Adjacency Matrix Method Research Articles

Graph Database and Matrix-Based Intelligent Generation of the Assembly Sequence of Prefabricated Building Components

The assembly of prefabricated components is a critical process in prefabricated building construction, influencing both progress and accuracy. However, the assembly sequence planning and optimization (ASPO) of prefabricated components have yet to receive sufficient attention from researchers, and current research has displayed limited automation and poor generalization capabilities. Therefore, this paper proposes a framework for intelligently generating assembly sequences for prefabricated components based on graph databases and matrices. The framework utilizes an adjacency matrix and interference matrix-based modeling method to comprehensively describe the connections and constraint relationships between components, enabling better evaluation of assembly difficulty during optimization. The graph database serves as the central hub for data exchange, facilitating component information storage, automatic querying, and summarization. The obtained assembly sequence and progress plan are fed back into the graph database. To accomplish assembly sequence optimization, a genetic algorithm based on the double-elite strategy is employed. Furthermore, the effectiveness of the proposed framework is validated through an actual engineering case. The results demonstrate that the framework can effectively find an optimal assembly sequence to mitigate the assembly challenge of a prefabricated building.

Bayesian spatio-temporal modelling of child anemia in Ethiopia using conditional autoregressive model

Anemia is a common health problem for women and under five children in low income countries. According to the WHO, anemia is considered a serious public health problem when the prevalence is greater than 40%. The prevalence of anemia among children under five in Ethiopia changes over time, and is spatially correlated because it is influenced by environmental, socio-economic and other related factors. However, to our knowledge, there is no small area level estimates of anemia among children under five in Ethiopia. Therefore, this study aimed to assess zonal level estimates of anemia using a Bayesian spatio-temporal conditional autoregressive modeling approach. The data for the study was extracted from the Ethiopian Demographic and Health Surveys (EDHS) from 2005 to 2016. A sample of 18,939 children aged 6–59 months were considered for this study. A Bayesian spatio-temporal conditional autoregressive model was implemented to identify the risk of child anemia. Smoothed relative risks along with the 95% credible interval were reported. The queen’s adjacency matrix method was used in spatial smoothing and in estimating the relative risk. The prevalence of anemia among children aged 6–59 months in Ethiopia was 54% in 2005, 44% in 2011 and 57% in 2016. This study showed that low maternal education, low socio-economic status of women, and maternal anemia at zone level were strongly associated with child anemia in Ethiopia. Therefore, enhancing education for women, improving women's socioeconomic status, and mitigating maternal anemia are crucial to reduce the prevalence of childhood anemia in Ethiopia.

GPU-accelerated N-1 static security analysis based on fine-grained parallelism HELM

With the increment of scale of power system, the accuracy and efficiency requirements of N-1 static security analysis (SSA) keep increasing. In order to satisfy these requirements, this paper proposed a GPU-accelerated N-1 SSA method to reduce computation burden and ensure the accuracy of alternating current power flow (ACPF) and connectivity test simultaneously. First, in the algorithm, ACPF is performed by holomorphic embedding load flow method (HELM). The construction and solution of sparse linear system both adopts fine-grained parallelism. According to the mathematical lemma of combining linear equations, this paper performs fine-grained parallelism Padé approximation of HELM. Second, considering the high time complexity of the original search-based algorithm and adjacency matrix method which is not suitable for sparse graph, this paper proposes a GPU-accelerated Union Set algorithm. Its main advantage is lower time complexity compared to other graph theory methods. And most importantly, it is very suitable for parallelization. Shared memory can be used in this algorithm well. Therefore, it is not complicated to perform a block-level parallelism in GPU-accelerated Union Set. Finally, the overall framework of GPU-accelerated N-1 SSA method is shown in this paper. It has been tested on large-scale power systems of up to 2869 buses. The computation results are compared with MATPOWER and the execution times are compared with other mainstream method to show the improvement in performance.

