Optimal weighted Bonferroni tests and their graphical extensions.

Regulatory guidelines mandate the strong control of the familywise error rate in confirmatory clinical trials with primary and secondary objectives. Bonferroni tests are one of the popular choices for multiple comparison procedures and are building blocks of more advanced procedures. It is usually of interest to find the optimal weighted Bonferroni split for multiple hypotheses. We consider two popular quantities as the optimization objectives, which are the disjunctive power and the conjunctive power. The former is the probability to reject at least one false hypothesis and the latter is the probability to reject all false hypotheses. We investigate the behavior of each of them as a function of different Bonferroni splits, given assumptions about the alternative hypotheses and correlations between test statistics. Under independent tests, unique optimal Bonferroni weights exist; under dependence, optimal Bonferroni weights may not be unique based on a fine grid search. In general, we propose an optimization algorithm based on constrained nonlinear optimization and multiple starting points. The proposed algorithm efficiently identifies optimal Bonferroni weights to maximize the disjunctive or conjunctive power. In addition, we apply the proposed algorithm to graphical approaches, which include many Bonferroni-based multiple comparison procedures. Utilizing the closed testing principle, we adopt a two-step approach to find optimal graphs using the disjunctive power. We also identify a class of closed test procedures that optimize the conjunctive power. We apply the proposed algorithm to a case study to illustrate the utility of optimal graphical approaches that reflect study objectives.

On SOCP-based disjunctive cuts for solving a class of integer bilevel nonlinear programs.

We study a class of integer bilevel programs with second-order cone constraints at the upper-level and a convex-quadratic objective function and linear constraints at the lower-level. We develop disjunctive cuts (DCs) to separate bilevel-infeasible solutions using a second-order-cone-based cut-generating procedure. We propose DC separation strategies and consider several approaches for removing redundant disjunctions and normalization. Using these DCs, we propose a branch-and-cut algorithm for the problem class we study, and a cutting-plane method for the problem variant with only binary variables. We present an extensive computational study on a diverse set of instances, including instances with binary and with integer variables, and instances with a single and with multiple linking constraints. Our computational study demonstrates that the proposed enhancements of our solution approaches are effective for improving the performance. Moreover, both of our approaches outperform a state-of-the-art generic solver for mixed-integer bilevel linear programs that is able to solve a linearized version of our binary instances. Supplementary Information: The online version contains supplementary material available at 10.1007/s10107-023-01965-1.

Improved NMR-data-compliant protein structure modeling captures context-dependent variations and expands the scope of functional inference.

Nuclear magnetic resonance (NMR) spectroscopy can reveal conformational states of a protein in physiological conditions. However, sparsely available NMR data for a protein with large degrees of freedom can introduce structural artifacts in the built models. Currently used state-of-the-art methods deriving protein structure and conformation from NMR deploy molecular dynamics (MD) coupled with simulated annealing for building models. We provide an alternate graph-based modeling approach, where we first build substructures from NMR-derived distance-geometry constraints combined in one shot to form the core structure. The remaining molecule with inadequate data is modeled using a hybrid approach respecting the observed distance-geometry constraints. One-shot structure building is rarely undertaken for large and sparse data systems, but our data-driven bottom-up approach makes this uniquely feasible by suitable partitioning of the problem. A detailed comparison of select models with state-of-art methods reveals differences in the secondary structure regions wherein the correctness of our models is confirmed by NMR data. Benchmarking of 106 protein-folds covering 38-282 length structures shows minimal experimental-constraint violations while conforming to other structure quality parameters such as the proper folding, steric clash, and torsion angle violation based on Ramachandran plot criteria. Comparative MD studies using select protein models from a state-of-art method and ours under identical experimental parameters reveal distinct conformational dynamics that could be attributed to protein structure-function. Our work is thus useful in building enhanced NMR-evidence-based models that encapsulate the contextual secondary and tertiary structure variations present during the experimentation and expand the scope of functional inference.

CHOmpact: A reduced metabolic model of Chinese hamster ovary cells with enhanced interpretability.

