Model-free Parameters Research Articles

Bulk density of small meteoroids

Aims. Here we report on precise metric and photometric observations of 107 optical meteors, which were simultaneously recorded at multiple stations using three different intensified video camera systems. The purpose is to estimate bulk meteoroid density, link small meteoroids to their parent bodies based on dynamical and physical density values expected for different small body populations, to better understand and explain the dynamical evolution of meteoroids after release from their parent bodies. Methods. The video systems used had image sizes ranging from 640 × 480 to 1360 × 1036 pixels, with pixel scales from 0.01 ◦ per pixel to 0.05 ◦ per pixel, and limiting meteor magnitudes ranging from Mv =+ 2.5 to +6.0. We find that 78% of our sample show noticeable deceleration, allowing more robust constraints to be placed on density estimates. The density of each meteoroid is estimated by simultaneously fitting the observed deceleration and lightcurve using a model based on thermal fragmentation, conservation of energy and momentum. The entire phase space of the model free parameters is explored for each event to find ranges of parameters which fit the observations within the measurement uncertainty. Results. (a) We have analysed our data by first associating each of our events with one of the five meteoroid classes. The average density of meteoroids whose orbits are asteroidal and chondritic (AC) is 4200 kg m −3 suggesting an asteroidal parentage, possibly related to the high-iron content population. Meteoroids with orbits belonging to Jupiter family comets (JFCs) have an average density of 3100 ± 300 kg m −3 . This high density is found for all meteoroids with JFC-like orbits and supports the notion that the refractory material reported from the Stardust measurements of 81P/Wild 2 dust is common among the broader JFC population. This high density is also the average bulk density for the 4 meteoroids with orbits belonging to the Ecliptic shower-type class (ES) also related to JFCs. Both categories we suggest are chondritic based on their high bulk density. Meteoroids of HT (Halley type) orbits have a minimum bulk density value of 360 +400 −900 kg m −3 . This is consistent with many previous works which suggest bulk cometary meteoroid density is low. SA (Sun-approaching)-type meteoroids show a density spread from 1000 kg m −3 to 4000 kg m −3 , reflecting multiple origins. (b) We found two different meteor showers in our sample: Perseids (10 meteoroids, ∼11% of our sample) with an average bulk density of 620 kg m −3 and Northern Iota Aquariids (4 meteoroids) with an average bulk density of 3200 kg m −3 , consistent with the notion that the NIA derive from 2P/Encke.

The effect of temporal wave averaging on the performance of an empirical shoreline evolution model

The effect of using time-averaged wave statistics in a simple empirical model for shoreline change is investigated. The model was first calibrated with a six-year time series of hourly wave conditions and weekly shoreline position at the Gold Coast, Australia. The model was then recalibrated with the hourly waves averaged over intervals up to 1 year. With wave averaging up to 2 days, model performance was approximately constant (squared correlation r 2 ~ 0.61–0.62), with only small changes in the values of empirical model parameters (e.g. the beach response coefficient c varied by less than 4%). With between 2 and 40 day averaging, individual storms are not resolved; model skill decreased only modestly (r 2 ~ 0.55), but c varied erratically by up to 40% of the original value. That is, optimal model coefficients depend on wave averaging, an undesirable result. With increased averaging (> 40 days) seasonal variability in the wave field is not resolved well and model skill declined markedly. Thus, temporal averaging of wave conditions increases numerical efficiency, but over-averaging degrades model performance and distorts best-fit values of model free parameters.

ASSIMILATING MODELS AND DATA TO ENHANCE PREDICTIONS OF SHORELINE EVOLUTION

A modeling system that considers both long- and short-term process-driven shoreline change is presented. The modeling system is integrated into a data assimilation framework that uses sparse observations of shoreline change to correct a model forecast and to determine unobserved model variables and free parameters. Application of the assimilation algorithm also provides quantitative statistical estimates of uncertainty that can be applied to coastal hazard and vulnerability assessments. Significant attention is given to the estimation of four non-observable quantities using the data assimilation framework that utilizes only one observable process (i.e. ,shoreline change). The general framework discussed here can be applied to many other geophysical processes by simply changing the model component to one applicable to the processes of interest.

