Empirical Graph Research Articles

A New CRITIC-GRA Model for Stope Dimension Optimization Considering Open Stoping Stability, Mining Capacity and Costs

In the long-hole stage open stoping with subsequent backfill mining of underground metal mines, the selection or optimization of stope dimension parameters is significant for safe and economic mining operations. To analyze the optimal stope sizes, the Mathews empirical graph method and FLAC3D numerical method can be used, but the analyzed safety results of the two methods are generally independent from each other. More importantly, economic indicators including production capacity and mining costs should be considered simultaneously to optimize the stope dimension which was mostly ignored in previous reports. In this paper, a new CRITIC-GRA model was proposed for the first time to build up a multi-factor quantitative optimization for stope dimension, which allows for a comprehensive analysis with preset influential safety and economic indicators. The indicators considered include the safety indicators such as stability probability for the side walls and roof of the open stope via the updated Mathews graph method, maximum displacement, plastic zones volume and maximum principal stress via FLAC3D simulations, as well as economic indicators such as mining costs and stope production capacity in mine operations. The model was then illustrated in an underground iron mine. With the given rockmass quality in the mine, the overall stability of the open stope can be improved instead of reduced to enlarge the single stage stope height (60 m) to a double stage height (120 m) by reducing the stope width from 20 m to 15 m, thereby significantly increasing the mineable ore amount and improving the stope safety. An integrated evaluation of open stope stability, mining capacity and costs objectively determined that scheme No. 10, with a slope length of 50 m, a width of 15 m and a height of 120 m, was the optimum out of the 20 preset schemes. The new CRITIC-GRA model offers a dependable reference tool for determining the optimal stope dimensions in similar underground mines.

Comprehensive analysis of protein-protein interactions (PPIs) with structure prediction program for breast cancer determination

Breast cancer is a prevalent disease that primarily affects women, with significant implications for public health. Early detection improves survival rates, and technological advancements can enhance early diagnosis. Protein structure prediction methods can provide valuable insights into the structure of proteins involved in breast cancer, including human epidermal growth factor receptor-2 (HER2). HER2 is a known protein receptor that plays a critical role in breast cancer development and is a target for therapy. Predicting the binding affinity between HER2 and potential ligands can help identify novel treatment options. This study aimed to predict the structure of HER2 using I-TASSER and determine potential ligands using empirical graph neural network-based scoring functions. Molecular docking simulations were performed to evaluate the binding conformation and stability of the HER2-ligand complexes. The results showed the potential ligands identified by I-TASSER: AEE, UUU, and Mg2+. Afterward, their binding affinity with HER2 was assessed, yielding AEE as the best binding with the lowest vina score.

De-sounding echo chambers: Simulation-based analysis of polarization dynamics in social networks

As online social networks have become dominant platforms for public discourse worldwide, there is growing anecdotal evidence of a concurrent rise in social antagonisms. Yet, while the increase in polarization is evident, the extent to which these digital communication ecosystems are driving this shift remains elusive. A dominant scholarly perspective suggests that digital social media lead to the compartmentalization of information channels, potentially culminating in the emergence of echo chambers. However, a growing body of empirical research suggests that the mechanisms influencing ideological demarcation are more complex than a complete communicative decoupling of user groups. This study introduces two intertwined principles that elucidate the dynamics of digital communication: First, socio-cognitive biases of social group formation enforce internal congruence of ideological communities by demarcation from outsiders. Second, algorithmic personalization of content contributes to ideological network formation by creating social redundancy, wherein the same individuals frequently interact in various roles, such as authors, recipients, or disseminators of messages, leading to a surplus of shared ideological fragments. Leveraging these insights, we pioneer a computational simulation model, integrating machine learning based on behavioral data and established recommendation technologies, to explore the evolution of social network structures in digital exchanges. Utilizing advanced methods in opinion dynamics, our model uniquely captures both the algorithmic delivery and the subsequent dissemination of messages by users. Our findings reveal that in ambiguous debate scenarios, the dual components of our model are essential to accurately capture the emergence of social polarization. Consequently, our model offers a forward-looking perspective on the evolution of network communication, facilitating nuanced comparisons with empirical graph benchmarks.

