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Parameter estimation for chaotic systems using a hybrid adaptive cuckoo search with simulated annealing algorithm
This paper introduces a novel hybrid optimization algorithm to establish the parameters of chaotic systems. In order to deal with the weaknesses of the traditional cuckoo search algorithm, the proposed adaptive cuckoo search with simulated annealing algorithm is presented, which incorporates the adaptive parameters adjusting operation and the simulated annealing operation in the cuckoo search algorithm. Normally, the parameters of the cuckoo search algorithm are kept constant that may result in decreasing the efficiency of the algorithm. For the purpose of balancing and enhancing the accuracy and convergence rate of the cuckoo search algorithm, the adaptive operation is presented to tune the parameters properly. Besides, the local search capability of cuckoo search algorithm is relatively weak that may decrease the quality of optimization. So the simulated annealing operation is merged into the cuckoo search algorithm to enhance the local search ability and improve the accuracy and reliability of the results. The functionality of the proposed hybrid algorithm is investigated through the Lorenz chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the method can estimate parameters efficiently and accurately in the noiseless and noise condition. Finally, the results are compared with the traditional cuckoo search algorithm, genetic algorithm, and particle swarm optimization algorithm. Simulation results demonstrate the effectiveness and superior performance of the proposed algorithm.
ESTIMATION OF DISTANCES TO STARS WITH STELLAR PARAMETERS FROM LAMOST
We present a method to estimate distances to stars with spectroscopically derived stellar parameters. The technique is a Bayesian approach with likelihood estimated via comparison of measured parameters to a grid of stellar isochrones, and returns a posterior probability density function for each star’s absolute magnitude. This technique is tailored specifically to data from the Large Sky Area Multi-object Fiber Spectroscopic Telescope (LAMOST) survey. Because LAMOST obtains roughly 3000 stellar spectra simultaneously within each ∼5° diameter “plate” that is observed, we can use the stellar parameters of the observed stars to account for the stellar luminosity function and target selection effects. This removes biasing assumptions about the underlying populations, both due to predictions of the luminosity function from stellar evolution modeling, and from Galactic models of stellar populations along each line of sight. Using calibration data of stars with known distances and stellar parameters, we show that our method recovers distances for most stars within ∼20%, but with some systematic overestimation of distances to halo giants. We apply our code to the LAMOST database, and show that the current precision of LAMOST stellar parameters permits measurements of distances with ∼40% error bars. This precision should improve as the LAMOST data pipelines continue to be refined.
A Comparison of Cosmological Parameters Determined from CMB Temperature Power Spectra from the South Pole Telescope and the Planck Satellite
The Planck cosmic microwave background temperature data are best fit with a Lambda CDM model that mildly contradicts constraints from other cosmological probes. The South Pole Telescope (SPT) 2540 deg(2) SPT-SZ survey offers measurements on sub-degree angular scales (multipoles 650 <= l <= 2500) with sufficient precision to use as an independent check of the Planck data. Here we build on the recent joint analysis of the SPT-SZ and Planck data in Hou et al. by comparing Lambda CDM parameter estimates using the temperature power spectrum from both data sets in the SPT-SZ survey region. We also restrict the multipole range used in parameter fitting to focus on modes measured well by both SPT and Planck, thereby greatly reducing sample variance as a driver of parameter differences and creating a stringent test for systematic errors. We find no evidence of systematic errors from these tests. When we expand the maximum multipole of SPT data used, we see low-significance shifts in the angular scale of the sound horizon and the physical baryon and cold dark matter densities, with a resulting trend to higher Hubble constant. When we compare SPT and Planck data on the SPT-SZ sky patch to Planck full-sky data but keep the multipole range restricted, we find differences in the parameters n(s) and A(s)e(-2 tau). We perform further checks, investigating instrumental effects and modeling assumptions, and we find no evidence that the effects investigated are responsible for any of the parameter shifts. Taken together, these tests reveal no evidence for systematic errors in SPT or Planck data in the overlapping sky coverage and multipole range and at most weak evidence for a breakdown of Lambda CDM or systematic errors influencing either the Planck data outside the SPT-SZ survey area or the SPT data at l > 2000.
Inference of reaction rate parameters based on summary statistics from experiments
Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H 2 /O 2 -mechanism chain branching reaction H + O 2 → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the given summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize Gauss-Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity in the model, the consistent data sets all res ult in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogen-air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.
