Number Of Free Parameters Research Articles

Ill-posed problem and regularization in reconstruction of radiobiological parameters from serial tumor imaging data

The main objective of this article is to improve the stability of reconstruction algorithms for estimation of radiobiological parameters using serial tumor imaging data acquired during radiation therapy. Serial images of tumor response to radiation therapy represent a complex summation of several exponential processes as treatment induced cell inactivation, tumor growth rates, and the rate of cell loss. Accurate assessment of treatment response would require separation of these processes because they define radiobiological determinants of treatment response and, correspondingly, tumor control probability. However, the estimation of radiobiological parameters using imaging data can be considered an inverse ill-posed problem because a sum of several exponentials would produce the Fredholm integral equation of the first kind which is ill posed. Therefore, the stability of reconstruction of radiobiological parameters presents a problem even for the simplest models of tumor response. To study stability of the parameter reconstruction problem, we used a set of serial CT imaging data for head and neck cancer and a simplest case of a two-level cell population model of tumor response. Inverse reconstruction was performed using a simulated annealing algorithm to minimize a least squared objective function. Results show that the reconstructed values of cell surviving fractions and cell doubling time exhibit significant nonphysical fluctuations if no stabilization algorithms are applied. However, after applying a stabilization algorithm based on variational regularization, the reconstruction produces statistical distributions for survival fractions and doubling time that are comparable to published in vitro data. This algorithm is an advance over our previous work where only cell surviving fractions were reconstructed. We conclude that variational regularization allows for an increase in the number of free parameters in our model which enables development of more-advanced parameter reconstruction algorithms.

Model flexibility analysis.

A good fit of model predictions to empirical data are often used as an argument for model validity. However, if the model is flexible enough to fit a large proportion of potential empirical outcomes, finding a good fit becomes less meaningful. We propose a method for estimating the proportion of potential empirical outcomes that the model can fit: Model Flexibility Analysis (MFA). MFA aids model evaluation by providing a metric for gauging the persuasiveness of a given fit. We demonstrate that MFA can be more informative than merely discounting the fit by the number of free parameters in the model, and show how the number of free parameters does not necessarily correlate with the flexibility of the model. Additionally, we contrast MFA with other flexibility assessment techniques, including Parameter Space Partitioning, Model Mimicry, Minimum Description Length, and Prior Predictive Evaluation. Finally, we provide examples of how MFA can help to inform modeling results and discuss a variety of issues relating to the use of MFA in model validation. (PsycINFO Database Record

Flight-Path Tracking Control of an Aircraft Using Backstepping Controller

For transportation aircraft, the primary control objective for an autopilot system engaged during approach and landing is relative to the flight path tracking on the basis of highly simplified linear models of flight dynamics. The dynamics governing the flight path of an aircraft are in general highly nonlinear and involve complex physics for which no accurate models are available. In this paper a nonlinear model describing the longitudinal equations of motion in strick feedback form is derived. Backstepping is utilized for the construction of a globally stabilizing controller with a number of free parameters. It is implemented a controller with an internal loop controls involving the pitch rate of the aircraft and an external loop which includes angle of attack, path angle and pitch angle. Finally, nonlinear simulation results for a longitudinal model of a transportation aircraft are displayed and discussed.

Flight-Path Tracking Control of an Aircraft Using Backstepping Controller

For transportation aircraft, the primary control objective for an autopilot system engaged during approach and landing is relative to the flight path tracking on the basis of highly simplified linear models of flight dynamics. The dynamics governing the flight path of an aircraft are in general highly nonlinear and involve complex physics for which no accurate models are available. In this paper a nonlinear model describing the longitudinal equations of motion in strick feedback form is derived. Backstepping is utilized for the construction of a globally stabilizing controller with a number of free parameters. It is implemented a controller with an internal loop controls involving the pitch rate of the aircraft and an external loop which includes angle of attack, path angle and pitch angle. Finally, nonlinear simulation results for a longitudinal model of a transportation aircraft are displayed and discussed.

