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Journal articles on the topic 'Graphons de probabilités'

Author: Grafiati

Published: 14 December 2024

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1

McMillan, Audra, and Adam Smith. "When is non-trivial estimation possible for graphons and stochastic block models?‡." Information and Inference: A Journal of the IMA 7, no. 2 (2017): 169–81. http://dx.doi.org/10.1093/imaiai/iax010.

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Abstract Block graphons (also called stochastic block models) are an important and widely studied class of models for random networks. We provide a lower bound on the accuracy of estimators for block graphons with a large number of blocks. We show that, given only the number $k$ of blocks and an upper bound $\rho$ on the values (connection probabilities) of the graphon, every estimator incurs error ${\it{\Omega}}\left(\min\left(\rho, \sqrt{\frac{\rho k^2}{n^2}}\right)\right)$ in the $\delta_2$ metric with constant probability for at least some graphons. In particular, our bound rules out any non-trivial estimation (that is, with $\delta_2$ error substantially less than $\rho$) when $k\geq n\sqrt{\rho}$. Combined with previous upper and lower bounds, our results characterize, up to logarithmic terms, the accuracy of graphon estimation in the $\delta_2$ metric. A similar lower bound to ours was obtained independently by Klopp et al.

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2

HATAMI, HAMED, and SERGUEI NORINE. "The Entropy of Random-Free Graphons and Properties." Combinatorics, Probability and Computing 22, no. 4 (2013): 517–26. http://dx.doi.org/10.1017/s0963548313000175.

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Every graphon defines a random graph on any given number n of vertices. It was known that the graphon is random-free if and only if the entropy of this random graph is subquadratic. We prove that for random-free graphons, this entropy can grow as fast as any subquadratic function. However, if the graphon belongs to the closure of a random-free hereditary graph property, then the entropy is O(n log n). We also give a simple construction of a non-step-function random-free graphon for which this entropy is linear, refuting a conjecture of Janson.

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3

Backhausz, Ágnes, and Dávid Kunszenti-Kovács. "On the dense preferential attachment graph models and their graphon induced counterpart." Journal of Applied Probability 56, no. 2 (2019): 590–601. http://dx.doi.org/10.1017/jpr.2019.34.

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AbstractLetting ℳ denote the space of finite measures on ℕ, and μλ ∊ ℳ denote the Poisson distribution with parameter λ, the function W : [0, 1]2 → ℳ given by W(x, y) = μc log x log y is called the PAG graphon with density c. It is known that this is the limit, in the multigraph homomorphism sense, of the dense preferential attachment graph (PAG) model with edge density c. This graphon can then in turn be used to generate the so-called W-random graphs in a natural way, and similar constructions also work in the slightly more general context of the so-called PAGκ models. The aim of this paper is to compare these dense PAGκ models with the W-random graph models obtained from the corresponding graphons. Motivated by the multigraph limit theory, we investigate the expected jumble-norm distance of the two models in terms of the number of vertices n. We present a coupling for which the expectation can be bounded from above by O(log3/2n · n−1/2), and provide a universal lower bound that is coupling-independent, but without the logarithmic term.

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4

Kalampakas, Antonios. "Graph Automata and Graph Colorability." European Journal of Pure and Applied Mathematics 16, no. 1 (2023): 112–20. http://dx.doi.org/10.29020/nybg.ejpam.v16i1.4629.

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Automata recognizing graphs can be constructed by employing the algebraic structure of graphoids. For the construction of a graph automaton, the relations over the Kleene star of the state set must constitute a graphoid. Hence different kinds of graphoids produce graph automata with diverse operation and recognition capacity. In this paper we show that graph colorability is recognized by automata operating over the simplest possible abelian graphoid.

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5

Zhang, Yuan, Elizaveta Levina, and Ji Zhu. "Estimating network edge probabilities by neighbourhood smoothing." Biometrika 104, no. 4 (2017): 771–83. http://dx.doi.org/10.1093/biomet/asx042.