K-ε Turbulence Model Parameter Estimates Using an Approximate Self-similar Jet-in-Crossflow Solution
The k-ε turbulence model has been described as perhaps “the most widely used complete turbulence model.” This family of heuristic Reynolds Averaged Navier-Stokes (RANS) turbulence closures is supported by a suite of model parameters that have been estimated by demanding the satisfaction of well-established canonical flows such as homogeneous shear flow, log-law behavior, etc. While this procedure does yield a set of so-called nominal parameters, it is abundantly clear that they do not provide a universally satisfactory turbulence model that is capable of simulating complex flows. Recent work on the Bayesian calibration of the k-ε model using jet-in-crossflow wind tunnel data has yielded parameter estimates that are far more predictive than nominal parameter values. In this paper, we develop a self-similar asymptotic solution for axisymmetric jet-in-crossflow interactions and derive analytical estimates of the parameters that were inferred using Bayesian calibration. The self-similar method utilizes a near field approach to estimate the turbulence model parameters while retaining the classical far-field scaling to model flow field quantities. Our parameter values are seen to be far more predictive than the nominal values, as checked using RANS simulations and experimental measurements. They are also closer to the Bayesian estimates than the nominal parameters. A traditional simplified jet trajectory model is explicitly related to the turbulence model parameters and is shown to yield good agreement with measurement when utilizing the analytical derived turbulence model coefficients. Finally, the close agreement between the turbulence model coefficients obtained via Bayesian calibration and the analytically estimated coefficients derived in this paper is consistent with the contention that the Bayesian calibration approach is firmly rooted in the underlying physical description.
Consequences of CCD imperfections for cosmology determined by weak lensing surveys: from laboratory measurements to cosmological parameter bias
Weak gravitational lensing causes subtle changes in the apparent shapes of galaxies due to the bending of light by the gravity of foreground masses. By measuring the shapes of large numbers of galaxies (millions in recent surveys, up to tens of billions in future surveys) we can infer the parameters that determine cosmology. Imperfections in the detectors used to record images of the sky can introduce changes in the apparent shapes of galaxies, which in turn can bias the inferred cosmological parameters. In this paper we consider the effect of two widely discussed sensor imperfections: tree rings, due to impurity gradients that cause transverse electric fields in the charge-coupled devices (CCDs), and pixel size variation, due to periodic CCD fabrication errors. These imperfections can be observed when the detectors are subject to uniform illumination (flat-field images). We develop methods to determine the spurious shear and convergence (due to the imperfections) from the flat-field images. We calculate how the spurious shear when added to the lensing shear will bias the determination of cosmological parameters. We apply our methods to candidate sensors of the Large Synoptic Survey Telescope (LSST) as a timely and important example, analyzing flat-field images recorded with LSST prototype CCDs in the laboratory. We find that tree rings and periodic pixel size variation present in the LSST CCDs will introduce negligible bias to cosmological parameters determined from the lensing power spectrum, specifically w, Ω{sub m}, and σ{sub 8}.
Automated extraction of physical parameters from experimentally obtained thermal profiles using a machine learning approach
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Reionization history and CMB parameter estimation
We study how uncertainty in the reionization history of the universe affects estimates of other cosmological parameters from the Cosmic Microwave Background. We analyze WMAP7 data and synthetic Planck-quality data generated using a realistic scenario for the reionization history of the universe obtained from high-resolution numerical simulation. We perform parameter estimation using a simple sudden reionization approximation, and using the Principal Component Analysis (PCA) technique proposed by Mortonson and Hu. We reach two main conclusions: (1) Adopting a simple sudden reionization model does not introduce measurable bias into values for other parameters, indicating that detailed modeling of reionization is not necessary for the purpose of parameter estimation from future CMB data sets such as Planck. (2) PCA analysis does not allow accurate reconstruction of the actual reionization history of the universe in a realistic case.
On the parameter combinations that matter and on those that do not: data-driven studies of parameter (non)identifiability
Abstract We present a data-driven approach to characterizing nonidentifiability of a model’s parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal combinations of parameters required to characterize the output behavior of a chemical system: a set of effective parameters for the model. Furthermore, we introduce and use a Conformal Autoencoder Neural Network technique, as well as a kernel-based Jointly Smooth Function technique, to disentangle the redundant parameter combinations that do not affect the output behavior from the ones that do. We discuss the interpretability of our data-driven effective parameters, and demonstrate the utility of the approach both for behavior prediction and parameter estimation. In the latter task, it becomes important to describe level sets in parameter space that are consistent with a particular output behavior. We validate our approach on a model of multisite phosphorylation, where a reduced set of effective parameters (nonlinear combinations of the physical ones) has previously been established analytically.
Impact of Detailed Parameter Modeling of Open-Cycle Gas Turbines on Production Cost Simulation: Preprint
Flexible resources are increasingly important as variable renewable energy deployment in the power system increases. Although many systems are transitioning away from fossil fuels, open-cycle gas turbines are likely to play an important balancing role for some time, thus requiring accurate modeling of their operational parameters. This paper explores the impact of detailed representation of three operational parameters - start- up costs, run-up rates, and forced outage rates - in the production cost model of a system as it adopts higher levels of wind and solar. Using PLEXOS simulations of the NREL-118 bus test system, the study examines how more detailed parameter modeling affects outcomes such as the number of start-ups and shutdowns, ramping and total generation costs for open-cycle gas turbines, as renewable energy levels increase. The results suggest the value of detailed parameter modeling and continued research on combustion turbines' ability to provide flexibility.
