Hispanic Thrifty Food Plan (H-TFP): Healthy, Affordable, and Culturally Relevant.

The USDA Thrifty Food Plan (TFP) is a federal estimate of a healthy diet at lowest cost for US population groups defined by gender and age. The present goal was to develop a version of the TFP that was more tailored to the observed dietary patterns of self-identified Hispanic participants in NHANES 2013-16. Analyses used the same national food prices and nutrient composition data as the TFP 2021. Diet quality was measured using the Healthy Eating Index 2015. The new Hispanic TFP (H-TFP) was cost-neutral with respect to TFP 2021 and fixed at $186/week for a family of four. Two H-TFP models were created using a quadratic programming (QP) algorithm. Fresh pork was modeled separately from other red meats. Hispanic NHANES participants were younger, had lower education and incomes, but had similar or higher HEI 2015 scores than non-Hispanics. Their diet included more pulses, beans, fruit, 100% juice, grain-based dishes, and soups, but less pizza, coffee, candy, and desserts. The H-TFP market basket featured more pork, whole grains, 100% fruit juice, and cheese. The second TFP model showed that pork could replace both poultry and red meat, while satisfying all nutrient needs. A vegetarian H-TFP proved infeasible for most age-gender groups. Healthy, affordable, and culturally relevant food plans can be developed for US population subgroups.

Low-carbon diets across diverse dietary patterns: Addressing population heterogeneity under constrained optimization.

Mathematical optimization is a useful tool for modeling diets that fulfill requirements for health and environmental sustainability, however, population-based optimization approaches fail to account for underlying dietary diversity in populations. This study proposes a methodological approach to consider diverse dietary intake patterns in mathematical optimization of nutritionally adequate low-carbon diets and investigates the differences between different population groups, along with trade-offs between greenhouse gas emission (GHGE) reduction and the inconvenience of dietary changes required to achieve optimized diets. A k-means clustering analysis was applied to individual dietary intake data from Denmark, which resulted in four clusters with different dietary patterns. This was followed by quadratic programming, wherein the total dietary changes required from the observed diet within each cluster were used as a proxy for consumer inconvenience (i.e., "inconvenience index") and were minimized while fulfilling nutrient constraints and incrementally tightened GHGE constraints. Across clusters, a steep increase of the inconvenience index was observed at GHGE levels below approximately 3 kg CO2e/10 MJ, corresponding to GHGE reductions of 24-36 % in different clusters. In all clusters, the optimized diets with nutritional and GHGE constraints showed common traits of increased content of cereals and starches, eggs, and fish and decreased amounts of beef and lamb, cheese, animal-based fats, and alcoholic beverages, but differences across clusters were also observed, maintaining characteristics of the clusters' baselines. When additional health-based targets for food amounts were applied as constraints, the optimized diets converged towards the same type of diet. The total inconvenience of dietary changes required to fulfill constraints differed between clusters, indicating that specific sub-populations may be more effective targets for dietary transition. The method has potential for future integration of more sustainability aspects and different consumer preferences.

A hybrid, nonlinear programming approach for optimizing passive shimming in MRI.

BACKGROUND: In magnetic resonance imaging (MRI), maintaining a highly uniform main magnetic field (B0) is essential for producing detailed images of human anatomy. Passive shimming (PS) is a technique used to enhance B0 uniformity by strategically arranging shimming iron pieces inside the magnet bore. Traditionally, PS optimization has been implemented using linear programming (LP), posing challenges in balancing field quality with the quantity of iron used for shimming. PURPOSE: In this work, we aimed to improve the efficacy of passive shimming that has the advantages of balancing field quality, iron usage, and harmonics in an optimal manner and leads to a smoother field profile. METHODS: This study introduces a hybrid algorithm that combines particle swarm optimization with sequential quadratic programming (PSO-SQP) to enhance shimming performance. Additionally, a regularization method is employed to reduce the iron pieces' weight effectively. RESULTS: The simulation study demonstrated that the magnetic field was improved from 462  to 3.6 ppm, utilizing merely 1.2 kg of iron in a 40 cm diameter spherical volume (DSV) of a 7T MRI magnet. Compared to traditional optimization techniques, this method notably enhanced magnetic field uniformity by 96.7% and reduced the iron weight requirement by 81.8%. CONCLUSION: The results indicated that the proposed method is expected to be effective for passive shimming.

