Impact of Noise on a Dynamical System: Prediction and Uncertainties from a Swarm-Optimized Neural Network.

PubMed

López-Caraballo, C H; Lazzús, J A; Salfate, I; Rojas, P; Rivera, M; Palma-Chilla, L

2015-01-01

An artificial neural network (ANN) based on particle swarm optimization (PSO) was developed for the time series prediction. The hybrid ANN+PSO algorithm was applied on Mackey-Glass chaotic time series in the short-term x(t + 6). The performance prediction was evaluated and compared with other studies available in the literature. Also, we presented properties of the dynamical system via the study of chaotic behaviour obtained from the predicted time series. Next, the hybrid ANN+PSO algorithm was complemented with a Gaussian stochastic procedure (called stochastic hybrid ANN+PSO) in order to obtain a new estimator of the predictions, which also allowed us to compute the uncertainties of predictions for noisy Mackey-Glass chaotic time series. Thus, we studied the impact of noise for several cases with a white noise level (σ(N)) from 0.01 to 0.1.

Generalized Polynomial Chaos Based Uncertainty Quantification for Planning MRgLITT Procedures

PubMed Central

Fahrenholtz, S.; Stafford, R. J.; Maier, F.; Hazle, J. D.; Fuentes, D.

2014-01-01

Purpose A generalized polynomial chaos (gPC) method is used to incorporate constitutive parameter uncertainties within the Pennes representation of bioheat transfer phenomena. The stochastic temperature predictions of the mathematical model are critically evaluated against MR thermometry data for planning MR-guided Laser Induced Thermal Therapies (MRgLITT). Methods Pennes bioheat transfer model coupled with a diffusion theory approximation of laser tissue interaction was implemented as the underlying deterministic kernel. A probabilistic sensitivity study was used to identify parameters that provide the most variance in temperature output. Confidence intervals of the temperature predictions are compared to MR temperature imaging (MRTI) obtained during phantom and in vivo canine (n=4) MRgLITT experiments. The gPC predictions were quantitatively compared to MRTI data using probabilistic linear and temporal profiles as well as 2-D 60 °C isotherms. Results Within the range of physically meaningful constitutive values relevant to the ablative temperature regime of MRgLITT, the sensitivity study indicated that the optical parameters, particularly the anisotropy factor, created the most variance in the stochastic model's output temperature prediction. Further, within the statistical sense considered, a nonlinear model of the temperature and damage dependent perfusion, absorption, and scattering is captured within the confidence intervals of the linear gPC method. Multivariate stochastic model predictions using parameters with the dominant sensitivities show good agreement with experimental MRTI data. Conclusions Given parameter uncertainties and mathematical modeling approximations of the Pennes bioheat model, the statistical framework demonstrates conservative estimates of the therapeutic heating and has potential for use as a computational prediction tool for thermal therapy planning. PMID:23692295

A Stochastic Tick-Borne Disease Model: Exploring the Probability of Pathogen Persistence.

PubMed

Maliyoni, Milliward; Chirove, Faraimunashe; Gaff, Holly D; Govinder, Keshlan S

2017-09-01

We formulate and analyse a stochastic epidemic model for the transmission dynamics of a tick-borne disease in a single population using a continuous-time Markov chain approach. The stochastic model is based on an existing deterministic metapopulation tick-borne disease model. We compare the disease dynamics of the deterministic and stochastic models in order to determine the effect of randomness in tick-borne disease dynamics. The probability of disease extinction and that of a major outbreak are computed and approximated using the multitype Galton-Watson branching process and numerical simulations, respectively. Analytical and numerical results show some significant differences in model predictions between the stochastic and deterministic models. In particular, we find that a disease outbreak is more likely if the disease is introduced by infected deer as opposed to infected ticks. These insights demonstrate the importance of host movement in the expansion of tick-borne diseases into new geographic areas.

Analytical approximations for spatial stochastic gene expression in single cells and tissues

PubMed Central

Smith, Stephen; Cianci, Claudia; Grima, Ramon

2016-01-01

Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction–diffusion master equation (RDME) describing stochastic reaction–diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction–diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues. PMID:27146686

Uncertainty-accounting environmental policy and management of water systems.

PubMed

Baresel, Christian; Destouni, Georgia

2007-05-15

Environmental policies for water quality and ecosystem management do not commonly require explicit stochastic accounts of uncertainty and risk associated with the quantification and prediction of waterborne pollutant loads and abatement effects. In this study, we formulate and investigate a possible environmental policy that does require an explicit stochastic uncertainty account. We compare both the environmental and economic resource allocation performance of such an uncertainty-accounting environmental policy with that of deterministic, risk-prone and risk-averse environmental policies under a range of different hypothetical, yet still possible, scenarios. The comparison indicates that a stochastic uncertainty-accounting policy may perform better than deterministic policies over a range of different scenarios. Even in the absence of reliable site-specific data, reported literature values appear to be useful for such a stochastic account of uncertainty.

Stochastic model stationarization by eliminating the periodic term and its effect on time series prediction

NASA Astrophysics Data System (ADS)

Moeeni, Hamid; Bonakdari, Hossein; Fatemi, Seyed Ehsan

2017-04-01

Because time series stationarization has a key role in stochastic modeling results, three methods are analyzed in this study. The methods are seasonal differencing, seasonal standardization and spectral analysis to eliminate the periodic effect on time series stationarity. First, six time series including 4 streamflow series and 2 water temperature series are stationarized. The stochastic term for these series obtained with ARIMA is subsequently modeled. For the analysis, 9228 models are introduced. It is observed that seasonal standardization and spectral analysis eliminate the periodic term completely, while seasonal differencing maintains seasonal correlation structures. The obtained results indicate that all three methods present acceptable performance overall. However, model accuracy in monthly streamflow prediction is higher with seasonal differencing than with the other two methods. Another advantage of seasonal differencing over the other methods is that the monthly streamflow is never estimated as negative. Standardization is the best method for predicting monthly water temperature although it is quite similar to seasonal differencing, while spectral analysis performed the weakest in all cases. It is concluded that for each monthly seasonal series, seasonal differencing is the best stationarization method in terms of periodic effect elimination. Moreover, the monthly water temperature is predicted with more accuracy than monthly streamflow. The criteria of the average stochastic term divided by the amplitude of the periodic term obtained for monthly streamflow and monthly water temperature were 0.19 and 0.30, 0.21 and 0.13, and 0.07 and 0.04 respectively. As a result, the periodic term is more dominant than the stochastic term for water temperature in the monthly water temperature series compared to streamflow series.

Mixed Effects Modeling Using Stochastic Differential Equations: Illustrated by Pharmacokinetic Data of Nicotinic Acid in Obese Zucker Rats.

PubMed

Leander, Jacob; Almquist, Joachim; Ahlström, Christine; Gabrielsson, Johan; Jirstrand, Mats

2015-05-01

Inclusion of stochastic differential equations in mixed effects models provides means to quantify and distinguish three sources of variability in data. In addition to the two commonly encountered sources, measurement error and interindividual variability, we also consider uncertainty in the dynamical model itself. To this end, we extend the ordinary differential equation setting used in nonlinear mixed effects models to include stochastic differential equations. The approximate population likelihood is derived using the first-order conditional estimation with interaction method and extended Kalman filtering. To illustrate the application of the stochastic differential mixed effects model, two pharmacokinetic models are considered. First, we use a stochastic one-compartmental model with first-order input and nonlinear elimination to generate synthetic data in a simulated study. We show that by using the proposed method, the three sources of variability can be successfully separated. If the stochastic part is neglected, the parameter estimates become biased, and the measurement error variance is significantly overestimated. Second, we consider an extension to a stochastic pharmacokinetic model in a preclinical study of nicotinic acid kinetics in obese Zucker rats. The parameter estimates are compared between a deterministic and a stochastic NiAc disposition model, respectively. Discrepancies between model predictions and observations, previously described as measurement noise only, are now separated into a comparatively lower level of measurement noise and a significant uncertainty in model dynamics. These examples demonstrate that stochastic differential mixed effects models are useful tools for identifying incomplete or inaccurate model dynamics and for reducing potential bias in parameter estimates due to such model deficiencies.

Incorporating Wind Power Forecast Uncertainties Into Stochastic Unit Commitment Using Neural Network-Based Prediction Intervals.

PubMed

Quan, Hao; Srinivasan, Dipti; Khosravi, Abbas

2015-09-01

Penetration of renewable energy resources, such as wind and solar power, into power systems significantly increases the uncertainties on system operation, stability, and reliability in smart grids. In this paper, the nonparametric neural network-based prediction intervals (PIs) are implemented for forecast uncertainty quantification. Instead of a single level PI, wind power forecast uncertainties are represented in a list of PIs. These PIs are then decomposed into quantiles of wind power. A new scenario generation method is proposed to handle wind power forecast uncertainties. For each hour, an empirical cumulative distribution function (ECDF) is fitted to these quantile points. The Monte Carlo simulation method is used to generate scenarios from the ECDF. Then the wind power scenarios are incorporated into a stochastic security-constrained unit commitment (SCUC) model. The heuristic genetic algorithm is utilized to solve the stochastic SCUC problem. Five deterministic and four stochastic case studies incorporated with interval forecasts of wind power are implemented. The results of these cases are presented and discussed together. Generation costs, and the scheduled and real-time economic dispatch reserves of different unit commitment strategies are compared. The experimental results show that the stochastic model is more robust than deterministic ones and, thus, decreases the risk in system operations of smart grids.

Site correction of stochastic simulation in southwestern Taiwan

NASA Astrophysics Data System (ADS)

Lun Huang, Cong; Wen, Kuo Liang; Huang, Jyun Yan

2014-05-01

Peak ground acceleration (PGA) of a disastrous earthquake, is concerned both in civil engineering and seismology study. Presently, the ground motion prediction equation is widely used for PGA estimation study by engineers. However, the local site effect is another important factor participates in strong motion prediction. For example, in 1985 the Mexico City, 400km far from the epicenter, suffered massive damage due to the seismic wave amplification from the local alluvial layers. (Anderson et al., 1986) In past studies, the use of stochastic method had been done and showed well performance on the simulation of ground-motion at rock site (Beresnev and Atkinson, 1998a ; Roumelioti and Beresnev, 2003). In this study, the site correction was conducted by the empirical transfer function compared with the rock site response from stochastic point-source (Boore, 2005) and finite-fault (Boore, 2009) methods. The error between the simulated and observed Fourier spectrum and PGA are calculated. Further we compared the estimated PGA to the result calculated from ground motion prediction equation. The earthquake data used in this study is recorded by Taiwan Strong Motion Instrumentation Program (TSMIP) from 1991 to 2012; the study area is located at south-western Taiwan. The empirical transfer function was generated by calculating the spectrum ratio between alluvial site and rock site (Borcheret, 1970). Due to the lack of reference rock site station in this area, the rock site ground motion was generated through stochastic point-source model instead. Several target events were then chosen for stochastic point-source simulating to the halfspace. Then, the empirical transfer function for each station was multiplied to the simulated halfspace response. Finally, we focused on two target events: the 1999 Chi-Chi earthquake (Mw=7.6) and the 2010 Jiashian earthquake (Mw=6.4). Considering the large event may contain with complex rupture mechanism, the asperity and delay time for each sub-fault is to be concerned. Both the stochastic point-source and the finite-fault model were used to check the result of our correction.

Comparison of linear–stochastic and nonlinear–deterministic algorithms in the analysis of 15-minute clinical ECGs to predict risk of arrhythmic death

PubMed Central

Skinner, James E; Meyer, Michael; Nester, Brian A; Geary, Una; Taggart, Pamela; Mangione, Antoinette; Ramalanjaona, George; Terregino, Carol; Dalsey, William C

2009-01-01

Objective: Comparative algorithmic evaluation of heartbeat series in low-to-high risk cardiac patients for the prospective prediction of risk of arrhythmic death (AD). Background: Heartbeat variation reflects cardiac autonomic function and risk of AD. Indices based on linear stochastic models are independent risk factors for AD in post-myocardial infarction (post-MI) cohorts. Indices based on nonlinear deterministic models have superior predictability in retrospective data. Methods: Patients were enrolled (N = 397) in three emergency departments upon presenting with chest pain and were determined to be at low-to-high risk of acute MI (>7%). Brief ECGs were recorded (15 min) and R-R intervals assessed by three nonlinear algorithms (PD2i, DFA, and ApEn) and four conventional linear-stochastic measures (SDNN, MNN, 1/f-Slope, LF/HF). Out-of-hospital AD was determined by modified Hinkle–Thaler criteria. Results: All-cause mortality at one-year follow-up was 10.3%, with 7.7% adjudicated to be AD. The sensitivity and relative risk for predicting AD was highest at all time-points for the nonlinear PD2i algorithm (p ≤0.001). The sensitivity at 30 days was 100%, specificity 58%, and relative risk >100 (p ≤0.001); sensitivity at 360 days was 95%, specificity 58%, and relative risk >11.4 (p ≤0.001). Conclusions: Heartbeat analysis by the time-dependent nonlinear PD2i algorithm is comparatively the superior test. PMID:19707283

A Unified Statistical Rain-Attenuation Model for Communication Link Fade Predictions and Optimal Stochastic Fade Control Design Using a Location-Dependent Rain-Statistic Database

NASA Technical Reports Server (NTRS)

Manning, Robert M.

