Number Of Free Model Parameters Research Articles

Entropy and Information Content of Geostatistical Models

Geostatistical models quantify spatial relations between model parameters and can be used to estimate and simulate properties away from known observations. The underlying statistical model, quantified through a joint probability density, most often consists of both an assumed statistical model and the specific choice of algorithm, including tuning parameters controlling the algorithm. Here, a theory is developed that allows one to compute the entropy of the underlying multivariate probability density when sampled using sequential simulation. The self-information of a single realization can be computed as the sum of the conditional self-information. The entropy is the average of the self-information obtained for many independent realizations. For discrete probability mass functions, a measure of the effective number of free model parameters, implied by a specific choice of probability mass function, is proposed. Through a few examples, the entropy measure is used to quantify the information content related to different choices of simulation algorithms and tuning parameters.

Ionization quenching in scintillators used for dosimetry of mixed particle fields

Ionization quenching in ion beam dosimetry is often related to the fluence- or dose-averaged linear energy transfer (LET). Both quantities are however averaged over a wide LET range and a mixed field of primary and secondary ions. We propose a novel method to correct the quenched luminescence in scintillators exposed to ion beams. The method uses the energy spectrum of the primaries and accounts for the varying quenched luminescence in heavy, secondary ion tracks through amorphous track structure theory. The new method is assessed against more traditional approaches by correcting the quenched luminescence response from the BCF-12, BCF-60, and 81-0084 plastic scintillators exposed to a 100 MeV pristine proton beam in order to compare the effects of the averaged LET quantities and the secondary ions. Calculations and measurements show that primary protons constitute more than 92% of the energy deposition but account for more than 95% of the luminescence signal in the scintillators. The quenching corrected luminescence signal is in better agreement with the dose measurement when the secondary particles are taken into account. The Birks model provided the overall best quenching corrections, when the quenching corrected signal is adjusted for the number of free model parameters. The quenching parameter kB for the BCF-12 and BCF-60 scintillators is in agreement with literature values and was found to be m keV−1 for the 81-0084 scintillator. Finally, a fluence threshold for the 100 MeV proton beam was calculated to be of the order of 1010 cm−2, corresponding to 110 Gy, above which the quenching increases non-linearly and the Birks model no longer is applicable.

Explicit failure model for boron carbide ceramics under shock loading

Ceramic materials have a long-term industrial demand due to their high mechanical hardness and chemical and temperature resistance. They are brittle and tend to lose strength under heavy loads which complicates the development of a comprehensive material model for simulation of engineering prototypes containing ceramic parts. We developed an improved failure model of ceramics based on the well-known Johnson–Holmquist approach. This model redefines the damage rate equation using a consistent definition of the total plastic strain in the failed material. It reduces the number of free model parameters and enables the plastic strain to be explicitly accumulated during the failure process. The corresponding non-iterative algorithm utilizing this explicit failure model is developed. It is successfully validated by simulation of the wave profiles obtained in plate-impact experiments with boron carbide using the contact smoothed particle hydrodynamic method.

Research Article. On memory, dimension, and atmospheric teleconnections

AbstractUsing reanalysed atmospheric data and applying a data-driven multiscale approximation to non-stationary dynamical processes, we undertake a systematic examination of the role of memory and dimensionality in defining the quasi-stationary states of the troposphere over the recent decades. We focus on the role of teleconnections characterised by either zonally-oriented wave trains or meridional dipolar structures. We consider the impact of various strategies for dimension reduction based on principal component analysis, diagonalization and truncation.We include the impact of memory by consideration of Bernoulli, Markovian and non-Markovian processes. We a priori explicitly separate barotropic and baroclinic processes and then implement a comprehensive sensitivity analysis to the number and type of retained modes. Our results show the importance of explicitly mitigating the deleterious impacts of signal degradation through ill-conditioning and under sampling in preference to simple strategies based on thresholds in terms of explained variance. In both hemispheres, the results obtained for the dominant tropospheric modes depend critically on the extent to which the higher order modes are retained, the number of free model parameters to be fitted, and whether memory effects are taken into account. Our study identifies the primary role of the circumglobal teleconnection pattern in both hemispheres for Bernoulli and Markov processes, and the transient nature and zonal structure of the Southern Hemisphere patterns in relation to their Northern Hemisphere counterparts. For both hemispheres, overfitted models yield structures consistent with the major teleconnection modes (NAO, PNA and SAM), which give way to zonally oriented wavetrains when either memory effects are ignored or where the dimension is reduced via diagonalising. Where baroclinic processes are emphasised, circumpolar wavetrains are manifest.