Research on Trajectory Planning of Autonomous Vehicles in Constrained Spaces.

This paper addresses the challenge of trajectory planning for autonomous vehicles operating in complex, constrained environments. The proposed method enhances the hybrid A-star algorithm through back-end optimization. An adaptive node expansion strategy is introduced to handle varying environmental complexities. By integrating Dijkstra's shortest path search, the method improves direction selection and refines the estimated cost function. Utilizing the characteristics of hybrid A-star path planning, a quadratic programming approach with designed constraints smooths discrete path points. This results in a smoothed trajectory that supports speed planning using S-curve profiles. Both simulation and experimental results demonstrate that the improved hybrid A-star search significantly boosts efficiency. The trajectory shows continuous and smooth transitions in heading angle and speed, leading to notable improvements in trajectory planning efficiency and overall comfort for autonomous vehicles in challenging environments.

Solving general convex quadratic multi-objective optimization problems via a projection neurodynamic model.

A neural network model is constructed to solve convex quadratic multi-objective programming problem (CQMPP). The CQMPP is first converted into an equivalent single-objective convex quadratic programming problem by the mean of the weighted sum method, where the Pareto optimal solution (POS) are given by diversifying values of weights. Then, for given various values weights, multiple projection neural networks are employded to search for Pareto optimal solutions. Based on employing Lyapunov theory, the proposed neural network approach is established to be stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the single-objective problem. The simulation results also show that the presented model is feasible and efficient.

Adaptive fractional-order nonsingular terminal sliding mode control and sequential quadratic programming torque distribution for lateral stability of FWID-EVs with actuator constraints.

This paper proposes a novel sliding mode control (SMC) algorithm for direct yaw moment control of four-wheel independent drive electric vehicles (FWID-EVs). The algorithm integrates adaptive law theory, fractional-order theory, and nonsingular terminal sliding mode reaching law theory to reduce chattering, handle uncertainty, and avoid singularities in the SMC system. A sequential quadratic programming (SQP) method is also proposed to optimize the yaw moment distribution under actuator constraints. The performance of the proposed algorithm is evaluated by a hardware-in-the-loop test with two driving maneuvers and compared with two existing SMC-based schemes together with the cases with the change of vehicle parameters and disturbances. The results demonstrate that the proposed algorithm can eliminate chattering and achieve the best lateral stability as compared with the existing schemes.

Fault-Tolerant Control of Autonomous Underwater Vehicle Actuators Based on Takagi and Sugeno Fuzzy and Pseudo-Inverse Quadratic Programming under Constraints.

Autonomous Underwater Vehicles (AUVs) play a significant role in ocean-related research fields as tools for human exploration and the development of marine resources. However, the uncertainty of the underwater environment and the complexity of underwater motion pose significant challenges to the fault-tolerant control of AUV actuators. This paper presents a fault-tolerant control strategy for AUV actuators based onTakagi and Sugeno (T-S) fuzzy logic and pseudo-inverse quadratic programming under control constraints, aimed at addressing potential actuator faults. Firstly, considering the steady-state performance and dynamic performance of the control system, a T-S fuzzy controller is designed. Next, based on the redundant configuration of the actuators, the propulsion system is normalized, and the fault-tolerant control of AUV actuators is achieved using the pseudo-inverse method under thrust allocation. When control is constrained, a quadratic programming approach is used to compensate for the input control quantity. Finally, the effectiveness of the fuzzy control and fault-tolerant control allocation methods studied in this paper is validated through mathematical simulation. The experimental results indicate that in various fault scenarios, the pseudo-inverse combined with a nonlinear quadratic programming algorithm can compensate for the missing control inputs due to control constraints, ensuring the normal thrust of AUV actuators and achieving the expected fault-tolerant effect.

