Quadratic Index Research Articles

Proportional Retarded Control of Robot Manipulators

In the present contribution, a methodology to solve the tracking control problem of robot manipulators through the use of a Proportional Retarded plus Gravity (PR+G) compensation scheme is presented. The main advantage of the proposal is to avoid the necessity of velocity measurements or their estimation, which is commonly used in most control schemes, such as the proportional derivative-type controllers or the computed torque control. The design of the PR+G controller is addressed via σ-stability analysis and its performance is tested in an experimental platform that consists of 2 degrees of the freedom robot manipulator. The proposed controller is compared with a classic proportional derivative plus gravity compensation scheme. The results are analyzed from a frequency perspective and measured by a quadratic error index.

A Fuzzy Sharpness Metric for Magnetic Resonance Images

A fuzzy-based sharpness metric for the objective measurement of sharpness of Magnetic Resonance (MR) images is proposed in this paper. In the proposed metric, Quadratic Index of fuzziness (QIF) is used to quantitatively express image sharpness. The proposed metric is found to be superior to Maximum Local Variation (MLV) metric, Perceptual Sharpness Index (PSI), Second order Derivative based Measure of Enhancement (SDME), Blanchet’s Sharpness Index (BSI) and Roffet’s Blur Metric (RBM) in terms of correlation with subjective quality ratings and computational time.

Spatiotemporal autofocused chirped Pearcey Pearcey Gaussian wave packets with an adjustable focus in a quadratic-index medium

Here we investigate the propagation properties of spatiotemporal autofocused chirped Pearcey Pearcey Gaussian (PePeG) wavepackets by solving (3 + 1) D Schro¨dinger equation in a quadratic index medium. When the spatial distribution factor p and the temporal distribution factor f are the same, PePeG wavepackets can simultaneously autofocus in spatial and temporal domain and the peak intensity at the focus is more 28 times than that at the initial plane. With the increase of distribution factor p, the scope of the radius of trapped particles decreases.

Active Vibration Control of a Doubly Curved Composite Shell Stiffened by Beams Bonded With Discrete Macro Fiber Composite Sensor/Actuator Pairs

Doubly curved stiffened shells are essential parts of many large-scale engineering structures, such as aerospace, automotive and marine structures. Optimization of active vibration reduction has not been properly investigated for this important group of structures. This study develops a placement methodology for such structures under motion base and external force excitations to optimize the locations of discrete piezoelectric sensor/actuator pairs and feedback gain using genetic algorithms for active vibration control. In this study, fitness and objective functions are proposed based on the maximization of sensor output voltage to optimize the locations of discrete sensors collected with actuators to attenuate several vibrations modes. The optimal control feedback gain is determined then based on the minimization of the linear quadratic index. A doubly curved composite shell stiffened by beams and bonded with discrete piezoelectric sensor/actuator pairs is modeled in this paper by first-order shear deformation theory using finite element method and Hamilton's principle. The proposed methodology is implemented first to investigate a cantilever composite shell to optimize four sensor/actuator pairs to attenuate the first six modes of vibration. The placement methodology is applied next to study a complex stiffened composite shell to optimize four sensor/actuator pairs to test the methodology effectiveness. The results of optimal sensor/actuator distribution are validated by convergence study in genetic algorithm program, ANSYS package and vibration reduction using optimal linear quadratic control scheme.

Evaluation of the estimate bias magnitude of the Rao's quadratic diversity index.

Rao’s quadratic diversity index is one of the most widely applied diversity indices in functional and phylogenetic ecology. The standard way of computing Rao’s quadratic diversity index for an ecological assemblage with a group of species with varying abundances is to sum the functional or phylogenetic distances between a pair of species in the assemblage, weighted by their relative abundances. Here, using both theoretically derived and observed empirical datasets, we show that this standard calculation routine in practical applications will statistically underestimate the true value, and the bias magnitude is derived accordingly. The underestimation will become worse when the studied ecological community contains more species or the pairwise species distance is large. For species abundance data measured using the number of individuals, we suggest calculating the unbiased Rao’s quadratic diversity index.

