Experimental Design Criteria Research Articles

Advances in mass spectrometry for metabolomics: Strategies, challenges, and innovations in disease biomarker discovery.

Mass spectrometry (MS) plays a crucial role in metabolomics, especially in the discovery of disease biomarkers. This review outlines strategies for identifying metabolites, emphasizing precise and detailed use of MS techniques. It explores various methods for quantification, discusses challenges encountered, and examines recent breakthroughs in biomarker discovery. In the field of diagnostics, MS has revolutionized approaches by enabling a deeper understanding of tissue-specific metabolic changes associated with disease. The reliability of results is ensured through robust experimental design and stringent system suitability criteria. In the past, data quality, standardization, and reproducibility were often overlooked despite their significant impact on MS-based metabolomics. Progress in this field heavily depends on continuous training and education. The review also highlights the emergence of innovative MS technologies and methodologies. MS has the potential to transform our understanding of metabolic landscapes, which is crucial for disease biomarker discovery. This article serves as an invaluable resource for researchers in metabolomics, presenting fresh perspectives and advancements that propels the field forward.

Clinical effect of botulinum toxin type A combined with autologous fat grafting in patients with nasolabial fold depression.

Nasolabial fold (NLF) depression can affect the facial appearance of patients to some extent and increase their psychological burdens. In recent years, autologous fat grafting (AFG) combined with botulinum toxin A (BTX-A) injection (AFG + BTX-A injection) has been gradually applied in the treatment of patients with NLF depression. Although studies have been conducted on the efficacy and safety of AFG + BTX-A injection in treating NLF depression, the experimental design, observational indicators, and sample enrollment criteria vary remarkably, making it difficult to draw convincing and consistent conclusions. Thus, further relevant research is warranted. To assess the esthetic improvement, efficacy, and safety of AFG + BTX-A injections in patients with NLF depression. This study included 60 patients with NLF depression who were treated in our hospital from February 2019 to April 2021. These patients were categorized into control (n = 30) and observation (n = 30) groups. The observation group received AFG + BTX-A injection, whereas the control group underwent AFG only. All patients were evaluated using the wrinkle severity rating scale (WSRS) and global aesthetic improvement scale. The compactness of facial contours, skin evaluation indexes, adverse reactions, and satisfaction of the two groups were evaluated 3 months postoperatively. The WSRS scores of the observation group at 1, 3, and 6 months postoperatively were lower than those of the control group (P < 0.05). Three months postoperatively, facial fine lines and pores showed obvious improvement and the skin index score was higher in the observation group than in the control group (P < 0.05). The compactness of facial contours was better in the observation group than in the control group (P < 0.05). In addition, no remarkable differences were noted in the incidence of postoperative adverse reactions such as facial stiffness, facial asymmetry, facial bruising, and facial concavity inequality (P > 0.05). AFG + BTX-A injection is a highly safe, cost-effective, effective, and long-lasting treatment for NLF depression with high esthetic value, which should be promoted in the future.

Lessons learned from using wild-caught and captive-reared lesser scaup (Aythya affinis) in captive experiments.

Waterfowl are housed in captivity for research studies that are infeasible in the wild. Accommodating the unique requirements of semi-aquatic species in captivity while meeting experimental design criteria for research questions can be challenging and may have unknown effects on animal health. Thus, testing and standardizing best husbandry and care practices for waterfowl is necessary to facilitate proper husbandry and humane care while ensuring reliable and repeatable research results. To inform husbandry practices for captive-reared and wild-caught lesser scaup (Aythya affinis; hereafter, scaup), we assessed body mass and fat composition across two different aspects of husbandry, source population (captive-reared or wild caught), and housing densities (birds/m2). Our results suggest that housing scaup at low densities (≤0.6 m2/bird, P = 0.049) relative to other species can minimize negative health effects. Captive-reared scaup were heavier (P = 0.027) with greater body fat (P < 0.001) and exhibited fewer signs of stress during handling than wild-caught scaup. In our experience, scaup which are captive-reared from eggs collected in the wild were better for long-term captivity studies as they maintained body mass between and recovered lost body mass following trials. Researchers would benefit from carefully evaluating the tradeoffs of using short- and long-term captive methods on their research question before designing projects, husbandry practices, and housing facilities for waterfowl.

