Cooperative Safe Trajectory Planning for Quadrotor Swarms.

In this paper, we propose a novel distributed algorithm based on model predictive control and alternating direction multiplier method (DMPC-ADMM) for cooperative trajectory planning of quadrotor swarms. First, a receding horizon trajectory planning optimization problem is constructed, in which the differential flatness property is used to deal with the nonlinear dynamics of quadrotors while we design a relaxed form of the discrete-time control barrier function (DCBF) constraint to balance feasibility and safety. Then, we decompose the original trajectory planning problem by ADMM and solve it in a fully distributed manner with peer-to-peer communication, which induces the quadrotors within the communication range to reach a consensus on their future trajectories to enhance safety. In addition, an event-triggered mechanism is designed to reduce the communication overhead. The simulation results verify that the trajectories generated by our method are real-time, safe, and smooth. A comprehensive comparison with the centralized strategy and several other distributed strategies in terms of real-time, safety, and feasibility verifies that our method is more suitable for the trajectory planning of large-scale quadrotor swarms.

Fast Trajectory Tracking Control Algorithm for Autonomous Vehicles Based on the Alternating Direction Multiplier Method (ADMM) to the Receding Optimization of Model Predictive Control (MPC).

In order to improve the real-time performance of the trajectory tracking of autonomous vehicles, this paper applies the alternating direction multiplier method (ADMM) to the receding optimization of model predictive control (MPC), which improves the computational speed of the algorithm. Based on the vehicle dynamics model, the output equation of the autonomous vehicle trajectory tracking control system is constructed, and the auxiliary variable and the dual variable are introduced. The quadratic programming problem transformed from the MPC and the vehicle dynamics constraints are rewritten into the solution of the ADMM form, and a decreasing penalty factor is used during the solution process. The simulation verification is carried out through the joint simulation platform of Simulink and Carsim. The results show that, compared with the active set method (ASM) and the interior point method (IPM), the algorithm proposed in this paper can not only improve the accuracy of trajectory tracking, but also exhibits good real-time performance in different prediction time domains and control time domains. When the prediction time domain increases, the calculation time shows no significant difference. This verifies the effectiveness of the ADMM in improving the real-time performance of MPC.

Identifying potential small molecule-miRNA associations via Robust PCA based on γ-norm regularization.

Dysregulation of microRNAs (miRNAs) is closely associated with refractory human diseases, and the identification of potential associations between small molecule (SM) drugs and miRNAs can provide valuable insights for clinical treatment. Existing computational techniques for inferring potential associations suffer from limitations in terms of accuracy and efficiency. To address these challenges, we devise a novel predictive model called RPCA$\Gamma $NR, in which we propose a new Robust principal component analysis (PCA) framework based on $\gamma $-norm and $l_{2,1}$-norm regularization and design an Augmented Lagrange Multiplier method to optimize it, thereby deriving the association scores. The Gaussian Interaction Profile Kernel Similarity is calculated to capture the similarity information of SMs and miRNAs in known associations. Through extensive evaluation, including Cross Validation Experiments, Independent Validation Experiment, Efficiency Analysis, Ablation Experiment, Matrix Sparsity Analysis, and Case Studies, RPCA$\Gamma $NR outperforms state-of-the-art models concerning accuracy, efficiency and robustness. In conclusion, RPCA$\Gamma $NR can significantly streamline the process of determining SM-miRNA associations, thus contributing to advancements in drug development and disease treatment.

Dim and Small Target Detection with a Combined New Norm and Self-Attention Mechanism of Low-Rank Sparse Inversion.

