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Hitchcock, \u201cThe expression of a tensor or a polyadic as a sum\nof products,\u201d Journal of Mathematics and Physics, vol. 6, no. 1-4, pp.\n164\u2013189, 1927. https:\/\/dx.doi.org\/10.1002\/sapm192761164","DOI":"10.1002\/sapm192761164"},{"key":"ref4","doi-asserted-by":"publisher","unstructured":"L. Grasedyck, D. Kressner, and C. Tobler, \u201cA literature survey of low-rank tensor approximation techniques,\u201d GAMM-Mitteilungen, vol. 36,\nno. 1, pp. 53\u201378, 2013. https:\/\/dx.doi.org\/10.1002\/gamm.201310004","DOI":"10.1002\/gamm.201310004"},{"key":"ref5","doi-asserted-by":"publisher","unstructured":"W. Hackbusch, Tensor spaces and numerical tensor calculus. Springer,\n2012, vol. 42, https:\/\/dx.doi.org\/10.1007\/978-3-030-35554-8.","DOI":"10.1007\/978-3-030-35554-8"},{"key":"ref6","doi-asserted-by":"publisher","unstructured":"J. Grabek and B. Cyganek, \u201cAn impact of tensor-based data\ncompression methods on deep neural network accuracy,\u201d in Position\nand Communication Papers of the 16th Conference on Computer\nScience and Intelligence Systems, ser. Annals of Computer Science and\nInformation Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, and\nD. \u015al\u0119zak, Eds., vol. 26. PTI, 2021. https:\/\/dx.doi.org\/10.15439\/2021F127 p. 3\u201311.\n[Online]. Available: http:\/\/dx.doi.org\/10.15439\/2021F127","DOI":"10.15439\/2021F127"},{"key":"ref7","doi-asserted-by":"publisher","unstructured":"D. T. Gillespie, \u201cA rigorous derivation of the chemical master equation,\u201d\nPhysica A: Statistical Mechanics and its Applications, vol. 188, no. 1-3,\npp. 404\u2013425, 1992. https:\/\/dx.doi.org\/10.1016\/0378-4371(92)90283-V","DOI":"10.1016\/0378-4371(92)90283-V"},{"key":"ref8","doi-asserted-by":"publisher","unstructured":"D. T. Gillespie, \u201cExact stochastic simulation of coupled chemical reactions,\u201d The\njournal of physical chemistry, vol. 81, no. 25, pp. 2340\u20132361, 1977. https:\/\/dx.doi.org\/10.1021\/j100540a008","DOI":"10.1021\/j100540a008"},{"key":"ref9","doi-asserted-by":"publisher","unstructured":"B. Munsky and M. Khammash, \u201cThe finite state projection algorithm for\nthe solution of the chemical master equation,\u201d The Journal of Chemical\nPhysics, vol. 124, no. 4, p. 044104, 2006. https:\/\/dx.doi.org\/10.1063\/1.2145882","DOI":"10.1063\/1.2145882"},{"key":"ref10","doi-asserted-by":"publisher","unstructured":"J. S. van Zon, M. J. Morelli, S. T\u01cenase-Nicola, and P. R. ten Wolde,\n\u201cDiffusion of transcription factors can drastically enhance the noise in\ngene expression,\u201d Biophysical Journal, vol. 91, no. 12, pp. 4350\u20134367,\n2006. https:\/\/dx.doi.org\/10.1529\/biophysj.106.086157","DOI":"10.1529\/biophysj.106.086157"},{"key":"ref11","doi-asserted-by":"publisher","unstructured":"N. Pavin, H. \u010c. Paljetak, and V. Krsti\u0107, \u201cMin-protein oscillations in Escherichia coli with spontaneous formation of two-stranded filaments in a\nthree-dimensional stochastic reaction-diffusion model,\u201d Physical Review\nE, vol. 73, no. 2, p. 021904, 2006. https:\/\/dx.doi.org\/10.1103\/PhysRevE.73.021904","DOI":"10.1103\/PhysRevE.73.021904"},{"key":"ref12","unstructured":"M. Smoluchowski, \u201cMathematical theory of the kinetics of the coagulation of colloidal solutions,\u201d Z. Phys. Chem., vol. 92, pp. 129\u2013168,\n1917."},{"key":"ref13","doi-asserted-by":"publisher","unstructured":"C. Gardiner, K. McNeil, D. Walls, and I. Matheson, \u201cCorrelations in\nstochastic theories of chemical reactions,\u201d Journal of Statistical Physics,\nvol. 14, pp. 307\u2013331, 1976. https:\/\/dx.doi.org\/10.1007\/BF01030197","DOI":"10.1007\/BF01030197"},{"key":"ref14","doi-asserted-by":"publisher","unstructured":"A. B. Stundzia and C. J. Lumsden, \u201cStochastic simulation of coupled\nreaction\u2013diffusion processes,\u201d Journal of Computational Physics, vol.\n127, no. 1, pp. 196\u2013207, 1996. https:\/\/dx.doi.org\/10.1006\/jcph.1996.0168","DOI":"10.1006\/jcph.1996.0168"},{"key":"ref15","doi-asserted-by":"publisher","unstructured":"M. M. Rahman and R. B. Sidje, \u201cA study of a metapopulation model\nusing the stochastic reaction diffusion master equation,\u201d in Southwest\nData Science Conference. Springer, 2023, pp. 242\u2013253, https:\/\/dx.doi.org\/10.1007\/978-3-031-61816-1_17.","DOI":"10.1007\/978-3-031-61816-1_17"},{"key":"ref16","doi-asserted-by":"publisher","unstructured":"M. M. Rahman, K. 