Functional modeling of the human auditory brainstem response to broadband stimulation.

Population responses such as the auditory brainstem response (ABR) are commonly used for hearing screening, but the relationship between single-unit physiology and scalp-recorded population responses are not well understood. Computational models that integrate physiologically realistic models of single-unit auditory-nerve (AN), cochlear nucleus (CN) and inferior colliculus (IC) cells with models of broadband peripheral excitation can be used to simulate ABRs and thereby link detailed knowledge of animal physiology to human applications. Existing functional ABR models fail to capture the empirically observed 1.2-2 ms ABR wave-V latency-vs-intensity decrease that is thought to arise from level-dependent changes in cochlear excitation and firing synchrony across different tonotopic sections. This paper proposes an approach where level-dependent cochlear excitation patterns, which reflect human cochlear filter tuning parameters, drive AN fibers to yield realistic level-dependent properties of the ABR wave-V. The number of free model parameters is minimal, producing a model in which various sources of hearing-impairment can easily be simulated on an individualized and frequency-dependent basis. The model fits latency-vs-intensity functions observed in human ABRs and otoacoustic emissions while maintaining rate-level and threshold characteristics of single-unit AN fibers. The simulations help to reveal which tonotopic regions dominate ABR waveform peaks at different stimulus intensities.

Nonlinear dynamic systems modeling using Gaussian processes: Predicting ionospheric total electron content over South Africa

[1] Two different implementations of Gaussian process (GP) models are proposed to estimate the vertical total electron content (TEC) from dual frequency Global Positioning System (GPS) measurements. The model falseness of GP and neural network models are compared using daily GPS TEC data from Sutherland, South Africa, and it is shown that the proposed GP models exhibit superior model falseness. The GP approach has several advantages over previously developed neural network approaches, which include seamless incorporation of prior knowledge, a theoretically principled method for determining the much smaller number of free model parameters, the provision of estimates of the model uncertainty, and a more intuitive interpretability of the model.

The Regionalization of National-Scale SPARROW Models for Stream Nutrients1

This analysis modifies the parsimonious specification of recently published total nitrogen (TN) and total phosphorus (TP) national-scale SPAtially Referenced Regressions On Watershed attributes models to allow each model coefficient to vary geographically among three major river basins of the conterminous United States. Regionalization of the national models reduces the standard errors in the prediction of TN and TP loads, expressed as a percentage of the predicted load, by about 6 and 7%. We develop and apply a method for combining national-scale and regional-scale information to estimate a hybrid model that imposes cross-region constraints that limit regional variation in model coefficients, effectively reducing the number of free model parameters as compared to a collection of independent regional models. The hybrid TN and TP regional models have improved model fit relative to the respective national models, reducing the standard error in the prediction of loads, expressed as a percentage of load, by about 5 and 4%. Only 19% of the TN hybrid model coefficients and just 2% of the TP hybrid model coefficients show evidence of substantial regional specificity (more than ±100% deviation from the national model estimate). The hybrid models have much greater precision in the estimated coefficients than do the unconstrained regional models, demonstrating the efficacy of pooling information across regions to improve regional models.