1990-01-01

A static and dynamic rain-attenuation model is presented which describes the statistics of attenuation on an arbitrarily specified satellite link for any location for which there are long-term rainfall statistics. The model may be used in the design of the optimal stochastic control algorithms to mitigate the effects of attenuation and maintain link reliability. A rain-statistics data base is compiled, which makes it possible to apply the model to any location in the continental U.S. with a resolution of 0-5 degrees in latitude and longitude. The model predictions are compared with experimental observations, showing good agreement.

Minimizing the stochasticity of halos in large-scale structure surveys

NASA Astrophysics Data System (ADS)

Hamaus, Nico; Seljak, Uroš; Desjacques, Vincent; Smith, Robert E.; Baldauf, Tobias

2010-08-01

In recent work (Seljak, Hamaus, and Desjacques 2009) it was found that weighting central halo galaxies by halo mass can significantly suppress their stochasticity relative to the dark matter, well below the Poisson model expectation. This is useful for constraining relations between galaxies and the dark matter, such as the galaxy bias, especially in situations where sampling variance errors can be eliminated. In this paper we extend this study with the goal of finding the optimal mass-dependent halo weighting. We use N-body simulations to perform a general analysis of halo stochasticity and its dependence on halo mass. We investigate the stochasticity matrix, defined as Cij≡⟨(δi-biδm)(δj-bjδm)⟩, where δm is the dark matter overdensity in Fourier space, δi the halo overdensity of the i-th halo mass bin, and bi the corresponding halo bias. In contrast to the Poisson model predictions we detect nonvanishing correlations between different mass bins. We also find the diagonal terms to be sub-Poissonian for the highest-mass halos. The diagonalization of this matrix results in one large and one low eigenvalue, with the remaining eigenvalues close to the Poisson prediction 1/n¯, where n¯ is the mean halo number density. The eigenmode with the lowest eigenvalue contains most of the information and the corresponding eigenvector provides an optimal weighting function to minimize the stochasticity between halos and dark matter. We find this optimal weighting function to match linear mass weighting at high masses, while at the low-mass end the weights approach a constant whose value depends on the low-mass cut in the halo mass function. This weighting further suppresses the stochasticity as compared to the previously explored mass weighting. Finally, we employ the halo model to derive the stochasticity matrix and the scale-dependent bias from an analytical perspective. It is remarkably successful in reproducing our numerical results and predicts that the stochasticity between halos and the dark matter can be reduced further when going to halo masses lower than we can resolve in current simulations.

Predicting the stochastic guiding of kinesin-driven microtubules in microfabricated tracks: a statistical-mechanics-based modeling approach.

PubMed

Lin, Chih-Tin; Meyhofer, Edgar; Kurabayashi, Katsuo

2010-01-01

Directional control of microtubule shuttles via microfabricated tracks is key to the development of controlled nanoscale mass transport by kinesin motor molecules. Here we develop and test a model to quantitatively predict the stochastic behavior of microtubule guiding when they mechanically collide with the sidewalls of lithographically patterned tracks. By taking into account appropriate probability distributions of microscopic states of the microtubule system, the model allows us to theoretically analyze the roles of collision conditions and kinesin surface densities in determining how the motion of microtubule shuttles is controlled. In addition, we experimentally observe the statistics of microtubule collision events and compare our theoretical prediction with experimental data to validate our model. The model will direct the design of future hybrid nanotechnology devices that integrate nanoscale transport systems powered by kinesin-driven molecular shuttles.

Development and validation of a stochastic model for potential growth of Listeria monocytogenes in naturally contaminated lightly preserved seafood.

PubMed

Mejlholm, Ole; Bøknæs, Niels; Dalgaard, Paw

2015-02-01

A new stochastic model for the simultaneous growth of Listeria monocytogenes and lactic acid bacteria (LAB) was developed and validated on data from naturally contaminated samples of cold-smoked Greenland halibut (CSGH) and cold-smoked salmon (CSS). During industrial processing these samples were added acetic and/or lactic acids. The stochastic model was developed from an existing deterministic model including the effect of 12 environmental parameters and microbial interaction (O. Mejlholm and P. Dalgaard, Food Microbiology, submitted for publication). Observed maximum population density (MPD) values of L. monocytogenes in naturally contaminated samples of CSGH and CSS were accurately predicted by the stochastic model based on measured variability in product characteristics and storage conditions. Results comparable to those from the stochastic model were obtained, when product characteristics of the least and most preserved sample of CSGH and CSS were used as input for the existing deterministic model. For both modelling approaches, it was shown that lag time and the effect of microbial interaction needs to be included to accurately predict MPD values of L. monocytogenes. Addition of organic acids to CSGH and CSS was confirmed as a suitable mitigation strategy against the risk of growth by L. monocytogenes as both types of products were in compliance with the EU regulation on ready-to-eat foods. Copyright © 2014 Elsevier Ltd. All rights reserved.

Stochastic does not equal ad hoc. [theories of lunar origin

NASA Technical Reports Server (NTRS)

Hartmann, W. K.

1984-01-01

Some classes of influential events in solar system history are class-predictable but not event-predictable. Theories of lunar origin should not ignore class-predictable stochastic events. Impacts and close encounters with large objects during planet formation are class-predictable. These stochastic events, such as large impacts that triggered ejection of Earth-mantle material into a circum-Earth cloud, should not be rejected as ad hoc. A way to deal with such events scientifically is to investigate their consequences; if it can be shown that they might produce the Moon, they become viable concepts in theories of lunar origin.

Inducing Tropical Cyclones to Undergo Brownian Motion

NASA Astrophysics Data System (ADS)

Hodyss, D.; McLay, J.; Moskaitis, J.; Serra, E.

2014-12-01

Stochastic parameterization has become commonplace in numerical weather prediction (NWP) models used for probabilistic prediction. Here, a specific stochastic parameterization will be related to the theory of stochastic differential equations and shown to be affected strongly by the choice of stochastic calculus. From an NWP perspective our focus will be on ameliorating a common trait of the ensemble distributions of tropical cyclone (TC) tracks (or position), namely that they generally contain a bias and an underestimate of the variance. With this trait in mind we present a stochastic track variance inflation parameterization. This parameterization makes use of a properly constructed stochastic advection term that follows a TC and induces its position to undergo Brownian motion. A central characteristic of Brownian motion is that its variance increases with time, which allows for an effective inflation of an ensemble's TC track variance. Using this stochastic parameterization we present a comparison of the behavior of TCs from the perspective of the stochastic calculi of Itô and Stratonovich within an operational NWP model. The central difference between these two perspectives as pertains to TCs is shown to be properly predicted by the stochastic calculus and the Itô correction. In the cases presented here these differences will manifest as overly intense TCs, which, depending on the strength of the forcing, could lead to problems with numerical stability and physical realism.

Dependence of Perpendicular Viscosity on Magnetic Fluctuations in a Stochastic Topology

NASA Astrophysics Data System (ADS)

Fridström, R.; Chapman, B. E.; Almagri, A. F.; Frassinetti, L.; Brunsell, P. R.; Nishizawa, T.; Sarff, J. S.

2018-06-01

In a magnetically confined plasma with a stochastic magnetic field, the dependence of the perpendicular viscosity on the magnetic fluctuation amplitude is measured for the first time. With a controlled, ˜ tenfold variation in the fluctuation amplitude, the viscosity increases ˜100 -fold, exhibiting the same fluctuation-amplitude-squared dependence as the predicted rate of stochastic field line diffusion. The absolute value of the viscosity is well predicted by a model based on momentum transport in a stochastic field, the first in-depth test of this model.

Responses to single photons in visual cells of Limulus

PubMed Central

Borsellino, A.; Fuortes, M. G. F.

1968-01-01

1. A system proposed in a previous article as a model of responses of visual cells has been analysed with the purpose of predicting the features of responses to single absorbed photons. 2. As a result of this analysis, the stochastic variability of responses has been expressed as a function of the amplification of the system. 3. The theoretical predictions have been compared to the results obtained by recording electrical responses of visual cells of Limulus to flashes delivering only few photons. 4. Experimental responses to single photons have been tentatively identified and it was shown that the stochastic variability of these responses is similar to that predicted for a model with a multiplication factor of at least twenty-five. 5. These results lead to the conclusion that the processes responsible for visual responses incorporate some form of amplification. This conclusion may prove useful for identifying the physical mechanisms underlying the transducer action of visual cells. PMID:5664231

Forecasting stochastic neural network based on financial empirical mode decomposition.

PubMed

Wang, Jie; Wang, Jun

2017-06-01

In an attempt to improve the forecasting accuracy of stock price fluctuations, a new one-step-ahead model is developed in this paper which combines empirical mode decomposition (EMD) with stochastic time strength neural network (STNN). The EMD is a processing technique introduced to extract all the oscillatory modes embedded in a series, and the STNN model is established for considering the weight of occurrence time of the historical data. The linear regression performs the predictive availability of the proposed model, and the effectiveness of EMD-STNN is revealed clearly through comparing the predicted results with the traditional models. Moreover, a new evaluated method (q-order multiscale complexity invariant distance) is applied to measure the predicted results of real stock index series, and the empirical results show that the proposed model indeed displays a good performance in forecasting stock market fluctuations. Copyright © 2017 Elsevier Ltd. All rights reserved.

Improved ensemble-mean forecasting of ENSO events by a zero-mean stochastic error model of an intermediate coupled model

NASA Astrophysics Data System (ADS)

Zheng, Fei; Zhu, Jiang

2017-04-01

How to design a reliable ensemble prediction strategy with considering the major uncertainties of a forecasting system is a crucial issue for performing an ensemble forecast. In this study, a new stochastic perturbation technique is developed to improve the prediction skills of El Niño-Southern Oscillation (ENSO) through using an intermediate coupled model. We first estimate and analyze the model uncertainties from the ensemble Kalman filter analysis results through assimilating the observed sea surface temperatures. Then, based on the pre-analyzed properties of model errors, we develop a zero-mean stochastic model-error model to characterize the model uncertainties mainly induced by the missed physical processes of the original model (e.g., stochastic atmospheric forcing, extra-tropical effects, Indian Ocean Dipole). Finally, we perturb each member of an ensemble forecast at each step by the developed stochastic model-error model during the 12-month forecasting process, and add the zero-mean perturbations into the physical fields to mimic the presence of missing processes and high-frequency stochastic noises. The impacts of stochastic model-error perturbations on ENSO deterministic predictions are examined by performing two sets of 21-yr hindcast experiments, which are initialized from the same initial conditions and differentiated by whether they consider the stochastic perturbations. The comparison results show that the stochastic perturbations have a significant effect on improving the ensemble-mean prediction skills during the entire 12-month forecasting process. This improvement occurs mainly because the nonlinear terms in the model can form a positive ensemble-mean from a series of zero-mean perturbations, which reduces the forecasting biases and then corrects the forecast through this nonlinear heating mechanism.

On the comparison of stochastic model predictive control strategies applied to a hydrogen-based microgrid

NASA Astrophysics Data System (ADS)

Velarde, P.; Valverde, L.; Maestre, J. M.; Ocampo-Martinez, C.; Bordons, C.

2017-03-01

In this paper, a performance comparison among three well-known stochastic model predictive control approaches, namely, multi-scenario, tree-based, and chance-constrained model predictive control is presented. To this end, three predictive controllers have been designed and implemented in a real renewable-hydrogen-based microgrid. The experimental set-up includes a PEM electrolyzer, lead-acid batteries, and a PEM fuel cell as main equipment. The real experimental results show significant differences from the plant components, mainly in terms of use of energy, for each implemented technique. Effectiveness, performance, advantages, and disadvantages of these techniques are extensively discussed and analyzed to give some valid criteria when selecting an appropriate stochastic predictive controller.

Financial Time Series Prediction Using Elman Recurrent Random Neural Networks

PubMed Central

Wang, Jie; Wang, Jun; Fang, Wen; Niu, Hongli

2016-01-01

In recent years, financial market dynamics forecasting has been a focus of economic research. To predict the price indices of stock markets, we developed an architecture which combined Elman recurrent neural networks with stochastic time effective function. By analyzing the proposed model with the linear regression, complexity invariant distance (CID), and multiscale CID (MCID) analysis methods and taking the model compared with different models such as the backpropagation neural network (BPNN), the stochastic time effective neural network (STNN), and the Elman recurrent neural network (ERNN), the empirical results show that the proposed neural network displays the best performance among these neural networks in financial time series forecasting. Further, the empirical research is performed in testing the predictive effects of SSE, TWSE, KOSPI, and Nikkei225 with the established model, and the corresponding statistical comparisons of the above market indices are also exhibited. The experimental results show that this approach gives good performance in predicting the values from the stock market indices. PMID:27293423

Financial Time Series Prediction Using Elman Recurrent Random Neural Networks.