Multi-parameter optimization of piezoelectric actuators for multi-mode active vibration control of cylindrical shells

A novel technique for the multi-parameter optimization of distributed piezoelectric actuators is presented in this paper. The proposed method is designed to improve the performance of multi-mode vibration control in cylindrical shells. The optimization parameters of actuator patch configuration include position, size, and tilt angle. The modal control force of tilted orthotropic piezoelectric actuators is derived and the multi-parameter cylindrical shell optimization model is established. The linear quadratic energy index is employed as the optimization criterion. A geometric constraint is proposed to prevent overlap between tilted actuators, which is plugged into a genetic algorithm to search the optimal configuration parameters. A simply-supported closed cylindrical shell with two actuators serves as a case study. The vibration control efficiencies of various parameter sets are evaluated via frequency response and transient response simulations. The results show that the linear quadratic energy indexes of position and size optimization decreased by 14.0% compared to position optimization; those of position and tilt angle optimization decreased by 16.8%; and those of position, size, and tilt angle optimization decreased by 25.9%. It indicates that, adding configuration optimization parameters is an efficient approach to improving the vibration control performance of piezoelectric actuators on shells.

Self-repeating properties of four-petal Gaussian vortex beams in quadratic index medium

In this paper, we investigate the propagation properties of four-petal Gaussian vortex (FPGV) beams propagating through the quadratic index medium, obtaining the analytical expression of FPGV beams. The effects of beam order n, topological charge m and beam waist ω0 are investigated. Results show that quadratic index medium support periodic distributions of FPGV beams. A hollow optical wall or an optical central principal maximum surrounded by symmetrical sidelobes will occur at the center of a period. At length, they will evolve into four petals structure, exactly same as the intensity distributions at source plane.

Application of a partitioning procedure based on Rao quadratic entropy index to characterize the temporal evolution of in situ varietal and genetic diversity of bread wheat in France over the period 1981-2006.

We present and highlight a partitioning procedure based on the Rao quadratic entropy index to assess temporal in situ inter-annual varietal and genetic changes of crop diversity. For decades, Western-European agroecosystems have undergone profound changes, among which a reduction of crop genetic diversity. These changes have been highlighted in numerous studies, but no unified partitioning procedure has been proposed to compute the inter-annual variability in both varietal and genetic diversity. To fill this gap, we tested, adjusted and applied a partitioning procedure based on the Rao quadratic entropy index that made possible to describe the different components of crop diversity as well as to account for the relative acreages of varieties. To emphasize the relevance of this procedure, we relied on a case study focusing on the temporal evolution of bread wheat diversity in France over the period 1981-2006 at both national and district scales. At the national scale, we highlighted a decrease of the weighted genetic replacement indicating that varieties sown in the most recent years were more genetically similar than older ones. At the district scale, we highlighted sudden changes in weighted genetic replacement in some agricultural regions that could be due to fast shifts of successive leading varieties over time. Other regions presented a relatively continuous increase of genetic similarity over time, potentially due to the coexistence of a larger number of co-leading varieties that got closer genetically. Based on the partitioning procedure, we argue that a tendency of in situ genetic homogenization could be compared to some of its potential causes, such as a decrease in the speed of replacement or an increase in between-variety genetic similarity over time.

QSPR/QSAR Studies of 2-Furylethylenes Using Bond-Level Quadratic Indices and Comparison with Other Computational Approaches

The recently introduced, non-stochastic and stochastic quadratic indices (Marrero-Ponce et al. J. Comp. Aided Mol. Des. 2006, 20, 685-701) were applied to QSAR/QSPR studies of heteroatomic molecules. These novel bond-based molecular descriptors (MDs) were used for the prediction of the partition coefficient (log P), and the antibacterial activity of 34 derivatives of 2-furylethylenes. Two statistically significant QSPR models using non-stochastic and stochastic bond-based quadratic indices were obtained (R2 = 0.971, s = 0.137 and R2 = 0.986, s = 0.096). These models showed good stability to data variation in leave-one-out (LOO) cross-validation experiment (q2 = 0.9975, sCV = 0.164 and q2 = 0.947, sCV = 0.114). The best two discriminant models computed using the non-stochastic and stochastic molecular descriptors had globally good classification of 94.12% in the training set. The external prediction sets had accuracies of 100% in both cases. The comparison with other approaches (edge- and vertexbased connectivity indices, total and local spectral moments, quantum chemical descriptors as well as with other TOMOCOMD-CARDD MDs) revealed the good performance of our method in this QSPR study. The obtained results suggest that it is possible to obtain a good estimation of physical, chemical and physicochemical properties for organic compounds with the present approach.

