Linear Fitting Function Research Articles

Temperature Correction around Anchorage Zones of Cable-Stayed Bridge in Field Test

Based on the working principle of vibration wire strain gauge, two influence factors were analyzed and the temperature correcting equation was given. Furthermore combined with the anchorage zones model test of Xiaoshawan Yellow River Bridge in Inner Mongolia, temperature correction coefficients of test dates were found by linear fitting function of MATLAB, and then the test datum were corrected that achieved very good effects.

On the Semi-Automatic Retrieval of Biophysical Parameters Based on Spectral Index Optimization

Regression models based on spectral indices are typically empirical formulae enabling the mapping of biophysical parameters derived from Earth Observation (EO) data. Due to its empirical nature, it remains nevertheless uncertain to what extent a selected regression model is the most appropriate one, until all band combinations and curve fitting functions are assessed. This paper describes the application of a Spectral Index (SI) assessment toolbox in the Automated Radiative Transfer Models Operator (ARTMO) package. ARTMO enables semi-automatic retrieval and mapping of biophysical parameters from optical remote sensing observations. The SI toolbox facilitates the assessment of biophysical parameter retrieval accuracy of established as well as new and generic SIs. For instance, based on the SI formulation used, all possible band combinations of formulations with up to ten bands can be defined and evaluated. Several options are available in the SI assessment: calibration/validation data partitioning, the addition of noise and the definition of curve fitting models. To illustrate its functioning, all two-band combinations according to simple ratio (SR) and normalized difference (ND) formulations as well as various fitting functions (linear, exponential, power, logarithmic, polynomial) have been assessed. HyMap imaging spectrometer (430–2490 nm) data obtained during the SPARC-2003 campaign in Barrax, Spain, have been used to extract leaf area index (LAI) and leaf chlorophyll content (LCC) estimates. For both SR and ND formulations the most sensitive regions have been identified for two-band combinations of green (539–570 nm) with longwave SWIR (2421–2453 nm) for LAI (r2: 0.83) and far-red (692 nm) with NIR (1340 nm) or shortwave SWIR (1661–1686 nm) for LCC (r2: 0.93). Polynomial, logarithmic and linear fitting functions led to similar best correlations, though spatial differences emerged when applying the functions to HyMap imagery. We suggest that a systematic SI assessment is a strong requirement in the quality assurance approach for accurate biophysical parameter retrieval.

Analytical functions for beta and gamma absorbed fractions of iodine-131 in spherical and ellipsoidal volumes.

The beta and gamma absorbed fractions in organs and tissues are the important key factors of radionuclide internal dosimetry based on Medical Internal Radiation Dose (MIRD) approach. The aim of this study is to find suitable analytical functions for beta and gamma absorbed fractions in spherical and ellipsoidal volumes with a uniform distribution of iodine-131 radionuclide. MCNPX code has been used to calculate the energy absorption from beta and gamma rays of iodine-131 uniformly distributed inside different ellipsoids and spheres, and then the absorbed fractions have been evaluated. We have found the fit parameters of a suitable analytical function for the beta absorbed fraction, depending on a generalized radius for ellipsoid based on the radius of sphere, and a linear fit function for the gamma absorbed fraction. The analytical functions that we obtained from fitting process in Monte Carlo data can be used for obtaining the absorbed fractions of iodine-131 beta and gamma rays for any volume of the thyroid lobe. Moreover, our results for the spheres are in good agreement with the results of MIRD and other scientific literatures.

Analysis on performance characteristics of ejector with variable area-ratio for multi-evaporator refrigeration system based on experimental data

This paper presents a study on experiment and analysis of variable area-ratio ejector used in a multi-evaporator refrigeration system (MERS). The experimental rig and method are described, and the entrainment and pressure recovery performances of the variable ejector are measured at various operating and geometric conditions. The critical area ratio is proposed as an indicator of pressure recovery status; area ratios smaller than the critical ones are required to make sure that the system operates at energy saving mode. The investigation results indicate that the entrainment ratio, pressure recovery ratio and critical area ratio are strongly affected by the primary pressure and secondary pressure. Greater entrainment ratio can be obtained by increasing the secondary pressure or decreasing primary pressure. The opposite trends are found for pressure recovery ratio. Moreover, the critical area ratio varies greatly with the operation condition, and can be predicted by a linear fitting function of primary pressure or a power function in terms of secondary pressure.

