Efficient data indexing and exact k-nearest-neighbor (kNN) retrieval are still challenging tasks in high-dimensional spaces. This work highlights the difficulties of indexing in high-dimensional and tightly-clustered dataspaces by exploring several important tunable parameters for optimizing kNN query performance using the iDistance and iDStar algorithms. We experiment on real and synthetic dat...

Summary In this article, we formalize in Mizar [1], [2] the topological properties of finite-dimensional real normed spaces. first section, Bolzano-Weierstrass theorem, which states that a bounded sequence points an n-dimensional Euclidean space has certain subsequence converges to point. As corollary, it is also shown equivalence between subset being compact and closed bounded. next definition...

A detailed analysis of minimax estimates of arbitrary linear functionals based on infinite dimensional Gaussian models has been provided by Donoho and Liu. In particular it has been shown that if the parameter space is convex then linear estimates can always be found which have maximum mean squared error within a small constant multiple of the minimax value. These linear estimates do however ha...

Tumor cell growth models involve high-dimensional parameter spaces that require computationally tractable methods to solve. To address a proposed tumor growth dynamics mathematical model, an instance of the particle swarm optimization method was implemented to speed up the search process in the multi-dimensional parameter space to find optimal parameter values that fit experimental data from mi...