Best-fit Approximation Research Articles

Bicubic regression analysis a novel approach for estimation of physicochemical properties of skin cancer drugs through degree based entropy

Skin cancer poses a significant risk to the healthcare system worldwide and is projected to increase substantially over the next two decades, particularly if not detected in its early stages. The primary aim of this study is to construct a quantitative structure-property relationship (QSPR) by correlating calculated entropies with topological indices and specific physical-chemical properties of pharmaceuticals, in order to enhance their usefulness. The bicubic regression model is constructed through degree-based topological entropies to perform the QSPR analysis for the prediction of physiochemical properties like polar surface area, complexity, molar refractivity, boiling point, and polarity of skin cancer drugs. It is also examined that degree-based entropies provide best-fit models for skin cancer physiochemical properties. We inspected five physio-chemical properties of these anticancer drugs and found this methodology suitable for predicting best-fit approximations regarding R2 value. It is expected that this approach will be very favourable to examining problems related to mathematical chemistry.

Adaptive Channel Assignment for Maneuvering Target Tracking in Multistatic Passive Radar

In this paper, two adaptive channel assignment (CA) schemes are proposed for maneuvering target tracking (MTT) in multistatic passive radar. For a predetermined total number of channels w.r.t. each receiver, (a) the first scheme selects <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> channels to achieve the highest MTT accuracy; (b) the second scheme minimizes the number of channels while guaranteeing a required MTT performance. By utilizing the best-fitting Gaussian approximation, we derive the predicted conditional Cramér-Rao lower bound to evaluate the impact of CA on MTT performance, and formulate CA schemes as convex integer program problems, since channel variables are in binary form. The objective in the first CA problem is smooth, so we apply the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{2}$</tex-math></inline-formula> -box alternating direction method of multipliers to divide it into several simple subproblems and alternatively solve them in continuous domains without the introduction of relaxation error. The second CA problem may be infeasible when the required accuracy cannot be met with available channels. To tackle it, we introduce a linear rectification function w.r.t the performance constraint, and equivalently reformulate it as a feasible one. Then, a fast multi-start add-one-channel policy is designed to minimize the gap between the actual accuracy and the accuracy requirement. These algorithms offer considerable reductions in computational complexity compared with the branch and bound method and may achieve near-optimal performance. Simulation results demonstrate that these schemes can either achieve the highest MTT accuracy with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> channels or reduce the number of channels while guaranteeing MTT performance, compared with the traditional random channel allocation scheme.

Hybrid controller for mid-range mid-power audio application

A major reason for compromised audio quality with a coil-type loudspeaker is its complex impedance profile, which disturbs the intended algebraic linearity or linear phase behavior between the amplifier input and speaker driving force. Though switch-mode amplifiers are increasingly preferred in such audio systems owing to their superior energy efficiency, their inherent non-linearity and finite internal impedance further degrade audio reproduction. This paper investigates the effect of stated impedance on the loudspeaker driving current, hence on the loudspeaker driving force, and proposes a Hybrid controller-amplifier to enhance the proportionality between the audio reference and driving force without compromising on loudspeaker damping. The Hybrid amplifier combines a sliding mode controlled amplifier (SMCA) and a linear controller, designed after exhaustive modeling of the input–output behavior of the SMCA and best-fit approximation of the loudspeaker impedance. An 8 W, 500 Hz to 20 kHz prototype of the proposed amplifier is fabricated on the basis of the presented design. Time and frequency-domain results obtained with the experimental hardware are presented to validate the performance improvement.

Determining Chemical Reaction Systems in Plasma-Assisted Conversion of Methane Using Genetic Algorithms

Even for processes with only a few gas species involved the detailed description of plasma-assisted conversion processes in gas mixtures requires a large amount of processes to be taken into account and a large number of neutral and charged particles must be considered. In addition, setting up the corresponding reaction kinetics model needs the knowledge of the rate coefficients and their temperature dependence for all possible reactions between those species. Reduced reaction networks offer a simplified and pragmatic way to obtain an overall reaction kinetics model, already useful for the analysis of experimental data even if not all details of chemistry can be covered. In this paper we present a derivation of a data driven reduced model for plasma-assisted conversion of methane in an helium environment. By consideration of a small number of elementary reactions, a simple model is set up. Experimental data are analyzed by a genetic algorithm that provides best-fit approximations for the open parameters of the model. In a further step non-relevant parameters of the model are identified and a further model reduction is achieved. The data driven analysis of methane conversion serves as an illustrative example of the proposed method. The parameters and reaction channels found are compared with known results from the literature. The method is described in detail. The main goal of this work is to present the potential of this data driven method for a simplified and pragmatic modeling in the increasingly important field of plasma-assisted catalytic processes.

