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Jain, Brijnesh J. "Statistical graph space analysis." Pattern Recognition 60 (December 2016): 802–12. http://dx.doi.org/10.1016/j.patcog.2016.06.023.
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Martins, Maria Maria Pereira, Carolina Fernandes de Carvalho, and Carlos Eduardo Ferreira Monteiro. "The analysis of statistical graphs constructed by primary school teachers." Acta Scientiae 23, no. 6 (November 18, 2021): 28–57. http://dx.doi.org/10.17648/acta.scientiae.6762.
Повний текст джерелаАнотація:
Background: Statistical graphs are widely used in society and are important in presenting data related to different topics. Statistics education aims improve the teaching and learning of statistics, which include the approaches to statistics graphs. Objectives: This article analyses the construction of statistical graphs by in-service teachers and their reasons for choosing these graphs. Design: It was conducted an empirical study from a qualitative perspective which investigated teachers’ choices and constructions of statistical graphs. Setting and Participants: The participants were 22 primary school teachers from public schools located in Recife Metropolitan Area, Brazil. They expressed their intention to be interviewed when they responded to a questionnaire applied among a larger number of teachers. Data collection and analysis: The interviews were composed of two tasks comprised of statistical data in which participants had to choose a type of graph, justify the choice, and construct a graph of a chosen type. It was carried out a content analysis of speech protocols. Results: The reasons for participants’ choices seemed to be related to their familiarity with the type of graph, and they constructed graphs with high levels of complexity. Conclusions: The results of this study emphasised the importance of primary school teachers developing specific knowledge about graphs through pre-service and in-service elementary school teacher education. The results from this research study offer new questions concerning the construction and the choice for statistical graphs, which include the influence of new technologies and the use of textbooks.
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Nowicki, Krzysztof. "Asymptotic Poisson distributions with applications to statistical analysis of graphs." Advances in Applied Probability 20, no. 02 (June 1988): 315–30. http://dx.doi.org/10.1017/s0001867800016992.
Повний текст джерелаАнотація:
Various types of graph statistics for graphs and digraphs are presented as numerators of incompleteU-statistics, with symmetric and asymmetric kernels, respectively. Thus, asymptotic Poisson limits of these statistics are provided by using limit theorems for the sums of dissociated random variables. Several applications to statistical analysis of graphs are given.
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Nowicki, Krzysztof. "Asymptotic Poisson distributions with applications to statistical analysis of graphs." Advances in Applied Probability 20, no. 2 (June 1988): 315–30. http://dx.doi.org/10.2307/1427392.
Повний текст джерелаАнотація:
Various types of graph statistics for graphs and digraphs are presented as numerators of incomplete U-statistics, with symmetric and asymmetric kernels, respectively. Thus, asymptotic Poisson limits of these statistics are provided by using limit theorems for the sums of dissociated random variables. Several applications to statistical analysis of graphs are given.
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Lin, Zhenxian, Jiagang Wang, and Chengmao Wu. "Robust Spectral Clustering Incorporating Statistical Sub-Graph Affinity Model." Axioms 11, no. 6 (June 5, 2022): 269. http://dx.doi.org/10.3390/axioms11060269.
Повний текст джерелаАнотація:
Hyperspectral image (HSI) clustering is a challenging work due to its high complexity. Subspace clustering has been proven to successfully excavate the intrinsic relationships between data points, while traditional subspace clustering methods ignore the inherent structural information between data points. This study uses graph convolutional subspace clustering (GCSC) for robust HSI clustering. The model remaps the self-expression of the data to non-Euclidean domains, which can generate a robust graph embedding dictionary. The EKGCSC model can achieve a globally optimal closed-form solution by using a subspace clustering model with the Frobenius norm and a Gaussian kernel function, making it easier to implement, train, and apply. However, the presence of noise can have a noteworthy negative impact on the segmentation performance. To diminish the impact of image noise, the concept of sub-graph affinity is introduced, where each node in the primary graph is modeled as a sub-graph describing the neighborhood around the node. A statistical sub-graph affinity matrix is then constructed based on the statistical relationships between sub-graphs of connected nodes in the primary graph, thus counteracting the uncertainty image noise by using more information. The model used in this work was named statistical sub-graph affinity kernel graph convolutional subspace clustering (SSAKGCSC). Experiment results on Salinas, Indian Pines, Pavia Center, and Pavia University data sets showed that the SSAKGCSC model can achieve improved segmentation performance and better noise resistance ability.
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Hora, Akihito. "Central Limit Theorems and Asymptotic Spectral Analysis on Large Graphs." Infinite Dimensional Analysis, Quantum Probability and Related Topics 01, no. 02 (April 1998): 221–46. http://dx.doi.org/10.1142/s0219025798000144.
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Regarding the adjacency matrix of a graph as a random variable in the framework of algebraic or noncommutative probability, we discuss a central limit theorem in which the size of a graph grows in several patterns. Various limit distributions are observed for some Cayley graphs and some distance-regular graphs. To obtain the central limit theorem of this type, we make combinatorial analysis of mixed moments of noncommutative random variables on one hand, and asymptotic analysis of spectral structure of the graph on the other hand.
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Kalikova, A. "Statistical analysis of random walks on network." Scientific Journal of Astana IT University, no. 5 (July 27, 2021): 77–83. http://dx.doi.org/10.37943/aitu.2021.99.34.007.
Повний текст джерелаАнотація:
This paper describes an investigation of analytical formulas for parameters in random walks. Random walks are used to model situations in which an object moves in a sequence of steps in randomly chosen directions. Given a graph and a starting point, we select a neighbor of it at random, and move to this neighbor; then we select a neighbor of this point at random, and move to it etc. It is a fundamental dynamic process that arise in many models in mathematics, physics, informatics and can be used to model random processes inherent to many important applications. Different aspects of the theory of random walks on graphs are surveyed. In particular, estimates on the important parameters of hitting time, commute time, cover time are discussed in various works. In some papers, authors have derived an analytical expression for the distribution of the cover time for a random walk over an arbitrary graph that was tested for small values of n. However, this work will show the simplified analytical expressions for distribution of hitting time, commute time, cover time for bigger values of n. Moreover, this work will present the probability mass function and the cumulative distribution function for hitting time, commute time.
