Optimal Free Parameters Research Articles

Refinement of Global Coronal and Interplanetary Magnetic Field Extrapolations Constrained by Remote-sensing and In Situ Observations at the Solar Minimum

Solar magnetic fields are closely related to various physical phenomena on the Sun, which can be extrapolated with different models from photospheric magnetograms. However, the open flux problem (OFP), the underestimation of the magnetic field derived from the extrapolated model, is still unsolved. To minimize the impact of the OFP, we propose three evaluation parameters to quantitatively evaluate magnetic field models and determine the optimal free parameters in the models by constraining the coronal magnetic fields and the interplanetary magnetic fields (IMFs) with real observations. Although the OFP still exists, we find that magnetic field lines traced from the coronal models effectively capture the intricate topological configurations observed in the corona, including streamers and plumes. The OFP is lessened by using the Helioseismic and Magnetic Imager synoptic map instead of the Global Oscillation Network Group daily synoptic maps, and the potential field source surface + potential field current sheet (PFSS+PFCS) model instead of the current sheet source surface (CSSS) model. For Carrington Rotation 2231 at the solar minimum, we suggest that the optimal parameters for the PFSS+PFCS model are R ss = 2.2–2.5 R ☉ and R scs = 10.5–14.0 R ☉, as well as for the CSSS model, are R cs = 2.0–2.4 R ☉, R ss = 11.0–14.7 R ☉, and a = 1.0 R ☉. Despite the IMFs at 1 au being consistent with the measurements by artificially increasing the polar magnetic fields, the IMFs near the Sun are still underestimated. The OFP might be advanced by improving the accuracy of both the weak magnetic fields and polar magnetic fields, especially considering magnetic activities arising from interplanetary physical processes.

Optimal H2 Moment Matching-Based Model Reduction for Linear Systems through (Non)convex Optimization

In this paper, we compute a (local) optimal reduced order model that matches a prescribed set of moments of a stable linear time-invariant system of high dimension. We fix the interpolation points and parametrize the models achieving moment-matching in a set of free parameters. Based on the parametrization and using the H2-norm of the approximation error as the objective function, we derive a nonconvex optimization problem, i.e., we search for the optimal free parameters to determine the model yielding the minimal H2-norm of the approximation error. Furthermore, we provide the necessary first-order optimality conditions in terms of the controllability and the observability Gramians of a minimal realization of the error system. We then propose two gradient-type algorithms to compute the (local) optimal models, with mathematical guarantees on the convergence. We also derive convex semidefinite programming relaxations for the nonconvex Problem, under the assumption that the error system admits block-diagonal Gramians, and derive sufficient conditions to guarantee the block diagonalization. The solutions resulting at each step of the proposed algorithms guarantee the achievement of the imposed moment matching conditions. The second gradient-based algorithm exhibits the additional property that, when stopped, yields a stable approximation with a reduced H2-error norm. We illustrate the theory on a CD-player and on a discretized heat equation.

Simple derivation and closed-form frequency-domain design of wideband length-8 interpolation kernel

This paper proposes a frequency-domain method for designing a wide-band length-8 interpolator in the weighted-least-squares (WLS) sense. The length-8 interpolator is even-symmetric and it consists of the fourth-order piecewise polynomials. In this paper, we first present a simple method for deriving its closed-form frequency response, and then formulate a frequency-domain WLS design with the C0-continuity constraint. Since the length-8 interpolator contains a total of 20 parameters, and the C0-continuity imposes 8 constraints on the design, the remaining 12 parameters can be taken as free parameters. After expressing the frequency response as the function of the 12 free parameters, the optimal free parameters can be found in the frequency-domain by minimizing the weighted squared error between the ideal and actual frequency responses, where a non-negative weighting function is adopted for emphasizing important frequency bands and ignoring unimportant bands. Consequently, the WLS design can yield an extremely accurate wide-band length-8 interpolator. Three interpolation examples are given to verify that the designed length-8 wide-band interpolator can achieve the highest accuracy in both the frequency-domain and time-domain as compared to other existing interpolators.