Metabolic modeling has emerged as a key tool for the characterization of biopharmaceutical cell culture processes. Metabolic models have also been instrumental in identifying genetic engineering targets and developing feeding strategies that optimize the growth and productivity of Chinese hamster ovary (CHO) cells. Despite their success, metabolic models of CHO cells still present considerable challenges. Genome-scale metabolic models (GeMs) of CHO cells are very large (>6000 reactions) and are difficult to constrain to yield physiologically consistent flux distributions. The large scale of GeMs also makes the interpretation of their outputs difficult. To address these challenges, we have developed CHOmpact, a reduced metabolic network that encompasses 101 metabolites linked through 144 reactions. Our compact reaction network allows us to deploy robust, nonlinear optimization and ensure that the computed flux distributions are physiologically consistent. Furthermore, our CHOmpact model delivers enhanced interpretability of simulation results and has allowed us to identify the mechanisms governing shifts in the anaplerotic consumption of asparagine and glutamate as well as an important mechanism of ammonia detoxification within mitochondria. CHOmpact, thus, addresses key challenges of large-scale metabolic models and will serve as a platform to develop dynamic metabolic models for the control and optimization of biopharmaceutical cell culture processes.

Hierarchical Trajectory Planning for Narrow-Space Automated Parking with Deep Reinforcement Learning: A Federated Learning Scheme.

Collision-free trajectory planning in narrow spaces has become one of the most challenging tasks in automated parking scenarios. Previous optimization-based approaches can generate accurate parking trajectories, but these methods cannot compute feasible solutions with extremely complex constraints in a limited time. Recent research uses neural-network-based approaches that can generate time-optimized parking trajectories in linear time. However, the generalization of these neural network models in different parking scenarios has not been considered thoroughly and the risk of privacy compromise exists in the case of centralized training. To address the above issues, this paper proposes a hierarchical trajectory planning method with deep reinforcement learning in the federated learning scheme (HALOES) to rapidly and accurately generate collision-free automated parking trajectories in multiple narrow spaces. HALOES is a federated learning based hierarchical trajectory planning method to fully exert high-level deep reinforcement learning and the low-level optimization-based approach. HALOES further fuse the deep reinforcement learning model parameters to improve the generalization capabilities with a decentralized training scheme. The federated learning scheme in HALOES aims to protect the privacy of the vehicle's data during model parameter aggregation. Simulation results show that the proposed method can achieve efficient automatic parking in multiple narrow spaces, improve planning time from 12.15% to 66.02% compared to other state-of-the-art methods (e.g., hybrid A*, OBCA) and maintain the same level of trajectory accuracy while having great model generalization.

A Concurrent Framework for Constrained Inverse Kinematics of Minimally Invasive Surgical Robots.

Minimally invasive surgery has undergone significant advancements in recent years, transforming various surgical procedures by minimizing patient trauma, postoperative pain, and recovery time. However, the use of robotic systems in minimally invasive surgery introduces significant challenges related to the control of the robot's motion and the accuracy of its movements. In particular, the inverse kinematics (IK) problem is critical for robot-assisted minimally invasive surgery (RMIS), where satisfying the remote center of motion (RCM) constraint is essential to prevent tissue damage at the incision point. Several IK strategies have been proposed for RMIS, including classical inverse Jacobian IK and optimization-based approaches. However, these methods have limitations and perform differently depending on the kinematic configuration. To address these challenges, we propose a novel concurrent IK framework that combines the strengths of both approaches and explicitly incorporates RCM constraints and joint limits into the optimization process. In this paper, we present the design and implementation of concurrent inverse kinematics solvers, as well as experimental validation in both simulation and real-world scenarios. Concurrent IK solvers outperform single-method solvers, achieving a 100% solve rate and reducing the IK solving time by up to 85% for an endoscope positioning task and 37% for a tool pose control task. In particular, the combination of an iterative inverse Jacobian method with a hierarchical quadratic programming method showed the highest average solve rate and lowest computation time in real-world experiments. Our results demonstrate that concurrent IK solving provides a novel and effective solution to the constrained IK problem in RMIS applications.

Detection, Location, and Classification of Multiple Dipole-like Magnetic Sources Based on L2 Norm of the Vertical Magnetic Gradient Tensor Data.

In recent years, there has been a growing interest in the detection, location, and classification (DLC) of multiple dipole-like magnetic sources based on magnetic gradient tensor (MGT) data. In these applications, the tilt angle is usually used to detect the number of sources. We found that the tilt angle is only suitable for the scenario where the positive and negative signs of the magnetic sources' inclination are the same. Therefore, we map the L2 norm of the vertical magnetic gradient tensor on the arctan function, denoted as the VMGT2 angle, to detect the number of sources. Then we use the normalized source strength (NSS) to narrow the parameters' search space and combine the differential evolution (DE) algorithm with the Levenberg-Marquardt (LM) algorithm to solve the sources' locations and magnetic moments. Simulation experiments and a field demonstration show that the VMGT2 angle is insensitive to the sign of inclination and more accurate in detecting the number of magnetic sources than the tilt angle. Meanwhile, our method can quickly locate and classify magnetic sources with high precision.

