Convex Hull Research Articles

Biogeographic dynamics of graptolites during the Late Ordovician Mass Extinction in South China

Studying the temporal and spatial distributions and dynamics of fossils is crucial for understanding macroevolution processes in geological history. Biodiversity data provide an overview of faunal changes during extinction events, but it cannot differentiate the impact of extinction events on different species. Biogeographic study complements these data by offering more detailed insights into evolutionary patterns. A dataset of 704 graptolite occurrence records for the Late Ordovician Mass Extinction (LOME) was compiled from 60 localities in South China. The geographic distributions of 26 species across four graptolite biochrons (from late Katian to Hirnantian) were quantitatively reconstructed using ArcGIS. Two types of geographic range indexes, including convex hull areas and maximum distribution distances, were calculated for each species in each time slice. Based on the variations in the geographic ranges, the graptolites can be divided into three types. The geographic ranges of the first type shrank before the extinction, that of the second type expanded before the extinction but shrank during the extinction, and that of the third type expanded during the extinction. The first two types include Diplograptina species; and the third of Neograptina species. The study revealed that the extinction event affected all diplograptid graptolite species, as evidenced by the rate of decrease in geographic ranges. Interestingly, the impact of the major extinction appeared to be uniform across all graptolite species, irrespective of their initial geographic range size. The distribution centers of the graptolite species remained relatively stable and predominantly surrounded the center of the sea during the LOME. The substantial reduction in the geographic ranges of diplograptid species might be due to the global factors rather than local sea level decline.

Carathéodory Number of P 3 -Convexity of Claw-Free Graphs

Given a connected simple undirected graph G = ( V , E ) , a subset S of V is P 3 -convex if each vertex of G not in S has at most one neighbor in S . The P 3 -convex hull ⟨ S ⟩ of S is the smallest P 3 -convex set containing S . A Carathéodory set of G is a set S ⊆ V such that ⟨ S ⟩ ∖ ⋃ w ∈ S ⟨ S ∖ { w } ⟩ is non-empty. The Carathéodory number of G , denoted by C ( G ) , is the largest cardinality of a Carathéodory set of G . In this paper, we settle the conjecture posed by Barbosa et al. appeared in [SIAM J. Discrete Math. 26 (2012) 929–939] in the affirmative, which states that for a claw-free graph G of order n ( G ) , the Carathéodory number C ( G ) of the P 3 -convexity satisfies C ( G ) ≤ 2 n ( G ) + 6 5 . Furthermore, we determine all graphs attaining the bound.

A Nonlinear Hybrid Modeling Method for Pump Turbines by Integrating Delaunay Triangulation Interpolation and an Improved BP Neural Network

In order to solve the problem that the data processing accuracy of the characteristic curves is not high, which affects the accuracy of the simulation of variable-speed pumped storage units, this paper proposes a nonlinear hybrid modeling method for pump turbines by integrating Delaunay triangulation interpolation and an improved back-propagation neural network. Firstly, the improved Sutter transform is used to preprocess the original curve, and the convex hull of the transformed curve is calculated. With the unknown point inside the convex hull, Delaunay triangulation interpolation is used to model the transformed curve. With the unknown point outside the convex hull, the back-propagation neural network is first established based on the input and output, and then the initial weights and thresholds of the network are determined using the mind evolution algorithm to complete the modeling and simulation of the curve. Simulation results show that the proposed method fully integrates the high-precision features of interpolation and the powerful nonlinear fitting ability of the neural network, which greatly improves the efficiency and accuracy of pump turbine modeling.