Multi-Domain Generalized Graph Meta Learning

Graph meta learning aims to learn historical knowledge from training graph neural networks (GNNs) models and adapt it to downstream learning tasks in a target graph, which has drawn increasing attention due to its ability of knowledge transfer and fast adaptation. While existing graph meta learning approaches assume the learning tasks are from the same graph domain but lack the solution for multi-domain adaptation. In this paper, we address the multi-domain generalized graph meta learning problem, which is challenging due to non-Euclidean data, inequivalent feature spaces, and heterogeneous distributions. To this end, we propose a novel solution called MD-Gram for multi-domain graph generalization. It introduces an empirical graph generalization method that uses empirical vectors to form a unified expression of non-Euclidean graph data. Then it proposes a multi-domain graphs transformation approach to transform the learning tasks from multiple source-domain graphs with inequivalent feature spaces into a common domain, where graph meta learning is conducted to learn generalized knowledge. It further adopts a domain-specific GNN enhancement method to learn a customized GNN model to achieve fast adaptation in the unseen target domain. Extensive experiments based on four real-world graph domain datasets show that the proposed method significantly outperforms the state-of-the-art in multi-domain graph meta learning tasks.

Leveraging scaffold information to predict protein-ligand binding affinity with an empirical graph neural network.

Protein-ligand binding affinity prediction is an important task in structural bioinformatics for drug discovery and design. Although various scoring functions (SFs) have been proposed, it remains challenging to accurately evaluate the binding affinity of a protein-ligand complex with the known bound structure because of the potential preference of scoring system. In recent years, deep learning (DL) techniques have been applied to SFs without sophisticated feature engineering. Nevertheless, existing methods cannot model the differential contribution of atoms in various regions of proteins, and the relationship between atom properties and intermolecular distance is also not fully explored. We propose a novel empirical graph neural network for accurate protein-ligand binding affinity prediction (EGNA). Graphs of protein, ligand and their interactions are constructed based on different regions of each bound complex. Proteins and ligands are effectively represented by graph convolutional layers, enabling the EGNA to capture interaction patterns precisely by simulating empirical SFs. The contributions of different factors on binding affinity can thus be transparently investigated. EGNA is compared with the state-of-the-art machine learning-based SFs on two widely used benchmark data sets. The results demonstrate the superiority of EGNA and its good generalization capability.

Quantum mechanics of particles trapped in a Lamé circle or Lamé sphere shaped potential well

Ground state and 1st excited state energies and wave functions were calculated for systems of one or two electrons in a 2D and 3D potential well having a shape intermediate between a circle and a square or a sphere and a cube. One way to define such a potential well is with a step potential and a bounding surface of form $|x|^q+|y|^q+|z|^q = |r|^q$, which converts from a sphere to a cube when $q$ increases from $2$ to infinity. This kind of geometrical object is called a Lam\'{e} surface. The calculations were done either with implicit finite difference time stepping in the direction of negative imaginary time axis or with quantum diffusion Monte Carlo. The results demonstrate how the volume and depth of the potential well affect the $E_0$ more than the shape parameter $q$ does. Functions of two and three parameters were found to be sufficient for fitting an empirical graph to the ground state energy data points as a function of well depth $V_0$ or exponent $q$. The ground state and first excited state energy of one particle in a potential well of this type appeared to be very closely approximated with an exponential function depending on $q$, when the well depth and area or volume was kept constant while changing the value of $q$. The model is potentially useful for describing quantum dots that deviate from simple geometric shapes, or for demonstrating methods of computational quantum mechanics to undergraduate students.

Introducing a new classification of soft rocks based on the main geological and engineering aspects