A Multi-Dimensional Graph Convolution Network for EEG Emotion Recognition

Due to the changeable, high-dimensional, non-stationary, and other characteristics of electroencephalography (EEG) signals, the recognition of EEG signals is mostly limited to independent individuals. To deal with these issues, we propose a multi-dimensional graph convolution network (MD-GCN), which integrates EEG signals’ temporal and spatial characteristics and can classify emotions more accurately. First, we use that the asymmetry of neuron activity in the left and right hemispheres is very important for emotion prediction to initialize the adjacency matrix and perform preliminary edge prediction without considering node features. Then, we perform the feature fusion on the Inception network and then input it into the graph convolution network to learn the interrelationship between channels. Finally, we visually analyze the adjacency matrix. To evaluate the performance of the model, we conduct experiments on the SEED dataset and the SEED-IV dataset. The results show that the pre-defined adjacency matrix method can improve the accuracy of emotion recognition and the graph convolution has better performance than the same type of convolution. It also theoretically shows that the emotional state is mainly by the interaction of important brain regions.

Optimization of mine ventilation network feature graph.

A ventilation network feature graph can directly and quantitatively represent the features of a ventilation network. To ensure the stability of airflow in a mine and improve ventilation system analysis, we propose a new algorithm to draw ventilation network feature graphs. The independent path method serves as the algorithm's main frame, and an improved adaptive genetic algorithm is embedded so that the graph may be drawn better. A mathematical model based on the node adjacency matrix method for unidirectional circuit discrimination is constructed as the drawing algorithm may not be valid in such cases. By modifying the edge-seeking strategy, the improved depth-first search algorithm can be used to determine all of the paths in the ventilation network with unidirectional circuits, and the equivalent transformation method of network topology relations is used to draw the ventilation network feature graph. Through the analysis of the topological relation of a ventilation network, a simplified mathematical model is constructed, and network simplification technology makes the drawing concise and hierarchical. The rapid and intuitive drawing of the ventilation network feature graphs is significant for optimization of the ventilation system and day-to-day management.

Port Recommendation System for Alternative Container Port Destinations Using a Novel Neural Language-Based Algorithm

Shipping containers are tokens of multimodal international transportation and rapid logistics. Container deliveries are scheduled to satisfy rapidly changing requirements. Unpredictable increases in costs and unforeseeable events such as pandemics compel ship owners and managers to adopt risk minimization measures. This study addresses one issue: how to determine an alternative port of call from massive data to offer a realistic destination change recommendation for a container vessel. Recommendation algorithms have become ubiquitous and are used effectively in other fields, but there is no such model for the port of call selection or recommendation. Large scale automatic identification system (AIS) data are readily available. We developed a computational framework based on a novel natural language programming algorithm that was tailored to support port recommendation rather than use a conventional adjacency matrix method. We mined large scale AIS data to construct sequential berth records for container vessels and mapped each port onto a vector in an embedded space. The natural language neural programming algorithm can suggest ports similar to the scheduled ports of call that were unable to offer service. The recommendations were validated with geo-analysis of sailing distance and could offer viable alternative ports to shipping managers.

Zeon and Idem-Clifford Formulations of Boolean Satisfiability

The Boolean satisfiability problem (SAT) is the problem of determining whether the variables of a given Boolean formula can be consistently replaced by true or false in such a way that the formula evaluates to true. In fact, SAT was the first known NP-complete problem. In recent years, SAT has found numerous industrial applications, particularly in model checking tools. In the current work, three approaches to Boolean satisfiability based on Clifford subalgebras are presented. In the first approach, an “idem-Clifford” algebraic test for satisfiability is presented. This test is straightforward to implement symbolically (e.g., using Mathematica), but does not yield the specific solution sets for a given formula. In the second approach, nilpotent adjacency matrix methods are extended to Boolean formulas in order to determine not only whether or not a Boolean formula is satisfiable but to explicitly obtain all solutions. This approach requires the construction of a graph associated with a given Boolean formula. Finally, a “new” algebraic framework is developed that combines the convenience of the first approach with the power of the second, recovering explicit solutions without the need to construct graphs. The algebraic formalism presented here readily lends itself to symbolic computations and provides the theoretical basis of a Clifford-algebraic SAT solver.

