Set Of Points Research Articles

A Central Local Metric Dimension of Generalized Fan Graph, Generalized Broken Fan Graph, and Cm ⊙ K¯m

The central local metric dimension is a new variation of local metric dimension that introduced in 2023. The central local metric dimension is a new concept that enriches research studies in graph theory, especially in the field of metric dimension. This concept combines the concept of local metric dimension by involving central points in the local metric set so that the existence of central points can strengthen the position of the local metric set in distinguishing every two neighboring points in a graph. The methodology of this research is study literature and observation. We find the central vertex of each graph and also find the local metric set of its graph, then we applied it to the related theorem to find the lower bound of central local metric dimension. Let 𝐺 be a connected graph with order 𝑛 and vertex set is 𝑉(𝐺). A subset 𝑊={𝑥1,𝑥2,…,𝑥𝑘}⊆𝑉(𝐺) is a local metric set of graph 𝐺 if the metric code of every two adjacent vertices 𝑢,𝑣 in 𝐺 are 𝑟(𝑢|𝑊)≠𝑟(𝑣|𝑊), where 𝑟(𝑢|𝑊)=(𝑑(𝑢,𝑥1),𝑑(𝑢,𝑥2),…,𝑑(𝑢,𝑥𝑘)) and 𝑟(𝑣|𝑊)=(𝑑(𝑣,𝑥1),𝑑(𝑣,𝑥2),…,𝑑(𝑣,𝑥𝑘)). A vertex 𝑥∈𝑉(𝐺) is a central vertex in 𝐺 if 𝑥 have the the shorthest distance to the another all vertices in 𝐺. If 𝑊 consist of all central vertices in 𝐺, then 𝑊 is called a central local metric set of 𝐺. The minimal cardinality of 𝑊 is called a central basis local set of 𝐺 and its cardinality is called central local metric dimension of 𝐺 or denoted by 𝑙𝑚𝑑𝑠(𝐺). In this paper we explored the central local metric dimension on generalized fan graph, generalized broken fan graph, and a graph resulting from corona operation Cm ⊙ K¯n. The result show that the central local metric dimension of generalized fan graph is equal with its order because the diameter and radius are equal. Different with it, the central local metric dimension of generalized broken fan is equal with its local metric dimension plus cardinality of central set, and the central local metric dimension of Cm ⊙ K¯n are equal with the central local metric dimension of 𝐶𝑚.

Memory loss can prevent chaos in games dynamics.

Recent studies have raised concerns on the inevitability of chaos in congestion games with large learning rates. We further investigate this phenomenon by exploring the learning dynamics in simple two-resource congestion games, where a continuum of agents learns according to a simplified experience-weighted attraction algorithm. The model is characterized by three key parameters: a population intensity of choice (learning rate), a discount factor (recency bias or exploration parameter), and the cost function asymmetry. The intensity of choice captures agents' economic rationality in their tendency to approximately best respond to the other agent's behavior. The discount factor captures a type of memory loss of agents, where past outcomes matter exponentially less than the recent ones. Our main findings reveal that while increasing the intensity of choice destabilizes the system for any discount factor, whether the resulting dynamics remains predictable or becomes unpredictable and chaotic depends on both the memory loss and the cost asymmetry. As memory loss increases, the chaotic regime gives place to a periodic orbit of period 2 that is globally attracting except for a countable set of points that lead to the equilibrium. Therefore, memory loss can suppress chaotic behaviors. The results highlight the crucial role of memory loss in mitigating chaos and promoting predictable outcomes in congestion games, providing insights into designing control strategies in resource allocation systems susceptible to chaotic behaviors.