Statistical assessment of non‐Gaussian diffusion models

In human brain diffusion measurements, there are deviations from monoexponential signal decay at high values of the diffusion-weighting factor b. This is known as non-Gaussian diffusion and can provide novel kinds of image contrast. We evaluated quantitatively the goodness-of-fit of five popular diffusion models. Because of the Rician signal distribution and physiological noise, the measurement errors are unknown. This precludes standard χ(2) testing. By repeating the measurement 25 times, the errors were estimated. Hypothesis testing based on the residual after least squares curve fitting was then carried out. Systematic errors originating from the Rician signal bias were eliminated in the fitting procedure. We performed diffusion measurements on four healthy volunteers with b-values ranging from 0 to 5000 s/mm(2) . The data were analyzed voxelwise. The null hypothesis of a given model being adequate was rejected, if the residual after fitting exceeded a limit that corresponds to a significance level of 1%. The fraction of rejected voxels depended strongly on the number of free model parameters. The rejected fraction was: monoexponential model with two parameters, 94%; statistical model with three parameters, 29%; stretched exponential model with three parameters, 35%; cumulant model with three parameters, 48%; cumulant model with four parameters, 11%; biexponential model with four parameters, 2.9%.

Optically inspired biomechanical model of the human eyeball

Currently available biomechanical models of the human eyeball focus mainly on the geometries and material properties of its components while little attention has been given to its optics--the eye's primary function. We postulate that in the evolution process, the mechanical structure of the eyeball has been influenced by its optical functions. We develop a numerical finite element analysis-based model in which the eyeball geometry and its material properties are linked to the optical functions of the eye. This is achieved by controlling in the model all essential optical functions while still choosing material properties from a range of clinically available data. In particular, it is assumed that in a certain range of intraocular pressures, the eye is able to maintain focus. This so-called property of optical self-adjustments provides a more constrained set of numerical solutions in which the number of free model parameters significantly decreases, leading to models that are more robust. Further, we investigate two specific cases of a model that satisfies optical self-adjustment: (1) a full model in which the cornea is flexibly attached to sclera at the limbus, and (2) a fixed cornea model in which the cornea is not allowed to move at the limbus. We conclude that for a biomechanical model of the eyeball to mimic the optical function of a real eye, it is crucial that the cornea is allowed to move at the limbal junction, that the materials used for the cornea and sclera are strongly nonlinear, and that their moduli of elasticity remain in a very close relationship.

Electroproduction of kaons from the proton in a Regge-plus-resonance approach

We present a Regge-plus-resonance (RPR) description of the p(e,e′K+)Y processes (Y=Λ,Σ0) in the resonance region. The background contributions to the RPR amplitude are constrained by the high-energy p(γ,K+)Y data. As a result, the number of free model parameters in the resonance region is considerably reduced compared to typical effective-Lagrangian approaches. We compare a selection of RPR model variants, originally constructed to describe KY photoproduction, with the world electroproduction database. The electromagnetic form factors of the intermediate N*s and Δ*s are computed in the Bonn constituent-quark model. With this input, we find a reasonable description of the p(e,e′K+)Y data without adding or readjusting any parameters. It is demonstrated that the electroproduction response functions are extremely useful for fine-tuning both the background and resonant contributions to the reaction dynamics.

Models of large-scale viscous flow in the Earth's mantle with constraints from mineral physics and surface observations