Optimizing heat source distribution in sintering molds: Integrating response surface model with sequential quadratic programming.

The sintering mold imposes strict requirements for temperature uniformity. The mold geometric parameters and the power configuration of heating elements exert substantial influence. In this paper, we introduce an optimization approach that combines response surface models with the sequential quadratic programming algorithm to optimize the geometric parameters and heating power configuration of a heating system for sintering mold. The response surface models of the maximum temperature difference, maximum temperature, and minimum temperature of the sintering area are constructed utilizing the central composite design method. The model's reliability is rigorously confirmed through variance analysis, residual analysis, and generalization capability validation. The models demonstrate remarkable predictive accuracy within the design space. A nonlinear constrained optimization model is established based on the response surface models, and the optimal parameters are obtained after 9 iterations using the sequential quadratic programming algorithm. Under the optimal parameters, the maximum temperature difference is maintained at less than 5 °C, confirming exceptional temperature uniformity. We conduct parameter analysis based on standardized effects to determine the main influencing factors of temperature uniformity, revealing that the distance between adjacent heating rods and the power density of the inner heating rods exert significant influence. Enhanced temperature uniformity can be achieved by adopting a larger distance between heating rods and configuring the power density of the heating rods to a relatively modest level. This work introduces a practical approach to optimize the heating systems for sintering molds, with potential applications in various industrial mold optimization.

Shape restricted additive hazards models: Monotone, unimodal, and U-shape hazard functions.

We consider estimation of the semiparametric additive hazards model with an unspecified baseline hazard function where the effect of a continuous covariate has a specific shape but otherwise unspecified. Such estimation is particularly useful for a unimodal hazard function, where the hazard is monotone increasing and monotone decreasing with an unknown mode. A popular approach of the proportional hazards model is limited in such setting due to the complicated structure of the partial likelihood. Our model defines a quadratic loss function, and its simple structure allows a global Hessian matrix that does not involve parameters. Thus, once the global Hessian matrix is computed, a standard quadratic programming method can be applicable by profiling all possible locations of the mode. However, the quadratic programming method may be inefficient to handle a large global Hessian matrix in the profiling algorithm due to a large dimensionality, where the dimension of the global Hessian matrix and number of hypothetical modes are the same order as the sample size. We propose the quadratic pool adjacent violators algorithm to reduce computational costs. The proposed algorithm is extended to the model with a time-dependent covariate with monotone or U-shape hazard function. In simulation studies, our proposed method improves computational speed compared to the quadratic programming method, with bias and mean square error reductions. We analyze data from a recent cardiovascular study.

A framework for the analysis of skin sores disease using evolutionary intelligent computing approach.

The most common and contagious bacterial skin disease i.e. skin sores (impetigo) mostly affects newborns and young children. On the face, particularly around the mouth and nose area, as well as on the hands and feet, it typically manifests as reddish sores. In this study, a neuro-evolutionary global algorithm is introduced to solve the dynamics of nonlinear skin sores disease model (SSDM) with the help of an artificial neural network. The global genetic algorithm is integrated with local sequential quadratic programming (GA-LSQP) to obtain the optimal solution for the proposed model. The designed differential model of skin sores disease is comprised of susceptible (S), infected (I), and recovered (R) categories. An activation function based neural network modeling is exploited for skin sores system through mean square error to achieve best trained weights. The integrated approach is validated and verified through the comparison of results of reference Adam strategy with absolute error analysis. The absolute error results give accuracy of around 10-11 to 10-5, demonstrating the worthiness and efficacy of proposed algorithm. Additionally, statistical investigations in form of mean absolute deviation, root mean square error, and Theil's inequality coefficient are exhibited to prove the consistency, stability, and convergence criteria of the integrated technique. The accuracy of the proposed solver has been examined from the smaller values of minimum, median, maximum, mean, semi-interquartile range, and standard deviation, which lie around 10-12 to 10-2.