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Turab, Ali, Wutiphol Sintunavarat, and Jong-Suk Ro. "On Novel Mathematical Modeling for Studying a Class of Nonlinear Caputo-Type Fractional-Order Boundary Value Problems Emerging in CGT." Fractal and Fractional 7, no. 2 (January 17, 2023): 99. http://dx.doi.org/10.3390/fractalfract7020099.
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Chemical graph theory (CGT) is a field of mathematical science that applies classical graph theory to chemical structures and processes. Chemical graphs are the principal data format used in cheminformatics to illustrate chemical interactions. Several researchers have addressed boundary-value problems using star graphs. Star graphs were used since their method requires a central point linked to other vertices but not to itself. Our objective is to expand the mechanism by introducing the idea of an isobutane graph that has the chemical formula C4H10 and CAS number 75-28-5. By using the appropriate fixed point theory findings, this paper investigates the existence of solutions to fractional boundary value problems of Caputo type on such graphs. Additionally, two examples are provided to strengthen our important conclusions.
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Zhao, Jin-Hua. "A local algorithm and its percolation analysis of bipartite z-matching problem." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 5 (May 1, 2023): 053401. http://dx.doi.org/10.1088/1742-5468/acd105.
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Abstract A z-matching on a bipartite graph is a set of edges, among which each vertex of two types of the graph is adjacent to at most 1 and at most z ( ⩾ 1 ) edges, respectively. The z-matching problem concerns finding z-matchings with the maximum size. Our approach to this combinatorial optimization problem is twofold. From an algorithmic perspective, we adopt a local algorithm as a linear approximate solver to find z-matchings on any graph instance, whose basic component is a generalized greedy leaf removal procedure in graph theory. From a theoretical perspective, on uncorrelated random bipartite graphs, we develop a mean-field theory for the percolation phenomenon underlying the local algorithm, leading to an analytical estimation of z-matching sizes on random graphs. Our analytical theory corrects the prediction by belief propagation algorithm at zero-temperature limit in (Kreačić and Bianconi 2019 Europhys. Lett. 126 028001). Besides, our theoretical framework extends a core percolation analysis of k-XORSAT problems to a general context of uncorrelated random hypergraphs with arbitrary degree distributions of factor and variable nodes.
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Ghazwani, Haleemah, Muhammad Faisal Nadeem, Faiza Ishfaq, and Ali N. A. Koam. "On Entropy of Some Fractal Structures." Fractal and Fractional 7, no. 5 (April 30, 2023): 378. http://dx.doi.org/10.3390/fractalfract7050378.
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Shannon entropy, also known as information entropy or entropy, measures the uncertainty or randomness of probability distribution. Entropy is measured in bits, quantifying the average amount of information required to identify an event from the distribution. Shannon’s entropy theory initiates graph entropies and develops information-theoretic magnitudes for structural computational evidence of organic graphs and complex networks. Graph entropy measurements are valuable in several scientific fields, such as computing, chemistry, biology, and discrete mathematics. In this study, we investigate the entropy of fractal-type networks by considering cycle, complete, and star networks as base graphs using degree-based topological indices.
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M, Obli Karthi. "Exploratory Data Analysis on Indian economy using Python." International Journal for Research in Applied Science and Engineering Technology 10, no. 6 (June 30, 2022): 4435–44. http://dx.doi.org/10.22214/ijraset.2022.44959.
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Abstract: The research aims to study the dataset of overall country's economy considering factors such as GDP (gross domestic product), FDI (foreign direct investment), import value, export value and to analyse the data using exploratory data analysis technique. The data analysis is done using Python. The mentioned parameters are compared and analysed using statistical tools and visual analysis. Since Python is a high-level language, they give more feasible approach to the statistical analysis. Technically for data computing and plotting statistical analysis were tested by scatter plotting. The data are compared and plotted in graphs using python. GDP growth of India from the year 1960 to 2020 were analysed and studied in the form of graph. Variations of parameters like FDI, Trade balance, Export, import with respect to GDP were analysed from the year 1960 to 2020. State-wise GDP contribution for top 5 and least 5 states were discussed from the year 2012 to 2019. Sector-wise FDI contribution were studied for various important sectors were studied from the year 2013 to 2017. Line graph, Scatter plot, Bar graphs were used to interpret the data and analysis results.
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Arsic, Branko, Dragos Cvetkovic, Slobodan Simic, and Milan Skaric. "Graph spectral techniques in computer sciences." Applicable Analysis and Discrete Mathematics 6, no. 1 (2012): 1–30. http://dx.doi.org/10.2298/aadm111223025a.
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We give a survey of graph spectral techniques used in computer sciences. The survey consists of a description of particular topics from the theory of graph spectra independently of the areas of Computer science in which they are used. We have described the applications of some important graph eigenvalues (spectral radius, algebraic connectivity, the least eigenvalue etc.), eigenvectors (principal eigenvector, Fiedler eigenvector and other), spectral reconstruction problems, spectra of random graphs, Hoffman polynomial, integral graphs etc. However, for each described spectral technique we indicate the fields in which it is used (e.g. in modelling and searching Internet, in computer vision, pattern recognition, data mining, multiprocessor systems, statistical databases, and in several other areas). We present some novel mathematical results (related to clustering and the Hoffman polynomial) as well.
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Pallauta, Jocelyn D., Pedro Arteaga, and José A. Garzón-Guerrero. "Secondary School Students’ Construction and Interpretation of Statistical Tables." Mathematics 9, no. 24 (December 11, 2021): 3197. http://dx.doi.org/10.3390/math9243197.
Повний текст джерелаАнотація:
Understanding statistical tables is a main component of statistical literacy, although related research dealing with secondary school students is scarce. The purpose of this study was to investigate secondary school students’ performance when translating graphs to tables and then interpreting the resulting table. Using content analysis of the responses to a questionnaire given to a sample of Spanish students, we analysed the correctness of the constructed table, the semiotic conflicts that appeared in their construction, the interpretation of the table elements, the ability to argue on the basis of the information in the table, and the reading level exhibited by the student in this task. Most students correctly translated a pictogram to a frequency table, and a half of them a double bar graph to a two-way table. The main semiotic conflicts were misinterpretation of the icon in the pictogram and incorrect computation of marginal frequencies. About 40% of the sample correctly justified a statement using the data in the graph and then reached the upper reading level of the graph and table, but only a minority achieved that level when the question required knowledge of the context. The findings of the study suggested points to reinforce the teaching of statistical graphs and tables.
