Convex Hull Research Articles

Real-time MPC with Control Barrier Functions for Autonomous Driving using Safety Enhanced Collocation

The autonomous driving industry is continuously dealing with safety-critical scenarios, and nonlinear model predictive control (NMPC) is a powerful control strategy for handling such situations. However, standard safety constraints are not scalable and require a long NMPC horizon. Moreover, the adoption of NMPC in the automotive industry is limited by the heavy computation of numerical optimization routines. To address those issues, this paper presents a real-time capable NMPC for automated driving in urban environments, using control barrier functions (CBFs). Furthermore, the designed NMPC is based on a novel collocation transcription approach, named RESAFE/COL, that allows to reduce the number of optimization variables while still guaranteeing the continuous time (nonlinear) inequality constraints satisfaction, through regional convex hull approximation. RESAFE/COL is proven to be 5 times faster than multiple shooting and more tractable for embedded hardware without a decrease in the performance, nor accuracy and safety of the numerical solution. We validate our NMPC-CBF with RESAFE/COL on digital twins of the vehicle and the urban environment and show the safe controller's ability to improve crash avoidance by 91%. Supplementary visual material can be found at https://youtu.be/_EnbfYwljp4.

Trophic history of Hawaiian green turtles as revealed by stable isotope ratios (δ13C, δ15N and δ34S) in the bones of museum specimens

Abstract Understanding consumer trophic status and long‐term dietary changes can yield information about impacts of altered habitats on their ecology. In Hawai'i, coastal ecosystems have been significantly modified by the introduction of invasive seaweeds and mangroves, high nutrient load and overfishing, but so far, much is still to be understood about how these changes have affected the green turtle (Chelonia mydas). This study analyzed stable carbon, nitrogen, and sulfur isotope ratios in the bone tissue of modern and museum specimens of green turtles collected from 1901 to 2020 in Oahu and the North‐western Hawaiian Islands to understand how their isotopic niche has changed through time, a crucial step towards restoring the ecological role of a formerly decimated species. The standard ellipse size and the total area of the convex hull of the isotopic niche of green turtles in three periods (1901–1951, 1992–2008, and 2018–2020) were calculated. The stable isotope values of ancient green turtles (1901–1951) suggest that they relied heavily on macroalgae even before the introduction of exotic species and eutrophication promoted the development of algal pastures. However, a few ancient green turtles relied heavily on seagrasses, and others complemented their macroalgae‐based diets with significant amounts of animal matter. Such diet specialists were missing from the sample of current green sea turtles, suggesting that these foraging strategies are less common or perhaps even absent in the current population. The results suggest that green turtles have converged on the use of the most abundant resource, red macroalgae, likely because of the homogenization and simplification of coastal habitats and food webs due to anthropogenic influences. Restoring the population size of herbivorous fishes and a more diverse ecosystem structure may be necessary to recover the array of trophic strategies formerly present in the Hawaiian green turtle population.

A systematic study on the phase diagram and superconductivity of ternary clathrate Ca-Sc-H at high pressures.

This work explores potential high-temperature superconductor materials in hydrogen-rich systems. Here, the crystal structure stabilities of ternary Ca-Sc-H systems under high-pressure (P = 100-250 GPa) and their superconductivities are investigated using the particle swarm optimization methodology combined with first-principles calculations. For the predicted candidate structures of Ca-Sc-H systems, the pressure-dependent phase diagram and thermodynamic convex hull were investigated across a wide range of compositions; the electronic properties of all the predicted phases were analyzed in detail to study the bonding behavior of these stable phases. We identified the crystal structures of four thermodynamically stable compounds: R3̄m-CaScH6, Immm-CaSc2H9,C2/m-Ca2ScH10, and R3̄m-CaScH12. Among them, R3̄m-CaScH12 was predicted to have the highest Tc value (i.e., 173 K) at 200 GPa. The discovery of this previously unreported pressure-induced decomposition of Ca-Sc-H systems will pave the way for investigations on the nature of hydrogen-metal interactions.

