Minimum Path Research Articles

Surface tension gradient invoked path selection.

Certain active particles execute continuous self-propelled motion at the air-water interface due to Marangoni forces. Here, we report motion of camphor and pentanol infused disks in an L-shaped two path and a Y-shaped three path channel. These channels are open to the sink. In both the cases, these channels have asymmetry in arm-lengths while the arm-widths are equal. The active disks are introduced in the decision region (center) of the channel from where they elect to move along a particular path towards the sink. We observe that these active disks show a preference for reaching the sink along the minimal (in length) path. The camphor disk prefers the minimal path 80% of the time in the two-path and 68% of the time in the three-path channels, while for the pentanol disk, the preference rates for the minimal path selection are 88% and 74%, respectively. Furthermore, we perform numerical analysis to validate the experimental observations.

Study Some Methods To Measure The Reliability System Neutrosophically

Industry has developed greatly nowadays, and it has been accompanied by great complexity in machines and devices. Researches that seeks to obtain high efficiencies for these machines have emerged , such as reliability theory. Due to the verity and complexity of the machines, we resort to using the neutrosophic reliability that includes cases excluded from classical reliability. The aim of this paper is to define the neutrosophic parallel system and study neutrosophic methods of calculating the neutrosophic reliability, where the basic concept neutrosophic adjacency matrix of system are present by defined neutrosophic adjacency matrix of neutrosophic graph. Two methods for calculate the neutrosophic reliability are defined conformity to neutrosophic logic which are neutrosophic minimal path method and neutrosophic tracing method. some applications have been introduced.

Determining reliability signature by minimal cut method for complex-parallel network

The process of counting minimal cut sets (MCS) in a network is typically more difficult than finding minimal path sets (MPS). The first aim of this work is to provide a precise and effective method for counting the (MCS) of directed networks. The second aim is to calculate the effectiveness of a complex-parallel network using the (MCM) to evaluate the reliability of a complex-parallel network. The (MCM) has been applied for predicting network reliability, minimal (MS), tails signatures (TS), signatures, and Barlow-Brochan indexes.

Generated admissible orders for intervals by matrices and continuous functions

In this paper, we systematically study the algebraic structures of the spaces L([0,1]), encompassing all closed subintervals of [0,1], under the generated admissible orders. We first prove that the admissible order on L([0,1]) generated by a non-degenerate matrix must be the form of two weighted averaging operators. As a corollary, we deduce that each admissible order on L([0,1]) generated by a non-degenerate matrix and the standard order ≤ on [0,1] are not isomorphic. Furthermore, we show that each admissible order on L([0,1]) derived from two continuous mappings and the standard order ≤ on [0,1] are not isomorphic, partially answering a conjecture proposed by Santana et al. (2020) [38]. Besides, we prove that L([0,1]) is a complete lattice under the admissible order generated by two continuous mappings. This is the first result regarding the completeness of L([0,1]). Finally, we apply the admissible orders to solve a minimal path problem within the context of interval-valued fuzzy weighted graph. The above results theoretically refine the study of the classification, non-isomorphism, and completeness of admissible orders, while expanding the scope of interval-valued fuzzy sets in practical applications.

A new hybrid inequality BAT for comprehensive all-level d-MP identification using minimal paths in Multistate Flow Network reliability analysis

In various network applications like wireless sensors, utilities, IoT, and transport systems, multistate flow networks (MFNs) serve as valuable models. A d-level minimal path (d-MP) is a unique type of MFN characterized by having a maximum flow of d without any redundant arcs. Assessing MFN reliability is critical and often relies on the d-MP algorithm, a foundational method for calculating reliability. Existing d-MP algorithms, however, lack the capability to concurrently identify all-level d-MPs. We propose a novel algorithm, the Hybrid Inequality Binary-Addition-Tree (IBAT), which overcomes existing limitations by concurrently discovering all-level d-MPs (decision-making points), thus enabling more informed decision-making. This hybrid IBAT combines the IBAT with several key techniques: the path-based layered-search algorithm (PLSA), sequential verification, the MP-to-arc state transformation, the cycle test, and the logarithmic prime pairwise comparison method (LPM). In contrast to existing methods, our BAT-based approach consistently showcases superior performance in the parallelized retrieval of all-level d-MPs, as substantiated through experiments conducted on 12 benchmark MFNs. Compared to existing methods, our BAT-based approach demonstrates superior performance in parallelized retrieval of all-level d-MPs in the execution times in discovering d-MPs across all levels, as validated by experiments on 12 benchmark MFNs.