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Wang, Yong. "Statistical analysis of frequency graph for traveling salesman problem." Journal of Intelligent & Fuzzy Systems 28, no. 3 (2015): 1109–18. http://dx.doi.org/10.3233/ifs-141394.
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Das, Soumya, D. Vijay Anand, and Moo K. Chung. "Topological data analysis of human brain networks through order statistics." PLOS ONE 18, no. 3 (March 13, 2023): e0276419. http://dx.doi.org/10.1371/journal.pone.0276419.
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Understanding the common topological characteristics of the human brain network across a population is central to understanding brain functions. The abstraction of human connectome as a graph has been pivotal in gaining insights on the topological properties of the brain network. The development of group-level statistical inference procedures in brain graphs while accounting for the heterogeneity and randomness still remains a difficult task. In this study, we develop a robust statistical framework based on persistent homology using the order statistics for analyzing brain networks. The use of order statistics greatly simplifies the computation of the persistent barcodes. We validate the proposed methods using comprehensive simulation studies and subsequently apply to the resting-state functional magnetic resonance images. We found a statistically significant topological difference between the male and female brain networks.
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Dong, Keqiang, Haowei Che, and Zhi Zou. "Multiscale Horizontal Visibility Graph Analysis of Higher-Order Moments for Estimating Statistical Dependency." Entropy 21, no. 10 (October 16, 2019): 1008. http://dx.doi.org/10.3390/e21101008.
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The horizontal visibility graph is not only a powerful tool for the analysis of complex systems, but also a promising way to analyze time series. In this paper, we present an approach to measure the nonlinear interactions between a non-stationary time series based on the horizontal visibility graph. We describe how a horizontal visibility graph may be calculated based on second-order and third-order statistical moments. We compare the new methods with the first-order measure, and then give examples including stock markets and aero-engine performance parameters. These analyses suggest that measures derived from the horizontal visibility graph may be of particular relevance to the growing interest in quantifying the information exchange between time series.
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Hoyer, Peter, and Zhan Yu. "Analysis of lackadaisical quantum walks." Quantum Information and Computation 20, no. 13&14 (November 2020): 1138–53. http://dx.doi.org/10.26421/qic20.13-14-4.
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The lackadaisical quantum walk is a quantum analogue of the lazy random walk obtained by adding a self-loop to each vertex in the graph. We analytically prove that lackadaisical quantum walks can find a unique marked vertex on any regular locally arc-transitive graph with constant success probability quadratically faster than the hitting time. This result proves several speculations and numerical findings in previous work, including the conjectures that the lackadaisical quantum walk finds a unique marked vertex with constant success probability on the torus, cycle, Johnson graphs, and other classes of vertex-transitive graphs. Our proof establishes and uses a relationship between lackadaisical quantum walks and quantum interpolated walks for any regular locally arc-transitive graph.
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Hung-Hsiang, Chou, Shen Jianhua, and Lisa Heyes. "15. Statistical Analysis of Shang Meteorology." Early China 9, S1 (1986): 34–35. http://dx.doi.org/10.1017/s0362502800003023.
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ABSTRACTThe authors see their paper as an attempt to analyze Shang meteorology through statistics, but explicitly not to reconstruct Shang weather. It is essentially an amplified study of the oracle-bone record along the lines pioneered by Wittfogel in his “Meteorological Records from the Divination Inscriptions of Shang” (1940), which has been followed up by contributions from Chinese scholars, notably Hu Houxuan. Compiling the data into a graph, the authors, whose research is still preliminary, conclude that during Shang times, there was more rainfall, that it took place during every month of the year, and that the weather was warmer.
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Ghoniem, Mohammad, Jean-Daniel Fekete, and Philippe Castagliola. "On the Readability of Graphs Using Node-Link and Matrix-Based Representations: A Controlled Experiment and Statistical Analysis." Information Visualization 4, no. 2 (May 12, 2005): 114–35. http://dx.doi.org/10.1057/palgrave.ivs.9500092.
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In this article, we describe a taxonomy of generic graph related tasks along with a computer-based evaluation designed to assess the readability of two representations of graphs: matrix-based representations and node-link diagrams. This evaluation encompasses seven generic tasks and leads to insightful recommendations for the representation of graphs according to their size and density. Typically, we show that when graphs are bigger than twenty vertices, the matrix-based visualization outperforms node-link diagrams on most tasks. Only path finding is consistently in favor of node-link diagrams throughout the evaluation.
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Kuzminets, Nikolai, and Yurii Dubovenko. "Constraints of optimization of statistical analysis of data of engineerig monitoring of transport networks." Automobile Roads and Road Construction, no. 109 (2021): 157–65. http://dx.doi.org/10.33744/0365-8171-2021-109-157-165.
Повний текст джерелаАнотація:
Time series for the technical monitoring of the transportation networks include interference and omissions. Their analysis requires the special statistical analysis. Known statistical packages do not contain a full cycle for processing of large time series. The linear timeline for the processing of periodic data is not available in digital statistics. The sliding window approach is suitable for processing of interrupted time series. Its disadvantage is the restriction on the length of the row and the sensitivity to data gaps. The graph of the time series processing needs the internal optimization. The necessary steps for optimizing of the time series processing graph are determined. They are as follows: store data in an internal database, build the data samples on a single time scale, sampling based on the meta-description of the series, averaging in a sliding window, calendar bindings and omission masks, generalization of graphs, storage of graphics in vector format and so on. The conditions for the study of series are revealed such as the database, calendar structure of data, processing of the gaps, a package of numerical methods of analysis, processing in a sliding window.
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Ghafouri, Saeid, and Seyed Hossein Khasteh. "A survey on exponential random graph models: an application perspective." PeerJ Computer Science 6 (April 6, 2020): e269. http://dx.doi.org/10.7717/peerj-cs.269.
Повний текст джерелаАнотація:
The uncertainty underlying real-world phenomena has attracted attention toward statistical analysis approaches. In this regard, many problems can be modeled as networks. Thus, the statistical analysis of networked problems has received special attention from many researchers in recent years. Exponential Random Graph Models, known as ERGMs, are one of the popular statistical methods for analyzing the graphs of networked data. ERGM is a generative statistical network model whose ultimate goal is to present a subset of networks with particular characteristics as a statistical distribution. In the context of ERGMs, these graph’s characteristics are called statistics or configurations. Most of the time they are the number of repeated subgraphs across the graphs. Some examples include the number of triangles or the number of cycle of an arbitrary length. Also, any other census of the graph, as with the edge density, can be considered as one of the graph’s statistics. In this review paper, after explaining the building blocks and classic methods of ERGMs, we have reviewed their newly presented approaches and research papers. Further, we have conducted a comprehensive study on the applications of ERGMs in many research areas which to the best of our knowledge has not been done before. This review paper can be used as an introduction for scientists from various disciplines whose aim is to use ERGMs in some networked data in their field of expertise.