Estimation of plant's morphological parameters using terrestrial laser scanning-based three-dimensional point cloud data

The yield of crop is very important for sustainable agriculture to meet continuously growing demand of food. The morphological parameters, such as plant height (PH), projected leaf area (PLA), and plant volume (PV) are important metrics to estimate crop yield. In this paper, a multi-step methodology is proposed to estimate parameters PH, PLA and PLA using state-of-the-art three-dimensional (3D) mapping technique: terrestrial laser scanning (TLS). The proposed methodology consists of three well-designed steps: pre-processing, ground filtering and clustering, and estimation of plant's morphological parameters. In pre-processing TLS-derived laser scans acquired from multiple scan stations to cover the selected agricultural test site registered and coordinate transformation is performed to convert the TLS point cloud into total station (TS)-based locally defined coordinate system. The second step transformed point cloud data is processed to generate ground and non-ground points, where subsequently Euclidean clustering is employed to generate clusters of non-ground points. The clustered data is cleaned based on geometrical constraints and cabbage plant's clusters are extracted, which are processed using height-based analysis and convex hull algorithm to estimate PH, PLA and PLA of each cluster. The proposed methodology performance was evaluated using TLS point cloud data of selected agricultural field of cabbage plants, and PH, PLA and PLA estimation was performed at RMSE of 0.005 m, 0.012 m2 and 0.0063 m3 respectively. The proposed methodology is efficient and easy to implement step-wise approach from data collection to processing for plant's geometrical analysis, thus it has potential to be used as one of the industrial tools for precision agriculture.

Research on trimming path for forked carrots using contour‐based machine learning methods

AbstractForked carrots are often used as animal feed or discarded directly, which affects ​the economic returns of growers and leads to resource waste and environmental pollution. After trimming, forked carrots become easier to peel and can be further processed. However, the lack of relevant studies and equipment hinders the full use of forked carrots, and the identification of fork points and determination of the trimming path are the main challenges in trimming forked carrots with unique and diverse shapes. Therefore, an automatic carrot‐trimming path recognition solution based on contour analysis and machine learning was proposed in this study to address the above challenges. Specifically, a cascaded model and a parallel model consisting of Multilayer Perceptron (MLP) and Support Vector Machine (SVM) were constructed to identify fork points, and three trimming path determination methods based on fork points and carrot contours were proposed. The results demonstrated cascaded and parallel models achieved 100% and 92.7% recall rates, respectively, with accuracy rates of 90.4% and 100% and repetition rates of 97.1% and 96.4%. Among the trimming path determination methods, both the dynamic convex hull method and the static convex hull method achieved a convexity of 94.7%, surpassing 93.1% for the slope method. The static convex hull method exhibited the fastest speed in determining the trimming path, taking only 0.0032 s per carat. The parallel model and the static convex hull method could be effectively used for online determination of the trimming path for forked carrots.Practical applicationsTrimming forked carrots enhances usability, reduces resource wastage, and mitigates environmental pollution. Leveraging contour‐based machine learning algorithms, we achieved precise fork point recognition with broad applicability. Using fork point and carrot contour data, we determined trimming paths that render carrots convex for mechanical peeling. This approach contributes to advancing sustainable agriculture by optimizing resource utilization.

An integrated method for phenotypic analysis of wheat based on multi-view image sequences: from seedling to grain filling stages.

Wheat exhibits complex characteristics during its growth, such as extensive tillering, slender and soft leaves, and severe organ cross-obscuration, posing a considerable challenge in full-cycle phenotypic monitoring. To address this, this study presents a synthesized method based on SFM-MVS (Structure-from-Motion, Multi-View Stereo) processing for handling and segmenting wheat point clouds, covering the entire growth cycle from seedling to grain filling stages. First, a multi-view image acquisition platform was constructed to capture image sequences of wheat plants, and dense point clouds were generated using SFM-MVS technology. High-quality dense point clouds were produced by implementing improved Euclidean clustering combined with centroids, color filtering, and statistical filtering methods. Subsequently, the segmentation of wheat plant stems and leaves was performed using the region growth segmentation algorithm. Although segmentation performance was suboptimal during the tillering, jointing, and booting stages due to the glut leaves and severe overlap, there was a salient improvement in wheat leaf segmentation efficiency over the entire growth cycle. Finally, phenotypic parameters were analyzed across different growth stages, comparing automated measurements of plant height, leaf length, and leaf width with actual measurements. The results demonstrated coefficients of determination ( ) of 0.9979, 0.9977, and 0.995; root mean square errors (RMSE) of 1.0773 cm, 0.2612 cm, and 0.0335 cm; and relative root mean square errors (RRMSE) of 2.1858%, 1.7483%, and 2.8462%, respectively. These results validate the reliability and accuracy of our proposed workflow in processing wheat point clouds and automatically extracting plant height, leaf length, and leaf width, indicating that our 3D reconstructed wheat model achieves high precision and can quickly, accurately, and non-destructively extract phenotypic parameters. Additionally, plant height, convex hull volume, plant surface area, and Crown area were extracted, providing a detailed analysis of dynamic changes in wheat throughout its growth cycle. ANOVA was conducted across different cultivars, accurately revealing significant differences at various growth stages. This study proposes a convenient, rapid, and quantitative analysis method, offering crucial technical support for wheat plant phenotypic analysis and growth dynamics monitoring, applicable for precise full-cycle phenotypic monitoring of wheat.