Generalized 3-D Rigid Point Set Registration With Bidirectional Hybrid Mixture Models

Generalized 3-D Rigid Point Set Registration With Bidirectional Hybrid Mixture Models

An Integer Programming Algorithm for Constructing Maximin Distance Designs From Good Lattice Point Sets

An Integer Programming Algorithm for Constructing Maximin Distance Designs From Good Lattice Point Sets

Convergence of a Fast Hierarchical Alternating Least Squares Algorithm for Nonnegative Matrix Factorization

The hierarchical alternating least squares (HALS) algorithms are powerful tools for nonnegative matrix factorization (NMF), among which the Fast-HALS, proposed in [A. Cichocki and A.-H. Phan, 2009], is one of the most efficient. This paper investigates the convergence of Fast-HALS. First, a more general weak convergence (converged subsequences exist and converge to the stationary point set) is established without any assumption, while most existing results assume all the columns of iterates are strictly away from the origin. Then, a simplified strong convergence (the entire sequence converges to a stationary point) proof is provided. The existing strong convergence is attributed to the block prox-linear (BPL) method, which is a more general framework including Fast-HALS as a special case. So, the convergence proof under BPL is quite complex. Our simplified proof explores the structure of Fast-HALS and can be regarded as a complement to the results under BPL. In addition, some numerical verifications are presented.

Pyramid Point: A Multi-Level Focusing Network for Revisiting Feature Layers

We present a mcthod to lcarn a diverse group of object categories from an unordcrcd point set. We propose our Pyramid Point network, which uses a dense pyramid structure instead of thc traditional ’U’ shape, typically seen in semantic segmentation networks. This pyramid structure gives a second look, allowing thc network to revisit different layers creating from various leveis on the network, allowing for feature propagation. We introduce a Focused Kemel Point convolution (FKP Conv), which expands on the traditional point convolutions by adding an attention mcchanism to the kemel outputs. This FKP Conv increases our feature quality and allows us to weigh thc kemel outputs dynamically. These FKP Convs are the central part of our Recurrent FKP Bottlcneck block, which makes up thc backbonc of our encoder. With this distinct network, we demonstrate competitive performance on threc benchmark data sets.

PSD-SQ: Point Set Decoding Based on Semantic Query for Object Detection in Remote Sensing Images

PSD-SQ: Point Set Decoding Based on Semantic Query for Object Detection in Remote Sensing Images

LPOT: Locality-Preserving Gromov-Wasserstein Discrepancy for Nonrigid Point Set Registration.

The main problems in point registration involve recovering correspondences and estimating transformations, especially in a fully unsupervised way without any feature descriptors. In this work, we propose a robust point matching method using discrete optimal transport (OT), which is a natural and useful approach for assignment tasks, to recover the underlying correspondences and improve the nonrigid registration in the presence of unknown global transformations. Specifically, we cast the registration problem as a joint estimation over local transport couplings and global transformations, observing that the local neighborhood topology structures should be preserved strongly and stably for nonrigid transformations. By solving the Gromov-Wasserstein discrepancy, a smooth assignment matrix from one point set to another can be recovered in a fully unsupervised way. Registration performance can be improved by applying an unsupervised map to guide the transformation estimate under the alternating optimization. Experimental results on several datasets reveal how the presented method is superior to the state-of-the-art methods when facing large data degradations.

Accurate Registration of Cross-Modality Geometry via Consistent Clustering.

The registration of unitary-modality geometric data has been successfully explored over past decades. However, existing approaches typically struggle to handle cross-modality data due to the intrinsic difference between different models. To address this problem, in this article, we formulate the cross-modality registration problem as a consistent clustering process. First, we study the structure similarity between different modalities based on an adaptive fuzzy shape clustering, from which a coarse alignment is successfully operated. Then, we optimize the result using fuzzy clustering consistently, in which the source and target models are formulated as clustering memberships and centroids, respectively. This optimization casts new insight into point set registration, and substantially improves the robustness against outliers. Additionally, we investigate the effect of fuzzier in fuzzy clustering on the cross-modality registration problem, from which we theoretically prove that the classical Iterative Closest Point (ICP) algorithm is a special case of our newly defined objective function. Comprehensive experiments and analysis are conducted on both synthetic and real-world cross-modality datasets. Qualitative and quantitative results demonstrate that our method outperforms state-of-the-art approaches with higher accuracy and robustness. Our code is publicly available at https://github.com/zikai1/CrossModReg.

