Convex Hull Research Articles

A cardiac audio classification method based on image expression of multidimensional features.

Heart sound auscultation plays a crucial role in the early diagnosis of cardiovascular diseases. In recent years, great achievements have been made in the automatic classification of heart sounds, but most methods are based on segmentation features and traditional classifiers and do not fully exploit existing deep networks. This paper proposes a cardiac audio classification method based on image expression of multidimensional features (CACIEMDF). First, a 102-dimensional feature vector is designed by combining the characteristics of heart sound data in the time domain, frequency domain and statistical domain. Based on the feature vector, a two-dimensional feature projection space is constructed by PCA dimensionality reduction and the convex hull algorithm, and 102 pairs of coordinate representations of the feature vector in the two-dimensional space are calculated. Each one-dimensional component of the feature vector corresponds to a pair of 2D coordinate representations. Finally, the one-dimensional feature component value and its divergence into categories are used to fill the three channels of a color image, and a Gaussian model is used to dye the image to enrich its content. The color image is sent to a deep network such as ResNet50 for classification. In this paper, three public heart sound datasets are fused, and experiments are conducted using the above methods. The results show that for the two-classification/five-classification task of heart sounds, the method in this paper can achieve a classification accuracy of 95.68%/94.53% when combined with the current deep network.

Event-driven intelligent fault-tolerant containment control for nonlinear multiagent systems with unknown disturbances

This paper investigates the event-driven intelligent fault-tolerant containment control problem for nonlinear multiagent systems affected by unknown disturbances, and conducts a comprehensive analysis of the dynamic stability of the system. Reduced-order modelling is employed for system modelling and identification, while radial basis function neural networks are utilised to estimate the nonlinear functions of the system model. An event-driven control scheme is designed based on the backstepping method and Lyapunov functional approach. In contrast to existing consensus control schemes, the proposed event-driven control schemes are specifically tailored to improve the energy efficiency and endurance of nonlinear multiagent systems operating in complex environments. Under the proposed control law, the output of each follower is converge to the convex hull spanned by the outputs of the leaders. The effectiveness of the proposed method is rigorously validated through numerical simulations. Furthermore, a practical example involving the design of a marine surface vehicle using advanced robotics technology is presented to further substantiate the efficacy of the proposed method.

A Fast Grasp Planning Algorithm for Humanoid Robot Hands.

Grasp planning is crucial for robots to perform precision grasping tasks, where determining the grasp points significantly impacts the performance of the robotic hand. Currently, the majority of grasp planning methods based on analytic approaches solve the problem by transforming it into a nonlinear constrained planning problem. This method often requires performing convex hull computations, which tend to have high computational complexity. This paper proposes a new algorithm for calculating multi-finger force-closure grasps of three-dimensional objects based on humanoid multi-fingered hands. Firstly, sufficient conditions for the multi-finger force-closure grasps of three-dimensional objects are derived from a point contact model with friction. These three-dimensional force-closure conditions are then transformed into two-dimensional plane conditions, leading to a simple algorithm for multi-finger force-closure determination. This method is purely based on geometric analysis, resulting in low computational demands and enabling the rapid assessment of force-closure grasps, which are beneficial for real-time applications. Finally, the algorithm is validated through two case studies, demonstrating its feasibility and effectiveness.

A comparison of home range estimates using the time local convex hull (T‐LoCoH) and minimum convex polygon (MCP) methods for African savannah elephants in a semi‐arid protected area

A comparison of home range estimates using the time local convex hull (T‐LoCoH) and minimum convex polygon (MCP) methods for African savannah elephants in a semi‐arid protected area

Diel movement patterns in nominally nocturnal coral reef fishes (Haemulidae and Lutjanidae): Intra vs. Interspecific variation