Estimation of foliar pigment concentration in floating macrophytes using hyperspectral vegetation indices

Foliar pigment concentrations of chlorophylls and cartenoids are important indicators of plant physiological status, photosynthesis rate, and net primary productivity. Although the utility of hyperspectral derived vegetation indices for estimating foliar pigment concentration has been documented for many vegetation types, floating macrophytes have not been assessed despite their ecological importance. This study surveyed 39 wetland species (12 floating macrophytes (FM), 8 grasses/sedges/rushes (GSR), and 19 herbs/wildflowers (HWF)) to determine whether foliar pigment concentrations could be estimated from hyperspectral reflectance. Hyperspectral reflectance of samples was recorded using an ASD FieldSpec3 Max portable spectroradiometer with the plant probe attachment or via a typical laboratory set-up. A semi-empirical relationship was established using either a linear, second-degree polynomial or logarithmic function between 13 candidate vegetation indices and chl-a, chl-b, Car, and chl-a + b pigment concentrations. Vegetation indices R-M, CI-Red, and MTCI were strongly correlated with foliar pigment concentrations using a linear fitting function. Chl-a + b and chl-b concentrations for all samples were reasonably estimated by the R-M index (R2 = 0.66 and 0.64), although Chl-a and Car concentration estimates using CI-Red were weaker (R2 = 0.63 and 0.51). Regression results indicate that pooled samples to estimate individual foliar pigments were less correlated than when each type of vegetation type was treated separately. For instance, chl-a + b was best estimated by CI-Red for FM (R2 = 0.80), MTCI for HWF (R2 = 0.77), and R-M for GSR (R2 = 0.67). Although floating macrophytes feature unique adaptions to their aquatic environment, their foliar pigment concentrations and spectral signatures were comparable to other wetland vegetation types. Overall, vegetation indices that exploit the red-edge region were a reasonable compromise, having good explanatory power for estimation of foliar pigments across the sampled wetland vegetation types and with CI-Red the best suited index for floating macrophytes.

Experimental Study of Short-Term Creep Characteristics Base on Step Loading-Unloading Method for Hard Rock

Based on experimental results of uniaxial compression and short-term creep using 8-step loading-unloading method, fine sandstone specimen, which lower creep limit is 27MPa, present typical brittle breakage properties of hard rock. The correlative coefficients of linear regression function for isochronous stress-strain curve are all higher than 0. 92, and the ratio of long-term strength to instantaneous strength reaches 94. 39%，which indicate that the whole creep of fine sandstone specimen is weak. The average correlative coefficients of linear regression function for isochronous stress- axial strain curve are 3. 92% higher than that of average correlative coefficients of linear regression function for isochronous stress- radial strain curve, so nonlinear creep property of the fine sandstone specimen in axial direction is correspondingly weaker than that in radial direction. Negative Gauss distribution can be applied collectively to nonlinear creep of fine sandstone specimen, which has obvious time effect.With increasing loading, the reduction degrees of average correlative coefficients of linear fitting functions of isochronous stress-axial strain curve and isochronous stress-radial strain curve are 0. 97% and 0. 67% respectively, which indicates the linear correlation decreases commonly. Thus, the degree of nonlinear creep for fine sandstone specimen increases along with loading stress with obvious stress effect.