Optimized pharmacokinetic modeling for the detection of perfusion differences in skeletal muscle with DCE‐MRI: Effect of contrast agent size

The goal of this study was to optimize dynamic contrast-enhanced (DCE)-MRI analysis for differently sized contrast agents and to evaluate the sensitivity for microvascular differences in skeletal muscle. In rabbits, pathophysiological perfusion differences between hind limbs were induced by unilateral femoral artery ligation. On days 14 and 21, DCE-MRI was performed using a medium-sized contrast agent (MCA) (Gadomer) or a small contrast agent (SCA) (Gd-DTPA). Acquisition protocols were adapted to the pharmacokinetic properties of the contrast agent. Model-based data analysis was optimized by selecting the optimal model, considering fit error, estimation uncertainty, and parameter interdependency from three two-compartment pharmacokinetic models (normal and extended generalized kinetic models and Patlak model). Model-based parameters were compared to the model-free parameter area-under-curve (AUC). Finally, the sensitivity of transfer constant Krans and AUC for physiological and pathophysiological microvascular differences was evaluated. For the MCA, the optimal model included Ktrans and plasma fraction nu(p). For the SCA, Ktrans and interstitial fraction nu(e) should be incorporated. For the MCA, Ktrans were (4.8 +/- 0.2) x 10(-3) min(-1) (mean standard error) and (3.6 +/- 0.1) x 10(-3) min(-1) for the red soleus and white tibialis muscle, respectively, p < 0.01. With the SCA, Ktrans were (81 +/- 5) x 10(-3) min(-1) (soleus) and (66 +/- 5) x 10(-3) min(-1) (tibialis) p < 0.01. In the ischemic limb, Ktrans was significantly decreased relative to the control limb (soleus: 15%-20%; tibialis: 5%-10%). Similar differences in AUC were found for both contrast agents. For optimal estimation of microvascular parameters, both model-based and model-free analysis should be adapted to the pharmacokinetic properties of the contrast agent. The detection of microvascular differences based on both Ktrans and AUC was most sensitive when the analysis strategy was tailored to the contrast agent used. The MCA was equally sensitive for microvascular differences as the SCA, with the advantage of improved spatial resolution.

Lung Cancer from Radon: A Two-Stage Model Analysis of the WISMUT Cohort, 1955–1998

A biologically based two-stage carcinogenesis model is applied to epidemiological data for lung cancer mortality in a large uranium miner cohort of the WISMUT company (Germany). To date, this is the largest uranium miner cohort analyzed by a mechanistic model, comprising 35,084 workers among whom 461 died from lung cancer in the follow-up period 1955-1998. It comprises only workers who were first employed between 1955 and 1989 and contains information on annual exposures to radon progeny. We fitted the model's free parameters, including the average growth time of one malignant cell into a lethal tumor. This lag time has an extraordinary value of 13 to 14 years, larger than that previously used or found in miner studies. Even though cohort-wide information on smoking habits is limited and the calendar-year dependence of tobacco smoke exposure was only implicitly accounted for by a birth cohort effect, we find good agreement between the modeled (expected) and empirical (observed) lung cancer mortality. Model calculations of excess relative lung cancer death risk agree well with those from the descriptive, BEIR VI-type exposure-age-concentration model for WISMUT miners. The large variety of exposure profiles in the cohort leads to a well-determined mechanistic model that in principle allows for an extrapolation from occupational to indoor radon exposure.

Assessment of liver function in primary biliary cirrhosis using Gd-EOB-DTPA-enhanced liver MRI

ObjectivesGd-EOB-DTPA (gadolinium ethoxybenzyl diethylenetriaminepentaacetic acid) is a gadolinium-based hepatocyte-specific contrast agent for magnetic resonance imaging (MRI). The aim of this study was to determine whether the hepatic uptake and excretion of Gd-EOB-DTPA differ between patients with primary biliary cirrhosis (PBC) and healthy controls, and whether differences could be quantified. MethodsGd-EOB-DTPA-enhanced liver MRI was performed in 20 healthy volunteers and 12 patients with PBC. The uptake of Gd-EOB-DTPA was assessed using traditional semi-quantitative parameters (Cmax, Tmax and T1/2), as well as model-free parameters derived after deconvolutional analysis (hepatic extraction fraction [HEF], input-relative blood flow [irBF] and mean transit time [MTT]). In each individual, all parameters were calculated for each liver segment and the median of the segmental values was used to define a global liver median (GLM). ResultsAlthough the PBC patients had relatively mild disease according to their Model for End-stage Liver Disease (MELD), Child–Pugh and Mayo risk scores, they had significantly lower HEF and shorter MTT values compared with the healthy controls. These differences significantly increased with increasing MELD and Child–Pugh scores. ConclusionsDynamic hepatocyte-specific contrast-enhanced MRI (DHCE-MRI) has a potential role as an imaging-based liver function test. The high spatial resolution of MRI enables hepatic function to be assessed on segmental and sub-segmental levels.