Performance Evaluation of Underground Mining Machinery: A Case Study

Unexpected occurrence of uneven breakdowns and their consequences have a significant influence on the equipment life. Hence, there is a need to discover the motives for the happening of critical potential failures and required repair or replacement action to control. Reliability analysis is utilized to approximate the performance of the equipment. In this study, the performance of the underground mining machinery known as load haul dumper (LHD) has been estimated with reliability analysis. The best-fit distribution of the data sets was selected by testing the numerous statistical distributions using the Kolmogorov–Smirnov (K-S) test. The percentage of reliability of each subsystem of the LHD machine was computed based on the best-fit approximation. The overall system reliability of the equipment was estimated using a series configuration-based reliability block diagram (RBD) approach. The reliability-based preventive maintenance (PM) time intervals were also computed for estimated 90.00% reliability. To accomplish the desired level of reliability, a review on maintenance programs should be made. Possible recommendations were made to the maintenance department in the industry for improvement in equipment.

Determination of macroscopic stress from diffraction experiments: A critical discussion

The paper is motivated by some inconsistencies and contradictions present in the literature on the calculation of the so-called diffraction elastic constants. In an attempt at unifying the views that the two communities of Materials Science and Mechanics of Materials have on the subject, we revisit and define the terminology used in the field. We also clarify the limitations of the commonly used approaches and show that a unified methodology is also applicable to textured materials with a nearly arbitrary grain shape. We finally compare the predictions based on this methodology with experimental data obtained by in situ synchrotron radiation diffraction on additively manufactured Ti-6Al-4V alloy. We show that (a) the transverse isotropy of the material yields good agreement between the best-fit isotropy approximation (equivalent to the classic Kröner's model) and the experimental data and (b) the use of a general framework allows the calculation of all components of the tensor of diffraction elastic constants, which are not easily measurable by diffraction methods. This allows us to extend the current state-of-the-art with a predictive tool.

Bi-Radial Curvature Morphology of the Healthy Talus

Category:AnkleIntroduction/Purpose:In order to design an implant for the ankle joint that mimics normal joint motion, the condylar geometry of the talus must be anatomically accurate. Previous attempts to describe the curvature of the talus have typically involved fitting single-radius arcs to the medial and lateral facets. The purpose of this investigation was to determine if the curvature of the medial and lateral sides of the talus can be more accurately described by dividing the condyles into anterior and posterior regions, thus creating bi-radial curves for both the medial and lateral sides of the talus.Methods:After IRB approval, 18 subjects (9 male, 9 female; mean age 34.5 years) underwent weight-bearing CT scans at mid- stance of simulated gait. All subjects were deemed to have a healthy right ankle by the surgeon investigator. CT images were used to generate 3D models of each talus. A coordinate system was defined and the articular surface of the talus was separated into four sections: medial-anterior (MA), medial-posterior (MP), lateral-anterior (LA) and lateral-posterior (LP). The curvature of each section was defined by selecting points on the articular surface at 10° intervals. The extent of each radius was 30° of arc and the magnitude of each radius was selected to minimize the gaps between the radii and the spline curve to define a best-fit bi-radial approximation to the spline curve using geometry that could be easily used to define the articular surface of the talus. Ratios of the aforementioned radii were calculated.Results:The average MA, MP, LA and LP radii were 18.3 mm, 26.6 mm, 21.5 mm and 25.1 mm, respectively. The medial (A/P), lateral (A/P), anterior (M/L) and posterior (M/L) radii ratios were 0.70, 0.87, 0.88 and 1.07, respectively. The anterior and posterior ratios were compared using a paired t-test and found to be statistically different (P=.019). Further, the data were compared against a hypothesized value of 1 using a one-tailed one-sample t-test. The anterior ratio was significantly lower than 1 (P=.014) while the posterior ratio was significantly greater (P=.037). On the lateral side, 83.3% of the subjects exhibited a larger posterior radius than anterior radius. Only one subject (5.6%) had a larger anterior radius than posterior radius on the medial side.Conclusion:This study shows that the radius increases in the sagittal plane from the anterior portion to the posterior portion of both the medial and lateral sides of the talus. Furthermore, the MA radius is smaller than the LA radius. Conversely, the MP radius is larger than the LP radius. These results substantiate the validity of an implant design that incorporates a condylar radius ratio that is smaller for the anterior dorsiflexion surface and greater for the posterior plantar flexion surface. Implants with more accurate anatomical geometry may allow for more normal kinematics and potentially prolong the life of the implant.