EMUlator: An Elementary Metabolite Unit (EMU) Based Isotope Simulator Enabled by Adjacency Matrix.

Stable isotope based metabolic flux analysis is currently the unique methodology that allows the experimental study of the integrated responses of metabolic networks. This method primarily relies on isotope labeling and modeling, which could be a challenge in both experimental and computational biology. In particular, the algorithm implementation for isotope simulation is a critical step, limiting extensive usage of this powerful approach. Here, we introduce EMUlator a Python-based isotope simulator which is developed on Elementary Metabolite Unit (EMU) algorithm, an efficient and powerful algorithm for isotope modeling. We propose a novel adjacency matrix method to implement EMU modeling and exemplify it stepwise. This method is intuitively straightforward and can be conveniently mastered for various customized purposes. We apply this arithmetic pipeline to understand the phosphoketolase flux in the metabolic network of an industrial microbe Clostridium acetobutylicum. The resulting design enables a high-throughput and non-invasive approach for estimating phosphoketolase flux in vivo. Our computational insights allow the systematic design and prediction of isotope-based metabolic models and yield a comprehensive understanding of their limitations and potentials.

A method of calculating the degree of freedom of foldable plate rigid origami with adjacency matrix

The mechanism with good fold performance derived from rigid origami is widely used in the field of engineering. In this article, the adjacency matrix method was proposed to analyze the degree of freedom of foldable plate rigid origami. This method can also judge the number of redundant constraints while calculating the degree of freedom of the rigid origami. First, the adjacency matrix between vertices of origami structure was established. Then the elimination matrix was introduced, and the process of determining the motion state of vertices was described by matrix product. The degree of freedom of rigid origami was determined by calculating the number of constraints introduced. A method for judging redundant constraints of rigid origami was proposed, and the number of redundant constraints was determined by computing the sum of the row elements corresponding to the vertices. The motion state of the cross-crease vertex was analyzed, and the computational error of the degree of freedom at the cross-crease vertex was avoided by the method of classification and simplification. The degree of freedom of the ring pattern was discussed, and the calculation method of the degree of freedom of whole pattern with many ring patterns was summarized. Finally, the degree of freedom of typical rigid origami was analyzed.

Zeons, Orthozeons, and Graph Colorings

Nilpotent adjacency matrix methods have proven useful for counting self-avoiding walks (paths, trails, cycles, and circuits) in finite graphs. In the current work, these methods are extended for the first time to problems related to graph colorings. Nilpotent-algebraic formulations of graph coloring problems include necessary and sufficient conditions for k-colorability, enumeration (counting) of heterogeneous and homogeneous paths, trails, cycles, and circuits in colored graphs, and a matrix-based greedy coloring algorithm. Introduced here also are the orthozeons and their application to counting monochromatic self-avoiding walks in colored graphs. The algebraic formalism easily lends itself to symbolic computations, and Mathematica-computed examples are presented throughout.

Steganalysis of images based on spatial domain and two-dimensional JPEG array

The aim of digital image steganalysis is to detect hidden information (which can be a message or an image) in a steganographic image. An ideal steganography method encrypts the information in the image such that it cannot be easily detected. Currently, a wide variety of different steganography techniques are being used; therefore, more advanced steganalysis methods are needed that can detect the steganographic images coded by different techniques. A typical steganalysis technique consists of two parts: (1) feature extraction and (2) classification. In this paper, a new steganalysis technique based on the Markov chain process is proposed. In the proposed technique, after extraction of the new features, a non-linear classifier named support vector machine is applied to classify clean and encrypted images. Analysis of variance is used to reduce the dimensions of the proposed features. The performance of the proposed technique is compared against subtractive DCT coefficient adjacency matrix (SDAM) and subtractive pixel adjacency matrix (SPAM) methods using an image database prepared by three strong steganography techniques called yet another steganographic scheme, model based, and perturbed quantization. The obtained results show that the proposed method provides better performance than SDAM and SPAM methods.