Methods for detecting small infrared targets in complex scenes are widely utilized across various domains. Traditional methods have drawbacks such as a poor clutter suppression ability and a high number of edge residuals in the detection results in complex scenes. To address these issues, we propose a method based on a joint new norm and self-attention mechanism of low-rank sparse inversion. Firstly, we propose a new tensor nuclear norm based on linear transformation, which globally constrains the low-rank characteristics of the image background and makes full use of the structural information among tensor slices to better approximate the rank of the non-convex tensor, thus achieving effective background suppression. Secondly, we construct a self-attention mechanism in order to constrain the sparse characteristics of the target, which further eliminates any edge residuals in the detection results by transforming the local feature information into a weight matrix to further constrain the target component. Finally, we use the alternating direction multiplier method to decompose the newly reconstructed objective function and introduce a reweighted strategy to accelerate the convergence speed of the model. The average values of the three evaluation metrics, SSIM, BSF, and SNR, for the algorithm proposed in this paper are 0.9997, 467.23, and 11.72, respectively. Meanwhile, the proposed detection method obtains a higher detection rate compared with other algorithms under the same false alarm rate.

Joint Learning of Correlation-Constrained Fuzzy Clustering and Discriminative Non-Negative Representation for Hyperspectral Band Selection.

Hyperspectral band selection plays an important role in overcoming the curse of dimensionality. Recently, clustering-based band selection methods have shown promise in the selection of informative and representative bands from hyperspectral images (HSIs). However, most existing clustering-based band selection methods involve the clustering of original HSIs, limiting their performance because of the high dimensionality of hyperspectral bands. To tackle this problem, a novel hyperspectral band selection method termed joint learning of correlation-constrained fuzzy clustering and discriminative non-negative representation for hyperspectral band selection (CFNR) is presented. In CFNR, graph regularized non-negative matrix factorization (GNMF) and constrained fuzzy C-means (FCM) are integrated into a unified model to perform clustering on the learned feature representation of bands rather than on the original high-dimensional data. Specifically, the proposed CFNR aims to learn the discriminative non-negative representation of each band for clustering by introducing GNMF into the model of the constrained FCM and making full use of the intrinsic manifold structure of HSIs. Moreover, based on the band correlation property of HSIs, a correlation constraint, which enforces the similarity of clustering results between neighboring bands, is imposed on the membership matrix of FCM in the CFNR model to obtain clustering results that meet the needs of band selection. The alternating direction multiplier method is adopted to solve the joint optimization model. Compared with existing methods, CFNR can obtain a more informative and representative band subset, thus can improve the reliability of hyperspectral image classifications. Experimental results on five real hyperspectral datasets demonstrate that CFNR can achieve superior performance compared with several state-of-the-art methods.

Lie symmetry analysis, particular solutions and conservation laws of a (2+1)-dimensional KdV4 equation.

In this paper, a (2+1)-dimensional KdV4 equation is considered. We obtain Lie symmetries of this equation by utilizing Lie point symmetry analysis method, then use them to perform symmetry reductions. By using translation symmetries, two fourth-order ordinary differential equations are obtained. Solutions of one fourth order ordinary differential equation are presented by using direct integration method and $ (G'/G) $-expansion method respectively. Furthermore, the corresponding solutions are depicted with appropriate graphical representations. The other fourth-order ordinary differential equation is solved by using power series technique. Finally, two kinds of conserved vectors of this equation are presented by invoking the multiplier method and Noether's theorem respectively.

Hierarchical Multi-Objective Optimization for Dedicated Bus Punctuality and Supply-Demand Balance Control.

Public transportation is a crucial component of urban transportation systems, and improving passenger sharing rates can help alleviate traffic congestion. To enhance the punctuality and supply-demand balance of dedicated buses, we propose a hierarchical multi-objective optimization model to optimize bus guidance speeds and bus operation schedules. Firstly, we present an intelligent decision-making method for bus driving speed based on the mathematical description of bus operation states and the application of the Lagrange multiplier method, which improves the overall punctuality rate of the bus line. Secondly, we propose an optimization method for bus operation schedules that respond to passenger needs by optimizing departure time intervals and station schedules for supply-demand balance. The experiments were conducted in Future Science City, Beijing, China. The results show that the bus line's punctuality rate has increased to 90.53%, while the retention rate for platform passengers and the intersection stop rate have decreased by 36.22% and 60.93%, respectively. These findings verify the effectiveness and practicality of the proposed hierarchical multi-objective optimization model.

An inertial neural network approach for loco-manipulation trajectory tracking of mobile robot with redundant manipulator.