Optimal control of uncertain nonlinear quadratic systems

This paper addresses the problem of robust and optimal control for the class of nonlinear quadratic systems subject to norm-bounded parametric uncertainties and disturbances. By using an approach based on the guaranteed cost control theory, a technique is proposed to design a state feedback controller ensuring for the closed-loop system: (i) the local exponential stability of the zero equilibrium point; (ii) the inclusion of a given region into the domain of exponential stability of the equilibrium point; (iii) the satisfaction of a guaranteed level of performance, in terms of boundedness of some optimality indexes. In particular, a sufficient condition for the existence of a state feedback controller satisfying a prescribed integral–quadratic index is provided, followed by a sufficient condition for the existence of a state feedback controller satisfying a given L2-gain disturbance rejection constraint. By the proposed design procedures, the optimal control problems dealt with here can be efficiently solved as Linear Matrix Inequality (LMI) optimization problems.

Land use effects on the functional structure of aquatic insect communities in Neotropical streams

Land use and occupation by human populations can cause many environmental changes in streams, which affect not only the number and abundance of species but also the biological characteristics or functional traits of the individuals. Here we investigated the influence of different land uses (agriculture and urbanization) on taxonomic and functional diversity of aquatic insects in drift samples from Neotropical streams. To this end, we used 2 diversity metrics: the Shannon-Wiener diversity index (H′) to quantify taxonomic diversity and Rao’s quadratic entropy index (Q) to measure functional diversity. In addition, we analyzed the importance of environmental variables on functional traits composition. The high heterogeneity of habitats in rural streams contributed to the occurrence of sensitive taxa (i.e., specialist taxa), which mostly do not share the same categories of functional traits, providing higher functional diversity in these streams. Conversely, the impacts resulting from urbanization processes changed the abiotic variables and led to habitat simplification, favoring the dominance of tolerant (generalist) taxa, which share more traits, thus reducing the taxonomic and functional diversity in these sites. Assessing the functional diversity of aquatic insects under the influence of different land uses is of utmost importance to better understand the functioning of aquatic communities impacted by land use change.

Soil attributes structure plant assemblages across an Atlantic forest mosaic

Community assembly persists as a key topic in ecology due to the complex variation in the relative importance of assembly forces and mechanisms across spatio-temporal scales and ecosystems. Here we address a forest–savanna vegetation mosaic in the Brazilian Atlantic forest to examine the role played by soil attributes as determinants of community assembly and organization at a landscape spatial scale. We examined soil and plant assemblage attributes across 23 plots of forest and savanna in a 1600 km² landscape exposed to the same climatic conditions in the Atlantic forest region of northeast Brazil. Assemblage attributes included species richness, taxonomic and functional composition (community weighted mean, CWM) and functional diversity (quadratic diversity; Rao’s quadratic entropy index) relative to plant leaf area, specific leaf area, leaf dry matter content, thickness and succulence. Our results suggest that forest and savanna patches exposed to the same climatic conditions clearly differ in terms of soil attributes, plant assemblage structure, taxonomic and functional composition. By selecting particular plant strategies relative to resource economy, soil potentially affects community structure, with forest assemblages bearing more acquisitive resource-use strategies, while conservative plant strategies are more frequent in savannas. Accordingly, savanna–forest mosaics in the Atlantic forest region represent spatially organized plant assemblages in terms of taxonomic and functional features, with a signal of trait convergence in both vegetation types. Soil-mediated filtering thus emerges as a potential deterministic assembly force affecting the spatial organization of savanna–forest boundaries and mosaics.

Propagation properties of spatiotemporal chirped Airy Gaussian vortex wave packets in a quadratic index medium.