PubMed

Wang, Jie; Wang, Jun; Fang, Wen; Niu, Hongli

2016-01-01

In recent years, financial market dynamics forecasting has been a focus of economic research. To predict the price indices of stock markets, we developed an architecture which combined Elman recurrent neural networks with stochastic time effective function. By analyzing the proposed model with the linear regression, complexity invariant distance (CID), and multiscale CID (MCID) analysis methods and taking the model compared with different models such as the backpropagation neural network (BPNN), the stochastic time effective neural network (STNN), and the Elman recurrent neural network (ERNN), the empirical results show that the proposed neural network displays the best performance among these neural networks in financial time series forecasting. Further, the empirical research is performed in testing the predictive effects of SSE, TWSE, KOSPI, and Nikkei225 with the established model, and the corresponding statistical comparisons of the above market indices are also exhibited. The experimental results show that this approach gives good performance in predicting the values from the stock market indices.

Stochastic Growth Theory of Type 3 Solar Radio Emission

NASA Technical Reports Server (NTRS)

Robinson, P. A.; Carins, I. H.

1993-01-01

The recently developed stochastic growth theory of type 3 radio sources is extended to predict their electromagnetic volume emissivities and brightness temperatures. Predicted emissivities are consistent with spacecraft observations and independent theoretical constraints.

The Stochastic predictability limits of GCM internal variability and the Stochastic Seasonal to Interannual Prediction System (StocSIPS)

NASA Astrophysics Data System (ADS)

Del Rio Amador, Lenin; Lovejoy, Shaun

2017-04-01

Over the past ten years, a key advance in our understanding of atmospheric variability is the discovery that between the weather and climate regime lies an intermediate "macroweather" regime, spanning the range of scales from ≈10 days to ≈30 years. Macroweather statistics are characterized by two fundamental symmetries: scaling and the factorization of the joint space-time statistics. In the time domain, the scaling has low intermittency with the additional property that successive fluctuations tend to cancel. In space, on the contrary the scaling has high (multifractal) intermittency corresponding to the existence of different climate zones. These properties have fundamental implications for macroweather forecasting: a) the temporal scaling implies that the system has a long range memory that can be exploited for forecasting; b) the low temporal intermittency implies that mathematically well-established (Gaussian) forecasting techniques can be used; and c), the statistical factorization property implies that although spatial correlations (including teleconnections) may be large, if long enough time series are available, they are not necessarily useful in improving forecasts. Theoretically, these conditions imply the existence of stochastic predictability limits in our talk, we show that these limits apply to GCM's. Based on these statistical implications, we developed the Stochastic Seasonal and Interannual Prediction System (StocSIPS) for the prediction of temperature from regional to global scales and from one month to many years horizons. One of the main components of StocSIPS is the separation and prediction of both the internal and externally forced variabilities. In order to test the theoretical assumptions and consequences for predictability and predictions, we use 41 different CMIP5 model outputs from preindustrial control runs that have fixed external forcings: whose variability is purely internally generated. We first show that these statistical assumptions hold with relatively good accuracy and then we performed hindcasts at global and regional scales from monthly to annual time resolutions using StocSIPS. We obtained excellent agreement between the hindcast Mean Square Skill Score (MSSS) and the theoretical stochastic limits. We also show the application of StocSIPS to the prediction of average global temperature and compare our results with those obtained using multi-model ensemble approaches. StocSIPS has numerous advantages including a) higher MSSS for large time horizons, b) the from convergence to the real - not model - climate, c) much higher computational speed, d) no need for data assimilation, e) no ad hoc post processing and f) no need for downscaling.

Quantum Stochastic Trajectories: The Fokker-Planck-Bohm Equation Driven by the Reduced Density Matrix.

PubMed

Avanzini, Francesco; Moro, Giorgio J

2018-03-15

The quantum molecular trajectory is the deterministic trajectory, arising from the Bohm theory, that describes the instantaneous positions of the nuclei of molecules by assuring the agreement with the predictions of quantum mechanics. Therefore, it provides the suitable framework for representing the geometry and the motions of molecules without neglecting their quantum nature. However, the quantum molecular trajectory is extremely demanding from the computational point of view, and this strongly limits its applications. To overcome such a drawback, we derive a stochastic representation of the quantum molecular trajectory, through projection operator techniques, for the degrees of freedom of an open quantum system. The resulting Fokker-Planck operator is parametrically dependent upon the reduced density matrix of the open system. Because of the pilot role played by the reduced density matrix, this stochastic approach is able to represent accurately the main features of the open system motions both at equilibrium and out of equilibrium with the environment. To verify this procedure, the predictions of the stochastic and deterministic representation are compared for a model system of six interacting harmonic oscillators, where one oscillator is taken as the open quantum system of interest. The undeniable advantage of the stochastic approach is that of providing a simplified and self-contained representation of the dynamics of the open system coordinates. Furthermore, it can be employed to study the out of equilibrium dynamics and the relaxation of quantum molecular motions during photoinduced processes, like photoinduced conformational changes and proton transfers.

Stochasticity of bacterial attachment and its predictability by the extended derjaguin-landau-verwey-overbeek theory.

PubMed

Chia, Teck Wah R; Nguyen, Vu Tuan; McMeekin, Thomas; Fegan, Narelle; Dykes, Gary A

2011-06-01

Bacterial attachment onto materials has been suggested to be stochastic by some authors but nonstochastic and based on surface properties by others. We investigated this by attaching pairwise combinations of two Salmonella enterica serovar Sofia (S. Sofia) strains (with different physicochemical and attachment properties) with one strain each of S. enterica serovar Typhimurium, S. enterica serovar Infantis, or S. enterica serovar Virchow (all with similar physicochemical and attachment abilities) in ratios of 0.428, 1, and 2.333 onto glass, stainless steel, Teflon, and polysulfone. Attached bacterial cells were recovered and counted. If the ratio of attached cells of each Salmonella serovar pair recovered was the same as the initial inoculum ratio, the attachment process was deemed stochastic. Experimental outcomes from the study were compared to those predicted by the extended Derjaguin-Landau-Verwey-Overbeek (XDLVO) theory. Significant differences (P < 0.05) between the initial and the attached ratios for serovar pairs containing S. Sofia S1296a for all different ratios were apparent for all materials. For S. Sofia S1635-containing pairs, 7 out of 12 combinations of serovar pairs and materials had attachment ratios not significantly different (P > 0.05) from the initial ratio of 0.428. Five out of 12 and 10 out of 12 samples had attachment ratios not significantly different (P > 0.05) from the initial ratios of 1 and 2.333, respectively. These results demonstrate that bacterial attachment to different materials is likely to be nonstochastic only when the key physicochemical properties of the bacteria were significantly different (P < 0.05) from each other. XDLVO theory could successfully predict the attachment of some individual isolates to particular materials but could not be used to predict the likelihood of stochasticity in pairwise attachment experiments.

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

PubMed

Fakir, Hatim; Hlatky, Lynn; Li, Huamin; Sachs, Rainer

2013-12-01

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. 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. 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. 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.

Robust and Adaptive Online Time Series Prediction with Long Short-Term Memory

PubMed Central

Tao, Qing

2017-01-01

Online time series prediction is the mainstream method in a wide range of fields, ranging from speech analysis and noise cancelation to stock market analysis. However, the data often contains many outliers with the increasing length of time series in real world. These outliers can mislead the learned model if treated as normal points in the process of prediction. To address this issue, in this paper, we propose a robust and adaptive online gradient learning method, RoAdam (Robust Adam), for long short-term memory (LSTM) to predict time series with outliers. This method tunes the learning rate of the stochastic gradient algorithm adaptively in the process of prediction, which reduces the adverse effect of outliers. It tracks the relative prediction error of the loss function with a weighted average through modifying Adam, a popular stochastic gradient method algorithm for training deep neural networks. In our algorithm, the large value of the relative prediction error corresponds to a small learning rate, and vice versa. The experiments on both synthetic data and real time series show that our method achieves better performance compared to the existing methods based on LSTM. PMID:29391864

Robust and Adaptive Online Time Series Prediction with Long Short-Term Memory.

PubMed

Yang, Haimin; Pan, Zhisong; Tao, Qing

2017-01-01

Online time series prediction is the mainstream method in a wide range of fields, ranging from speech analysis and noise cancelation to stock market analysis. However, the data often contains many outliers with the increasing length of time series in real world. These outliers can mislead the learned model if treated as normal points in the process of prediction. To address this issue, in this paper, we propose a robust and adaptive online gradient learning method, RoAdam (Robust Adam), for long short-term memory (LSTM) to predict time series with outliers. This method tunes the learning rate of the stochastic gradient algorithm adaptively in the process of prediction, which reduces the adverse effect of outliers. It tracks the relative prediction error of the loss function with a weighted average through modifying Adam, a popular stochastic gradient method algorithm for training deep neural networks. In our algorithm, the large value of the relative prediction error corresponds to a small learning rate, and vice versa. The experiments on both synthetic data and real time series show that our method achieves better performance compared to the existing methods based on LSTM.

Thermal and Driven Stochastic Growth of Langmuir Waves in the Solar Wind and Earth's Foreshock

NASA Technical Reports Server (NTRS)

Cairns, Iver H.; Robinson, P. A.; Anderson, R. R.

2000-01-01

Statistical distributions of Langmuir wave fields in the solar wind and the edge of Earth's foreshock are analyzed and compared with predictions for stochastic growth theory (SGT). SGT quantitatively explains the solar wind, edge, and deep foreshock data as pure thermal waves, driven thermal waves subject to net linear growth and stochastic effects, and as waves in a pure SGT state, respectively, plus radiation near the plasma frequency f(sub p). These changes are interpreted in terms of spatial variations in the beam instability's growth rate and evolution toward a pure SGT state. SGT analyses of field distributions are shown to provide a viable alternative to thermal noise spectroscopy for wave instruments with coarse frequency resolution, and to separate f(sub p) radiation from Langmuir waves.

GW150914: Implications for the Stochastic Gravitational-Wave Background from Binary Black Holes

NASA Astrophysics Data System (ADS)

Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Aiello, L.; Ain, A.; Ajith, P.; Allen, B.; Allocca, A.; Altin, P. A.; Anderson, S. B.; Anderson, W. G.; Arai, K.; Araya, M. C.; Arceneaux, C. C.; Areeda, J. S.; Arnaud, N.; Arun, K. G.; Ascenzi, S.; Ashton, G.; Ast, M.; Aston, S. M.; Astone, P.; Aufmuth, P.; Aulbert, C.; Babak, S.; Bacon, P.; Bader, M. K. M.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Barayoga, J. C.; Barclay, S. E.; Barish, B. C.; Barker, D.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barta, D.; Bartlett, J.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Baune, C.; Bavigadda, V.; Bazzan, M.; Behnke, B.; Bejger, M.; Bell, A. S.; Bell, C. J.; Berger, B. K.; Bergman, J.; Bergmann, G.; Berry, C. P. L.; Bersanetti, D.; Bertolini, A.; Betzwieser, J.; Bhagwat, S.; Bhandare, R.; Bilenko, I. A.; Billingsley, G.; Birch, J.; Birney, R.; Biscans, S.; Bisht, A.; Bitossi, M.; Biwer, C.; Bizouard, M. A.; Blackburn, J. K.; Blair, C. D.; Blair, D. G.; Blair, R. M.; Bloemen, S.; Bock, O.; Bodiya, T. P.; Boer, M.; Bogaert, G.; Bogan, C.; Bohe, A.; Bojtos, P.; Bond, C.; Bondu, F.; Bonnand, R.; Boom, B. A.; Bork, R.; Boschi, V.; Bose, S.; Bouffanais, Y.; Bozzi, A.; Bradaschia, C.; Brady, P. R.; Braginsky, V. B.; Branchesi, M.; Brau, J. E.; Briant, T.; Brillet, A.; Brinkmann, M.; Brisson, V.; Brockill, P.; Brooks, A. F.; Brown, D. D.; Brown, N. M.; Buchanan, C. C.; Buikema, A.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Buskulic, D.; Buy, C.; Byer, R. L.; Cadonati, L.; Cagnoli, G.; Cahillane, C.; Bustillo, J. Calderón; Callister, T.; Calloni, E.; Camp, J. B.; Cannon, K. C.; Cao, J.; Capano, C. D.; Capocasa, E.; Carbognani, F.; Caride, S.; Diaz, J. Casanueva; Casentini, C.; Caudill, S.; Cavaglià, M.; Cavalier, F.; Cavalieri, R.; Cella, G.; Cepeda, C. B.; Baiardi, L. Cerboni; Cerretani, G.; Cesarini, E.; Chakraborty, R.; Chalermsongsak, T.; Chamberlin, S. J.; Chan, M.; Chao, S.; Charlton, P.; Chassande-Mottin, E.; Chen, H. Y.; Chen, Y.; Cheng, C.; Chincarini, A.; Chiummo, A.; Cho, H. S.; Cho, M.; Chow, J. H.; Christensen, N.; Chu, Q.; Chua, S.; Chung, S.; Ciani, G.; Clara, F.; Clark, J. A.; Cleva, F.; Coccia, E.; Cohadon, P.-F.; Colla, A.; Collette, C. G.; Cominsky, L.; Constancio, M.; Conte, A.; Conti, L.; Cook, D.; Corbitt, T. R.; Cornish, N.; Corsi, A.; Cortese, S.; Costa, C. A.; Coughlin, M. W.; Coughlin, S. B.; Coulon, J.-P.; Countryman, S. T.; Couvares, P.; Cowan, E. E.; Coward, D. M.; Cowart, M. J.; Coyne, D. C.; Coyne, R.; Craig, K.; Creighton, J. D. E.; Cripe, J.; Crowder, S. G.; Cumming, A.; Cunningham, L.; Cuoco, E.; Canton, T. Dal; Danilishin, S. L.; D'Antonio, S.; Danzmann, K.; Darman, N. S.; Dattilo, V.; Dave, I.; Daveloza, H. P.; Davier, M.; Davies, G. S.; Daw, E. J.; Day, R.; DeBra, D.; Debreczeni, G.; Degallaix, J.; De Laurentis, M.; Deléglise, S.; Del Pozzo, W.; Denker, T.; Dent, T.; Dereli, H.; Dergachev, V.; DeRosa, R. T.; De Rosa, R.; DeSalvo, R.; Dhurandhar, S.; Díaz, M. C.; Di Fiore, L.; Di Giovanni, M.; Di Lieto, A.; Di Pace, S.; Di Palma, I.; Di Virgilio, A.; Dojcinoski, G.; Dolique, V.; Donovan, F.; Dooley, K. L.; Doravari, S.; Douglas, R.; Downes, T. P.; Drago, M.; Drever, R. W. P.; Driggers, J. C.; Du, Z.; Ducrot, M.; Dwyer, S. E.; Edo, T. B.; Edwards, M. C.; Effler, A.; Eggenstein, H.-B.; Ehrens, P.; Eichholz, J.; Eikenberry, S. S.; Engels, W.; Essick, R. C.; Etzel, T.; Evans, M.; Evans, T. M.; Everett, R.; Factourovich, M.; Fafone, V.; Fair, H.; Fairhurst, S.; Fan, X.; Fang, Q.; Farinon, S.; Farr, B.; Farr, W. M.; Favata, M.; Fays, M.; Fehrmann, H.; Fejer, M. M.; Ferrante, I.; Ferreira, E. C.; Ferrini, F.; Fidecaro, F.; Fiori, I.; Fiorucci, D.; Fisher, R. P.; Flaminio, R.; Fletcher, M.; Fournier, J.-D.; Franco, S.; Frasca, S.; Frasconi, F.; Frei, Z.; Freise, A.; Frey, R.; Frey, V.; Fricke, T. T.; Fritschel, P.; Frolov, V. V.; Fulda, P.; Fyffe, M.; Gabbard, H. A. G.; Gair, J. R.; Gammaitoni, L.; Gaonkar, S. G.; Garufi, F.; Gatto, A.; Gaur, G.; Gehrels, N.; Gemme, G.; Gendre, B.; Genin, E.; Gennai, A.; George, J.; Gergely, L.; Germain, V.; Ghosh, Archisman; Ghosh, S.; Giaime, J. A.; Giardina, K. D.; Giazotto, A.; Gill, K.; Glaefke, A.; Goetz, E.; Goetz, R.; Gondan, L.; González, G.; Castro, J. M. Gonzalez; Gopakumar, A.; Gordon, N. A.; Gorodetsky, M. L.; Gossan, S. E.; Gosselin, M.; Gouaty, R.; Graef, C.; Graff, P. B.; Granata, M.; Grant, A.; Gras, S.; Gray, C.; Greco, G.; Green, A. C.; Groot, P.; Grote, H.; Grunewald, S.; Guidi, G. M.; Guo, X.; Gupta, A.; Gupta, M. K.; Gushwa, K. E.; Gustafson, E. K.; Gustafson, R.; Hacker, J. J.; Hall, B. R.; Hall, E. D.; Hammond, G.; Haney, M.; Hanke, M. M.; Hanks, J.; Hanna, C.; Hannam, M. D.; Hanson, J.; Hardwick, T.; Haris, K.; Harms, J.; Harry, G. M.; Harry, I. W.; Hart, M. J.; Hartman, M. T.; Haster, C.-J.; Haughian, K.; Heidmann, A.; Heintze, M. C.; Heitmann, H.; Hello, P.; Hemming, G.; Hendry, M.; Heng, I. S.; Hennig, J.; Heptonstall, A. W.; Heurs, M.; Hild, S.; Hoak, D.; Hodge, K. A.; Hofman, D.; Hollitt, S. E.; Holt, K.; Holz, D. E.; Hopkins, P.; Hosken, D. J.; Hough, J.; Houston, E. A.; Howell, E. J.; Hu, Y. M.; Huang, S.; Huerta, E. A.; Huet, D.; Hughey, B.; Husa, S.; Huttner, S. H.; Huynh-Dinh, T.; Idrisy, A.; Indik, N.; Ingram, D. R.; Inta, R.; Isa, H. N.; Isac, J.-M.; Isi, M.; Islas, G.; Isogai, T.; Iyer, B. R.; Izumi, K.; Jacqmin, T.; Jang, H.; Jani, K.; Jaranowski, P.; Jawahar, S.; Jiménez-Forteza, F.; Johnson, W. W.; Jones, D. I.; Jones, R.; Jonker, R. J. G.; Ju, L.; Kalaghatgi, C. V.; Kalogera, V.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Karki, S.; Kasprzack, M.; Katsavounidis, E.; Katzman, W.; Kaufer, S.; Kaur, T.; Kawabe, K.; Kawazoe, F.; Kéfélian, F.; Kehl, M. S.; Keitel, D.; Kelley, D. B.; Kells, W.; Kennedy, R.; Key, J. S.; Khalaidovski, A.; Khalili, F. Y.; Khan, I.; Khan, S.; Khan, Z.; Khazanov, E. A.; Kijbunchoo, N.; Kim, C.; Kim, J.; Kim, K.; Kim, Nam-Gyu; Kim, Namjun; Kim, Y.-M.; King, E. J.; King, P. J.; Kinzel, D. L.; Kissel, J. S.; Kleybolte, L.; Klimenko, S.; Koehlenbeck, S. M.; Kokeyama, K.; Koley, S.; Kondrashov, V.; Kontos, A.; Korobko, M.; Korth, W. Z.; Kowalska, I.; Kozak, D. B.; Kringel, V.; Królak, A.; Krueger, C.; Kuehn, G.; Kumar, P.; Kuo, L.; Kutynia, A.; Lackey, B. D.; Landry, M.; Lange, J.; Lantz, B.; Lasky, P. D.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; Lebigot, E. O.; Lee, C. H.; Lee, H. K.; Lee, H. M.; Lee, K.; Lenon, A.; Leonardi, M.; Leong, J. R.; Leroy, N.; Letendre, N.; Levin, Y.; Levine, B. M.; Li, T. G. F.; Libson, A.; Littenberg, T. B.; Lockerbie, N. A.; Logue, J.; Lombardi, A. L.; Lord, J. E.; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lough, J. D.; Lück, H.; Lundgren, A. P.; Luo, J.; Lynch, R.; Ma, Y.; MacDonald, T.; Machenschalk, B.; MacInnis, M.; Macleod, D. M.; Magaña-Sandoval, F.; Magee, R. M.; Mageswaran, M.; Majorana, E.; Maksimovic, I.; Malvezzi, V.; Man, N.; Mandel, I.; Mandic, V.; Mangano, V.; Mansell, G. L.; Manske, M.; Mantovani, M.; Marchesoni, F.; Marion, F.; Márka, S.; Márka, Z.; Markosyan, A. S.; Maros, E.; Martelli, F.; Martellini, L.; Martin, I. W.; Martin, R. M.; Martynov, D. V.; Marx, J. N.; Mason, K.; Masserot, A.; Massinger, T. J.; Masso-Reid, M.; Matichard, F.; Matone, L.; Mavalvala, N.; Mazumder, N.; Mazzolo, G.; McCarthy, R.; McClelland, D. E.; McCormick, S.; McGuire, S. C.; McIntyre, G.; McIver, J.; McManus, D. J.; McWilliams, S. T.; Meacher, D.; Meadors, G. D.; Meidam, J.; Melatos, A.; Mendell, G.; Mendoza-Gandara, D.; Mercer, R. A.; Merilh, E.; Merzougui, M.; Meshkov, S.; Messenger, C.; Messick, C.; Meyers, P. M.; Mezzani, F.; Miao, H.; Michel, C.; Middleton, H.; Mikhailov, E. E.; Milano, L.; Miller, J.; Millhouse, M.; Minenkov, Y.; Ming, J.; Mirshekari, S.; Mishra, C.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Moggi, A.; Mohan, M.; Mohapatra, S. R. P.; Montani, M.; Moore, B. C.; Moore, C. J.; Moraru, D.; Moreno, G.; Morriss, S. R.; Mossavi, K.; Mours, B.; Mow-Lowry, C. M.; Mueller, C. L.; Mueller, G.; Muir, A. W.; Mukherjee, Arunava; Mukherjee, D.; Mukherjee, S.; Mukund, N.; Mullavey, A.; Munch, J.; Murphy, D. J.; Murray, P. G.; Mytidis, A.; Nardecchia, I.; Naticchioni, L.; Nayak, R. K.; Necula, V.; Nedkova, K.; Nelemans, G.; Neri, M.; Neunzert, A.; Newton, G.; Nguyen, T. T.; Nielsen, A. B.; Nissanke, S.; Nitz, A.; Nocera, F.; Nolting, D.; Normandin, M. E. N.; Nuttall, L. K.; Oberling, J.; Ochsner, E.; O'Dell, J.; Oelker, E.; Ogin, G. H.; Oh, J. J.; Oh, S. H.; Ohme, F.; Oliver, M.; Oppermann, P.; Oram, Richard J.; O'Reilly, B.; O'Shaughnessy, R.; Ottaway, D. J.; Ottens, R. S.; Overmier, H.; Owen, B. J.; Pai, A.; Pai, S. A.; Palamos, J. R.; Palashov, O.; Palomba, C.; Pal-Singh, A.; Pan, H.; Pankow, C.; Pannarale, F.; Pant, B. C.; Paoletti, F.; Paoli, A.; Papa, M. A.; Paris, H. R.; Parker, W.; Pascucci, D.; Pasqualetti, A.; Passaquieti, R.; Passuello, D.; Patricelli, B.; Patrick, Z.; Pearlstone, B. L.; Pedraza, M.; Pedurand, R.; Pekowsky, L.; Pele, A.; Penn, S.; Perreca, A.; Phelps, M.; Piccinni, O.; Pichot, M.; Piergiovanni, F.; Pierro, V.; Pillant, G.; Pinard, L.; Pinto, I. M.; Pitkin, M.; Poggiani, R.; Popolizio, P.; Post, A.; Powell, J.; Prasad, J.; Predoi, V.; Premachandra, S. S.; Prestegard, T.; Price, L. R.; Prijatelj, M.; Principe, M.; Privitera, S.; Prodi, G. A.; Prokhorov, L.; Puncken, O.; Punturo, M.; Puppo, P.; Pürrer, M.; Qi, H.; Qin, J.; Quetschke, V.; Quintero, E. A.; Quitzow-James, R.; Raab, F. J.; Rabeling, D. S.; Radkins, H.; Raffai, P.; Raja, S.; Rakhmanov, M.; Rapagnani, P.; Raymond, V.; Razzano, M.; Re, V.; Read, J.; Reed, C. M.; Regimbau, T.; Rei, L.; Reid, S.; Reitze, D. H.; Rew, H.; Reyes, S. D.; Ricci, F.; Riles, K.; Robertson, N. A.; Robie, R.; Robinet, F.; Rocchi, A.; Rolland, L.; Rollins, J. G.; Roma, V. J.; Romano, J. D.; Romano, R.; Romanov, G.; Romie, J. H.; Rosińska, D.; Rowan, S.; Rüdiger, A.; Ruggi, P.; Ryan, K.; Sachdev, S.; Sadecki, T.; Sadeghian, L.; Salconi, L.; Saleem, M.; Salemi, F.; Samajdar, A.; Sammut, L.; Sanchez, E. J.; Sandberg, V.; Sandeen, B.; Sanders, J. R.; Sassolas, B.; Sathyaprakash, B. S.; Saulson, P. R.; Sauter, O.; Savage, R. L.; Sawadsky, A.; Schale, P.; Schilling, R.; Schmidt, J.; Schmidt, P.; Schnabel, R.; Schofield, R. M. S.; Schönbeck, A.; Schreiber, E.; Schuette, D.; Schutz, B. F.; Scott, J.; Scott, S. M.; Sellers, D.; Sentenac, D.; Sequino, V.; Sergeev, A.; Serna, G.; Setyawati, Y.; Sevigny, A.; Shaddock, D. A.; Shah, S.; Shahriar, M. S.; Shaltev, M.; Shao, Z.; Shapiro, B.; Shawhan, P.; Sheperd, A.; Shoemaker, D. H.; Shoemaker, D. M.; Siellez, K.; Siemens, X.; Sigg, D.; Silva, A. D.; Simakov, D.; Singer, A.; Singer, L. P.; Singh, A.; Singh, R.; Singhal, A.; Sintes, A. M.; Slagmolen, B. J. J.; Smith, J. R.; Smith, N. D.; Smith, R. J. E.; Son, E. J.; Sorazu, B.; Sorrentino, F.; Souradeep, T.; Srivastava, A. K.; Staley, A.; Steinke, M.; Steinlechner, J.; Steinlechner, S.; Steinmeyer, D.; Stephens, B. C.; Stone, R.; Strain, K. A.; Straniero, N.; Stratta, G.; Strauss, N. A.; Strigin, S.; Sturani, R.; Stuver, A. L.; Summerscales, T. Z.; Sun, L.; Sutton, P. J.; Swinkels, B. L.; Szczepańczyk, M. J.; Tacca, M.; Talukder, D.; Tanner, D. B.; Tápai, M.; Tarabrin, S. P.; Taracchini, A.; Taylor, R.; Theeg, T.; Thirugnanasambandam, M. P.; Thomas, E. G.; Thomas, M.; Thomas, P.; Thorne, K. A.; Thorne, K. S.; Thrane, E.; Tiwari, S.; Tiwari, V.; Tokmakov, K. V.; Tomlinson, C.; Tonelli, M.; Torres, C. V.; Torrie, C. I.; Töyrä, D.; Travasso, F.; Traylor, G.; Trifirò, D.; Tringali, M. C.; Trozzo, L.; Tse, M.; Turconi, M.; Tuyenbayev, D.; Ugolini, D.; Unnikrishnan, C. S.; Urban, A. L.; Usman, S. A.; Vahlbruch, H.; Vajente, G.; Valdes, G.; van Bakel, N.; van Beuzekom, M.; van den Brand, J. F. J.; Van Den Broeck, C.; Vander-Hyde, D. C.; van der Schaaf, L.; van Heijningen, J. V.; van Veggel, A. A.; Vardaro, M.; Vass, S.; Vasúth, M.; Vaulin, R.; Vecchio, A.; Vedovato, G.; Veitch, J.; Veitch, P. J.; Venkateswara, K.; Verkindt, D.; Vetrano, F.; Viceré, A.; Vinciguerra, S.; Vine, D. J.; Vinet, J.-Y.; Vitale, S.; Vo, T.; Vocca, H.; Vorvick, C.; Voss, D.; Vousden, W. D.; Vyatchanin, S. P.; Wade, A. R.; Wade, L. E.; Wade, M.; Walker, M.; Wallace, L.; Walsh, S.; Wang, G.; Wang, H.; Wang, M.; Wang, X.; Wang, Y.; Ward, R. L.; Warner, J.; Was, M.; Weaver, B.; Wei, L.-W.; Weinert, M.; Weinstein, A. J.; Weiss, R.; Welborn, T.; Wen, L.; Weßels, P.; Westphal, T.; Wette, K.; Whelan, J. T.; White, D. J.; Whiting, B. F.; Williams, R. D.; Williamson, A. R.; Willis, J. L.; Willke, B.; Wimmer, M. H.; Winkler, W.; Wipf, C. C.; Wittel, H.; Woan, G.; Worden, J.; Wright, J. L.; Wu, G.; Yablon, J.; Yam, W.; Yamamoto, H.; Yancey, C. C.; Yap, M. J.; Yu, H.; Yvert, M.; ZadroŻny, A.; Zangrando, L.; Zanolin, M.; Zendri, J.-P.; Zevin, M.; Zhang, F.; Zhang, L.; Zhang, M.; Zhang, Y.; Zhao, C.; Zhou, M.; Zhou, Z.; Zhu, X. J.; Zucker, M. E.; Zuraw, S. E.; Zweizig, J.; LIGO Scientific Collaboration; Virgo Collaboration