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Summary The estimation of probabilities of network edges from the observed adjacency matrix has important applications to the prediction of missing links and to network denoising. It is usually addressed by estimating the graphon, a function that determines the matrix of edge probabilities, but this is ill-defined without strong assumptions on the network structure. Here we propose a novel computationally efficient method, based on neighbourhood smoothing, to estimate the expectation of the adjacency matrix directly, without making the structural assumptions that graphon estimation requires. The neighbourhood smoothing method requires little tuning, has a competitive mean squared error rate and outperforms many benchmark methods for link prediction in simulated and real networks.

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Shi, Tan, Qing Peng, Zhitong Bai, Fei Gao, and Igor Jovanovic. "Proton irradiation of graphene: insights from atomistic modeling." Nanoscale 11, no. 43 (2019): 20754–65. http://dx.doi.org/10.1039/c9nr06502d.

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Peng, Songang, Zhi Jin, Dayong Zhang, Jingyuan Shi, Yanhui Zhang, and Guanghui Yu. "Evidence of electric field-tunable tunneling probability in graphene and metal contact." Nanoscale 9, no. 27 (2017): 9520–28. http://dx.doi.org/10.1039/c7nr02502e.

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8

Yoder, J. W., E. Littell, and B. T. Williams. "Probability Graphics Support for Medical Reasoning." Methods of Information in Medicine 32, no. 03 (1993): 229–32. http://dx.doi.org/10.1055/s-0038-1634928.

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Abstract:Graphic displays of data from clinical observations and laboratory testing provide important support to the health practitioner in managing an increasing amount of complex information. A graphic display program is described that preserves much of the context of data that is important to their evaluation, and that maintains a sense of the strength of the signal when aberrant data are encountered.

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VANTAGGI, BARBARA. "CONDITIONAL INDEPENDENCE STRUCTURES AND GRAPHICAL MODELS." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 11, no. 05 (2003): 545–71. http://dx.doi.org/10.1142/s0218488503002326.

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In this paper we study conditional independence structures arising from conditional probabilities and lower conditional probabilities. Such models are based on notions of stochastic independence apt to manage also those situations where zero evaluations on possible events are present: this is particularly crucial for lower probability. The "graphoid" properties of such models are investigated, and the representation problem of conditional independence structures is dealt with by generalizing the wellknown classic separation criteria for undirected and directed acyclic graphs. Our graphical models describe the independence statements and the possible logical dependencies among the random variables.

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10

Raturi, Ashish, and Sudhanshu Choudhary. "Simulation Study on Understanding the Spin Transport in MgO Adsorbed Graphene Based Magnetic Tunnel Junction." SPIN 06, no. 03 (2016): 1650011. http://dx.doi.org/10.1142/s2010324716500119.

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First principles calculations of spin-dependent electronic transport properties of magnetic tunnel junction (MTJ) consisting of MgO adsorbed graphene nanosheet sandwiched between two CrO2 half-metallic ferromagnetic (HMF) electrodes is reported. MgO adsorption on graphene opens bandgap in graphene nanosheet which makes it more suitable for use as a tunnel barrier in MTJs. It was found that MgO adsorption suppresses transmission probabilities for spin-down channel in case of parallel configuration (PC) and also suppresses transmission in antiparallel configuration (APC) for both spin-up and spin-down channel. Tunnel magneto-resistance (TMR) of 100% is obtained at all bias voltages in MgO adsorbed graphene-based MTJ which is higher than that reported in pristine graphene-based MTJ. HMF electrodes were found suitable to achieve perfect spin filtration effect and high TMR. I–V characteristics for both parallel and antiparallel magnetization states of junction are calculated. High TMR suggests its usefulness in spin valves and other spintronics-based applications.

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11

Sedeeq, Bekhal Samad, and Zhiyan Muhsin Jalal. "Estimation and Prediction the Probability of Failure with Application." Tikrit Journal of Administrative and Economic Sciences 17, no. 54, 3 (2021): 493–508. http://dx.doi.org/10.25130/tjaes.17.54.3.31.