THE AGE–REDSHIFT RELATIONSHIP OF OLD PASSIVE GALAXIES

We use 32 age measurements of passively evolving galaxies as a function of redshift to test and compare the standard model ($\Lambda$CDM) with the $R_{\rm h}=ct$ Universe. We show that the latter fits the data with a reduced $\chi^2_{\rm dof}=0.435$ for a Hubble constant $H_{0}= 67.2_{-4.0}^{+4.5}$ km $\rm s^{-1}$ $\rm Mpc^{-1}$. By comparison, the optimal flat $\Lambda$CDM model, with two free parameters (including $\Omega_{\rm m}=0.12_{-0.11}^{+0.54}$ and $H_{0}=94.3_{-35.8}^{+32.7}$ km $\rm s^{-1}$ $\rm Mpc^{-1}$), fits the age-\emph{z} data with a reduced $\chi^2_{\rm dof}=0.428$. Based solely on their $\chi^2_{\rm dof}$ values, both models appear to account for the data very well, though the optimized $\Lambda$CDM parameters are only marginally consistent with those of the concordance model ($\Omega_{\rm m}=0.27$ and $H_{0}= 70$ km $\rm s^{-1}$ $\rm Mpc^{-1}$). Fitting the age-$z$ data with the latter results in a reduced $\chi^2_{\rm dof}=0.523$. However, because of the different number of free parameters in these models, selection tools, such as the Akaike, Kullback and Bayes Information Criteria, favour $R_{\rm h}=ct$ over $\Lambda$CDM with a likelihood of $\sim 66.5\%-80.5\%$ versus $\sim 19.5\%-33.5\%$. These results are suggestive, though not yet compelling, given the current limited galaxy age-$z$ sample. We carry out Monte Carlo simulations based on these current age measurements to estimate how large the sample would have to be in order to rule out either model at a $\sim 99.7\%$ confidence level. We find that if the real cosmology is $\Lambda$CDM, a sample of $\sim 45$ galaxy ages would be sufficient to rule out $R_{\rm h}=ct$ at this level of accuracy, while $\sim 350$ galaxy ages would be required to rule out $\Lambda$CDM if the real Universe were instead $R_{\rm h}=ct$.

White matter compartment models for in vivo diffusion MRI at 300 mT/m

This paper compares a range of compartment models for diffusion MRI data on in vivo human acquisitions from a standard 60mT/m system (Philips 3T Achieva) and a unique 300mT/m system (Siemens Connectom). The key aim is to determine whether both systems support broadly the same models or whether the Connectom higher gradient system supports significantly more complex models. A single volunteer underwent 8h of acquisition on each system to provide uniquely wide and dense sampling of the available space of pulsed-gradient spin-echo (PGSE) measurements. We select a set of promising models from the wide set of possible three-compartment models for in vivo white matter (WM) that previous work and preliminary experiments suggest as strong candidates, but extend them to fit for compartmental T2 and diffusivity. We focus on the corpus callosum where the WM fibre architecture is simplest and compare their ability to explain the measured data, using Akaike's information criterion (AIC), and to predict unseen data, using cross-validation. We also compare the stability of parameter estimates in the presence of i) noise, using bootstrapping, and ii) spatial variation, using visual assessment and comparison with anatomical knowledge. Broadly similar models emerge from the AIC and cross-validation experiments in both data sets. Specifically, a three-compartment model consisting of either a Bingham distribution of sticks or a Cylinder for the intracellular compartment, an anisotropic diffusion tensor (DT) model for the extracellular compartment, as well as an isotropic CSF compartment, performs consistently well. However, various other models also perform well and no single model emerges as clear winner. The WM data (with virtually no CSF contamination) do not support compartmental T2 but partially support compartmental diffusivity. Evaluation of parameter stability favours simpler models than those identified by AIC or cross-validation. They suggest that the level of complexity in models underpinning currently popular microstructure imaging techniques such as NODDI, CHARMED, or ActiveAx, where the number of free parameters is about 4 or 5 rather than 10 or 11, may reflect the level of complexity achievable for a useful technique on current systems, although the 300mT/m data may support more complex models.

MLPNN Training via a Multiobjective Optimization of Training Error and Stochastic Sensitivity.

The training of a multilayer perceptron neural network (MLPNN) concerns the selection of its architecture and the connection weights via the minimization of both the training error and a penalty term. Different penalty terms have been proposed to control the smoothness of the MLPNN for better generalization capability. However, controlling its smoothness using, for instance, the norm of weights or the Vapnik-Chervonenkis dimension cannot distinguish individual MLPNNs with the same number of free parameters or the same norm. In this paper, to enhance generalization capabilities, we propose a stochastic sensitivity measure (ST-SM) to realize a new penalty term for MLPNN training. The ST-SM determines the expectation of the squared output differences between the training samples and the unseen samples located within their Q -neighborhoods for a given MLPNN. It provides a direct measurement of the MLPNNs output fluctuations, i.e., smoothness. We adopt a two-phase Pareto-based multiobjective training algorithm for minimizing both the training error and the ST-SM as biobjective functions. Experiments on 20 UCI data sets show that the MLPNNs trained by the proposed algorithm yield better accuracies on testing data than several recent and classical MLPNN training methods.