Algebras of polynomials generated by linear operators

Let $E$ be a Banach space and $A$ be a commutative Banach algebra with identity. Let $\mathbb{P}(E, A)$ be the space of $A$-valued polynomials on $E$ generated by bounded linear operators (an $n$-homogenous polynomial in $\mathbb{P}(E,A)$ is of the form $P=\sum_{i=1}^\infty T^n_i$, where $T_i:E\to A$, $1\leq i <\infty$, are bounded linear operators and $\sum_{i=1}^\infty \|T_i\|^n < \infty$). For a compact set $K$ in $E$, we let $\mathbb{P}(K, A)$ be the closure in $\mathscr{C}(K,A)$ of the restrictions $P|_K$ of polynomials $P$ in $\mathbb{P}(E,A)$. It is proved that $\mathbb{P}(K, A)$ is an $A$-valued uniform algebra and that, under certain conditions, it is isometrically isomorphic to the injective tensor product $\mathcal{P}_N(K){\widehat\otimes}_\epsilon A$, where $\mathcal{P}_N(K)$ is the uniform algebra on $K$ generated by nuclear scalar-valued polynomials. The character space of $\mathbb{P}(K, A)$ is then identified with $\hat{K}_N\times \mathfrak{M}(A),$ where $\hat K_N$ is the nuclear polynomially convex hull of $K$ in $E$, and $\mathfrak{M}(A)$ is the character space of $A$.

Circuit-theoretic joint parameter-state estimation—Balancing optimality and AC feasibility

AC State Estimation (ACSE) is widely recognized as a practical approach for determining the grid states in steady-state conditions. It serves as a fundamental analysis to ensure grid security and is a reference for market dispatch. As grid complexity increases with rapid electrification and decarbonization, there is a growing need for more accurate knowledge of the grid operating state. However, existing ACSE algorithms have technical gaps. Critically, current ACSE algorithms are susceptible to erroneous system parameters, which are assumed to be fixed in traditional approaches. In this paper, we build a novel circuit-theoretic joint parameter-state estimation algorithm to address this limitation. The innovative algorithm builds an analogous equivalent circuit of the grid with states and certain parameters unknown. It solves a circuit-constrained optimization to estimate the most likely grid states and parameters given a set of measurements. Further, it quantifies the goodness of the estimated output by formulating tight convex envelopes around the original non-convex problem to quantify the quality of estimates. We compare the various proposed approaches on systems with up to 2869 nodes while demonstrating a tradeoff between solution optimality and model fidelity.

Design and Experiment of a Soil-Covering and -Pressing Device for Planters

In response to the practical production challenges posed by the unreliable operation of the V-shaped squeezing soil-covering and -pressing device (VCP) for planters under clay soil conditions in Northeast China, incomplete seed furrow closure, and severe soil adhesion on pressing wheels, this study proposes a device with star-toothed concave discs for soil-covering and -pressing (STCP) with the aim of enhancing the soil-covering quality of planters. The main working principles of STCP were expounded, and its main structural and installation parameters were determined and designed. Based on bionics, with the dung beetle’s protruding head structure as the research object and UHMWPE as the material, an optimized protuberance-type bionic pressing wheel was designed. A Box–Behnken experiment was conducted by taking the width of the compression wheel, the spring deformation, and the installation angle as experimental factors, as well as the weight of the soil adhered to the surface of the pressing wheel (SW) and the soil compactness (SC) as the evaluation indicators. The optimal structural parameters of the pressing device were determined as follows: the width of the pressing wheel was 60.57 mm, the spring deformation was 55.19 mm, and the installation angle was 10.70°. The field comparison tests of soil covering performance showed that the star-tooth concave disc soil-covering device can effectively solve the problem of seed “hanging” and “drying”. The average covered soil weight of the star-tooth concave disc soil-covering device was 241.46 g, and the average covered soil weight of VCP was 223.56 g. Compared with VCP, the average covered soil weight of STCP increased by 8.01%. The variation coefficient of covered soil weight after the operation of the star-tooth concave disc soil-covering device was 3.71%, which was more uniform than VCP. The field comparison tests of soil-covering thickness showed that the uniformity of soil-covering thickness can be significantly improved by adding a star-tooth concave disc soil-covering device to VCP. The comparative tests of soil anti-adhesive showed that the convex hull type pressing wheels optimized by bionics had better soil anti-adhesive performance, and the soil adhesion weight was reduced by 43.68% compared with VCP. The field comparative tests of seedling emergence showed that the seedling emergence rate after STCP operation was 3.9% higher than that of VCP.

An Advanced Lung Carcinoma Prediction and Risk Screening Model Using Transfer Learning.