Dynamic Properties of Evolutionary Multi-player Games in Finite Populations

William D. Hamilton famously stated that “human life is a many person game and not just a disjoined collection of two person games”. However, most of the theoretical results in evolutionary game theory have been developed for two player games. In spite of a multitude of examples ranging from humans to bacteria, multi-player games have received less attention than pairwise games due to their inherent complexity. Such complexities arise from the fact that group interactions cannot always be considered as a sum of multiple pairwise interactions. Mathematically, multi-player games provide a natural way to introduce non-linear, polynomial fitness functions into evolutionary game theory, whereas pairwise games lead to linear fitness functions. Similarly, studying finite populations is a natural way of introducing intrinsic stochasticity into population dynamics. While these topics have been dealt with individually, few have addressed the combination of finite populations and multi-player games so far. We are investigating the dynamical properties of evolutionary multi-player games in finite populations. Properties of the fixation probability and fixation time, which are relevant for rare mutations, are addressed in well mixed populations. For more frequent mutations, the average abundance is investigated in well mixed as well as in structured populations. While the fixation properties are generalizations of the results from two player scenarios, addressing the average abundance in multi-player games gives rise to novel outcomes not possible in pairwise games.

A Wireless Sensor Readout System—Circuit Concept, Simulation, and Accuracy

In this paper, we present an electronic readout system for wireless passive sensors based on inductively coupled LC resonant circuits. The proposed system consists of a reader coil inductively coupled to the sensor circuit, an analog frontend circuit, and a digital signal processing unit. The analog frontend circuit generates a dc voltage representing the sensor resonance curve. The frequency of the reader coil driving signal is continuously readjusted by the digital signal processing unit. Based on analytical calculation and system simulation, we derive a model for the achievable accuracy of the overall sensor and readout system. The accuracy is limited by noise and systematic errors due to the measurement principle. We show how to design the digital signal processing system for optimal insensitivity to voltage noise. The noise sensitivity of the measurement system is inversely proportional to the square of the quality factor of the LC sensor. This means that minimizing the losses of the sensor is of crucial importance to obtain a wireless measurement system with a high range and a good insensitivity to noise. Subsequently, we outline an approach to calculate the sensor resonance frequency, quality factor, and inductive coupling factor from the available voltage signals in the signal processing unit using linear fitting functions. The accuracy of our approach is exemplified by a system simulation for typical sensor parameters. For the system studied, we show that the relative linearization error of the sensor resonance frequency measurement is below 0.02%. Taking the general models presented for both the noise sensitivity and linearization error into account, it is possible to estimate the maximum distance and accuracy for any wireless sensor system based on an inductively coupled LC resonator.

Contribution of magnetotail reconnection to the cross-polar cap electric potential drop

[1] Since the work of Dungey (1961), the global circulation pattern with two (dayside and nightside) reconnection regions has become a classic concept. However, the contributions of dayside and nightside sources to the cross-polar cap potential (PCP) are not fully understood, particularly, the relative role and specifics of the nightside source are poorly investigated both in quantitative and qualitative terms. To fill this gap, we address the contributions of dayside and nightside sources to the PCP by conducting global MHD simulations with both idealized solar wind input and an observed event input. The dayside source was parameterized by solar wind–based “dayside merging potential” Φd = LeffVBt sin4(θ/2), whereas to characterize the nightside source we integrated across the tail the dawn-dusk electric field in the plasma sheet (to obtain the “cross-tail potential” Φn). For the idealized run we performed simulations using four MHD codes available at the Community Coordinated Modeling Center to show that contribution of the nightside source is a code-independent feature (although there are many differences in the outputs provided by different codes). Particularly, we show that adding a nightside source to the linear fit function for the ionospheric potential (i.e., using the fit function Φfit = KdΦd + KnΦn + Φ0) considerably improves the fitting results both in the idealized events as well as in the simulation of an observed event. According to these simulations the nightside source contribution to the PCP has a fast response time (<5 min) and a modest efficiency (potential transmission factor from tail to the ionosphere is small, Kn < 0.2), which is closely linked to the primarily inductive character of strong electric field generated in the plasma sheet. The latter time intervals are marked by strongly enhanced nightside (lobe) reconnection and can be associated with substorm expansion phases. This association is further strengthened by the simulated patterns of precipitation, the R1-type field-aligned substorm current wedge currents and Hall electrojet currents, which are consistent with the known substorm signatures.