2016-04-01

The LIGO detection of the gravitational wave transient GW150914, from the inspiral and merger of two black holes with masses ≳30 M⊙, suggests a population of binary black holes with relatively high mass. This observation implies that the stochastic gravitational-wave background from binary black holes, created from the incoherent superposition of all the merging binaries in the Universe, could be higher than previously expected. Using the properties of GW150914, we estimate the energy density of such a background from binary black holes. In the most sensitive part of the Advanced LIGO and Advanced Virgo band for stochastic backgrounds (near 25 Hz), we predict ΩGW(f =25 Hz )=1. 1-0.9+2.7×10-9 with 90% confidence. This prediction is robustly demonstrated for a variety of formation scenarios with different parameters. The differences between models are small compared to the statistical uncertainty arising from the currently poorly constrained local coalescence rate. We conclude that this background is potentially measurable by the Advanced LIGO and Advanced Virgo detectors operating at their projected final sensitivity.

GW150914: Implications for the Stochastic Gravitational-Wave Background from Binary Black Holes.

PubMed

Abbott, B P; Abbott, R; Abbott, T D; Abernathy, M R; Acernese, F; Ackley, K; Adams, C; Adams, T; Addesso, P; Adhikari, R X; Adya, V B; Affeldt, C; Agathos, M; Agatsuma, K; Aggarwal, N; Aguiar, O D; Aiello, L; Ain, A; Ajith, P; Allen, B; Allocca, A; Altin, P A; Anderson, S B; Anderson, W G; Arai, K; Araya, M C; Arceneaux, C C; Areeda, J S; Arnaud, N; Arun, K G; Ascenzi, S; Ashton, G; Ast, M; Aston, S M; Astone, P; Aufmuth, P; Aulbert, C; Babak, S; Bacon, P; Bader, M K M; Baker, P T; Baldaccini, F; Ballardin, G; Ballmer, S W; Barayoga, J C; Barclay, S E; Barish, B C; Barker, D; Barone, F; Barr, B; Barsotti, L; Barsuglia, M; Barta, D; Bartlett, J; Bartos, I; Bassiri, R; Basti, A; Batch, J C; Baune, C; Bavigadda, V; Bazzan, M; Behnke, B; Bejger, M; Bell, A S; Bell, C J; Berger, B K; Bergman, J; Bergmann, G; Berry, C P L; Bersanetti, D; Bertolini, A; Betzwieser, J; Bhagwat, S; Bhandare, R; Bilenko, I A; Billingsley, G; Birch, J; Birney, R; Biscans, S; Bisht, A; Bitossi, M; Biwer, C; Bizouard, M A; Blackburn, J K; Blair, C D; Blair, D G; Blair, R M; Bloemen, S; Bock, O; Bodiya, T P; Boer, M; Bogaert, G; Bogan, C; Bohe, A; Bojtos, P; Bond, C; Bondu, F; Bonnand, R; Boom, B A; Bork, R; Boschi, V; Bose, S; Bouffanais, Y; Bozzi, A; Bradaschia, C; Brady, P R; Braginsky, V B; Branchesi, M; Brau, J E; Briant, T; Brillet, A; Brinkmann, M; Brisson, V; Brockill, P; Brooks, A F; Brown, D D; Brown, N M; Buchanan, C C; Buikema, A; Bulik, T; Bulten, H J; Buonanno, A; Buskulic, D; Buy, C; Byer, R L; Cadonati, L; Cagnoli, G; Cahillane, C; Bustillo, J Calderón; Callister, T; Calloni, E; Camp, J B; Cannon, K C; Cao, J; Capano, C D; Capocasa, E; Carbognani, F; Caride, S; Diaz, J Casanueva; Casentini, C; Caudill, S; Cavaglià, M; Cavalier, F; Cavalieri, R; Cella, G; Cepeda, C B; Baiardi, L Cerboni; Cerretani, G; Cesarini, E; Chakraborty, R; Chalermsongsak, T; Chamberlin, S J; Chan, M; Chao, S; Charlton, P; Chassande-Mottin, E; Chen, H Y; Chen, Y; Cheng, C; Chincarini, A; Chiummo, A; Cho, H S; Cho, M; Chow, J H; Christensen, N; Chu, Q; Chua, S; Chung, S; Ciani, G; Clara, F; Clark, J A; Cleva, F; Coccia, E; Cohadon, P-F; Colla, A; Collette, C G; Cominsky, L; Constancio, M; Conte, A; Conti, L; Cook, D; Corbitt, T R; Cornish, N; Corsi, A; Cortese, S; Costa, C A; Coughlin, M W; Coughlin, S B; Coulon, J-P; Countryman, S T; Couvares, P; Cowan, E E; Coward, D M; Cowart, M J; Coyne, D C; Coyne, R; Craig, K; Creighton, J D E; Cripe, J; Crowder, S G; Cumming, A; Cunningham, L; Cuoco, E; Canton, T Dal; Danilishin, S L; D'Antonio, S; Danzmann, K; Darman, N S; Dattilo, V; Dave, I; Daveloza, H P; Davier, M; Davies, G S; Daw, E J; Day, R; DeBra, D; Debreczeni, G; Degallaix, J; De Laurentis, M; Deléglise, S; Del Pozzo, W; Denker, T; Dent, T; Dereli, H; Dergachev, V; DeRosa, R T; De Rosa, R; DeSalvo, R; Dhurandhar, S; Díaz, M C; Di Fiore, L; Di Giovanni, M; Di Lieto, A; Di Pace, S; Di Palma, I; Di Virgilio, A; Dojcinoski, G; Dolique, V; Donovan, F; Dooley, K L; Doravari, S; Douglas, R; Downes, T P; Drago, M; Drever, R W P; Driggers, J C; Du, Z; Ducrot, M; Dwyer, S E; Edo, T B; Edwards, M C; Effler, A; Eggenstein, H-B; Ehrens, P; Eichholz, J; Eikenberry, S S; Engels, W; Essick, R C; Etzel, T; Evans, M; Evans, T M; Everett, R; Factourovich, M; Fafone, V; Fair, H; Fairhurst, S; Fan, X; Fang, Q; Farinon, S; Farr, B; Farr, W M; Favata, M; Fays, M; Fehrmann, H; Fejer, M M; Ferrante, I; Ferreira, E C; Ferrini, F; Fidecaro, F; Fiori, I; Fiorucci, D; Fisher, R P; Flaminio, R; Fletcher, M; Fournier, J-D; Franco, S; Frasca, S; Frasconi, F; Frei, Z; Freise, A; Frey, R; Frey, V; Fricke, T T; Fritschel, P; Frolov, V V; Fulda, P; Fyffe, M; Gabbard, H A G; Gair, J R; Gammaitoni, L; Gaonkar, S G; Garufi, F; Gatto, A; Gaur, G; Gehrels, N; Gemme, G; Gendre, B; Genin, E; Gennai, A; George, J; Gergely, L; Germain, V; Ghosh, Archisman; Ghosh, S; Giaime, J A; Giardina, K D; Giazotto, A; Gill, K; Glaefke, A; Goetz, E; Goetz, R; Gondan, L; González, G; Castro, J M Gonzalez; Gopakumar, A; Gordon, N A; Gorodetsky, M L; Gossan, S E; Gosselin, M; Gouaty, R; Graef, C; Graff, P B; Granata, M; Grant, A; Gras, S; Gray, C; Greco, G; Green, A C; Groot, P; Grote, H; Grunewald, S; Guidi, G M; Guo, X; Gupta, A; Gupta, M K; Gushwa, K E; Gustafson, E K; Gustafson, R; Hacker, J J; Hall, B R; Hall, E D; Hammond, G; Haney, M; Hanke, M M; Hanks, J; Hanna, C; Hannam, M D; Hanson, J; Hardwick, T; Haris, K; Harms, J; Harry, G M; Harry, I W; Hart, M J; Hartman, M T; Haster, C-J; Haughian, K; Heidmann, A; Heintze, M C; Heitmann, H; Hello, P; Hemming, G; Hendry, M; Heng, I S; Hennig, J; Heptonstall, A W; Heurs, M; Hild, S; Hoak, D; Hodge, K A; Hofman, D; Hollitt, S E; Holt, K; Holz, D E; Hopkins, P; Hosken, D J; Hough, J; Houston, E A; Howell, E J; Hu, Y M; Huang, S; Huerta, E A; Huet, D; Hughey, B; Husa, S; Huttner, S H; Huynh-Dinh, T; Idrisy, A; Indik, N; Ingram, D R; Inta, R; Isa, H N; Isac, J-M; Isi, M; Islas, G; Isogai, T; Iyer, B R; Izumi, K; Jacqmin, T; Jang, H; Jani, K; Jaranowski, P; Jawahar, S; Jiménez-Forteza, F; Johnson, W W; Jones, D I; Jones, R; Jonker, R J G; Ju, L; Kalaghatgi, C V; Kalogera, V; Kandhasamy, S; Kang, G; Kanner, J B; Karki, S; Kasprzack, M; Katsavounidis, E; Katzman, W; Kaufer, S; Kaur, T; Kawabe, K; Kawazoe, F; Kéfélian, F; Kehl, M S; Keitel, D; Kelley, D B; Kells, W; Kennedy, R; Key, J S; Khalaidovski, A; Khalili, F Y; Khan, I; Khan, S; Khan, Z; Khazanov, E A; Kijbunchoo, N; Kim, C; Kim, J; Kim, K; Kim, Nam-Gyu; Kim, Namjun; Kim, Y-M; King, E J; King, P J; Kinzel, D L; Kissel, J S; Kleybolte, L; Klimenko, S; Koehlenbeck, S M; Kokeyama, K; Koley, S; Kondrashov, V; Kontos, A; Korobko, M; Korth, W Z; Kowalska, I; Kozak, D B; Kringel, V; Królak, A; Krueger, C; Kuehn, G; Kumar, P; Kuo, L; Kutynia, A; Lackey, B D; Landry, M; Lange, J; Lantz, B; Lasky, P D; Lazzarini, A; Lazzaro, C; Leaci, P; Leavey, S; Lebigot, E O; Lee, C H; Lee, H K; Lee, H M; Lee, K; Lenon, A; Leonardi, M; Leong, J R; Leroy, N; Letendre, N; Levin, Y; Levine, B M; Li, T G F; Libson, A; Littenberg, T B; Lockerbie, N A; Logue, J; Lombardi, A L; Lord, J E; Lorenzini, M; Loriette, V; Lormand, M; Losurdo, G; Lough, J D; Lück, H; Lundgren, A P; Luo, J; Lynch, R; Ma, Y; MacDonald, T; Machenschalk, B; MacInnis, M; Macleod, D M; Magaña-Sandoval, F; Magee, R M; Mageswaran, M; Majorana, E; Maksimovic, I; Malvezzi, V; Man, N; Mandel, I; Mandic, V; Mangano, V; Mansell, G L; Manske, M; Mantovani, M; Marchesoni, F; Marion, F; Márka, S; Márka, Z; Markosyan, A S; Maros, E; Martelli, F; Martellini, L; Martin, I W; Martin, R M; Martynov, D V; Marx, J N; Mason, K; Masserot, A; Massinger, T J; Masso-Reid, M; Matichard, F; Matone, L; Mavalvala, N; Mazumder, N; Mazzolo, G; McCarthy, R; McClelland, D E; McCormick, S; McGuire, S C; McIntyre, G; McIver, J; McManus, D J; McWilliams, S T; Meacher, D; Meadors, G