Mechanistic modelling of separating dispersions in pipes using model-based design of experiments techniques

This work presents a parametric study on a mechanistic model for separating liquid–liquid dispersions in pipes. The model considers drop-settling, drop-interface coalescence and drop-drop coalescence, predicting the evolution of four characteristic layers during separation. Parameter estimation, parametric sensitivity analysis (PSA), and model-based design of experiments (MBDoE) techniques are employed to acquire precise parameter estimates and propose optimal experimental conditions, thereby enhancing the accuracy of existing models. Experimental data from literature using oil-in-water dispersions are used for parameter estimation. PSA reveals regions of high sensitivity of the model outputs to uncertain parameters, which are corresponding to favourable sampling locations. Manipulating the mixture velocity, the dispersed phase fraction, and the layer heights at the inlet influences these sensitive regions. Clustered measurements around highly sensitive regions in the pipe enhance the information content they provide. MBDoE demonstrates that either of the A-, D-, or E-optimal experimental design criteria improves the expected parameter precision.

Temperature Experiment and Parameter Optimization of Cemented Carbide Tool in Milling 508III Steel

In machining 508III steel, the cemented carbide tool is subjected to a strong periodic thermal load impact, leading to serious tool-chip adhesion and shortening the tool life. Considering the influence of cutting parameters on temperature, temperature experiments and finite element (FE) simulations were carried out based on Box-Behnken experimental design criteria in the response surface method (RSM). Based on the experimental results, A second-order polynomial regression prediction model for temperature was constructed as the optimization objective function based on RSM. A temperature prediction model based on GA-SVM was established to predict temperature change. Taking cutting temperature and efficiency as evaluation indicators, the elitist nondominated sorting genetic algorithm was used to optimize cutting parameters. These findings may be important for the tool life improvement and reasonable parameter selection.

Exact Bayesian inference for the detection of graft-mobile transcripts from sequencing data.

The long-distance transport of messenger RNAs (mRNAs) has been shown to be important for several developmental processes in plants. A popular method for identifying travelling mRNAs is to perform RNA-Seq on grafted plants. This approach depends on the ability to correctly assign sequenced mRNAs to the genetic background from which they originated. The assignment is often based on the identification of single-nucleotide polymorphisms (SNPs) between otherwise identical sequences. A major challenge is therefore to distinguish SNPs from sequencing errors. Here, we show how Bayes factors can be computed analytically using RNA-Seq data over all the SNPs in an mRNA. We used simulations to evaluate the performance of the proposed framework and demonstrate how Bayes factors accurately identify graft-mobile transcripts. The comparison with other detection methods using simulated data shows how not taking the variability in read depth, error rates and multiple SNPs per transcript into account can lead to incorrect classification. Our results suggest experimental design criteria for successful graft-mobile mRNA detection and show the pitfalls of filtering for sequencing errors or focusing on single SNPs within an mRNA.

Separating the Effects of Nonorthogonal Variables on the Hot-Injection Synthesis of Core/Thick-Shell (“Giant”) CdTe/CdS Quantum Dots

“Giant” core/thick-shell quantum dot (QD) nanostructures are of interest due to their unusual optical properties and importance as components of more advanced heterostructures tailored to achieve increasingly complex optical functions. However, reliable one-step seeded growth of these structures poses a significant challenge: one must balance multiple competing reaction processes to find the growth regime that realizes spherical shells of both the target size and high crystalline quality. Adjusting synthesis conditions in thicker-shelled reactions is further complicated by multiple nonorthogonal variables that impact the reaction mechanism. These variables include the reaction volume, reaction concentration, and oleic acid (ligand) concentration. Here, we investigate the seeded growth of core/thick-shell CdTe/CdS QDs by adapting a “flash” shelling method. We systematically vary three key reaction parameters (particle concentration, oleic acid:Cd ratio, and Cd–S:CdTe core ratio) over 30+ different thick-shelling reactions to elucidate the separate and intersecting impacts of these parameters on shell growth. Our analysis of the resulting particle quality reveals that the particle concentration of the reaction plays a critical role in the shell growth mechanism. We find the impact of oleic acid to be dependent on the particle concentration for a given shell thickness. We also find that the optimal conditions shift when targeting increasingly thick shells. The results demonstrate the importance of testing and controlling for synthesis variables across a multidimensional parameter space. We develop and present general experimental design criteria to help guide efficient development of new seeded growth reactions that enable reliable synthesis of thick-shelled nanostructures.