Study of Project Duration Risk in the Network Diagram Based on Matrix Algorithm

The probable route sets in the network diagram were calculated by adjacency matrix method, and based on the assumption that activity becoming the key obeyed 0-1 distribution, a probable route matrix was established. A random variable matrix was structed by monte carlo simulation under condition of activity time independent distribution. A matrix algorithm model was built by isolating activity times impact on activity becoming the key for the first time. This model with a simple and optimal algorithm avoided the computation complexity of network planning time parameter, to evaluate project duration risk rapidly and statistical analyze the probability of activity becoming the key and the influence degree of activity time fluctuation impacting on project duration, providing theoretical and data support for decisions. Empirical research on a tunnel engineering project verified its practicability and feasibility, providing a new powerful tool for assessing project duration risk in the network diagram quickly.

The Reliability Evaluation Method Study of Power System Communication Networks in Case of Ice Storm

This paper is divided into two cases to study the communication transmission equipment reliability in the state of the ice storm, according to the huge losses of power system communication caused by the ice storm. For the nodes or links which are not affected by the ice storm, we use the calculation with “the mean time between failures (MTBF)” and “the mean time to repair” (MTTR) to put forward the calculation methods; for the OPGW cable which influenced greater in ice storm, we use the fiber excess length and the elongation of fiber optic cable. It obtains all the paths of the network through improved adjacency matrix method, and then it uses binary decision diagram to obtain the overall reliability of the network. By testing the network nodes and links using “N-1” inspection, the key nodes and key links can be obtained. Finally, considering the importance degree of network transmission business, the reliability evaluation method of power system communication network based on the risk theory in the case of the ice storm has been put forward, and the example to verify that the method can provide the basis for the reliability assessment of the power system communication in the case of the ice storm has been given.

Docking System Design and Self-Assembly Control of Distributed Swarm Flying Robots

This paper presents a novel docking system design and the distributed self-assembly control strategy for a Distributed Swarm Flying Robot (DSFR). The DSFR is a swarm robot comprising many identical robot modules that are able to move on the ground, dock with each other and fly coordinately once self-assembled into a robotic structure. A generalized adjacency matrix method is proposed to describe the configurations of robotic structures. Based on the docking system and the adjacency matrix, experiments are performed to demonstrate and verify the self-assembly control strategy.

Complexity of counting cycles using zeons

Nilpotent adjacency matrix methods are employed to count k -cycles in simple graphs on n vertices for any k ≤ n . The worst-case time complexity of counting k -cycles in an n -vertex simple graph is shown to be O ( n α + 1 2 n ) , where α ≤ 3 is the exponent representing the complexity of matrix multiplication. When k is fixed, the counting of all k -cycles in an n -vertex graph is of time complexity O ( n α + k − 1 ) . Letting Ω = ( n 2 ) , the average-case time complexity of counting k -cycles in an n -vertex, e -edge graph where e ≤ q ( Ω k − 1 ) for fixed 0 < q < 1 is found to be O ( n 4 ( 1 + q ) n ) . The storage complexity of the approach detailed herein is O ( n 2 2 n ) . For reference, experimental results detailing computation times (in seconds) are included alongside similar computations performed with algorithms based on the approaches of Bax and Tarjan.

Optimal Scheduling and Simulation of Snow Removers for Airfield Pavement Based on Breadth-First Search

In this paper, the Breadth-First Search algorithm is adopted to optimize the scheduling of Snow Removers for Airfield Pavement in large airports, as a result, the efficiency of cleaning work can be improved and the delayed time of the airport open can be decreased. The designed function of the automatic formation of plaque, the Airport Road area of adjacency matrix method, weight matrix, completed the snow removal vehicle scheduling model. Finally, an example, show that the algorithm of the allocation of airport runway snow removal vehicles, the optimized performance, as the airport runway snow removal vehicles provide a new strategy for optimal operation.