Chlorinated solvents source identification by nonlinear optimization method.

In this work, chloride ions were used as conservative tracers and supplemented with conservative amounts of chloroethenes (PCE, TCE, Cis-DCE, 1,1-DCE), chloroethanes (1,1,1-TCA, 1,1-DCA), and the carbon isotope ratios of certain compounds, the most representative on the sites studied, which is a novelty compared to the optimization methods developed in the scientific literature so far. A location of the potential missing sources is then proposed in view of the balances of the calculated mixing fractions. A test of the influence of measurement errors on the results shows that the uncertainties in the calculation of the mixture fractions are less than 11%, indicating that the source identification method developed is a robust tool for identifying sources of chlorinated solvents in groundwater.

Robust 6-DoF Pose Estimation under Hybrid Constraints.

To solve the problem of the insufficient accuracy and stability of the two-stage pose estimation algorithm using heatmap in the problem of occluded object pose estimation, a new robust 6-DoF pose estimation algorithm under hybrid constraints is proposed in this paper. First, a new loss function suitable for heatmap regression is formulated to improve the quality of the predicted heatmaps and increase keypoint accuracy in complex scenes. Second, the heatmap regression network is expanded and a translation regression branch is added to constrain the pose further. Finally, a robust pose optimization module is used to fuse the heatmap and translation estimates and improve the pose estimation accuracy. The proposed algorithm achieves ADD(-S) accuracy rates of 93.5% and 46.2% on the LINEMOD dataset and the Occlusion LINEMOD dataset, which are better than other state-of-the-art algorithms. Compared with the conventional two-stage heatmap-based pose estimation algorithms, the mean estimation error is greatly reduced, and the stability of pose estimation is improved. The proposed algorithm can run at a maximum speed of 22 FPS, thus constituting both a performant and efficient method.

Mobile Robot Localization and Mapping Algorithm Based on the Fusion of Image and Laser Point Cloud.

Given the lack of scale information of the image features detected by the visual SLAM (simultaneous localization and mapping) algorithm, the accumulation of many features lacking depth information will cause scale blur, which will lead to degradation and tracking failure. In this paper, we introduce the lidar point cloud to provide additional depth information for the image features in estimating ego-motion to assist visual SLAM. To enhance the stability of the pose estimation, the front-end of visual SLAM based on nonlinear optimization is improved. The pole error is introduced in the pose estimation between frames, and the residuals are calculated according to whether the feature points have depth information. The residuals of features reconstruct the objective function and iteratively solve the robot's pose. A keyframe-based method is used to optimize the pose locally in reducing the complexity of the optimization problem. The experimental results show that the improved algorithm achieves better results in the KITTI dataset and outdoor scenes. Compared with the pure visual SLAM algorithm, the trajectory error of the mobile robot is reduced by 52.7%. The LV-SLAM algorithm proposed in this paper has good adaptability and robust stability in different environments.

PLI-VINS: Visual-Inertial SLAM Based on Point-Line Feature Fusion in Indoor Environment.

In indoor low-texture environments, the point feature-based visual SLAM system has poor robustness and low trajectory accuracy. Therefore, we propose a visual inertial SLAM algorithm based on point-line feature fusion. Firstly, in order to improve the quality of the extracted line segment, a line segment extraction algorithm with adaptive threshold value is proposed. By constructing the adjacent matrix of the line segment and judging the direction of the line segment, it can decide whether to merge or eliminate other line segments. At the same time, geometric constraint line feature matching is considered to improve the efficiency of processing line features. Compared with the traditional algorithm, the processing efficiency of our proposed method is greatly improved. Then, point, line, and inertial data are effectively fused in a sliding window to achieve high-accuracy pose estimation. Finally, experiments on the EuRoC dataset show that the proposed PLI-VINS performs better than the traditional visual inertial SLAM system using point features and point line features.

A Resilient Method for Visual-Inertial Fusion Based on Covariance Tuning.