Lung cancer, also known as lung carcinoma, has a high death rate, but an early diagnosis can substantially reduce this risk. In the current era, prediction models face challenges such as low accuracy, excessive noise, and low contrast. To resolve these problems, an advanced lung carcinoma prediction and risk screening model using transfer learning is proposed. Our proposed model initially preprocesses lung computed tomography images for noise removal, contrast stretching, convex hull lung region extraction, and edge enhancement. The next phase segments the preprocessed images using the modified Bates distribution coati optimization (B-RGS) algorithm to extract key features. The PResNet classifier then categorizes the cancer as normal or abnormal. For abnormal cases, further risk screening determines whether the risk is low or high. Experimental results depict that our proposed model performs at levels similar to other state-of-the-art models, achieving enhanced accuracy, precision, and recall rates of 98.21%, 98.71%, and 97.46%, respectively. These results validate the efficiency and effectiveness of our suggested methodology in early lung carcinoma prediction and risk assessment.

Verification of the person’s dynamic signature on a limited number of samples

Objectives. The goal of the research is to develop a new person-dependent method for verification of a signature of one person made on a tablet with a stylus in the presence of a limited number of signature samples of this person.Methods. The paper shows how to construct an individual pattern of the dynamic signatures of any person, which is described by points in a multidimensional feature space and is intended for subsequent verification of the authenticity of the signatures of a given person. It is constructed using 5<N<20 samples of genuine human signatures. The pattern forms a convex object in a multidimensional feature space. It describes the peculiar properties of a signature performed by a specific person.Results . The dynamics of signature execution is represented by three discrete parametric functions: coordinates of the stylus X, Y and its pressure on the tablet P, recorded at fixed time intervals. In the process of research, a number of secondary functions-features were selected and calculated from them. Since these data sets have different lengths, the dynamic time warping algorithm is used to compare them. The results of this transformation are distances between the dynamic features of two signatures, which serve as coordinates of a point in the feature space that describes the similarity of these signatures. The set of such points describes similarity of all pairs of genuine human signatures presented for verification in a multidimensional feature space. The convex hull of the cloud of these points is used as a pattern of a particular person's signature. The genuine signatures of any person are always different from each other; significant differences between them can distort the verification result.Conclusion. Experimental studies performed on genuine and fake signatures of 498 people from the largest available database of dynamic signatures, DeepSignDB, showed a verification accuracy of about 98 % when analyzing 24,900 signatures. Half of them are genuine, half are fake

Hybrid A-Star Path Planning Method Based on Hierarchical Clustering and Trichotomy

Aiming to improve on the poor smoothness and longer paths generated by the traditional Hybrid A-star algorithm in unstructured environments with multiple obstacles, especially in confined areas for autonomous vehicles, a Hybrid A-star path planning method based on hierarchical clustering and trichotomy is proposed. This method first utilizes the Prewitt compass gradient operator (Prewitt operator) to identify obstacle boundaries and discretize boundaries. Then, it employs a single linkage hierarchical clustering algorithm to cluster obstacles based on boundaries. Subsequently, the clustered points are enveloped using a convex hull algorithm, considering collision safety for vehicle expansion. This fundamentally addresses the ineffective expansion issue of the traditional Hybrid A-star algorithm in U-shaped obstacle clusters. Finally, the expansion strategy of Hybrid A-star algorithm nodes is improved based on the trichotomy method. Simulation results demonstrate that the improved algorithm can search for a shorter and smoother path without significantly increasing the computational time.

Extraction of crop canopy features and decision-making for variable spraying based on unmanned aerial vehicle LiDAR data