Atrial fibrillation detection using support vector machine and electrocardiographic descriptive statistics

This paper proposes a new technique for detecting atrial fibrillation (AF). The method employs electrocardiographic features and support vector machine (SVM). The features include descriptive statistics of electrocardiographic RR interval. The RR interval is the distance in time between two consecutive R-peaks of electrocardiogram. AF detections using SVM with different electrocardiographic features and different SVM free parameters are explored. Employing SVM with the optimal free parameters and all the proposed electrocardiographic features, we find an AF detection technique with a comparable performance. The best performance obtained by the technique is 98.47% and 97.84%, in terms of sensitivity and specificity.

Atrial fibrillation detection using support vector machine and electrocardiographic descriptive statistics

This paper proposes a new technique for detecting atrial fibrillation (AF). The method employs electrocardiographic features and support vector machine (SVM). The features include descriptive statistics of electrocardiographic RR interval. The RR interval is the distance in time between two consecutive R-peaks of electrocardiogram. AF detections using SVM with different electrocardiographic features and different SVM free parameters are explored. Employing SVM with the optimal free parameters and all the proposed electrocardiographic features, we find an AF detection technique with a comparable performance. The best performance obtained by the technique is 98.47% and 97.84%, in terms of sensitivity and specificity.

Support Vector Machine and regression analysis to predict the field hydraulic conductivity of sandy soil

Saturated hydraulic conductivity is one of the key parameters in soil physics and hydrological modeling. This study explores the use of Support Vector Machine (SVM) and a nonlinear statistical regression approach for the purpose of predicting the field saturated soil hydraulic conductivity (Kfield) of sandy soil based on basic soil properties of saline and alkaline soil data sets. Considering the significance of soil properties, both methods used the following levels of input soil data, which are easily measurable in the laboratory: hydraulic conductivity, clay/silt ratio, liquid limit, hydro carbonate anions, chloride ions, and calcium carbonate content. The influence of three kernel functions (linear, radial basis and sigmoid) on the performance of the SVM model was investigated. An adaptive genetic algorithm is used to determine the optimal free parameters of the SVM models. The results indicated that the SVM with the RBF model has better accuracy compared to the linear- and sigmoid-based models. The RBF model performed satisfactorily with a modeling efficiency of 0.972 and a correlation coefficient of 0.976. According to all of the performance measures, the different SVM models are a powerful tool and have better performance than statistical regression models. The excellent performance of the SVM with the RBF model demonstrated its potential to function as a useful tool for the indirect estimation of Kfield to assess maximum obtainable prediction accuracy.

On different numerical inverse Laplace methods for solute transport problems

Numerical inversion is required when Laplace transform cannot be inverted analytically by manipulating tabled formulas of special cases. However, the numerical inverse Laplace transform is generally an ill-posed problem, and there is no universal method which works well for all problems. In this study, we selected seven commonly used numerical inverse Laplace transform methods to evaluate their performance for dealing with solute transport in the subsurface under uniform or radial flow condition. Such seven methods included the Stehfest, the de Hoog, the Honig–Hirdes, the Talbot, the Weeks, the Simon and the Zakian methods. We specifically investigated the optimal free parameters of each method, including the number of terms used in the summation and the numerical tolerance. This study revealed that some commonly recommended values of the free parameters in previous studies did not work very well, especially for the advection-dominated problems. Instead, we recommended new values of the free parameters for some methods after testing their robustness. For the radial dispersion, the de Hoog, the Talbot, and the Simon methods worked very well, regardless of the dispersion-dominated or advection-dominated situations. The Weeks method can be used to solve the dispersion-dominated problems, but not the advection-dominated problems. The Stehfest, the Honig–Hirdes, and the Zakian methods were recommended for the dispersion-dominated problems. The Zakian method was efficient, while the de Hoog method was time-consuming under radial flow condition. Under the uniform flow condition, all the methods could present somewhat similar results when the free parameters were given proper values for dispersion-dominated problems; while only the Simon method, the Weeks method, and the de Hoog method worked well for advection-dominated problems.