GECO: Galaxy Evolution COde – A new semi-analytical model of galaxy formation

We present a new semi-analytical model of galaxy formation, GECO (Galaxy Evolution COde), aimed at a better understanding of when and how the two processes of star formation and galaxy assembly have taken place. Our model is structured into a Monte Carlo algorithm based on the Extended Press-Schechter theory, for the representation of the merging hierarchy of dark matter halos, and a set of analytic algorithms for the treatment of the baryonic physics, including classical recipes for the gas cooling, the star formation time-scales, galaxy mergers and SN feedback. Together with the galaxies, the parallel growth of BHs is followed in time and their feedback on the hosting galaxies is modelled. We set the model free parameters by matching with data on local stellar mass functions and the BH-bulge relation at z=0. Based on such local boundary conditions, we investigate how data on the high-redshift universe constrain our understanding of the physical processes driving the evolution, focusing in particular on the assembly of stellar mass and on the star formation history. Since both processes are currently strongly constrained by cosmological near- and far-IR surveys, the basic physics of the Lambda CDM hierarchical clustering concept of galaxy formation can be effectively tested by us by comparison with the most reliable set of observables. Our investigation shows that when the time-scales of the stellar formation and mass assembly are studied as a function of dark matter halo mass and the single galaxy stellar mass, the 'downsizing' fashion of star formation appears to be a natural outcome of the model, reproduced even in the absence of the AGN feedback. On the contrary, the stellar mass assembly history turns out to follow a more standard hierarchical pattern progressive in cosmic time, with the more massive systems assembled at late times mainly through dissipationless mergers.

Effects of Atomic Mixing in Inertial Confinement Fusion by Multifluid Interpenetration Mix Model

The effects of atomic-level mixing are systemically investigated in a multifluid interpenetration mix model, and results are compared with the single-fluid model's simulations and experimental data. It is shown that increasing the model free parameter α, shock Mach number, and the initial density discontinuity makes the mix length and fraction of mixing particle increase, resulting in the lower shock temperatures compared with the results of single-fluid model without mixing. Recent high-compressibility direct-drive spherical implosions on OMEGA are simulated by the interpenetration mix model. The calculations with atomic mixing between fuel and shell match quite well with the observations. Without considering any mixing, the calculated neutron yields and ion temperatures are overpredicted; while inclusion of the interpenetration mix model with the adjustable parameter α could fit the simulated neutron yields and ion temperatures well with experimental data.

Equilibrium shoreline response: Observations and modeling

Shoreline location and incident wave energy, observed for almost 5 years at Torrey Pines beach, show seasonal fluctuations characteristic of southern California beaches. The shoreline location, defined as the cross‐shore position of the mean sea level contour, retreats by almost 40 m in response to energetic winter waves and gradually recovers during low‐energy summer waves. Hourly estimates of incident wave energy and weekly to monthly surveys of the shoreline location are used to develop and calibrate an equilibrium‐type shoreline change model. By hypothesis, the shoreline change rate depends on both the wave energy and the wave energy disequilibrium with the shoreline location. Using calibrated values of four model free parameters, observed and modeled shoreline location are well correlated at Torrey Pines and two additional survey sites. Model free parameters can be estimated with as little as 2 years of monthly observations or with about 5 years of ideally timed, biannual observations. Wave energy time series used to calibrate and test the model must resolve individual storms, and model performance is substantially degraded by using weekly to monthly averaged wave energy. Variations of free parameter values between sites may be associated with variations in sand grain size, sediment availability, and other factors. The model successfully reproduces shoreline location for time periods not used in tuning and can be used to predict beach response to past or hypothetical future wave climates. However, the model will fail when neglected geologic factors are important (e.g., underlying bedrock limits erosion or sand availability limits accretion).