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Yu, Binyan, and Yongshun Liang. "On the Lower and Upper Box Dimensions of the Sum of Two Fractal Functions." Fractal and Fractional 6, no. 7 (July 20, 2022): 398. http://dx.doi.org/10.3390/fractalfract6070398.
Повний текст джерелаАнотація:
Let f and g be two continuous functions. In the present paper, we put forward a method to calculate the lower and upper Box dimensions of the graph of f+g by classifying all the subsequences tending to zero into different sets. Using this method, we explore the lower and upper Box dimensions of the graph of f+g when the Box dimension of the graph of g is between the lower and upper Box dimensions of the graph of f. In this case, we prove that the upper Box dimension of the graph of f+g is just equal to the upper Box dimension of the graph of f. We also prove that the lower Box dimension of the graph of f+g could be an arbitrary number belonging to a certain interval. In addition, some other cases when the Box dimension of the graph of g is equal to the lower or upper Box dimensions of the graph of f have also been studied.
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Cranmer, Skyler J., and Bruce A. Desmarais. "Inferential Network Analysis with Exponential Random Graph Models." Political Analysis 19, no. 1 (2011): 66–86. http://dx.doi.org/10.1093/pan/mpq037.
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Methods for descriptive network analysis have reached statistical maturity and general acceptance across the social sciences in recent years. However, methods for statistical inference with network data remain fledgling by comparison. We introduce and evaluate a general model for inference with network data, the Exponential Random Graph Model (ERGM) and several of its recent extensions. The ERGM simultaneously allows both inference on covariates and for arbitrarily complex network structures to be modeled. Our contributions are three-fold: beyond introducing the ERGM and discussing its limitations, we discuss extensions to the model that allow for the analysis of non-binary and longitudinally observed networks and show through applications that network-based inference can improve our understanding of political phenomena.
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Zhminko, A. E., V. A. Sergeeva, and A. A. Shelakova. "Statistical analysis of internal migration processes in Russia." Bulletin of the Academy 1, no. 68 (2022): 54–60. http://dx.doi.org/10.36871/v.a.2022.03.01.007.
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Purpose of the article. The article analyzes the data of the current migration situation in the Russian Federation. Materials and methods. The main problem of migration movements is identified and their relevance in the present reality is reflected both in the whole world and in Russia. In particular, the migration movement within the borders of the Russian Federation is considered. One of the main types of migration is considered – internal. Results. With the help of Rosstat data for 2010-2020, the growth trend of migration flows and their impact on the development and economy of the state is characterized. The data of the arriving and departing population within the country were analyzed, as well as the migration growth was calculated and a graph of the dynamics of migration processes in Russia was constructed. The controversial definition of the concept of «migration», the main reasons for its appearance, classification, types and consequences after it are revealed and studied. Calculations of the following indicators were carried out: absolute change, growth coefficient, growth rate, growth rate, value of 1% to increase, - for the entire study period according to the basic and chain indices. Conclusion. The results of calculations and absolute changes in the graphs are reflected and confirmed, as well as the results of the research and analysis are summarized.
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SMALTER, AARON, JUN HUAN, and GERALD LUSHINGTON. "GRAPH WAVELET ALIGNMENT KERNELS FOR DRUG VIRTUAL SCREENING." Journal of Bioinformatics and Computational Biology 07, no. 03 (June 2009): 473–97. http://dx.doi.org/10.1142/s0219720009004187.
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In this paper, we introduce a novel statistical modeling technique for target property prediction, with applications to virtual screening and drug design. In our method, we use graphs to model chemical structures and apply a wavelet analysis of graphs to summarize features capturing graph local topology. We design a novel graph kernel function to utilize the topology features to build predictive models for chemicals via Support Vector Machine classifier. We call the new graph kernel a graph wavelet-alignment kernel. We have evaluated the efficacy of the wavelet-alignment kernel using a set of chemical structure–activity prediction benchmarks. Our results indicate that the use of the kernel function yields performance profiles comparable to, and sometimes exceeding that of the existing state-of-the-art chemical classification approaches. In addition, our results also show that the use of wavelet functions significantly decreases the computational costs for graph kernel computation with more than ten fold speedup.
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Liang, Jun, Jun Hua Zhao, Xian Quan Han, and Bo Li. "Automatic Statistic of Rock Mass Discontinuity Attitude Elements Based on K-Mean Clustering Analysis." Applied Mechanics and Materials 170-173 (May 2012): 348–51. http://dx.doi.org/10.4028/www.scientific.net/amm.170-173.348.
Повний текст джерелаАнотація:
The rock attitude elements play important role in the fields of both mechanical properties and stability analysis. The traditional statistical graphs such as rose diagram, isopycnic graph and angle histogram are displayed which can roughly estimate the dip direction and angle of rock mass. And k-mean clustering analysis is applied to rock mass discontinuity attitude automatic statistic which can determine the the dip direction of rock mass accurately and estimate the proportion of gathered data. The K-mean clustering analysis is a beneficial supplement of traditional statistical methods, which has a prospect of engineering application.
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Ri, Song-Il, Vasileios Drakopoulos, and Song-Min Nam. "Fractal Interpolation Using Harmonic Functions on the Koch Curve." Fractal and Fractional 5, no. 2 (April 5, 2021): 28. http://dx.doi.org/10.3390/fractalfract5020028.
Повний текст джерелаАнотація:
The Koch curve was first described by the Swedish mathematician Helge von Koch in 1904 as an example of a continuous but nowhere differentiable curve. Such functions are now characterised as fractal since their graphs are in general fractal sets. Furthermore, it can be obtained as the graph of an appropriately chosen iterated function system. On the other hand, a fractal interpolation function can be seen as a special case of an iterated function system thus maintaining all of its characteristics. Fractal interpolation functions are continuous functions that can be used to model continuous signals. An in-depth discussion on the theory of affine fractal interpolation functions generating the Koch Curve by using fractal analysis as well as its recent development including some of the research made by the authors is provided. We ensure that the graph of fractal interpolation functions on the Koch Curve are attractors of an iterated function system constructed by non-constant harmonic functions.
