Cost Function Research Articles

Elliptical Halbach magnet and gradient modules for low-field portable magnetic resonance imaging.

This study aims to develop methods to design the complete magnetic system for a truly portable MRI scanner for neurological and musculoskeletal (MSK) applications, optimized for field homogeneity, field of view (FoV), and gradient performance compared to existing low-weight configurations. We explore optimal elliptic-bore Halbach configurations based on discrete arrays of permanent magnets. In this way, we seek to improve the field homogeneity and remove constraints to the extent of the gradient coils typical of Halbach magnets. Specifically, we have optimized a tightly packed distribution of magnetic Nd2Fe14B cubes with differential evolution algorithms and a second array of shimming magnets with interior point and differential evolution methods. We have also designed and constructed an elliptical set of gradient coils that extend over the whole magnet length, maximizing the distance between the lobe centers. These are optimized with a target field method minimizing a cost function that considers also heat dissipation. We have employed the new toolbox to build the main magnet and gradient modules for a portable MRI scanner designed for point-of-care and residential use. The elliptical Halbach bore has semi-axes of 10 and 14& cm, and the magnet generates a field of 87& mT homogeneous down to 5700& ppm (parts per million) in a 20-cm diameter FoV; it weighs 216& kg and has a width of 65& cm and a height of 72& cm. Gradient efficiencies go up to around 0.8& mT/m/A, for a maximum of 12& mT/m within 0.5& ms with 15& A and 15& V amplifier. The distance between lobes is 28& cm, significantly increased with respect to other Halbach-based scanners. Heat dissipation is around 25& W at maximum power, and gradient deviations from linearity are below 20% in a 20-cm sphere. Elliptic-bore Halbach magnets enhance the ergonomicity and field distribution of low-cost portable MRI scanners, while allowing for full-length gradient support to increase the FoV. This geometry can be potentially adapted for a prospective low-cost whole-body technology.

Robust Underwater Direction-of-Arrival Estimation Method Using Acoustic Sensor Array under Unknown Swing Deviation Elements

This paper presents a strategy called the alternating iterative minimization method (AIMM), aimed at enhancing the precision of direction of arrival (DOA) estimation when utilizing an acoustic vector sensor array (AVSA) with unknown swing deviation elements (SDEs). The AVSA model with unknown SDEs is formulated by incorporating the swing deviation parameter. Later, to estimate the swing deviation matrix (SDM) and the sparse signal power by using the alternating iteration method, the auxiliary cost functions with respect to SDM and the sparse signal power are formulated based on the regularized weighted least squares (RWLS) and regularized covariance matrix fitting (RCMF) criteria. Furthermore, their analytical expressions have also been quantified. In order to mitigate the effect of unknown SDEs on the accuracy of DOA estimation, any sub-time segment (STS) in the dataset is selected as the reference to convert the received data of different STS into the reference STS using the estimated SDM. The simulation and experimental outcomes conclusively represent the effectiveness of the suggested TSIM approach using AVSA in handling unknown SDEs.

Efficient nonlinear model predictive and active disturbance rejection control for trajectory tracking of unmanned vehicles

This article proposes an efficient trajectory tracking control strategy of unmanned vehicles. The method is based on nonlinear model predictive control (NMPC) and active disturbance reject control (ADRC). The designed control algorithm considers three challenges including nonlinear characteristics, multiple constraints, and external disturbance. First, NMPC method is presented for the nonlinear vehicle model with multiple constraints. To relax inequality constraints and reduce the heavy calculation burden, the penalty term with the variable factor is added to the cost function, an improved continuous/generalized minimum residual method is proposed to solve NMPC online optimization problem. Then, an ADRC scheme is designed to estimate the unknown disturbance via extended state observer, and compensate them by feedback control law in real time, the corresponding parameters are obtained by a novel particle swarm optimization algorithm to further improve the control precision. It ensures the stability to a certain extent. Finally, the results indicate the designed algorithm can raise the calculation efficiency and meet the real-time requirements, and obviously increase the tracking accuracy and robustness performance.

