Local Minimum Point Research Articles

Computing Quadratic Eigenvalues and Solvent by a New Minimization Method and a Split-Linearization Technique

To solve quadratic eigenvalue problems (QEPs), especially the gyroscopic systems, two methods are proposed: an iterative direct detection method (DDM) of the complex eigenvalues of the original QEP, and a split-linearization method (SLM) for finding the solvent matrix, which results to a standard linear eigenvalue problem (LEP) being solved to compute all eigenvalues by the symmetry extension. Reducing the dimension to one-half, the LEP is recast in a simpler QEP involving the square of the solvent. We set up two new merit functions which are minimized to detect the complex eigenvalues from the original QEP and a simpler QEP. For each eigen-parameter the merit function consists of the Euclidean norm of each derived eigen-equation, whose vector variable is solved from a derived inhomogeneous linear system. Then, the golden section search algorithm is employed to minimize the merit functions and locate the complex eigenvalue as a local minimal point. The results are compared with that computed by the cyclic-reduction-based solvent (CRS) method.

3D-AMM: a 3D artificial moment method for path planning of manipulator in multiple obstacles scenario

PurposeIn response to the issue of traditional algorithms often falling into local minima or failing to find feasible solutions in manipulator path planning. The purpose of this paper is to propose a 3D artificial moment method (3D-AMM) for obstacle avoidance for the robotic arm's end-effector.Design/methodology/approachA new method for constructing temporary attractive points in 3D has been introduced using the vector triple product approach, which generates the attractive moments that attract the end-effector to move toward it. Second, distance weight factorization and spatial projection methods are introduced to improve the solution of repulsive moments in multiobstacle scenarios. Third, a novel motion vector-solving mechanism is proposed to provide nonzero velocity for the end-effector to solve the problem of limiting the solution of the motion vector to a fixed coordinate plane due to dimensionality constraints.FindingsA comparative analysis was conducted between the proposed algorithm and the existing methods, the improved artificial potential field method and the rapidly-random tree method under identical simulation conditions. The results indicate that the 3D-AMM method successfully plans paths with smoother trajectories and reduces the path length by 20.03% to 36.9%. Additionally, the experimental comparison outcomes affirm the feasibility and effectiveness of this method for obstacle avoidance in industrial scenarios.Originality/valueThis paper proposes a 3D-AMM algorithm for manipulator path planning in Cartesian space with multiple obstacles. This method effectively solves the problem of the artificial potential field method easily falling into local minimum points and the low path planning success rate of the rapidly-exploring random tree method.

Desingularization of 2D elliptic free-boundary problem with non-autonomous nonlinearity

In this paper, we consider the existence and limiting behaviour of solutions to a semilinear elliptic equation arising from confined plasma problem in dimension two \[ \begin{cases} -\Delta u=\lambda k(x)f(u) & \text{in}\ D,\\ u= c & \displaystyle\text{on}\ \partial D,\\ \displaystyle - \int_{\partial D} \frac{\partial u}{\partial \nu}\,{\rm d}s=I, \end{cases} \] where $D\subseteq \mathbb {R}^2$ is a smooth bounded domain, $\nu$ is the outward unit normal to the boundary $\partial D$ , $\lambda$ and $I$ are given constants and $c$ is an unknown constant. Under some assumptions on $f$ and $k$ , we prove that there exists a family of solutions concentrating near strict local minimum points of $\Gamma (x)=({1}/{2})h(x,\,x)- ({1}/{8\pi })\ln k(x)$ as $\lambda \to +\infty$ . Here $h(x,\,x)$ is the Robin function of $-\Delta$ in $D$ . The prescribed functions $f$ and $k$ can be very general. The result is proved by regarding $k$ as a $measure$ and using the vorticity method, that is, solving a maximization problem for vorticity and analysing the asymptotic behaviour of maximizers. Existence of solutions concentrating near several points is also obtained.

Quasi Strongly $ E $-preinvexity and its relationships with non-linear programming

In this paper, we extend the class of strongly $ E $-preinvex and strongly $ E $-invex functions to quasi strongly $ E $-preinvex, quasi strongly $ E $-invex and pseudo strongly $ E $-invex functions. Some non-trivial suitable examples have been constructed in support of our definitions. Several interesting properties and relationships of these functions are discussed. Furthermore, to show the application of our results, we consider a non-linear programming problem and show that the local minimum point is also a strictly global minimum.