Movement of animals, habitat connectivity, and nutrient transport are key elements in the ecological functioning of coral reef ecosystems. However, most studies have focused on the diurnal component of these aspects; nocturnal patterns are less known. Our study aims to address this knowledge gap by assessing diel movement patterns in ecologically and commercially important nocturnal coral reef fishes. We evaluate 122-days of acoustic telemetry data from 4 nocturnal species in 2 coral reef fish families (Haemulidae and Lutjanidae) on the Great Barrier Reef. For all species, we found a clear division between daytime resting areas on the reef and a move towards off-reef areas at night. This was highlighted in the low number of detections at night and the high average transitions between receivers at twilight. Over our study period, average nocturnal space use area (minimum convex polygon) of Plectorhincus gibbosus was 328,089 m2, Plectorhincus lineatus 28,828 m2, and Lutjanus carponotatus 20,369 m2. However, results from a Principal Component Analysis revealed that space use, and movement, varied substantially within species; for 3 of the 4 species the main axis of variation correlated with individual-level behaviour. These large differences in individual space use patterns highlight the need for caution when using species averages when considering ecosystem functions. Overall, our preliminary observations provide a glimpse into the large spatial extent, potential habitat connectivity, and intra and interspecific variation in activity patterns among large nocturnal Indo-Pacific reef fishes. This highlights their potential importance in maintaining ecosystem links between coral reefs and adjacent habitats.

Ultrafast Yttrium Hydride Chemistry at High Pressures via Non-equilibrium States Induced by an X-ray Free Electron Laser.

Controlling the formation and stoichiometric content of the desired phases of materials has become of central interest for a variety of fields. The possibility of accessing metastable states by initiating reactions by X-ray-triggered mechanisms over ultrashort time scales has been enabled by the development of X-ray free electron lasers (XFELs). Utilizing the exceptionally high-brilliance X-ray pulses from the EuXFEL, we report the synthesis of a previously unobserved yttrium hydride under high pressure, along with nonstoichiometric changes in hydrogen content as probed at a repetition rate of 4.5 MHz using time-resolved X-ray diffraction. Exploiting non-equilibrium pathways, we synthesize and characterize a hydride in a Weaire-Phelan structure type at pressures as low as 125 GPa, predicted using a crystal structure search, with a hydrogen content of 4.0-5.75 hydrogens per cation, that is enthalpically metastable on the convex hull.

Measuring exploration: evaluation of modelling to generate alternatives methods in capacity expansion models

Abstract As decarbonisation agendas mature, macro-energy systems modelling studies have increasingly focused on enhanced decision support methods that move beyond least-cost modelling to improve consideration of additional objectives and tradeoffs. One candidate is modelling to generate alternatives (MGA), which systematically explores new objectives without explicit stakeholder elicitation. This paper provides comparative testing of four existing MGA methodologies and proposes a new Combination vector selection approach. We examine each existing method’s runtime, parallelizability, new solution discovery efficiency, and spatial exploration in lower dimensional (N ⩽ 100) spaces, as well as spatial exploration for all methods in a three-zone, 8760 h capacity expansion model case. To measure convex hull volume expansion, this paper formalizes a computationally tractable high-dimensional volume estimation algorithm. We find random vector provides the broadest exploration of the near-optimal feasible region and variable Min/Max provides the most extreme results, while the two tie on computational speed. The new Combination method provides an advantageous mix of the two. Additional analysis is provided on MGA variable selection, in which we demonstrate MGA problems formulated over generation variables fail to retain cost-optimal dispatch and are thus not reflective of real operations of equivalent hypothetical capacity choices. As such, we recommend future studies utilize a parallelized combined vector approach over the set of capacity variables for best results in computational speed and spatial exploration while retaining optimal dispatch.

Topologies related to (I)-envelopes

We investigate the question whether the (I)-envelope of any subset of a dual to a Banach space X may be described as the closed convex hull in a suitable topology. If X contains no copy of ℓ1 then the weak topology generated by functionals of the first Baire class in the weak⁎ topology works. On the other hand, if X contains a complemented copy of ℓ1 or X=C([0,1]) no locally convex topology works. If we do not require the topology to be locally convex, the problem is still open. We further introduce and compare several natural intermediate closure operators on a dual Banach space. Finally, we collect several intriguing open problems related to (I)-envelopes.