Cognitive dissonance and introversion effects on opinion dynamics and echo chamber formation

Bounded confidence models (BCM) are extensively used to model continuous opinion dynamics in social networks. Typically, these models are analysed on static networks where edges do not vary over time. Following in the footsteps of adaptive voter models, further research has considered BCMs in the setting where agents are able to dynamically adjust their edges, which subsequently feedback into the opinion dynamics of the network. Several methods of updating connections have been proposed ranging from random rewiring to more sophisticated approaches based on concordant edges, homophily and cognitive dissonance. We present a modified form of the bounded confidence model, termed the selfish agent opinion (SAO) model, where connection updates are evaluated using a general cost function. Agents in the SAO model maintain two classes of relationships, friends and acquaintances, based on which they update their opinions and edges to optimise a payoff function that may include multiple social factors. This paper explores the effects, which we describe as “cognitive dissonance” and “introversion” that attempt to mimic postulated behaviours associated with the social concepts of the same name, on social network and opinion dynamics. We find that the SAO model naturally produces echo chambers for social networks with increased sensitivity to cognitive dissonance, whilst introversion produces high levels of fragmentation and low opinion mobility. Additionally, the effect of tolerant agents and inquisitive social encounters is investigated. It is found that both the presence of very small numbers of tolerant agents and inquisitive encounters are able to strongly promote consensus formation.

Considering the Cost-Effectiveness of Accredited Continuing Medical Education: A Landscape Analysis of Economic Concepts in Continuing Medical Education Research.

In health care, cost-effectiveness analysis evaluates changes in health outcomes as a function of costs. The cost-effectiveness of continuing professional development for health care providers has not been historically well characterized despite substantial investment. This literature review identified publications considering the costs and cost-effectiveness of accredited continuing medical education activities. Searches were conducted for English language records in PubMed and the gray literature using a 10-year lookback period from March 10, 2023. Search terms included concepts related to continuing medical education, cost, effect, and utilization. One reviewer conducted title/abstract screening, full-text review, and data extraction, with direction and adjudication of search and screening concepts provided by the lead advisor. Publications were categorized as related to costs of an educational intervention (Concept 1) and/or the impact of education on health care costs (Concept 2). Results were summarized using descriptive statistics. A total of 668 database records were screened, 125 (19%) underwent full-text review, and 25 of 125 (20%) were accepted; 7 of 351 (2%) gray literature sources were accepted for a total of 32 included records. The most common reason for rejection was not being an accredited activity. Of the 32 records, 27 (84%) were related to Concept 1 only, 3 (9%) to Concept 2 only, and 2 (6%) to both Concepts 1 and 2. Approximately half (n = 19, 59%) mentioned costs without supporting data. These findings show that considerations of cost and cost-effectiveness are rare in the accredited continuing medical education literature, which may limit how the value of continuing medical education is characterized.

OPTIMIZATION OF LOADING AND UNLOADING WORKS AND PLACEMENT OF TARED AND PIECE CARGOES IN VEHICLES AND WAREHOUSES USING THE METHODS OF ERGONOMICS AND THEORY OF SYSTEMS