Selective image segmentation driven by region, edge and saliency functions

Present active contour methods often struggle with the segmentation of regions displaying variations in texture, color, or intensity a phenomenon referred to as inhomogeneities. These limitation impairs their ability to precisely distinguish and outline diverse components within an image. Further some of these methods employ intricate mathematical formulations for energy minimization. Such complexity introduces computational sluggishness, making these methods unsuitable for tasks requiring real-time processing or rapid segmentation. Moreover, these methods are susceptible to being trapped in energy configurations corresponding to local minimum points. Consequently, the segmentation process fails to converge to the desired outcome. Additionally, the efficacy of these methods diminishes when confronted with regions exhibiting weak or subtle boundaries. To address these limitations comprehensively, our proposed approach introduces a fresh paradigm for image segmentation through the synchronization of region-based, edge-based, and saliency-based segmentation techniques. Initially, we adapt an intensity edge term based on the zero crossing feature detector (ZCD), which is used to highlight significant edges of an image. Secondly, a saliency function is formulated to detect salient regions from an image. We have also included a globally tuned region based SPF (signed pressure force) term to move contour away and capture homogeneous regions. ZCD, saliency and global SPF are jointly incorporated with some scaled value for the level set evolution to develop an effective image segmentation model. In addition, proposed method is capable to perform selective object segmentation, which enables us to choose any single or multiple objects inside an image. Saliency function and ZCD detector are considered feature enhancement tools, which are used to get important features of an image, so this method has a solid capacity to segment nature images (homogeneous or inhomogeneous) precisely. Finally, the adaption of the Gaussian kernel removes the need of any penalization term for level set reinitialization. Experimental results will exhibit the efficiency of the proposed method.

An early indicator index of tornadic storms for Euro-Mediterranean region

Tornadoes are the most violent and destructive of all the severe weather phenomena that localized convective storms produce. There is a requirement in operational meteorology increasing nowadays that an indicator index which allows to reduce the uncertainty of severe convective storms and tornadoes in the scope of climate change adaptation strategies. The main intention is not to replace or substitute mesoscale modeling approaches, or composite indexes, but to warn operationally to draw attention to the Eastern Mediterranean and Türkiye in particular a few days in advance. The development of some indicators using atmospheric variables can undertake a crucial role by enabling such numerical models to be run only at certain time intervals, thus enduring lower computational costs. In this study, Eastern Mediterranean oscillation index (EMEDOi) has been developed in order to be able to detect the presence of ULLs (upper-level low) and frontogenesis approach is employed for selected tornadic storm events in Türkiye. EMEDOi has 7 different its variations (members) which these members have been developed to detect differences depending on the entry directions of cyclones and storms influencing Türkiye from the west of the country. In line with the GDAS data analysis, values of geopotential height are derived for the requirement of EMEDOi in a limited area. A few of the results from the study are as in the following: 86% of the trained tornado events revealed that the EMEDO-Oper index was in negative phase at the time a tornado was reported, regardless of whether the events featured a supercell mesoscale convective storm or a frontal movement. The hourly period until the local minimum is obtained can be described and characterized as the process by which the EMEDO-Oper index value decreases continuously. The time required to reach the local minimum varies based on the tornado occurrence. Based on the tornadic storm scenario in the test cluster in 2022 and the train cluster, this timeframe is predicted to be roughly 33.2 h on average. In western Türkiye, there is a 79% chance of a tornado occurring between six and forty-two hours after the EMEDO-Oper index reaches its local minimum. In particular, the projected chance for this period is 63% between 12 and 30 h after the local minimum is obtained. Besides, the majority of the tornado incidents with EMEDO-Oper values below − 0.75 were evaluated. After an EMEDO-Oper index value falls below that threshold, it is likely to forecast the risk period of a tornado in Türkiye with a probability of 79% and the local minimum point must be identified.

Concentration of nodal solutions for semiclassical quadratic Choquard equations

In this article concerns the semiclassical Choquard equation \(-\varepsilon^2 \Delta u +V(x)u = \varepsilon^{-2}( \frac{1}{|\cdot|}* u^2)u\) for \(x \in \mathbb{R}^3\) and small \(\varepsilon\). We establish the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function \(V\), by means of the perturbation method and the method of invariant sets of descending flow. For more information see https://ejde.math.txstate.edu/Volumes/2023/75/abstr.html

Research on Fast Multi-Threshold Image Segmentation Technique Using Histogram Analysis

This paper investigates a method for the multi-threshold segmentation of grayscale imaging using the local minimum points of a histogram curve as the segmentation threshold. By smoothing the histogram curve and judging the conditions, the expected peaks and valleys are identified, and the corresponding minimum points are used as segmentation thresholds to achieve fast multi-threshold image segmentation. Compared to the OTSU method (maximum between-class variance) for multi-threshold segmentation and the region growing method, this method has less computational complexity. In the recognition and segmentation process of solder pads with adhesion of underfill in LED Chips, the segmentation time is less than one percent of that of the OTSU method and the region growing method. The segmentation effect is better than the OTSU method and the region growing method, and it can achieve fast multi-threshold segmentation of images. Moreover, it has strong adaptability to the differences in the overall grayscale of images, meeting the requirements for high UPH (Units Per Hour) in industrial production lines.