Evaluating the effectiveness factor from a 1D approximation fitted at high Thiele modulus: Spanning commercial pellet shapes with linear kinetics

In the present contribution a one-dimensional model (1D model) is employed to account for the effect of pellet shape in the solution of diffusion–catalytic reaction problems. The 1D model free parameter ( σ) is fitted so as to match the second term of the series for the effective reaction rate at fast kinetic conditions. The performance of the model was evaluated for a large collection of pellets available commercially, covering almost all the main shapes offered by catalyst manufacturers. For isothermal linear kinetics the effectiveness factors calculated by the 1D model differ at most by 3% from those of the actual 3D pellets.

HIGHLY ACCELERATED DIAMAGNETIC PLASMOIDS: A NEW X-RAY PRODUCTION MECHANISM FOR OB STELLAR WINDS

The observed X-ray source temperature distributions in OB stellar winds, as determined from high energy resolution Chandra observations, show that the highest temperatures occur near the star, and then steadily decrease outward through the wind. To explain this unexpected behavior, we propose a shock model concept that utilizes a well-known magnetic propulsion mechanism: the surface ejection of diamagnetic plasmoids into a diverging external magnetic field. This produces rapidly accelerating self-contained structures that plow through an ambient wind and form bow shocks that generate a range in X-ray temperatures determined by the plasmoid-wind relative velocities. The model free parameters are the plasmoid initial Alfven speed, the initial plasma-β of the external medium, and the divergence rate of the external field. These are determined by fitting the predicted bow shock temperatures with the observed OB supergiant X-ray temperature distribution. We find that the initial external plasma-β has a range between 0 and 2, and the assumed radially decreasing external magnetic field strength that scales as r –S has a value of S lying between 2 and 3. Most importantly, the initial plasmoid Alfven speed is found to be well constrained at a value of 0.6V ∞, which appears to represent an upper limit for all normal OB stars. This intriguing new limit on OB magnetic properties, as derived from Chandra observations, emphasizes the need for further studies of magnetic propulsion mechanisms in these stars.

Model-independent interpretation of NMR relaxation data for unfolded proteins: the acid-denatured state of ACBP

We have investigated the acid-unfolded state of acyl-coenzyme A binding protein (ACBP) using 15N laboratory frame nuclear magnetic resonance (NMR) relaxation experiments at three magnetic field strengths. The data have been analyzed using standard model-free fitting and models involving distribution of correlation times. In particular, a model-independent method of analysis that does not assume any analytical form for the correlation time distribution is proposed. This method explains correlations between model-free parameters and the analytical distribution parameters found by other authors. The analysis also shows that the relaxation data are consistent with and complementary to information obtained from other parameters, especially secondary chemical shifts and residual dipolar couplings, and strengthens the conclusions of previous observations that three out of the four regions that form helices in the native structure appear to contain residual secondary structure also in the acid-denatured state.

Monitoring Aromatic Picosecond to Nanosecond Dynamics in Proteins via 13C Relaxation: Expanding Perturbation Mapping of the Rigidifying Core Mutation, V54A, in Eglin c

Long-range effects, such as allostery, have evolved in proteins as a means of regulating function via communication between distal sites. An NMR-based perturbation mapping approach was used to more completely probe the dynamic response of the core mutation V54A in the protein eglin c by monitoring changes in picosecond to nanosecond aromatic side-chain dynamics and H/D exchange stabilities. Previous side-chain dynamics studies on this mutant were limited to methyl-bearing residues, most of which were found to rigidify on the picosecond to nanosecond time scale in the form of a contiguous "network". Here, high precision (13)C relaxation data from 13 aromatic side chains were acquired by applying canonical relaxation experiments to a newly developed carbon labeling scheme [Teilum et al. (2006) J. Am. Chem. Soc. 128, 2506-2507]. The fitting of model-free parameters yielded S (2) variability which is intermediate with respect to backbone and methyl-bearing side-chain variability and tau e values that are approximately 1 ns. Inclusion of the aromatic dynamic response results in an expanded network of dynamically coupled residues, with some aromatics showing increases in flexibility, which partially offsets the rigidification in methyl side chains. Using amide hydrogen exchange, dynamic propagation on a slower time scale was probed in response to the V54A perturbation. Surprisingly, regional stabilization (slowed exchange) 10-12 A from the site of mutation was observed despite a global destabilization of 1.5 kcal x mol (-1). Furthermore, this unlikely pocket of stabilized residues colocalizes with increases in aromatic flexibility on the faster time scale. Because the converse is also true (destabilized residues colocalize with rigidification on the fast time scale), a plausible entropy-driven mechanism is discussed for relating colocalization of opposing dynamic trends on vastly different time scales.