This paper proposes a novel constrained optimization model to address the loco-manipulation problem of mobile robot with redundant manipulator for trajectory tracking. To alleviate the accumulative error of the end-effector's position, a new control law is designed to eliminate the negative effect from the deviation of the initial position, leading to better performance than existing ones. To deal with the locomotion constraints in the loco-manipulation problem, the optimization model is converted to an augmented Lagrangian primal-dual problem. Furthermore, an inertial neural network approach is used to solve the problem and the corresponding Lyapunov proof guarantees the convergence of variables. The numerical simulations show that the proposed approach is more suitable for application since the model is more effective and the algorithm has better convergence rate.

Estimating Productivity Loss from Breast and Non-Small-Cell Lung Cancer among Working-Age Patients and Unpaid Caregivers: A Survey Study Using the Multiplier Method.

Background. Traditional approaches to capturing health-related productivity loss (e.g., the human capital method) focus only on the foregone wages of affected patients, overlooking the losses caregivers can incur. This study estimated the burden of productivity loss among breast cancer (BC) and non-small-cell lung cancer (NSCLC) patients and individuals caring for such patients using an augmented multiplier method. Design. A cross-sectional survey of BC and NSCLC patients and caregivers measured loss associated with time absent from work (absenteeism) and reduced effectiveness (presenteeism). Respondents reported pre- and postcancer diagnosis income, hours worked, and time to complete tasks. Exploratory multivariable analyses examined correlations between respondents' clinical/demographic characteristics-including industry of employment-and postdiagnosis productivity. Results. Of 204 patients (104 BC, 100 NSCLC) and 200 caregivers (100 BC, 100 NSCLC) who completed the survey, 319 participants (162 BC, 157 NSCLC) working ≥40 wk/y prediagnosis were included in the analysis. More than one-third of the NSCLC (33%) and BC (43%) patients left the workforce postdiagnosis, whereas only 15% of caregivers did. The traditional estimate for the burden of productivity loss was 66% lower on average than the augmented estimate (NSCLC patients: 60%, BC patients: 69%, NSCLC caregivers: 59%, and BC caregivers: 73%). Conclusions. Although patients typically experience greater absenteeism, productivity loss incurred by caregivers is also substantial. Failure to account for such impacts can result in substantial underestimation of productivity gains novel cancer treatments may confer by enabling patients and caregivers to remain in the workforce longer. Our results underscore the importance of holistic approaches to understanding this impact on both patients and their caregivers and accounting for such considerations when making decisions about treatment and treatment value. Highlights: Cancer can have a profound impact on productivity. This study demonstrates how the disease affects not only patients but also the informal or unpaid individuals who care for patients.An augmented approach to calculating health-related productivity loss suggests that productivity impacts are much larger than previously understood.A more comprehensive understanding of the economic burden of cancer for both patients and their caregivers suggests the need for more support in the workplace for these individuals and a holistic approach to accounting for these impacts in treatment decision making.

Estimating the Prevalence of Recreational Opioid Use in Spain Using a Multiplier Method.

Acknowledgement of the prevalence of recreational opioid use (PROU) is key to the planning and evaluation of care services. However, in Spain, the prevalence of PROU in recent years is unknown. The objective of this study was to estimate the PROU between 2005 and 2019 in the general populations of six Spanish cities. A benchmark-multiplier methodology was used to estimate the PROU population size. The benchmark used was overdose deaths from recreational opioid use in Spain's six most populated cities. The multiplier was the overdose death rate in a cohort of heroin users. Linear regression was used to estimate the trend of the PROU estimate over the set period of years. In 2005, the PROU was 4.78 (95%CI 3.16-7.91) per 1000 people. The estimated trend decreased, with the two lowest values being 2.35 per 1000 in 2015 and 2.29 in 2018. In 2019 the PROU was 2.60 per 1000 (95%CI 1.72-4.31), 45% lower than in 2005. While the decline in the PROU continues, its deceleration over the last four years calls for increased vigilance, especially in light of the opioid crisis in North America that has occurred over the last few years.