Improved artificial potential field method for local minima

With the development of autonomous driving technology, its applications permeate many aspects of work and life, providing convenience while reducing labor costs. Path planning has always been important for autonomous driving, where APF is widely used thanks to its simplicity of calculation and effectiveness. However, therere still problems existing such as local minima, influenced by initial positions and parameters, and so on. In this study, a better approach to solving the local minimum issue is suggested. Firstly, the odometry method is used for the determination of falling into local minima by saving and computing the relationships between adjacent steps. Subsequently, a variable step length method is designed for escaping local minimum points and bypassing obstacles in front. The feasibility and robustness of the method were verified by simulations, and this method proved capable of solving the local minima and planning a reasonable trajectory.

Analysis of the Ink-Stream Break-Up Phenomenon in Continuous Inkjet Printing.

The ink-stream break-up phenomenon in continuous inkjet printers has been studied herein. A numerical model has been developed to reproduce and analyze the non-monotonic behavior of ink-stream break-up length (BUL) against the amplitude of piezo-actuator oscillation. That is, when the amplitude is increased, the BUL initially decreases to a local minimum point, then increases to a local maximum point, and finally decreases again. The developed model is split into two stages, first being the emergence of periodic "initial indentation" on ink stream caused by piezo-oscillation and the second being the growth of indentation. Finally, the calculated results of BUL against oscillation amplitude is compared with experimental data. We confirmed that the model well reproduces the characteristic of BUL and clarified the emergence mechanism of its local minimum and maximum points.

Reconsidering Multi-Branch Aggregation for Semantic Segmentation

For semantic segmentation tasks, there are problems in using multi-branch structures to enrich feature maps and aggregate different branches of feature maps in a certain network depth, such as the insufficient richness of feature maps and the incomplete aggregation of feature maps. Given multi-branch feature maps and branch aggregation, this study proposes a lightweight method, called multi-branch aggregation atrous spatial pyramidal pooling, by introducing an attention mechanism and CARAFE to enrich the features of the feature maps, giving the feature maps adaptive parameters, periodically adjusting the adaptive parameters, and aggregating the feature maps in both the vertical and horizontal directions. First, the atrous pyramid is retained and the attention mechanism and CARAFE are used to handle the pooling features to obtain 10 different feature maps. Secondly, giving each feature map a cascaded adaptive parameter and periodically adjusting the adaptive parameter to promote or suppress certain feature maps prevents the model from being at a local minimum or saddle point for long periods due to aleatory uncertainty. Finally, the feature maps are vertically aggregated, horizontally aggregated, and weighted for summation. This work demonstrates a competitive performance on the benchmark dataset, with an improvement of 1.88% in MPA, 0.66% in FWIoU, and 1.29% in MIoU compared to atrous spatial pyramid pooling. The benchmark datasets include PASCAL VOC 2012 and CIFAR-100.

On the Improvement of the Heuristic Algorithm for Packing Circles into a Circle of Minimum Radius