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One of the reasons that reduces the production of factories is the failure of these machines that are used for production. One of the reasons for these failures is due to failures of the components of the machines, which is due to all the stress that these components face while working. That is why trying to make the life of these machines longer we need to know the (Probability of Failure) and (Cycle of Failure) for the components of these machines. The Researcher, to achieve and obtain the main goal of this study, after very hard work started to collect data on five components (time of failure and repair) of these components in a steel company, the company that is in Erbil City Kurdistan Region of Iraq. The Researcher reached a conclusion finding the probability of failure and cycle to failure for each component in these machines, also estimating the value of cycle to failure for nine specific values of the probability of failure. We also designed a model for predicting the probability of failure for each machine including all the components together through using Factor Analysis and Multiple Regression Analysis. STAT Graphics, SPSS and Microsoft Excel have been used for all the calculations, graphics, and analysis.

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12

Saunders, D. J. "Computer graphics and animations for teaching probability and statistics." International Journal of Mathematical Education in Science and Technology 17, no. 5 (1986): 561–68. http://dx.doi.org/10.1080/0020739860170505.

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Tan, Choo-Kim, Madhubala Bava Harji, and Siong-Hoe Lau. "Fostering positive attitude in probability learning using graphing calculator." Computers & Education 57, no. 3 (2011): 2011–24. http://dx.doi.org/10.1016/j.compedu.2011.05.005.

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14

Pudlak, Mihal, Jan Smotlacha, and Rashid Nazmitdinov. "On Symmetry Properties of The Corrugated Graphene System." Symmetry 12, no. 4 (2020): 533. http://dx.doi.org/10.3390/sym12040533.

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The properties of the ballistic electron transport through a corrugated graphene system are analysed from the symmetry point of view. The corrugated system is modelled by a curved surface (an arc of a circle) connected from both sides to flat sheets. The spin–orbit couplings, induced by the curvature, give rise to equivalence between the transmission (reflection) probabilities of the transmitted (reflected) electrons with the opposite spin polarisation, incoming from opposite system sides. We find two integrals of motion that explain the chiral electron transport in the considered system.

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15

Vanderplas, Susan, Dianne Cook, and Heike Hofmann. "Testing Statistical Charts: What Makes a Good Graph?" Annual Review of Statistics and Its Application 7, no. 1 (2020): 61–88. http://dx.doi.org/10.1146/annurev-statistics-031219-041252.

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It has been approximately 100 years since the very first formal experimental evaluations of statistical charts were conducted. In that time, technological changes have impacted both our charts and our testing methods, resulting in a dizzying array of charts, many different taxonomies to classify graphics, and several different philosophical approaches to testing the efficacy of charts and graphs experimentally. Once rare, charts and graphical displays are now everywhere—but do they help us understand? In this article we review the history of graphical testing across disciplines, discuss different direct approaches to testing graphics, and contrast direct tests with visual inference, which requires that the viewer determine both the question and the answer. Examining the past 100 years of graphical testing, we summarize best practices for creating effective graphics and discuss what the future holds for graphics and empirical testing of interactive statistical visualizations.

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16

Xu, Zhi-Cheng, and Wei-Rong Zhong. "Probability of self-healing in damaged graphene bombarded by fullerene." Applied Physics Letters 104, no. 26 (2014): 261907. http://dx.doi.org/10.1063/1.4886580.

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17

Zhang, Kongsheng. "On the application of projection threading method in the teaching of probability theory." Journal of Education and Educational Research 1, no. 1 (2022): 14–17. http://dx.doi.org/10.54097/jeer.v1i1.2063.

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The probability density function of the sum of random variables and marginal density function are important and difficult concepts in the course of probability theory. The key to calculate them is to determine the range of interested variables and integral variables. Combined with graphics, the range of those variables can be determined quickly by using projection threading method. The proposed method is intuitive and easy to master.

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18

Wood, Eric. "Probability, Problem Solving, and “The Price Is Right”." Mathematics Teacher 85, no. 2 (1992): 103–9. http://dx.doi.org/10.5951/mt.85.2.0103.

