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1

Xu, Feng, and Oliver E. Jensen. "Drop spreading with random viscosity." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2194 (October 2016): 20160270. http://dx.doi.org/10.1098/rspa.2016.0270.

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We examine theoretically the spreading of a viscous liquid drop over a thin film of uniform thickness, assuming the liquid’s viscosity is regulated by the concentration of a solute that is carried passively by the spreading flow. The solute is assumed to be initially heterogeneous, having a spatial distribution with prescribed statistical features. To examine how this variability influences the drop’s motion, we investigate spreading in a planar geometry using lubrication theory, combining numerical simulations with asymptotic analysis. We assume diffusion is sufficient to suppress solute concentration gradients across but not along the film. The solute field beneath the bulk of the drop is stretched by the spreading flow, such that the initial solute concentration immediately behind the drop’s effective contact lines has a long-lived influence on the spreading rate. Over long periods, solute swept up from the precursor film accumulates in a short region behind the contact line, allowing patches of elevated viscosity within the precursor film to hinder spreading. A low-order model provides explicit predictions of the variances in spreading rate and drop location, which are validated against simulations.
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2

Galam, S. "Minority opinion spreading in random geometry." European Physical Journal B 25, no. 4 (February 2002): 403–6. http://dx.doi.org/10.1140/epjb/e20020045.

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3

Vojta, Thomas, and Michael Schreiber. "Damage spreading in random field systems." Computer Physics Communications 121-122 (September 1999): 750. http://dx.doi.org/10.1016/s0010-4655(06)70153-9.

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4

Giorno, Virginia, and Serena Spina. "Rumor spreading models with random denials." Physica A: Statistical Mechanics and its Applications 461 (November 2016): 569–76. http://dx.doi.org/10.1016/j.physa.2016.06.070.

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5

Panagiotou, K., and L. Speidel. "Asynchronous Rumor Spreading on Random Graphs." Algorithmica 78, no. 3 (August 1, 2016): 968–89. http://dx.doi.org/10.1007/s00453-016-0188-x.

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6

Vojta, Thomas. "Damage spreading in random field systems." Journal of Physics A: Mathematical and General 30, no. 18 (September 21, 1997): L643—L649. http://dx.doi.org/10.1088/0305-4470/30/18/006.

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7

Chang, Ching-Lueh, and Yuh-Dauh Lyuu. "Spreading of Messages in Random Graphs." Theory of Computing Systems 48, no. 2 (March 9, 2010): 389–401. http://dx.doi.org/10.1007/s00224-010-9258-7.

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8

Clementi, Andrea, Pierluigi Crescenzi, Carola Doerr, Pierre Fraigniaud, Francesco Pasquale, and Riccardo Silvestri. "Rumor spreading in random evolving graphs." Random Structures & Algorithms 48, no. 2 (March 30, 2015): 290–312. http://dx.doi.org/10.1002/rsa.20586.

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9

Verdu, S., and S. Shamai. "Spectral efficiency of CDMA with random spreading." IEEE Transactions on Information Theory 45, no. 2 (March 1999): 622–40. http://dx.doi.org/10.1109/18.749007.

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10

Chiang, P. H., D. B. Lin, and H. J. Li. "SINR for DS-CDMA with random spreading." IEE Proceedings - Communications 153, no. 3 (2006): 419. http://dx.doi.org/10.1049/ip-com:20045235.

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11

Pu, Cunlai, Siyuan Li, and Jian Yang. "Epidemic spreading driven by biased random walks." Physica A: Statistical Mechanics and its Applications 432 (August 2015): 230–39. http://dx.doi.org/10.1016/j.physa.2015.03.035.

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12

Solna, Knut. "Acoustic Pulse Spreading in a Random Fractal." SIAM Journal on Applied Mathematics 63, no. 5 (January 2003): 1764–88. http://dx.doi.org/10.1137/s0036139902404657.

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13

Saif, M. Ali, M. A. Shukri, and F. H. Al-makhedhi. "Dynamics of SIR Model on Random Networks." مجلة جامعة عمران 4, no. 7 (May 23, 2024): 10. http://dx.doi.org/10.59145/jaust.v4i7.91.