Using a Node–Child Matrix to Address the Quickest Path Problem in Multistate Flow Networks under Transmission Cost Constraints

The quickest path problem in multistate flow networks, which is also known as the quickest path reliability problem (QPRP), aims at calculating the probability of successfully sending a minimum of d flow units/data/commodity from a source node to a destination node via one minimal path (MP) within a specified time frame of T units. Several exact and approximative algorithms have been proposed in the literature to address this problem. Most of the exact algorithms in the literature need prior knowledge of all of the network’s minimal paths (MPs), which is considered a weak point. In addition to the time, the budget is always limited in real-world systems, making it an essential consideration in the analysis of systems’ performance. Hence, this study considers the QPRP under cost constraints and provides an efficient approach based on a node–child matrix to address the problem without knowing the MPs. We show the correctness of the algorithm, compute the complexity results, illustrate it through a benchmark example, and describe our extensive experimental results on one thousand randomly generated test problems and well-established benchmarks to showcase its practical superiority over the available algorithms in the literature.

A flow-directed minimal path sets method for success path planning and performance analysis

Emergency operation plans are indispensable elements for effective process safety management especially when unanticipated events occur under extreme situations. In the paper, a synthesis framework is proposed for the integration success path planning and performance analysis. Within the synthesis framework, success path planning is implemented through flow-directed signal tracing, renaming and reconstruction from a complete collection of Minimal Path Sets (MPSs) that are obtained using graph traversal search on GO-FLOW model diagram. The performance of success paths is then evaluated and prioritized according to the task complexity and probability calculation of MPSs for optimum action plans identification. Finally, an Auxiliary Feed Water System of Pressurized Water Reactor (PWR-AFWS) is taken as an example system to demonstrate the flow-directed MPSs search method for success path planning and performance analysis. It is concluded that the synthesis framework is capable of providing procedural guidance for emergency response and safety management with optimal success path planning under extreme situations.

An Improved Method to Search All Minimal Paths in Networks

Minimal paths (MPs) play an important role in system reliability analysis, such as binary network reliability evaluation and multistate network reliability evaluation. Searching all MPs is an NP-hard problem. The direct-search-based algorithm implements the depth-first search (DFS) mechanism to find all MPs, which is a simple and efficient method. The current efficient DFS algorithm is based on backtracking and linked list by nodes. In this article, we propose several improvements to speed up the current algorithm. First, we find that the relative positional information of the network can be used to avoid visiting some unnecessary nodes. Thus, we improve the algorithm by incorporating the point in the polygon algorithm to avoid visiting nodes surrounded by other nodes in a network. Second, we further improve the current backtracking condition in which the time complexity of implementing each backtrack is reduced. In addition, we find that different search branches from a similar node are independent and can be executed in parallel. A parallel search mechanism is proposed and incorporated to speed up the searching process. Through computational experiments on several benchmark networks and real transportation networks, we demonstrate that the improved algorithm is more efficient than the existing algorithm. The proposed algorithm becomes more advantageous as the size of the network grows.

Computing the Reliability of a Multistate Flow Network with Flow Loss Effect

Multistate flow networks (MFNs) and their reliability problem have been studied extensively. However, most of the research on MFN reliability assumes that flow into and out of any arc is equal. In practical applications, flow may experience loss during transmission such that flow into and out of an arc may not be equal. Thus, this article concentrates on the reliability of an MFN with flow loss effect, defined as the probability that the sink node can receive a flow of at least <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> units when the flow experiences loss without replenishment during transmission. Using minimal paths, a simple method is put forth to compute this reliability index, and the solution procedure is illustrated via a simple network example. Finally, computational experiments are provided to investigate the impact of flow loss on network reliability.

Facies conditional simulation based on VAE-GAN model and image quilting algorithm

Characterization of complex reservoir structures by using limited observations is challenging in geosciences because it requires to reproduce geological realism. We propose a novel method to reconstruct complex structures by combining variational autoencoder and generative adversarial networks (VAE-GAN) with conditional image quilting algorithm. It improves the stability of traditional GAN-based simulation method without decreasing the quality of patterns. Firstly, we construct a VAE-GAN model to extract the high-dimensional features of facies patterns and to create abundant new patterns. The VAE-GAN-based learning method has a good ability in feature learning from training patches and accurately reproduce new facies patterns. Finally, these new patterns are spliced together to reconstruct a complex geological structure by employing the conditional image quilting algorithm, in which patterns are pasted to the simulated areas based on the calculated minimum cost path. During this process, conditioning is also considered. Since the pattern is generated by using the deep learning method rather than directly extracted from the training image, the diversity of realizations is enhanced without losing reproducibility. Based on synthetic training image, several examples are described and analyzed in detail, demonstrating the effectiveness and reliability of the present method. In addition, the new method is applied to a real training image. The complex heterogeneous structures are well reproduced by our method, indicating its practicability.