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The document Academic Preparation in Mathematics (Kilpatrick 1985) sets out in some detail the mathematical topics that students entering college in the 1990s need to know. One point that is made rather forcefully is that students should have some grounding in statistics, probability, and computer simulation, a theme that is echoed in Standard 11 in the Curriculum and Evaluation Standards for School Mathematics (1989). Furnishing such experiences and at the same time ensuring that the material is both relevant and at an appropriate level of difficulty is often a challenge in the typical high school classroom. This article discusses the analysis of a decision-making problem faced by contestants on the popular game show “The Price Is Right.” An analysis of the original and related problems involves pattern searching, inductive reasoning, quadratric functions, and graphing, as well as presents an intrinsically interesting question in elementary probability that can be investigated by students at many different grade levels.

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19

Li, Ker-Chau, and R. Dennis Cook. "Regression Graphics: Ideas for Studying Regression through Graphics." Journal of the American Statistical Association 94, no. 447 (1999): 980. http://dx.doi.org/10.2307/2670012.

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20

Melgar, Angel Salvatierra, José Nieto Gamboa, César Daniel Escuza Mesías, Paola Gissella Orozco-Vargas, and Linda Shardin-Flores. "Micro worlds: learning about probabilities in simulated contexts." Revista Tempos e Espaços em Educação 14, no. 33 (2021): e15122. http://dx.doi.org/10.20952/revtee.v14i33.15122.

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In this study, the learning processes of the concepts of the probability topic are based on the use and simulation of the micro world tools by the learning actors, who demonstrated creativity, selection of the objects visible in the interface, and the introduction of basic programming principles associated with the topic in question. For the development of the study, we proceeded by the experimental design of a pre-experimental type of an intact group made up of 50 students from the 5th academic semester of the Professional School of Education of a Public University. The data were collected by an academic test before and after the experimentation, to later be processed and analyzed through the Student's t-statistic expression for related samples, reaching the following conclusion. The experimentation with micro worlds as active learning strategies based on the theory of constructionism, presents a high degree of interactivity associated with sounds, silhouettes, graphics and activities, which allowed to promote the conceptualization, resolution of exercises and problems of the topic in an experiential way in environments natural simulated by the computer.

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21

Dhar, Purbarun, Ankur Chattopadhyay, Lakshmi Sirisha Maganti, and Anilakkad Raman Harikrishnan. "Streamer evolution arrest governed amplified AC breakdown strength of graphene and CNT colloids." European Physical Journal Applied Physics 85, no. 3 (2019): 30402. http://dx.doi.org/10.1051/epjap/2019180360.

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The present paper explores the concept of improving the AC dielectric breakdown strength of insulating mineral oils by the addition of graphene or carbon nanotubes (CNTs) to form stable dispersions. Experimental observations of graphene and CNT nano-oils show that not only improved average breakdown voltage, but also significantly improved reliability and survival probabilities of the oils under AC high voltage stressing is achieved. Improvement of the tune of ∼70–80% in the AC breakdown voltage of the oils has been obtained. The study examines the reliability of such nano-colloids using a two-parameter Weibull distribution and the oils show greatly augmented electric field bearing capacity. The fundamental mechanism responsible for such observed outcomes is reasoned to be delayed streamer development and reduced streamer growth rates due to effective electron scavenging. A mathematical model based on the principles of electron scavenging is proposed to quantify the amount of electrons scavenged by the nanostructures.

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22

Murrell, Paul. "R Graphics." Wiley Interdisciplinary Reviews: Computational Statistics 1, no. 2 (2009): 216–20. http://dx.doi.org/10.1002/wics.22.

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23

Goldberg, Kenneth P. "Applications: Using Technology to Understand the Jury Decision-making Process." Mathematics Teacher 87, no. 2 (1994): 110–14. http://dx.doi.org/10.5951/mt.87.2.0110.

