Least-squares Procedure Research Articles

A Novel Ephemeris Model for Martian Moons Incorporating Their Free Rotation

High-precision ephemerides not only support space missions, but can also be used to study the origin and future of celestial bodies. In this paper, a coupled orbit-rotation dynamics model that fully takes into account the rotation of the Martian moons is developed. Phobos and Deimos’ rotations are first described by Eulerian rotational equations, and integrated simultaneously with the orbital motion equations. Orbital and orientational parameters of Mars satellites were simultaneously obtained by numerical integration for the first time. In order to compare the differences between our newly developed model and the one now used in the ephemerides, we first reproduced and simulated the current model using our own parameters, and then fit it to the Institut de Mécanique Céleste et de Calcul des Éphémérides ephemerides using least-square procedures. The adjustment test simulations show Phobos and Deimos’ orbital differences between the refined model and the current model are no more than 300 m and 125 m, respectively. The orientation parameters are confirmed and the results are in good agreement with the International Astronomical Union results. Moreover, we simulated two perturbations (main asteroids and mutual torques) which were not included in our refined model, and find that their effects on the orbits are completely negligible. As for the effect on rotation, we propose to take care of the role of mutual attraction in future models.

One-Port Coaxial Line Sample Holder Characterisation Method of Dielectric Spectra.

A technique for solving the one-port closed coaxial transmission line sample holder scattering equation for complex permittivity inversion for lossy materials is presented. A non-linear least-squares procedure is used for the determination of parameters for the specification of the spectral functional form of the complex permittivity. The method allows for accurate retrieval of many low- and high-permittivity dielectric materials in the frequency range of 1 GHz to 3 GHz inserted into the coaxial cell. Using this method, the complex permittivity of a number of liquids and a Maltese soil known as Bajjad soil have been extracted by measurements using a short terminated coaxial transmission line sample holder. The proposed novel inversion method is mainly based on the reflection coefficient of the test material. The measured results of the complex permittivity of liquid dielectrics such as ethanol, methanol, and TX100 are validated and compared with previously published data obtained from measurements made by the National Physical Laboratory (NPL) using a two-port measurement setup made with the same commercial coaxial transmission line sample holder used in the one-port setup. Since the technique allows broadband measurements, it has been used to characterise the soil dielectric spectrum in the frequency range of 1-3 GHz, which is also compared with results from a two-port setup of the same coaxial line. The experimental results are a validation of the proposed approach for different types of materials.

Uncertainty of the initial phase estimation of a sinewave in the presence of phase noise, additive noise or jitter

This paper presents the derivation of a simple analytical expression for the precision of the initial phase estimates obtained through a least-squares procedure. That expression depends on number of samples, phase noise standard deviation and additive noise standard deviation. This study is applicable to the estimates obtained through the sine fitting algorithm with known frequency and to the Discrete Fourier Transform algorithm. The analytical expression supplied was verified using a Monte Carlo simulation with numerically created data. The non-ideal phenomena treated in this work is the presence of jitter in the sampling instant, phase noise in the oscillator and additive noise in the system both of which must be normally distributed with a known value of standard deviation. It is useful information for an engineer in order to choose the proper number of samples to acquire to achieve a desired level of precision on the estimates made and thus carry out an efficient data acquisition with no unnecessary samples thus optimizing the test duration.