A type of chirped Airy Gaussian vortex (CAiGV) localized wave packets in a quadratic index medium are studied by solving the paraxial differential equation. For the first time, the propagation properties of spatiotemporal CAiGV light bullets in the quadratic index medium are demonstrated. Some typical examples of the obtained solutions are based on the temporal and spatial chirp parameters, the initial velocity, the distribution factor, and the topological charge. The radiation force of the spatial CAiGV wave packet on a Rayleigh dielectric particle has the periodically reversion and recovery abilities due to the quadratic potential. What we report here can obtain different radiation force trajectory and may have potential application in optical tweezing and bio-medical field.

Influence of a variable Rayleigh scattering-loss coefficient on the light backscattering in multimode optical fibers.

The recently developed diffraction technique of analytical investigation of the Rayleigh backscattering produced by an incident fundamental mode in a multimode optical fiber with an arbitrary refractive index profile is supplemented by taking into account the Rayleigh scattering-loss coefficient, which could be variable within the fiber cross section. The relative changes in various radial and azimuthal modes' excitation levels, due to some typical radial dependences of this coefficient, are computed for the quadratic- and step-index fibers. It is stated that the excitation efficiency could either rise or decay for different modes. The effect of the variable Rayleigh scattering-loss coefficient is shown to be more noticeable in the fibers with a quadratic refractive index profile, whereas it is negligible in actual multimode step-index fibers.

Enhancement of the efficiency of the automatic control system to control the thermal load of steam boilers fired with fuels of several types

An automatic control system to control the thermal load (ACS) in a drum-type boiler under random fluctuations in the blast-furnace and coke-oven gas consumption rates and to control action on the natural gas consumption is considered. The system provides for use of a compensator by the basic disturbance, the blast-furnace gas consumption rate. To enhance the performance of the system, it is proposed to use more accurate mathematical second-order delay models of the channels of the object under control in combination with calculation by frequency methods of the controller parameters as well as determination of the structure and parameters of the compensator considering the statistical characteristics of the disturbances and using simulation. The statistical characteristics of the random blast-furnace gas consumption signal based on experimental data are provided. The random signal is presented in the form of the low-frequency (LF) and high-frequency (HF) components. The models of the correlation functions and spectral densities are developed. The article presents the results of calculating the optimal settings of the control loop with the controlled variable in the form of the “heat” signal with the restricted frequency variation index using three variants of the control performance criteria, viz., the linear and quadratic integral indices under step disturbance and the control error variance under random disturbance by the blastfurnace gas consumption rate. It is recommended to select a compensator designed in the form of series connection of two parts, one of which corresponds to the operator inverse to the transfer function of the PI controller, i.e., in the form of a really differentiating element. This facilitates the realization of the second part of the compensator by the invariance condition similar to transmitting the compensating signal to the object input. The results of simulation under random disturbance by the blast-furnace gas consumption are reported. Recommendations are made on the structure and parameters of the shaping filters for modeling the LF and HF components of the random signal. The results of the research may find applications in the systems to control the thermal processes with compensation of basic disturbances, in particular, in boilers for combustion of accompanying gases.

Positive effects of tree species richness on fine-root production in a subtropical forest in SE-China

Aims: Fine roots play an important role in the biogeochemical cycles of terrestrial ecosystems and are vital for understanding forest ecosystem functioning and services. Higher plant species diversity has been largely reported to increase aboveground community biomass, but how biodiversity affects fine-root production and the related mechanisms in forests remain unclear. In this study, we aim to answer two questions: (i) does fine-root production increase with tree species richness? (ii) Can this effect be explained by niche complementarity among species? Methods: We analyzed data from a large forest biodiversity experiment (BEF-China) with 5-year-old trees. Fine-root growth was measured as standing biomass and annual fine-root regrowth was estimated using ingrowth cores. Moreover, relative yield was calculated to test whether over- or under-yielding occurred when mixtures were compared with the average monoculture of the species included in the mixtures. We calculated functional diversity for fine-root (≤2mm in diameter) traits by Rao’s quadratic entropy index for each species mixture. The effects of manipulated tree species richness and identity on fine-root traits were analyzed with linear mixed-effects models. Mixed models were also used to test the relationships between tree species richness and fine-root standing biomass, annual regrowth and vertical heterogeneity. Important Findings: Fine roots of more than one species were found in half of the soil cores in mixtures indicating that belowground interactions in these young forest stands occurred much earlier than canopy closure. We found significant differences among species in fine-root traits such as diameter and specific root length (SRL), which suggested different resource-use strategies and niche partitioning among species. Mean fine-root diameter of species ranged from 0.31 to 0.74mm, mean SRL ranged from 12.43 m·g−1 to 70.22 m·g−1 and mean vertical distribution index β ranged from 0.68 to 0.93. There was a significant positive relationship between species richness and the evenness of the vertical distribution of fine-root standing biomass. Moreover, marginally significant positive relationships existed between species richness and standing biomass as well as annual regrowth of fine roots. Relative yields and Rao’s quadratic entropy index were both not significantly affected by species richness. However, the relative yield of fine-root standing biomass was marginally correlated with Rao’s quadratic entropy index, implying that belowground niche complementarity between species does contribute to diversity effects. In conclusion, our study showed positive effects of species richness on the filling of soil volume by fine roots in the studied experimental forest communities. This has positive effects on fine-root standing biomass and may also lead to increased aboveground biomass.