A Hybrid Sparse Representation Model for Image Restoration.

Group-based sparse representation (GSR) uses image nonlocal self-similarity (NSS) prior to grouping similar image patches, and then performs sparse representation. However, the traditional GSR model restores the image by training degraded images, which leads to the inevitable over-fitting of the data in the training model, resulting in poor image restoration results. In this paper, we propose a new hybrid sparse representation model (HSR) for image restoration. The proposed HSR model is improved in two aspects. On the one hand, the proposed HSR model exploits the NSS priors of both degraded images and external image datasets, making the model complementary in feature space and the plane. On the other hand, we introduce a joint sparse representation model to make better use of local sparsity and NSS characteristics of the images. This joint model integrates the patch-based sparse representation (PSR) model and GSR model, while retaining the advantages of the GSR model and the PSR model, so that the sparse representation model is unified. Extensive experimental results show that the proposed hybrid model outperforms several existing image recovery algorithms in both objective and subjective evaluations.

A BAYESIAN HIERARCHICAL MODEL FOR COMBINING MULTIPLE DATA SOURCES IN POPULATION SIZE ESTIMATION.

To combat the HIV/AIDS pandemic effectively, targeted interventions among certain key populations play a critical role. Examples of such key populations include sex workers, people who inject drugs, and men who have sex with men. While having accurate estimates for the size of these key populations is important, any attempt to directly contact or count members of these populations is difficult. As a result, indirect methods are used to produce size estimates. Multiple approaches for estimating the size of such populations have been suggested but often give conflicting results. It is, therefore, necessary to have a principled way to combine and reconcile these estimates. To this end, we present a Bayesian hierarchical model for estimating the size of key populations that combines multiple estimates from different sources of information. The proposed model makes use of multiple years of data and explicitly models the systematic error in the data sources used. We use the model to estimate the size of people who inject drugs in Ukraine. We evaluate the appropriateness of the model and compare the contribution of each data source to the final estimates.

Reliability-based tolerance redesign of mechanical assemblies using Jacobian-Torsor model.

The purpose of this paper is to present a new method to redesign dimensional and geometric tolerances of mechanical assemblies at a lower cost and with higher reliability. A parametric Jacobian-Torsor model is proposed to conduct tolerance analysis of mechanical assembly. A reliability-based tolerance optimization model is established. Differing from previous studies of fixed process parameters, this research determines the optimal process variances of tolerances, which provide basis for the subsequent assembly tolerance redesign. By using the Lambert W function and the Lagrange multiplier method, the analytical solution of the parametric tolerance optimization model is obtained. A numerical example is presented to demonstrate the effectiveness of the model, while the results indicate that the total cost is reduced by 10.93% and assembly reliability improves by 2.12%. This study presents an efficient reliability-based tolerance optimization model. The proposed model of tolerance redesign can be used for mechanical assembly with a better economic effect and higher reliability.

Estimates of people who injected drugs within the last 12 months in Belgium based on a capture-recapture and multiplier method.

BACKGROUND: For Belgium, available estimates of the number of people who inject drugs (PWID) are based on data from more than fifteen years ago and apply only to those who report ever injecting drugs. As a result, no reliable baseline data exist to determine the scale of services for PWID. METHODS: We obtained pseudo-anonymized identifier information from treatment and harm reduction service providers and a fieldwork study between February and April 2019 in Brussels. We estimated the number of PWID, defined as people who injected within the last 12 months, in Brussels using capture-recapture (CRC) methodology. To obtain national estimates, we scaled the proportion of PWID in Brussels to the total number of this population in Belgium based on two existing drug treatment registers, which were then multiplied with the result of the CRC. RESULTS: The total population of PWID is estimated to be 703 (95 %CI 538-935) for Brussels and between 6620 (95 %CI 4711 - 8576) and 7018 (95 %CI 4794 - 9527) for Belgium. CONCLUSIONS: These estimates provide crucial information to ensure that services to PWID are adequately maintained. They clearly indicate the need to maximize efforts to achieve the targets set by WHO for 2030 on the provision of 300 sterile needles and syringes per PWID per year, a 90 % reduction of new HCV infections, and a 65 % reduction of liver-related mortality.

