Quadratic Index Research Articles

Taxonomic and functional diversity of macroinvertebrates in sediment and macrophyte habitats: A case study, the Ibrahimia Canal, Nile River, Egypt

The taxonomic and functional diversities of macroinvertebrates are a critical indicator of ecosystem health. This study focuses on the taxonomic and functional diversities of the assemblage structure of macroinvertebrates in the Ibrahimia Canal, Egypt. They were compared across two different substrate habitats: sediment-associated and macrophytes-associated habitats. Significant variations in the taxonomic and biological trait community composition in the two substrate habitats were recorded, with high taxa abundance in sediment substrate and increased diversity in macrophyte substrate. In sediment substrates, burrow dweller and collector-filterer taxa were the main characteristics, while tube dweller and collector-gatherer were the main traits of macrophytes substrate. The taxonomic and functional indices tended to increase from sediment to macrophytes substrate; however, there was an increase in Rao’s quadratic entropy index (RaoQ) for sediment substrate habitat. Redundancy analyses explained the association between environmental factors and macroinvertebrate taxa and traits. Total suspended solids, dissolved oxygen, chemical demand oxygen, and phosphate were the key environmental drivers of the taxonomic and functional diversities of macroinvertebrates. Integration between the approaches to taxonomic and functional diversity is recommended to give insight into explaining and managing the freshwater ecosystem.

Selection of a discrete quadratic quality index when calculating a digital tracking system with a finite decay time of a free process at a given astatism order

Selection of a discrete quadratic quality index when calculating a digital tracking system with a finite decay time of a free process at a given astatism order

An unbiased function‐based Poisson adaptive EWMA control chart for monitoring range of shifts

AbstractFor monitoring the number of nonconformities per unit in industrial processes during the inspection, Poisson control charts are most widely deployed. These charting structures are referred to as attribute control charts as the quality characteristic under study is based on a nominal scale other than a quantitative or measured scale. In this study, Poisson adaptive exponentially weighted moving average (PAEWMA) has been designed and the performance of the said chart under a steady‐state situation along with the zero‐state condition has been studied for detecting changes over an unknown range of shifts. The enactment of the proposed PAEWMA design with existing schemes has been evaluated and compared using run‐length (RL) profiles such as; average RL (ARL), the standard deviation of RL (SDRL), and some percentile points of the RL distribution. The extra quadratic loss and relative mean index measures have been used for comparing the range of shifts. The comparison reveals that the proposed PAEWMA chart under the steady‐state situations performs far better than the competitors. The effect of estimation of the process parameter is also a part of the study. The three applications of the proposal have been included; which are taken from the artificial dataset, from past study monitoring dataset, and the other from the aircraft accident monitoring data for the implementation of the proposal.

Assessing Moisture Content and Its Mitigating Effect in an Urban Area Using the Land Surface Temperature–Vegetation Index Triangle Method

Nowadays, climate change and heat extremes are becoming highly challenging problems in many cities across the globe. One of the solutions to overcome this problem is the use of vegetation, and, in particular, extending the range of overgrown areas, which are sometimes referred to as “urban green areas.” In this paper, the moisture condition and its mitigating effect on Land Surface Temperature in urban areas were examined in Warsaw, Poland, using satellite data. To do so, the so-called “Triangle Method” was employed. The triangle method is based on a Land Surface Temperature–Normalized Difference Vegetation Index (LST-NDVI) scatterplot to calculate the Temperature Vegetation Dryness Index (TVDI) and its modification–quadratic Temperature Vegetation Dryness Index (qTVDI). This article discusses, in detail, the usefulness of the triangle method for the analyses of built-up areas. The drought satellite indices TVDI and qTVDI compared with those of LST, NDVI, and NDBI (Normalized Difference Building Index). The study shows that the triangle method based on LST-NDVI scatterplot analysis is a promising tool for establishing moisture conditions over urban areas and for studying the effect of vegetation impact on urban heat islands. Detailed analysis shows that over an urban area, qTVDI shows better agreement with LST than classic TVDI.