A new pressure-densified orthogonal hard superconducting phase of RhB4.

A new hard superconducting phase of RhB4 with the space group Cmca is predicted, and the phase transition and mechanical and superconducting properties of RhB4 under 300 GPa are studied using first principles. We predict a new high-pressure phase of RhB4 by substituting the most stable Cmca structure of OsB4, known for its excellent mechanical properties. The calculated enthalpy shows that above 112.6 GPa, Cmca is superior to Pmmn as was previously predicted by particle swarm optimization. The stability of the predicted phase is checked using formation enthalpy, elastic constant and phonon dispersion. Additionally, the convex hull of the Rh-B system confirms that the phase is expected to be synthesized experimentally. The Cmca phase is an incompressible hard material with a hardness of 23.75 GPa at 300 GPa attributed to strong intralayer covalent B-B bonds. Furthermore, the phase is a relatively pressure-insensitive superconductor, with a Tc of 8.6 K at 112.6 GPa and a pressure-dependent coefficient of -0.03 K GPa-1. The finding reveals a superconducting hard material that is well-suited for extreme high-pressure environments.

How smooth can the convex hull of a Lévy path be?

How smooth can the convex hull of a Lévy path be?

Simplicial decomposition of variational inequalities with multiple nonlinear column generation

<abstract> <p>Simplicial decomposition (SD) of variational inequalities experiences the long-tail convergence property. That is, the equilibrium solution rapidly progresses at first but then tails off, making only a tiny amount of progress per column generation iteration, which is a drawback of SD-VI. In the context of Dantzig-Wolfe of LP, it is reported that the more proposals are used to initialize the algorithm, the faster the solution can be found by reducing the number of decomposition steps. Therefore, I proposed to solve multiple nonlinear column generation (mNCG) subproblems in each SD-VI iteration (SD-VI-mNCG) instead of solving only one subproblem as in SD-VI. Generating multiple column generation subproblem solutions in each SD-VI iteration enabled the corresponding convex hull to be rapidly enlarged. Consequently, the number of SD-VI iterations could be greatly reduced. A transportation network equilibrium problem was used to study the performance of the SD-VI-mNCG.</p> </abstract>

Foundations of neutrosophic convex structures

In this paper an idea of neutrosophic convex structures (briefly, NC-structures) is given and some of their properties are explored. Also, NC-sets, neutrosophic concave sets and neutrosophic convex hull are defined and their properties are investigated. Moreover, the notions of NC-derived operator and NC-base are studied and their relationship to NC-structures are established.

Pygmy Blue Whale Home Ranges and Their Overlaps with Indonesian and Australian Marine Protected Areas: Comparison between a-LoCoH and BBMM Methods

Information on the distribution of marine migratory species is lacking, and for a long time, these species have been overlooked in the designation of Marine Protected Areas (MPAs). This study analysed the home range of pygmy blue whales (PBWs) from western Australia to eastern Indonesia to be able to assess the overlap with current MPAs. In this study, data from 11 individual PBWs tagged in the Perth Canyon were used. Two home range methods, adaptive Local Convex Hull (a-LoCoH) and Brownian Bridge Movement Model (BBMM), were performed and compared to identify core use areas and connections between these areas (i.e., migration corridors). By assessing the relative properties and visually inspecting the home ranges, 90% BBMM (home range and migration corridor) and 50% BBMM (core use area) are chosen as the best results, because they cover the connected core-use areas to a large extent. The home ranges that were covered by current MPAs were only 2% in Indonesia and 16% in Australia. Important migration corridors without current protection are in the east Savu Sea, south of Timor Island, and wider Banda Sea. It is noteworthy that comparing methods is relevant to be able to choose the most suitable method for the data used and the goal of this study. The limited overlap between the calculated home ranges and the MPAs of the Indonesian waters articulates the importance of in-depth scientific studies to be able to evaluate, implement and develop marine conservation planning.

Constrained Maximum Cross-Domain Likelihood for Domain Generalization.