Use of the multiplier method to estimate the size of populations most at risk of human immunodeficiency virus infection in China: a systematic review.

OBJECTIVE: United Nations Programme on human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome and World Health Organization believe that some of the benchmark numbers collected may be inaccurate when using the multiplier method to estimate the size of populations most at risk of acquiring HIV. Here, study data have been evaluated to characterize the inaccurate benchmark numbers. STUDY DESIGN: The study design used is a systematic review. METHODS: Studies published from 1 January 2004 to 1 December 2019 using the multiplier method to estimate the population proportions of men who have sex with men (MSM) and female sex workers (FSWs) in China were reviewed. Five electronic bibliographic databases were searched: Medline, the China National Knowledge Infrastructure, VIP Database for Chinese Technical Periodicals, Wanfang Data, and the Chinese BioMedical Literature Database. RESULTS: In all eight studies of FSW, six of the estimated population proportions fell within the range of national estimates. However, the estimated MSM population proportions of all 18 studies fell outside the range of national estimates. CONCLUSIONS: When estimating the MSM population, the use of benchmark numbers from homosexual websites or MSM-frequented sites usually led to an inaccurate estimation. Therefore, benchmark numbers from services/programs that meet fundamental needs, such as those dealing with health and wellness, should be used.

Assessing Bias in Population Size Estimates Among Hidden Populations When Using the Service Multiplier Method Combined With Respondent-Driven Sampling Surveys: Survey Study.

BACKGROUND: Population size estimates (PSEs) for hidden populations at increased risk of HIV, including female sex workers (FSWs), are important to inform public health policy and resource allocation. The service multiplier method (SMM) is commonly used to estimate the sizes of hidden populations. We used this method to obtain PSEs for FSWs at 9 sites in Zimbabwe and explored methods for assessing potential biases that could arise in using this approach. OBJECTIVE: This study aimed to guide the assessment of biases that arise when estimating the population sizes of hidden populations using the SMM combined with respondent-driven sampling (RDS) surveys. METHODS: We conducted RDS surveys at 9 sites in late 2013, where the Sisters with a Voice program (the program), which collects program visit data of FSWs, was also present. Using the SMM, we obtained PSEs for FSWs at each site by dividing the number of FSWs who attended the program, based on program records, by the RDS-II weighted proportion of FSWs who reported attending this program in the previous 6 months in the RDS surveys. Both the RDS weighting and SMM make a number of assumptions, potentially leading to biases if the assumptions are not met. To test these assumptions, we used convergence and bottleneck plots to assess seed dependence of RDS-II proportion estimates, chi-square tests to assess if there was an association between the characteristics of FSWs and their knowledge of program existence, and logistic regression to compare the characteristics of FSWs attending the program with those recruited to RDS surveys. RESULTS: The PSEs ranged from 194 (95% CI 62-325) to 805 (95% CI 456-1142) across 9 sites from May to November 2013. The 95% CIs for the majority of sites were wide. In some sites, the RDS-II proportion of women who reported program use in the RDS surveys may have been influenced by the characteristics of selected seeds, and we also observed bottlenecks in some sites. There was no evidence of association between characteristics of FSWs and knowledge of program existence, and in the majority of sites, there was no evidence that the characteristics of the populations differed between RDS and program data. CONCLUSIONS: We used a series of rigorous methods to explore potential biases in our PSEs. We were able to identify the biases and their potential direction, but we could not determine the ultimate direction of these biases in our PSEs. We have evidence that the PSEs in most sites may be biased and a suggestion that the bias is toward underestimation, and this should be considered if the PSEs are to be used. These tests for bias should be included when undertaking population size estimation using the SMM combined with RDS surveys.

Size Estimation of high-risk groups for hiv infection in india based on data from national integrated bio-behavioral surveillance and targeted interventions.

