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We propose boundary conditions for the diffusion equation that maintain the initial mean and the total mass of a discrete data sample in the density estimation process.
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1D Inhomogenious Diffusion Equation solution with FEM. Patarroyo K. available online. http://nbviewer.jupyter.org/github/MrKeithPatarroyo/Example/blob/master/FEM-Public/1D%20Heat%20Equation%20FEM-Public.ipynb
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Botev, Z. I. , Grotowski, J. F. and Kroese, D. P. (2010). Kernel density estimation via Diffusion. Ann. Statist, Vol. 38, No. 5, 2916–2957
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Olver, P. (2014). Introduction to Partial Differential Equations. Springer-Verlag, 1st Ed
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Gómez, F., Torres, A. , Galvis, J., Camargo, J. and Martínez, O. (2016). Hotspot mapping for Perception of Security. Smart Cities Conference (ISC2), 2016 IEEE International
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