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El-Mesady, A., and Omar Bazighifan. "Construction of Mutually Orthogonal Graph Squares Using Novel Product Techniques." Journal of Mathematics 2022 (October 10, 2022): 1–16. http://dx.doi.org/10.1155/2022/9722983.
Повний текст джерелаАнотація:
Sets of mutually orthogonal Latin squares prescribe the order in which to apply different treatments in designing an experiment to permit effective statistical analysis of results, they encode the incidence structure of finite geometries, they encapsulate the structure of finite groups and more general algebraic objects known as quasigroups, and they produce optimal density error-correcting codes. This paper gives some new results on mutually orthogonal graph squares. Mutually orthogonal graph squares generalize orthogonal Latin squares interestingly. Mutually orthogonal graph squares are an area of combinatorial design theory that has many applications in optical communications, wireless communications, cryptography, storage system design, algorithm design and analysis, and communication protocols, to mention just a few areas. In this paper, novel product techniques of mutually orthogonal graph squares are considered. Proposed product techniques are the half-starters’ vectors Cartesian product, half-starters’ function product, and tensor product of graphs. It is shown that by taking mutually orthogonal subgraphs of complete bipartite graphs, one can obtain enough mutually orthogonal subgraphs in some larger complete bipartite graphs. Also, we try to find the minimum number of mutually orthogonal subgraphs for certain graphs based on the proposed product techniques. As a direct application to the proposed different product techniques, mutually orthogonal graph squares for disjoint unions of stars are constructed. All the constructed results in this paper can be used to generate new graph-orthogonal arrays and new authentication codes.
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Fatkina, Anna, Maxim Gonchar, Anastasia Kalitkina, Liudmila Kolupaeva, Dmitry Naumov, Dmitry Selivanov, and Konstantin Treskov. "GNA: new framework for statistical data analysis." EPJ Web of Conferences 214 (2019): 05024. http://dx.doi.org/10.1051/epjconf/201921405024.
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We report on the status of GNA — a new framework for fitting large-scale physical models. GNA utilizes the data flow concept within which a model is represented by a directed acyclic graph. Each node is an operation on an array (matrix multiplication, derivative or cross section calculation, etc). The framework enables the user to create flexible and efficient large-scale lazily evaluated models, handle large numbers of parameters, propagate parameters’ uncertainties while taking into account possible correlations between them, fit models, and perform statistical analysis. The main goal of the paper is to give an overview of the main concepts and methods as well as reasons behind their design. Detailed technical information is to be published in further works.
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Bhaduri, Susmita, and Dipak Ghosh. "Azimuthal Anisotropy in High-Energy Nuclear Collision: An Approach Based on Complex Network Analysis." Advances in High Energy Physics 2018 (2018): 1–9. http://dx.doi.org/10.1155/2018/8347408.
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Recently, a complex network based method of visibility graph has been applied to confirm the scale-freeness and presence of fractal properties in the process of multiplicity fluctuation. Analysis of data obtained from experiments on hadron-nucleus and nucleus-nucleus interactions results in values of Power of Scale-Freeness of Visibility Graph (PSVG) parameter extracted from the visibility graphs. Here, the relativistic nucleus-nucleus interaction data have been analysed to detect azimuthal anisotropy by extending the visibility graph method and extracting the average clustering coefficient, one of the important topological parameters, from the graph. Azimuthal-distributions corresponding to different pseudorapidity regions around the central pseudorapidity value are analysed utilising the parameter. Here we attempt to correlate the conventional physical significance of this coefficient with respect to complex network systems, with some basic notions of particle production phenomenology, like clustering and correlation. Earlier methods for detecting anisotropy in azimuthal distribution were mostly based on the analysis of statistical fluctuation. In this work, we have attempted to find deterministic information on the anisotropy in azimuthal distribution by means of precise determination of topological parameter from a complex network perspective.
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Ganea, Ion. "Model of statistical data analysis on nitrogen content in soybeans (Glicine Max Merrill) in Clavera variety." Journal of Engineering Science 30, no. 1 (April 2023): 165–77. http://dx.doi.org/10.52326/jes.utm.2023.30(1).14.
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Climate change, drought and high temperatures lately have led to the need to increase the adaptation capacities of plants to these changes. The purpose of the research is to gain knowledge regarding the influence of the biologically active substances Reglalg (compound of algal nature) and Biovit (compound of humic nature) on plant development, productivity and adaptation of plants to new climatic conditions. The research was based on decision support systems, machine learning and graph databases. These systems allow in-depth processing of unstructured data and making the necessary decisions. In this sense, an intelligent model was developed for the processing of biological data as part of a Decision Support System. For data analysis and knowledge generation, a graph database was developed to determine relationships and connections between entities, phenomena or events. Graphs allow the representation of complex information in a simple and intuitive way, which makes it easier to perform and analyze them. The use of Machine Learning methods allows the highlighting of laws and interactions between different elements, which can lead to the discovery of patterns and trends that can be easily identified. The paper presents the structure and functions of some components of the decision support system for the study of nitrogen content in soybean.
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Hayat, Sakander, and Farwa Asmat. "Sharp Bounds on the Generalized Multiplicative First Zagreb Index of Graphs with Application to QSPR Modeling." Mathematics 11, no. 10 (May 11, 2023): 2245. http://dx.doi.org/10.3390/math11102245.
Повний текст джерелаАнотація:
Degree sequence measurements on graphs have attracted a lot of research interest in recent decades. Multiplying the degrees of adjacent vertices in graph Ω provides the multiplicative first Zagreb index of a graph. In the context of graph theory, the generalized multiplicative first Zagreb index of a graph Ω is defined as the product of the sum of the αth powers of the vertex degrees of Ω, where α is a real number such that α≠0 and α≠1. The focus of this work is on the extremal graphs for several classes of graphs including trees, unicyclic, and bicyclic graphs, with respect to the generalized multiplicative first Zagreb index. In the initial step, we identify a set of operations that either increases or decreases the generalized multiplicative first Zagreb index for graphs. We then involve analysis of the generalized multiplicative first Zagreb index achieving sharp bounds by characterizing the maximum or minimum graphs for those classes. We present applications of the generalized multiplicative first Zagreb index Π1α for predicting the π-electronic energy Eπ(β) of benzenoid hydrocarbons. In particular, we answer the question concerning the value of α for which the predictive potential of Π1α with Eπ for lower benzenoid hydrocarbons is the strongest. In fact, our statistical analysis delivers that Π1α correlates with Eπ of lower benzenoid hydrocarbons with correlation coefficient ρ=−0.998, if α=−0.00496. In QSPR modeling, the value ρ=−0.998 is considered to be considerably significant.