Planck-Benzinger Thermal Work Function: Thermodynamic Characterization of the Carboxy-Terminus of P53 Peptide Fragments

The thermodynamic parameters for six p53 carboxy-terminus peptide fragments as determined by analytical ultracentrifugal analysis were compared over the experimental temperature range of 275-310 K to evaluate the Gibbs free energy change as a function of temperature, ΔGo(T), from 0 to 400 K using our general linear third-order fitting function, ΔGo(T) = α + βT2 + γT3. Data obtained at the typical experimental temperature range are not sufficient to accurately describe the variations observed in the oligomerization of these p53 fragments. It is necessary to determine a number of thermodynamic parameters, all of which can be precisely assessed using this general third-order linear fitting function. These are the heat of reaction, innate temperature-invariant enthalpy, compensatory temperatures and the thermodynamic molecular switch occurring at the thermal set point. The temperature-invariant enthalpy for each of the six p53 peptide fragments was found to be: Lys319-Ala347, 10.92 kcal mol−1; Lys319-Lys351, 24.75; Lys319-Gly360, 54.86; Lys319-Asp393, 203.20; Ser303-Asp393, 140.43; and Ser303-Gly360, 49.69 kcal mol−1. While the role of the C-terminus in sequence-specific DNA binding has been debated, these results suggest that the C-terminal end has a significant influence on the degree of oligomerization in p53. When p53 is considered in vivo, it would seem that the C-terminus has an additional role, that of protecting the tetramerization domain. These thermodynamic values can be used to distinguish the characteristic structure and stability not only of p53 carboxy-terminal fragments or other p53 mutants, but also in the analysis of site-direct mutagenesis or other fragmentation, deletion mutation, and truncation reactions. In fact the parameters determined with this universal linear third-order fitting function are essential for the thermodynamic characterization of any interacting biological system. No other experimental method offers a similar degree of accuracy.

High Temperature X-Ray Diffraction Studies Of The Sample Heating Units

By means of the in situ high temperature X-ray diffraction (HT-XRD), sample heating units (Pt) is studied as the standard sample for temperature correction in the temperature range 28–1050°C. The interpla according to method provided by Rigaku and method of copper target Kα radiation(Kα1, Kα2). By linear fitting, polynomial fitting and custom function fitting, the lattice parameters at each temperature point are also calculated and compared. Besides, different views are put forward for three aspects about the temperature correction in Rigaku diffractometer manual, and the complex phenomenon of the experiment are preliminarily discussed using the theoretical calculation and experimental diffraction data. Theory and experiment show that Custom fitting has higher accuracy, Selection of the degree of the Fitting polynomial must be greater than or equal to 3, the lattice constant of Platinum nonlinear increases with temperature. In the process of heating, Pt and environmental elements may be coupled reaction, platinum is oxidized to form a new oxide Pt3O2.

Planck-Benzinger Thermal Work Function: Thermodynamic Characterization of the Carboxy-Terminus of p53 Peptide Fragments

The thermodynamic parameters for six p53 carboxy-terminus peptide fragments as determined by analytical ultracentrifugal analysis were compared over the experimental temperature range of 275-310 K to evaluate the Gibbs free energy change as a function of temperature, ΔG°(T), from 0 to 400 K using our general linear third-order fitting function, ΔG°(T) = α + βT² + γT³. Data obtained at the typical experimental temperature range are not sufficient to accurately describe the variations observed in the oligomerization of these p53 fragments. It is necessary to determine a number of thermodynamic parameters, all of which can be precisely assessed using this general third-order linear fitting function. These are the heat of reaction, innate temperature-invariant enthalpy, compensatory temperatures and the thermodynamic molecular switch occurring at the thermal set point. This methodology can be used to distinguish the characteristic structure and stability of p53 carboxy-terminal fragments or other p53 mutants. It should be used for the thermodynamic characterization of any interacting biological system.