Network-Wide Optimization of Traffic Signals Using Mixed Integer Programming

<div class=""abs_img""><img src=""[disp_template_path]/JRM/abst-image/00260005/09.jpg"" width=""300"" />Network with four intersections</div> In this paper a network-wide traffic signal control scheme in a model predictive control framework using mixed integer programming is presented. A concise model of traffic is proposed to describe a signalized road network considering conservation of traffic. In the model, the traffic of two sections that belong to a traffic signal group of a junction are represented by a single continuous variable. Therefore, the number of variables required to describe traffic in the network becomes half compared with the models that describe section wise traffic flows. The traffic signal at the junction is represented by a binary variable to express a signal state either green or red. The proposed model is transformed into a mixed logical dynamical system to describe the traffic flows in a finite horizon, and traffic signals are optimized using mixed integer linear programming (MILP) for a given performance index. The scheme simultaneously optimizes all traffic signals in a network in the context of model predictive control by successively extending or terminating a green or red signal of each junction. Consequently, traffic signal patterns with the optimal free parameters, i.e., the cycle times, the split times and the offsets, are realized. Use of the proposed concise traffic model significantly reduces the computation time of the scheme without compromising the performance as it is evaluated on a small road network and compared with a previously proposed scheme. </span>

Investigation of statistical iterative reconstruction for dedicated breast CT

Dedicated breast CT has great potential for improving the detection and diagnosis of breast cancer. Statistical iterative reconstruction (SIR) in dedicated breast CT is a promising alternative to traditional filtered backprojection (FBP). One of the difficulties in using SIR is the presence of free parameters in the algorithm that control the appearance of the resulting image. These parameters require tuning in order to achieve high quality reconstructions. In this study, the authors investigated the penalized maximum likelihood (PML) method with two commonly used types of roughness penalty functions: hyperbolic potential and anisotropic total variation (TV) norm. Reconstructed images were compared with images obtained using standard FBP. Optimal parameters for PML with the hyperbolic prior are reported for the task of detecting microcalcifications embedded in breast tissue. Computer simulations were used to acquire projections in a half-cone beam geometry. The modeled setup describes a realistic breast CT benchtop system, with an x-ray spectra produced by a point source and an a-Si, CsI:Tl flat-panel detector. A voxelized anthropomorphic breast phantom with 280 μm microcalcification spheres embedded in it was used to model attenuation properties of the uncompressed woman's breast in a pendant position. The reconstruction of 3D images was performed using the separable paraboloidal surrogates algorithm with ordered subsets. Task performance was assessed with the ideal observer detectability index to determine optimal PML parameters. The authors' findings suggest that there is a preferred range of values of the roughness penalty weight and the edge preservation threshold in the penalized objective function with the hyperbolic potential, which resulted in low noise images with high contrast microcalcifications preserved. In terms of numerical observer detectability index, the PML method with optimal parameters yielded substantially improved performance (by a factor of greater than 10) compared to FBP. The hyperbolic prior was also observed to be superior to the TV norm. A few of the best-performing parameter pairs for the PML method also demonstrated superior performance for various radiation doses. In fact, using PML with certain parameter values results in better images, acquired using 2 mGy dose, than FBP-reconstructed images acquired using 6 mGy dose. A range of optimal free parameters for the PML algorithm with hyperbolic and TV norm-based potentials is presented for the microcalcification detection task, in dedicated breast CT. The reported values can be used as starting values of the free parameters, when SIR techniques are used for image reconstruction. Significant improvement in image quality can be achieved by using PML with optimal combination of parameters, as compared to FBP. Importantly, these results suggest improved detection of microcalcifications can be obtained by using PML with lower radiation dose to the patient, than using FBP with higher dose.

Traffic Signal Control in an MPC Framework Using Mixed Integer Programming

This paper presents network wide traffic signal control in a model predictive control framework using mixed integer programming. A concise model of traffic is proposed to describe the traffic flows in a signalized road network. In the model, the traffic signal at a junction is represented by a binary variable to express a signal state either green or red, and the traffic of two sections that belong to a traffic signal group at the junction are represented by a continuous variable. Therefore, less number of variables are required to describe traffic in the network than any model that describes each section traffic individually. The traffic signal control framework using the proposed traffic model is evaluated on a small road network that experiences varying traffic flows over time. The framework simultaneously generates all traffic signals in the network by turning them flexibly to red and green that optimize the traffic flows in the context of model predictive control. Successive generations of red and green signals at all junctions create traffic signal patterns with optimal free parameters, i.e., the cycle times, the split times and the offsets, depending on the traffic flow conditions in the network. Use of the concise traffic model reduces the computation time of mixed integer programming significantly.

