Project URA-HPC

[1] J. Acebrón, J. Herrero, J. Monteiro. "A highly parallel algorithm for computing the action of a matrix exponential on a vector based on a multilevel Monte Carlo method." Computers and Mathematics with Applications, February 2020.

[2] J. Acebrón. "A probabilistic linear solver based on a multilevel Monte Carlo method". J. Sci. Comput. 82 (2020) 65.

[3] F. Magalhães, J. Acebrón, J. Herrero, J. Monteiro. "A distributed Monte Carlo based linear algebra solver applied to the analysis of large complex networks". Future Generation Computer Systems, Volume 127, pp. 320-330, February 2022.

[4] J. Pinto, S. Nunes, M. Bianciardi, A. Dias, L. M. Silveira, L. Wald, P. Figueiredo, "Improved 7 Tesla resting-state fMRI connectivity measurements by cluster-based modeling of respiratory volume and heart rate effects", Neuroimage, vol. 153, pp. 262-272, Elsevier, Apr. 2017.

[5] N. Guidotti, P. Ceyrat, J. Barreto, J. Monteiro, R. Rodrigues, R. Fonseca, X. Martorell, A. Peña, "Particle-In-Cell Simulation using Asynchronous Tasking", in the 27th International European Conference on Parallel and Distributed Computing (Euro-Par 21), Aug. 2021.

[6] R. Leland, J. Ang, D. Barnette, B. Benner, S. Goudy, B. Malins, M. Rajan, C. Vaughan, A. Black, D. Doerfler, S. Domino, B. Franke, A. Ganti, T. Laub, H. Meyer, R. Scott, J. Stevenson, J. Sturtevant, M. Taylor. “Performance, Efficiency and Effectiveness of Supercomputers“. Sandia National Laboratories Report 2016.

[7] N. Higham, and A. Al-Mohy, “Functions of matrices: Theory and Computation“, SIAM, 2008.

[8] G. Forsythe, and R. Leibler, “Matrix inversion by a Monte Carlo method“, Math. Tables Other Aids Comput., 4 (1950) pp. 127-129.

[9] M. Giles, “Multilevel Monte Carlo methods“. Acta Numerica, 24 (2015) 259-328.

[10] M. Botchev, V. Grimm, and M. Hochbruck, “Residual, restarting, and Richardson iteration for the matrix exponential“, SIAM J. Sci. Comput, 35 (2013) A1376-A1397

[11] I. Dimov, “Monte Carlo methods for applied scientists“, World Scientific, 2007.

[12] H. Ji, M. Mascagni, and Y. Li, “Convergence Analysis of Markov Chain Monte Carlo Linear Solvers Using Ulam-von Neumann Algorithm“, SIAM J. Numer. Anal., 51 (2013) 2107- 2122.

[13] M. Benzi, T. Evans, S. Hamilton, M. Pasini, and S. Slattery, “Analysis of Monte Carlo accelerated iterative methods for sparse linear systems“, Numerical Linear Algebra with Appl., 24 (2017).

[14] I. Dimov, V. Alexandrov, and A. Karaivanova, “Parallel resolvent Monte Carlo algorithms for linear algebra problems“, Mathematics and Computers in Simulation, vol. 39, pp. 25- 35, 2015.

[15] S. Weng, Q. Chen and C. Cheng, "Time-Domain Analysis of Large-Scale Circuits by Matrix Exponential Method With Adaptive Control," in IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 31, no. 8, pp. 1180-1193, Aug. 2012.

[16] H. Zhuang, W. Yu, S. Weng, I. Kang, J. Lin, X. Zhang, R. Coutts, C. Cheng, “Simulation Algorithms With Exponential Integration for Time-Domain Analysis of Large-Scale Power Delivery Networks“, Computer-Aided Design of Integrated Circuits and Systems IEEE Transactions on, vol. 35, no. 10, pp. 1681-1694, 2016.