Tracking of group targets using multiple models GGIW-PHD algorithm based on best-fitting Gaussian approximation and strong tracking filter

Gamma Gaussian inverse Wishart probability hypothesis density (GGIW-PHD) filter algorithm is always used for tracking group targets with unknown number and variable measurement rates in the presence of cluttered measurements and missing detections. Aiming at the defect that the tracking error of GGIW-PHD filter algorithm will increase greatly in the maneuvering stage, a multiple model GGIW-PHD (MM-GGIW-PHD) algorithm is proposed in this paper based on the best-fitting Gaussian approximation and strong tracking filter. Firstly, on the basis of measurement set partition, the best-fitting Gaussian approximation method is proposed to implement the fusion of multiple models in the PHD predict stage. And a fading factor of strong tracking filter is proposed to correct the predicted covariance matrix of the GGIW component. Then, the estimation of kinematic state and extension state are deduced in the frame of multiple models. The probability of different tracking models is updated by the modified likelihood functions. The simulation results show that the MM-GGIW-PHD algorithm based on best-fitting Gaussian approximation and strong tracking filter can decrease the tracking error of group targets in the maneuvering stage and treated with the combination/spawning of group effectively.

Determination of the significant wave height from shadowing in synthetic radar images

Radar imagery is nowadays used to observe ocean waves despite the fact that radar images contain invisible areas because of the shadowing effect in the radar mechanism. Moreover, the radar images show the radar intensity which is not directly related to the wave height. This paper deals with the subject to estimate the significant wave height Hs from (synthetic) radar images and will show that the change of shadowing with distance from the radar is the key property to estimate Hs. In fact, the extent of shadowing, quantified by a visibility function, depends on various physical variables, but most notably on two dimensionless quantities: the ratio of radar height and Hs in the vertical direction, and the normalized distance in the horizontal direction. Assuming the normalized sea spectrum to be known, or approximating the spectrum, visibility functions can be determined for various Hs, defining the ingredients of a database. Comparing an observed visibility from successive images with the elements of the database, a best-fit approximation will provide an estimate of the Hs of the observed sea. Randomness of the sea will only slightly affect the observed visibility and Monte Carlo simulations will annihilate these effects in the database.

Group Targets Tracking Using Multiple Models GGIW-CPHD Based on Best-Fitting Gaussian Approximation and Strong Tracking Filter

Gamma Gaussian inverse Wishart cardinalized probability hypothesis density (GGIW-CPHD) algorithm was always used to track group targets in the presence of cluttered measurements and missing detections. A multiple models GGIW-CPHD algorithm based on best-fitting Gaussian approximation method (BFG) and strong tracking filter (STF) is proposed aiming at the defect that the tracking error of GGIW-CPHD algorithm will increase when the group targets are maneuvering. The best-fitting Gaussian approximation method is proposed to implement the fusion of multiple models using the strong tracking filter to correct the predicted covariance matrix of the GGIW component. The corresponding likelihood functions are deduced to update the probability of multiple tracking models. From the simulation results we can see that the proposed tracking algorithm MM-GGIW-CPHD can effectively deal with the combination/spawning of groups and the tracking error of group targets in the maneuvering stage is decreased.

Fault modelling of the early-2014 ~ M6 Earthquakes in Cephalonia Island (W. Greece) based on GPS measurements

Modelling of ground deformation was performed based on GPS measurements that were collected in the western part of Cephalonia (Paliki Peninsula) which had experienced two moderate magnitude earthquakes in early 2014. Both events of magnitudes Mw=6.1 (Jan. 26) and Mw=5.9 (Feb. 3) had the same right-lateral character of motion with a small thrust component, but different focal depth of 16km and 5km, respectively. The GPS results show large amplitudes of displacement in both horizontal (6–40cm) and vertical (8–15cm) components in the vicinity of Paliki for the period 2010–2014, which is attributed primarily to those earthquakes. Various scenarios of activated faults were considered to model the observed ground deformation that was associated with those events. The most plausible case that accounts for a realistic and best-fit approximation of the measured displacement vectors has a solution of two activated faults of SSW–NNE trending direction that are separated by a small offset. Consistent with the lack of surface exposure of the seismogenic faults, the best-fit model assumes two easterly dipping fault planes at burial depths of 0.8km and 0.5km and at angles of 72° and 65°, respectively. The GPS deduced models clearly resolved the plane ambiguities associated with the focal mechanism solutions of the two major events. A small “normal-fault” component along the upper part of the fault planes should be considered to further improve the best-fit approximation of the observed vertical deformation. It was also found that a non-negligible deformational component from aftershocks is inherent in the observed data mainly from Paliki.