A comprehensive network meta-analysis: comparison of long-term outcomes between intravascular ultrasound, optical coherence tomography, and angiography-guided stent implantation

Abstract Background Intravascular ultrasonography (IVUS) and optical coherence tomography (OCT) guided stent implantations are alternative techniques that are adjunct to angiography-guided (ANG) percutaneous coronary interventions in patients with coronary artery disease (CAD), especially for optimal stent deployment. We aimed to conduct a network meta-analysis including studies comparing those three techniques. Methods We searched PubMed, Scopus, and Cochrane libraries for eligible studies that compared IVUS, OCT, and angiography-guided stent implantation in patients with CAD. After excluding studies, which were irrelevant, duplicated, and had inappropriate results, 54 randomized, propensity-score matched, and observational studies with 232.181 patients were included in this meta-analysis. Results Number of studies compared ANG and IVUS was higher than the other two comparisons. Indirect evidence of network estimates between OCT and IVUS was higher than direct estimate (60% vs. 40%). Minimal parallelism and mean path length of each estimation was suitable with numbers low than 2 for both for comparisons. ANG had higher MACE (RR =1.30; 1.22-1.39, p&amp;lt;0.001), all cause-death (RR=1.45;1.30-1.61, p&amp;lt;0.001), cardiac death (RR=1.72;1.54-1.92, p&amp;lt;0.001), myocardial infarction (RR=1.34; 1.23-1.45, p&amp;lt;0.001), target lesion revascularization (RR=1.20; 1.13-1.26, p&amp;lt;0.001), and stent thrombosis (RR=1.58;1.34-1.85, p&amp;lt;0.001) risks compared to IVUS. There was no difference between OCT and IVUS regarding all outcomes. MACE (RR=1.51;1.26-1.81, p&amp;lt;0.001), cardiac death (RR=2.13;1.41-3.21, p&amp;lt;0.001), and myocardial infarction (RR=1.42;1.05-1.93, p&amp;lt;0.001) risks were higher in ANG groups than in OCT group. Highest benefit was established with OCT for MACE (p-score = 0.973), with IVUS for all-cause death (p-score= 0.792), with OCT for cardiac death (p-score=0.921), with OCT for myocardial infarction (p-score =0.823), with IVUS for target lesion revascularization (p-score=0.865), and with IVUS for stent thrombosis (p-score=0.930). Heterogeneity was appropriate for all outcomes (I2 &amp;lt;70%). There was no publication bias for all outcomes. Conclusion This comprehensive network meta-analysis indicated that angiography-guided stent implantation had higher risk of MACE, cardiac death, myocardial infarction, target lesion-revascularization, and stent thrombosis when compared to IVUS and had higher risk of MACE, cardiac death, and myocardial infarction than OCT.

Improved Genetic Algorithm Based on Oscillation Factor to Solve the AUV Path Planning Problem

In this paper, the bi-objective AUV path planning problem considering the shortest path and the minimum path smoothness is studied. Firstly, a mathematical model of the problem is established and a two-dimensional Cartesian coordinate system model is used to model the AUV working environment. Then the dual objective is normalized and transformed into an adaptation function by dimensionality reduction. An improved Genetic Algorithm is proposed to solve the problem according to its characteristics. An initial solution generation strategy for the n-1 equipartition method based on the improved oscillation factor is designed, and an elite retention strategy with simulated annealing operation is introduced to improve the genetic strategy. To verify the effectiveness of the improved algorithm in this paper, simulation experiments were conducted by the Microsoft Visual Studio platform. After the comparison and analysis of the three algorithms, the algorithm proposed in this paper has shorter and smoother paths, faster convergence speed, and more obvious advantages in the quality of the solution.