Optimal placement of distribution-level synchrophasor sensors for distribution system

This paper proposes a new method for the placement of the important synchrophasor sensors, the distribution-level phasor measurement units (DPMUs). A new objective function is developed to achieve minimization of distribution system state estimation errors where the limited number of DPMUs, the zero injection buses, the limited DPMU channels and the supervisory control and data acquisition measurements are taken into account. The A-optimal experimental design criterion is used to formulate the proposed objective function and constraints. The state estimates are obtained by using the maximum likelihood estimator where both Gaussian and non-Gaussian measurement noise scenarios are studied. The performance of the proposed method is demonstrated by simulations on IEEE 34-bus and 123-bus distribution systems.

Experimental Investigation on Proppant Transport Behavior in Hydraulic Fractures of Tight Oil and Gas Reservoir

Proppant concentration and fracture surface morphology are two significant fractures that can affect proppant transport and deposition behavior especially in tight and oil and gas reservoirs. This paper proposed a new set of similarity criteria for proppant experimental design by incorporating proppant concentration and fracture roughness. Based on the proposed criterion, proppant transport experiments in hydraulic fractures of tight oil and gas reservoirs were conducted to explore the proppant placement behavior and identify the key parameters that affected the fracture propping efficiency. Results showed that the proposed similarity criterion can be used to evaluate the onsite proppant transport behavior and optimize hydraulic fracturing parameters. Results showed that the fracture placement efficiency of LD C7 tight oil reservoir is mainly affected by sand ratio and fracturing fluid viscosity. The sand ratio in the LD C7 tight oil reservoir should not be less than 8%, and the optimal carrying fluid viscosity is 5 mPa s. The proppant placement efficiency of the SLG H8 tight gas reservoir is mainly affected by the displacement rate and frac fluid viscosity. The displacement rate of SLG H8 tight gas reservoir should not be less than 3.5 m3/min, and the optimal carrying fluid viscosity is 15 mPa s.

Systematic review and meta-analysis: analysis of variables influencing the interpretation of clinical trial results in NAFLD

BackgroundNAFLD clinical trials have shown suboptimal results, particularly for liver fibrosis, despite the robust preclinical drug development. We aimed to assess the histological response after the experimental treatment versus placebo by carrying out a meta-analysis of NAFLD clinical trials.MethodsAfter a systematic review of NAFLD clinical trials to May 2021, applying strict selection criteria, the following primary outcomes were observed: (a) NASH resolution, with no worsening of fibrosis when available; (b) fibrosis improvement ≥ 1 stage, with no worsening of NAS when available; (c) worsening of NAS; (d) worsening of liver fibrosis ≥ 1 stage, including the progression to cirrhosis on histopathology. Other histological, clinical, and biochemical outcomes were considered secondary endpoints. Heterogeneity was explored by subgroup and sensitivity analyses, and univariable meta-regression.ResultsTwenty-seven randomized clinical trials were included. The pooled efficacy for NASH resolution receiving experimental therapy was 19% (95%CI 15–23; I2 96.2%) compared with placebo 10% (95%CI 7–12; I2 85.8%) (OR 1.66 (95%CI 1.24–2.21); I2 57.8%), while it was 26% (95%CI 22–29); I2 90%)) versus 18% (95%CI 15–21; I2 59%)) for fibrosis improvement (OR 1.34 (95%CI 1.13–1.58); I2 25.4%). For these outcomes, the therapy showed higher efficacy in trials longer than 48 weeks, with < 60% of diabetic population, and when it targeted FXR, PPAR, and antidiabetic mechanisms, and with a NAS < 5 for NASH resolution. Also, NASH (OR 0.57 (95%CI 0.39–0.84); I2 67%) and fibrosis worsening (OR 0.65 (95%CI 0.46–0.92); I2 61.9%) were prevented with the therapy.ConclusionThis meta-analysis provides information about the efficacy of the therapy versus placebo by comparing different and combined trial outcomes such as NASH resolution, fibrosis improvement, and NAS and fibrosis worsening. Changes in the experimental design and selection criteria of the clinical trials might be suitable to increase the efficacy.