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Two of the recommendations of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) are to use technology to enhance teaching and learning mathematics and to relate school mathematics to the world in which the students Jive through developing and interpreting mathematical models. This article demonstrates how computer or graphing-calculator technology can be used to help students develop and interpret three increasingly realistic models of jwy behavior and explore the potential effect of such decisions as changing jury size. The only mathematics required is an understanding of simple binomial probabilities and the use of sigma, or summation, notation

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24

Sivasamy, R., K. Setlhare, W. B. Molefe, and Olebogeng Mokgwar. "A Discrete Time Geometric Queue Attached to an Inventory under a (0, Q) Policy." International Journal of Membrane Science and Technology 10, no. 2 (2023): 3439–49. http://dx.doi.org/10.15379/ijmst.v10i2.3148.

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This paper describes how a threshold policy, or TP = [(0, Q), 1]-based inventory management, economically offers customers a single product with a discrete time geometric queue attached to a Geo/Geo/1 service base. The order for Q units starts when inventory I(t) at time ’t’ drops to the level ’0’, and the length of the queueing process X(t) is at least one. We focus on the process Z(t) = (X(t), I(t)), t [0, ?). We then analyse the steady state probabilities and then provides a numerical study for graphing the economic order quantity.

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25

Wickham, Hadley, and Dianne Cook. "R Graphics." American Statistician 61, no. 1 (2007): 99–100. http://dx.doi.org/10.1198/tas.2007.s72.

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26

Tomov, Stanimire, Michael McGuigan, Robert Bennett, Gordon Smith, and John Spiletic. "Benchmarking and implementation of probability-based simulations on programmable graphics cards." Computers & Graphics 29, no. 1 (2005): 71–80. http://dx.doi.org/10.1016/j.cag.2004.11.008.

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27

Tan, Choo-Kim. "Effects of the application of graphing calculator on students’ probability achievement." Computers & Education 58, no. 4 (2012): 1117–26. http://dx.doi.org/10.1016/j.compedu.2011.11.023.

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28

Su, Cong, Mukesh Tripathi, Qing-Bo Yan, et al. "Engineering single-atom dynamics with electron irradiation." Science Advances 5, no. 5 (2019): eaav2252. http://dx.doi.org/10.1126/sciadv.aav2252.

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Atomic engineering is envisioned to involve selectively inducing the desired dynamics of single atoms and combining these steps for larger-scale assemblies. Here, we focus on the first part by surveying the single-step dynamics of graphene dopants, primarily phosphorus, caused by electron irradiation both in experiment and simulation, and develop a theory for describing the probabilities of competing configurational outcomes depending on the postcollision momentum vector of the primary knock-on atom. The predicted branching ratio of configurational transformations agrees well with our atomically resolved experiments. This suggests a way for biasing the dynamics toward desired outcomes, paving the road for designing and further upscaling atomic engineering using electron irradiation.

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29

Klopp, Olga, and Nicolas Verzelen. "Optimal graphon estimation in cut distance." Probability Theory and Related Fields 174, no. 3-4 (2018): 1033–90. http://dx.doi.org/10.1007/s00440-018-0878-1.

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30

Fan, Mingming, and Yunsong Li. "The application of computer graphics processing in visual communication design." Journal of Intelligent & Fuzzy Systems 39, no. 4 (2020): 5183–91. http://dx.doi.org/10.3233/jifs-189003.

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The purpose of this paper is to improve the existing computer graphics image processing technology, so that designers can produce more inspiration, improve the author’s ability to innovate. Based on the information in the field of graphics visual communication as the research object, through the elaboration of graphical information characteristics, development course, and the visual communication of computer graphical related, such as cognitive psychology, semiology theory research, analyzes the computer graphics into a kind of economic and effective way of conveying information, the significance of interface design for mobile media. Experiments demonstrate the unique advantages of graphics in the process of information transmission. In 2022, the market size of computer graphics and vision will expand to 755.5 million RMB. It can be known that the communication mode integrating information and graphics, as the future development trend, will also be applied to more fields and play a greater role.

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31

Unwin, Antony, and Pedro Valero-Mora. "Ensemble Graphics." Journal of Computational and Graphical Statistics 27, no. 1 (2018): 157–65. http://dx.doi.org/10.1080/10618600.2017.1383264.