Nucleon Structure Including High Fock States in AdS/QCD Models

We discuss a holographic soft-wall model that consider several Fock states in nucleon description. In our approach nucleon structure is a superposition of a three-valence quark state with high Fock states including an adjustable number of partons (quarks, antiquarks and gluons). With a minimal number of free parameters (dilaton scale parameter, mixing parameters of partial contributions of Fock states, coupling constants in the effective Lagrangian) we achieve a reasonable agreement with data.

Exactly solvable model of resonance tunneling of an electromagnetic wave in plasma containing short-scale inhomogeneities

Different variants of resonance tunneling of a transverse electromagnetic wave through a plasma layer containing short-scale (subwavelength) inhomogeneities, including evanescence regions to which approximate methods are inapplicable, are analyzed in the framework of an exactly solvable one-dimensional model. Complex plasma density profiles described by a number of free parameters determining the permittivity modulation depth, the characteristic scale lengths of plasma structures, their number, and the thickness of the inhomogeneous plasma layer are considered. It is demonstrated that reflection-free propagation of the wave incident on the layer from vacuum (the effect of wave-barrier transillumination) can be achieved for various sets of such structures, including plasma density profiles containing a stochastic component. Taking into account cubic nonlinearity, it is also possible to obtain an exact solution to the one-dimensional problem on the nonlinear transillumination of nonuniform plasma. In this case, the thicknesses of the evanescence regions decrease appreciably. The problem of resonance tunneling of electromagnetic waves through such barriers is of interest for a number of practical applications.

LEAVING THE DARK AGES WITH AMIGA

We present an Analytic Model of Intergalactic-medium and GAlaxy evolution since the dark ages. AMIGA is in the spirit of the popular semi-analytic models of galaxy formation, although it does not use halo merger trees but interpolates halo properties in grids that are progressively built. This strategy is less memory-demanding and allows one to start the modeling at redshifts high enough and halo masses low enough to have trivial boundary conditions. The number of free parameters is minimized by making the causal connection between physical processes usually treated as independent from each other, which leads to more reliable predictions. But the strongest points of AMIGA are: i) the inclusion of molecular cooling and metal-poor, population III (Pop III) stars, with the most dramatic feedback, and ii) the accurate follow-up of the temperature and volume filling factor of neutral, singly, and doubly ionized regions, taking into account the distinct halo mass functions in those environments. We find the following general results. Massive Pop III stars determine the IGM metallicity and temperature, and the growth of spheroids and disks is self-regulated by that of massive black holes developed from the remnants of those stars. Yet, the properties of normal galaxies and active galactic nuclei appear to be quite insensitive to Pop III star properties owing to the much higher yield of ordinary stars compared to Pop III stars and the dramatic growth of MBHs when normal galaxies begin to develop, which cause the memory loss of the initial conditions.

Theoretical and Phenomenological Status of Neutrino Physics: A Brief Review

We present an overview of recent progress in the theoretical and phenomenological studies of neutrino masses, lepton avor mixing, and CP violation. Firstly, We discuss the status of neutrino mass with in the Standard Model (SM) of particle physics. Then the possible ways in which neutrino mass terms can be included in the SM are discussed. The inclusion of new physics beyond the SM inevitably brings new parameters which are not constrained by the present experimental data on neutrino masses and mixing angles and, thus, are free parameters of the theory. We, also, discuss various theoretically motivated phenomenological approaches which can be used to reduce the number of free parameters and, thus, provide an excellent tool to understand the underlying physics of neutrino masses and mixings. Current experimental constraints on the neutrino mass spectrum and the lepton avor mixing parameters, including the recent observation of nonzeroθ13, have been summarized. Finally, We discuss the renewed interest in the possible existence of one or more sterile neutrinos and their phenomenology.

Energy Dependence of Slope Parameter in Elastic Nucleon-Nucleon Scattering

The diffraction slope parameter is investigated for elastic proton-proton and proton-antiproton scattering based on all the available experimental data at low and intermediate momentum transfer values. Energy dependence of the elastic diffraction slope is approximated by various analytic functions. The expanded “standard” logarithmic approximations with minimum number of free parameters allow description of the experimental slopes in all the available energy range reasonably. The estimations of asymptotic shrinkage parameterαP′are obtained for various|t|domains based on all the available experimental data. Various approximations differ from each other both in the low energy and very high energy domains. Predictions for diffraction slope parameter are obtained for elastic proton-proton scattering from NICA up to future collider (FCC/VLHC) energies, for proton-antiproton elastic reaction in FAIR energy domain for various approximation functions.