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Oksiiuk, Oleksandr, Larysa Myrutenko, and Yanina Shestak. "PRACTICAL INTRODUCTION OF INFORMATION SYSTEMS BASED ON ASSESSMENT OF EXTERNAL INFLUENCES." Information systems and technologies security, no. 1 (1) (2019): 27–35. http://dx.doi.org/10.17721/ists.2019.1.27-35.
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The article highlighted the advantage of information systems in front of centralized systems in terms of ensuring the security of network infrastructure, data transmitted, and procedures used in the software environment of the complex. It was pointed out the technical simplicity of the methods of expansion of information systems and, accordingly, their scalability. A multilevel energy balance scheme and computing resources of the information system infrastructure, based on the optimization of the task graph, have been developed. The methods of estimating the optimization of the graph of tasks, which are based on the indicators of the normalized graph normalized distribution of energy, are determined. The results of mathematical modeling in comparison with statistical data for such methods of working with task graphs as calculations by hierarchical structure, graph split algorithms, methods based on algebraic theory of graphs, structuring of "Diamond Dags" type. The analysis was conducted for such types of distribution as uniform distribution, binomial distribution, geometric distribution. The results of the comparison point to a sufficiently upstart prediction accuracy at the level of mathematical modeling. In most cases, the value of the maximum deviation, presented as a relative error, between simulation results and statistical data remains within 10%, which shows the adequacy of the simulation. Nevertheless, for the four pairs of functions of the length of the normalized graph and the normalized energy distribution, the maximum deviation is greater than 10%, indicating the need for a revision of the model and further statistical studies. It is proposed to use in organizing the protection of resources of the information system of clusterization methods, which allow to construct a transparent scheme of functioning of the complex and to construct monitoring algorithms
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Pattabiraman, K., B. Devayani, M. Sowmiya, and B. Santhiya. "Statistical Investigation for Some Classes of Alkanes Through Graph Indices." Journal of Statistics and Mathematical Engineering 9, no. 1 (January 19, 2023): 15–28. http://dx.doi.org/10.46610/josme.2023.v09i01.002.
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Topological indices are numerical descriptors that may be produced from a molecular graph to thoroughly analyze the medications. They are frequently employed in the analysis and forecasting of the physicochemical features of several pharmaceuticals. Numerous forms of polynomials and topological indices are computed, which serves as representations of chemical structure, and are crucial to chemical graph theory. The findings already obtained may be improved, and there may be a greater link to the various physical features of chemical substances, as a consequence of modifications and generalizations of the conventional topological indices. We suggest seven brand-new distance-based topological indices in this communication. We further investigate these suggested topological indices for several frequently occurring chemical structures from chemical graph theory.
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Yap, Timothy Tzen Vun, Ting Fong Ho, Hu Ng, and Vik Tor Goh. "Exploratory graph analysis of the network data of the Ethereum blockchain." F1000Research 10 (September 9, 2021): 908. http://dx.doi.org/10.12688/f1000research.73141.1.
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Background: This research uses exploratory graph analysis to analyze the transaction data of the Ethereum network. This is achieved through network visualization and mathematical and statistical modelling of the network data. Methods: The dataset used in this study was extracted from the Ethereum in the BigQuery public dataset, specifically selected transactions in July 2019. The transactions were firstly modelled as network graphs and then visualized using the Kamada-Kawai and force-directed graphs layouts. Further modelling was explored with classical random graph and network block, with emphasis on network cohesion, hierarchical clustering and community membership. Results: Looking at the network visualization and hierarchical clustering of the data, the network shows 170 clusters, the largest having 135 members. Through random graph modelling the optimum number of clusters is shown to be 95. Referring to the generated dendrograms, notable large transactions center around the DRINK token, the Maximine Exchange, the Upbit2 Exchange and the IDEX Exchange, identified through public disclosure of their Ethereum addresses. The network graphs tend to go towards the DRINK smart contract and the Maximine Exchange, indicating deposit actions, while it is the opposite for the IDEX Exchange. Further analysis also shows a different number of communities than the expected number. Falling short of the expected 170 clusters, the model is not able to capture additional mechanism that may be present at the density and social interaction distribution level of the network. On the other hand, network block modelling shows only four major clusters out of the 170 expected clusters, an indication that the model is not able to capture the network sufficiently. Conclusions: The study was able to capture and model the interconnectedness of the system with its notion of elements, in this case, the transactions on the network.
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Guasch, Oriol, Àngels Aragonès, and Marcel Janer. "A graph cut strategy for transmission path problems in statistical energy analysis." Mechanical Systems and Signal Processing 30 (July 2012): 343–55. http://dx.doi.org/10.1016/j.ymssp.2011.10.006.
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McLean, Alan L. "Concepts and Practice of Statistics: Part 3 - Graphics." Australasian Orthodontic Journal 10, no. 1 (March 1, 1987): 15–20. http://dx.doi.org/10.2478/aoj-1987-0003.
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Abstract The process of analysis of a set data aims to detect patterns, especially relationships between variables, in the data. Statistical techniques can be described broadly as techniques to detect particular types of patterns, and to test whether such patterns ‘really exist’. The use of graphs to aid in pattern detection is long established. A picture can be used to make a point quickly and easily. In the context of data analysis, it is making the point more powerfully than does a table of data. A well chosen and well drawn graph makes its point - reveals a pattern - very powerfully. Equally, a badly chosen or dishonestly drawn graph makes a point incorectly - but equally powerfully.
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Korney, A. O., and E. N. Kryuchkova. "Text Categorization Based on Condensed Graph." INFORMACIONNYE TEHNOLOGII 27, no. 3 (March 15, 2021): 138–46. http://dx.doi.org/10.17587/it.27.138-146.