On the evaluation of effective reaction rates on commercial catalyst by means of a one-dimensional model

A one-dimensional model (1D), called generalized cylinder (GC), for the diffusion–reaction problem in commercial catalytic pellets is presented. The GC model free parameter ( σ) is fitted so as to reproduce the behaviour of the actual pellet at high reaction rates. A simple analytical expression allows obtaining σ straightforwardly and the maximum deviation of the GC model is evaluated at around 2%.

Glandular Function in Sjögren Syndrome: Assessment with Dynamic Contrast-enhanced MR Imaging and Tracer Kinetic Modeling—Initial Experience

To prospectively use dynamic contrast material-enhanced magnetic resonance (MR) imaging and a tracer kinetic model to compare parotid gland microvascular characteristics in patients who have Sjögren syndrome (SS) with those in healthy volunteers. The local research ethics committee approved the study, and written informed consent was obtained from all participants. Twenty-one patients (19 women, two men; age range, 31-73 years) with a diagnosis of SS and 11 healthy volunteers (10 women, one man; age range, 41-68 years) underwent three-dimensional T1-weighted dynamic contrast-enhanced MR imaging of the parotid gland at 1.5 T. A voxel-wise tracer kinetic model and a model-free analysis were applied to the dynamic MR data. Parameter medians and standard deviations were computed to summarize gland microvascular characteristics and gland heterogeneity, respectively. Differences were investigated by using multivariate analysis of variance, t, or U tests. Further investigation was performed by using linear discriminant and receiver operating characteristic analyses. Compared with the healthy volunteers, the patients with SS had highly significant elevations (P << .001) in the model-free parameter initial area under the curve and in tracer kinetic model parameters, including transcapillary contrast agent transfer constant (P < .001) and extracellular extravascular volume (P < .001). Gland heterogeneity was significantly greater (P < .001) in the patients with SS. Parameter medians and standard deviations enabled excellent differentiation (areas under receiver operating characteristic curve, 0.96 and 1.00, respectively) between the patients with SS and the healthy volunteers. Dynamic contrast-enhanced MR imaging has the potential to be used in clinical settings to quantify microvascular function in SS and to differentiate between patients with and those without SS.

Optimisation of NMR dynamic models II. A new methodology for the dual optimisation of the model-free parameters and the Brownian rotational diffusion tensor

Finding the dynamics of an entire macromolecule is a complex problem as the model-free parameter values are intricately linked to the Brownian rotational diffusion of the molecule, mathematically through the autocorrelation function of the motion and statistically through model selection. The solution to this problem was formulated using set theory as an element of the universal set {mathfrak{U}}—the union of all model-free spaces (d’Auvergne EJ and Gooley PR (2007) Mol BioSyst 3(7), 483–494). The current procedure commonly used to find the universal solution is to initially estimate the diffusion tensor parameters, to optimise the model-free parameters of numerous models, and then to choose the best model via model selection. The global model is then optimised and the procedure repeated until convergence. In this paper a new methodology is presented which takes a different approach to this diffusion seeded model-free paradigm. Rather than starting with the diffusion tensor this iterative protocol begins by optimising the model-free parameters in the absence of any global model parameters, selecting between all the model-free models, and finally optimising the diffusion tensor. The new model-free optimisation protocol will be validated using synthetic data from Schurr JM et al. (1994) J Magn Reson B 105(3), 211–224 and the relaxation data of the bacteriorhodopsin (1–36)BR fragment from Orekhov VY (1999) J Biomol NMR 14(4), 345–356. To demonstrate the importance of this new procedure the NMR relaxation data of the Olfactory Marker Protein (OMP) of Gitti R et al. (2005) Biochem 44(28), 9673–9679 is reanalysed. The result is that the dynamics for certain secondary structural elements is very different from those originally reported.Electronic supplementary materialThe online version of this article (doi:10.1007/s10858-007-9213-3) contains supplementary material, which is available to authorized users.