Rayleigh backscattering from the fundamental mode in step-index multimode optical fibers.

The Rayleigh backscattering produced by an incident fundamental mode in a multimode step-index optical fiber was analyzed using a recently developed diffraction technique. The complete set of backward propagating modes, both radial and azimuthal, was determined and regarded. For this type of fiber, normalized mode functions were constructed in an explicit form, thus providing a unified power scale to characterize the relationships between various excited modes. The dependencies of the mode excitation efficiencies on the technical parameters of the fiber and the frequency of the launched radiation were studied. A comparison of the mode excitation efficiencies was performed with those in the fiber with quadratic refractive index profiles.

Prediction of Aquatic Toxicity of Benzene Derivatives to Tetrahymena pyriformis According to OECD Principles.

Many QSAR studies have been developed to predict acute toxicity over several biomarkers like Pimephales promelas, Daphnia magna and Tetrahymena pyriformis. Regardless of the progress made in this field there are still some gaps to be resolved such as the prediction of aquatic toxicity over the protozoan T. pyriformis still lack a QSAR study focused in accomplish the OECD principles. Atom-based quadratic indices are used to obtain quantitative structure-activity relationship (QSAR) models for the prediction of aquatic toxicity. Our models agree with the principles required by the OECD for QSAR models to regulatory purposes. The database employed consists of 392 substituted benzenes with toxicity values measured in T. pyriformis (defined endpoint), was divided using cluster analysis in two series (training and test sets). We obtain (with an unambiguous algorithm) two good multiple linear regression models for non-stochastic (R2=0.807 and s=0.334) and stochastic (R2=0.817 and s=0.321), quadratic indices. The models were internally validated using leave-one-out, bootstrapping as well as Y-scrambling experiments. We also perform an external validation using the test set, achieving values of R2 pred values of 0.754 and 0.760, showing that our models have appropriate measures of goodness- of-fit, robustness and predictivity. Moreover, we define a domain of applicability for our best models. The achieved results demonstrated that, the atom-based quadratic indices could provide an attractive alternative to the experiments currently used for determining toxicity, which are costly and time-consuming.

Slices method to describe ray propagation in inhomogeneous media

We describe an alternative method that numerically calculates the trajectory followed by a light ray in rotationally symmetric inhomogeneous media in the paraxial approximation. The medium is divided into thin parallel slices and a radial quadratic refractive index is considered for each slice. The ABCD matrix is calculated in each slice and the trajectory of the ray was obtained. The method is demonstrated considering media with a refractive index distribution used to describe the human eye lens. The results are compared with the exact numerical solution for each particular distribution. In all cases, a good agreement is obtained for the proposed method and the exact numerical solution.

Calculation of eigenfunctions of bounded waveguide with quadratic refractive index

In this work, the one-dimensional finite fractional Fourier transform has been considered in application to gradient optical waveguides. The eigenfunctions of it has been discussed. The relation between obtained functions, Hermite-Gaussian modes and spheroidal functions has been shown. The dependence of input domain width and number of nonzero eigenfunctions of transformation has been demonstrated. The functions which recover its form at given distance from the front plane have been calculated.