A group decision making approach based on the multi-dimensional Steiner point

<abstract> <p>The social division of labor has become increasingly specialized, and there are more and more group decision-making problems participated by multiple decision-makers. With respect to the multi-attribute group decision making problem, including two-tuple linguistic information, based on the theory and method of group decision making, Steiner point constraint and plant growth simulation algorithm, we establish a novel multi-attribute group decision making approach based on two-tuple linguistic information aggregation. We introduce Steiner points into group consensus decision making and use the PGSA algorithm to seek the global optimal point. The method seeks set points that are both mathematically and geometrically meaningful to reduce set bias. In this paper, to begin with, according to the constraints of multi-dimensional Steiner point, we map the evaluation vectors of the group experts over the alternatives into multi-dimensional space and then we propose a two-tuple linguistic information aggregation model. Moreover, we construct a comprehensive evaluation decision making approach and then design a plant growth simulation algorithm to select the optimal alternative. Finally, a case verifies the validity and rationality of the proposed model.</p> </abstract>

A Resilience Enhanced Secondary Control for AC Micro-Grids

Communication-based distributed secondary control is deemed necessary to restore the state of islanding AC microgrids to set points. As its limited global information, the microgrids become vulnerable to cyber-attacks, which by falsifying the communicating singles, like the angular frequency, can disturb the power dispatch in the microgrids or even induce blackout by pushing the microgrids beyond the safe operation area and triggering the protection. To make the microgrids more cyber secure, adaptive resilient control for the secondary frequency regulation is proposed. It assumes that each converter is communicating with its adjacent converters. With the proposed control, the weight of the communication channel being attacked is automatically reduced, and the more the communicating signals are falsified, the further the weight of that communication channel is weakened. The proposed approach does not rely on attack detection and thereby is easy to implement; Besides, it still works when challenged by a combination of multi-attack signals; Moreover, it applies to multiple communication lines getting attacked cases. Finally, the effectiveness and feasibility of the proposed resilient control scheme are validated by both simulations and experimental results.

Optimization of Food Delivery Robot Using the PID Method Ziegler Nichols Type 2 and Fuzzy Logic Mamdani

In this research in this research, the Ziegler-Nichols Type 2 PID method was used in the development of a food delivery robot that has a line follower sensor. The PID control system is used to correct input variable (sensor) measurement errors so that the system output matches the set point value to produce the smallest possible error. Ziegler-Nichols Type 2 is used for path detection optimization. Fuzzy is used to adjust the speed of the robot’s movement based on the type and weight of food against obstacles in the path. In this research, a food delivery robot containing 0% liquid and 100% liquid will be tested. The calculation of this method results in Kp 1.2, Ki 7.038, and Kd 0.051, the overshoot value is 45.2581, and the rise time is 64.2857. The optimization was carried out using the trial-and-error method, and the results obtained were Kp 0.06, Ki 0.032, Kd 0.0001, the overshoot value was 40.7109, and the rise time was 45.2286. In the fuzzy logic test, it was found that the fastest time to reach a distance of 200 cm was 3.74 seconds at the initial PWM 47% with no food load, and the longest time was 17.41 seconds at the initial PWM 31.4% with a food load of 1300gram. This occurred when delivering food that contains 100% liquid, and the success rate in food delivery is 87.5%.

Peach LAZY1 and DRO1 protein-protein interactions and co-expression with PRAF/RLD family support conserved gravity-related protein interactions across plants.