Zhang equivalency of inequation-to-inequation type for constraints of redundant manipulators.

In solving specific problems, physical laws and mathematical theorems directly express the connections between variables with equations/inequations. At times, it could be extremely hard or not viable to solve these equations/inequations directly. The PE (principle of equivalence) is a commonly applied pragmatic method across multiple fields. PE transforms the initial equations/inequations into simplified equivalent equations/inequations that are more manageable to solve, allowing researchers to achieve their objectives. The problem-solving process in many fields benefits from the use of PE. Recently, the ZE (Zhang equivalency) framework has surfaced as a promising approach for addressing time-dependent optimization problems. This ZEF (ZE framework) consolidates constraints at different tiers, demonstrating its capacity for the solving of time-dependent optimization problems. To broaden the application of ZEF in time-dependent optimization problems, specifically in the domain of motion planning for redundant manipulators, the authors systematically investigate the ZEF-I2I (ZEF of the inequation-to-inequation) type. The study concentrates on transforming constraints (i.e., joint constraints and obstacles avoidance depicted in different tiers) into consolidated constraints backed by rigorous mathematical derivations. The effectiveness and applicability of the ZEF-I2I are verified through two optimization motion planning schemes, which consolidate constraints in the velocity-tier and acceleration-tier. Schemes are required to accomplish the goal of repetitive motion planning within constraints. The firstly presented optimization motion planning schemes are then reformulated as two time-dependent quadratic programming problems. Simulative experiments conducted on the basis of a six-joint redundant manipulator confirm the outstanding effectiveness of the firstly presented ZEF-I2I in achieving the goal of motion planning within constraints.

First/second-order predefined-time convergent ZNN models for time-varying quadratic programming and robotic manipulator application.

Zeroing neural network (ZNN) model, an important class of recurrent neural network, has been widely applied in the field of computation and optimization. In this paper, two ZNN models with predefined-time convergence are proposed for the time-varying quadratic programming (TVQP) problem. First, in the framework of the traditional ZNN model, the first-order predefined-time convergent ZNN (FPTZNN) model is proposed in combination with a predefined-time controller. Compared with the existing ZNN models, the proposed ZNN model is error vector combined with sliding mode control technique. Then, the FPTZNN model is further extended and the second-order predefined-time convergent ZNN (SPTZNN) model is developed. Combined with the Lyapunov method and the concept of predefined-time stability, it is shown that the proposed FPTZNN and SPTZNN models have the properties of predefined-time convergence, and their convergence time can be flexibly adjusted by predefined-time control parameters. Finally, the proposed FPTZNN and SPTZNN models are compared with the existing ZNN models for the TVQP problem in simulation experiment, and the simulation experiment results verify the effectiveness and superior performance of the proposed FPTZNN and SPTZNN models. In addition, the proposed FPTZNN model for robot motion planning problem is applied and successfully implemented to verify the practicality of the model.

Endoscope Automation Framework with Hierarchical Control and Interactive Perception for Multi-Tool Tracking in Minimally Invasive Surgery.

In the context of Minimally Invasive Surgery, surgeons mainly rely on visual feedback during medical operations. In common procedures such as tissue resection, the automation of endoscopic control is crucial yet challenging, particularly due to the interactive dynamics of multi-agent operations and the necessity for real-time adaptation. This paper introduces a novel framework that unites a Hierarchical Quadratic Programming controller with an advanced interactive perception module. This integration addresses the need for adaptive visual field control and robust tool tracking in the operating scene, ensuring that surgeons and assistants have optimal viewpoint throughout the surgical task. The proposed framework handles multiple objectives within predefined thresholds, ensuring efficient tracking even amidst changes in operating backgrounds, varying lighting conditions, and partial occlusions. Empirical validations in scenarios involving single, double, and quadruple tool tracking during tissue resection tasks have underscored the system's robustness and adaptability. The positive feedback from user studies, coupled with the low cognitive and physical strain reported by surgeons and assistants, highlight the system's potential for real-world application.