To improve localization and pose precision of visual-inertial simultaneous localization and mapping (viSLAM) in complex scenarios, it is necessary to tune the weights of the visual and inertial inputs during sensor fusion. To this end, we propose a resilient viSLAM algorithm based on covariance tuning. During back-end optimization of the viSLAM process, the unit-weight root-mean-square error (RMSE) of the visual reprojection and IMU preintegration in each optimization is computed to construct a covariance tuning function, producing a new covariance matrix. This is used to perform another round of nonlinear optimization, effectively improving pose and localization precision without closed-loop detection. In the validation experiment, our algorithm outperformed the OKVIS, R-VIO, and VINS-Mono open-source viSLAM frameworks in pose and localization precision on the EuRoc dataset, at all difficulty levels.

Research on Positioning Method in Underground Complex Environments Based on Fusion of Binocular Vision and IMU.

Aiming at the failure of traditional visual slam localization caused by dynamic target interference and weak texture in underground complexes, an effective robot localization scheme was designed in this paper. Firstly, the Harris algorithm with stronger corner detection ability was used, which further improved the ORB (oriented FAST and rotated BRIEF) algorithm of traditional visual slam. Secondly, the non-uniform rational B-splines algorithm was used to transform the discrete data of inertial measurement unit (IMU) into second-order steerable continuous data, and the visual sensor data were fused with IMU data. Finally, the experimental results under the KITTI dataset, EUROC dataset, and a simulated real scene proved that the method used in this paper has the characteristics of stronger robustness, better localization accuracy, small size of hardware equipment, and low power consumption.

A complex Gaussian approach to molecular photoionization.

We develop and implement a Gaussian approach to calculate partial cross-sections and asymmetry parameters for molecular photoionization. Optimal sets of complex Gaussian-type orbitals (cGTOs) are first obtained by nonlinear optimization, to best fit sets of Coulomb or distorted continuum wave functions for relevant orbital quantum numbers. This allows us to represent the radial wavefunction for the outgoing electron with accurate cGTO expansions. Within a time-independent partial wave approach, we show that all the necessary transition integrals become analytical, in both length and velocity gauges, thus facilitating the numerical evaluation of photoionization observables. Illustrative results, presented for NH3 and H2 O within a one-active-electron monocentric model, validate numerically the proposed strategy based on a complex Gaussian representation of continuum states.

Design and Implementation of Symmetric Legged Robot for Highly Dynamic Jumping and Impact Mitigation.

Aiming at highly dynamic locomotion and impact mitigation, this paper proposes the design and implementation of a symmetric legged robot. Based on the analysis of the three-leg topology in terms of force sensitivity, force production, and impact mitigation, the symmetric leg was designed and equipped with a high torque density actuator, which was assembled by a custom motor and two-stage planetary. Under the kinematic and dynamic constraints of the robot system, a nonlinear optimization for high jumping and impact mitigation is proposed with consideration of the peak impact force at landing. Finally, experiments revealed that the robot achieved a jump height of 1.8 m with a robust landing, and the height was equal to approximately three times the leg length.

A model predictive control approach to optimally devise a two-dose vaccination rollout: A case study on COVID-19 in Italy.

The COVID-19 pandemic has led to the unprecedented challenge of devising massive vaccination rollouts, toward slowing down and eventually extinguishing the diffusion of the virus. The two-dose vaccination procedure, speed requirements, and the scarcity of doses, suitable spaces, and personnel, make the optimal design of such rollouts a complex problem. Mathematical modeling, which has already proved to be determinant in the early phases of the pandemic, can again be a powerful tool to assist public health authorities in optimally planning the vaccination rollout. Here, we propose a novel epidemic model tailored to COVID-19, which includes the effect of nonpharmaceutical interventions and a concurrent two-dose vaccination campaign. Then, we leverage nonlinear model predictive control to devise optimal scheduling of first and second doses, accounting both for the healthcare needs and for the socio-economic costs associated with the epidemics. We calibrate our model to the 2021 COVID-19 vaccination campaign in Italy. Specifically, once identified the epidemic parameters from officially reported data, we numerically assess the effectiveness of the obtained optimal vaccination rollouts for the two most used vaccines. Determining the optimal vaccination strategy is nontrivial, as it depends on the efficacy and duration of the first-dose partial immunization, whereby the prioritization of first doses and the delay of second doses may be effective for vaccines with sufficiently strong first-dose immunization. Our model and optimization approach provide a flexible tool that can be adopted to help devise the current COVID-19 vaccination campaign, and increase preparedness for future epidemics.

