Qian, Xinwu, "Big data analytics with NYC taxicab data" (2014). Open Access Theses. 669.

In this work, Voronoi diagrams, Fortune algorithm and diagrams in the Taxicab plane are investigated.

In this article, we make use of some known method to investigate some properties of the numbers represented as sums of two equal odd powers, i.e., the equation x + y = N for n ≥ 3. It was originated in developing algorithms to search new taxicab numbers (i.e., naturals that can be represented as a sum of positive cubes in many different ways) and to verify their minimality. We discuss propertie...

Two kinds of optimal convergence orders in L1-norm to a self-similar solution are proved or conjectured for various evolutionary problems so far. The first convergence order is of the magnitude of the similarity solution itself and the second one is of order 1/t . Employing a potential comparison technique to scalar conservation laws we may easily see that these asymptotic convergence orders ar...

This paper considers the problem of finding the least cost rectilinear distance path in the presence of convex polygonal congested regions. An upper bound for the number of entry/exit points for a congested region is obtained. Based on this key finding, we demonstrate that there are a finite, though exponential number of potential least cost paths between a specified pair of origin-destination ...

In this paper, block distance matrices are introduced. Suppose F is a square block matrix in which each block is a symmetric matrix of some given order. If F is positive semidefinite, the block distance matrix D is defined as a matrix whose (i, j)-block is given by Dij = Fii+Fjj−2Fij . When each block in F is 1 × 1 (i.e., a real number), D is a usual Euclidean distance matrix. Many interesting ...

The τ -temperature is a measure of disorder of bipartite networks that is based on the total Manhattan distance of the adjacency matrix. Two proper­ ties of this measure are that it does not depend on permutations of lines or columns that have the same connectivity and it is completely determined by connectivities of lines and columns. The normalisation of τ is done by an uni­ form random matri...

This paper presents various regularization functions, which are employed to overcome instabilities of system identification problems. Since a regularization function define the solution space of a given problem, it should well represent both mathematical and physical characteristics of the original problem. The regularization function can be derived from the integrability condition of the solut...

Let W ( ) be either the number of descents or inversions of a permutation 2 Sn. Stein's method is applied to bound the sup-norm distance between the distribution of W and the standard normal distribution. This appears to be the rst use of Stein's method in theory of permutation statistics. The construction of an exchangeable pair (W;W 0) used in Stein's method is non-trivial and may be of indep...