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we focus on studying the dynamics of infectious disease spreading SIR model on random networks. We investigate how various parameters of the network influence the behavior of spreading and analyze the occurrence of phase transitions within this networkframework. Our analysis reveals the critical role of network connectivity in shaping the dynamics of disease transmission and highlights the presence of mean-field phase transitions.Additionally, we employ both analytical techniques and simulation methods to extract critical thresholds for the model and compare them for validation. By delving into the intricate dynamics of disease spreading on random networks, this work offers valuableinsights into the mechanisms driving epidemic propagation and provides a theoretical foundation for studying disease control strategies and public health interventions.
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14

Liu, Zhaoxia, Wenhui Bian, Gang Pan, Pengcheng Li, and Wenxin Li. "Influences on Shotcrete Rebound from Walls with Random Roughness." Advances in Materials Science and Engineering 2018 (October 23, 2018): 1–12. http://dx.doi.org/10.1155/2018/7401358.

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Concrete slurry can be sprayed on walls for reinforcement; however, there is a certain amount of rebound which is hazardous, lowers production quality, and wastes material. To investigate this problem, we studied single slurry droplets at the mesoscopic level. We deduced the factors influencing droplet spreading and wall adhesion to create models of shotcrete rebound. Then, a numerical simulation orthogonal experiment investigating droplet-wall impacts was performed. The relationship between the spreading coefficient and each influencing factor is discussed, and numerical models are presented. Finally, the obtained models are verified by physical experiments. The results show that the spreading coefficient can be used to better characterize the effect of slurry droplet adhesion to walls. Modeled and experimentally observed droplet-wall impacts showed good consistency. The influence of each factor on the spreading coefficient was determined in the following order of strength: droplet velocity and viscosity, wall roughness, and surface tension. The spreading coefficient increases with velocity, decreases with viscosity and roughness, and increases first and then decreases with surface tension. This study improves the fluid dynamics-based theory of multiphase flow in concrete slurry and provides a theoretical basis for mitigating shotcrete rebound.
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15

Illahi, Ramadian Ridho, Fakhrudin Nugroho, and Pekik Nurwantoro. "Spreading Dynamics of Corrosion on Material Surface Using Site Percolation Model." Materials Science Forum 901 (July 2017): 69–75. http://dx.doi.org/10.4028/www.scientific.net/msf.901.69.

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Spreading phenomenon is usually characterized by existence of two competing processes. On the spreading of corrosion, competition occurs between the power of solution to corrode with the resistance level of a metal surface against corrosion. In the present study, we simulate a corrosion process using site percolation model to determine the spreading pattern of corrosion. The simulation results showed different spreading patterns and dynamics of corrosion when the value of corrode molecules were varied. The simulation results also indicate the emergence of two regimes that happens, smooth regime and random regime. Smooth regime characterized by the shape of its corrosion face is almost the same as before. While random regime characterized by the appearance of random spreading pattern on the shape of corrosion face.
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16

Bestehorn, Michael, Alejandro P. Riascos, Thomas M. Michelitsch, and Bernard A. Collet. "A Markovian random walk model of epidemic spreading." Continuum Mechanics and Thermodynamics 33, no. 4 (January 16, 2021): 1207–21. http://dx.doi.org/10.1007/s00161-021-00970-z.

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17

Ahmadi, Mohammad Javad, and Tolga M. Duman. "Random Spreading for Unsourced MAC With Power Diversity." IEEE Communications Letters 25, no. 12 (December 2021): 3995–99. http://dx.doi.org/10.1109/lcomm.2021.3119424.

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18

Choi, Jinho. "NOMA-Based Compressive Random Access Using Gaussian Spreading." IEEE Transactions on Communications 67, no. 7 (July 2019): 5167–77. http://dx.doi.org/10.1109/tcomm.2019.2907623.

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19

Gbur, Greg, and Emil Wolf. "Spreading of partially coherent beams in random media." Journal of the Optical Society of America A 19, no. 8 (August 1, 2002): 1592. http://dx.doi.org/10.1364/josaa.19.001592.

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20

Lahtinen, Jani, János Kertész, and Kimmo Kaski. "Random spreading phenomena in annealed small world networks." Physica A: Statistical Mechanics and its Applications 311, no. 3-4 (August 2002): 571–80. http://dx.doi.org/10.1016/s0378-4371(02)00625-8.

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21

Clouet, J. F., and J. P. Fouque. "Spreading of a Pulse Travelling in Random Media." Annals of Applied Probability 4, no. 4 (November 1994): 1083–97. http://dx.doi.org/10.1214/aoap/1177004904.

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22

Biggins, J. D. "Spreading speeds in reducible multitype branching random walk." Annals of Applied Probability 22, no. 5 (October 2012): 1778–821. http://dx.doi.org/10.1214/11-aap813.