Purpose. The tasks of optimizing the placement of tared and piece cargoes (or the task of loading) in a limited volume (capacity) are typical for cases of loading with tared and piece cargoes (mainly large-sized) of transport containers, car bodies, ship holds in the merchant fleet, transport aircraft, railway wagons, areas of the warehouse complex. At the same time, the safe and efficient performance of loading and unloading operations with tared and piece cargoes, including large-sized ones, in a limited space is directly related to taking into account the requirements and using ergonomic methods. The purpose of this paper is to develop a mathematical model for the optimization of the placement of tared and piece cargoes (or about loading) in a limited volume (capacity), which is used to select a subset of cargo units with the maximum relative utility, while observing the limit on the total volume (or mass) of cargo. Methods. The analysis of literary sources made it possible to establish that for modeling and solving the problem of optimizing the placement of cargo (or loading) in a limited volume (capacity), it is rational to use one of the exact solution methods (dynamic programming method), the number of stages of which is the number of types of cargo. The work uses the method of dynamic programming, methods of theory of systems, and linear optimization. Results. The article presents a mathematical model of the problem of optimal placement of tared and piece cargoes (or about loading) in a limited volume, and for the case of placing weapons, ammunition, weapons, it is proposed to maximize not the function of the total cost (value) of the cargo, but the function that would take into account the relative usefulness of each cargo. The relative usefulness of each cargo is proposed to be determined by expert methods of systems theory, for example, the Delphi method, which is well formalized and suitable for computer processing of results. Scientific novelty. The scientific novelty consists in the development of a mathematical model that allows solving the problem of optimal placement of container loads (or loading) in a limited volume, and the target function of the optimization model is proposed to be the total relative usefulness of the cargo. Practical significance. Defined ergonomic requirements for cargo operations with tared and piece cargoes in a limited space (vehicles, warehouses). A method of numerical calculation based on the model is proposed (the case of loading a car body with tared and piece cargoes). In further research, the obtained results will be used for computer simulation according to the developed model using the Solver tool of Microsoft Excel.

An iterative learning-based integrated motion planning and control method for autonomous patrolling of unmanned surface vehicles

Abstract The minimization of maritime patrol durations and the optimization of patrol trajectories are still a prevailing challenge for autonomous navigation of unmanned surface vehicles (USVs). In this paper, we propose an integrated trajectory planning and control method to achieve time-optimal autonomous patrol of USVs by a data-efficient iterative learning-based predictive control algorithm. We build the optimization problem of the algorithm by introducing a local cost and a local safe constraint set for closed-loop efficient data-driven learning. To guarantee recursive feasibility, stability and convergence properties of the optimization algorithm at each iteration, the local cost and the local constraint set are designed and update iteratively using the historical vehicle states at previous iterations as a dataset. Different from traditional optimization methods, the proposed method does not require a reference path. The cost function of the optimization method decreases monotonically and converge to obtain a time-optimal control law for trajectory planning and tracking of USVs only after several iterations. The proposed approach is validated on the robotic operation system in typical maritime patrol scenarios. The results show that the proposed method implement a 5% reduction of patrol time, fewer lateral track errors, and smoother trajectories compared to the traditional MPC algorithm under water flow conditions. In addition, Enhancements in patrol operation efficiency of USVs are achieved by the algorithm, even under the constraints of varied patrol paths, attesting to its versatility.

Automatic Optimal Robotic Base Placement for Collaborative Industrial Robotic Car Painting

This paper investigates the problem of optimal base placement in collaborative robotic car painting. The objective of this problem is to find the optimal fixed base positions of a collection of given articulated robotic arms on the factory floor/ceiling such that the possibility of vehicle paint coverage is maximized while the possibility of robot collision avoidance is minimized. Leveraging the inherent two-dimensional geometric features of robotic car painting, we construct two types of cost functions that formally capture the notions of paint coverage maximization and collision avoidance minimization. Using these cost functions, we formulate a multi-objective optimization problem, which can be readily solved using any standard multi-objective optimizer. Our resulting optimal base placement algorithm decouples base placement from motion/trajectory planning. In particular, our computationally efficient algorithm does not require any information from motion/trajectory planners a priori or during base placement computations. Rather, it offers a hierarchical solution in the sense that its generated results can be utilized within already available robotic painting motion/trajectory planners. Our proposed solution’s effectiveness is demonstrated through simulation results of multiple industrial robotic arms collaboratively painting a Ford F-150 truck.