SUMMARY Modelling the geoid has been a widely used and successful approach in constraining flow and viscosity in the Earth’s mantle. However, details of the viscosity structure cannot be tightly constrained with this approach. Here, radial viscosity variations in four to five mantle layers (lithosphere, upper mantle, one to two transition zone layers, lower mantle) are computed with the aid of independent mineral physics results. A density model is obtained by converting s-wave anomalies from seismic tomography to density anomalies. Assuming both are of thermal origin, conversion factors are computed based on mineral physics results. From the density and viscosity model, a model of mantle flow, and the resulting geoid and radial heat flux profile are computed. Absolute viscosity values in the mantle layers are treated as free parameters and determined by minimizing a misfit function, which considers fit to geoid, ‘Haskell average’ determined from post-glacial rebound and the radial heat flux profile and penalizes if at some depth computed heat flux exceeds the estimated mantle heat flux 33 TW. Typically, optimized models do not exceed this value by more than about 20 per cent and fit the Haskell average well. Viscosity profiles obtained show a characteristic hump in the lower mantle, with maximum viscosities of about 10 23 Pa s just above the D �� layer— several hundred to about 1000 times the lowest viscosities in the upper mantle. This viscosity contrast is several times higher than what is inferred when a constant lower mantle viscosity is assumed. The geoid variance reduction obtained is up to about 80 per cent—similar to previous results. However, because of the use of mineral physics constraints, a rather small number of free model parameters is required, and at the same time, a reasonable heat flux profile is obtained. Results are best when the lowest viscosities occur in the transition zone. When viscosity is lowest in the asthenosphere, variance reduction is about 70‐75 per cent. Best results were obtained with a viscous lithosphere with a few times 10 22 Pa s. The optimized models yield a core-mantle boundary excess ellipticity several times higher than observed, possibly indicating that radial stresses are partly compensated due to non-thermal lateral variations within the lowermost mantle.

Quantifying Parsimonyin Structural Equation Modeling

Fitting propensity (FP) is defined as a model's average ability to fit diverse data patterns, all else being equal. The relevance of FP to model selection is examined in the context of structural equation modeling (SEM). In SEM it is well known that the number of free model parameters influences FP, but other facets of FP are routinely excluded from consideration. It is shown that models possessing the same number of free parameters but different structures may exhibit different FPs. The consequences of this fact are demonstrated using illustrative examples and models culled from published research. The case is made that further attention should be given to quantifying FP in SEM and considering it in model selection. Practical approaches are suggested.

Climate sensitivity to changes in solar insolation in a simple coupled climate model

A simple coupled ocean, atmosphere and sea-ice model is presented. The idealised model consists of a zonally averaged land and ocean strip of constant angular width extending from pole to pole. The meridional energy transport in the ocean is modelled by contributions from the large scale thermohaline overturning cells and from horizontal diffusive fluxes. The atmospheric meridional energy transports are parametrised as diffusive fluxes in addition to advective transports in the Hadley domain. This parametrisation resolves the equatorward moisture transport as well as the poleward transport of potential energy in the upper branch of the Hadley circulation. The model reproduces the annual averaged meridional energy transports in the climate system with a small number of free model parameters. The basic feedbacks between the three climatic components are studied by investigating the model's sensitivity towards reductions in the solar insolation. It is found that the meridional energy transport in the ocean does not amplify the ice albedo feedback. This has important implications for modelling the climate sensitivity in atmosphere-only models, as these would exaggerate the sensitivity to changes in the solar insolation if their parametrisations of the meridional energy transport are constrained by surface temperatures. The role of the dependence of the atmospheric transports on the meridional temperature gradient is shown to have a significant influence on the sensitivity on the coupled model, and the inclusion of seasonal cycles greatly increase the models sensitivity. The Hadley circulation does significantly alter the strength of the ice-albedo feedback in the coupled model. The idealised configuration of the model makes it a useful tool for studying the feedbacks in the ocean-atmosphere-sea ice system in the context of the "Snowball Earth" hypothesis.

Lattice dynamic of alpha -quartz. II. Theory

The recently determined phonon dispersion curves of alpha -quartz have been analysed with various polarizable-ion, bond-charge and shell models, the shell models giving a very satisfactory account of the dispersion curves as well as of the scattering intensities. Due to the use of interatomic potentials the number of free model parameters can be kept small. Investigating the dielectric constants in the framework of the developed shell models yields an ionic charge of about -2e for the oxygen ion, indicating a strongly ionic crystal. The polarizability of the O2- pseudo-ion in quartz should be close to 1.8 AA3. The physical significance of the obtained potentials has been tested by studying the equilibrium conditions. It turns out that additional valence forces of the Keating type improve the fulfilment of the equilibrium conditions, but that it is not possible to satisfy them completely.