[17] H. Zhuang, S. Weng, C. Cheng, “Power grid simulation using matrix exponential method with rational Krylov subspaces“, Proc. IEEE Int. Conf. ASIC, pp. 1-4, 2013.

[18] M. Pusa, and J. Leppanen, “Computing the matrix exponential in burnup calculations“, Nuclear Sci. and Eng, 164 (2010) 140-150.

[19] R. Sidjea, and W. Stewart, “A numerical study of large sparse matrix exponentials arising in Markov chains“, Comput. Stat. Data Anal., 29 (1999) 345-368.

[20] R. Mattheij, S. Rienstra, and J. Boonkkamp, “Partial Differential Equations: Modeling, Analysis, Computation“, SIAM, 2005.

[21] M. Benzi, E. Estrada, and C. Klymko, “Ranking hubs and authorities using matrix functions“, Linear Algebra and Its Applications, 438 (2013) 2447-2474.

[22] M. Evans, and T. Swartz, “Approximating Integrals Via Monte Carlo and Deterministic Methods“, Oxford University Press, 2000.

[23] M. Newman, “Networks: an introduction“. University Press, 2010.

[24] L. Katz, “A new status index derived from sociometric analysis“, Psychometrika, vol. 18, no. 1, pp. 39-43, 1953.

[25] C. Hubbell, “An input-output approach to clique identification“, Sociometry, vol. 28, no. 4, pp. 377-399, 1965.

[26] R. Valiullim, “Diffusion NMR of Confined Systems: Fluid

[26] R. Valiullim, “Diffusion NMR of Confined Systems: Fluid Transport in Porous Solids and Heterogeneous Materials (New Developments in NMR)“, Royal Society of Chemistry (2016).

[27] S. Capuani, and M. Palombo, “Mini review on anomalous diffusion by MRI: potential advantages, pitfalls, limitations, nomenclature and correct interpretation of literature“, Front. Phys. 7:248 (2020).

[28] B. Guo, X. Pu, and F. Huang, “Fractional Partial Differential Equations and Their Numerical Solutions“, World Scientific (2015).

[29] D. Belomestny, and T. Nagapetyan. “Variance reduced multilevel path simulation: going beyond the complexity epsilon^-2“, arXiv preprint arXiv:1412.4045.

[30] C. Lemieux, “Monte Carlo and Quasi-Monte Carlo Sampling“. Springer (2009).

[31] D. Watts and S. Strogatz, “Collective dynamics of ’small- world’ networks“, Nature, vol. 393, pp. 440-442, Jun 1998.

[32] J. Leskovec, D. Chakrabarti, J. Kleinberg, C. Faloutsos, and Z. Ghahramani, “Kronecker Graphs: an Approach to Modeling Networks“, J. Mach. Learn. Res., vol. 11, pp. 985-1042, Mar. 2010.

[33] N. Cusimano, F. del Teso, L. Gerardo-Giorda, and G. Pagnini, “Discretizations of the spectral fractional Laplacian on general domains with Dirichlet, Neumann, and Robin boundary conditions“, SIAM Journal on Numerical Analysis 56 (3), 1243- 1272 (2018).

[34] N. Masuda, and L. Rocha, “A Gillespie Algorithm for Non- Markovian Stochastic Processes”, SIAM Review 2018 60:1, 95-115.

[35] R. Iakymchuk, A. Faustino, A. Emerson, J. Barreto, V. Bartsch, R. Rodrigues, J. Monteiro, “Efficient and Eventually Consistent Collective Operations”, in Advances in Parallel and Distributed Computational Models, a workshop of the 35th IEEE International Parallel and Distributed Processing Symposium, May 2021.

[36] J. Silva, J. Phillips and L. M. Silveira, "Efficient simulation of power grids", IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 29 (10), pp. 1523-1532, Oct. 2010.

[37] H. Niu, Y. Chen 2, and B.J. West ,"Why Do Big Data and Machine Learning Entail the Fractional Dynamics?", Entropy 23, 297 (2021).

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