Symmetry Parameter Constraints from a Lower Bound on Neutron-matter Energy
We propose the existence of a lower bound on the energy of pure neutron matter (PNM) on the basis of unitary-gas considerations. We discuss its justification from experimental studies of cold atoms as well as from theoretical studies of neutron matter. We demonstrate that this bound results in limits to the density-dependent symmetry energy, which is the difference between the energies of symmetric nuclear matter and PNM. In particular, this bound leads to a lower limit to the volume symmetry energy parameter S {sub 0}. In addition, for assumed values of S {sub 0} above this minimum, this bound implies both upper and lower limits to the symmetry energy slope parameter L , which describes the lowest-order density dependence of the symmetry energy. A lower bound on neutron-matter incompressibility is also obtained. These bounds are found to be consistent with both recent calculations of the energies of PNM and constraints from nuclear experiments. Our results are significant because several equations of state that are currently used in astrophysical simulations of supernovae and neutron star mergers, as well as in nuclear physics simulations of heavy-ion collisions, have symmetry energy parameters that violate these bounds. Furthermore, below the nuclear saturation density, the bound on neutron-matter energies leads to a lower limit to the density-dependent symmetry energy, which leads to upper limits to the nuclear surface symmetry parameter and the neutron-star crust–core boundary. We also obtain a lower limit to the neutron-skin thicknesses of neutron-rich nuclei. Above the nuclear saturation density, the bound on neutron-matter energies also leads to an upper limit to the symmetry energy, with implications for neutron-star cooling via the direct Urca process.
Diffusion and perfusion MR parameters to assess preoperative short-course radiotherapy response in locally advanced rectal cancer: a comparative explorative study among Standardized Index of Shape by DCE-MRI, intravoxel incoherent motion- and diffusion kurtosis imaging-derived parameters
Purpose: To assess preoperative short-course radiotherapy (SCR) tumor response in locally advanced rectal cancer (LARC) by means of Standardized Index of Shape (SIS) by dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), apparent diffusion coefficient (ADC), intravoxel incoherent motion (IVIM) and diffusion kurtosis imaging (DKI) parameters derived from diffusion-weighted MRI (DW-MRI). Materials and methods: Thirty-four patients with LARC who underwent MRI scans before and after SCR followed by delayed surgery, retrospectively, were enrolled. SIS, ADC, IVIM parameters [tissue diffusion (D{sub t}), pseudo-diffusion (D{sub p}), perfusion fraction (f{sub p})] and DKI parameters [mean diffusivity (MD), mean of diffusional kurtosis (MK)] were calculated for each patient. IVIM parameters were estimated using two methods, namely conventional biexponential fitting (CBFM) and variable projection (VARPRO). After surgery, the pathological TNM and tumor regression grade (TRG) were estimated. For each parameter, percentage changes between before and after SCR were evaluated. Furthermore, an artificial neural network was trained for outcome prediction. Nonparametric sample tests and receiver operating characteristic curve (ROC) analysis were performed. Results: Fifteen patients were classified as responders (TRG ≤ 2) and 19 as not responders (TRG > 3). Seven patients had TRG 1 (pathological complete response, pCR). Mean and standard deviation values of pre-treatment CBFM D{sub p} and mean value of VARPRO D{sub p} pre-treatment showed statistically significant differences to predict pCR. (p value at Mann–Whitney test was 0.05, 0.03 and 0.008, respectively.) Exclusively SIS percentage change showed significant differences between responder and non-responder patients after SCR (p value << 0.001) and to assess pCR after SCR (p value << 0.001). The best results to predict pCR were obtained by VARPRO Fp mean value pre-treatment with area under ROC of 0.84, a sensitivity of 96.4%, a specificity of 71.4%, a positive predictive value (PPV) of 92.9%, a negative predictive value (NPV) of 83.3% and an accuracy of 91.2%. The best results to assess after treatment complete pathological response were obtained by SIS with an area under ROC of 0.89, a sensitivity of 85.7%, a specificity of 92.6%, a PPV of 75.0%, a NPV of 96.1% and an accuracy of 91.2%. Moreover, the best results to differentiate after treatment responders vs. non-responders were obtained by SIS with an area under ROC of 0.94, a sensitivity of 93.3%, a specificity of 84.2%, a PPV of 82.4%, a NPV of 94.1% and an accuracy of 88.2%. Promising initial results were obtained using a decision tree tested with all ADC, IVIM and DKI extracted parameter: we reached high accuracy to assess pathological complete response after SCR in LARC (an accuracy of 85.3% to assess pathological complete response after SCR using VARPRO D{sub p} mean value post-treatment, ADC standard deviation value pre-treatment, MD standard deviation value post-treatment). Conclusion: SIS is a hopeful DCE-MRI angiogenic biomarker to assess preoperative treatment response after SCR with delayed surgery. Furthermore, an important prognostic role was obtained by VARPRO F{sub p} mean value pre-treatment and by a decision tree composed by diffusion parameters derived by DWI and DKI to assess pathological complete response.