FLEXMG: A new library of multigrid preconditioners for a spectral/finite element incompressible flow solver

AbstractA new library called FLEXMG has been developed for a spectral/finite element incompressible flow solver called SFELES. FLEXMG allows the use of various types of iterative solvers preconditioned by algebraic multigrid methods. Two families of algebraic multigrid preconditioners have been implemented, namely smooth aggregation‐type and non‐nested finite element‐type. Unlike pure gridless multigrid, both of these families use the information contained in the initial fine mesh. A hierarchy of coarse meshes is also needed for the non‐nested finite element‐type multigrid so that our approaches can be considered as hybrid. Our aggregation‐type multigrid is smoothed with either a constant or a linear least‐square fitting function, whereas the non‐nested finite element‐type multigrid is already smooth by construction. All these multigrid preconditioners are tested as stand‐alone solvers or coupled with a GMRES method. After analyzing the accuracy of the solutions obtained with our solvers on a typical test case in fluid mechanics, their performance in terms of convergence rate, computational speed and memory consumption is compared with the performance of a direct sparse LU solver as a reference. Finally, the importance of using smooth interpolation operators is also underlined in the study. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Solution of the Crow-Kimura and Eigen Models for Alphabets of Arbitrary Size by Schwinger Spin Coherent States

To represent the evolution of nucleic acid and protein sequence, we express the parallel and Eigen models for molecular evolution in terms of a functional integral representation with an $h$-letter alphabet, lifting the two-state, purine/pyrimidine assumption often made in quasi-species theory. For arbitrary $h$ and a general mutation scheme, we obtain the solution of this model in terms of a maximum principle. Euler's theorem for homogeneous functions is used to derive this `thermodynamic' formulation of evolution. The general result for the parallel model reduces to known results for the purine/pyrimidine $h=2$ alphabet and the nucleic acid $h=4$ alphabet for the Kimura 3 ST mutation scheme. Examples are presented for the $h=4$ and $h=20$ cases. We derive the maximum principle for the Eigen model for general $h$. The general result for the Eigen model reduces to a known result for $h=2$. Examples are presented for the nucleic acid $h=4$ and the amino acid $h=20$ alphabet. An error catastrophe phase transition occurs in these models, and the order of the phase transition changes from second to first order for smooth fitness functions when the alphabet size is increased beyond two letters to the generic case. As examples, we analyze the general analytic solution for sharp peak, linear, quadratic, and quartic fitness functions.

Tribological interaction between multi-walled carbon nanotubes and silica surface using lateral force microscopy

This work presents the tribological interaction between multi-walled carbon nanotubes (MWCNTs) and silica surface using lateral manipulation in the atomic force microscope (AFM). The MWCNT is mechanically manipulated by a pyramidal silicon probe of an AFM using the same scan mechanism as in the imaging mode. With a controlled normal force of the AFM probe, it was found that lateral force applied to the MWCNT could overcome the tribological adhesion between MWCNT and silica surface, causing individual MWCNT to rotate on the silica. According to the results, the shear stresses due to tribological interacting with the MWCNTs and the silica are 59.6 MPa and 64.8 MPa for the MWCNT 1 (100 nm diameter) and the MWCNT 2 (60 nm diameter), respectively. Experimental results show that the shear stress increases with the increasing rotation angle for each manipulation, from which we determine the linear fitting function. In addition, we determine the relationship between push point and pivot point to realize the rotation behavior. The implications of tribological interaction between the MWCNTs and silica surface are discussed in detail.

QSAR Analyses of Skin Penetration Enhancers.

AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract, please click on HTML or PDF.

