial variation in biodiversity under changing climate.

Wang, Jianjun↗
DOE OSTI2018

Analytic Analysis for Dynamic System Frequency in Power Systems Under Uncertain Variability

In this paper, a new systematic method is proposed to analyze the system frequency in power systems under uncertain variability (UV). UV gradually increases in power systems, which originates from the renewable energy generation, random loads, frequency measurement, and communication channels, exerting noteworthy impacts on dynamic system frequency. The UV is modeled as a stochastic process in this paper. Then, the stochastic differential equations are used to describe the dynamic system frequency response (SFR) of a power system under UV, which is based on the SFR model. To assess system frequency dynamics under UV, an index of intra-range probability is put forward. Based on stochastic analysis theory, an analytic method is proposed to analyze the system frequency under UV, by which the intra-range probability can be analytically solved. Compared with Monte Carlo simulation in a typical SFR case and the Iceland electricity transmission network, the proposed method shows almost the same results using much less computation resource. Finally, insights for improving the SFR under UV are provided. The proposed method can be used to quickly verify whether the system frequency could withstand the UV and stay in the security range.

42 ENGINEERING↗
NASA NTRS1996

Discrete Deterministic and Stochastic Petri Nets

Petri nets augmented with timing specifications gained a wide acceptance in the area of performance and reliability evaluation of complex systems exhibiting concurrency, synchronization, and conflicts. The state space of time-extended Petri nets is mapped onto its basic underlying stochastic process, which can be shown to be Markovian under the assumption of exponentially distributed firing times. The integration of exponentially and non-exponentially distributed timing is still one of the major problems for the analysis and was first attacked for continuous time Petri nets at the cost of structural or analytical restrictions. We propose a discrete deterministic and stochastic Petri net (DDSPN) formalism with no imposed structural or analytical restrictions where transitions can fire either in zero time or according to arbitrary firing times that can be represented as the time to absorption in a finite absorbing discrete time Markov chain (DTMC). Exponentially distributed firing times are then approximated arbitrarily well by geometric distributions. Deterministic firing times are a special case of the geometric distribution. The underlying stochastic process of a DDSPN is then also a DTMC, from which the transient and stationary solution can be obtained by standard techniques. A comprehensive algorithm and some state space reduction techniques for the analysis of DDSPNs are presented comprising the automatic detection of conflicts and confusions, which removes a major obstacle for the analysis of discrete time models.

MATHEMATICAL MODELS↗
DOE OSTI2014

Karhunen–Loève treatment to remove noise and facilitate data analysis in sensing, spectroscopy and other applications

Resolving weak spectral variations in the dynamic response of materials that are either dominated or excited by stochastic processes remains a challenge. Responses that are thermal in origin are particularly relevant examples due to the delocalized nature of heat. Despite its inherent properties in dealing with stochastic processes, the Karhunen–Loève expansion has not been fully exploited in measurement of systems that are driven solely by random forces or can exhibit large thermally driven random fluctuations. Here in this paper, we present experimental results and analysis of the archetypes (a) the resonant excitation and transient response of an atomic force microscope probe by the ambient random fluctuations and nanoscale photothermal sample response, and (b) the photothermally scattered photons in pump–probe spectroscopy. In each case, the dynamic process is represented as an infinite series with random coefficients to obtain pertinent frequency shifts and spectral peaks and demonstrate spectral enhancement for a set of compounds including the spectrally complex biomass. The considered cases find important applications in nanoscale material characterization, biosensing, and spectral identification of biological and chemical agents.

47 OTHER INSTRUMENTATION↗