D; Meidam, J; Melatos, A; Mendell, G; Mendoza-Gandara, D; Mercer, R A; Merilh, E; Merzougui, M; Meshkov, S; Messenger, C; Messick, C; Meyers, P M; Mezzani, F; Miao, H; Michel, C; Middleton, H; Mikhailov, E E; Milano, L; Miller, J; Millhouse, M; Minenkov, Y; Ming, J; Mirshekari, S; Mishra, C; Mitra, S; Mitrofanov, V P; Mitselmakher, G; Mittleman, R; Moggi, A; Mohan, M; Mohapatra, S R P; Montani, M; Moore, B C; Moore, C J; Moraru, D; Moreno, G; Morriss, S R; Mossavi, K; Mours, B; Mow-Lowry, C M; Mueller, C L; Mueller, G; Muir, A W; Mukherjee, Arunava; Mukherjee, D; Mukherjee, S; Mukund, N; Mullavey, A; Munch, J; Murphy, D J; Murray, P G; Mytidis, A; Nardecchia, I; Naticchioni, L; Nayak, R K; Necula, V; Nedkova, K; Nelemans, G; Neri, M; Neunzert, A; Newton, G; Nguyen, T T; Nielsen, A B; Nissanke, S; Nitz, A; Nocera, F; Nolting, D; Normandin, M E N; Nuttall, L K; Oberling, J; Ochsner, E; O'Dell, J; Oelker, E; Ogin, G H; Oh, J J; Oh, S H; Ohme, F; Oliver, M; Oppermann, P; Oram, Richard J; O'Reilly, B; O'Shaughnessy, R; Ottaway, D J; Ottens, R S; Overmier, H; Owen, B J; Pai, A; Pai, S A; Palamos, J R; Palashov, O; Palomba, C; Pal-Singh, A; Pan, H; Pankow, C; Pannarale, F; Pant, B C; Paoletti, F; Paoli, A; Papa, M A; Paris, H R; Parker, W; Pascucci, D; Pasqualetti, A; Passaquieti, R; Passuello, D; Patricelli, B; Patrick, Z; Pearlstone, B L; Pedraza, M; Pedurand, R; Pekowsky, L; Pele, A; Penn, S; Perreca, A; Phelps, M; Piccinni, O; Pichot, M; Piergiovanni, F; Pierro, V; Pillant, G; Pinard, L; Pinto, I M; Pitkin, M; Poggiani, R; Popolizio, P; Post, A; Powell, J; Prasad, J; Predoi, V; Premachandra, S S; Prestegard, T; Price, L R; Prijatelj, M; Principe, M; Privitera, S; Prodi, G A; Prokhorov, L; Puncken, O; Punturo, M; Puppo, P; Pürrer, M; Qi, H; Qin, J; Quetschke, V; Quintero, E A; Quitzow-James, R; Raab, F J; Rabeling, D S; Radkins, H; Raffai, P; Raja, S; Rakhmanov, M; Rapagnani, P; Raymond, V; Razzano, M; Re, V; Read, J; Reed, C M; Regimbau, T; Rei, L; Reid, S; Reitze, D H; Rew, H; Reyes, S D; Ricci, F; Riles, K; Robertson, N A; Robie, R; Robinet, F; Rocchi, A; Rolland, L; Rollins, J G; Roma, V J; Romano, J D; Romano, R; Romanov, G; Romie, J H; Rosińska, D; Rowan, S; Rüdiger, A; Ruggi, P; Ryan, K; Sachdev, S; Sadecki, T; Sadeghian, L; Salconi, L; Saleem, M; Salemi, F; Samajdar, A; Sammut, L; Sanchez, E J; Sandberg, V; Sandeen, B; Sanders, J R; Sassolas, B; Sathyaprakash, B S; Saulson, P R; Sauter, O; Savage, R L; Sawadsky, A; Schale, P; Schilling, R; Schmidt, J; Schmidt, P; Schnabel, R; Schofield, R M S; Schönbeck, A; Schreiber, E; Schuette, D; Schutz, B F; Scott, J; Scott, S M; Sellers, D; Sentenac, D; Sequino, V; Sergeev, A; Serna, G; Setyawati, Y; Sevigny, A; Shaddock, D A; Shah, S; Shahriar, M S; Shaltev, M; Shao, Z; Shapiro, B; Shawhan, P; Sheperd, A; Shoemaker, D H; Shoemaker, D M; Siellez, K; Siemens, X; Sigg, D; Silva, A D; Simakov, D; Singer, A; Singer, L P; Singh, A; Singh, R; Singhal, A; Sintes, A M; Slagmolen, B J J; Smith, J R; Smith, N D; Smith, R J E; Son, E J; Sorazu, B; Sorrentino, F; Souradeep, T; Srivastava, A K; Staley, A; Steinke, M; Steinlechner, J; Steinlechner, S; Steinmeyer, D; Stephens, B C; Stone, R; Strain, K A; Straniero, N; Stratta, G; Strauss, N A; Strigin, S; Sturani, R; Stuver, A L; Summerscales, T Z; Sun, L; Sutton, P J; Swinkels, B L; Szczepańczyk, M J; Tacca, M; Talukder, D; Tanner, D B; Tápai, M; Tarabrin, S P; Taracchini, A; Taylor, R; Theeg, T; Thirugnanasambandam, M P; Thomas, E G; Thomas, M; Thomas, P; Thorne, K A; Thorne, K S; Thrane, E; Tiwari, S; Tiwari, V; Tokmakov, K V; Tomlinson, C; Tonelli, M; Torres, C V; Torrie, C I; Töyrä, D; Travasso, F; Traylor, G; Trifirò, D; Tringali, M C; Trozzo, L; Tse, M; Turconi, M; Tuyenbayev, D; Ugolini, D; Unnikrishnan, C S; Urban, A L; Usman, S A; Vahlbruch, H; Vajente, G; Valdes, G; van Bakel, N; van Beuzekom, M; van den Brand, J F J; Van Den Broeck, C; Vander-Hyde, D C; van der Schaaf, L; van Heijningen, J V; van Veggel, A A; Vardaro, M; Vass, S; Vasúth, M; Vaulin, R; Vecchio, A; Vedovato, G; Veitch, J; Veitch, P J; Venkateswara, K; Verkindt, D; Vetrano, F; Viceré, A; Vinciguerra, S; Vine, D J; Vinet, J-Y; Vitale, S; Vo, T; Vocca, H; Vorvick, C; Voss, D; Vousden, W D; Vyatchanin, S P; Wade, A R; Wade, L E; Wade, M; Walker, M; Wallace, L; Walsh, S; Wang, G; Wang, H; Wang, M; Wang, X; Wang, Y; Ward, R L; Warner, J; Was, M; Weaver, B; Wei, L-W; Weinert, M; Weinstein, A J; Weiss, R; Welborn, T; Wen, L; Weßels, P; Westphal, T; Wette, K; Whelan, J T; White, D J; Whiting, B F; Williams, R D; Williamson, A R; Willis, J L; Willke, B; Wimmer, M H; Winkler, W; Wipf, C C; Wittel, H; Woan, G; Worden, J; Wright, J L; Wu, G; Yablon, J; Yam, W; Yamamoto, H; Yancey, C C; Yap, M J; Yu, H; Yvert, M; Zadrożny, A; Zangrando, L; Zanolin, M; Zendri, J-P; Zevin, M; Zhang, F; Zhang, L; Zhang, M; Zhang, Y; Zhao, C; Zhou, M; Zhou, Z; Zhu, X J; Zucker, M E; Zuraw, S E; Zweizig, J

2016-04-01

The LIGO detection of the gravitational wave transient GW150914, from the inspiral and merger of two black holes with masses ≳30M_{⊙}, suggests a population of binary black holes with relatively high mass. This observation implies that the stochastic gravitational-wave background from binary black holes, created from the incoherent superposition of all the merging binaries in the Universe, could be higher than previously expected. Using the properties of GW150914, we estimate the energy density of such a background from binary black holes. In the most sensitive part of the Advanced LIGO and Advanced Virgo band for stochastic backgrounds (near 25 Hz), we predict Ω_{GW}(f=25  Hz)=1.1_{-0.9}^{+2.7}×10^{-9} with 90% confidence. This prediction is robustly demonstrated for a variety of formation scenarios with different parameters. The differences between models are small compared to the statistical uncertainty arising from the currently poorly constrained local coalescence rate. We conclude that this background is potentially measurable by the Advanced LIGO and Advanced Virgo detectors operating at their projected final sensitivity.

Ground motion simulation for the 23 August 2011, Mineral, Virginia earthquake using physics-based and stochastic broadband methods

USGS Publications Warehouse

Sun, Xiaodan; Hartzell, Stephen; Rezaeian, Sanaz

2015-01-01

Three broadband simulation methods are used to generate synthetic ground motions for the 2011 Mineral, Virginia, earthquake and compare with observed motions. The methods include a physics‐based model by Hartzell et al. (1999, 2005), a stochastic source‐based model by Boore (2009), and a stochastic site‐based model by Rezaeian and Der Kiureghian (2010, 2012). The ground‐motion dataset consists of 40 stations within 600 km of the epicenter. Several metrics are used to validate the simulations: (1) overall bias of response spectra and Fourier spectra (from 0.1 to 10 Hz); (2) spatial distribution of residuals for GMRotI50 peak ground acceleration (PGA), peak ground velocity, and pseudospectral acceleration (PSA) at various periods; (3) comparison with ground‐motion prediction equations (GMPEs) for the eastern United States. Our results show that (1) the physics‐based model provides satisfactory overall bias from 0.1 to 10 Hz and produces more realistic synthetic waveforms; (2) the stochastic site‐based model also yields more realistic synthetic waveforms and performs superiorly for frequencies greater than about 1 Hz; (3) the stochastic source‐based model has larger bias at lower frequencies (<0.5  Hz) and cannot reproduce the varying frequency content in the time domain. The spatial distribution of GMRotI50 residuals shows that there is no obvious pattern with distance in the simulation bias, but there is some azimuthal variability. The comparison between synthetics and GMPEs shows similar fall‐off with distance for all three models, comparable PGA and PSA amplitudes for the physics‐based and stochastic site‐based models, and systematic lower amplitudes for the stochastic source‐based model at lower frequencies (<0.5  Hz).