Cosmic Type Ia supernova rate and constraints on supernova Ia progenitors

Type Ia supernovae play a key role in the evolution of galaxies by polluting the interstellar medium with a fraction of iron peak elements larger than that released in the core-collapse supernova events. Their light curve, moreover, is widely used in cosmological studies as it constitutes a reliable distance indicator on extragalactic scales. Among the mechanisms proposed to explain the Type Ia supernovae (SNe), the single- and double-degenerate channels are thought to be the dominant ones, which implies a different distribution of time delays between the progenitor formation and the explosion. In this paper, we aim to determine the dominant mechanism by comparing a compilation of Type Ia SN rates with those computed from various cosmic star-formation histories coupled with different delay-time distribution functions. We also evaluate the relative contributions of both channels. By using a least-squares fitting procedure, we modeled the observations of Type Ia SN rates assuming different combinations of three recent cosmic star-formation rates and seven delay-time distributions. The goodness of these fits are statistically quantified by the $ test. For two of the three cosmic star-formation rates, the single degenerate scenario provides the most accurate explanation for the observations, while a combination of 34<!PCT!> single-degenerate- and 66<!PCT!> double-degenerate delay-time distributions is more plausible for the remaining tested cosmic star-formation rates. Though dependent on the assumed cosmic star-formation rate, we find arguments in favor of the single-degenerate model. From the theoretic point of view, at least sim 34<!PCT!> of the Type Ia SN must have been produced through the single-degenerate channel to account for the observations. The wide, double-degenerate mechanism slightly under-predicts the observations at redshift $z 1$, unless the cosmic SFR flattens in that regime. On the contrary, although the purely close double-degenerate scenario can be ruled out, we cannot rule out a mixed scenario with single- and double-degenerate progenitors.

Polynomial preserving recovery for the finite volume element methods under simplex meshes

The recovered gradient, using the polynomial preserving recovery (PPR), is constructed for the finite volume element method (FVEM) under simplex meshes. Regarding the main results of this paper, there are two aspects. Firstly, we investigate the supercloseness property of the FVEM, specifically examining the quadratic FVEM under tetrahedral meshes. Secondly, we present several guidelines for selecting computing nodes such that the least-squares fitting procedure of the PPR admits a unique solution. Numerical experiments demonstrate that the recovered gradient by the PPR exhibits superconvergence.

The anion photoelectron spectrum and diabatization of tetrazolyl.

The potential energy surface of tetrazolyl [cyclic (N4CH)] has a conical intersection seam between the two lowest-energy electronic states near the ground state minimum geometry. This work treats that molecule. The potential energy surfaces used in this study are based on a least-squares fitting procedure that includes abinitio energies, energy gradients, and derivative couplings described using polynomials up to fourth-order and abinitio data obtained from multireference configuration interaction wave functions. A five-electronic-state description was generated with a root mean square absolute energy error of 9.6cm-1, compared to 326.8cm-1 when only second-order terms were used. The time-independent multimode vibronic coupling in the KDC approximation was used to simulate and analyze the anion ultraviolet photoelectron spectrum of tetrazolide.

Spectroscopic evaluation of Nd3+ doped cadmium-boro-phosphate glasses for near-IR (1060 nm) laser applications

Neodymium-doped Cadmium-boro-phosphate glasses were synthesized using the melt quenching procedure to investigate their lasing capacities. The FTIR results reveal the different functional groups and structural units of our glass system. Physical parameters such as density (ρ), molar volume (VM), refractive index (n), Urbach energy (ΔE), and band gap (Eg) were measured, and computed. The results demonstrated that our glasses have indirect-allowed transitions with low localized states. The photoluminescence and absorption spectra were measured and the results suggest that the Nd3+ ions have a uniform distribution throughout the glass network. The Judd-Ofelt parameters (Ω2, Ω4, and Ω6) were obtained using the least-squares procedure. The spectroscopic quality factor (χ), the emission-peak-wavelength (λp), the radiative-transition-probability (Ar), the radiative lifetime (τrad), the radiative and experimental branching-ratio (βrad, βexp), the effective-bandwidth (Δλeff), the stimulated-emission-cross-section (σ(λp)), the gain-bandwidth (σ(λp), × Δλeff) and the optical-gain (σ(λp) x τrad) were measured, computed and compared with other famous reported glasses. The current glass showed low χ values (=0.45), high βexp (=0.7), and high optical gain (15.8 × 10− 24 cm2 s). According to its spectroscopic and radiative properties, our glass system shows remarkable potential for lasing around 1057 nm.

Influence of night shift work on circadian heart-rate rhythm in nurses: using a Holter electrocardiogram that can be continuously measured for two weeks.

