We present a novel data structure called T-Cube which dramatically improves response time to ad-hoc time series queries against large datasets. We have tested T-Cube on both synthetic and real world data (emergency room patient visits, pharmacy sales) containing millions of records. The results indicate that T-Cube responds to complex queries 1,000 times faster when compared to the state-of-the...

We show that in d-dimensional Euclidean space the maximum number of non-overlapping translates of a d-dimensional convex body K that can touch K and can lie in a closed supporting half-space of K is always at most 2 ·3d−1−1, with this bound to be reached only if K is an affine image of a d-cube. Such onesided Hadwiger configurations occur at the boundary of finite packings or near the holes in ...

This paper presents an optical interconnect model for k-ary n-cube network topologies based on free-space analysis. This model integrates relevant parameters inherent to optics with traditional network parameters to make it applicable for performance evaluation of parallel processor optical network designs. We apply this model to a free-space diffractive-reflective optical interconnect design a...

This paper addresses the solution of instationary parabolic evolution equations simultaneously in space and time. As a model problem we consider the heat equation posed on the unit cube in Euclidean space of moderately high dimension. An a priori stable minimal residual Petrov-Galerkin variational formulation of the heat equation in space-time results in a generalized least squares problem. Thi...

An imaginary cube is a three dimensional object which has square projections in three orthogonal directions just as a cube has. In this paper, we study imaginary cubes and present sculptures based on imaginary cubes. We show that there are 16 kinds of minimal convex imaginary cubes. The list of 16 representative minimal convex imaginary cubes contains, as well as a regular tetrahedron and a cub...

in this paper, using the tight-binding model, we extend the real-space renormalization group method to time-dependent hamiltonians. we drive the time-dependent recursion relations for the renormalized tight-binding hamiltonian by decimating selective sites of lattice iteratively. the formalism is then used for the calculation of the local density of electronic states for a one dimensional quant...

Analysts examining large-scale information security repositories for propagating network events are interested in quickly identifying temporal and spatial (IP address and/or port) regions containing interesting phenomena, or correlating events from different time periods. The size of these datasets strains current query capabilities provided by, for example, relational databases. We introduce a...

We prove an inequality for functions on the discrete cube {0, 1} extending the edgeisoperimetric inequality for sets. This inequality turns out to be equivalent to the following claim about random walks on the cube: Subcubes maximize ’mean first exit time’ among all subsets of the cube of the same cardinality.

We prove that for the space of functions with mixed rst derivatives bounded in L 1 norm, the weighted integration problem over bounded or unbounded regions is equivalent to the corresponding classical integration problem over the unit cube. This correspondence yields tractability of the general weighted integration problem. 1. Introduction In recent years there has been great interest in the tr...