Clinical Observation of SGLT2 Inhibitor Therapy for Cardiac Arrhythmia and Related Cardiovascular Disease in Diabetic Patients with Controlled Hypertension.

Sodium-glucose transporter 2 (SGLT2) inhibitors are new glucose-lowering agents that have been proven to be beneficial for patients with cardiovascular diseases, heart failure, and sudden cardiac death. However, the possible protective effects of cardiac arrhythmia have not yet been clarified in clinical practice. In this study, we attempted to demonstrate the effects of SGLT2 inhibitors on cardiac arrhythmia by medical records from a single center. This retrospective study included patients diagnosed with type 2 diabetes mellitus (DM) and controlled hypertension who prescribed the indicated glucose-lowering agents based on medical records from 2016 to 2019 from Kaohsiung Medical University Hospital. These patients were divided into two groups. Group one patients were defined as patients with SGLT2 inhibitor therapy, and group two patients were defined as patients without SGLT2 inhibitor therapy. Baseline characteristics were collected from medical records. Univariate, multivariate, and match-paired statistical analyses were performed for the study endpoints. The primary study outcome was the incidence of cardiac arrhythmias, including atrial and ventricular arrhythmias, after SGLT2 inhibitor therapy. The secondary study outcomes were the incidence of stroke, heart failure, and myocardial infarction after SGLT2 inhibitor therapy. From the initial 62,704 medical records, a total of 9609 people who met our experimental design criteria were included. The mean follow-up period was 51.50 ± 4.23 months. Group one included 3203 patients who received SGLT2 inhibitors for treatment, and group two included 6406 patients who received non-SGLT2 inhibitors for treatment. Multivariate analysis showed that group one patients had significantly lower incidences of total cardiac arrhythmia (hazard ratio (HR): 0.58, 95% confidence interval (CI): 0.38–0.89, p = 0.013) and atrial fibrillation (HR: 0.56, 95% CI: 0.35–0.88, p = 0.013) than those of group two patients. The secondary outcome analysis showed that group one patients also had a significantly lower risk of stroke (HR: 0.48, 95% CI: 0.33–0.7; p < 0.001), heart failure (HR: 0.54, 95% CI: 0.41–0.7, p < 0.001), and myocardial infarction (HR: 0.47, 95% CI: 0.31–0.72, p < 0.001). A time-to-event analysis showed that treatment of type 2 DM patients with SGLT2 inhibitors could reduce the probability of total cardiac arrhythmia and related cardiovascular disease, such as atrial fibrillation, stroke, heart failure, or myocardial infarction, by 0.5%~0.8%. This databank analysis showed that SGLT2 inhibitor therapy reduced the incidence of total cardiac arrhythmia and atrial fibrillation in type 2 DM patients and decreased the incidence of related cardiovascular diseases, such as stroke, heart failure, and myocardial infarction. However, additional investigations are needed to confirm this hypothesis.

Evaluating acute toxicity in enriched nitrifying cultures: Lessons learned

Toxicological batch assays are essential to assess a compound's acute effect on microorganisms. This methodology is frequently employed to evaluate the effect of contaminants in sensitive microbial communities from wastewater treatment plants (WWTPs), such as autotrophic nitrifying populations. However, despite nitrifying batch assays being commonly mentioned in the literature, their experimental design criteria are rarely reported or overlooked. Here, we found that slight deviations in culture preparations and conditions impacted bacterial community performance and could skew assay results.From pre-experimental trials and experience, we determined how mishandling and treatment of cultures could affect nitrification activity. While media and biomass preparations are needed to establish baseline conditions (e.g., biomass washing), we found extensive centrifugation selectively destabilised nitrification activities. Further, it is paramount that the air supply is adjusted to minimise nitrite build-up in the culture and maintain suitable aeration levels without sparging ammonia. DMSO and acetone up to 0.03% (v/v) were suitable organic solvents with minimal impact on nitrification activity. In the nitrification assays with allylthiourea (ATU), dilute cultures exhibited more significant inhibition than concentrated cultures. So there were biomass-related effects; however, these differences minimally impacted the EC50 values. Using different nutrient-media compositions had a minimal effect; however, switching mineral media for the toxicity test from the original cultivation media is not recommended because it reduced the original biomass nitrification capacity.Our results demonstrated that these factors substantially impact the performance of the nitrifying inoculum used in acute bioassays, and consequently, affect the response of AOB-NOB populations during the toxicant exposure. These are not highlighted in operation standards, and unfortunately, they can have significant consequential impacts on the determinations of toxicological endpoints. Moreover, the practical procedures tested here could support other authors in developing testing methodologies, adding quality checks in the experimental framework with minimal waste of time and resources.