Approximate effect of parameter pseudonoise intensity on rate of convergence for EKF parameter estimators
When using parameter estimation methods based on extended Kalman filter (EKF) theory, it is common practice to assume that the unknown parameter values behave like a random process, such as a random walk, in order to guarantee their identifiability by the filter. The present work is the result of an ongoing effort to quantitatively describe the effect that the assumption of a fictitious noise (called pseudonoise) driving the unknown parameter values has on the parameter estimate convergence rate in filter-based parameter estimators. The initial approach is to examine a first-order system described by one state variable with one parameter to be estimated. The intent is to derive analytical results for this simple system that might offer insight into the effect of the pseudonoise assumption for more complex systems. Such results would make it possible to predict the estimator error convergence behavior as a function of the assumed pseudonoise intensity, and this leads to the natural application of the results to the design of filter-based parameter estimators. The results obtained show that the analytical description of the convergence behavior is very difficult.
Gaussian Mixture Model-Based Ensemble Kalman Filter for Machine Parameter Calibration
This letter proposes a novel Gaussian mixture model-based ensemble Kalman filter (GMM-EnKF) approach to the accurate calibration of the parameters of machine dynamic models. This approach aims to overcome some practical challenges of machine parameter calibration. Results show the proposed approach can provide high-accuracy calibrated parameters even when the machine operates under unbalanced network conditions and the measurement noises are non-Gaussian.
Cosmic shear results from the deep lens survey. II. Full cosmological parameter constraints from tomography
We present a tomographic cosmic shear study from the Deep Lens Survey (DLS), which, providing a limiting magnitude r{sub lim}∼27 (5σ), is designed as a precursor Large Synoptic Survey Telescope (LSST) survey with an emphasis on depth. Using five tomographic redshift bins, we study their auto- and cross-correlations to constrain cosmological parameters. We use a luminosity-dependent nonlinear model to account for the astrophysical systematics originating from intrinsic alignments of galaxy shapes. We find that the cosmological leverage of the DLS is among the highest among existing >10 deg{sup 2} cosmic shear surveys. Combining the DLS tomography with the 9 yr results of the Wilkinson Microwave Anisotropy Probe (WMAP9) gives Ω{sub m}=0.293{sub −0.014}{sup +0.012}, σ{sub 8}=0.833{sub −0.018}{sup +0.011}, H{sub 0}=68.6{sub −1.2}{sup +1.4} km s{sup −1} Mpc{sup −1}, and Ω{sub b}=0.0475±0.0012 for ΛCDM, reducing the uncertainties of the WMAP9-only constraints by ∼50%. When we do not assume flatness for ΛCDM, we obtain the curvature constraint Ω{sub k}=−0.010{sub −0.015}{sup +0.013} from the DLS+WMAP9 combination, which, however, is not well constrained when WMAP9 is used alone. The dark energy equation-of-state parameter w is tightly constrained when baryonic acoustic oscillation (BAO) data are added, yielding w=−1.02{sub −0.09}{sup +0.10} with the DLS+WMAP9+BAO joint probe. The addition of supernova constraints further tightens the parameter to w=−1.03±0.03. Our joint constraints are fully consistent with the final Planck results and also with the predictions of a ΛCDM universe.
Nuclear Fission: from more phenomenology and adjusted parameters to more fundamental theory and increased predictive power
Two major recent developments in theory and computational resources created the favorable conditions for achieving a microscopic description of fission dynamics in classically allowed regions of the collective potential energy surface, almost eighty years after its discovery in 1939 by Hahn and Strassmann [1]. The first major development was in theory, the extension of the Time-Dependent Density Functional Theory (TDDFT) [2–5] to superfluid fermion systems [6]. The second development was in computing, the emergence of powerful enough supercomputers capable of solving the complex systems of equations describing the time evolution in three dimensions without any restrictions of hundreds of strongly interacting nucleons. Thus the conditions have been created to renounce phenomenological models and incomplete microscopic treatments with uncontrollable approximations and/or assumptions in the description of the complex dynamics of fission. Even though the available nuclear energy density functionals (NEDFs) are phenomenological still, their accuracy is improving steadily and the prospects of being able to perform calculations of the nuclear fission dynamics and to predict many properties of the fission fragments, otherwise not possible to extract from experiments.