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32

Eddy, William F., William S. Cleveland, and Marylyn E. McGill. "Dynamic Graphics for Statistics." Journal of the American Statistical Association 85, no. 410 (1990): 599. http://dx.doi.org/10.2307/2289818.

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33

Wegman, Edward J., and Leland Wilkinson. "The Grammar of Graphics." Journal of the American Statistical Association 95, no. 451 (2000): 1009. http://dx.doi.org/10.2307/2669493.

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34

Bradstreet, Thomas E. "The Grammar of Graphics." Journal of the American Statistical Association 101, no. 476 (2006): 1719–20. http://dx.doi.org/10.1198/jasa.2006.s138.

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35

Qian, Weikang, Marc D. Riedel, Hongchao Zhou, and Jehoshua Bruck. "Transforming Probabilities With Combinational Logic." IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 30, no. 9 (2011): 1279–92. http://dx.doi.org/10.1109/tcad.2011.2144630.

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36

BAI, CHUNXU, JUNTAO WANG, JING ZHANG, and YANLING YANG. "CONDUCTANCE IN GRAPHENE-BASED STRUCTURE WITH THE SPATIALLY-MODULATED STRENGTH OF SPIN–ORBIT INTERACTIONS." International Journal of Modern Physics B 25, no. 23n24 (2011): 3199–209. http://dx.doi.org/10.1142/s021797921110179x.

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Based on the transfer-matrix method, the transport properties of electrons in the multilayers structure with the spatially-modulated strength of spin–orbit interactions (SOIs) have been investigated. We show that the transmission and the conductance oscillate with the parameters of the structure and the incident energy. In particular, when only the Rashba spin–orbit interaction (RSOI) exists, in sharp contrast to its counterpart in conventional junctions, the minima of the normal transmission probabilities just reach a constant value 0.5.

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Murrell, Paul, and Velvet Ly. "Debugging grid Graphics." R Journal 4, no. 2 (2012): 19. http://dx.doi.org/10.32614/rj-2012-013.

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Coll-Serrano, V., O. Blasco-Blasco, and J. A. Alvarez-Jareno. "Dynamic graphics in Excel for teaching statistics: understanding the probability density function." Teaching Mathematics and its Applications 30, no. 4 (2011): 222–26. http://dx.doi.org/10.1093/teamat/hrr016.

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Vittaldev, Vivek, and Ryan P. Russell. "Space Object Collision Probability via Monte Carlo on the Graphics Processing Unit." Journal of the Astronautical Sciences 64, no. 3 (2017): 285–309. http://dx.doi.org/10.1007/s40295-017-0113-9.

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40

Mohammed Ismail, Wazim, and Chung-chieh Shan. "Deriving a probability density calculator (functional pearl)." ACM SIGPLAN Notices 51, no. 9 (2016): 47–59. http://dx.doi.org/10.1145/3022670.2951922.

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41

Boston, Brett, Adrian Sampson, Dan Grossman, and Luis Ceze. "Probability type inference for flexible approximate programming." ACM SIGPLAN Notices 50, no. 10 (2015): 470–87. http://dx.doi.org/10.1145/2858965.2814301.

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42

Bhat, Sooraj, Ashish Agarwal, Richard Vuduc, and Alexander Gray. "A type theory for probability density functions." ACM SIGPLAN Notices 47, no. 1 (2012): 545–56. http://dx.doi.org/10.1145/2103621.2103721.

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43

Wilkinson, Leland. "The grammar of graphics." Wiley Interdisciplinary Reviews: Computational Statistics 2, no. 6 (2010): 673–77. http://dx.doi.org/10.1002/wics.118.

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44

Chen, Jim X. "Rendering in computer graphics." WIREs Computational Statistics 2, no. 1 (2010): 120–26. http://dx.doi.org/10.1002/wics.60.

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Hintze, Jerry. "NCSS-Graphics: An Advanced Statistical Graphics Package for MS-DOS Microcomputers." American Statistician 42, no. 3 (1988): 230. http://dx.doi.org/10.2307/2685023.