High-resolution in vivo MR-STAT using a matrix-free and parallelized reconstruction algorithm.

MR-STAT is a recently proposed framework that allows the reconstruction of multiple quantitative parameter maps from a single short scan by performing spatial localisation and parameter estimation on the time-domain data simultaneously, without relying on the fast Fourier transform (FFT). To do this at high resolution, specialized algorithms are required to solve the underlying large-scale nonlinear optimisation problem. We propose a matrix-free and parallelized inexact Gauss-Newton based reconstruction algorithm for this purpose. The proposed algorithm is implemented on a high-performance computing cluster and is demonstrated to be able to generate high-resolution (1 mm × 1 mm in-plane resolution) quantitative parameter maps in simulation, phantom, and in vivo brain experiments. Reconstructed T1 and T2 values for the gel phantoms are in agreement with results from gold standard measurements and, for the in vivo experiments, the quantitative values show good agreement with literature values. In all experiments, short pulse sequences with robust Cartesian sampling are used, for which MR fingerprinting reconstructions are shown to fail.

Multi-Feature Nonlinear Optimization Motion Estimation Based on RGB-D and Inertial Fusion.

To achieve a high precision estimation of indoor robot motion, a tightly coupled RGB-D visual-inertial SLAM system is proposed herein based on multiple features. Most of the traditional visual SLAM methods only rely on points for feature matching and they often underperform in low textured scenes. Besides point features, line segments can also provide geometrical structure information of the environment. This paper utilized both points and lines in low-textured scenes to increase the robustness of RGB-D SLAM system. In addition, we implemented a fast initialization process based on the RGB-D camera to improve the real-time performance of the proposed system and designed a new backend nonlinear optimization framework. By minimizing the cost function formed by the pre-integrated IMU residuals and re-projection errors of points and lines in sliding windows, the state vector is optimized. The experiments evaluated on public datasets show that our system achieves higher accuracy and robustness on trajectories and in pose estimation compared with several state-of-the-art visual SLAM systems.

On Stable Parameter Estimation and Forecasting in Epidemiology by the Levenberg-Marquardt Algorithm with Broyden's Rank-one Updates for the Jacobian Operator.

Rigorously calibrating dynamic models with time-series data can pose roadblocks. Oftentimes, the problem is ill-posed and one has to rely on appropriate regularization techniques to ensure stable parameter estimation from which forward projections with quantified uncertainty could be generated. If the inversion procedure is cast as nonlinear least squares constrained by a system of nonlinear differential equations, then the system has to be solved numerically at every step of the iterative process and the corresponding parameter-to-data map cannot be used to evaluate the Fréchet derivative analytically. To address challenges related to both instability and Jacobian approximation, we propose a novel regularized Levenberg-Marquardt algorithm with iterative rank-one updates for computation of the derivative operator. In order to test the efficiency of this scheme, we conduct numerical experiments using a mathematical model of infectious disease transmission and real incidence data of historic measles outbreaks in the UK.

Methodology for improving reliability of river discharge measurements.

Programs to monitor water characteristics are undertaken to identify any possible water pollution of a river. To compute reliable water pollution loads, accurate river discharge and pollutant/tracer concentrations are required. When pollutants/tracers are measured with sufficient precision, the accuracy of river discharge measurements becomes the most critical parameter of the pollutant load computation, as well as the largest error source. The absence of permanent measuring equipment in many rivers is a common difficulty for the implementation of monitoring programs. Alternatively, quick measurement methods which are low in cost and reliability (e.g. floats) are often employed to get an estimate of river discharges, when there are budgetary and time restrictions. In this paper, an original technique, mainly for use in ungauged rivers, is proposed for correcting river discharge measurements which have low levels of accuracy; this in turn would correct pollutant concentrations. A nonlinear optimization problem is developed based on water volume and pollutant mass conservation principles for river balance nodes, taking into consideration non-measurable latent quantities. Parallel measurements of discharge and tracers for representative cross-sections of a river and its tributaries are required. The measurement conditions should refer to the steady-state hydraulic conditions usually prevailing in the flow under consideration. In order to test the reliability of the method, a virtual river example is built, defining the real values of water characteristics and generating measurement sets via Monte-Carlo simulations combining random and systematic errors. For more than 92% of the generated measurement sets, the proposed technique results in a successful and acceptable correction for the total of the measured cross-sections. Finally, the method is applied to a real river and the measurements are corrected successfully.