A new model predictive current control strategy for PMSM based on extended control set and dynamic cost function

A new model predictive current control strategy for PMSM based on extended control set and dynamic cost function

Optimizing Performance in Wireless Sensor Networks through a Multi-Objective Rendezvous Points Selection Algorithm

Wireless sensor networks (WSNs) play a vital role in modern research and applications due to their potential to gather data from various environments. Because sensor nodes (SNs) within WSNs have limited battery life, those in close proximity to the sink often experience rapid power depletion, leading to the emergence of hotspot issues. To address this, the concept of a mobile sink (MS) has emerged as a potential solution, effectively mitigating power usage in SNs and thereby extending the network’s overall lifespan. Furthermore, many sensor-based applications necessitate specific data collection timeframes, underscoring the necessity of effective strategies. Leveraging rendezvous points (RPs) to enhance network efficiency becomes imperative in enabling the MS to efficiently collect data from all SNs within designated time periods. A sophisticated cost function is employed to strategically determine RPs, considering multiple factors that influence the efficacy of each RP. This process culminates in the selection of RPs, optimizing for the longest path with minimal delays. Through the proposed hybrid mobile vehicle (HMV) method, compared against the prevailing MOOVor method, significant enhancements are observed in terms of sensor coverage and reduced hop count within the network.

Strategic manipulation of preferences in the rank minimization mechanism

We consider one-sided matching problems, where agents are allocated items based on stated preferences. Posing this as an assignment problem, the average rank of obtained matchings can be minimized using the rank minimization (RM) mechanism. RM matchings can have significantly better rank distributions than matchings obtained by mechanisms with random priority, such as Random Serial Dictatorship. However, these matchings are sensitive to preference manipulation from strategic agents. In this work we consider a scenario where agents aim to be matched to their top-n preferred items using the RM mechanism, and strategically manipulate their preferences to achieve this. We derive a best response strategy for an agent to be assigned to their n most preferred items using the Hungarian algorithm, under a simplified cost function. This strategy is then extended to a first-order heuristic strategy for being matched to the top-n items in a setup that minimizes the average rank. Based on this finding, an empirical study is conducted examining the impact of the first-order heuristic strategy. The study utilizes data from both simulated markets and real-world matching markets in Amsterdam, taking into account variations in item popularity, fractions of strategic agents, and the preferences for the n most favored items. For most scenarios, RM yields more rank efficient matches than Random Serial Dictatorship, even when agents apply the first-order heuristic strategy. However, although highly market dependent, the matching performance can become worse when 50% of agents or more want to be matched to their top-1 or top-2 preferred items and apply the first-order heuristic strategy to achieve this.

ℓ 1 -Regularized ICA: A Novel Method for Analysis of Task-Related fMRI Data.

We propose a new method of independent component analysis (ICA) in order to extract appropriate features from high-dimensional data. In general, matrix factorization methods including ICA have a problem regarding the interpretability of extracted features. For the improvement of interpretability, sparse constraint on a factorized matrix is helpful. With this background, we construct a new ICA method with sparsity. In our method, the ℓ1-regularization term is added to the cost function of ICA, and minimization of the cost function is performed by a difference of convex functions algorithm. For the validity of our proposed method, we apply it to synthetic data and real functional magnetic resonance imaging data.

Enhancing Autoencoder-Based Machine Learning through the Use of Process Control Gain and Relative Gain Arrays as Cost Functions

Enhancing Autoencoder-Based Machine Learning through the Use of Process Control Gain and Relative Gain Arrays as Cost Functions

Source Range Estimation Using Linear Frequency-Difference Matched Field Processing in a Shallow Water Waveguide

Matched field processing (MFP) is an established technique for source localization in known multipath acoustic environments. Unfortunately, in many situations, imperfect knowledge of the actual propagation environment and sidelobes due to modal interference prevent accurate propagation modeling and source localization via MFP. To suppress the sidelobes and improve the method’s robustness, a linear frequency-difference matched field processing (LFDMFP) method for estimating the source range is proposed. A two-neighbor-frequency high-order cross-spectrum between the measurement and the replica of each hydrophone of the vertical line array is first computed. The cost function can then be derived from the dual summation or double integral of the high-order cross-spectrum with respect to the depth of the hydrophones and the candidate sources of the replicas, where the range that corresponds to the minimum is the optimal estimation. Because of the larger modal interference distances, LFDMFP can efficiently provide only one optimal range within the same range search interval rather than some conventional matched field processing. The efficiency of the presented method was verified using simulations and experiments. The LFDMFP unambiguously estimated the source range in two experimental datasets with average relative errors of 2.2 and 1.9%.