Analysis and design of control systems via parameter‐based approach

Analysis and design of control systems via parameter‐based approach

Inventory Management in Supply Chains Based on a Linear Discrete System with a Quadratic Quality Criterion

Purpose of research. To analyze theoretical studies of models and methods used in the theory of inventory management and directions of their practical implementation. To present the problem of optimal inventory management as a discrete control problem. Tasks of this type are formulated in cases where there is a need to form strategies of management of material and production inventories in supply chains, taking into account their organization at a certain time interval. To propose a method for solving the corresponding management problem.Methods. As a basic model, we consider the process of inventory management in the warehouse, in which a certain balance between the products released from the warehouse into production, released for sale, as well as its residues, which form the inventory of the next period must be fulfilled. The process of inventory management in supply chains during the planning period is based on the procedure of finding the appropriate control action for a linear discrete controlled system with a quadratic quality index. Implementation of control uses the principle of feedback. The computer algebra system Wolfram Mathematica is chosen as a tool for implementing the control.Results. Within the framework of studying the methods of finding the optimal control, two solution methods were singled out - the method of finding the optimal program control and the method of determining the optimal control according to the feedback principle. In the process of verification of the obtained solution, several model examples with different initial conditions were considered.Conclusion. The results of testing the proposed discrete model showed that the feedback method makes it possible to quite efficiently solve the inventory management problem with different initial conditions, which is described by a system of difference equations.

A Class of Algorithms for Recovery of Continuous Relaxation Spectrum from Stress Relaxation Test Data Using Orthonormal Functions.

The viscoelastic relaxation spectrum provides deep insights into the complex behavior of polymers. The spectrum is not directly measurable and must be recovered from oscillatory shear or relaxation stress data. The paper deals with the problem of recovery of the relaxation spectrum of linear viscoelastic materials from discrete-time noise-corrupted measurements of relaxation modulus obtained in the stress relaxation test. A class of robust algorithms of approximation of the continuous spectrum of relaxation frequencies by finite series of orthonormal functions is proposed. A quadratic identification index, which refers to the measured relaxation modulus, is adopted. Since the problem of relaxation spectrum identification is an ill-posed inverse problem, Tikhonov regularization combined with generalized cross-validation is used to guarantee the stability of the scheme. It is proved that the accuracy of the spectrum approximation depends both on measurement noises and the regularization parameter and on the proper selection of the basis functions. The series expansions using the Laguerre, Legendre, Hermite and Chebyshev functions were studied in this paper as examples. The numerical realization of the scheme by the singular value decomposition technique is discussed and the resulting computer algorithm is outlined. Numerical calculations on model data and relaxation spectrum of polydisperse polymer are presented. Analytical analysis and numerical studies proved that by choosing an appropriate model through selection of orthonormal basis functions from the proposed class of models and using a developed algorithm of least-square regularized identification, it is possible to determine the relaxation spectrum model for a wide class of viscoelastic materials. The model is smoothed and robust on measurement noises; small model approximation errors are obtained. The identification scheme can be easily implemented in available computing environments.

Finite‐frequency output feedback MPC for Markov jump systems

AbstractThis paper investigates a general design framework of dynamic output feedback model predictive control (DOFMPC) for Markov jump systems within both time and frequency domain. Such a design with guaranteed H∞ and quadratic performance is formulated by a standard semi‐definite programming (SDP), and it is achieved by employing a special congruence transformation. The SDP condition greatly reduces the computational effort by eliminating bilinear matrix inequalities or equation constraints reported in existing references. Specifically, the H∞ norm of the transfer function is optimized within three types of frequency ranges on account of generalized Kalman–Yakubovic–Popov (GKYP) lemma. The quadratic index is optimized online via SDP. Finally, we verify the feasibility and effectiveness of the proposed method from both theoretical and practical point of view.

Event-Triggered Cost-Guaranteed Control for Linear Repetitive Processes Under Probabilistic Constraints

In this article, the event-triggered cost-guaranteed control problem is investigated for a class of shift-varying linear repetitive processes (LRPs) with multiplicative noises under probabilistic constraints. First, in order to relieve the communication burden and improve the communication efficiency, the event-triggered mechanism is exploited for the shift-varying LRPs over the communication network of limited bandwidth. By constructing a novel event generator function, the order of the event triggering sequence is identified on two independent directions. Then, the probabilistic constraint is enforced onto the shift-varying LRPs under the influence of the event-triggered mechanism. With the aid of the Chi-square distribution and the completing-the-square technique, a controller design algorithm is proposed to ensure that both the probabilistic constraints and the quadratic cost index are satisfied by using the actual information at the triggering instants. Sufficient conditions are derived to guarantee the existence of event-based controllers, and the controller gains are obtained at each step by solving a series of matrix inequalities. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed controller design method.