Communication: Limitations of the stochastic quasi-steady-state approximation in open biochemical reaction networks

NASA Astrophysics Data System (ADS)

Thomas, Philipp; Straube, Arthur V.; Grima, Ramon

2011-11-01

It is commonly believed that, whenever timescale separation holds, the predictions of reduced chemical master equations obtained using the stochastic quasi-steady-state approximation are in very good agreement with the predictions of the full master equations. We use the linear noise approximation to obtain a simple formula for the relative error between the predictions of the two master equations for the Michaelis-Menten reaction with substrate input. The reduced approach is predicted to overestimate the variance of the substrate concentration fluctuations by as much as 30%. The theoretical results are validated by stochastic simulations using experimental parameter values for enzymes involved in proteolysis, gluconeogenesis, and fermentation.

Stochastic associative memory

NASA Astrophysics Data System (ADS)

Baumann, Erwin W.; Williams, David L.

1993-08-01

Artificial neural networks capable of learning and recalling stochastic associations between non-deterministic quantities have received relatively little attention to date. One potential application of such stochastic associative networks is the generation of sensory 'expectations' based on arbitrary subsets of sensor inputs to support anticipatory and investigate behavior in sensor-based robots. Another application of this type of associative memory is the prediction of how a scene will look in one spectral band, including noise, based upon its appearance in several other wavebands. This paper describes a semi-supervised neural network architecture composed of self-organizing maps associated through stochastic inter-layer connections. This 'Stochastic Associative Memory' (SAM) can learn and recall non-deterministic associations between multi-dimensional probability density functions. The stochastic nature of the network also enables it to represent noise distributions that are inherent in any true sensing process. The SAM architecture, training process, and initial application to sensor image prediction are described. Relationships to Fuzzy Associative Memory (FAM) are discussed.

Stochastic Spectral Descent for Discrete Graphical Models

DOE PAGES

Carlson, David; Hsieh, Ya-Ping; Collins, Edo; ...

2015-12-14

Interest in deep probabilistic graphical models has in-creased in recent years, due to their state-of-the-art performance on many machine learning applications. Such models are typically trained with the stochastic gradient method, which can take a significant number of iterations to converge. Since the computational cost of gradient estimation is prohibitive even for modestly sized models, training becomes slow and practically usable models are kept small. In this paper we propose a new, largely tuning-free algorithm to address this problem. Our approach derives novel majorization bounds based on the Schatten- norm. Intriguingly, the minimizers of these bounds can be interpreted asmore » gradient methods in a non-Euclidean space. We thus propose using a stochastic gradient method in non-Euclidean space. We both provide simple conditions under which our algorithm is guaranteed to converge, and demonstrate empirically that our algorithm leads to dramatically faster training and improved predictive ability compared to stochastic gradient descent for both directed and undirected graphical models.« less

Predicting Rift Valley Fever Inter-epidemic Activities and Outbreak Patterns: Insights from a Stochastic Host-Vector Model

PubMed Central

Pedro, Sansao A.; Abelman, Shirley; Tonnang, Henri E. Z.

2016-01-01

Rift Valley fever (RVF) outbreaks are recurrent, occurring at irregular intervals of up to 15 years at least in East Africa. Between outbreaks disease inter-epidemic activities exist and occur at low levels and are maintained by female Aedes mcintoshi mosquitoes which transmit the virus to their eggs leading to disease persistence during unfavourable seasons. Here we formulate and analyse a full stochastic host-vector model with two routes of transmission: vertical and horizontal. By applying branching process theory we establish novel relationships between the basic reproduction number, R0, vertical transmission and the invasion and extinction probabilities. Optimum climatic conditions and presence of mosquitoes have not fully explained the irregular oscillatory behaviour of RVF outbreaks. Using our model without seasonality and applying van Kampen system-size expansion techniques, we provide an analytical expression for the spectrum of stochastic fluctuations, revealing how outbreaks multi-year periodicity varies with the vertical transmission. Our theory predicts complex fluctuations with a dominant period of 1 to 10 years which essentially depends on the efficiency of vertical transmission. Our predictions are then compared to temporal patterns of disease outbreaks in Tanzania, Kenya and South Africa. Our analyses show that interaction between nonlinearity, stochasticity and vertical transmission provides a simple but plausible explanation for the irregular oscillatory nature of RVF outbreaks. Therefore, we argue that while rainfall might be the major determinant for the onset and switch-off of an outbreak, the occurrence of a particular outbreak is also a result of a build up phenomena that is correlated to vertical transmission efficiency. PMID:28002417

Predicting Rift Valley Fever Inter-epidemic Activities and Outbreak Patterns: Insights from a Stochastic Host-Vector Model.

PubMed

Pedro, Sansao A; Abelman, Shirley; Tonnang, Henri E Z

2016-12-01

Rift Valley fever (RVF) outbreaks are recurrent, occurring at irregular intervals of up to 15 years at least in East Africa. Between outbreaks disease inter-epidemic activities exist and occur at low levels and are maintained by female Aedes mcintoshi mosquitoes which transmit the virus to their eggs leading to disease persistence during unfavourable seasons. Here we formulate and analyse a full stochastic host-vector model with two routes of transmission: vertical and horizontal. By applying branching process theory we establish novel relationships between the basic reproduction number, R0, vertical transmission and the invasion and extinction probabilities. Optimum climatic conditions and presence of mosquitoes have not fully explained the irregular oscillatory behaviour of RVF outbreaks. Using our model without seasonality and applying van Kampen system-size expansion techniques, we provide an analytical expression for the spectrum of stochastic fluctuations, revealing how outbreaks multi-year periodicity varies with the vertical transmission. Our theory predicts complex fluctuations with a dominant period of 1 to 10 years which essentially depends on the efficiency of vertical transmission. Our predictions are then compared to temporal patterns of disease outbreaks in Tanzania, Kenya and South Africa. Our analyses show that interaction between nonlinearity, stochasticity and vertical transmission provides a simple but plausible explanation for the irregular oscillatory nature of RVF outbreaks. Therefore, we argue that while rainfall might be the major determinant for the onset and switch-off of an outbreak, the occurrence of a particular outbreak is also a result of a build up phenomena that is correlated to vertical transmission efficiency.

Revisiting the cape cod bacteria injection experiment using a stochastic modeling approach

USGS Publications Warehouse

Maxwell, R.M.; Welty, C.; Harvey, R.W.

2007-01-01

Bromide and resting-cell bacteria tracer tests conducted in a sandy aquifer at the U.S. Geological Survey Cape Cod site in 1987 were reinterpreted using a three-dimensional stochastic approach. Bacteria transport was coupled to colloid filtration theory through functional dependence of local-scale colloid transport parameters upon hydraulic conductivity and seepage velocity in a stochastic advection - dispersion/attachment - detachment model. Geostatistical information on the hydraulic conductivity (K) field that was unavailable at the time of the original test was utilized as input. Using geostatistical parameters, a groundwater flow and particle-tracking model of conservative solute transport was calibrated to the bromide-tracer breakthrough data. An optimization routine was employed over 100 realizations to adjust the mean and variance ofthe natural-logarithm of hydraulic conductivity (InK) field to achieve best fit of a simulated, average bromide breakthrough curve. A stochastic particle-tracking model for the bacteria was run without adjustments to the local-scale colloid transport parameters. Good predictions of mean bacteria breakthrough were achieved using several approaches for modeling components of the system. Simulations incorporating the recent Tufenkji and Elimelech (Environ. Sci. Technol. 2004, 38, 529-536) correlation equation for estimating single collector efficiency were compared to those using the older Rajagopalan and Tien (AIChE J. 1976, 22, 523-533) model. Both appeared to work equally well at predicting mean bacteria breakthrough using a constant mean bacteria diameter for this set of field conditions. Simulations using a distribution of bacterial cell diameters available from original field notes yielded a slight improvement in the model and data agreement compared to simulations using an average bacterial diameter. The stochastic approach based on estimates of local-scale parameters for the bacteria-transport process reasonably captured the mean bacteria transport behavior and calculated an envelope of uncertainty that bracketed the observations in most simulation cases. ?? 2007 American Chemical Society.

A developmental basis for stochasticity in floral organ numbers

PubMed Central

Kitazawa, Miho S.; Fujimoto, Koichi

2014-01-01

Stochasticity ubiquitously inevitably appears at all levels from molecular traits to multicellular, morphological traits. Intrinsic stochasticity in biochemical reactions underlies the typical intercellular distributions of chemical concentrations, e.g., morphogen gradients, which can give rise to stochastic morphogenesis. While the universal statistics and mechanisms underlying the stochasticity at the biochemical level have been widely analyzed, those at the morphological level have not. Such morphological stochasticity is found in foral organ numbers. Although the floral organ number is a hallmark of floral species, it can distribute stochastically even within an individual plant. The probability distribution of the floral organ number within a population is usually asymmetric, i.e., it is more likely to increase rather than decrease from the modal value, or vice versa. We combined field observations, statistical analysis, and mathematical modeling to study the developmental basis of the variation in floral organ numbers among 50 species mainly from Ranunculaceae and several other families from core eudicots. We compared six hypothetical mechanisms and found that a modified error function reproduced much of the asymmetric variation found in eudicot floral organ numbers. The error function is derived from mathematical modeling of floral organ positioning, and its parameters represent measurable distances in the floral bud morphologies. The model predicts two developmental sources of the organ-number distributions: stochastic shifts in the expression boundaries of homeotic genes and a semi-concentric (whorled-type) organ arrangement. Other models species- or organ-specifically reproduced different types of distributions that reflect different developmental processes. The organ-number variation could be an indicator of stochasticity in organ fate determination and organ positioning. PMID:25404932

Stochastic point-source modeling of ground motions in the Cascadia region

USGS Publications Warehouse

Atkinson, G.M.; Boore, D.M.

1997-01-01

A stochastic model is used to develop preliminary ground motion relations for the Cascadia region for rock sites. The model parameters are derived from empirical analyses of seismographic data from the Cascadia region. The model is based on a Brune point-source characterized by a stress parameter of 50 bars. The model predictions are compared to ground-motion data from the Cascadia region and to data from large earthquakes in other subduction zones. The point-source simulations match the observations from moderate events (M 100 km). The discrepancy at large magnitudes suggests further work on modeling finite-fault effects and regional attenuation is warranted. In the meantime, the preliminary equations are satisfactory for predicting motions from events of M < 7 and provide conservative estimates of motions from larger events at distances less than 100 km.

Comparing 2-nt 3' overhangs against blunt-ended siRNAs: a systems biology based study.

PubMed

Ghosh, Preetam; Dullea, Robert; Fischer, James E; Turi, Tom G; Sarver, Ronald W; Zhang, Chaoyang; Basu, Kalyan; Das, Sajal K; Poland, Bradley W

2009-07-07

In this study, we formulate a computational reaction model following a chemical kinetic theory approach to predict the binding rate constant for the siRNA-RISC complex formation reaction. The model allowed us to study the potency difference between 2-nt 3' overhangs against blunt-ended siRNA molecules in an RNA interference (RNAi) system. The rate constant predicted by this model was fed into a stochastic simulation of the RNAi system (using the Gillespie stochastic simulator) to study the overall potency effect. We observed that the stochasticity in the transcription/translation machinery has no observable effects in the RNAi pathway. Sustained gene silencing using siRNAs can be achieved only if there is a way to replenish the dsRNA molecules in the cell. Initial findings show about 1.5 times more blunt-ended molecules will be required to keep the mRNA at the same reduced level compared to the 2-nt overhang siRNAs. However, the mRNA levels jump back to saturation after a longer time when blunt-ended siRNAs are used. We found that the siRNA-RISC complex formation reaction rate was 2 times slower when blunt-ended molecules were used pointing to the fact that the presence of the 2-nt overhangs has a greater effect on the reaction in which the bound RISC complex cleaves the mRNA.

Comparing 2-nt 3' overhangs against blunt-ended siRNAs: a systems biology based study

PubMed Central

Ghosh, Preetam; Dullea, Robert; Fischer, James E; Turi, Tom G; Sarver, Ronald W; Zhang, Chaoyang; Basu, Kalyan; Das, Sajal K; Poland, Bradley W

2009-01-01

In this study, we formulate a computational reaction model following a chemical kinetic theory approach to predict the binding rate constant for the siRNA-RISC complex formation reaction. The model allowed us to study the potency difference between 2-nt 3' overhangs against blunt-ended siRNA molecules in an RNA interference (RNAi) system. The rate constant predicted by this model was fed into a stochastic simulation of the RNAi system (using the Gillespie stochastic simulator) to study the overall potency effect. We observed that the stochasticity in the transcription/translation machinery has no observable effects in the RNAi pathway. Sustained gene silencing using siRNAs can be achieved only if there is a way to replenish the dsRNA molecules in the cell. Initial findings show about 1.5 times more blunt-ended molecules will be required to keep the mRNA at the same reduced level compared to the 2-nt overhang siRNAs. However, the mRNA levels jump back to saturation after a longer time when blunt-ended siRNAs are used. We found that the siRNA-RISC complex formation reaction rate was 2 times slower when blunt-ended molecules were used pointing to the fact that the presence of the 2-nt overhangs has a greater effect on the reaction in which the bound RISC complex cleaves the mRNA. PMID:19594876

Improved Modeling of Finite-Rate Turbulent Combustion Processes in Research Combustors

NASA Technical Reports Server (NTRS)

VanOverbeke, Thomas J.

