Search NASA⌕ Search

SEARCH · Search NASA

Results for “Markov process”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Counting generations in birth and death processes with competing Erlang and exponential waiting times

Lymphocyte populations, stimulated in vitro or in vivo, grow as cells divide. Stochastic models are appropriate because some cells undergo multiple rounds of division, some die, and others of the same type in the same conditions do not divide at all. If individual cells behave independently, then each cell can be imagined as sampling from a probability density of times to division and death. The exponential density is the most mathematically and computationally convenient choice. It has the advantage of satisfying the memoryless property, consistent with a Markov process, but it overestimates the probability of short division times. With the aim of preserving the advantages of a Markovian framework while improving the representation of experimentally-observed division times, we consider a multi-stage model of cellular division and death. We use Erlang-distributed (or, more generally, phase-type distributed) times to division, and exponentially distributed times to death. We classify cells into generations, using the rule that the daughters of cells in generation n are in generation n + 1. In some circumstances, our representation is equivalent to established models of lymphocyte dynamics. We find the growth rate of the cell population by calculating the proportions of cells by stage and generation. The exponent describing the late-time cell population growth, and the criterion for extinction of the population, differs from what would be expected if N steps with rate λ were equivalent to a single step of rate λ/N. We link with a published experimental dataset, where cell counts were reported after T cells were transferred to lymphopenic mice, using Approximate Bayesian Computation. In the comparison, the death rate is assumed to be proportional to the generation and the Erlang time to division for generation 0 is allowed to differ from that of subsequent generations. The multi-stage representation is preferred to a simple exponential in posterior distributions, and the mean time to first division is estimated to be longer than the mean time to subsequent divisions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2014

Anomaly Detection in Dynamic Networks

Anomaly detection in dynamic communication networks has many important security applications. These networks can be extremely large and so detecting any changes in their structure can be computationally challenging; hence, computationally fast, parallelisable methods for monitoring the network are paramount. For this reason the methods presented here use independent node and edge based models to detect locally anomalous substructures within communication networks. As a first stage, the aim is to detect changes in the data streams arising from node or edge communications. Throughout the thesis simple, conjugate Bayesian models for counting processes are used to model these data streams. A second stage of analysis can then be performed on a much reduced subset of the network comprising nodes and edges which have been identified as potentially anomalous in the first stage. The first method assumes communications in a network arise from an inhomogeneous Poisson process with piecewise constant intensity. Anomaly detection is then treated as a changepoint problem on the intensities. The changepoint model is extended to incorporate seasonal behavior inherent in communication networks. This seasonal behavior is also viewed as a changepoint problem acting on a piecewise constant Poisson process. In a static time frame, inference is made on this extended model via a Gibbs sampling strategy. In a sequential time frame, where the data arrive as a stream, a novel, fast Sequential Monte Carlo (SMC) algorithm is introduced to sample from the sequence of posterior distributions of the change points over time. A second method is considered for monitoring communications in a large scale computer network. The usage patterns in these types of networks are very bursty in nature and don’t fit a Poisson process model. For tractable inference, discrete time models are considered, where the data are aggregated into discrete time periods and probability models are fitted to the communication counts. In a sequential analysis, anomalous behavior is then identified from outlying behavior with respect to the fitted predictive probability models. Seasonality is again incorporated into the model and is treated as a changepoint model on the transition probabilities of a discrete time Markov process. Second stage analytics are then developed which combine anomalous edges to identify anomalous substructures in the network.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Deep Generative Model for Non-Intrusive Identification of EV Charging Profiles

The proliferation of electric vehicles (EVs) brings environmental benefits and technical challenges to power grids. An identification algorithm which can accurately extract individual EV charging profiles out of widely available smart meter measurements has attracted great interests. This paper proposes a non-intrusive identification framework for EV charging profile extraction, which is driven by deep generative models (DGM). First, the proposed DGM is designed as a representation layer embedded into the Markov process and used to model the joint probability distribution of available time-series data. A novel contribution is to approximate posterior distributions by neural networks whose parameters are obtained by variational inference and supervised learning. Second, the EV charging status is inferred from the DGM via dynamic programming. Lastly, the desired EV charging profile can be reconstructed by the rated power of EV models and inferred status. Compared with the benchmark Hidden Markov Models, the proposed framework can better handle noise in data with less computational complexity and better overall accuracy performances with smaller recall. The proposed framework is validated by numerical experiments on the Pecan Street dataset.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2025