Further generalized energies for the application of an energy criterion of conditional stability

A previously proposed energy criterion for predicting the conditional stability of incompressible flows, which is based on properly defined generalized energies, is considered. An extension of the procedure for the construction of generalized energies is proposed here, leading to the definition of a broader class of generalized energies which may depend on several free parameters. The optimal free parameters are computed by searching the value for which the energetic stability criterion predicts the maximum critical L 2 energy. The capabilities of the resulting stability criterion are appraised through the application to low-dimensional non-linear quadratic models, mimicking the subcritical instability behavior of particular incompressible flows. Many shear flows are characterized by a subcritical instability regime, in which the stability of the base flow is guaranteed only if the initial amplitude of a given disturbance is lower than a critical threshold value. This value is a decreasing function of Re between Reg and ReL , ReL being the critical Reynolds number predicted by linear stability and Reg being the Reynolds number of global stability, i.e., for Re < Reg all disturbances, whatever their initial amplitude, decay asymptotically in time. In several cases, the classical energetic stabil- ity theory does not give any useful information concerning the subcritical regime, since it predicts a critical Reynolds number (ReE ) which is significantly lower than Reg. As discussed in the literature, this failure is mainly due to two major flaws. First, the non-normality of the linearized Navier-Stokes (NS) operator leads to the well-known transient growth of the disturbance energy, which eventually may decrease to zero, while the energetic criterion requires the disturbance energy to decrease monotonically in time. Second, for many flows, the nonlinear part of the NS operator and, consequently, the amplitude of the disturbance do not play a role in the computation of ReE . An energetic criterion was proposed in (1) in which the problems related to the non-normality of the linear operator are bypassed and the amplitude of the disturbance is taken into account in the problem. This criterion is based on a procedure which consists of two main steps. First, a generalized energy is defined through a perturbation of the classical L 2 energy, which is aimed at overcoming the non-normality of the linearized operator. Indeed, the metric perturbation is such that the time variation of the generalized energy due to the linear term of the disturbance evolution equation is negative definite. Second, by imposing the monotonic decay of the generalized energy, a criterion of conditional stability is obtained for each Reynolds number up

Support vector machines experts for time series forecasting

This paper proposes using the support vector machines (SVMs) experts for time series forecasting. The generalized SVMs experts have a two-stage neural network architecture. In the first stage, self-organizing feature map (SOM) is used as a clustering algorithm to partition the whole input space into several disjointed regions. A tree-structured architecture is adopted in the partition to avoid the problem of predetermining the number of partitioned regions. Then, in the second stage, multiple SVMs, also called SVM experts, that best fit partitioned regions are constructed by finding the most appropriate kernel function and the optimal free parameters of SVMs. The sunspot data, Santa Fe data sets A, C and D, and the two building data sets are evaluated in the experiment. The simulation shows that the SVMs experts achieve significant improvement in the generalization performance in comparison with the single SVMs models. In addition, the SVMs experts also converge faster and use fewer support vectors.

Particle counting by fluorescence correlation spectroscopy. Simultaneous measurement of aggregation and diffusion of molecules in solutions and in membranes

A method for simultaneous determination of molar weights (M) and lateral diffusion constants (D) of particles in three- and two-dimensional systems is described. Spontaneous concentration fluctuations in space and time are analyzed, by monitoring fluctuations in the fluorescence from fluorescein-labeled molecules (1 dye/molecule is sufficient), excited by a rotating laser spot. For particles in solution, M values are determined over the range of 3 x 10(2) to 3 x 10(11) daltons, and D values can be determined from approximately 10(-7) to 10(-10) cm2/s. The time for a determination is approximately 1 min. Aggregation can be followed by changes of either M or D. This method is used to study the calcium dependence of vesicle aggregation or fusion, and the time course of aggregate formation of porin (an Escherichia Coli outer membrane protein) in lipid monolayers. Essential parameters for the development of the method are described. Equations to estimate the signal-to-noise ratios and to find the optimal free parameters for a specific application are derived. The theoretical predictions for the correlation function of the signal and for the signal-to-noise ratio are compared with observed values.