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Elf, \u201cStochastic reaction-diffusion simulation\nwith MesoRD,\u201d Bioinformatics, vol. 21, no. 12, pp. 2923\u20132924, 2005.\nhttps:\/\/dx.doi.org\/10.1093\/bioinformatics\/bti431","DOI":"10.1093\/bioinformatics\/bti431"},{"key":"ref19","doi-asserted-by":"publisher","unstructured":"J. Elf and M. Ehrenberg, \u201cSpontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases,\u201d Systems biology,\nvol. 1, no. 2, pp. 230\u2013236, 2004. https:\/\/dx.doi.org\/10.1049\/sb:20045021","DOI":"10.1049\/sb:20045021"},{"key":"ref20","unstructured":"M. M. Rahman, \u201cA numerical study of the stochastic reaction-diffusion\nmaster equation using tensors and parallelism with application to biological models,\u201d Ph.D. dissertation, The University of Alabama, 2025."},{"key":"ref21","doi-asserted-by":"publisher","unstructured":"L. De Lathauwer, B. De Moor, and J. Vandewalle, \u201cA multilinear singular value decomposition,\u201d SIAM Journal on Matrix Analysis and Applications, vol. 21, no. 4, pp. 1253\u20131278, 2000. https:\/\/dx.doi.org\/10.1137\/S089547989630569","DOI":"10.1137\/S089547989630569"},{"key":"ref22","doi-asserted-by":"publisher","unstructured":"T. G. Kolda and B. W. Bader, \u201cTensor decompositions and applications,\u201d SIAM Review, vol. 51, no. 3, pp. 455\u2013500, 2009. https:\/\/dx.doi.org\/10.1137\/07070111X","DOI":"10.1137\/07070111X"},{"key":"ref23","doi-asserted-by":"publisher","unstructured":"T. G. Kolda, \u201cMultilinear operators for higher-order decompositions,\u201d\nSandia National Laboratories (SNL), Albuquerque, NM, and Livermore,\nCA (United States), Tech. Rep., 2006, https:\/\/dx.doi.org\/10.2172\/923081.","DOI":"10.2172\/923081"},{"key":"ref24","doi-asserted-by":"publisher","unstructured":"I. V. Oseledets, \u201cTensor-train decomposition,\u201d SIAM Journal on\nScientific Computing, vol. 33, no. 5, pp. 2295\u20132317, 2011. https:\/\/dx.doi.org\/10.1137\/090752286","DOI":"10.1137\/090752286"},{"key":"ref25","doi-asserted-by":"publisher","unstructured":"T. Dinh and R. B. Sidje, \u201cAn adaptive solution to the chemical master\nequation using quantized tensor trains with sliding windows,\u201d Physical\nBiology, vol. 17, no. 6, p. 065014, 2020. https:\/\/dx.doi.org\/10.1088\/1478-3975\/aba1d2","DOI":"10.1088\/1478-3975\/aba1d2"},{"key":"ref26","doi-asserted-by":"publisher","unstructured":"H. D. Vo and R. B. Sidje, \u201cAn adaptive solution to the chemical master\nequation using tensors,\u201d The Journal of Chemical Physics, vol. 147,\nno. 4, 2017. https:\/\/dx.doi.org\/10.1063\/1.4994917","DOI":"10.1063\/1.4994917"},{"key":"ref27","unstructured":"K. Burrage, M. Hegland, S. Macnamara, and R. B. Sidje, \u201cA Krylov-based finite state projection algorithm for solving the chemical master\nequation arising in the discrete modelling of biological systems,\u201d in Proc.\nof The AA Markov 150th Anniversary Meeting, no. 21-37, 2006."},{"key":"ref28","doi-asserted-by":"publisher","unstructured":"M. Hegland and J. Garcke, \u201cOn the numerical solution of the chemical\nmaster equation with sums of rank one tensors,\u201d ANZIAM Journal,\nvol. 52, pp. C628\u2013C643, 2010. https:\/\/dx.doi.org\/10.21914\/anziamj.v52i0.3895","DOI":"10.21914\/anziamj.v52i0.3895"},{"key":"ref29","doi-asserted-by":"publisher","unstructured":"V. Kazeev, M. Khammash, M. Nip, and C. Schwab, \u201cDirect solution of the chemical master equation using quantized tensor trains,\u201d\nPLoS computational biology, vol. 10, no. 3, p. e1003359, 2014. https:\/\/dx.doi.org\/10.1371\/journal.pcbi.1003359","DOI":"10.1371\/journal.pcbi.1003359"},{"key":"ref30","doi-asserted-by":"publisher","unstructured":"V. Colizza, R. Pastor-Satorras, and A. Vespignani, \u201cReaction\u2013diffusion\nprocesses and metapopulation models in heterogeneous networks,\u201d Nature Physics, vol. 3, no. 4, pp. 276\u2013282, 2007. https:\/\/dx.doi.org\/10.1038\/nphys560","DOI":"10.1038\/nphys560"},{"key":"ref31","doi-asserted-by":"publisher","unstructured":"R. Anderson, R. May, and B. Anderson, Infectious Diseases of Humans:\nDynamics and Control. Oxford University Press, 1992, https:\/\/dx.doi.org\/10.1093\/oso\/9780198545996.001.0001.","DOI":"10.1093\/oso\/9780198545996.001.0001"},{"key":"ref32","doi-asserted-by":"publisher","unstructured":"S. Smith and R. Grima, \u201cBreakdown of the reaction-diffusion master\nequation with nonelementary rates,\u201d Phys. Rev. E, vol. 93, p. 052135,\nMay 2016. https:\/\/dx.doi.org\/10.1103\/PhysRevE.93.052135. [Online]. 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