Implementation of precision agriculture aerial applications using unmanned aerial vehicles (UAVs) represents a pivotal technological aspect in precision agriculture. However, current UAV applications are still far from realizing true precision variable spraying. The use of UAVs to analyze and model crop growth, pest and disease conditions, and other pertinent information to enable targeted precision spraying poses a formidable challenge. Herein, a UAV variable-rate spray system with adaptive flow control based on crop canopy morphology was developed using a UAV equipped with a light detection and ranging (LiDAR) sensor to support precision spraying of cotton. Point cloud data captured by the LiDAR sensor initially undergo processing using the simple morphological filter (SMRF) algorithm and feature extraction function. Subsequently, cotton canopy volumes measured by the alpha shape algorithm, convex hull by slices shape algorithm, and voxel-based method were compared with manual measurements with coefficient of determination R2 values of 0.89, 0.78, and 0.82, respectively. The results of the validation experiments denote that the cotton canopy volume obtained using the alpha shape algorithm is in good agreement with that obtained using manual measurements; thus, this algorithm is employed for volume calculations in this design. Models were constructed to relate UAV flight parameters, cotton canopy volume, and spraying parameters to the duty cycle of variable control signals, which enabled the UAV to adjust the flow rate in real time to match the cotton canopy structure. In addition, a polygonal prescription map decoding algorithm based on the cotton canopy morphology was introduced. This algorithm is used for real-time decoding of prescription maps and extraction of flow, latitude, and longitude information. Finally, field experiments were conducted, and the results indicate that the UAV variable-rate spray system designed in this study exhibits biological efficacy (effective application thresholds provided by the pesticide manufacturer) comparable to that of the constant-rate spray system at a lower application rate. Furthermore, it exhibited superior spray deposition efficiency and coverage compared with the constant-rate spray system. Notably, the use of the variable-rate spray system in cotton crops resulted in a 43.37% reduction in spray volume while maintaining high application quality, providing an opportunity for pesticide and labor cost savings.

A network flow approach to a common generalization of Clar and Fries numbers

Clar number and Fries number are two thoroughly investigated parameters of plane graphs emerging from mathematical chemistry to measure stability of organic molecules. First, we introduce a common generalization of these two concepts for bipartite plane graphs, and then we extend it further to the notion of source-sink pairs of subsets of nodes in a general (not necessarily planar) directed graph. The main result is a min-max formula for the maximum weight of a source-sink pair. The proof is based on the recognition that the convex hull of source-sink pairs can be obtained as the projection of a network tension polyhedron. The construction makes it possible to apply any standard cheapest network flow algorithm to compute both a maximum weight source-sink pair and a minimizer of the dual optimization problem formulated in the min-max theorem. As a consequence, our approach gives rise to the first purely combinatorial, strongly polynomial algorithm to compute a largest (or even a maximum weight) Fries-set of a perfectly matchable plane bipartite graph and an optimal solution to the dual minimization problem.

Satellite Image Cloud Automatic Annotator with Uncertainty Estimation

In satellite imagery, clouds obstruct the ground information, directly impacting various downstream applications. Thus, cloud annotation/cloud detection serves as the initial preprocessing step in remote sensing image analysis. Recently, deep learning methods have significantly improved in the field of cloud detection, but training these methods necessitates abundant annotated data, which requires experts with professional domain knowledge. Moreover, the influx of remote sensing data from new satellites has further led to an increase in the cost of cloud annotation. To address the dependence on labeled datasets and professional domain knowledge, this paper proposes an automatic cloud annotation method for satellite remote sensing images, CloudAUE. Unlike traditional approaches, CloudAUE does not rely on labeled training datasets and can be operated by users without domain expertise. To handle the irregular shapes of clouds, CloudAUE firstly employs a convex hull algorithm for selecting cloud and non-cloud regions by polygons. When selecting convex hulls, the cloud region is first selected, and points at the edges of the cloud region are sequentially selected as polygon vertices to form a polygon that includes the cloud region. Then, the same selection is performed on non-cloud regions. Subsequently, the fast KD-Tree algorithm is used for pixel classification. Finally, an uncertainty method is proposed to evaluate the quality of annotation. When the confidence value of the image exceeds a preset threshold, the annotation process terminates and achieves satisfactory results. When the value falls below the threshold, the image needs to undergo a subsequent round of annotation. Through experiments on two labeled datasets, HRC and Landsat 8, CloudAUE demonstrates comparable or superior accuracy to deep learning algorithms, and requires only one to two annotations to obtain ideal results. An unlabeled self-built Google Earth dataset is utilized to validate the effectiveness and generalizability of CloudAUE. To show the extension capabilities in various fields, CloudAUE also achieves desirable results on a forest fire dataset. Finally, some suggestions are provided to improve annotation performance and reduce the number of annotations.