1998-01-01

The objective of this thesis is to further develop and test a stochastic model of turbulent combustion in recirculating flows. There is a requirement to increase the accuracy of multi-dimensional combustion predictions. As turbulence affects reaction rates, this interaction must be more accurately evaluated. In this work a more physically correct way of handling the interaction of turbulence on combustion is further developed and tested. As turbulence involves randomness, stochastic modeling is used. Averaged values such as temperature and species concentration are found by integrating the probability density function (pdf) over the range of the scalar. The model in this work does not assume the pdf type, but solves for the evolution of the pdf using the Monte Carlo solution technique. The model is further developed by including a more robust reaction solver, by using accurate thermodynamics and by more accurate transport elements. The stochastic method is used with Semi-Implicit Method for Pressure-Linked Equations. The SIMPLE method is used to solve for velocity, pressure, turbulent kinetic energy and dissipation. The pdf solver solves for temperature and species concentration. Thus, the method is partially familiar to combustor engineers. The method is compared to benchmark experimental data and baseline calculations. The baseline method was tested on isothermal flows, evaporating sprays and combusting sprays. Pdf and baseline predictions were performed for three diffusion flames and one premixed flame. The pdf method predicted lower combustion rates than the baseline method in agreement with the data, except for the premixed flame. The baseline and stochastic predictions bounded the experimental data for the premixed flame. The use of a continuous mixing model or relax to mean mixing model had little effect on the prediction of average temperature. Two grids were used in a hydrogen diffusion flame simulation. Grid density did not effect the predictions except for peak temperature and tangential velocity. The hybrid pdf method did take longer and required more memory, but has a theoretical basis to extend to many reaction steps which cannot be said of current turbulent combustion models.

Two Stochastic Phases of Tick-wise Price Fluctuation and the Price Prediction Generator

NASA Astrophysics Data System (ADS)

Tanaka-Yamawaki, Mieko; Tokuoka, Seiji

2007-07-01

We report in this paper the existence of two different stochastic phases in the tick-wise price fluctuations. Based on this observation, we improve our old method of developing the evolutional strategy to predict the direction of the tick-wise price movements. We obtain a stable predictive power even in the region where the old method had a difficulty.

Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

NASA Technical Reports Server (NTRS)

Williams Colin P.

1999-01-01

Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

A stochastic multiple imputation algorithm for missing covariate data in tree-structured survival analysis.

PubMed

Wallace, Meredith L; Anderson, Stewart J; Mazumdar, Sati

2010-12-20

Missing covariate data present a challenge to tree-structured methodology due to the fact that a single tree model, as opposed to an estimated parameter value, may be desired for use in a clinical setting. To address this problem, we suggest a multiple imputation algorithm that adds draws of stochastic error to a tree-based single imputation method presented by Conversano and Siciliano (Technical Report, University of Naples, 2003). Unlike previously proposed techniques for accommodating missing covariate data in tree-structured analyses, our methodology allows the modeling of complex and nonlinear covariate structures while still resulting in a single tree model. We perform a simulation study to evaluate our stochastic multiple imputation algorithm when covariate data are missing at random and compare it to other currently used methods. Our algorithm is advantageous for identifying the true underlying covariate structure when complex data and larger percentages of missing covariate observations are present. It is competitive with other current methods with respect to prediction accuracy. To illustrate our algorithm, we create a tree-structured survival model for predicting time to treatment response in older, depressed adults. Copyright © 2010 John Wiley & Sons, Ltd.

State-dependent anisotrophy: Comparison of quasi-analytical solutions with stochastic results for steady gravity drainage

USGS Publications Warehouse

Green, Timothy R.; Freyberg, David L.

1995-01-01

Anisotropy in large-scale unsaturated hydraulic conductivity of layered soils changes with the moisture state. Here, state-dependent anisotropy is computed under conditions of large-scale gravity drainage. Soils represented by Gardner's exponential function are perfectly stratified, periodic, and inclined. Analytical integration of Darcy’s law across each layer results in a system of nonlinear equations that is solved iteratively for capillary suction at layer interfaces and for the Darcy flux normal to layering. Computed fluxes and suction profiles are used to determine both upscaled hydraulic conductivity in the principal directions and the corresponding “state-dependent” anisotropy ratio as functions of the mean suction. Three groups of layered soils are analyzed and compared with independent predictions from the stochastic results of Yeh et al. (1985b). The small-perturbation approach predicts appropriate behaviors for anisotropy under nonarid conditions. However, the stochastic results are limited to moderate values of mean suction; this limitation is linked to a Taylor series approximation in terms of a group of statistical and geometric parameters. Two alternative forms of the Taylor series provide upper and lower bounds for the state-dependent anisotropy of relatively dry soils.

Effects of stochastic noise on dynamical decoupling procedures

NASA Astrophysics Data System (ADS)

Bernád, J. Z.; Frydrych, H.

2014-06-01

Dynamical decoupling is an important tool to counter decoherence and dissipation effects in quantum systems originating from environmental interactions. It has been used successfully in many experiments; however, there is still a gap between fidelity improvements achieved in practice compared to theoretical predictions. We propose a model for imperfect dynamical decoupling based on a stochastic Ito differential equation which could explain the observed gap. We discuss the impact of our model on the time evolution of various quantum systems in finite- and infinite-dimensional Hilbert spaces. Analytical results are given for the limit of continuous control, whereas we present numerical simulations and upper bounds for the case of finite control.

The use of copulas to practical estimation of multivariate stochastic differential equation mixed effects models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rupšys, P.

A system of stochastic differential equations (SDE) with mixed-effects parameters and multivariate normal copula density function were used to develop tree height model for Scots pine trees in Lithuania. A two-step maximum likelihood parameter estimation method is used and computational guidelines are given. After fitting the conditional probability density functions to outside bark diameter at breast height, and total tree height, a bivariate normal copula distribution model was constructed. Predictions from the mixed-effects parameters SDE tree height model calculated during this research were compared to the regression tree height equations. The results are implemented in the symbolic computational language MAPLE.

A comparison of the stochastic and machine learning approaches in hydrologic time series forecasting

NASA Astrophysics Data System (ADS)

Kim, T.; Joo, K.; Seo, J.; Heo, J. H.

2016-12-01

Hydrologic time series forecasting is an essential task in water resources management and it becomes more difficult due to the complexity of runoff process. Traditional stochastic models such as ARIMA family has been used as a standard approach in time series modeling and forecasting of hydrological variables. Due to the nonlinearity in hydrologic time series data, machine learning approaches has been studied with the advantage of discovering relevant features in a nonlinear relation among variables. This study aims to compare the predictability between the traditional stochastic model and the machine learning approach. Seasonal ARIMA model was used as the traditional time series model, and Random Forest model which consists of decision tree and ensemble method using multiple predictor approach was applied as the machine learning approach. In the application, monthly inflow data from 1986 to 2015 of Chungju dam in South Korea were used for modeling and forecasting. In order to evaluate the performances of the used models, one step ahead and multi-step ahead forecasting was applied. Root mean squared error and mean absolute error of two models were compared.

On the reach of perturbative descriptions for dark matter displacement fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baldauf, Tobias; Zaldarriaga, Matias; Schaan, Emmanuel, E-mail: baldauf@ias.edu, E-mail: eschaan@astro.princeton.edu, E-mail: matiasz@ias.edu

We study Lagrangian Perturbation Theory (LPT) and its regularization in the Effective Field Theory (EFT) approach. We evaluate the LPT displacement with the same phases as a corresponding N-body simulation, which allows us to compare perturbation theory to the non-linear simulation with significantly reduced cosmic variance, and provides a more stringent test than simply comparing power spectra. We reliably detect a non-vanishing leading order EFT coefficient and a stochastic displacement term, uncorrelated with the LPT terms. This stochastic term is expected in the EFT framework, and, to the best of our understanding, is not an artifact of numerical errors ormore » transients in our simulations. This term constitutes a limit to the accuracy of perturbative descriptions of the displacement field and its phases, corresponding to a 1% error on the non-linear power spectrum at k = 0.2 h{sup −1}Mpc at z = 0. Predicting the displacement power spectrum to higher accuracy or larger wavenumbers thus requires a model for the stochastic displacement.« less

Modelling daily water temperature from air temperature for the Missouri River.

PubMed

Zhu, Senlin; Nyarko, Emmanuel Karlo; Hadzima-Nyarko, Marijana

2018-01-01

The bio-chemical and physical characteristics of a river are directly affected by water temperature, which thereby affects the overall health of aquatic ecosystems. It is a complex problem to accurately estimate water temperature. Modelling of river water temperature is usually based on a suitable mathematical model and field measurements of various atmospheric factors. In this article, the air-water temperature relationship of the Missouri River is investigated by developing three different machine learning models (Artificial Neural Network (ANN), Gaussian Process Regression (GPR), and Bootstrap Aggregated Decision Trees (BA-DT)). Standard models (linear regression, non-linear regression, and stochastic models) are also developed and compared to machine learning models. Analyzing the three standard models, the stochastic model clearly outperforms the standard linear model and nonlinear model. All the three machine learning models have comparable results and outperform the stochastic model, with GPR having slightly better results for stations No. 2 and 3, while BA-DT has slightly better results for station No. 1. The machine learning models are very effective tools which can be used for the prediction of daily river temperature.

? filtering for stochastic systems driven by Poisson processes

NASA Astrophysics Data System (ADS)

Song, Bo; Wu, Zheng-Guang; Park, Ju H.; Shi, Guodong; Zhang, Ya

2015-01-01

This paper investigates the ? filtering problem for stochastic systems driven by Poisson processes. By utilising the martingale theory such as the predictable projection operator and the dual predictable projection operator, this paper transforms the expectation of stochastic integral with respect to the Poisson process into the expectation of Lebesgue integral. Then, based on this, this paper designs an ? filter such that the filtering error system is mean-square asymptotically stable and satisfies a prescribed ? performance level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.

Hill functions for stochastic gene regulatory networks from master equations with split nodes and time-scale separation

NASA Astrophysics Data System (ADS)

Lipan, Ovidiu; Ferwerda, Cameron

2018-02-01

The deterministic Hill function depends only on the average values of molecule numbers. To account for the fluctuations in the molecule numbers, the argument of the Hill function needs to contain the means, the standard deviations, and the correlations. Here we present a method that allows for stochastic Hill functions to be constructed from the dynamical evolution of stochastic biocircuits with specific topologies. These stochastic Hill functions are presented in a closed analytical form so that they can be easily incorporated in models for large genetic regulatory networks. Using a repressive biocircuit as an example, we show by Monte Carlo simulations that the traditional deterministic Hill function inaccurately predicts time of repression by an order of two magnitudes. However, the stochastic Hill function was able to capture the fluctuations and thus accurately predicted the time of repression.

Ensemble superparameterization versus stochastic parameterization: A comparison of model uncertainty representation in tropical weather prediction

NASA Astrophysics Data System (ADS)

Subramanian, Aneesh C.; Palmer, Tim N.

2017-06-01

Stochastic schemes to represent model uncertainty in the European Centre for Medium-Range Weather Forecasts (ECMWF) ensemble prediction system has helped improve its probabilistic forecast skill over the past decade by both improving its reliability and reducing the ensemble mean error. The largest uncertainties in the model arise from the model physics parameterizations. In the tropics, the parameterization of moist convection presents a major challenge for the accurate prediction of weather and climate. Superparameterization is a promising alternative strategy for including the effects of moist convection through explicit turbulent fluxes calculated from a cloud-resolving model (CRM) embedded within a global climate model (GCM). In this paper, we compare the impact of initial random perturbations in embedded CRMs, within the ECMWF ensemble prediction system, with stochastically perturbed physical tendency (SPPT) scheme as a way to represent model uncertainty in medium-range tropical weather forecasts. We especially focus on forecasts of tropical convection and dynamics during MJO events in October-November 2011. These are well-studied events for MJO dynamics as they were also heavily observed during the DYNAMO field campaign. We show that a multiscale ensemble modeling approach helps improve forecasts of certain aspects of tropical convection during the MJO events, while it also tends to deteriorate certain large-scale dynamic fields with respect to stochastically perturbed physical tendencies approach that is used operationally at ECMWF.