Sensitivity analysis of large-eddy simulations to subgrid-scale-model parametric uncertainty using polynomial chaos

We address the sensitivity of large-eddy simulations (LES) to parametric uncertainty in the subgrid-scale model. More specifically, we investigate the sensitivity of the LES statistical moments of decaying homogeneous isotropic turbulence to the uncertainty in the Smagorinsky model free parameterCs(i.e. the Smagorinsky constant). Our sensitivity methodology relies on the non-intrusive approach of the generalized Polynomial Chaos (gPC) method; the gPC is a spectral non-statistical numerical method well-suited to representing random processes not restricted to Gaussian fields. The analysis is carried out at Reλ, =, 100 and for different grid resolutions andCsdistributions. Numerical predictions are also compared to direct numerical simulation evidence. We have shown that the different turbulent scales of the LES solution respond differently to the variability inCs. In particular, the study of the relative turbulent kinetic energy distributions for differentCsdistributions indicates that small scales are mainly affected by changes in the subgrid-model parametric uncertainty.

Route to non-Gaussian statistics in convective turbulence

Motivated by the work of Li and Meneveau [Phys. Rev. Lett. 95, 164502 (2005)], we propose and solve a model for the Lagrangian evolution of both longitudinal and transverse velocity and temperature increments for Boussinesq convection. From this model, the short-time evolution of an initially imposed Gaussian joint probability density function (PDF) of both velocity and temperature increments is computed analytically and the trend to non-Gaussian statistics shown in a quantitative way. Predictions for moments of the joint PDF are obtained and their behavior analyzed with respect to known experimental and numerical results. The obtained results do not depend on the model free parameters, a fact in favor of their robustness.

Assessing the tilt of the solar magnetic field axis through Faraday rotation observations

Context: Faraday rotation measurements of extragalactic radio sources during coronal occultation allow assessment of both the electron density distribution and the three-dimensional magnetic field topology in the outer solar corona. Aims: We simulate the three-dimensional structure of both the coronal magnetic field and the electron density distribution in order to reproduce the excess Faraday rotation measures (RMs) of the occulted radio sources observed during solar activity minimum. In particular, we infer the tilt of the solar magnetic axis with respect to the rotation axis. Methods: We compare the output of the model with Very Large Array (VLA) radio polarimetric measurements of a sample of extragalactic sources observed in May 1997. Information on the magnetic field geometry can be retrieved by fine-tuning the set of model free parameters that best describe the observations. Results: We find that predicted and observed Faraday rotation measures are in excellent agreement, thus supporting the model. Our best-fitting model yields a tilt angle $\theta_{RB}=3.3^{\circ}$ of the solar magnetic axis with respect to the solar rotation axis around Carrington Rotation 1923. This result is consistent with analogous but independent estimates computed from the expansion coefficients of the photospheric field observed at the Wilcox Solar Observatory (WSO).

Set theory formulation of the model-free problem and the diffusion seeded model-free paradigm

Model-free analysis of NMR relaxation data, which describes the motion of individual atoms, is a problem intricately linked to the Brownian rotational diffusion of the macromolecule. The diffusion tensor parameters strongly influence the optimisation of the various model-free models and the subsequent model selection between them. Finding the optimal model of the dynamics of the system among the numerous diffusion and model-free models is hence quite complex. Using set theory, the entirety of this global problem has been encapsulated by the universal set Ll, and its resolution mathematically formulated as the universal solution Ll. Ever since the original Lipari and Szabo papers the model-free dynamics of a molecule has most often been solved by initially estimating the diffusion tensor. The model-free models which depend on the diffusion parameter values are then optimised and the best model is chosen to represent the dynamics of the residue. Finally, the global model of all diffusion and model-free parameters is optimised. These steps are repeated until convergence. For simplicity this approach to Ll will be labelled the diffusion seeded model-free paradigm. Although this technique suffers from a number of problems many have been solved. All aspects of the diffusion seeded paradigm and its consequences, together with a few alternatives to the paradigm, will be reviewed through the use of set notation.