A mathematical primer to classical deep learning

This manuscript synthesizes the statistical foundations of classical deep learning by integrating insights from eight seminal works. It covers matrix calculus, neuron layers, weight and bias indexing, cost functions, differentiation of neuron operations, activation functions, bias functions, gradient descent, and backpropagation algorithms. The synthesis aims to provide a comprehensive understanding of the mathematical and statistical principles underpinning deep learning models, facilitating their application and further development in various domains.

Automatic multi-storey building partitioning from point cloud via bidirectional cloth simulation

With the advancements in scanning technology, the rapid acquisition of point cloud spanning multiple storeys of buildings has become feasible. Accurately dividing the building into individual storeys deepens the understanding of the building environment, accelerates the processing of the vast point cloud, and is crucial for numerous fields such as model reconstruction, indoor navigation, and building management. However, it remains a challenge to handle the building with rooms across multiple storeys. This study presents a novel method to partition complex multi-storey building from cluttered point cloud. First, the non-vertical structural elements are detected by taking the difference of height and normal vector as growth conditions. Next, we iteratively employ bidirectional cloth with height variation constraints to simulate the floor and ceiling trend surface. In this step, candidate ceiling patches are obtained through the optimization of a cost function. Finally, the irregular boundary between adjacent storeys that used for partitioning the point cloud is rasterized in terms of the ceilings at lower storey and the floors at upper storey. Each point is orderly classified into the correspond storey with reference to the elevation of the estimated boundary. Through comprehensive evaluation and analysis, our method has demonstrated its effectiveness and adaptability across various datasets. Our method yields superior results compared to the advanced methods, achieving an approximate value of 99 % on the weighted recall, weighted precision and weighted F1-score. Besides, the proposed method is not limited to Manhattan world buildings and requires only the spatial coordinate of points.

Uncertainty Estimation for Dual View X-ray Mammographic Image Registration Using Deep Ensembles.

Techniques are developed for generating uncertainty estimates for convolutional neural network (CNN)-based methods for registering the locations of lesions between the craniocaudal (CC) and mediolateral oblique (MLO) mammographic X-ray image views. Multi-view lesion correspondence is an important task that clinicians perform for characterizing lesions during routine mammographic exams. Automated registration tools can aid in this task, yet if the tools also provide confidence estimates, they can be of greater value to clinicians, especially in cases involving dense tissue where lesions may be difficult to see. A set of deep ensemble-based techniques, which leverage a negative log-likelihood (NLL)-based cost function, are implemented for estimating uncertainties. The ensemble architectures involve significant modifications to an existing CNN dual-view lesion registration algorithm. Three architectural designs are evaluated, and different ensemble sizes are compared using various performance metrics. The techniques are tested on synthetic X-ray data, real 2D X-ray data, and slices from real 3D X-ray data. The ensembles generate covariance-based uncertainty ellipses that are correlated with registration accuracy, such that the ellipse sizes can give a clinician an indication of confidence in the mapping between the CC and MLO views. The results also show that the ellipse sizes can aid in improving computer-aided detection (CAD) results by matching CC/MLO lesion detects and reducing false alarms from both views, adding to clinical utility. The uncertainty estimation techniques show promise as a means for aiding clinicians in confidently establishing multi-view lesion correspondence, thereby improving diagnostic capability.