As a recent noticeable topic, domain generalization aims to learn a generalizable model on multiple source domains, which is expected to perform well on unseen test domains. Great efforts have been made to learn domain-invariant features by aligning distributions across domains. However, existing works are often designed based on some relaxed conditions which are generally hard to satisfy and fail to realize the desired joint distribution alignment. In this article, we propose a novel domain generalization method, which originates from an intuitive idea that a domain-invariant classifier can be learned by minimizing the Kullback-Leibler (KL)-divergence between posterior distributions from different domains. To enhance the generalizability of the learned classifier, we formalize the optimization objective as an expectation computed on the ground-truth marginal distribution. Nevertheless, it also presents two obvious deficiencies, one of which is the side-effect of entropy increase in KL-divergence and the other is the unavailability of ground-truth marginal distributions. For the former, we introduce a term named maximum in-domain likelihood to maintain the discrimination of the learned domain-invariant representation space. For the latter, we approximate the ground-truth marginal distribution with source domains under a reasonable convex hull assumption. Finally, a constrained maximum cross-domain likelihood (CMCL) optimization problem is deduced, by solving which the joint distributions are naturally aligned. An alternating optimization strategy is carefully designed to approximately solve this optimization problem. Extensive experiments on four standard benchmark datasets, i.e., Digits-DG, PACS, Office-Home, and miniDomainNet, highlight the superior performance of our method.

Non-Iterative Solution for Coordinated Optimal Dispatch via Equivalent Projection—Part II: Method and Applications

This two-part paper develops a non-iterative coordinated optimal dispatch framework, i.e., free of iterative information exchange, via the innovation of the equivalent projection (EP) theory. The EP eliminates internal variables from technical and economic operation constraints of the subsystem and obtains an equivalent model with reduced scale, which is the key to the non-iterative coordinated optimization. In Part II of this paper, a novel projection algorithm with the explicit error guarantee measured by the Hausdorff distance is proposed, which characterizes the EP model by the convex hull of its vertices. This algorithm is proven to yield a conservative approximation within the prespecified error tolerance and can obtain the exact EP model if the error tolerance is set to zero, which provides flexibility to balance the computation accuracy and effort. Applications of the EP-based coordinated dispatch are demonstrated based on the multi-area coordination and transmission-distribution coordination. Case studies with a wide range of system scales verify the superiority of the proposed projection algorithm in terms of computational efficiency and scalability, and validate the effectiveness of the EP-based coordinated dispatch in comparison with the joint optimization.

CrO<sub>2</sub> monolayer: a two-dimensional ferromagnet with high Curie temperature and half-metallicity

Owing to the complete spin-polarization of electronic states near Fermi energy, half-metallic ferromagnets, especially two-dimensional half-metallic ferromagnets, have garnered significant attention in the field of spintronics. However, the practical applications of these materials are greatly hindered by their low Curie temperatures. Therefore, the exploration of high Curie temperature half-metallic ferromagnets poses a necessary and challenging task. In this study, we predict a two-dimensional transition metal oxide, CrO<sub>2</sub> monolayer, and employ first-principles calculations to investigate the crystal structure, electronic properties, magnetic ground state, and ferromagnetic phase transition. The calculations of phonon spectrum, elastic constant, and molecular dynamics simulations indicate that CrO<sub>2</sub> monolayer is dynamically, mechanically, and thermally stable. The convex hull diagram of Cr-O systems shows that the hull energy of the predicted CrO<sub>2</sub> layer is only 0.18 eV, further confirming the structural stability and large possibility for experimental fabrication. More importantly, the electronic and magnetic properties of CrO<sub>2</sub> monolayer demonstrate that it is a two-dimensional ferromagnetic half-metal with wide band gap. Five d suborbitals are divided into E<sub>g</sub> and T<sub>2g</sub> orbitals because of the crystal field of Cr atom in the center of O tetrahedron, and the spin-polarizations of E<sub>g</sub> orbitals make a major contribution to the moment around Cr atom. The ferromagnetic coupling along Cr-O-Cr chain is dominated by the superexchange interaction bridged by O 2p orbitals, similar to the typical Mn-O-Mn superexchange model. The magnetic behavior of the Cr spin lattice in a CrO<sub>2</sub> monolayer is described by a two-dimensional Heisenberg model, in which the exchange coupling anisotropy is ignored and the single ion anisotropy is the main consideration. By solving the Heisenberg model through using the Monte Carlo simulation method, the Curie temperature is determined to be over 400 K. The high Curie temperature ferromagnetism is rare in two-dimensional ferromagnetic materials and even rarer in semi-metallic materials, which makes it an ideal material for fabricating spintronic devices and studying spin quantum effects.