A star selection strategy based on MDS and fast convex hull algorithm in COSPAS-SARSAT system

Abstract The space segment of the current COSPAS-SARSAT system is mainly supported by the Galileo system, and the positioning technology used is generally three-star time-difference positioning. Most of the antennas equipped in the Mission Control Centre (MCC) are not omnidirectional. In the case of Source of Search and Rescue (SAR) in a heavily shaded environment, it is necessary to use the different orbit time-sharing single satellite geolocations using TDOA, and the time-sharing will generate more satellite position data. In order to achieve the higher positioning accuracy of the solution, it is necessary to select the appropriate time and optimal geometrical distribution from the satellite positions. In this paper, we propose a satellite selection strategy based on Multiple Dimensional scaling (MDS) data degradation and a fast convex hull algorithm. The three-dimensional satellite data are downscaled to two-dimensional while maintaining their relative positional relationships, and the two-dimensional convex hull algorithm is used for Geometric Dilution of Precision (GDOP) minimum search star selection. By simulating the satellite position data in different orbits and time-sharing to complete the localization solution, the results show that compared with the traditional satellite selection method, the satellite selection strategy proposed in this paper is able to achieve better localization accuracy in a shorter period of time.

Observer-Based Fault-Tolerant Finite-Time Control of Nonlinear Multiagent Systems.

In this article, an adaptive neural containment control for a class of nonlinear multiagent systems considering actuator faults is introduced. By using the general approximation property of neural networks, a neuro-adaptive observer is designed to estimate unmeasured states. In addition, in order to reduce the computational burden, a novel event-triggered control law is designed. Furthermore, the finite-time performance function is presented to improve the transient and steady-state performance of the synchronization error. Utilizing the Lyapunov stability theory, it will be shown that the closed-loop system is cooperatively semiglobally uniformly ultimately bounded (CSGUUB), and the followers' outputs reach the convex hull constructed by the leaders. Moreover, it is shown that the containment errors are limited to the prescribed level in a finite time. Eventually, a simulation example is presented to corroborate the capability of the proposed scheme.

Optimized Backstepping-Based Containment Control for Multiagent Systems With Deferred Constraints Using a Universal Nonlinear Transformation.

This article investigates an optimized containment control problem for multiagent systems (MASs), where all followers are subject to deferred full-state constraints. A universal nonlinear transformation is proposed for simultaneously handling the cases with and without constraints. Particularly, for the constrained case, initial values of states are flexibly managed to the midpoint between upper and lower boundaries by utilizing a state-shifting function, thus eliminating the initial restriction conditions. By deferred constraints, the state is forced to fall back into the restrictive boundaries within a preassigned time. A neural network (NN)-based reinforcement learning (RL) algorithm is executed under the identifier-critic-actor architecture, where the Hamilton-Jacobi-Bellman (HJB) equation is built in every subsystem to optimize control performance. For actor and critic NNs, updating laws are simplified, since the gradient descent method is performed based on a simple positive function rather than square of Bellman residual error. In view of the Lyapunov stability theorem and graph theory, it is proved that all signals are bounded and the outputs of followers can eventually enter into the convex hull constituted by leaders. Finally, simulations confirm the validity of the proposed approach.

Efficiency of the convex hull of the columns of certain triple perturbed consistent matrices

Efficiency of the convex hull of the columns of certain triple perturbed consistent matrices

Divisible convex sets with properly embedded cones

AbstractIn this article we construct many examples of properly convex irreducible domains divided by Zariski dense relatively hyperbolic groups in every dimension at least 3. This answers a question of Benoist. Relative hyperbolicity and non-strict convexity are captured by a family of properly embedded cones (convex hulls of points and ellipsoids) in the domain. Our construction is most flexible in dimension 3 where we give a purely topological criterion for the existence of a large deformation space of geometrically controlled convex projective structures with totally geodesic boundary on a compact 3-manifold.

Pricing balancing ancillary services for low-inertia power systems under uncertainty and nonconvexity

In renewable-rich power systems, declining rotational inertia and unpredictable power fluctuations make the system vulnerable to contingencies. Recently, this issue has garnered significant attention in practice and academia, aiming to enhance power system reliability through market mechanisms. This paper proposes a day-ahead joint market that integrates energy, reserve, inertia, and frequency response services. A frequency-constrained unit commitment (UC) model is developed employing a distributionally robust chance-constrained (DRCC) approach to account for the uncertainties in wind farm outputs. Additionally, a convex hull pricing (CHP) model is introduced to minimize uplift payments associated with the nonconvex nature of commitment variables. Case studies conducted on a 5-bus and a 118-bus power system demonstrate the efficacy of the proposed market design in reducing operational costs and promoting renewable energy utilization. Furthermore, the results highlight the effectiveness of the CHP model in minimizing the uplifts and enhancing market transparency.

