Sharif Digital Repository

This paper describes the use of Quad-Tree Decomposition for upscaling of absolute permeability 2D geological models. Quad-Tree Decomposition is a data structure and generates an unstructured upscaled model that preserves the heterogeneity of the original geological model. In other words, in high-variability regions of the geological model, the gridblocks of the upscaled model remain small but in other regions that the permeability variation is low, the gridblocks of the upscaled model are coarsened. Quad-Tree Decomposition is a very simple, efficient and robust method that reduces the total number of gridblocks and results to high saving in time and memory required to flow simulation in the... 

In the context of differential privacy, a data holder has confidential information about users. The goal is to provide a randomized algorithm that takes this information as input and outputs an aggregation of the input. The algorithm must have the property that for any neighboring input pairs, the output distribution of the algorithm is close. One problem in differential privacy research is the release of shortest distances in a weighted graph. This model, first studied by Adam Sealfon, involves an edge-weighted graph G=(V, E) with weights w : E → R, where the topology of the graph is public and the private information is the weight of the edges. The aim is to provide an (ϵ, δ)-DP algorithm...