Robust Evaluation of ENSO in Climate Models: How Many Ensemble Members Are Needed?

AbstractLarge ensembles of model simulations require considerable resources, and thus defining an appropriate ensemble size for a particular application is an important experimental design criterion. We estimate the ensemble size (N) needed to assess a model’s ability to capture observed El Niño‐Southern Oscillation (ENSO) behavior by utilizing the recently developed International CLIVAR ENSO Metrics Package. Using the larger ensembles available from CMIP6 and the US CLIVAR Large Ensemble Working Group, we find that larger ensembles are needed to robustly capture baseline ENSO characteristics (N &gt; 50) and physical processes (N &gt; 50) than the background climatology (N ≥ 12) and remote ENSO teleconnections (N ≥ 6). While these results vary somewhat across metrics and models, our study quantifies how larger ensembles are required to robustly evaluate simulated ENSO behavior, thereby providing some guidance for the design of model ensembles.

DOPE: D-Optimal Pooling Experimental design with application for SARS-CoV-2 screening.

ObjectiveTesting individuals for the presence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the pathogen causing the coronavirus disease 2019 (COVID-19), is crucial for curtailing transmission chains. Moreover, rapidly testing many potentially infected individuals is often a limiting factor in controlling COVID-19 outbreaks. Hence, pooling strategies, wherein individuals are grouped and tested simultaneously, are employed. Here, we present a novel pooling strategy that builds on the Bayesian D-optimal experimental design criterion.Materials and MethodsOur strategy, called DOPE (D-Optimal Pooling Experimental design), is built on a novel Bayesian formulation of pooling. DOPE defines optimal pooled tests as those maximizing the mutual information between data and infection states. We estimate said mutual information via Monte-Carlo sampling and employ a discrete optimization heuristic to maximize it.ResultsWe compare DOPE to other, commonly used pooling strategies, as well as to individual testing. DOPE dominates the other strategies as it yields lower error rates while utilizing fewer tests. We show that DOPE maintains this dominance for a variety of infection prevalence values.DiscussionDOPE has several additional advantages over common pooling strategies: it provides posterior distributions of the probability of infection rather than only binary classification outcomes; it naturally incorporates prior information of infection probabilities and test error rates; and finally, it can be easily extended to include other, newly discovered information regarding COVID-19.ConclusionDOPE can substantially improve accuracy and throughput over current pooling strategies. Hence, DOPE can facilitate rapid testing and aid the efforts of combating COVID-19 and other future pandemics.

Iterative model‐based experimental design for spherical agglomeration processes

AbstractSpherical agglomeration (SA) is a process intensification strategy, which can reduce the number of unit operations in pharmaceutical manufacturing. SA merges drug substance crystallization with drug product wet granulation, reducing capital, and operating costs. However, SA is a highly nonlinear process, thus for its efficient operation model‐based design and control strategies are beneficial. These require the development of a high‐fidelity process model with appropriately estimated parameters. There are two major problems associated with the development of a high‐fidelity process models—(i) selection of the appropriate model corresponding to the underlying process mechanisms, and (ii) accurate estimation of the parameters. This work focuses on the identification of the best fitting model that correlates with experimental observations using cross‐validation experiments. Further, an iterative model‐based experimental design strategy is developed, which uses D‐optimal experimental design criterion to minimize the number of experiments necessary to obtain accurate parameter estimates.

Active learning in multiple-class classification problems via individualized binary models

We propose a unified algorithm for both categorical and ordinal labeled data in multiclass classification problems, where each subject belongs to one class only. In training an effective classification rule, it is critical that one have and rely on a sufficient amount of reliably labeled data. As information on the training sample sizes needed to obtain satisfactory performance is lacking, we adopt an adaptive subject recruiting scheme with an experimental design criterion to shorten the training process. Because this kind of active learning method is naturally conducted in a sequential manner, we adopt sequential analysis to control the required sample size and ensure the performance of the final classifier. Additionally, we report its statistical properties and numerical results from using synthesized and real data.