EMOKINE: A software package and computational framework for scaling up the creation of highly controlled emotional full-body movement datasets

EMOKINE is a software package and dataset creation suite for emotional full-body movement research in experimental psychology, affective neuroscience, and computer vision. A computational framework, comprehensive instructions, a pilot dataset, observer ratings, and kinematic feature extraction code are provided to facilitate future dataset creations at scale. In addition, the EMOKINE framework outlines how complex sequences of movements may advance emotion research. Traditionally, often emotional-‘action’-based stimuli are used in such research, like hand-waving or walking motions. Here instead, a pilot dataset is provided with short dance choreographies, repeated several times by a dancer who expressed different emotional intentions at each repetition: anger, contentment, fear, joy, neutrality, and sadness. The dataset was simultaneously filmed professionally, and recorded using XSENS® motion capture technology (17 sensors, 240 frames/second). Thirty-two statistics from 12 kinematic features were extracted offline, for the first time in one single dataset: speed, acceleration, angular speed, angular acceleration, limb contraction, distance to center of mass, quantity of motion, dimensionless jerk (integral), head angle (with regards to vertical axis and to back), and space (convex hull 2D and 3D). Average, median absolute deviation (MAD), and maximum value were computed as applicable. The EMOKINE software is appliable to other motion-capture systems and is openly available on the Zenodo Repository. Releases on GitHub include: (i) the code to extract the 32 statistics, (ii) a rigging plugin for Python for MVNX file-conversion to Blender format (MVNX=output file XSENS® system), and (iii) a Python-script-powered custom software to assist with blurring faces; latter two under GPLv3 licenses.

Data-Driven Containment Control for a Class of Nonlinear Multi-Agent Systems: A Model Free Adaptive Control Approach

This paper studies the containment control problem of heterogeneous multi-agent systems (MASs) with multiple leaders. The follower agent dynamics are assumed to be unknown and nonlinear. First, each follower is transformed into an incremental data description based on the dynamic linearization technique. Then, a distributed model-free adaptive containment control law is proposed such that all followers will be driven into the convex hull of the leaders. Furthermore, the algorithm is extended to the time-switching and dynamic leaders case. As a data-driven approach, the proposed controller design uses only the received input and output (I/O) data of these agents rather than agent mathematical models. Finally, to test the potential in real applications, three representative examples considering various environment factors, including external disturbances, are simulated to show the effectiveness and resilience of this method.

Studying the Thermodynamic Phase Stability of Organic-Inorganic Hybrid Perovskites Using Machine Learning.

As an important photovoltaic material, organic-inorganic hybrid perovskites have attracted much attention in the field of solar cells, but their instability is one of the main challenges limiting their commercial application. However, the search for stable perovskites among the thousands of perovskite materials still faces great challenges. In this work, the energy above the convex hull values of organic-inorganic hybrid perovskites was predicted based on four different machine learning algorithms, namely random forest regression (RFR), support vector machine regression (SVR), XGBoost regression, and LightGBM regression, to study the thermodynamic phase stability of organic-inorganic hybrid perovskites. The results show that the LightGBM algorithm has a low prediction error and can effectively capture the key features related to the thermodynamic phase stability of organic-inorganic hybrid perovskites. Meanwhile, the Shapley Additive Explanation (SHAP) method was used to analyze the prediction results based on the LightGBM algorithm. The third ionization energy of the B element is the most critical feature related to the thermodynamic phase stability, and the second key feature is the electron affinity of ions at the X site, which are significantly negatively correlated with the predicted values of energy above the convex hull (Ehull). In the screening of organic-inorganic perovskites with high stability, the third ionization energy of the B element and the electron affinity of ions at the X site is a worthy priority. The results of this study can help us to understand the correlation between the thermodynamic phase stability of organic-inorganic hybrid perovskites and the key features, which can assist with the rapid discovery of highly stable perovskite materials.

Maximum Consensus Floating Point Solutions for Infeasible Low-Dimensional Linear Programs with Convex Hull as the Intermediate Representation

Maximum Consensus Floating Point Solutions for Infeasible Low-Dimensional Linear Programs with Convex Hull as the Intermediate Representation

Tilted inequalities and facets of the set covering polytope: A theoretical analysis

Given a ground-set of elements and a family of subsets, the set covering problem consists in choosing a minimum number of elements such that each subset contains at least one of the chosen elements. This research focuses on the set covering polytope, which is the convex hull of integer solutions to the set covering problem. We investigate the connection between the study of the facets of the set covering polytope and tilting theory. This theory studies how inequalities can be rotated around their contact points with a polyhedron in order to obtain inequalities inducing higher dimensional faces. To study this connection, we introduce the concept of tilting vectors which characterize the degrees of freedom of rotation of an inequality. These vectors characterize facet-defining inequalities and can be used to tilt inequalities with a similar procedure to the one used for arbitrary polyhedra. Additionally, we demonstrate that the computational effort needed to tilt an inequality can be reduced when the inequality has many null coefficients. Finally, we use the tilting vectors to extend several necessary and/or sufficient conditions for facets of the set covering polytope presented by several previous works of the literature.