Soft rock masses represent a significant percentage of rock material on the earth’s crust. The engineering properties of these rocks are related to their composition, geological history, and degree of weathering. Mudrocks (claystone, mudstone, argillite), marl, shale, sandstone, and conglomerates with weak cementing material are the most common example of these rocks which can be subjected to a wide variation of their engineering properties. Generally, they can be grouped in a broad sense, as geological materials with very low intact rock properties, namely, high deformability and low strength that span the range between soils and hard rocks. This paper is organized to suggest a classification for these rocks, dealing with the main geological and engineering aspects and features that characterize these materials. The two indices of soft rock number (SRN) and soft rock activity (SRA) have been introduced in this classification. The SRN is obtained based on the geomechanical properties of soft rocks, and it is within a range from 0 to 100 (0 for very weak rocks and 100 for strong ones). On the other hand, the SRA index, which indicates how rocks respond to disturbance, is calculated using an empirical graph. This index can have values from 0 to 1. If the index is closer to 0, the rock mass will be less sensitive to disturbance. Based on the two indices, the weakest group of soft rocks, which is called swelling soft rocks, has SRNs less than 20 and SRAs higher than 0.8. Excavation of these rocks can be accompanied by various types of failures. Moreover, in high-strength soft rocks, SRNs and SRAs have values higher than 80 and lower than 0.25, respectively. These rocks have good geomechanical properties and the lowest sensitivity to disturbance, so excavation them results in the fewest failures.

A Simple Model to Relate the Elastic Ratio Gamma of a Critically Self-Organized Spring-Block Model with the Age of a Lithospheric Downgoing Plate in a Subduction Zone.

In 1980, Ruff and Kanamori (RK) published an article on seismicity and the subduction zones where they reported that the largest characteristic earthquake () of a subduction zone is correlated with two geophysical quantities: the rate of convergence between the oceanic and continental plates (V) and the age of the corresponding subducting oceanic lithosphere (T). This proposal was synthetized by using an empirical graph (RK-diagram) that includes the variables , V and T. We have recently published an article that reports that there are some common characteristics between real seismicity, sandpaper experiments and a critically self-organized spring-block model. In that paper, among several results we qualitatively recovered a RK-diagram type constructed with equivalent synthetic quantities corresponding to , V and T. In the present paper, we improve that synthetic RK-diagram by means of a simple model relating the elastic ratio γ of a critically self-organized spring-block model with the age of a lithospheric downgoing plate. In addition, we extend the RK-diagram by including some large subduction earthquakes occurred after 1980. Similar behavior to the former RK-diagram is observed and its SOC synthetic counterpart is obtained.

Method of Predicting Ore Dilution Based on a Neural Network and Its Application

A back-propagation neural network prediction model with three layers and six neurons in the hidden layer is established to overcome the limitation of the equivalent linear overbreak slough (ELOS) empirical graph method in estimating unplanned ore dilution. The modified stability number, hydraulic radius, average deviation of the borehole, and powder factor are taken as input variables and the ELOS of quantified unplanned ore dilution as the output variable. The training and testing of the model are performed using 120 sets of data. The average fitting degree r2 of the prediction model is 0.9761, the average mean square error is 0.0001, and the relative error of the prediction is approximately 6.2%. A method of calculating the unplanned ore dilution is proposed and applied to a test stope of the Sandaoqiao lead–zinc mine. The calculated unplanned ore dilution is 0.717 m, and the relative error (i.e., the difference between calculation and measurement of 0.70 m) is 2.4%, which is better than the relative errors for the empirical graph method and numerical simulation (giving dilution values of 0.8 and 0.55 m, respectively). The back-propagation neural network prediction model is confirmed to predict the unplanned ore dilution in real applications.

Exploring the Semantic Content of Unsupervised Graph Embeddings: An Empirical Study

Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Unsupervised graph embedding techniques aim to automatically create a low-dimensional representation of a given graph, which captures key structural elements in the resulting embedding space. However, to date, there has been little work exploring exactly which topological structures are being learned in the embeddings, which could be a possible way to bring interpretability to the process. In this paper, we investigate if graph embeddings are approximating something analogous to traditional vertex-level graph features. If such a relationship can be found, it could be used to provide a theoretical insight into how graph embedding approaches function. We perform this investigation by predicting known topological features, using supervised and unsupervised methods, directly from the embedding space. If a mapping between the embeddings and topological features can be found, then we argue that the structural information encapsulated by the features is represented in the embedding space. To explore this, we present extensive experimental evaluation with five state-of-the-art unsupervised graph embedding techniques, across a range of empirical graph datasets, measuring a selection of topological features. We demonstrate that several topological features are indeed being approximated in the embedding space, allowing key insight into how graph embeddings create good representations.