Distributed adaptive event-triggered finite-time fault-tolerant containment control for multi-UAVs with input constraints and actuator failures

This article investigates the distributed adaptive finite-time containment control problem for multi-UAVs with input constraints, actuator failures, communication limitations, and external disturbances. First, a new smoothing function is used to smooth the asymmetric input constraint signals so that the input constraint and actuator fault control problem can be transformed into a variable gain control problem. Subsequently, a new Nussbaum function is proposed to solve the variable gain control problem. A new adaptive event-triggered strategy is designed to solve the communication limitation problem, and the trigger threshold has the characteristic of adaptive adjustment that can be dynamically decreased. In response to external disturbances, an adaptive law is designed to estimate and compensate for the boundaries of disturbances. It follows from the analysis based on Lyapunov theory that under the proposed controller, the followers will converge to the convex envelope formed by the leaders in a finite time, and Zeno-free is achieved. Simulation results are provided to verify the effectiveness of the developed adaptive event-triggered finite-time fault-tolerant containment control laws.

Dead-reckoning facilitates determination of activity and habitat use: a case study with European badgers (Meles meles)

BackgroundStudies describing the movement of free-ranging animals often use remotely collected global positioning system (GPS) data. However, such data typically only include intermittent positional information, with a sampling frequency that is constrained by battery life, producing sub-sampling effects that have the potential to bias interpretation. GPS-enhanced ‘dead-reckoning’ of animal movements is an alternative approach that utilises combined information from GPS devices, tri-axial accelerometers, and tri-axial magnetometers. Continuous detailed information of animal movement, activity and habitat selection can then be inferred from finer-scale GPS-enhanced dead-reckoning. It is also a useful technique to reveal the minutiae of an animal’s movements such as path tortuosity. However, examples of studies using these approaches on terrestrial species are limited.MethodsCollars equipped with GPS, tri-axial accelerometer, and tri-axial magnetometer loggers were deployed on European badgers, Meles meles, to collect data on geo-position, acceleration and magnetic compass heading, respectively. This enabled us to compare GPS data with calculated GPS-enhanced dead-reckoned data. We also examined space use, distances travelled, speed of travel, and path tortuosity in relation to habitat type.ResultsNightly distances travelled were 2.2 times greater when calculated using GPS-enhanced dead-reckoned data than when calculated using GPS data alone. The use of dead-reckoned data reduced Kernel Density Estimates (KDE) of animal ranges to approximately half the size (0.21 km2) estimated using GPS data (0.46 km2). In contrast, Minimum Convex Polygon (MCP) methods showed that use of dead reckoned data yielded larger estimates of animal ranges than use of GPS-only data (0.35 and 0.27 km2, respectively).Analyses indicated that longer periods of activity were associated with greater travel distances and increased activity-related energy expenditure. Badgers also moved greater distances when they travelled at faster speeds and when the routes that they took were less tortuous. Nightly activity-related energy expenditure was not related to average travel speed or average ambient temperature but was positively related to the length of time individuals spent outside the sett (burrow). Badger activity varied with habitat type, with greater distance, speed, track tortuosity, and activity undertaken within woodland areas. Analyses of the effects of varying GPS sampling rate indicate that assessments of distance travelled depend on the sampling interval and the tortuosity of the animal’s track. Where animal paths change direction rapidly, it becomes more important to use dead-reckoned data rather than GPS data alone to determine space use and distances.ConclusionsThis study demonstrates the efficacy of GPS-enhanced dead-reckoning to collect high-resolution data on animal movements, activity, and locations and thereby identify subtle differences amongst individuals. This work also shows how the temporal resolution of position fixes plays a key role in the estimation of various movement metrics, such as travel speed and track tortuosity.