Fast, Nondestructive and Precise Biomass Measurements Are Possible Using Lidar-Based Convex Hull and Voxelization Algorithms

Light detection and ranging (lidar) scanning tools are available that can make rapid digital estimations of biomass. Voxelization and convex hull are two algorithms used to calculate the volume of the scanned plant canopy, which is correlated with biomass, often the primary trait of interest. Voxelization splits the scans into regular-sized cubes, or voxels, whereas the convex hull algorithm creates a polygon mesh around the outermost points of the point cloud and calculates the volume within that mesh. In this study, digital estimates of biomass were correlated against hand-harvested biomass for field-grown corn, broom corn, and energy sorghum. Voxelization (r = 0.92) and convex hull (r = 0.95) both correlated well with plant dry biomass. Lidar data were also collected in a large breeding trial with nearly 900 genotypes of energy sorghum. In contrast to the manual harvest studies, digital biomass estimations correlated poorly with yield collected from a forage harvester for both voxel count (r = 0.32) and convex hull volume (r = 0.39). However, further analysis showed that the coefficient of variation (CV, a measure of variability) for harvester-based estimates of biomass was greater than the CV of the voxel and convex-hull-based biomass estimates, indicating that poor correlation was due to harvester imprecision, not digital estimations. Overall, results indicate that the lidar-based digital biomass estimates presented here are comparable or more precise than current approaches.

Dispatchable region for distributed renewable energy generation in reconfigurable AC–DC distribution networks with soft open points

The dispatchable region (DR) describes the ability of a power system to adapt to the variability of distributed renewable energy (DRE) generation. Switchable devices such as soft open points (SOPs) and tie switches enable the AC–DC distribution network to flexibly cope with DRE power fluctuations. Currently, research on DRs seldom considers the effects of SOPs and reconfiguration with tie switches in AC–DC distribution networks, which prevents accurate evaluation of DR for this type of network. To bridge this gap, this paper formulates DRs for DRE generation in an AC–DC distribution network considering SOPs and reconfiguration with tie switches. The original model for deriving DRs is typically nonconvex, and the DR boundaries are intractable because of nonlinear power flow equations and binary variables of tie switches. Accordingly, this paper employs the outer polyhedral approximation and convex hull relaxation to approximate the original DR. An efficient adaptive constraint generation algorithm is developed to search for boundaries of the approximated DR. The numerical results show that the proposed model can effectively adapt to the DR of reconfigurable AC–DC distribution networks with SOPs and verify the accuracy and computational efficiency of the proposed method.

High-throughput assessment of stability and mechanical properties of medium- and high-entropy carbides: Bridging empirical criteria and ab-initio calculations

This study assesses the effectiveness of empirical stability descriptors — the normalized geometric packing parameter, lattice size difference, electronegativities mismatch, and the convex hull analysis based on information on mutually dissolving components, and ab-initio calculated entropy forming ability (EFA) for high-throughput materials discovery in high-entropy ceramics. A sample containing 53,130 medium and high-entropy carbide combinations from the Materials Project database has been analyzed, comparing solid solutions selected based on empirical descriptors and EFA calculations. The suitability of various electronegativity scales is evaluated, while Automatic FLOW (AFLOW) partial occupation (AFLOW-POCC) and special quasirandom structures (SQS) calculations provide insights into enthalpies, bulk moduli, and lattice parameters. It is shown that local distortions play a role in determining the stability of high-entropy ceramics and estimated lattice parameters, Young’s modulus, fracture toughness, and Vickers hardness by computational and experimental approaches. Our analysis demonstrates the efficacy of density functional theory (DFT) approaches for high-throughput screening and highlights the need for the further exploration of the cocktail effect on high-entropy ceramics’ mechanical properties.