Semi-Supervised Learning in Network-Structured Data via Total Variation Minimization

We propose and analyze a method for semi-supervised learning from partially-labeled network-structured data. Our approach is based on a graph signal recovery interpretation under a clustering hypothesis that labels of data points belonging to the same well-connected subset (cluster) are similar valued. This lends naturally to learning the labels by total variation (TV) minimization, which we solve by applying a recently proposed primal-dual method for non-smooth convex optimization. The resulting algorithm allows for a highly scalable implementation using message passing over the underlying empirical graph, which renders the algorithm suitable for big data applications. By applying tools of compressed sensing, we derive a sufficient condition on the underlying network structure such that TV minimization recovers clusters in the empirical graph of the data. In particular, we show that the proposed primal-dual method amounts to maximizing network flows over the empirical graph of the dataset. Moreover, the learning accuracy of the proposed algorithm is linked to the set of network flows between data points having known labels. The effectiveness and scalability of our approach is verified by numerical experiments.

Research on BatSLAM Algorithm for UAV Based on Audio Perceptual Hash Closed-Loop Detection

This research is aimed at the optimization of a two-dimensional (2D) empirical graph under a certain height and dark conditions for a UAV, using the bionic sonar system to replace the visual sensor’s BatSLAM mode and audio perceptual hash closed-loop detection. The BatSLAM model uses Sum of Absolute Difference (SAD) image processing methods to update the bionic sonar template. This method only judges whether the appearance of the two cochlear images is consistent and does not have geometric processing and feature extraction. Because the cochlear images produce various noises during the acquisition and transmission, there are some differences in cochlear maps obtained at the same position, which can lead to the distortion of the constructed empirical map. In this research, an audio perceptual hash closed-loop detection algorithm is developed to extract features of cochlea. It considers both the appearance and the energy difference between adjacent bands to improve the accuracy of closed-loop detection, thus solving the distortion problem and improving the experience map. The simulation experiment shows that the improved BatSLAM model based on the audio perceptual hash closed-loop detection can improve the 2D experience map for UAV under certain height and dark conditions, through improving the accuracy of the closed-loop detection to solve the distortion problem and thus implementing the optimization of the experience graph.

Fujitsu HIKARI, a Healthcare Decision Support System based on Biomedical Knowledge

Fujitsu HIKARI is an artificial intelligence solution to assist clinicians in medical decision making, developed in the context of a joint collaboration project between Fujitsu Laboratories of Europe and Hospital Clínico San Carlos. This decision support system leverages on data analytics combined with healthcare semantic information to provide health estimations for patients, improving care quality and personalized treatment. Fujitsu HIKARI stands on the shoulders of biomedical knowledge, which includes (i) theoretical knowledge extracted from scientific literature, domain expert knowledge, and health standards; and (ii) empirical knowledge extracted from real patient electronic health records. The theoretical knowledge combines a theoretical knowledge graph (TKG) and a biomedical document repository (BDR). The empirical knowledge is encoded in an empirical knowledge graph (EKG). One of the main functionalities of Fujitsu HIKARI is the patient mental health risks assessment, which is based on the exploitation of its underlying Biomedical Knowledge.

Using Graph and Vertex Entropy to Compare Empirical Graphs with Theoretical Graph Models

Over the years, several theoretical graph generation models have been proposed. Among the most prominent are: the Erdős–Renyi random graph model, Watts–Strogatz small world model, Albert–Barabási preferential attachment model, Price citation model, and many more. Often, researchers working with real-world data are interested in understanding the generative phenomena underlying their empirical graphs. They want to know which of the theoretical graph generation models would most probably generate a particular empirical graph. In other words, they expect some similarity assessment between the empirical graph and graphs artificially created from theoretical graph generation models. Usually, in order to assess the similarity of two graphs, centrality measure distributions are compared. For a theoretical graph model this means comparing the empirical graph to a single realization of a theoretical graph model, where the realization is generated from the given model using an arbitrary set of parameters. The similarity between centrality measure distributions can be measured using standard statistical tests, e.g., the Kolmogorov–Smirnov test of distances between cumulative distributions. However, this approach is both error-prone and leads to incorrect conclusions, as we show in our experiments. Therefore, we propose a new method for graph comparison and type classification by comparing the entropies of centrality measure distributions (degree centrality, betweenness centrality, closeness centrality). We demonstrate that our approach can help assign the empirical graph to the most similar theoretical model using a simple unsupervised learning method.