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23

Winzen, Carola. "Direction-reversing quasi-random rumor spreading with restarts." Information Processing Letters 113, no. 22-24 (November 2013): 921–26. http://dx.doi.org/10.1016/j.ipl.2013.09.006.

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24

Fountoulakis, Nikolaos, and Konstantinos Panagiotou. "Rumor spreading on random regular graphs and expanders." Random Structures & Algorithms 43, no. 2 (May 28, 2012): 201–20. http://dx.doi.org/10.1002/rsa.20432.

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25

Kurita, Osamu. "A Fire-Spreading Model with Random Points Associated with Random Break-Out Time." Journal of the City Planning Institute of Japan 42 (2007): 84. http://dx.doi.org/10.11361/cpij1.42.0.84.0.

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26

Kurita, Osamu. "A Fire-Spreading Model with Random Points Associated with Random Break-Out Time." Journal of the City Planning Institute of Japan 42.3 (2007): 499–504. http://dx.doi.org/10.11361/journalcpij.42.3.499.

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27

Higuchi, Yusuke, and Etsuo Segawa. "Spreading behavior of quantum walks induced by random walks." Quantum Information and Computation 17, no. 5&6 (April 2017): 399–414. http://dx.doi.org/10.26421/qic17.5-6-3.

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In this paper, we consider the quantum walk on Z with attachment of one-length path periodically. This small modification to Z provides localization of the quantum walk. The eigenspace causing this localization is generated by finite length round trip paths. We find that the localization is due to the eigenvalues of an underlying random walk. Moreover we find that the transience of the underlying random walk provides a slow down of the pseudo velocity of the induced quantum walk and a different limit distribution from the Konno distribution.
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28

Dall’Asta, Luca. "Inhomogeneous percolation models for spreading phenomena in random graphs." Journal of Statistical Mechanics: Theory and Experiment 2005, no. 08 (August 25, 2005): P08011. http://dx.doi.org/10.1088/1742-5468/2005/08/p08011.

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29

Huang, Yunhan, Li Ding, Yun Feng, and Jiangtian Pan. "Epidemic spreading in random walkers with heterogeneous interaction radius." Journal of Statistical Mechanics: Theory and Experiment 2016, no. 10 (October 26, 2016): 103501. http://dx.doi.org/10.1088/1742-5468/2016/10/103501.

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30

Jang, W. M., L. Nguyen, and M. Hempel. "Precoded Random Spreading Multiple Access System in AWGN Channels." IEEE Transactions on Wireless Communications 3, no. 5 (September 2004): 1477–80. http://dx.doi.org/10.1109/twc.2004.834686.

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31

Jitomirskaya, Svetlana, and Hermann Schulz-Baldes. "Upper Bounds On Wavepacket Spreading For Random Jacobi Matrices." Communications in Mathematical Physics 273, no. 3 (April 28, 2007): 601–18. http://dx.doi.org/10.1007/s00220-007-0252-0.

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32

Kurkova, Irina, Serguei Popov, and M. Vachkovskaia. "On Infection Spreading and Competition between Independent Random Walks." Electronic Journal of Probability 9 (2004): 293–315. http://dx.doi.org/10.1214/ejp.v9-197.

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33

Doerr, Benjamin, and Mahmoud Fouz. "A Time-Randomness Tradeoff for Quasi-Random Rumour Spreading." Electronic Notes in Discrete Mathematics 34 (August 2009): 335–39. http://dx.doi.org/10.1016/j.endm.2009.07.055.

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34

Doerr, Benjamin, and Mahmoud Fouz. "Quasi-random rumor spreading: Reducing randomness can be costly." Information Processing Letters 111, no. 5 (February 2011): 227–30. http://dx.doi.org/10.1016/j.ipl.2010.11.006.

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35

Kawai, Reiichiro. "Anomalous spreading and misidentification of spatial random walk models." Applied Mathematical Modelling 40, no. 9-10 (May 2016): 5283–91. http://dx.doi.org/10.1016/j.apm.2015.12.028.

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36

Zhu, Anding, Wanying Chen, Jinming Zhang, Xiaojie Zong, Wenmin Zhao, and Yi Xie. "Investor immunization to Ponzi scheme diffusion in social networks and financial risk analysis." International Journal of Modern Physics B 33, no. 11 (April 30, 2019): 1950104. http://dx.doi.org/10.1142/s0217979219501042.