Improved Best-fitting Gaussian Approximation PHD Filter

最适高斯近似概率假设密度滤波是一种新颖的多机动目标跟踪算法。然而，该算法存在模型概率先验固化问题，即在计算模型概率的过程中量测信息不起作用。针对以上问题，该文提出一种改进算法，通过引入模型概率更新过程，将后验量测信息加入模型概率的计算式中，根据似然函数在多个运动模型之间进行软切换，进而实现对多个机动目标的有效跟踪。实验结果表明，改进算法能够有效解决模型概率先验固化问题，在目标数估计和滤波精度方面均优于传统算法，具有良好的工程应用前景。

Modeling the chemical dynamics of chloride ion indicators

Fluorescent indicators have shown promise as a relatively non-invasive probe to measure cytosolic ion concentrations in brain slices and neuron cultures using microscopy imaging. Most fluorescent ion indicators bind selectively with a certain ion in solution causing a decrease in fluorescence in a process known as quenching. Under steady state conditions, a fluorescence measurement, made at a specific point and time, is directly related to the local ion concentration at the same point and time, typically via the Stern-Volmer relationship. However, this is usually no longer true under the dynamic conditions inside a cell when transmembrane currents are active. In our research, we are interested in measuring chloride (Cl-) channel currents because of their implication in substance abuse mechanisms. Useful probes have been found in Cl- sensitive dyes, such as N-(6-methoxyquinolyl) acetoethyl ester (MQAE) [1], and 6-methoxy-N-ethylquinolinium (MEQ) [3], and variants of the Yellow Fluorescent Protein (YFP) useful as a Cl- biosensor in dendritic compartments [4]. We have modeled jointly the Cl- flow as part of a Hodgkin-Huxley type model and the interaction of Cl- with a generic binding indicator as a system of non-linear differential equations derived from biophysical and chemical kinetic theory, using arbitrary parameters. Using the quenched indicator concentration as the given input signal, several approximate solutions can be derived for the corresponding output signal, the Cl- current of interest. To date, we have explored a simple quasi-linear approximation similar to that discussed in [2], as well as a best-fit model-based approximation in which the output is assumed to satisfy a sum of parameterized exponential curves (an assumption consistent with the theory of neuron excitation). We consider how both approximations can be optimally applied to a noisy input signal, and on their limitations in probing disparate time scales and small currents. We also test these methods on current experimental data obtained as part of study of the biophysics of drug addiction (Ingram et. al, in progress). Figure 1 Joint model of Cl- channel current and Cl- indicator binding. A) Concentration of quenched indicator due to current in B, with simulated noise. B) Cl- channel current reconstructed from noisy model (blue) and actual channel current (black).

Constraint Satisfaction Technology for Stacking Problem with Ordered Constraints

The stacking problem with ordered constraints (SPOC) is a typical combinatorial optimization problem and NP-hard character. In order to simplify problem, it is treated as a constraint satisfaction problem. A constraint satisfaction model is given. A hybrid solving algorithm is designed based on constraint satisfaction and Best-Fit approximation algorithm. The validity of the proposed solving algorithm is demonstrated by numerical simulation experiment from the production data in container yard.

Estimation of Roughness Parameters Within Sparse Urban-Like Obstacle Arrays

We conduct wind-tunnel experiments on three different uniform roughness arrays composed of sparsely distributed rectangular cylinders for the estimation of surface parameters. Roughness parameters such as the roughness length z 0 and zero-plane displacement d are extracted using a best-fit approximation of the measured wind velocity. We also perform a large-eddy simulation (LES) to confirm that four sampling points are sufficient to surrogate a space average above the canopy layer of the sparse roughness arrays. We propose a new morphological model from a systematic analysis of experimental data on the arrays. The friction velocity predicted by the proposed model agrees well with the peak value of the measured Reynolds shear stress $${(-\left )^{0.5}}$$ . The proposed model is further validated in an additional wind-tunnel experiment conducted on a scaled configuration of a real urban area exposed to four wind directions. The proposed model is found to perform very well particularly in the estimation of the friction velocity, readily leading to a better estimation of turbulence, which is essential for an accurate prediction of pollutant dispersion.