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The resonant world events of2020 led to an increase in the amount of information on the Internet, including criminal, fake news, and fake negative reviews. False negative information can spread very quickly, and methods are needed to suppress this process. The development of effective algorithms for automatic text analysis is especially relevant today. The most important subtasks include thematic catesorization, sentiment analysis, includins ABSA (aspect-based sentiment analysis). The paper proposes a combined semantic-statistical alsorithm for the aspect analysis of larse texts, based on the use of a semantic graph. The aspect extraction method contains the phases of selectins a set of sisnificant words, calculatins the weishts of the vertices of the semantic sraph by the relaxation method, filterins aspects based on the sradient method. The method proposed allows to extract domain-dependent aspect terms from trainins data. Different aspect term sets extracted from different domains have the same statistical features, and in the same time lexical diversity and structure are taken into account.
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Liu, Jia-Bao, Qing Xie, and Jiao-Jiao Gu. "Statistical Analyses of a Class of Random Pentagonal Chain Networks with respect to Several Topological Properties." Journal of Function Spaces 2023 (February 28, 2023): 1–17. http://dx.doi.org/10.1155/2023/6675966.
Повний текст джерелаАнотація:
There has been an upsurge of research on complex networks in recent years. The purpose of this paper is to study the mathematical properties of the random pentagonal chain networks PE C n with the help of graph theory. Based on the networks PE C n , we first obtain the expected value expressions of the Gutman index, Schultz index, multiplicative degree-Kirchhoff index, and additive degree-Kirchhoff index, and then, we get the explicit expression formulas of their variances. Finally, we find that their limiting distributions all have the probabilistic and statistical significance of normal distribution.
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Petruk, Victoria. "Zero Forcing Number of Some Families of Graphs." Mohyla Mathematical Journal 3 (January 29, 2021): 48–52. http://dx.doi.org/10.18523/2617-70803202048-52cs.
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The work is devoted to the study of the zero forcing number of some families of graphs. The concept of zero forcing is a relatively new research topic in discrete mathematics, which already has some practical applications, in particular, is used in studies of the minimum rank of the matrices of adjacent graphs. The zero forcing process is an example of the spreading process on graphs. Such processes are interesting not only in terms of mathematical and computer research, but also interesting and are used to model technical or social processes in other areas: statistical mechanics, physics, analysis of social networks, and so on. Let the vertices of the graph G be considered white, except for a certain set of S black vertices. We will repaint the vertices of the graph from white to black, using a certain rule.Colour change rule: A white vertex turns black if it is the only white vertex adjacent to the black vertex.[5] The zero forcing number Z(G) of the graph G is the minimum cardinality of the set of black vertices S required to convert all vertices of the graph G to black in a finite number of steps using the ”colour change rule”.It is known [10] that for any graph G, its zero forcing number cannot be less than the minimum degree of its vertices. Such and other already known facts became the basis for finding the zero forcing number for two given below families of graphs:A gear graph, denoted W2,n is a graph obtained by inserting an extra vertex between each pair of adjacent vertices on the perimeter of a wheel graph Wn. Thus, W2,n has 2n + 1 vertices and 3n edges.A prism graph, denoted Yn, or in general case Ym,n, and sometimes also called a circular ladder graph, is a graph corresponding to the skeleton of an n-prism.A wheel graph, denoted Wn is a graph formed by connecting a single universal vertex to all vertices of a cycle of length n.In this article some known results are reviewed, there is also a definition, proof and some examples of the zero forcing number and the zero forcing process of gear graphs and prism graphs.
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Roux, Jérôme, Nicolas Bez, Paul Rochet, Rocío Joo, and Stéphanie Mahévas. "Graphlet correlation distance to compare small graphs." PLOS ONE 18, no. 2 (February 15, 2023): e0281646. http://dx.doi.org/10.1371/journal.pone.0281646.
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Graph models are standard for representing mutual relationships between sets of entities. Often, graphs deal with a large number of entities with a small number of connections (e.g. social media relationships, infectious disease spread). The distances or similarities between such large graphs are known to be well established by the Graphlet Correlation Distance (GCD). This paper deals with small graphs (with potentially high densities of connections) that have been somewhat neglected in the literature but that concern important fora like sociology, ecology and fisheries, to mention some examples. First, based on numerical experiments, we study the conditions under which Erdős-Rényi, Fitness Scale-Free, Watts-Strogatz small-world and geometric graphs can be distinguished by a specific GCD measure based on 11 orbits, the GCD11. This is done with respect to the density and the order (i.e. the number of nodes) of the graphs when comparing graphs with the same and different orders. Second, we develop a randomization statistical test based on the GCD11 to compare empirical graphs to the four possible null models used in this analysis and apply it to a fishing case study where graphs represent pairwise proximity between fishing vessels. The statistical test rules out independent pairing within the fleet studied which is a standard assumption in fisheries. It also illustrates the difficulty to identify similarities between real-world small graphs and graph models.
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Younis, Mudasir, and Afrah Ahmad Noman Abdou. "Novel Fuzzy Contractions and Applications to Engineering Science." Fractal and Fractional 8, no. 1 (December 29, 2023): 28. http://dx.doi.org/10.3390/fractalfract8010028.
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The article outlines a creative approach by fusing ideas from fuzzy contractions, graph mappings, and Kannan mappings to create a brand-new notion known as “Kannan-graph-fuzzy contraction”. This combination of concepts makes it possible to create a unique framework for resolving real-world issues controlled by nonlinear models. It is anticipated that using Kannan-graph-fuzzy contractions will offer a fresh approach to discussing solution existence in situations where these ideas overlap. This strategy might have a significant impact on a lot of real-world applications, proving how practical multidisciplinary techniques are for tackling issues in the real world originating from technology and engineering. The article includes several illustrated examples based on computer simulations, making the results more explicit.
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Kudryakov, Roman I. "ANALYSIS OF THE STATE OF INNOVATION PROCESSES IN THE REGION: INDICATOR-GRAPHICAL APPROACH." Economy of the North-West: problems and prospects of development 3, no. 74 (November 24, 2023): 46–55. http://dx.doi.org/10.52897/2411-4588-2023-3-46-55.
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This study is devoted to the analysis of the state of innovation processes in the region using the graph theory method. The paper discusses the theoretical and conceptual apparatus, carried out a statistical analysis of the dynamics of innovation processes in the region of Vladimir region from 2013–2022, based on statistical data developed mathematical tools to determine the indicators of innovation processes, identified problems, applied the graph theory method to identify the causes of problematic aspects in the region, the industrial sector was chosen as an example of the application of the method, and the author’s recommendations for minimizing the impact of problematic moments in the selected sector of the economy are presented.