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Most illegal Ponzi schemes are ultimately out of control and lead to systemic financial risk. Risk education and precaution are similar to mass random immunization of epidemic spreading. In this study, the effect of random immunization strategy is evaluated based on the potential-investor–divestor (PID) spreading model in both homo- and inhomogeneous social networks. Fund flux function and system balance function are formulated. The zero point of system balance is used as the collapse point. The peak value of balance, the total number of investors involved and the total amount of principal involved are defined to compare the immunization effects in various scenarios. Mathematical derivation and numerical simulation show that the random immunization takes effect by postponing the peak position of the system balance as well as suppressing the peak values of the system balance. This kind of positive effect helps reduce the scheme’s scale of total number of investors involved and total amount of principal involved. The random immunization is more powerful towards the schemes with small spreading rate than those with medium and high spreading rates. Hence, it is suitable for the concentrated regulation on a large amount of small scale and slow spreading schemes in bulk.
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37

BUSCARINO, ARTURO, AGNESE DI STEFANO, LUIGI FORTUNA, MATTIA FRASCA, and VITO LATORA. "EFFECTS OF MOTION ON EPIDEMIC SPREADING." International Journal of Bifurcation and Chaos 20, no. 03 (March 2010): 765–73. http://dx.doi.org/10.1142/s0218127410026058.

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The study of social networks, and in particular those aspects related to disease spreading, has recently attracted considerable attention in the scientific community. In this paper, we investigate the effect of motion on the spread of diseases in dynamical networks of mobile agents. In order to simulate the long distance displacements empirically observed in real human movements, we consider different motion rules, such as random walks with the addition of jumps or Lévy flights. We compare the epidemic thresholds found in dynamical networks of mobile agents with the analogous expressions for static networks. We discuss the existing relations between dynamical networks of random walkers with jumps and static small-world networks, and those between systems of Lévy walkers and scale-free networks.
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38

Wang, Wanli, Eli Barkai, and Stanislav Burov. "Large Deviations for Continuous Time Random Walks." Entropy 22, no. 6 (June 22, 2020): 697. http://dx.doi.org/10.3390/e22060697.

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Recently observation of random walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the widely applicable continuous time random walk model and obtain the large deviation description of the propagator. Under mild conditions that the microscopic jump lengths distribution is decaying exponentially or faster i.e., Lévy like power law distributed jump lengths are excluded, and that the distribution of the waiting times is analytical for short waiting times, the spreading of particles follows an exponential decay at large distances, with a logarithmic correction. Here we show how anti-bunching of jump events reduces the effect, while bunching and intermittency enhances it. We employ exact solutions of the continuous time random walk model to test the large deviation theory.
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39

Kokin, Dmitry Sergeevich, and Oleg Gennadievich Ponomarev. "APPLICATION OF DETERMINATED NOISE IN A RADIO COMMUNICATION SYSTEM WITH DIGITAL MODULATION." Chronos 7, no. 4(66) (June 13, 2022): 52–54. http://dx.doi.org/10.52013/2658-7556-66-4-13.

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The article describes a communication system with digital pseudo-random modulation. The system is one of the variants of spread spectrum radio communication systems. This communication system uses deterministic noise as the spreading sequence. The noise immunity of the considered communication system can be changed by scaling the spreading factor — the length of the modulation symbol. By increasing the spreading factor, not only an increase in the noise immunity of the system is achieved, but also the possibility of separating subscribers simultaneously operating in a common frequency band. It has been established that for communication systems with digital pseudo-random modulation, the length of the modulation symbol (the value of the spreading factor) and the number of subscribers to be separated are related by a quadratic dependence.
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40

Mahmoud, Hosam. "A model for the spreading of fake news." Journal of Applied Probability 57, no. 1 (March 2020): 332–42. http://dx.doi.org/10.1017/jpr.2019.103.

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AbstractWe introduce a model for the spreading of fake news in a community of size n. There are $j_n = \alpha n - g_n$ active gullible persons who are willing to believe and spread the fake news, the rest do not react to it. We address the question ‘How long does it take for $r = \rho n - h_n$ persons to become spreaders?’ (The perturbation functions $g_n$ and $h_n$ are o(n), and $0\le \rho \le \alpha\le 1$ .) The setup has a straightforward representation as a convolution of geometric random variables with quadratic probabilities. However, asymptotic distributions require delicate analysis that gives a somewhat surprising outcome. Normalized appropriately, the waiting time has three main phases: (a) away from the depletion of active gullible persons, when $0< \rho < \alpha$ , the normalized variable converges in distribution to a Gumbel random variable; (b) near depletion, when $0< \rho = \alpha$ , with $h_n - g_n \to \infty$ , the normalized variable also converges in distribution to a Gumbel random variable, but the centering function gains weight with increasing perturbations; (c) at almost complete depletion, when $r = j -c$ , for integer $c\ge 0$ , the normalized variable converges in distribution to a convolution of two independent generalized Gumbel random variables. The influence of various perturbation functions endows the three main phases with an infinite number of phase transitions at the seam lines.
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41

Yamagami, Tomoki, Etsuo Segawa, Nicolas Chauvet, André Röhm, Ryoichi Horisaki, and Makoto Naruse. "Directivity of Quantum Walk via Its Random Walk Replica." Complexity 2022 (October 29, 2022): 1–14. http://dx.doi.org/10.1155/2022/9021583.