Cosmological tests using the angular size of galaxy clusters

We use measurements of the galaxy-cluster angular size versus redshift to test and compare the standard model (LCDM) and the R_h=ct Universe. We show that the latter fits the data with a reduced chi^2_dof=0.786 for a Hubble constant H_0= 72.6 (-3.4+3.8) km/s/Mpc, and H_0 is the sole parameter in this model. By comparison, the optimal flat LCDM model, with two free parameters (including Omega_m=0.50 and H_0=73.9 (-9.5+10.6) km/s/Mpc), fits the angular-size data with a reduced chi^2_dof=0.806. On the basis of their chi^2_dof values alone, both models appear to account for the data very well in spite of the fact that the R_h=ct Universe expands at a constant rate, while LCDM does not. However, because of the different number of free parameters in these models, selection tools, such as the Bayes Information Criterion, favour R_h=ct over LCDM with a likelihood of ~86% versus ~14%. These results impact the question of galaxy growth at large redshifts. Previous work suggested an inconsistency with the underlying cosmological model unless elliptical and disk galaxies grew in size by a surprisingly large factor ~6 from z~3 to 0. The fact that both LCDM and R_h=ct fit the cluster-size measurements quite well casts some doubt on the suggestion that the unexpected result with individual galaxies may be due to the use of an incorrect expansion scenario, rather than astrophysical causes, such as mergers and/or selection effects.

Data-driven HRF estimation for encoding and decoding models

Despite the common usage of a canonical, data-independent, hemodynamic response function (HRF), it is known that the shape of the HRF varies across brain regions and subjects. This suggests that a data-driven estimation of this function could lead to more statistical power when modeling BOLD fMRI data. However, unconstrained estimation of the HRF can yield highly unstable results when the number of free parameters is large. We develop a method for the joint estimation of activation and HRF by means of a rank constraint, forcing the estimated HRF to be equal across events or experimental conditions, yet permitting it to differ across voxels. Model estimation leads to an optimization problem that we propose to solve with an efficient quasi-Newton method, exploiting fast gradient computations. This model, called GLM with Rank-1 constraint (R1-GLM), can be extended to the setting of GLM with separate designs which has been shown to improve decoding accuracy in brain activity decoding experiments. We compare 10 different HRF modeling methods in terms of encoding and decoding scores on two different datasets. Our results show that the R1-GLM model outperforms competing methods in both encoding and decoding settings, positioning it as an attractive method both from the points of view of accuracy and computational efficiency.

A fuzzy logic controller applied to a diversity-based multi-objective evolutionary algorithm for single-objective optimisation

In recent years, Multi-Objective Evolutionary Algorithms (moeas) that consider diversity as an objective have been used to tackle single-objective optimisation problems. The ability to deal with premature convergence has been greatly improved with these schemes. However, they usually increase the number of free parameters that need to be tuned. To improve results and avoid the tedious hand-tuning of algorithms, the use of automated parameter control approaches that are able to adapt parameter values during the course of an evolutionary run are becoming more common in the field of Evolutionary Computation (ec). This research focuses on the application of parameter control approaches to diversity-based moeas. Two external parameter control methods are investigated; a novel method based on Fuzzy Logic and a recently proposed Hyper-heuristic. These are compared to an internal control method that uses self-adaptation. An extensive comparison of the three methods is carried out using a set of single-objective benchmark problems of diverse complexity. Analyses include comparisons to a wide range of schemes with fixed parameters and to a single-objective approach. The results show that the fuzzy logic and hyper-heuristic methods are able to find similar or better solutions than the fixed parameter methods for a significant number of problems, with considerable savings in computational resources and time, whereas the self-adaptive strategy provides little benefit. Finally, we also demonstrate that the controlled diversity-based moea outperforms the single-objective scheme in most cases, thus showing the benefits of solving single-objective problems through diversity-based multi-objective schemes.