Systematic tuning of parameters in support vector clustering

Clustering algorithms divide a set of observations into groups so that members of the same group share common features. In most of the algorithms, tunable parameters are set arbitrarily or by trial and error, resulting in less than optimal clustering. This paper presents a global optimization strategy for the systematic and optimal selection of parameter values associated with a clustering method. In the process, a performance criterion for the optimization model is proposed and benchmarked against popular performance criteria from the literature (namely, the Silhouette coefficient, Dunn’s index, and Davies–Bouldin index). The tuning strategy is illustrated using the support vector clustering (SVC) algorithm and simulated annealing. In order to reduce the computational burden, the paper also proposes an alternative to the adjacency matrix method (used for the assignment of cluster labels), namely the contour plotting approach. Datasets tested include the iris and the thyroid datasets from the UCI repository, as well as lymphoma and breast cancer data. The optimal tuning parameters are determined efficiently, while the contour plotting approach leads to significant reductions in computational effort (CPU time) especially for large datasets. The performance criteria comparisons indicate mixed results. Specifically, the Silhouette coefficient and the Davies–Bouldin index perform better, while the Dunn’s index is worse on average than the proposed performance index.

Bounding the diameter and the mean distance of a graph from its eigenvalues: Laplacian versus adjacency matrix methods

Recently, several results bounding above the diameter and/or the mean distance of a graph from its eigenvalues have been presented. They use the eigenvalues of either the adjacency or the Laplacian matrix of the graph. The main object of this paper is to compare both methods. As expected, they are equivalent for regular graphs. However, the situation is different for nonregular graphs: While no method has a definite advantage when bounding above the diameter, the use of the Laplacian matrix seems better when dealing with the mean distance. This last statement follows from improved bounds on the mean distance obtained in the paper.

Enumeration of connected spanning subgraphs of a planar graph

One of the important solved problems in graph theory is the enumeration of distinct connected spanning trees contained in a given connected graph; historically it was first solved by Kirchhoff. Since a tree graph contains no cycle by definition, the next question of importance is naturally the problem of enumeration, for a given connected graph, of connected spanning subgraphs each of which contains only a single cycle (besides the trees attached to the particular cycle). In general, the problems of interest are the enumeration of the connected spanning subgraphs having a preassigned cyclomatic number, i.e. each containing a fixed number of cycles (besides the trees attached), for a given graph. The enumeration of spanning trees for a labelled graph is usually computed by means of the adjaeeey matrix of the given graph. On the other hand, in contrast to the adjacency matrix method (or essentially the "incidence matrix" method), we approached the problem some years ago by a dual notion and derived a computational expression using the concept of cycles in defining the required matrix entries [1]. The duality is, of course, referred to that between the vertices and the cycles; the matrix entries are indexed by the vertices of the given graph in the adjacency matrix method, while they are indexed by the assigned cycles in the latter approach. It was already apparent to us, at that time, that the computational effectiveness of these two approaches depends critically on the nature of the given graph. Some examples were given in that paper [1] to point out that the adjacency matrix method is clearly not as effective as the "cycle matrix" method if the given graph involves many vertices but very few cycles (and vice versa). However, the formal expressions derived by either approach are of equal simplicity and elegance. In the present investigation, we rely on the concept of cycles. However, a direct application of cycle matrices [1] does not appear to be very effective. As it turns out, the problems can be handled efficiently by introducing the so-called cycle-adjacency matrix for a given connected graph after labelling the cycles considered. In carrying out the dual notion to the usual adjacency-matrix, it is necessary to impose the requirement that each edge of the graph can belong at most to two independent cycles. Using this matrix, together with some further auxiliary notions, we derive the explicit expressions for the enumeration of the connected subgraphs (of a planar graph) each containing one and two cycles. These explicit expressions suggest immediately the general expression for n cycles. Though it is natural to try to prove it by a mathematical induction on n, yet the involvement of determinants makes it computationally very complicated. We resolve this by introducing the i-th "annihilation operator" which deletes the i-th column and the i-th row in the cycle-adjacency matrix. Together with a formal procedure, the operator method provides a straight-