The article is devoted to investigation of a heuristic algorithm for solving the competitive problem "Circles Dense packing into a circle of minimum radius" and development of its improved version using Shor's r-algorithm with step dichotomy. The heuristic algorithm was developed by Bohdan Zadorozhnyi, a third-year student of Uzhhorod National University. The program implemented on its basis took second place in the competition and used less time than the maximum time, which, according to the competition, was allocated for a one-time launch of the program for 50 competitive tasks. The article describes the research results of how the Shor r-algorithm can be used to improve efficiency of the heuristic algorithm. The algorithm for improving the heuristic solution is implemented according to the following scheme. We start from the best arrangement of circles found by the heuristic algorithm. Then, we perform the following four stages of the algorithm: Stage 1. We set a rather large value of the initial step (we determine it depending on the input data or simply choose it as a large step); Stage 2. We run the r-algorithm from the starting point and find the local minimum of the corresponding nonlinear programming problem; Stage 3. If the local minimum found guarantees a smaller radius of the outer circle, then the local minimum point becomes the starting point; the local minimum found does not guarantee a smaller radius of the outer circle, then the size of the step h is reduced by half. Stage 4. If the step value is greater than the specified value, then we proceed to Stage 2. Otherwise, we finish work of the algorithm with solution improvement. Python 3.9.5 programming language and NumPy 1.24.2 library were used for software implementation of both algorithms. For 50 competitive tests and different number of iterations of the heuristic algorithm (10, 20, 30, 40 and 50 iterations), the analysis of the obtained results was conducted according to three parameters: the number of points obtained, program execution time and the number of exchanges of circles in one iteration of the heuristic algorithm. For most of the competitive tests, the refined algorithm allows you to get better results in points, in particular, in most cases the improvement is up to 2 points, and in some cases – from 3 to 6 points. The biggest improvements (6 points) are seen in tests, where the circles have the same or close radii. Here, the heuristic algorithm works not so effectively, therefore, for such tests, due to the algorithm with refinement, it is possible to significantly improve the results of competitive tasks in terms of points. Keywords: circle packing, heuristics, r-algorithm, Python 3.9.5, NumPy 1.24.2.

Path planning of mobile robot based on improved artificial potential field method

Artificial potential field method is widely used in robot path planning because of its simplicity, efficiency and smooth path generation. In this paper, based on the introduction of the basic principle of the artificial potential field method, the limitations of the algorithm are analysed in depth, and improvement methods are summarized for these problems. Aiming at the problem that the target near the obstacle is unreachable in the traditional artificial potential field method, an improved repulsive force potential field function is used to introduce the distance between the robot and the target point into the potential field function, so that the potential field of the target position is minimized in the global potential field, so that the robot can successfully reach the target. Using the obstacle connection method, the robot can quickly get rid of the local minimum point, go out of the local minimum area, and complete the path planning. The simulation results show that the method is effective.

Evaluating interfacial bonding quality of multilayered structure based on ultrasonic testing technology

An ultrasonic evaluation method of interfacial bonding quality from layered structures is proposed for enhancing the testing accuracy. The ultrasonic reflection and transmission characteristic is theoretically analyzed, which focus on the different quality of the single and double bonding interface with spring-type. The reflection coefficient and transmission coefficient mathematic models, which include multiple parameters, are derived from the transfer matrix. Taking the first, second, and the double bonding interface as the research objects, respectively, two types of resonant frequencies have been presented by numerical solving the model, namely, the first type resonance frequency (RFI) and the second type resonance frequency (RFII). The results show that the interval of the RFⅠ is related to medium thickness of the maximum acoustic impedance. Similarly, the interval of the RFⅡ depends on other layers’ thickness. In addition, the transmission coefficient shows a change in different trends with the bonding interface gradually tending to rigid. When the adhesive layer thickness is sufficiently small compared with the wavelength, the reflection coefficient shows many local minima points at a certain frequencies range, the frequency of local minimum point increases with the increase of the stiffness coefficient. The experimental results are in good agreement with the numerical solution results and finite element analysis results.

PDAS: Improving network pruning based on Progressive Differentiable Architecture Search for DNNs

Network pruning is an efficient approach to adapting large-scale deep neural networks (DNNs) to resource-constrained systems; the networks are pruned using the predefined pruning criteria or a flexible network structure is explored with the help of neural architecture search, (NAS). However, the former crucially relies on the human expert knowledge, while the latter usually requires one to make many simplifications to ensure the efficiency of the search, resulting in limited performance. This paper presents a new pruning approach called Progressive Differentiable Architecture Search (PDAS) that realizes a better balance between computation efficiency and model performance. First, a joint search-update scheme for search optimization is presented; it constantly refines the candidate number of channels in each layer by performing differentiable searching and evolutionary updating alternately. The latter can provide new high-probability candidates continuously to avoid local minimum point. Second, a two-stage constrained progressive search strategy is presented for some complex nonlinear networks (such as ResNet) that are more difficult to prune for existing approaches; it effectively avoids the over-fitting problem caused by the excessive search space and largely reduces the consumption of 1x1 convolution in the skip connections of the residual blocks with little accuracy loss. Extensive experiments on some representative datasets (such as CIFAR-10, CIFAR-100, and ImageNet) approve the superior performance of PDAS compared to most existing network pruning algorithms available. Notably, compared to the state-of-the-art LFPC, PDAS can even prune about 8% more FLOPs on ResNet-110 (on CIFAR-10) and ResNet-50 (on ImageNet), respectively, while coming with almost identical and ignorable accuracy losses.