Examining the effect of lab instructions on students' critical thinking during a chemical inquiry practical

Developing students’ critical thinking skills is often seen as an important educational goal for inquiry assignments. In this study, we investigated to what extent pre-laboratory activities of a chemical inquiry assignment influence students' independent critical thinking. We compared two forms of pre-laboratory activities that are frequently used in educational practice to prepare students for their inquiry assignments: on the one hand paved road pre-laboratory activities that lead students with sensemaking preparatory questions and on the other, critical-thinking pre-laboratory activities in which students start with the development of an experiment plan using provided information and criteria for a good experimental design. We conducted this study two years in succession in senior year Dutch high school chemistry classes during an inquiry assignment that involved the study of the relation between reaction kinetics and molecular reaction mechanisms of organic nucleophilic substitution reactions (SN1/SN2). We focused on aspects associated with critical thinking, such as the desire to understand what is observed and to be able to adjust an existing method or model on the basis of experimental data. The results show that the design of pre-laboratory activities strongly influence the critical thinking exhibited by students during their inquiry activities, whereby students who perform critical thinking pre-laboratory activities are more motivated to think more deeply about the meaning of their measurements than students that perform paved road pre-laboratory activities.

Multidimensional sum-up rounding for integer programming in optimal experimental design

We present a numerical method for approximating the solution of convex integer programs stemming from optimal experimental design. The statistical setup consists of a Bayesian framework for linear inverse problems for which the direct relationship is described by a discretized integral equation. Specifically, we aim to find the optimal sensor placement from a set of candidate locations where data are collected with measurement error. The convex objective function is a measure of the uncertainty, described here by the trace or log-determinant of the posterior covariance matrix, for the discretized linear inverse problem solution. The resulting convex integer program is relaxed, producing a lower bound. An upper bound is obtained by extending the sum-up rounding approach to multiple dimensions. For this extension, we analyze its accuracy as a function of the discretization mesh size for a rectangular domain. We show asymptotic optimality of the integer solution defining the upper bound for different experimental design criteria (A- and D-optimal), by proving the convergence to zero of the gap between the upper and lower bounds as the mesh size goes to zero. The technique is illustrated on a two-dimensional gravity surveying problem for both A-optimal and D-optimal sensor placement where our designs yield better results compared with a thresholding rounding approach.

Bregman divergences based on optimal design criteria and simplicial measures of dispersion

In previous work the authors defined the k-th order simplicial distance between probability distributions which arises naturally from a measure of dispersion based on the squared volume of random simplices of dimension k. This theory is embedded in the wider theory of divergences and distances between distributions which includes Kullback–Leibler, Jensen–Shannon, Jeffreys–Bregman divergence and Bhattacharyya distance. A general construction is given based on defining a directional derivative of a function $$\phi $$ from one distribution to the other whose concavity or strict concavity influences the properties of the resulting divergence. For the normal distribution these divergences can be expressed as matrix formula for the (multivariate) means and covariances. Optimal experimental design criteria contribute a range of functionals applied to non-negative, or positive definite, information matrices. Not all can distinguish normal distributions but sufficient conditions are given. The k-th order simplicial distance is revisited from this aspect and the results are used to test empirically the identity of means and covariances.

Optimal Path Planning for Two Unmanned Aerial Vehicles in DRSS Localization

Optimal path planning for three or more unmanned aerial vehicles (UAVs) in radio source localization has been studied extensively; but path planning for two UAVs in signal strength based localization is still a challenge. This paper investigates the autonomous path planning for a pair of UAVs equipped with received signal strength (RSS) sensors applying optimum experimental design criteria based on the fisher information matrix (FIM). The control strategy steers the UAVs along the paths that minimize the emitter location uncertainty. Since there is one differential received signal strength (DRSS) measurement (two RSS sensors) in each time step, the emitter location uncertainty is infinite for a single measurement and the FIM is singular. The FIM is approximated at successive waypoints using the estimated location of the emitter produced by the extended kalman filter (EKF). The objective of this paper is to propose path planning approaches for minimum number of UAVs in DRSS-based localization based on different optimum criteria including D-, E-, A-optimality and sensitivity. Each criterion is related to a different characteristic of the estimation uncertainty ellipsoid and consequently generates different trajectories. The proposed steering algorithms are evaluated through extensive simulations.