Gaussian mixture PHD filter for jump Markov models based on best-fitting Gaussian approximation

A new Gaussian mixture probability hypothesis density (PHD) filter is developed for tracking multiple maneuvering targets that follow jump Markov models. This approach is based on the best-fitting Gaussian approximation which has been shown to be an accurate predictor of the interacting multiple model (IMM) performance. Compared with the existing Gaussian mixture multiple model PHD filter without interacting, simulations show that the proposed filter achieves better results with much less computational expense.

Comment on "Negative refractive index in artificial metamaterials"

We dispute Grigorenko's statement [Opt. Lett. 31, 2483 (2006)] that measuring only the reflection intensity spectrum is sufficient for determining the effective refractive index. In addition, our simulations do not confirm his conclusions regarding the negative refractive index and the negative permeability of the nanopillar sample in the visible range.

Convergence results for the particle PHD filter

Bayesian single-target tracking techniques can be extended to a multiple-target environment by viewing the multiple-target state as a random finite set, but evaluating the multiple-target posterior distribution is currently computationally intractable for real-time applications. A practical alternative to the optimal Bayes multitarget filter is the probability hypothesis density (PHD) filter, which propagates the first-order moment of the multitarget posterior instead of the posterior distribution itself. It has been shown that the PHD is the best-fit approximation of the multitarget posterior in an information-theoretic sense. The method avoids the need for explicit data association, as the target states are viewed as a single global target state, and the identities of the targets are not part of the tracking framework. Sequential Monte Carlo approximations of the PHD using particle filter techniques have been implemented, showing the potential of this technique for real-time tracking applications. This paper presents mathematical proofs of convergence for the particle filtering algorithm and gives bounds for the mean-square error

Efficient Response Surface Modeling by Using Moving Least-Squares Method and Sensitivity

The response surface method (RSM) has currently become one of the better-known meta-modeling techniques. However, its approximation errors have placed several restrictions on designers as classical RSM uses the leastsquares method (LSM) to find the best-fitting approximation models from the given function data. We discuss how to construct RS models efficiently and accurately using the moving least-squares method (MLSM) combined with sensitivity information. The formulations for incorporating the sensitivity using the MLSM are derived. With this method, several parameters should be determined during the construction of response surfaces. The parametric study and optimization for these parameters are performed. However, because of the discontinuity problem of the optimization, a genetic algorithm is adopted. The correlation coefficient is used for the normalized comparison between the function and gradient errors. Also, the reciprocal condition number is applied to avoid illconditioned approximations. Several difficulties and their respective solutions during the approximation processes are described, and the numerical examples are then demonstrated to verify the accuracy and the efficiency of this method. If the sensitivity of each sampling point can be calculated efficiently by utilizing a cheap computation, the proposed method is recognized as very efficient and accurate.

Estimation of Nonlinear Time-dependent Soil Behavior in Strong Ground Motion Based on Vertical Array Data

To improve our understanding of nonlinear elastic properties of soils, a method is proposed of estimation of stress-strain relations of soils in situ in strong ground motion based on vertical array data. Strong motion records provided by seismic vertical arrays allow estimation of nonlinear stress-strain relations in soil layers at different depths, from the surface down to the location of the deepest device. As an example, records obtained during the main shock of the 1995 Kobe earthquake at Port-Island, SGK, and TKS sites were used to estimate the stress-strain relations in the soil profiles. For different layers, different types of nonlinear stress-strain relations were selected, according to the profiling data. To account for temporal changes in the soil behavior, consecutive parts of records were examined, and for successive time intervals, the relations were found showing the best-fit approximation to the observed data. At Port Island and SGK sites, where the strongest accelerations were recorded, the obtained stress-strain relations showed systematic changes in the upper layers (0–14 m), such as, a progressive reduction of the slopes of the stress-strain curves due to liquefaction at Port Island and reduction and recovery of the slopes at SGK and TKS sites. At the three sites, the stress-strain relations remained stable in layers below 11–14 m. Thus, the proposed approach gives us a representation of the soil behavior in layers at different depths in strong ground motion; it allows calculation of the propagation of arbitrary seismic signals in the studied profiles and estimation of nonlinear components in the ground response by the nonlinear system identification technique. The method can also be applied to evaluate the ground response at sites where profiling data are available and an imposed motion can be estimated.