Convex Hull Based Economic Operating Region for Power Grids Considering Uncertainties of Renewable Energy Sources

Convex Hull Based Economic Operating Region for Power Grids Considering Uncertainties of Renewable Energy Sources

Persistence in a dynamic moral hazard game

This paper explores how the persistence of past choices creates incentives in a continuous time stochastic game involving a large player (e.g., a firm) and a sequence of small players (e.g., customers). The large player faces moral hazard and her actions are distorted by a Brownian motion. Persistence refers to how actions impact a payoff‐relevant state variable (e.g., product quality depends on past investment). I characterize actions and payoffs in Markov perfect equilibria (MPE) for a fixed discount rate, show that the perfect public equilibrium (PPE) payoff set is the convex hull of the MPE payoff set, and derive sufficient conditions for a MPE to be the unique PPE. Persistence can serve as an effective channel for intertemporal incentives in a setting where traditional channels fail. Applications to persistent product quality and policy targeting demonstrate the impact of persistence on equilibrium behavior.

A Modular Event-Triggered Containment Control Scheme for Nonlinear Heterogeneous Multiagent Systems With Unknown Leaders.

This article addresses the containment control problem in multiagent systems with nonlinear heterogeneous followers and multiple unknown leaders whose dynamics are exclusively known to their neighbors. The primary goal is to ensure the convergence of each follower to the dynamic convex hull spanned by the leaders under the constraints of limited communication resources. To achieve this, this article introduces a modular event-triggered containment control scheme with three modules. The first module, Module I-signal generator, is designed for each follower to generate a reference signal asymptotically entering the dynamic convex hull without relying on follower dynamics. The second module, Module II-event-triggered mechanism, is tailored to save communication resources effectively by determining when to broadcast information based on perturbed system stability and input-to-state stability theories. The third module, Module III-tracking controller, treats each follower as an independent agent and is crafted to track the reference signal generated by Module I using an output regulation approach. It is established that the system achieves containment control without Zeno behavior under the influence of these modules, and the theoretical results are validated through simulation examples, demonstrating the practical validity of the proposed approach.

Convex Hull Triangle Mesh-Based Static Mapping in Highly Dynamic Environments

Convex Hull Triangle Mesh-Based Static Mapping in Highly Dynamic Environments

Adjustable Robust Low-Carbon Unit Commitment With Nonanticipativity by Linear Programming

Thermal power generation is the main source of carbon emissions. Adopting low-carbon dispatching and developing renewable energy sources (RESs) are effective ways to reduce carbon emissions. This article constructs a mixed-integer programming (MIP) model of low-carbon full-scenario unit commitment with nonanticipativity. To overcome the curse of dimensionality problem caused by the use of a massive number of scenarios, we employ the adjustable robust optimization approach (AROA) to reformulate the full-scenario unit commitment as a deterministic robust model. In addition, we establish the precise adjustable robust convex hull of generation constraints in a higher dimensional space and generate a relaxed linear programming (LP) formulation of the original MIP model. Then, we design a heuristic method for obtaining a near-optimal feasible solution by converting a large-scale MIP into an LP model that can be solved in polynomial time. The numerical experiments presented in this article demonstrate the effectiveness and efficiency of the proposed method.

Recent Patents on Manufacturing Microtextured Surface

Background: Surface microtextured technology is an expansion and extension of biomimicry in the tribology field, promoting vigorous development in microtextured tribology. Through artificial means, tiny convex hulls, craters, or stripes of specific size and arrangement are processed on the friction surfaces to change the morphology and contact angle of the surfaces and improve the surface contact state or the lubrication effect. The function and properties of microtextured surfaces are determined by optimizing their geometrical parameters, but the microtextured geometrical parameters require a high-level machining quality. It is necessary to analyze and summarize the existing research on manufacturing microtextured surfaces. By summarizing the preparation methods of microtextured surfaces in the past decade, some valuable conclusions are drawn to predict the future development of technology for manufacturing microtextured surfaces and provide a reference for researchers in related fields. This paper summarizes the representative patents related to the methods of manufacturing microtextured surfaces, analyzes the properties of the microtextured surfaces produced by each method, and discusses the advantages and disadvantages of these methods. The existing problems are summarised through the analyses of patents related to microtextured preparation methods. The future development of new preparation methods has prospected. By cooperating with various processing technologies and optimizing the processing methods, the microtextured surfaces can meet various functional requirements, and the manufacturing precision is higher than before. The processing method needs further improvement according to the working conditions. More new technologies will be invented to create microtextured surfaces.