The influence of night shift work on circadian heart-rate rhythm was examined in nurses engaged in shift work using a Holter electrocardiogram, continuously measured for two weeks, and cosine periodic regression analysis. We enrolled 11 nurses who were engaged in a two-shift system. The R2 value in the cosine regression curve of heart-rate rhythm (concordance rate), indicating the concordance rate between the actual heart rate over 24 h and the cosine regression curve approximated by the least-squares procedure, was significantly lower in the night shift (0.40 ± 0.15) than in the day shift (0.66 ± 0.19; p<0.001). Moreover, the amplitude was significantly lower and the acrophase was significantly delayed in the night shift. Thus, the circadian heart-rate rhythm was disrupted by the night shift work. Although the heart-rate acrophase recovered during the day and two days after the night shift, the concordance rate and amplitude did not recover, indicating that the influence of night shift work on circadian heart-rate rhythm might persist even two days after the night shift. Based on these results, adequate clinical attention should be paid to how to spend the day and two days after the night shift to correct the circadian heart-rate rhythm disruption caused by night shift work.

A Solution Verification Study for URANS Simulations of Flow Over a 5:1 Rectangular Cylinder Using Grid Convergence Index and Least Squares Procedures

Abstract A verification study was conducted for URANS (Unsteady Reynolds-Averaged Navier–Stokes) simulations of flow around a 5:1 rectangular cylinder at a Reynolds number of 56,700 (based on the cylinder depth) using the k–ω SST (shear stress transport) turbulence model and the γ−Reθ transition model for three types of grids (a fully structured grid and two hybrid grids generated using Delaunay and advancing front techniques). The grid convergence index (GCI) and least squares (LS) procedures were employed to estimate discretization error and associated uncertainties. The result indicates that the LS procedure provides the most reliable estimates of discretization error uncertainties for solution variables in the structured grid from the k–ω SST model. From the six solution variables of interest, the highest relative uncertainty was typically observed in the root-mean-square (rms) of lift coefficient, followed by time-averaged reattachment length and peak rms of pressure coefficient on the top and bottom surfaces of the cylinder. The solution variable with the lowest uncertainty was Strouhal number, followed by time-averaged drag coefficient. It is also noted that the GCI and LS procedures produce noticeably different uncertainty estimates, primarily due to inconsistences in their estimated observed orders of accuracy and safety factors. To successfully apply the procedures to practical problems, further research is required to reliably estimate uncertainties in solutions with “noisy” grid convergence behaviors and observed orders of accuracy.

Spectral modelling approach for crowd-rhythmic activities performed on steel-concrete composite floors

During the last decades, building floors have become sensitive to vibrations caused by human activities, especially when a group of individuals perform rhythmic activities in a coordinated manner. Resulting effects on floor occupants can range from a mere perception, can pass through discomfort and can even go so far to cause panic. The present paper proposes a spectral modelling approach for crowd-rhythmic activities applied on floor structures. The proposed model comprises a frequency domain model for a single person, combined with coordination factors to account for the lack of synchronization between individuals. The identification of this model was based on vibration experiments carried out on a floor specimen specifically designed for that purpose. Two particular types of rhythmic activity were investigated: jumping and skipping, and performed by up to 16 individuals, where realistic coordination stimulus was adopted. Using least-squares identification procedures, the single person load parameters were determined and predicted load models are in good agreement with their measured counterparts. Resulting parameters are dependent on the motion style of each investigated activity. Coordination factors are also derived from crowd forces and present a hyperbolic decrease by crowd size for jumping activities against an exponential decrease for skipping activities. Based on a closed-form expression using the established crowd model, a design-oriented method is proposed for a simplified evaluation of floor response due to crowd-rhythmic activities and verified against floor response measurements. Slight differences were found between measured and numerical responses due to the variabilities either encountered during experiments or resulting from the load identification process.