ICON-GEMs: integration of co-expression network in genome-scale metabolic models, shedding light through systems biology.

BACKGROUND: Flux Balance Analysis (FBA) is a key metabolic modeling method used to simulate cellular metabolism under steady-state conditions. Its simplicity and versatility have led to various strategies incorporating transcriptomic and proteomic data into FBA, successfully predicting flux distribution and phenotypic results. However, despite these advances, the untapped potential lies in leveraging gene-related connections like co-expression patterns for valuable insights. RESULTS: To fill this gap, we introduce ICON-GEMs, an innovative constraint-based model to incorporate gene co-expression network into the FBA model, facilitating more precise determination of flux distributions and functional pathways. In this study, transcriptomic data from both Escherichia coli and Saccharomyces cerevisiae were integrated into their respective genome-scale metabolic models. A comprehensive gene co-expression network was constructed as a global view of metabolic mechanism of the cell. By leveraging quadratic programming, we maximized the alignment between pairs of reaction fluxes and the correlation of their corresponding genes in the co-expression network. The outcomes notably demonstrated that ICON-GEMs outperformed existing methodologies in predictive accuracy. Flux variabilities over subsystems and functional modules also demonstrate promising results. Furthermore, a comparison involving different types of biological networks, including protein-protein interactions and random networks, reveals insights into the utilization of the co-expression network in genome-scale metabolic engineering. CONCLUSION: ICON-GEMs introduce an innovative constrained model capable of simultaneous integration of gene co-expression networks, ready for board application across diverse transcriptomic data sets and multiple organisms. It is freely available as open-source at https://github.com/ThummaratPaklao/ICOM-GEMs.git .

Optimal allocation of physicians improves accessibility and workload disparities in stroke care.

BACKGROUND: Inequalities in access to stroke care and the workload of physicians have been a challenge in recent times. This may be resolved by allocating physicians suitable for the expected demand. Therefore, this study analyzes whether reallocation using an optimization model reduces disparities in spatial access to healthcare and excessive workload. METHODS: This study targeted neuroendovascular specialists and primary stroke centers in Japan and employed an optimization model for reallocating neuroendovascular specialists to reduce the disparity in spatial accessibility to stroke treatment and workload for neuroendovascular specialists in Japan. A two-step floating catchment area method and an inverted two-step floating catchment area method were used to estimate the spatial accessibility and workload of neuroendovascular specialists as a potential crowdedness index. Quadratic programming has been proposed for the reallocation of neuroendovascular specialists. RESULTS: The reallocation of neuroendovascular specialists reduced the disparity in spatial accessibility and the potential crowdedness index. The standard deviation (SD) of the demand-weighted spatial accessibility index improved from 125.625 to 97.625. Simultaneously, the weighted median spatial accessibility index increased from 2.811 to 3.929. Additionally, the SD of the potential crowdedness index for estimating workload disparity decreased from 10,040.36 to 5934.275 after optimization. The sensitivity analysis also showed a similar trend of reducing disparities. CONCLUSIONS: The reallocation of neuroendovascular specialists reduced regional disparities in spatial accessibility to healthcare, potential crowdedness index, and disparities between facilities. Our findings contribute to planning health policies to realize equity throughout the healthcare system.

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.

On the Finite Complexity of Solutions in a Degenerate System of Quadratic Equations: Exact Formula.

The paper describes an application of the p-regularity theory to Quadratic Programming (QP) and nonlinear equations with quadratic mappings. In the first part of the paper, a special structure of the nonlinear equation and a construction of the 2-factor operator are used to obtain an exact formula for a solution to the nonlinear equation. In the second part of the paper, the QP problem is reduced to a system of linear equations using the 2-factor operator. The solution to this system represents a local minimizer of the QP problem along with its corresponding Lagrange multiplier. An explicit formula for the solution of the linear system is provided. Additionally, the paper outlines a procedure for identifying active constraints, which plays a crucial role in constructing the linear system.