Optimal representation of tree foliage for local urban climate modeling

Trees impact the local urban climate, notably at street level by intercepting solar radiation and providing shading. Evapotranspiration in foliage may reduce the air temperature although it may increase relative humidity and leaf drag may reduce wind speed, affecting thermal comfort. To document and quantify this impact, microclimate modeling with Computational Fluid Dynamics (CFD) simulations requires explicit information of the urban configuration, including trees. However, trees are complex individuals with a variety of shapes and a variety of foliage distribution. This study aims to investigate the sensibility to the tree modeling of the urban climate simulations. Starting with terrestrial LiDAR data from trees of different species, ages, and forms, we propose a systematic evaluation of the optimal representation of arboreal configurations in terms of local urban comfort. One way to represent the foliage of trees accurately is to apply Delaunay triangulation on the LiDAR data, which yields a convex envelope model. The resulting foliage shape is very close to the actual tree, but includes a high number of facets leading to complex objects to model numerically. Comparing four species and three maturity level of trees with this method, the paper shows that the size of the zone shadowed by a tree is the parameter with the largest impact on thermal comfort, as the ability of trees to absorb solar radiation is the main asset to improve thermal comfort. The UTCI could be up to 2.1°C lower for a mature ACPL than for a sapling, mainly because the zone covered by the tree is larger. In addition, polyhedron shape rhombicuboctahedron (RBC) produces accurate shadowed zones. Mostly, in literature, tree canopies are modeled with cubic representations while we see that they overestimate the size of the shadowed zone. To have reliable compromise between accuracy and time for conception and computational time, this paper shows that the RBC is the best alternative to common tree models. Despite requiring a good knowledge of the canopy geometry, RBC provides a strong capacity for accurately modelling complex canopy shapes of most tree species and offers large benefits in reduced complexity. We show that the RBC shape, thanks to its simple but flexible geometry, is an efficient and accurate methodological approach to model trees and allows savings in computational time (up to 15% faster than the convex envelope) and costs; and we expect that this method will improve the modeling of further parametric studies on vegetation impact on thermal urban comfort.

Convex Hull Pricing for Unit Commitment: Survey, Insights, and Discussions

Convex Hull Pricing for Unit Commitment: Survey, Insights, and Discussions

Identifying regions in wide-angle scattering via graph-theoretical approaches

The method of regions, which provides a systematic approach for computing Feynman integrals involving multiple kinematic scales, proposes that a Feynman integral can be approximated and even reproduced by summing over integrals expanded in certain regions. A modern perspective of the method of regions considers any given Feynman integral as a specific Newton polytope, defined as the convex hull of the points associated with Symanzik polynomials. The regions then correspond one-to-one with the lower facets of this polytope.As Symanzik polynomials correspond to the spanning trees and spanning 2-trees of the Feynman graph, a graph-theoretical study of these polynomials may allow us to identify the complete set of regions for a given expansion. In this work, our primary focus is on three specific expansions: the on-shell expansion of generic wide-angle scattering, the soft expansion of generic wide-angle scattering, and the mass expansion of heavy-to-light decay. For each of these expansions, we employ graph-theoretical approaches to derive the generic forms of the regions involved in the method of regions. The results, applicable to all orders, offer insights that can be leveraged to investigate various aspects of scattering amplitudes.

Secret image restoration with interpolation and social network search

Image restoration is an essential task in image processing. Due to the secret image extracted from the corrupted stego-image and its pixels may suffer different levels of damage, the type of noise is particular. Most of the existing methods have a challenge in directly removing this type of noise. Hence, we propose a corrupted secret image restoration algorithm with interpolation and social network search. Firstly, a corrupted secret image is divided into several blocks, and the convex hull of each block is calculated. For the corrupted pixels in the convex hull, the natural neighbor interpolation and bi-harmonic spline interpolation are utilized to generate the estimation values of corrupted pixels according to the density of the trusted pixels. For the corrupted pixels outside the convex hull, the social network search algorithm is applied to generate the estimated values of corrupted pixels. Finally, all corrupted pixels are recovered by the ones of their candidate values closest to their estimated values. The performance of the various methodologies was evaluated using the USCSIPI database, employing peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) indices, which demonstrated an enhancement of more than 0.78 dB and 0.0431, respectively. Experiments show that our algorithm outperforms other state-of-the-art (SOTA) algorithms.