Direct Adaptive Control for Stochastic Systems with Risk-Sensitive Indices

We propose a direct adaptive control law based on the adaptive dynamic programming (ADP) algorithm for continuous-time stochastic linear systems with partially unknown system dynamics and infinite horizon quadratic risk-sensitive indices. A control design methodology is employed to iteratively solve the generalized algebraic Riccati equation by using the online information of the state and input, and to directly learn the optimal control law. We prove the convergence of the online ADP algorithm and show that the direct adaptive control law approximates the optimal control law as time goes on. Finally, a numerical simulation example is presented to demonstrate the effectiveness of our algorithm.

Plate-Like Flexible Spacecraft Modeling and Distribution of Control Moment Gyroscopes

This study investigates the optimization configuration problem of control moment gyroscopes for flexible vibration suppression of large space structures. First, the structural dynamic model of an unconstrained plate-like flexible spacecraft with control moment gyroscopes is established using the Lagrangian method and the finite element method. Second, an optimization problem is established with the positions of control moment gyroscope array as variables and the linear quadratic index of mechanical energy during vibration process as the objective function. Additionally, an improved gray wolf optimizer is used to solve the optimization problem. The optimization results show that the control moment gyroscopes should be primarily placed on the corners of the spacecraft in a symmetrical manner. Finally, the priority of control moment gyroscope installation positions was studied using topological iteration. The results indicate that the control moment gyroscopes should be primarily installed on the corners, followed by the central positions, and then gradually expanded outward.

Computational discovery of novel anthelmintic natural compounds from Agave Brittoniana trel. Spp. Brachypus

Helminth infections are a medical problem in the world nowadays. This report used bond-based 2D quadratic indices, a bond-level QuBiLs-MAS molecular descriptor family, and Linear Discriminant Analysis (LDA) to obtain a quantitative linear model that discriminates between anthelmintic and non-anthelmintic drug-like organic-compounds. The model obtained correctly classified 87.46% and 81.82% of the training and external data sets, respectively. The developed model was used in a virtual screening to predict the biological activity of all chemicals (19) previously obtained and chemically characterized by some authors of this report from Agave brittoniana Trel. spp. Brachypus. The model identified several metabolites (12) as possible anthelmintics, and a group of 5 novel natural products was tested in an in vitro assay against Fasciola hepatica (100% effectivity at 500 µg/mL). Finally, the two best hits were evaluated in vivo in bald/c mice and the same helminth parasite using a 25 mg/kg dose. Compound 8 (Karatavinoside A) showed an efficacy of 92.2% in vivo. It is important to remark that this natural compound exhibits similar-to-superior activity as triclabendazole, the best human fasciolicide available in the market against Fasciola hepatica, resulting in a novel lead scaffold with anti-helminthic activity. Keywords: TOMOCOMD-CARDD Software; QuBiLs-MAS, nonstochastic and stochastic bond-based quadratic indices; LDA-based QSAR model; Computational Screening, Anthelmintic Agent; Agave brittoniana Trel. spp. Brachypus, Fasciola hepatica.

Effect of measurement uncertainty on combined quality control charts

The accuracy of the measurement system is vital for reliable process monitoring using statistical process control charts. The applied chart’s effectiveness depends on the measurement system's performance. Measurement uncertainty can lead to incorrect decisions like unnecessary stops or failure to intervene. In this paper, we investigated the effect of measurement errors on the performance of four well-established combined charts for monitoring the mean of normally distributed processes: Shewhart-CUSUM, Shewhart-Crosier’s CUSUM, Shewhart-EWMA and Shewhart-GWMA charts. To deal with measurement errors we considered the additive measurement error model. Detailed run length profiles of these charts are studied in terms of average run length (ARL), extra quadratic loss, relative ARL, and performance comparison index through Monte Carlo simulations under different sizes of measurement errors. It was found that measurement errors significantly reduce the power of the combined charts. Thus, multiple measurements scheme is incorporated as a remedy to this effect. The Shewhart-Crosier’s CUSUM performed best of four charts, while the Shewhart-EWMA chart did worst. To demonstrate the effect of measurement uncertainty and highlight implications further, a simulated dataset with a shift in the process mean is considered.