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De Amici, D., C. Klersy, and C. Tinelli. "Graphic Data Representation in Anaesthesiological Journals: A Proposed Methodology for Assessment of Appropriateness." Anaesthesia and Intensive Care 25, no. 6 (December 1997): 659–64. http://dx.doi.org/10.1177/0310057x9702500612.
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Few authors have addressed the topic of graphic data presentation. The purpose of our study was to combine several guidelines in order to evaluate three anaesthesiology journals listed in Index Medicus (Australian, American and Italian) in terms of the appropriateness and the quality of presentation of graphs. Our analysis was based on concepts expressed by Cox and Tufte. We calculated the optimization of the amount of information in each graph using two parameters: Data Density Index (DDI) and Data Ink Ratio (DIR). The correctness and clearness of each component of the graph (scale, title, axes, legends and abbreviations) was evaluated on the basis of a binary score. We analysed 300 exploratory plots, quantitative graphs and summaries of statistical analysis. About 50% of papers had more than three graphs. Mean scores were 3.22 for the Italian journal, 3.47 for the American journal and 3.82 for the Australian journal. Tufte parameters were calculated on 42 scatterplots: DDI was 5.4±13.9 and DIR was 0.7±0.1. The criteria applied in our study appear sufficiently sensitive to differentiate the quality of graphs.
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SABRI, MOSTAFA. "ANDERSON LOCALIZATION FOR A MULTI-PARTICLE QUANTUM GRAPH." Reviews in Mathematical Physics 26, no. 01 (January 13, 2014): 1350020. http://dx.doi.org/10.1142/s0129055x13500207.
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We study a multi-particle quantum graph with random potential. Taking the approach of multiscale analysis, we prove exponential and strong dynamical localization of any order in the Hilbert–Schmidt norm near the spectral edge. Apart from the results on multi-particle systems, we also prove Lifshitz-type asymptotics for single-particle systems. This shows in particular that localization for single-particle quantum graphs holds under a weaker assumption on the random potential than previously known.
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Riba, Pau. "Distilling Structure from Imagery:Graph-based Models for the Interpretation of Document Images." ELCVIA Electronic Letters on Computer Vision and Image Analysis 19, no. 2 (January 12, 2021): 9–10. http://dx.doi.org/10.5565/rev/elcvia.1313.
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From its early stages, the community of Pattern Recognition and Computer Vision has considered the importance of leveraging the structural information when understanding images. Usually, graphs have been proposed as a suitable model to represent this kind of information due to their flexibility and representational power able to codify both, the components, objects, or entities and their pairwise relationship. Even though graphs have been successfully applied to a huge variety of tasks, as a result of their symbolic and relational nature, graphs have always suffered from some limitations compared to statistical approaches. Indeed, some trivial mathematical operations do not have an equivalence in the graph domain. For instance, in the core of many pattern recognition applications, there is a need to compare two objects. This operation, which is trivial when considering feature vectors defined in ℝn, is not properly defined for graphs. In this thesis, we have investigated the importance of the structural information from two perspectives, the traditional graph-based methods and the new advances on Geometric Deep Learning. On the one hand, we explore the problem of defining a graph representation and how to deal with it on a large scale and noisy scenario. On the other hand, Graph Neural Networks are proposed to first redefine a Graph Edit Distance methodologies as a metric learning problem, and second, to apply them in a real use case scenario for the detection of repetitive patterns which define tables in invoice documents. As experimental framework, we have validated the different methodological contributions in the domain of Document Image Analysis and Recognition.
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Khan, Asad, Azmat Ullah Khan Niazi, Waseem Abbasi, Faryal Awan, and Anam Khan. "Fractional-Order Nonlinear Multi-Agent Systems: A Resilience-Based Approach to Consensus Analysis with Distributed and Input Delays." Fractal and Fractional 7, no. 4 (April 11, 2023): 322. http://dx.doi.org/10.3390/fractalfract7040322.
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In this article, a resilient consensus analysis of fractional-order nonlinear leader and follower systems with input and distributed delays is assumed. To make controller design more practical, it is considered that the controller is not implemented as it is, and a disturbance term is incorporated into the controller part. A multi-agent system’s topology ahead to a weighted graph which may be directed or undirected is used. The article examines a scenario of leader–follower consensus through the application of algebraic graph theory and the fractional-order Razumikhin method. Numerical simulations are also provided to show the effectiveness of the proposed design for the leader–follower consensus.
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Kislitsyn A.A., A. A., Yu N. Orlov, and M. V. Goguev. "Investigation of the Properties of First Nearest Neighbors’ Graphs." Scientific Visualization 15, no. 1 (April 2023): 17–28. http://dx.doi.org/10.26583/sv.15.1.02.
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In this study we present a benchmark of statistical distributions of the first nearest neighbors in random graphs. We consider distribution of such graphs by the number of disconnected fragments, fragments by the number of involved nodes, and nodes by their degrees. The statements about the asymptotic properties of these distributions for graphs of large dimension are proved. The problem under investigation is to estimate the probability of realization of a certain structure of the first nearest neighbors graph depending on the distribution function of distances between the elements of the studied set. It is shown that, up to isomorphism, the graph of the first nearest neighbors does not depend on the distance distribution. This fact makes it possible to conduct numerical experiments on the construction of basic statistics based on a uniform distribution of distances and obtain tabulated data as a result of numerical modeling. We also discuss the approximation of the distribution of graph vertices by degrees, which allows us to estimate the proportion of randomness for a particular structure resulting from clustering elements of a certain set by the nearest neighbor method. The asymptotic analysis of the fragment distribution is discussed.
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Bing Li, Ning Chen, and U. Schlichtmann. "Statistical Timing Analysis for Latch-Controlled Circuits With Reduced Iterations and Graph Transformations." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 31, no. 11 (November 2012): 1670–83. http://dx.doi.org/10.1109/tcad.2012.2202393.
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Xu, Yue, Tao Yu, and Bo Yang. "Reliability assessment of distribution networks through graph theory, topology similarity and statistical analysis." IET Generation, Transmission & Distribution 13, no. 1 (January 8, 2019): 37–45. http://dx.doi.org/10.1049/iet-gtd.2018.5520.
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