Finite volume effects in the chiral extrapolation of baryon masses

We perform an analysis of the QCD lattice data on the baryon octet and decuplet masses based on the relativistic chiral Lagrangian. The baryon self-energies are computed in a finite volume at next-to-next-to-next-to-leading order (${\mathrm{N}}^{3}\mathrm{LO}$), where the dependence on the physical meson and baryon masses is kept. The number of free parameters is reduced significantly down to 12 by relying on large-${N}_{c}$ sum rules. Altogether we describe accurately more than 220 data points from six different lattice groups, BMW, PACS-CS, HSC, LHPC, QCDSF-UKQCD and NPLQCD. Values for all counterterms relevant at ${\mathrm{N}}^{3}\mathrm{LO}$ are predicted. In particular we extract a pion-nucleon sigma term of ${39}_{\ensuremath{-}1}^{+2}\text{ }\text{ }\mathrm{MeV}$ and a strangeness sigma term of the nucleon of ${\ensuremath{\sigma}}_{sN}=8{4}_{\ensuremath{-}4}^{+28}\text{ }\mathrm{MeV}$. The flavor SU(3) chiral limit of the baryon octet and decuplet masses is determined with ($802\ifmmode\pm\else\textpm\fi{}4$) and $(1103\ifmmode\pm\else\textpm\fi{}6)\text{ }\mathrm{MeV}$. Detailed predictions for the baryon masses as currently evaluated by the ETM lattice QCD group are made.

Code optimization in FORM

We describe the implementation of output code optimization in the open source computer algebra system Form. This implementation is based on recently discovered techniques of Monte Carlo tree search to find efficient multivariate Horner schemes, in combination with other optimization algorithms, such as common subexpression elimination. For systems for which no specific knowledge is provided it performs significantly better than other methods we could compare with. Because the method has a number of free parameters, we also show some methods by which to tune them to different types of problems.

The Role of Spatial Information in Disentangling the Irradiance–Reflectance–Transmittance Ambiguity

In the satellite hyperspectral measures, the contributions of light, surface, and atmosphere are mixed. Applications need separate access to the sources. Conventional inversion techniques usually take a pixelwise spectral-only approach. However, recent improvements in retrieving surface and atmosphere characteristics use heuristic spatial smoothness constraints. In this paper, we theoretically justify such heuristics by analyzing the impact of spatial information on the uncertainty of the solution. The proposed analysis allows to assess in advance the uniqueness (or robustness) of the solution depending on the curvature of a likelihood surface. In situations where pixel-based approaches become unreliable, it turns out that the consideration of spatial information always makes the problem to be better conditioned. With the proposed analysis, this is easily understood since the curvature is consistent with the complexity of the sources measured in terms of the number of significant eigenvalues (or free parameters in the problem). In agreement with recent results in hyperspectral image coding, spatial correlations in the sources imply that the intrinsic complexity of the spatio-spectral representation of the signal is always lower than its spectral-only counterpart. According to this, the number of free parameters in the spatio-spectral inverse problem is smaller, so the spatio-spectral approaches are always better than spectral-only approaches. Experiments using ensembles of actual reflectance values and realistic MODTRAN irradiance and atmosphere radiance and transmittance values show that the proposed analysis successfully predicts the practical difficulty of the problem and the improved quality of spatio-spectral retrieval.

Single‐parameter model of vegetated aquatic flows

AbstractCoupled flows through and over permeable layers occur in a variety of natural phenomena including turbulent flows over submerged vegetation. In this work, we employ a two‐domain approach to model flow through and over submerged canopies. The model, amenable of a closed‐form solution, couples the log‐law and the Darcy‐Brinkman equation, and is characterized by a novel representation of the drag force which does not rely on a parametrization through an unknown drag coefficient. This approach limits to one, i.e., the obstruction permeability, the number of free parameters. Analytical expressions for the average velocity profile through and above the canopies, volumetric flow rate, penetration length, and canopy shear layer parameter are obtained in terms of the canopy layer effective permeability. The model suggests that appropriately rescaled velocities in the canopy and surface layers follow two different scaling laws. The analytical predictions match with the experimental data collected by Ghisalberti and Nepf (2004) and Nepf et al. (2007).

Joint optimization of algorithmic suites for EEG analysis.

Electroencephalogram (EEG) data analysis algorithms consist of multiple processing steps each with a number of free parameters. A joint optimization methodology can be used as a wrapper to fine-tune these parameters for the patient or application. This approach is inspired by deep learning neural network models, but differs because the processing layers for EEG are heterogeneous with different approaches used for processing space and time. Nonetheless, we treat the processing stages as a neural network and apply backpropagation to jointly optimize the parameters. This approach outperforms previous results on the BCI Competition II - dataset IV; additionally, it outperforms the common spatial patterns (CSP) algorithm on the BCI Competition III dataset IV. In addition, the optimized parameters in the architecture are still interpretable.