BACKGROUND: Targeted interventions (TIs) are one of the most effective strategies to control HIV/AIDS transmission, especially among the high-risk groups (HRGs). Implementation of HIV/AIDS control strategies relies heavily on estimation of the size of HRG population. Size estimation for key populations such as female sex workers (FSWs), men who have sex with men (MSM), and injecting drug users (IDUs) is a crucial component of national HIV strategic planning. OBJECTIVE: The objective of this study was to estimate the size of FSWs, MSM, and IDUs in various states of India. METHODS: The program multiplier method was used to estimate the size of FSWs, MSM, and IDUs across the country using two distinct but overlapping data sources - Integrated Bio-Behavioral Surveillance and TI program from the same geographical area at the same time period. RESULTS: In India, as on 2018-2019, there were nearly 18.2 lakhs estimated FSWs accounting to 0.53% among female population aged 15-49 years, with a highest in West Bengal (4.5 lakhs); 5.7 lakhs estimated MSM accounting to 0.16% among male population aged 15-49 years, with a highest in Gujarat (0.7 lakh); and 3.9 lakhs estimated IDUs accounting to 0.11% among male population aged 15-49 years, with a highest in Uttar Pradesh (0.5 lakh). CONCLUSIONS: The current size estimates on HRGs will support the development of projections and estimations of the HIV epidemic at national and state levels. These estimates also help in framing national guidelines such as HIV strategic planning, program design, allocation of resources, prioritizing the interventions, and monitoring and evaluation.

Multiplier method estimates of the population of men who have sex with men: the effect of privacy protection.

OBJECTIVES: The stigmatization of men who have sex with men (MSM) has led to an underestimation of their population size. To address this, the United Nations Programme on HIV/Acquired Immunodeficiency Syndrome and World Health Organization developed a multiplier method. However, nearly all multiplier method estimates of MSM population size in China are far below national estimates. This study explores how privacy protection to address and avoid MSM stigmatization can affect reliable estimates. METHODS: Data from an MSM website, a bar, and a peer-based HIV testing were used to produce three multiplier method estimates of the MSM population size in Taiyuan, China, in 2014. The effect of privacy protection on stigmatization was explored by comparing the peer-based HIV testing with other estimates. We used a national estimate as a reference to verify potential underestimation. RESULTS: The website and bar estimates were 5- to 10-times and 8- to 16-times lower than the Chinese national estimate range, respectively. Conversely, the peer-based HIV testing estimate was within the national estimate range. CONCLUSIONS: Though the multiplier method was developed to estimate the size of stigmatized populations, it might be affected by privacy protection addressing stigmatization; this should be considered when gathering data.

Long-term results and comparison of the Green-Anderson and multiplier growth prediction methods after permanent epiphysiodesis using Canale's technique.

PURPOSE: The aim of the study was to evaluate the accuracy and radiographic outcomes of Canale's method in patients with idiopathic leg-length discrepancy (LLD) following percutaneous epiphysiodesis. The accuracy of two common growth prediction methods was assessed. METHODS: A total of 18 patients with 26 affected bones (eight distal femur, two proximal tibia, five combined) were clinically and radiologically analyzed after reaching skeletal maturity. We compared the final effect of epiphysiodesis at maturity with the expected effect of epiphysiodesis before surgery; these measures were calculated using the Green-Anderson and multiplier methods, respectively. We furthermore compared pre- and postoperative frontal and lateral plane radiographs. RESULTS: The average LLD was 21.2 mm before surgery and 7.9 mm after epiphysiodesis. The final effect of both methods was not significantly different compared with the expected effect of epiphysiodesis before surgery. However, the prediction by the Green-Anderson method was closer to the definitive epiphysiodesis effect. The frontal plane radiographic deformity parameters did not change significantly after epiphysiodesis. The postoperative sagittal plane radiographic deformity parameters were in the normal range. CONCLUSION: The Canale technique is a reliable method to reduce LLD in children. With regards to growth prediction, the Green-Anderson method using bone age seems to be more accurate than the multiplier method using chronological age. However, a relative over-estimation was observed with both methods in several cases, which might result in an insufficient correction. LEVEL OF EVIDENCE: IV, Therapeutic study.