Evaluation and prediction of flyrock resulting from blasting operations using empirical and computational methods

Mines, quarries and construction sites face environmental impacts, such as flyrock, due to blasting operations. Flyrock may cause damage to structures and injury to human. Therefore, flyrock prediction is required to determine safe blasting zone. In this regard, 232 blasting operations were investigated in five granite quarries, Malaysia. Blasting parameters comprising maximum charge per delay and powder factor were prepared to predict flyrock using empirical and intelligent methods. An empirical graph was proposed to predict flyrock distance for different powder factor values. In addition, using the same datasets, two intelligent systems, namely artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) were used to predict flyrock. Considering some model performance indices including coefficient of determination (R2), value account for and root mean squared error and also using simple ranking procedure, the best flyrock prediction models were selected. It was found that the ANFIS model can predict flyrock with higher performance capacity compared to ANN predictive model. R2 values of testing datasets are 0.925 and 0.964 for ANN and ANFIS techniques, respectively, suggesting the superiority of the ANFIS technique in predicting flyrock.

Testing exponentiality against NBUE distributions with an application in environmental extremes

The test for exponentiality of a dataset in terms of a specific aging property constitutes an interesting problem in reliability analysis. To this end, a wide variety of tests are proposed in the literature. In this paper, the excess-wealth function is recalled and new asymptotic properties are studied. By using the characterization of the exponential distribution based on the excess-wealth function, a new exponentiality test is proposed. Through simulation techniques, it is shown that this new test works well on small sample sizes. The exact null distribution and normality asymptotic is also obtained for the statistic proposed. This test and a new empirical graph based on the excess-wealth function are applied to extreme-value examples.

Approximating the stope stability function using genetic algorithms and neural networks

The stability of stopes in underground mines is an active research area worldwide. Stope failures are the main cause of fatal accidents in the mining industry and the intensity of failures is likely to increase as the scale of underground mining activity increases. This work investigates stope stability using four multidisciplinary random variables. The stope stability function is approximated by training feed forward neural networks with a genetic algorithm and resilient back propagation. The proposed method is used to approximate the stope stability function of three existing bauxite stopes and is compared to results obtained from the empirical stability graph method, the voussoir beam analogue and discontinuous deformation analysis. The neural network model is shown to be superior to the other methods, as, unlike the conventional approaches, it predicts the failure or the likelihood of stope instabilities.

The method of moments and degree distributions for network models

Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a large class of probability models through empirical counts of certain patterns in a graph. We establish some general asymptotic properties of empirical graph moments and prove consistency of the estimates as the graph size grows for all ranges of the average degree including $\Omega(1)$. Additional results are obtained for the important special case of degree distributions.

Dynamic linkages among equity markets: local versus basket currencies

This article compares the stability of interrelationships among nine national equity markets by employing basket currencies versus individual base currencies to measure rates of return. We show that the average correlations of equity indexes based on basket currencies are much lower than the average correlations of equity indexes based on individual home base currencies. Additionally, empirical directed graph results from using basket currencies are more consistent with each other than the results from using different individual currencies. We conclude that basket currencies provide more robust results for studying equity market comovements than individual currencies. By implication, studies on equity market interrelationships, including studies on potential financial contagion between equity markets, should use basket currencies to avoid currency dependent results.

A Laboratory Exercise on Determining Dinosaur Speeds Using Dimensional Analysis

Measurements from a dinosaur trackway are used to estimate how fast the dinosaur track makers were moving. The exercise, which is appropriate for any introductory earth-science course at the secondary-school or college level, introduces students to dimensional analysis by having them construct an empirical graph of dimensionless stride length versus dimensionless velocity. The students then estimate the dimensionless stride length from the trackway data and use the dimensionless graph to determine the speeds of the dinosaurs. Experience with the exercise indicates that even students with little quantitative background are motivated by the challenge of determining whether they could outrun the dinosaurs and often begin to appreciate the power of dimensional analysis, a concept not usually presented in introductory courses.