Time-Varying Topology Formation Reconfiguration Control of the Multi-Agent System Based on the Improved Hungarian Algorithm

Distributed time-varying formation technology for multi-agent systems is recently become a research hotspot in formation control field. However, the formation reconfiguration control technology for agents that randomly appeared to fail during maneuvers is rarely studied. In this paper, the topological relations between intelligence are designed by graph theory to simplify the cooperative interaction between multi-agent systems. Moreover, this paper constructs the time-varying configuration of the target formation based on the rigidity graph theory and leader–follower strategy. Drawing on the establishment of the expert experience database in a collaborative process, we innovatively propose the establishment of a graphic library to help the multi-agent system quickly form an affine transformation as soon as it is disabled. Secondly, the improved Hungarian algorithm is adopted to allocate the target point when the first failure occurs. This algorithm incorporates a gradient weighting factor from the auction algorithm to improve the speed of system reconfiguration with minimum path cost. On this basis, a distributed multi-agent control law based on consistency theory is established, and the system’s stability can be guaranteed via Lyapunov functions. Finally, the simulation results demonstrate the feasibility and effectiveness of the proposed formation reconfiguration control algorithm in a collaborative environment.

Self-Directed Mobile Robot Navigation Based on Functional Firefly Algorithm (FFA)

This paper proposes an optimized mobile robot navigation strategy using a functional firefly algorithm (FFA) and choice function. This approach has two key advantages: first, the linear objective function performs efficiently with the single degree and finite-order polynomial time operation, and second, the cartesian constraint performs compactly with the chosen degree of freedom on the finite interval. This functional approach optimizes the size of operational parameters in context with key size, operation time, and a finite range of verification. The choice function achieves parameter order (size) reduction. The attraction characteristic of fireflies is represented by the choice function for optimizing the choice between low and high intensities of fireflies. In 2D and 3D environments, the proposed robot navigation performs well in an uncertain environment with static and dynamic obstacles. This efficiency includes the robot’s speed as determined by the choice function’s minimum path lengths. The collision-free path is achieved by the non-void family of non-void sets. The obtained results are optimal in terms of path length and navigational time. The proposed controller is also compared with the other existing controllers, and it is observed that the FFA gives the shortest path in less time for the same environmental condition.

An autonomous mobile robot path planning strategy using an enhanced slime mold algorithm.

Autonomous mobile robot encompasses modules such as perception, path planning, decision-making, and control. Among these modules, path planning serves as a prerequisite for mobile robots to accomplish tasks. Enhancing path planning capability of mobile robots can effectively save costs, reduce energy consumption, and improve work efficiency. The primary slime mold algorithm (SMA) exhibits characteristics such as a reduced number of parameters, strong robustness, and a relatively high level of exploratory ability. SMA performs well in path planning for mobile robots. However, it is prone to local optimization and lacks dynamic obstacle avoidance, making it less effective in real-world settings. This paper presents an enhanced SMA (ESMA) path-planning algorithm for mobile robots. The ESMA algorithm incorporates adaptive techniques to enhance global search capabilities and integrates an artificial potential field to improve dynamic obstacle avoidance. Compared to the SMA algorithm, the SMA-AGDE algorithm, which combines the Adaptive Guided Differential Evolution algorithm, and the Lévy Flight-Rotation SMA (LRSMA) algorithm, resulted in an average reduction in the minimum path length of (3.92%, 8.93%, 2.73%), along with corresponding reductions in path minimum values and processing times. Experiments show ESMA can find shortest collision-free paths for mobile robots in both static and dynamic environments.

Investigating the min‐cost minimum fleet problem through taxi data analysis

AbstractThe optimization of urban traffic efficiency and reduction of pollution through minimizing the number of taxis has become a topic of increasing interest. However, the problem of determining the minimum fleet that considers both time and distance efficiency has received limited attention. Furthermore, little research has been done on how this problem is influenced by factors such as city size and travel demand (i.e., the number of trips). This study extends the minimum fleet problem to the min‐cost minimum fleet problem, and proposes a method to address the problem by constructing a “dispatch network” and finding the minimum weight and minimum path cover of it. A comparative analysis of the method is conducted with the taxi trajectory data of three cities, New York, Chengdu, and Chicago, and the results show a reduction in the off‐load travel time of vehicles compared to the previous method, while maintaining the same fleet size. With the introduction of an emissions model and its combination with our methodology, emissions can also be minimized. Moreover, the relationship between min‐cost minimum fleet and city size and travel demand (number of trips) is studied. Experimental results indicate that fleet size and idle time (distance) vary linearly with the number of trips. Meanwhile, city size also has an essential impact on the algorithm's performance. Furthermore, these results indicate that the min‐cost minimum fleet will help small cities to achieve higher efficiency (smaller fleet and less connection time) than large cities. The acceleration of urbanization is driving changes in the transportation system. Our findings are expected to have significant implications for transport planning, resource conservation, and reducing pollution.

3D reconstruction of the scapula from biplanar X-rays for pose estimation and morphological analysis.