Hyper-reduction for Petrov–Galerkin reduced order models

Projection-based Reduced Order Models are based on the idea of minimizing the discrete residual of a “full order model” (FOM) while at the same time constraining the unknowns to live in a space of reduced dimension. For problems with symmetric positive definite (SPD) Jacobians, this minimization can be achieved optimally by projecting the full order residual onto the approximation basis (Galerkin Projection). This approach is sub-optimal for problems with non-SPD Jacobians since it only guarantees that the projection of the residual onto the chosen basis is minimized and not the residual itself. One possible alternative in such cases is to directly minimize the 2-norm of the residual. This minimization can be achieved either by using QR factorization to solve the resulting least-squares problem or by employing the method of the normal equations (LSPG) to the same end. The first approach involves constructing and factorizing a rectangular tall and skinny matrix of size proportional to the number of unknowns of the FOM. The LSPG method avoids the use of the large matrix by directly constructing the product by its transpose. Unfortunately, constructing such a product element by element is not feasible and requires the use of a complementary mesh, which adds an extra layer of complexity to the hyper-reduction process when performing mesh sampling. The main idea of this work is to propose an alternative technique based on the idea of Petrov–Galerkin minimization. Essentially, we choose a left basis so that a least-squares minimization procedure can be carried out on a reduced problem while guaranteeing that the discrete full order residual is minimized. The resulting procedure is applicable to problems with both SPD and non-SPD Jacobians. Additionally, the resulting minimization problem can be assembled element by element, avoiding the use of the complementary mesh and simplifying implementation in the context of finite elements. The resulting technique is amenable to hyper-reduction by the use of the Empirical Cubature Method and can be readily applied in the context of nonlinear reduction procedures.

Magma mingling and ascent in the minutes to hours before an explosive eruption as recorded by banded pumice

High-threat explosive silicic eruptions commonly contain banded pumice, reflecting magma mingling in the conduit prior to or during eruption. Heterogeneities in tuffs have been attributed to the draw-up of compositionally distinct magmas, in which low-viscosity magmas ascend more quickly than high-viscosity magmas. The Rattlesnake Tuff of the High Lava Plains in Oregon (northwestern United States) represents a zoned magma reservoir where at least five different rhyolite compositions are preserved in banded pumice samples in variable mingled combinations. Geochemical gradients recorded across band boundaries in pumice were modeled using a Monte Carlo least-square minimization procedure to find the complementary error function that best fit observed Si and Ba diffusion profiles by iteratively varying the concentration of each plateau (i.e., the concentration on either side of the band boundary), the center and spacing of the diffusion profile, diffusion length scale, and temperature. Modeling indicates maximum time scales between mingling and conduit ascent from minutes to hours. Viscosity calculations for each rhyolite composition confirm that highly viscous rhyolites have longer ascent times than low-viscosity magmas, strongly supporting a model of sequential tapping of a zoned chamber controlled by viscosity.

The efficient conversion between linear wave function expansions and nonlinear graphically contracted function expansions

Several algorithms are examined for the transformation of a graphically contracted function (GCF) to a configuration state function (CSF) vector, denoted , and for the reverse transformation from CSF vector to GCF, denoted . The initial implementation of these algorithms is applied to a sequence of full-CI wave functions of similar molecules. The most efficient transformation is based on a depth-first search (DFS) and scales as where is an average facet count for the GCF wave function, is the dimension of the vector x, and is the dimension of the GCF basis. Two different transformations are proposed, one based on a pairwise recursive merge algorithm and the other based on a least-squares fitting algorithm. The recursive merge is a reliable algorithm, but our initial implementation does not display the expected scaling behaviour with respect to . The iterative least-squares fitting algorithm is based on an efficient DFS procedure to compute the error ε and its gradient g. However, the resulting iterative least-squares optimisation is slowly convergent, requiring excessive iterations to converge to a target error tolerance. For most of the calculations in this case study, the recursive merge procedure is found to be more efficient than the least-squares optimisation procedure.