Post-hoc reweighting of hadron production in the Lund string model

We present a method for reweighting flavor selection in the Lund string fragmentation model. This is the process of calculating and applying event weights enabling fast and exact variation of hadronization parameters on pre-generated event samples. The procedure is post hoc, requiring only a small amount of additional information stored per event, and allowing for efficient estimation of hadronization uncertainties without repeated simulation. Weight expressions are derived from the hadronization algorithm itself, and validated against direct simulation for a wide range of observables and parameter shifts. The hadronization algorithm can be viewed as a hierarchical Markov process with stochastic rejections, a structure common to many complex simulations outside of high-energy physics. This perspective makes the method modular, extensible, and potentially transferable to other domains. We demonstrate the approach in Pythia, including both coverage considerations and timing benefits. For the purpose of this paper, our goal is to develop and demonstrate the the formalism, and we therefore exclude several model variations for baryon production (popcorn model, junction production) needed for proton collisions. These will be the topic of a future paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1971

Bayesian recursive image estimation.

A procedure for recursively estimating images that are characterized statistically by the mean and correlation functions associated with the random process representing the brightness level is proposed for the case where the images are corrupted by additive noise. First, a dynamic model is developed with a response characteristic which matches that of the scanner output (the input of the estimator is the output of a horizontal line scanner) in a statistical sense. Such models have the form of an ordinary differential or difference equation with white noise input. An insignificant approximation is introduced by using a constant-coefficient model. The appropriate model is a vector valued difference equation with the solution representing a vector Markov process. The next step is to obtain the minimum mean square estimate of the image by using a Kalman filter. Since the image estimation is an interpolation problem, two successive runs over the observation are performed in opposite directions and the resultant estimates are averaged. Examples are included for illustration.

Nahi, N. E.↗
NASA NTRS2019

Cellular Statistical Models of Broken Cloud Fields. Part IV: Effects of Pixel Size on Idealized Satellite Observations

In the fourth part of our “Cellular Statistical Models of Broken Cloud Fields” series we use the binary Markov processes framework for quantitative investigation of the effects of low resolution of idealized satellite observations on the statistics of the retrieved cloud masks. We assume that the cloud fields are Markovian and are characterized by the “actual” cloud fraction (CF) and scale length. We use two different models of observations: a simple discrete-point sampling and a more realistic “pixel” protocol. The latter is characterized by a state attribution function (SAF) which has the meaning of the probability that the pixel with a certain CF is declared cloudy in the observed cloud mask. The stochasticity of the SAF means that the cloud/clear attribution is not ideal and can be affected by external or unknown factors. We show that the observed cloud masks can be accurately described as Markov chains of pixels and use the master-matrix formalism (introduced in Part III of the series) for analytical computation of their parameters: the “observed” CF and scale length. This procedure allows us to establish a quantitative relationship (which is pixel-size dependent) between the actual and the observed cloud-field statistics. The feasibility of restoring the former from the latter is considered. The adequacy of our analytical approach to idealized observations is evaluated using numerical simulations. Comparison of the observed parameters of the simulated datasets with their theoretical expectations showed an agreement within 0.005 for the CF, while for the scale length it is within 1% in the sampling case and within 4% in the pixel case.

Mikhail D. Alexandrov↗
DOE OSTI2016

Thermodynamics, morphology, and kinetics of early-stage self-assembly of π-conjugated oligopeptides

Synthetic oligopeptides containing π-conjugated cores self-assemble novel materials with attractive electronic and photophysical properties. All-atom, explicit solvent molecular dynamics simulations of Asp-Phe-Ala-Gly-OPV3-Gly-Ala-Phe-Asp peptides were used to parameterize an implicit solvent model to simulate early-stage self-assembly. Under low-pH conditions, peptides assemble into β-sheet-like stacks with strongly favorable monomer association free energies of ΔF ≈ -25kBT. Aggregation at high-pH produces disordered aggregates destabilized by Coulombic repulsion between negatively charged Asp termini (ΔF ≈ -5kBT). In simulations of hundreds of monomers over 70 ns we observe the spontaneous formation of up to undecameric aggregates under low-pH conditions. Modeling assembly as a continuous-time Markov process, we infer transition rates between different aggregate sizes and microsecond relaxation times for early-stage assembly. Our data suggests a hierarchical model of assembly in which peptides coalesce into small clusters over tens of nanoseconds followed by structural ripening and diffusion limited aggregation on longer time scales. This work provides new molecular-level understanding of early-stage assembly, and a means to study the impact of peptide sequence and aromatic core chemistry upon the thermodynamics, assembly kinetics, and morphology of the supramolecular aggregates.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Streamflow Reconstruction in the Upper Missouri River Basin Using a Novel Bayesian Network Model