Patient-specific scapular shape in functional posture can be highly relevant to clinical research. Biplanar radiography is a relevant modality for that purpose with already two existing assessment methods. However, they are either time-consuming or lack accuracy. The aim of this study was to propose a new, more user-friendly and accurate method to determine scapular shape. The proposed method relied on simplified manual inputs and an upgraded version of the first 3D estimate based on statistical inferences and Moving-Least Square (MLS) deformation of a template. Then, manual adjustments, with real-time MLS algorithm and contour matching adjustments with an adapted minimal path method, were added to improve the match between the projected 3D model and the radiographic contours. The accuracy and reproducibility of the method were assessed (with 6 and 12 subjects, respectively). The shape accuracy was in average under 2mm (1.3mm in the glenoid region). The reproducibility study on the clinical parameters found intra-observer 95% confidence intervals under 3mm or 3° for all parameters, except for glenoid inclination and Critical Shoulder Angle, ranging between 3° and 6°. This method is a first step towards an accurate reconstruction of the scapula to assess clinical parameters in a functional posture. This can already be used in clinical research on non-pathologic bones to investigate the scapulothoracic joint in functional position.

Minimum dose path planning method for virtual nuclear facilities based on navigation mesh

The operation, maintenance and decommissioning of nuclear facilities have radiation risks. When workers work in the radiation area, it is necessary to carry out radiation protection through path planning. In order to optimize the dose field path planning algorithm, a virtual verification platform for dose field path planning is established based on the Unreal Engine. The platform includes virtual environment, dose field, and personnel dose assessment modules, which can meet the needs of dose field path planning algorithm research and optimization. Considering the complexity and variability of the environment in the operation process, a new dose minimum path planning algorithm based on navigation mesh is designed. Based on this algorithm, the number of grids for path planning in complex or large scenes is significantly reduced, and the calculation time of the algorithm is reduced while ensuring the optimal dose. The simulation results show that the minimum dose path planning method based on navigation mesh can effectively reduce path planning time and ensure the safety of personnel during the decommissioning of nuclear facilities.

Regret-Index Neural Network for Finding the Maximum Data Flow of Self-Powered Wireless Sensor Networks

There are many complex situations in self-powered wireless sensor networks. First, the signal fluctuation will cause the upper limit of the data transmission volume between the sensor and the base station to change at different times. In addition, with long-term use, equipment failure will cause the loss of some data during transmission, and the rate of data loss is usually undetermined. Based on the above complexity, to determine the maximum data flow of self-powered wireless sensor networks, the fuzzy-wastage time-varying maximum flow problem (FTMFP) is introduced in this paper. Existing algorithms are not suitable for solving the FTMFP due to the uncertainty and time-variation in the problem. To solve this problem, a regret-index neural network (RINN) algorithm is proposed in this paper. The unique minimum regret-index path selection mechanism of the RINN algorithm improves the accuracy when obtaining solutions. The parallel computing and training-free mode of the RINN algorithm improves the computational speed. The Utah channel impulse response wireless sensor network and the large-scale New York City road monitoring network are employed to evaluate the performance of the proposed RINN algorithm. The time-variance of the data transmission caused by signal fluctuations and the fuzzy loss ratio of data caused by equipment failures are considered in the network. Compared with the well investigated Ford-Fulkerson, Edmonds-Karp, and Cai-Sha algorithms, experimental results have proven the effectiveness of the RINN.

Neuronal branching is increasingly asymmetric near synapses, potentially enabling plasticity while minimizing energy dissipation and conduction time.

Neurons' primary function is to encode and transmit information in the brain and body. The branching architecture of axons and dendrites must compute, respond and make decisions while obeying the rules of the substrate in which they are enmeshed. Thus, it is important to delineate and understand the principles that govern these branching patterns. Here, we present evidence that asymmetric branching is a key factor in understanding the functional properties of neurons. First, we derive novel predictions for asymmetric scaling exponents that encapsulate branching architecture associated with crucial principles such as conduction time, power minimization and material costs. We compare our predictions with extensive data extracted from images to associate specific principles with specific biophysical functions and cell types. Notably, we find that asymmetric branching models lead to predictions and empirical findings that correspond to different weightings of the importance of maximum, minimum or total path lengths from the soma to the synapses. These different path lengths quantitatively and qualitatively affect energy, time and materials. Moreover, we generally observe that higher degrees of asymmetric branching-potentially arising from extrinsic environmental cues and synaptic plasticity in response to activity-occur closer to the tips than the soma (cell body).