Convexity constraints on linear background models for electron energy-loss spectra.

In this paper convexity constraints are derived for a background model of electron energy loss spectra (EELS) that is linear in the fitting parameters. The model outperforms a power-law both on experimental and simulated backgrounds, especially for wide energy ranges, and thus improves elemental quantification results. Owing to the model's linearity, the constraints can be imposed through fitting by quadratic programming. This has important advantages over conventional nonlinear power-law fitting such as high speed and a guaranteed unique solution without need for initial parameters. As such, the need for user input is significantly reduced, which is essential for unsupervised treatment of large datasets. This is demonstrated on a demanding spectrum image of a semiconductor device sample with a high number of elements over a wide energy range.

Exploring healthy and climate-friendly diets for Danish adults: an optimization study using quadratic programming.

Background: A transition to healthy and sustainable diets has the potential to improve human and planetary health but diets need to meet requirements for nutritional adequacy, health, environmental targets, and be acceptable to consumers. Objective: The objective of this study was to derive a nutritionally adequate and healthy diet that has the least deviation possible from the average observed diet of Danish adults while aiming for a greenhouse gas emission (GHGE) reduction of 31%, corresponding to the GHGE level of the Danish plant-rich diet, which lays the foundation for the current healthy and sustainable food-based dietary guidelines (FBDGs) in Denmark. Methods: With an objective function minimizing the departure from the average observed diet of Danish adults, four diet optimizations were run using quadratic programming, with different combinations of diet constraints: (1) nutrients only (Nutri), (2) nutrients and health-based targets for food amounts (NutriHealth), (3) GHGE only (GHGE), and finally, (4) combined nutrient, health and GHGE constraints (NutriHealthGHGE). Results: The GHGE of the four optimized diets were 3.93 kg CO2-eq (Nutri), 3.77 kg CO2-eq (NutriHealth) and 3.01 kg CO2-eq (GHGE and NutriHealthGHGE), compared to 4.37 kg CO2-eq in the observed diet. The proportion of energy from animal-based foods was 21%-25% in the optimized diets compared to 34% in the observed diet and 18% in the Danish plant-rich diet. Moreover, compared to the average Danish diet, the NutriHealthGHGE diet contained more grains and starches (44 E% vs. 28 E%), nuts (+230%), fatty fish (+89%), eggs (+47%); less cheese (-73%), animal-based fats (-76%), total meat (-42%); and very limited amounts of ruminant meat, soft drinks, and alcoholic beverages (all-90%), while the amounts of legumes and seeds were unchanged. On average, the mathematically optimized NutriHealthGHGE diet showed a smaller deviation from the average Danish diet compared to the Danish plant-rich diet (38% vs. 169%, respectively). Conclusion: The final optimized diet presented in this study represents an alternative way of composing a nutritionally adequate and healthy diet that has the same estimated GHGE as a diet consistent with the climate-friendly FBDGs in Denmark. As this optimized diet may be more acceptable for some consumers, it might help to facilitate the transition toward more healthy and sustainable diets in the Danish population.

Statistical Inference for Cox Proportional Hazards Models with a Diverging Number of Covariates.

For statistical inference on regression models with a diverging number of covariates, the existing literature typically makes sparsity assumptions on the inverse of the Fisher information matrix. Such assumptions, however, are often violated under Cox proportion hazards models, leading to biased estimates with under-coverage confidence intervals. We propose a modified debiased lasso method, which solves a series of quadratic programming problems to approximate the inverse information matrix without posing sparse matrix assumptions. We establish asymptotic results for the estimated regression coefficients when the dimension of covariates diverges with the sample size. As demonstrated by extensive simulations, our proposed method provides consistent estimates and confidence intervals with nominal coverage probabilities. The utility of the method is further demonstrated by assessing the effects of genetic markers on patients' overall survival with the Boston Lung Cancer Survival Cohort, a large-scale epidemiology study investigating mechanisms underlying the lung cancer.