A Bayesian model that uses the spatial dependence induced by the river network topology, and the leading principal components of regional tree ring chronologies for paleo-streamflow reconstruction is presented. In any river basin, a convergent, dendritic network of tributaries come together to form the main stem of a river. Consequently, it is natural to think of a spatial Markov process that recognizes this topological structure to develop a spatially consistent basin-scale streamflow reconstruction model that uses the information in streamflow and tree ring chronology data to inform the reconstructed flows, while maintaining the space-time correlation structure of flows that is critical for water resource assessments and management. Given historical data from multiple streamflow gauges along a river, their tributaries in a watershed, and regional tree ring chronologies, the model is fit and used to simultaneously reconstruct the full network of paleo-streamflow at all gauges in the basin progressing upstream to downstream along the river. Our application to 18 streamflow gauges in the Upper Missouri River Basin shows that the mean adjusted R 2 for the basin is approximately 0.5 with good overall cross-validated skill as measured by five different skill metrics. The spatial network structure produced a substantial reduction in the uncertainty associated with paleo-streamflow as one proceeds downstream in the network aggregating information from upstream gauges and tree ring chronologies. Uncertainty was reduced by more than 50% at six gauges, between 6% and 50% at one gauge, and by less than 5% at the remaining 11 gauges when compared with the traditional principal component regression reconstruction model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Impact of velocity correlation and distribution on transport in fractured media: Field evidence and theoretical model

Flow and transport through fractured geologic media often leads to anomalous (non-Fickian) transport behavior, the origin of which remains a matter of debate: whether it arises from variability in fracture permeability (velocity distribution), connectedness in the flow paths through fractures (velocity correlation), or interaction between fractures and matrix. Here we show that this uncertainty of distribution- versus correlation-controlled transport can be resolved by combining convergent and push-pull tracer tests because flow reversibility is strongly dependent on velocity correlation, whereas late-time scaling of breakthrough curves is mainly controlled by velocity distribution. We build on this insight, and propose a Lagrangian statistical model that takes the form of a continuous time random walk (CTRW) with correlated particle velocities. In this framework, velocity distribution and velocity correlation are quantified by a Markov process of particle transition times that is characterized by a distribution function and a transition probability. Our transport model accurately captures the anomalous behavior in the breakthrough curves for both push-pull and convergent flow geometries, with the same set of parameters. Thus, the proposed correlated CTRW modeling approach provides a simple yet powerful framework for characterizing the impact of velocity distribution and correlation on transport in fractured media.

58 GEOSCIENCES↗
DOE OSTI2016

Persistence and memory timescales in root‐zone soil moisture dynamics

Abstract The memory timescale that characterizes root‐zone soil moisture remains the dominant measure in seasonal forecasts of land‐climate interactions. This memory is a quasi‐deterministic timescale associated with the losses (e.g., evapotranspiration) from the soil column and is often interpreted as persistence in soil moisture states. Persistence, however, represents a distribution of time periods where soil moisture resides above or below some prescribed threshold and is therefore inherently probabilistic. Using multiple soil moisture data sets collected at high resolution (subhourly) across different biomes and climates, this paper explores the differences, underlying dynamics, and relative importance of memory and persistence timescales in root‐zone soil moisture. A first‐order Markov process, commonly used to interpret soil moisture fluctuations derived from climate simulations, is also used as a reference model. Persistence durations of soil moisture below the plant water‐stress level (chosen as the threshold), and the temporal spectrum of upcrossings and downcrossings of this threshold, are compared to the memory timescale and spectrum of the full time series, respectively. The results indicate that despite the differences between meteorological drivers, the spectrum of threshold‐crossings is similar across sites, and follows a unique relation with that of the full soil moisture series. The distribution of persistence times exhibits an approximate stretched exponential type and reflects a likelihood of exceeding the memory at all sites. However, the rainfall counterpart of these distributions shows that persistence of dry atmospheric periods is less likely at sites with long soil moisture memory. The cluster exponent, a measure of the density of threshold‐crossings in a time frame, reveals that the clustering tendency in rainfall events (on‐off switches) does not translate directly to clustering in soil moisture. This is particularly the case in climates where rainfall and evapotranspiration are out of phase, resulting in less ordered (more independent) persistence in soil moisture than in rainfall.

Ghannam, Khaled↗
DOE OSTI2017

An exponential–gamma mixture model for extreme Santa Ana winds

We analyze the behavior of extreme winds occurring in Southern California during the Santa Ana wind season using a latent mixture model. This mixture representation is formulated as a hierarchical Bayesian model and fit using Markov chain Monte Carlo. The two‐stage model results in generalized Pareto margins for exceedances and generates temporal dependence through a latent Markov process. This construction induces asymptotic independence in the response, while allowing for dependence at extreme, but subasymptotic, levels. We compare this model with a frequentist analogue where inference is performed via maximum pairwise likelihood. We use interval censoring to account for data quantization and estimate the extremal index and probabilities of multiday occurrences of extreme Santa Ana winds over a range of high thresholds.