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Quantum walks (QWs) exhibit different properties compared with classical random walks (RWs), most notably by linear spreading and localization. In the meantime, random walks that replicate quantum walks, which we refer to as quantum-walk-replicating random walks (QWRWs), have been studied in the literature where the eventual properties of QWRW coincide with those of QWs. However, we consider that the unique attributes of QWRWs have not been fully utilized in the former studies to obtain deeper or new insights into QWs. In this paper, we highlight the directivity of one-dimensional discrete quantum walks via QWRWs. By exploiting the fact that QWRW allows trajectories of individual walkers to be considered, we first discuss the determination of future directions of QWRWs, through which the effect of linear spreading and localization is manifested in another way. Furthermore, the transition probabilities of QWRWs can also be visualized and show a highly complex shape, representing QWs in a novel way. Moreover, we discuss the first return time to the origin between RWs and QWs, which is made possible via the notion of QWRWs. We observe that the first return time statistics of QWs are quite different from RWs, caused by both the linear spreading and localization properties of QWs.
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42

Oleś, K., E. Gudowska-Nowak, and A. Kleczkowski. "Cost-benefit Analysis of Epidemics Spreading on Clustered Random Networks." Acta Physica Polonica B 45, no. 1 (2014): 43. http://dx.doi.org/10.5506/aphyspolb.45.43.

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43

Feng, Yun, Li Ding, Yun-Han Huang, and Zhi-Hong Guan. "Epidemic spreading on random surfer networks with infected avoidance strategy." Chinese Physics B 25, no. 12 (November 29, 2016): 128903. http://dx.doi.org/10.1088/1674-1056/25/12/128903.

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44

Mishkovski, Igor, Miroslav Mirchev, Sanja Scepanovic, and Ljupco Kocarev. "Interplay Between Spreading and Random Walk Processes in Multiplex Networks." IEEE Transactions on Circuits and Systems I: Regular Papers 64, no. 10 (October 2017): 2761–71. http://dx.doi.org/10.1109/tcsi.2017.2700948.

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45

Cottatellucci, Laura, Ralf R. Muller, and Mérouane Debbah. "Asynchronous CDMA Systems With Random Spreading—Part I: Fundamental Limits." IEEE Transactions on Information Theory 56, no. 4 (April 2010): 1477–97. http://dx.doi.org/10.1109/tit.2010.2040890.

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46

Cottatellucci, Laura, Ralf R. Muller, and Mérouane Debbah. "Asynchronous CDMA Systems With Random Spreading—Part II: Design Criteria." IEEE Transactions on Information Theory 56, no. 4 (April 2010): 1498–520. http://dx.doi.org/10.1109/tit.2010.2040898.

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47

Ghasemi Nezhadhaghighi, M. "Anomalous statistics of particle spreading in quenched random velocity field." Physica A: Statistical Mechanics and its Applications 557 (November 2020): 124977. http://dx.doi.org/10.1016/j.physa.2020.124977.

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48

Li, Meili, Manting Wang, Shuyang Xue, and Junling Ma. "The influence of awareness on epidemic spreading on random networks." Journal of Theoretical Biology 486 (February 2020): 110090. http://dx.doi.org/10.1016/j.jtbi.2019.110090.

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49

Feng, Yun, Li Ding, and Ping Hu. "Epidemic spreading on random surfer networks with optimal interaction radius." Communications in Nonlinear Science and Numerical Simulation 56 (March 2018): 344–53. http://dx.doi.org/10.1016/j.cnsns.2017.06.031.

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50

van Rijn, Monique A., Johan Marinus, Hein Putter, Sarah R. J. Bosselaar, G. Lorimer Moseley, and Jacobus J. van Hilten. "Spreading of complex regional pain syndrome: not a random process." Journal of Neural Transmission 118, no. 9 (February 18, 2011): 1301–9. http://dx.doi.org/10.1007/s00702-011-0601-1.

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