Using the Rao's Q diversity index as an indicator of protected area effectiveness in conserving biodiversity

Developing innovative monitoring systems for biodiversity outcomes in protected areas (PAs) are important to enable effective adaptive management. Here we show how to quantitatively detect and monitor temporal and spatial patterns in environmental heterogeneity, an important indicator of ecological integrity and biodiversity patterns. We used a 28-year time series (1991–2018) generated from freely available Landsat satellite imagery and Rao's quadratic index to calculate relative heterogeneity and trends in heterogeneity for 41 PAs across South Africa. We selected PAs where mega-herbivore assemblages were similar and where management objectives were broadly aligned with South African legislation to protect biodiversity. There was a three-fold difference in heterogeneity among PAs, mainly linked to variation in topography and rainfall. Heterogeneity decreased in 12 (29%), increased in three (7%) and remained stable in 26 (64%) PA's. These trends were not explained by overall heterogeneity, PA size, or rainfall – i.e., PAs that were smaller, drier, and more homogenous were not more likely to show decreasing trends than PAs that were larger, wetter, and generally more heterogenous. Rather trends in heterogeneity are likely the result of interactions between regional process (e.g., rainfall) and local factors such fire regimes, megaherbivore densities, and park management. The framework presented here can be extended to include every PA nationally, or even globally, and the data product fully automated. This presents an opportunity for conservation management to incorporate this important biodiversity indicator in PA monitoring programs as well as other large-scale ecological monitoring initiatives.

Two dimensional gradient-index beam shapers fabricated using ultrafast laser inscription.

In this paper gradient-index beam shapers are fabricated using the ultrafast laser inscription method. This method enables the fabrication of two-dimensional refractive index profiles inside silica glass, resulting in highly robust and compact beam shapers. The magnitude of this refractive index change can be tailored by adjusting the laser pulse energy, enabling arbitrary two-dimensional refractive index profiles to be manufactured. The process is then demonstrated by fabricating planar waveguides with quadratic index profiles that predictably resize Gaussian beams. Then a more complex two-dimensional refractive index profile is fabricated to transform an input Gaussian beam into a super-Gaussian (flat-top) beam.

Task-Oriented Real-Time Optimization Method of Dynamic Force Distribution for Multi-Fingered Grasping

The dynamic force distribution is significant in multi-fingered hand operation. It is essential to choose the appropriate contact force between fingers and object to ensure both stability and power consumption requirements corresponding to the specific task. We describe nonlinear contact force distribution problems as smooth manifold optimization problems corresponding to a linearly constrained positive definite matrix. A quadratic index gradient flow approach is presented to optimize the contact force based on a low-dimensional description matrix. And, a task-oriented contact stability criterion is proposed to evaluate contact stability. A simple selection method of the weight parameters of the objective function is provided for the specified contact stability criterion. The proposed algorithm has better force optimization results and fewer iterations than the traditional gradient flow optimization algorithm under the same stability condition. Numerical examples demonstrate the correctness and effectiveness of the algorithm. The proposed method of dynamic force distribution can be used for the real-time application of multi-fingered grasping and manipulation.

Dynamic Evaluation of Intensive Land Use Based on Objective Empowerment by Entropy Method and Neural Network Algorithm.

In the past, the extreme value standardization of indicators, the traditional weighting method, and the multifactor comprehensive model of land intensive use inevitably linearly correlate the evaluation indicators with the evaluation objects, ignoring the direction differences of different indicators in different intervals. At the same time, these methods are also difficult to meet the change of evaluation index weight value with land use type, and cannot adapt to the actual situation of land use environment level and dynamic change. Considering the objectivity of nonlinear correlation moderate index and weight assignment, based on the standardization of quadratic function index and entropy assignment, this paper studies the intensive and dynamic use of land in development zones by different regions to improve the realistic fit of the evaluation model. The results show that the overall level of land intensive use in Chongqing center district and western Chongqing is better than that in northeast Chongqing and southeast Chongqing, roughly showing the state of “high in west and low in east.”