Bopp, Gregory P.↗
DOE OSTI2016

State Space Truncation with Quantified Errors for Accurate Solutions to Discrete Chemical Master Equation

The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEGs), we truncate the state space by limiting the total molecular copy numbers in each MEG. We further describe a theoretical framework for analysis of the truncation error in the steady-state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of (1) the birth and death model, (2) the single gene expression model, (3) the genetic toggle switch model, and (4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady-state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate our theories. Overall, the novel state space truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Interaction of a quantum field with a rotating heat bath

The linear coupling of a rotating heat bath to a quantum field is studied in the framework of the Markovian master equation for the field’s non-unitary time evolution. The bath’s rotation induces population inversion for the field’s low-energy modes. For bosons, this leads to superradiance, an irreversible process in which some of the bath’s kinetic energy is extracted by spontaneous and stimulated emission. We find the energy and entropy balance for such systems and apply our results to the theory of black hole radiation. We also comment on how this relates to classical self-oscillations, including shear flow instabilities in hydrodynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Calculating infinite-medium α-eigenvalue spectra with Monte Carlo using a transition rate matrix method

The time-dependent behavior of the energy spectrum in neutron transport was investigated with a formulation, based on continuous-time Markov processes, for computing α eigenvalues and eigenvectors in an infinite medium. In this study, a research Monte Carlo code called “TORTE” (To Obtain Real Time Eigenvalues) was created and used to estimate elements of a transition rate matrix. TORTE is capable of using both multigroup and continuous-energy nuclear data, and verification was performed. Eigenvalue spectra for infinite homogeneous mixtures were obtained, and an eigenfunction expansion was used to investigate transient behavior of the neutron energy spectrum.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Lectures on statistical mechanics

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

plasma dynamics↗
DOE OSTI2022

Computational Aspects of Single-Molecule Kinetics for Coupled Catalytic Cycles: A Spectral Analysis

Catalysis from single active sites is analyzed using methods developed from single molecule kinetics. Using a stochastic Markov state description, the observable properties of general catalytic networks of reactions are expressed using an eigenvalue decomposition of the transition matrix for the Markov process. By the use of a sensitivity analysis, the necessary eigenvalues and eigenvectors are related to the energies of controlling barriers and wells located along the reaction routes. A generalization of the energetic span theory allows the eigenvalues to be computed from several activation energies corresponding to distinct barrier-well pairings. The formalism is demonstrated accurately for model problems for a physically realistic mechanism for an alkene hydrogenation reaction on a single atom catalyst.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Controlling Complex Coacervation via Random Polyelectrolyte Sequences

The utilization of chemical sequence control in polymeric materials is key to enabling material design on par with biomacromolecular systems. One important avenue for scalable sequence-controlled polymers leverages the random copolymerization of distinct monomers, with the statistical distribution of the monomeric sequence arising from reaction kinetics following a first-order Markov process. Here we utilize the framework of the random phase approximation (RPA) to develop a theory for the phase behavior of symmetric polyelectrolyte coacervates whose chemical sequences are dictated by simple statistical distributions. We find that a high charge "blockiness" within the random sequences favors the formation of denser and more salt-resistant coacervates while simultaneously increasing the width of the two-phase region. Here, we trace these physical effects to the increased cooperativity of Coulomb interactions that results from increased charge blockiness in oppositely charged polyelectrolytes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Closed‐loop hierarchical control strategies for connected and autonomous hybrid electric vehicles with random errors

This study presents a closed‐loop hierarchical control strategy for a group of connected and autonomous hybrid electric vehicles (HEVs) with the purpose of optimising fuel economy while guaranteeing traffic mobility and vehicle safety. In the hierarchical control architecture, a decentralised stochastic model predictive control (SMPC)‐based higher level controller incorporating signal phase and timing information is formulated to optimise the velocity profile of each vehicle, and an adaptive equivalent consumption minimisation strategy based lower level controller is employed for the energy management control of the HEVs. Creatively, random errors of the control variable are considered in the SMPC framework. The errors are discretised and modelled as a Markov process and the state transition matrix of the errors is generated randomly to capture the error transition dynamics. To solve the SMPC problem more efficiently, a scenario‐based SMPC is employed. Moreover, the propulsion and recuperation efficiencies of the lower level controller are calculated at each time step with measurable variables, and fed back to the higher level controller for velocity optimisation in next time step. Simulation results validate the control effectiveness and advantages of the proposed control architecture.

Qiu, Shaolin↗