Molecular dynamics simulation of polymorphic transformation between ε-CL-20 and β-CL-20 by short range order and orientational order parameter

Phase transition simulation of molecular crystals is a challenge. In order to clarify the polymorphic transformation mechanism of molecular crystal, a molecular dynamics (MD) simulation of the transformation between ε-CL-20 and β-CL-20 was carried out by the short range order g(r) and local orientational order parameter (OPs) P2(cosθ) as well as the spatial orientation correlation function. The effects of the temperature on them were performed. The results indicate that the g(r), orientational OPs and spatial orientation correlation function, composed of the structural parameters from three CL-20 molecules in three different single crystal, could be used to simulate the process of the polymorphic transformation between ε-CL-20 and β-CL-20. Only at a high temperature, could two kinds of the CL-20 supercells realize the transformation of crystal form. Furthermore, there were local and global minimum energy points, indicating that there could be the metastable or stable crystal forms in the process of the transformation from β-CL-20 to ε-CL-20. The values of P2(cosθ) were well related to results of the surface electrostatic potentials (ESPs), suggesting that the ESPs have an influence on polymorphic transformation.

Applications of fractional gradient descent method with adaptive momentum in BP neural networks

A novel fractional gradient descent method with adaptive momentum is presented in this paper to improve the convergence speed and stability for BP neural network training. The fractional Grünwald-Letnikov derivative is used for the fractional gradient. The coefficient of the momentum term is set as an adaptive variable, depending on the fractional gradient of the current step and the weight change of the previous step. We give a detailed convergence proof of the proposed method. Experiments on MNIST data sets and XOR problem demonstrate that the fractional gradient descent method with adaptive momentum term can effectively improve convergence speed, maintain stability of BP neural network training, help escape from local minimum points, and enlarge the selection range of the learning rate.

Localized nodal solutions for system of critical Choquard equations

In this paper, we study the system of critical Choquard equations ɛ2Δvj−a(x)vj+∑i=1kβijɛ−α(∫RN|vi(y)|2α∗dy|x−y|N−α)|vj|2α∗−2vj+λj|vj|q−2vj=0,x∈RN,vj(x)→0as|x|→∞,j=1,…,k,where N≥3, λj>0,j=1,…,k,(N−4)+<α<N,2α∗=N+αN−2, max{2,2∗−1}<q<2∗=2NN−2, ɛ>0 is a small parameter and the potential function a is bounded and positive. By the truncation method and the method of invariant sets of descending flow, we establish for small ɛ the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function a.

A boreal wildfire and harvesting database with ensemble confidence attributes for Ontario (1972–2021+)

We present a repeatable workflow that produced a comprehensive wildfire and timber harvesting database for Ontario (1972–2021) that accommodates annual updates after each new fire season. Training sites for classification are identified at the individual scene-level to avoid spectral variations introduced by time and distance. ISODATA classification on the training data produces clusters that are modelled by a smooth polynomial function to identify a local minimum point along the classification clusters that distinguishes disturbances from non-disturbances. This threshold is then applied to map disturbances on independent scenes of Landsat MSS, TM, ETM+, or OLI imagery. Results are aggregated to 1.44 ha cells and converted to points for dissemination; we do not map explicit boundaries to avoid issues of context- and scale-dependence, or the realities of transitional boundaries. Disturbance points are cross-referenced through time, ensuring that the earliest date for each disturbance is recorded. Disturbance points are intersected with other harvesting and fire databases to assess their ensemble confidence which is attached to each mapped location. We present summaries of Ontario’s boreal disturbance mapping with respect to levels of assessed confidence.

A Novel Codebook Generation by Smart Fruit Fly Algorithm based on Exponential Flight

A codebook is a combination of vectors that represents a digital image best and very useful tool for compression. Besides the well-known techniques such as Linde-Buzo-Gray, C-Means, and Fuzzy C-Means the nature-inspired metaheuristic algorithms have also become alternate techniques for solving the codebook generation problem. Fruit Fly Optimization Algorithm (FFA) is a simple and efficient algorithm, but the capturing of an agent by a local minimum point is the main problem. Therefore, the fruit flies generally do not reach the global solution at the end of the iterations. In this study, the FFA is empowered with a smart exponential flight approach to finding out a global optimum codebook. In this approach, if a fruit fly agent is captured by a local minimum point accidentally, the smart exponential flight steps provide an opportunity to escape from it easily. In the experimental studies, successful compression results have been taken in terms of lower error rates. The numerical results prove that the proposed Smart Exponential flight-based Fruit Fly Algorithm (SE-FFA) is better than the variations of convolutional FFA by providing a global optimum codebook.