Evaluating the energy efficiency-enhancing potential of the digital economy: Evidence from China

Improving energy efficiency can go a long way in helping China address environmental problems it currently faces and help deliver on its pledge of achieving carbon neutrality by 2060. At the same time, innovative production technologies based on digital solutions continue to attract significant attention, owing to their potential to provide environmentally sustainable development opportunities. This study explores whether the digital economy can improve energy efficiency by facilitating input reallocation and promoting better information flows. We rely on a panel of 285 Chinese cities for the period 2010–2019 and a so-called slacks-based efficiency measure incorporating socially undesirable outputs to obtain energy efficiency from the decomposition of a productivity index. Our estimation results demonstrate that the digital economy can promote better energy use efficiency. More specifically, a 1-percentage point increase in the size of the digital economy leads to an average increase of around 14.65 percentage points in energy efficiency. This conclusion still holds under a two-stage least-squares procedure used to mitigate endogeneity. The efficiency-enhancing impact of digitalization is heterogeneous and depends on factors such as resource endowment, city size, and geographical location. Additionally, our results suggest that digital transformation within a particular region has an adverse effect on energy efficiency in that region's neighboring areas due to negative spatial spillover effects. These negative spillovers outweigh the positive direct effect on energy efficiency that can be attributed to a growing digital economy.

Dependence of turbulence estimations on nacelle lidar scanning strategies

Abstract. Through numerical simulations and the analysis of field measurements, we investigate the dependence of the accuracy and uncertainty of turbulence estimations on the main features of the nacelle lidars' scanning strategy, i.e., the number of measurement points, the half-cone opening angle, the focus distance and the type of the lidar system. We assume homogeneous turbulence over the lidar scanning area in front of a Vestas V52 wind turbine. The Reynolds stresses are computed via a least-squares procedure that uses the radial velocity variances of each lidar beam without the need to reconstruct the wind components. The lidar-retrieved Reynolds stresses are compared with those from a sonic anemometer at turbine hub height. Our findings from the analysis of both simulations and measurements demonstrate that to estimate the six Reynolds stresses accurately, a nacelle lidar system with at least six beams is required. Further, one of the beams of this system should have a different opening angle. Adding one central beam improves the estimations of the velocity components' variances. Assuming the relations of the velocity components' variances as suggested in the IEC standard, all considered lidars can estimate the along-wind variance accurately using the least-squares procedure and the Doppler radial velocity spectra. Increasing the opening angle increases the accuracy and reduces the uncertainty on the transverse components, while enlarging the measurement distance has opposite effects. All in all, a six-beam continuous-wave lidar measuring at a close distance with a large opening angle provides the best estimations of all Reynolds stresses. This work gives insights on designing and utilizing nacelle lidars for inflow turbulence characterization.

Elastic constants of titanium carbide films using surface Brillouin scattering

Surface Brillouin scattering (SBS) from surface phonons has been used for determining the dispersion curves of guided acoustic modes propagating along titanium carbide (TiC) films. Dispersion curves have been obtained by varying both the layer thickness and the angle of incidence. Elastic stiffnesses for the TiC on silicon and TiC on silicon carbide systems were determined from a least-squares fitting procedure of the velocity dispersion curves and used to simulate the respective SBS spectra. For each system there is good agreement between measured and calculated SBS spectra.

Calibration of Mean Wind Profiles Using Wind Lidar Measurements

This paper explores the applicability of Lidar wind measurements for the calibration of mean wind profiles depending on the extension in time and space of the available measurements. Starting from logarithmic wind speed profiles corresponding to different site conditions, pseudo-experimental wind speed profiles are generated artificially by adding a zero-mean Gaussian-distributed noise, representative of realistic measurement errors. Then, a least-square fitting procedure is applied to identify the roughness length and the zero-plane displacement. The results obtained show an increase in the scatter of the estimated parameters of the logarithmic law with increasing elevation of the lowest measurement point. Then, a parametric study is developed to analyse the influence of the number of available experimental profiles on the uncertainty associated with the estimated logarithmic law parameters. Based on the results obtained, it can be pointed out that the availability of measurements at low elevations is essential to identify the logarithmic mean wind profile using a reasonable number of observations.