IGT/LAZY proteins play a central role in determining gravitropic set point angle and orientation of lateral organs across plant species. Recent work in model systems has demonstrated that interactions between IGT/LAZY proteins and BREVIS RADIX (BRX)-domain containing proteins, such as PH, RCC1, AND FYVE/RCC1-LIKE DOMAIN (PRAF/RLD), and BREVIS RADIX LIKE (BRXL) family members, are mechanistically important for setting gravitropic set point angle. Here, we identified peach PRAF/RLD proteins as interactors of the peach IGT/LAZY proteins PpeLAZY1 and DEEPER ROOTING 1 (PpeDRO1) from a yeast-two-hybrid screen. We also show that the BRX domains of these interacting proteins have high sequence similarity with PRAF/RLD and BRX family proteins from rice and Arabidopsis. Further, PpeLAZY1 and the peach PRAF/RLD interactors are all expressed at relatively high levels in leaf, meristem, and shoot tip tissues. Together, this evidence supports the importance and conservation of IGT/LAZY-BRX-domain interactions, which underlie setting gravitropic set point angle across angiosperms.

Internal model control of cumene process using analytical rules and evolutionary computation

Cumene is a precursor for producing many organic chemicals and is thinner in paints and lacquers. Its production process involves one of the large-scale manufacturing processes with complex kinetics. Different classical control strategies have been implemented and compared in this process for the cumene reactor. As a system with large degrees of freedom, a novel approach for extracting the state space model from the COMSOL Multiphysics implementation of the system is adopted here. Internal Modern Control (IMC) based PI and PID controllers are derived for the system. The system is reduced to the FOPDT and SOPDT model structure to derive the controller setting using Skogestad half rules. The integral time is modified for excellent set point tracking and faster disturbance rejection. From the analysis, it can be stated that the PI controller suits more for this specific process. The particle swarm optimization (PSO) algorithm, an evolutionary computation technique, is also used to tune the PI settings. The PI controllers with IMC, Zeigler Nichols, and PSO tuning are compared, and it can be concluded that the PSO PI controller settles at 45 s without any oscillations and settles down faster for the disturbance of magnitude 0.5 applied at t = 800 s. However, it is computationally intensive compared to other controller strategies.

On Logarithmic Holder Condition and Local Extrema of Power Takagi Functions

This paper studies one class of real functions, which we call Takagi power functions. Such functions have one positive real parameter; they are continuous, but nowhere differentiable, and are given on a real line using functional series. These series are similar to the series defining the continuous, nowhere differentiable Takagi function described in 1903. For each parameter value, we derive a functional equation for functions related to Takagi power functions. Then, using this equation, we obtain an accurate two-sides estimate for the functions under study. Next, we prove that for parameter values not exceeding 1, Takagi power functions satisfy the Holder logarithmic condition, and find the smallest value of the constant in this condition. As a result, we get the usual Hölder condition, which follows from the logarithmic Hölder condition. Moreover, for parameter values ranging from 0 to 1, we investigate the behavior of Takagi power functions in the neighborhood of their global maximum points. Then we show that the functions under study reach a strict local minimum on the real axis at binary-rational points, and only at them. Finally, we describe the set of points at which our functions reach a strict local maximum. The benefit of our research lies in the development of methods applicable to continuous functions that cannot be differentiated anywhere. This can significantly expand the set of functions being studied.

Modeling of a Greenhouse Climatic Conditions Control System with PID Controller for Plant Growth Optimization

In modern agriculture, our focus is on optimising crop cultivation, particularly in greenhouses, to enhance productivity and resource efficiency. This paper investigates the pivotal role of temperature and humidity control in greenhouses for optimal plant growth. Our study employs a Matlab/Simulink-designed system for continuous monitoring, analysis, and real-time adjustments, connecting with various actuators and integrating external data. Results show the system efficiently corrects variations, ensuring temperature and humidity return to set points of 25°C and 60% respectively. This underscores the transformative potential of the control system in revolutionizing agriculture for increased efficiency and sustainability.