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46

Zheng, Shan Suo, Shun Li Che, Lei Zheng, Lei Li, and Jie Zheng. "Theoretical Analysis and Experimental Study on Damage Probability of HSHP Concrete." Key Engineering Materials 348-349 (September 2007): 849–52. http://dx.doi.org/10.4028/www.scientific.net/kem.348-349.849.

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Damage probability is a new concept in modern engineering design. If the cumulative damage probability of member or material is known, then the rational design can be realized. Based on study of high-strength and high-performance (HSHP) concrete applied to steel reinforced concrete (SRC) structures, the equation of the cumulative damage probability of HSHP concrete is derived by Weibull theory. The calculation and analysis indicate that the theoretical equation presented give a suitably mathematical limit for damage probability of specimens. At the same time, the new method for Weibull parameters is established, which depends on the theory of the damage probability and computer graphics technology. The comparison of experimental curves with theoretical curves shows that the established equation can properly simulate the damage evolution of HSHP concrete. Them value, one of Weibull parameters, is studied in detail, which reveals that it is a key parameter to quality control. At last, the effect of specimen volume upon damage probability is also discussed. The research provides methods and ideas to improve performance of concrete material and simulate damage probability of HSHP concrete.

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Sun, Jingang, Huchuan Lu, and Xiuping Liu. "Saliency Region Detection Based on Markov Absorption Probabilities." IEEE Transactions on Image Processing 24, no. 5 (2015): 1639–49. http://dx.doi.org/10.1109/tip.2015.2403241.

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Wang, Yangjie, and Jige Chen. "Square ice formation in CrOCl and graphene confinement." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 6 (2023): 063203. http://dx.doi.org/10.1088/1742-5468/acd693.

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Abstract The structure and thermodynamic properties of water in nanoscale confinement environment are greatly involved in the research field of material science and nanotechnology. However, a complete picture of the ordered structure formation and thermodynamics behavior of the confined water inside two parallel nanosheets with different surface atomic arrangement is still lacking. In this paper, by using molecular dynamics (MD) simulations, we study the structural variation and thermodynamics behavior for water molecules confined between two parallel CrOCl with a square surface atomic arrangement and two parallel graphene nanosheets with a hexagonal surface atomic arrangement. Square ice, with a lattice constant 2.1 and 2.0 Å, is observed inside the two parallel CrOCl and graphene nanosheets, respectively. By calculating the configuration entropy of the molecular dipoles St , it is found that, in the CrOCl confinement, St reaches a peak value and then is greatly reduced due to the square ice formation. On the other hand, in the graphene confinement, St continues to grow after the square ice formation and is then reduced after reaching its peak value. Interestingly, it is found that the square ice could be stable at a higher entropy state under the external pressure than the bulk water at ambient condition. By calculating the orientational order parameters M, it shows that the conventional tetrahedral geometry of hydrogen bonding between water molecules breaks due to the square ice formation. By analyzing the average number of hydrogen bonds of water molecules Nh , it is found that the hydrogen bond interaction of the square ice relies on the confinement environment, where Nh is reduced in the CrOCl confinement and increased in the graphene confinement. Probability distribution functions of the dipole orientation angles between the x- or z-axis and the projection of the oxygen atoms of the water molecules are also calculated. It is observed that the square ice structure is paralleled with the x-axis (unit cell axis) in the CrOCl confinement and tilted with the x-axis (the zigzag direction of graphene) at an angle 30° in the graphene confinement. Furthermore, the square ice formation is found to be insensitive to temperature. Our result reveals the peculiar ordered structure and thermodynamics behavior of water in different nanoscale confinement environments.

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Yandell, Brian S., Edward J. Wegman, and Douglas J. DePriest. "Statistical Image Processing and Graphics." Journal of the American Statistical Association 84, no. 405 (1989): 338. http://dx.doi.org/10.2307/2289893.

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50

Wainer, Howard, Peter Pashley, and Michael Friendly. "SAS System for Statistical Graphics." Journal of the American Statistical Association 87, no. 419 (1992): 899. http://dx.doi.org/10.2307/2290235.

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