Efficient Matrix Polynomial Expansion Detector for Large-Scale MIMO: An Inverse-Transform-Sampling Approach

Matrix polynomial expansion (MPE) based detector incurs either complicated computation of polynomial coefficients or slow convergence in uplink large-scale multiple-input and multiple-output (LS-MIMO) systems. To solve these issues, an improved MPE (IMPE) detector is proposed, which can speed up the convergence significantly with uncomplicated polynomial coefficients. However, a challenging problem of performing IMPE is needed to compute all the eigenvalues of channel covariance matrix in real time. Unfortunately, directly calculating the eigenvalues of the channel covariance matrix requires complexity, which is as costly as the matrix inverse. To this end, an inverse-transform-sampling based IMPE (ITS-IMPE) detector is proposed to enhance the convergence rate and accuracy in a simple way. First, the closed-form expression of the eigenvalue spectral cumulative distribution function of the channel covariance matrix is deduced analytically, which is a critical factor that influence the eigenvalues estimation. Second, the improved polynomial coefficients of ITS-IMPE are then introduced by a fast online ITS-based eigenvalues estimation algorithm and a least-squares fitting procedure, which achieve a well trade-off between precision and computation. Simulation results exhibit that ITS-IMPE detector is able to achieve a significant enhancement performance with much lower complexity compared with many reported detectors under Rayleigh fading channel and low spatial correlated channel.

The Impact of Fiber Size on the Sound Absorption Behavior of Composites Made from Sugarcane Bagasse Wastes Fibers

ABSTRACT Natural fibers obtained from the agricultural wastes are a promising source within the field of acoustic and have already shown favorable results for mitigating the noise pollution. Supported by the experimental data and via an eco-friendly approach, the current study evaluates the impact of fiber size on the sound absorption values of the samples fabricated from sugarcane bagasse (SCB) waste fibers. The samples were formed based on the fiber size and constant bulk densities and thicknesses. The empirical models such as Delany-Bazley (D-B model) along with Best-fit-Nelder-Mead method were also employed to predict the acoustic absorption coefficients of the samples. Therefore, the least-square fit procedure was taken to evaluate the results which is compatible with both the impedance test tube and prediction models. Hence, according to the analyses, the lowest fiber size measured the highest absorption performance (α≃0.63) and airflow resistivity (σ = 6750), indicating that the performance of the fibers reached peaks at lower frequency and slightly decreased at mid and high frequency ranges while the fiber size 0.29–0.37 mm saw a slight rise again. Also, airflow resistivity and sound absorption performance of the SCB fibers decreased with increased fiber sizes.

Mediating role of profitability relating financial leverage and stock returns

PurposeThis paper aims to highlight firms' profitability as an alternative channel by which changes in leverage could affect stock returns in an imperfect market setting. The author also analytically argues that the benefits of debt, if any, may accrue beyond the usual tax benefit channel.Design/methodology/approachThe author used multivariate regression models based on firms' characteristics and the models' changes along with a two-stage least-square (2SLS) type procedure to estimate the impact of leverage changes on stock returns. The author controls for the varying arbitrage risk that is measured by forecasted idiosyncratic volatility of stock prices and overcome simultaneous or endogenous determination by using inter-temporal non-synchronous variation in leverage and control variables.FindingsThe author finds that increase in leverage increase (decrease) stock returns for firms with the gross operating profitability higher (lower) than the cost of debt. The author also finds that the variation in arbitrage risk does not substitute for the primary effect of leverage changes on stock returns.Research limitations/implicationsThe author's findings provide tacit support to the recent literature attempting to resolve the empirically puzzling pattern of the negative relationship between profitability and leverage. The findings suggest inclusion of profitability as a crucial asset-pricing factor in the contemporary empirical models.Practical implicationsThe non-trivial role of profitability in determining the effect of leverage on firms' stock returns that may be useful to managers, credit analysts and policy makers to assess the impact of net profitability on any change in leverage and its ensuing consequences on firms' value.Originality/valueThe paper develops analytical insights into the marginal role of profitability in influencing the relationship between firms' financing decisions and firms' stock returns beyond the conventional mechanisms of tax benefits, bankruptcy costs and information asymmetry.