QSAR Analyses of Skin Penetration Enhancers

QSAR models for four skin penetration enhancer data sets of 61, 44, 42, and 17 compounds were constructed using classic QSAR descriptors and 4D-fingerprints. Three data sets involved skin penetration enhancement of hydrocortisone and hydrocortisone acetate. The other data set involved skin penetration enhancement of fluorouracil. The measure of penetration enhancement is the ratio of the net permeation of the penetrant with and without a common fixed concentration of enhancer. Significant QSAR models could be built using multidimensional linear regression fitting and genetic function model optimization for all four data sets when both classic and 4D-fingerprint descriptors were used in the trial descriptor pool. Reasonable QSAR models could be built when only 4D-fingerprint descriptors were employed, and no significant QSAR models could be built using only classic descriptors for two of the four data sets. Comparison analyses of the descriptor terms, and their respective regression coefficients, across the pairs of the best QSAR models of the four skin penetration enhancer data sets did not reveal any significant extent of similar terms. Overall, the QSAR models for the penetration-enhancer systems appear meaningfully different from one another, suggesting that there are distinct mechanisms of skin penetration enhancement that depend on the chemistry of both the enhancer and the penetrant.

A new multiobjective simulated annealing algorithm

A new multiobjective simulated annealing algorithm for continuous optimization problems is presented. The algorithm has an adaptive cooling schedule and uses a population of fitness functions to accurately generate the Pareto front. Whenever an improvement with a fitness function is encountered, the trial point is accepted, and the temperature parameters associated with the improving fitness functions are cooled. Beside well known linear fitness functions, special elliptic and ellipsoidal fitness functions, suitable for the generation on non-convex fronts, are presented. The effectiveness of the algorithm is shown through five test problems. The parametric study presented shows that more fitness functions as well as more iteration gives more non-dominated points closer to the actual front. The study also compares the linear and elliptic fitness functions. The success of the algorithm is also demonstrated by comparing the quality metrics obtained to those obtained for a well-known evolutionary multiobjective algorithm.

An Analysis of Mutative σ-Self-Adaptation on Linear Fitness Functions

This paper investigates sigma-self-adaptation for real valued evolutionary algorithms on linear fitness functions. We identify the step-size logarithm log sigma as a key quantity to understand strategy behavior. Knowing the bias of mutation, recombination, and selection on log sigma is sufficient to explain sigma-dynamics and strategy behavior in many cases, even from previously reported results on non-linear and/or noisy fitness functions. On a linear fitness function, if intermediate multi-recombination is applied on the object parameters, the i-th best and the i-th worst individual have the same sigma-distribution. Consequently, the correlation between fitness and step-size sigma is zero. Assuming additionally that sigma-changes due to mutation and recombination are unbiased, then sigma-self-adaptation enlarges sigma if and only if mu < lambda/2, given (mu, lambda)-truncation selection. Experiments show the relevance of the given assumptions.

First-principles study of structural stabilities, and electronic and optical properties ofCaF2under high pressure

An investigation into the structural stabilities and the electronic and optical properties of $\mathrm{Ca}{\mathrm{F}}_{2}$ under high pressure was conducted using first-principles calculations based on density functional theory. Our results demonstrate that the sequence of the pressure-induced phase transition of $\mathrm{Ca}{\mathrm{F}}_{2}$ is the fluorite structure $(Fm3m)$, the $\mathrm{Pb}{\mathrm{Cl}}_{2}$-type structure $(Pnma)$, and the ${\mathrm{Ni}}_{2}\mathrm{In}$-type structure $(P{6}_{3}∕mmc)$. At these phase transformations, the coordination number of ${\mathrm{Ca}}^{2+}$ increases from eight to nine and then to eleven. The mechanisms of the structure change were revealed from the $\mathrm{Pb}{\mathrm{Cl}}_{2}$-type phase to the ${\mathrm{Ni}}_{2}\mathrm{In}$-type phase. The energy band gap increases with pressure in the $Fm3m$ and the $Pnma$ phases, but decreases in the $P{6}_{3}∕mmc$ phase. The band gap pressure coefficients were obtained using a linear pressure-dependent fit function. In addition, the energy band overlap metallization does not occur up to $218\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. The static dielectric constants ${\ensuremath{\epsilon}}_{0}$ vs pressure are also discussed.