Experimental Evaluation of Damping and Stiffness in Optimized Active Sport Utility Vehicle Suspension Systems

On a flat city road, the specificity of the suspension poses a challenge. Sport utility vehicles (SUVs) have less flexibility compared to regular cars, despite providing a firm grip on asphalt and concrete. Constant adjustments to the center of gravity of SUVs are necessary. Surprisingly, they are less reliable and stable in urban settings due to this characteristic. In this study, a mathematical model of the suspension system of SUVs based on the Newtonian approach is introduced and validated with data from experiments carried out by the MTS machine system on the mono-tube (oil/air) mixed damper element. The model accurately predicts the performance of this damper, commonly used in SUVs, across various operating conditions, including different frequencies. A coil spring element, serving as a passive suspension unit with this damper, is also tested experimentally under similar conditions. By integrating passive suspension elements with the active actuator, the proposed modified design reduces the power consumption needed for the actuator to function and ensures a certain level of reliability. The effectiveness and performance of the modified active suspension system in comparison to the traditional passive suspension system are assessed using three different strategies: hybrid PID-LQR, linear quadratic regulator (LQR), and proportional-integral-derivative (PID). The genetic algorithm is utilized to determine the optimal parameter values for each controller by minimizing a cost function, maximizing performance, and minimizing energy consumption. Simulation results demonstrate that the active suspension system controlled by the PID-LQR controller offers significantly improved ride comfort and vehicle stability compared to other systems. This suggests that the performance of the active suspension system is greatly enhanced by the combined application of the hybrid PID-LQR controller compared to other systems.

Fast convergence to non-isolated minima: four equivalent conditions for $${\textrm{C}^{2}}$$ functions

AbstractOptimization algorithms can see their local convergence rates deteriorate when the Hessian at the optimum is singular. These singularities are inescapable when the optima are non-isolated. Yet, under the right circumstances, several algorithms preserve their favorable rates even when optima form a continuum (e.g., due to over-parameterization). This has been explained under various structural assumptions, including the Polyak–Łojasiewicz condition, Quadratic Growth and the Error Bound. We show that, for cost functions which are twice continuously differentiable ($$\textrm{C}^2$$ C 2 ), those three (local) properties are equivalent. Moreover, we show they are equivalent to the Morse–Bott property, that is, local minima form differentiable submanifolds, and the Hessian of the cost function is positive definite along its normal directions. We leverage this insight to improve local convergence guarantees for safe-guarded Newton-type methods under any (hence all) of the above assumptions. First, for adaptive cubic regularization, we secure quadratic convergence even with inexact subproblem solvers. Second, for trust-region methods, we argue capture can fail with an exact subproblem solver, then proceed to show linear convergence with an inexact one (Cauchy steps).

A comprehensive design pipeline for FCEV powertrain configuration considering the evolutionary development process and extreme economic performance

Due to stringent emission regulations, the zero-emission hydrogen fuel cell electric vehicles (FCEVs) are gaining significant attention, but their slow power response requires careful selection of auxiliary energy sources and power systems to optimize energy efficiency. This paper presents a comprehensive design pipeline for the FCEV powertrain, encompassing methods for powertrain configuration design, feasible domain design for component parameters, and parameter matching. Initially, a powertrain configuration design method based on evolutionary game theory is introduced, forecasting trends in energy-efficient powertrain configurations using a dynamic cost function that adjusts based on the proportions of different configurations. Next, a feasible domain design method is developed to establish fixed constraints on component parameters, ensuring a fair balance between performance needs and overall costs, including development and lifecycle expenses associated with the powertrain configuration. Subsequently, dynamic programming (DP) is used for parameter matching, assessing the utmost energy-saving potential. The cost function in this method incorporates the degradation cost of powertrain components, underscoring the economic performance of the target FCEV over its lifespan. Finally, simulation assessments indicate that the proposed design pipeline effectively identifies the optimal powertrain configuration for FCEVs, endowing each possible configuration with exceptional economic efficiency across different component parameters.