2-DOF Preview Feedforward Sliding Mode Controller for the Control of Multivariable Process with Dead Time

This paper proposes a 2-DOF preview feedforward sliding mode controller (PFFSMC), which has a combination of feedback and feedforward terms in the sliding surface, for controlling the multivariable process with dead time, for both set point tracking and disturbance rejection. The proposed controller is applied for the control of the Wood and Berry binary distillation column having the composition of top and bottom products. The performance of the 2-DOF PFFSMC is compared with that of the 1-DOF preview sliding mode controller. The proposed controller delivered better responses for set point tracking and for disturbance rejection. The performance of the proposed 2-DOF PFFSMC is compared with the other controllers reported in the literature and, it was found that there was a significant reduction in the settling time by more than 76%, without any overshoot in the closed loop response. The proposed controller was robust against ±5% parametric uncertainties in gain, time constant, and dead time when these uncertainties were considered alone and together. The stability of the proposed controller was verified using the Lyapunov stability criterion.

Genetic algorithm-enhanced linear quadratic control for balancing bicopter system with non-zero set point

Bicopter is an unmanned aerial vehicle (UAV) with the advantage of saving energy consumption. However, the unique two rotors design presents a challenge in designing a controller that achieves good stability, fast settling time, and the ability to overcome oscillations simultaneously. This article proposes a new control method for bicopter that uses a genetic algorithm optimization approach in the linear quadratic (LQ-GA) control method. The GA is used to search for the best weighting matrix parameters, Q and R, in the Linear Quadratic (LQ) control scheme. The proposed control method was tested on a balancing bicopter test platform with an input in the form of difference in pulse width modulation (PWM) signals for both rotors and an output in the form of roll angle. The control system was evaluated based on the stability of the transient response and the generated control signal. The results of the tests showed that the proposed LQ-GA control method has better stability, faster settling time, and smaller overshoot than the existing PI and standard LQ control methods. Therefore, the proposed LQ-GA control method is the most suitable for use in a balancing bicopter system with a non-zero setpoint.

On the computation of Delaunay triangulations via genetic algorithms

AbstractIn this work, we introduce a new approach for computing Delaunay triangulations. Delaunay triangulations have numerous applications in geolocation, communications and other ICT systems or practical applications. Having available various types of approaches for computing such structures is rather desired from an implementation and computational point of view. We adopt Genetic Algorithms for computing Delaunay triangulations and present the design and evaluation of our novel approach. We consider a set of points in the plane as vertices and connect them with edges, creating the point graph. We have developed in C++ an application framework based on genetic algorithms, called , which produces the Delaunay triangulation structure of a given set of points in the plane. considers a novel graph-based chromosome representation of desired solutions, creates an initial population of individuals (chromosomes), an initial generation, and produces from the original population (generation) new generations of individuals in each repetition of the genetic process of Reproduction. Each new generation emerges more robust than the previous one. Our evaluations have revealed that the Delaunay triangulation yielded by , achieves an accuracy of 98–100% of the optimal Delaunay triangulation, while maintaining good convergence speed. Despite its limitations in computational time and space, the proposed novel approach exhibits several complementary benefits to computational geometry based approaches, such as allowing the insertion of new points in the triangulation dynamically, leading to seamless adaptation to new conditions, parallelization of the computational process and tolerance to noise regarding the coordinates of the points. Therefore, this work provides a useful alternative approach for computing Delaunay triangulations.

Characterizations of the set of integer points in an integral bisubmodular polyhedron

In this note, we provide two characterizations of the set of integer points in an integral bisubmodular polyhedron. Our characterizations do not require the assumption that a given set satisfies the hole-freeness, i.e., the set of integer points in its convex hull coincides with the original set. One is a natural multiset generalization of the exchange axiom of a delta-matroid, and the other comes from the notion of the tangent cone of an integral bisubmodular polyhedron.