Ciliate Communities Respond via Their Traits to a Wastewater Treatment Plant With a Combined UASB–Activated Sludge System

Assessing functional diversity of communities is an efficient method to link community composition to ecosystem quality. Still, studies using functional traits of microeukaryote ciliate communities in biological wastewater treatment plants are lacking. The present work explores the functional diversity of the ciliate protist community in a wastewater treatment plant (WWTP) operating with a combined UASB-activated sludge system, and specifically to: 1) investigate the taxonomic and functional composition of the ciliate communities over time; 2) compare taxonomic and functional diversity indices with regard to its applicability in WWPS; 3) assess the relationship between the ciliate community’s functional composition and the WWTPs temporal conditions; and 4) investigate the potential use of functional diversity as an indicator of WWTP efficiency. Totally, we recorded 21 ciliate species throughout 37 samplings. The number of species was low compared to other plants. Bacterivorous and flake-forming species were the main functional strategies found in the samples. The correlation between taxonomic and functional richness was significant, indicating a functionally redundant community. There was a correlation between the Simpson and Rao’s quadratic entropy indexes suggesting that loss of taxonomic diversity leads to a loss of functional diversity. The homogeneity of the measured physical and chemical data led to functional homogenization and redundancy (homogenous CWM) of the ciliate community. The functional diversity is positively correlated with parameters of removal efficiency, indicating a promising application in WWTPs. Future studies will broaden knowledge on functional diversity in biological wastewater treatment systems, this being a first step with the unprecedented application of this methodology in artificial ecosystems.

A Quantitative Survey of Effect of Semi-Natural Habitat Composition and Configuration on Landscape Heterogeneity in Arable Land System

Arable land systems are complex ecosystems composed of cultivated land and semi-natural habitats. Retaining an appropriate proportion of semi-natural habitats in arable land systems is beneficial for enhancing landscape heterogeneity and biodiversity. However, it is unclear how many semi-natural habitats need to be retained in arable land systems to improve landscape heterogeneity. In this study, the land use data of four counties were used as the data source in the Lower Liaohe Plain, Liaoning Province, and Rao’s quadratic entropy index (Q) was used to quantitatively characterize the landscape heterogeneity. We aimed to explore the minimum proportion of semi-natural habitat required to maintain high landscape heterogeneity and determine the independent and interactive effects of semi-natural habitat composition and configuration on landscape heterogeneity. We found that (1) maintaining a 5% proportion of semi-natural habitats is the minimum threshold for achieving high landscape heterogeneity in arable land systems. Retaining a 10% share of semi-natural habitats is beneficial for both agricultural production and land ecology. (2) The combination of woodland, water and ditches was good for improving landscape heterogeneity. Connectivity in semi-natural habitats is critical to improving landscape heterogeneity. (3) The interaction of semi-natural habitat composition and configuration had a strong effect on landscape heterogeneity (53.1%). Semi-natural habitat configuration was found to be more important than composition for landscape heterogeneity. The role of semi-natural habitat composition and configuration in maintaining landscape heterogeneity and supporting the sustainability of land use therefore needs to be considered in arable land systems.

Functional Diversity and Its Influencing Factors in a Subtropical Forest Community in China

Functional diversity is considered a key link between ecosystem functions and biodiversity, and forms the basis for making community diversity conservation strategies. Here, we chose a subtropical forest community in China as the research object, which is unique in that other regions of the world at the same latitude have almost no vegetation cover. We measured 17 functional traits of 100 plant species and calculated seven different functional diversity indices, based on functional richness, evenness, and divergence. We found that most functional diversity and species diversity indices significantly differed with plant habit. There was a significant positive correlation among functional richness indices. However, functional divergence indices, multidimensional functional divergence (FDiv), and Rao’s quadratic entropy index (RaoQ) were significantly negatively correlated, and RaoQ and functional divergence indices (FDis) were uncorrelated. The correlations between three types (richness, evenness, and divergence) of functional diversity indices and three species diversity indices were different. Lineage regression results generally showed that three functional richness indices (Average distance of functional traits (MFAD), Functional volume (FRic) and Posteriori functional group richness (FGR)) were increased with three species diversity indices (species richness (S), Shannon-Wiener index (H) and Pielou index (E)). The functional evenness index (FEve) decreased with species richness (S), Shannon-Wiener index (H) and increased with species evenness (Pielou index (E)), but the change trends were small. All three types of functional diversity indices declined with altitude, although altitude had a weak influence on them. Other environmental factors affected the functional diversity of the community. Here, soil total phosphorus (TP) was the most critical environmental factor and the convex had the least effect on functional diversity in our subtropical forest community. These results will contribute to our understanding of functional diversity in subtropical forests, and provide a basis for biodiversity conservation in this region.