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...

We propose a novel heuristic algorithm for Cube Pruning running in linear time in the beam size. Empirically, we show a gain in running time of a standard machine translation system, at a small loss in accuracy.

Decision support applications involve complex queries on very large databases Since response times should be small query optimization is critical Users typically view the data as multi dimensional data cubes Each cell of the data cube is a view consisting of an aggregation of interest like total sales The values of many of these cells are dependent on the values of other cells in the data cube ...

Decision support applications involve complex queries on very large databases. Since response times should be small, query optimization is critical. Users typically view the data as multidimensional data cubes. Each cell of the data cube is a view consisting of an aggregation of interest, like total sales. The values of many of these cells are dependent on the values of other cells in the data ...

In this article, the authors propose to use the grid file to store multi-dimensional data cubes and answer rangesum queries. The grid file is enhanced with a dynamic splitting mechanism to accommodate insertions of data. It overcomes the drawback of the traditional grid file in storing uneven data while enjoying its advantages of simplicity and efficiency. The space requirement grows linearly w...

We prove the following results: (1) A unique smooth solution exists for short time for the heat equation associated with the MM obius energy of loops in a euclidean space, starting with any simple smooth loop. (2) A critical loop of the energy is smooth if it has cube-integrable curvature. Combining this with an earlier result of M. Freedman, Z. Wang and the author, any local minimizer of the e...

We give an expository account of our computational proof that every position of Rubik’s Cube can be solved in 20 moves or less, where a move is defined as any twist of any face. The roughly 4.3 × 1019 positions are partitioned into about two billion cosets of a specially chosen subgroup, and the count of cosets required to be treated is reduced by considering symmetry. The reduced space is sear...

A unit cube in k dimensional space (or k-cube in short) is defined as the Cartesian product R1 × R2 × · · · × Rk where Ri(for 1 ≤ i ≤ k) is a closed interval of the form [ai, ai + 1] on the real line. A k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that two vertices in G are adjacent if and only if their corresponding k-cubes have a non-empty intersection....

We prove a theorem whose countable version is that a zero-dimensional polyadic space of countable tightness is a Uniform Eberlein compact space. We prove that if a point p of a polyadic space Y has πχ(p, Y ) = κ > ω, then there exists K ⊂ Y such that p ∈ K and K is homeomorphic to the Cantor cube 2.

The crucial problem of cube attack is the selection of cube set, which also being the most time-consuming process. This paper designs a new search algorithm which generates several linear equations through one cube set and applies cube attack to simplified version of Grain-v1algorithem. Our attack directly recovers 14 bits of the secret key when the initialization rounds in Grain-v1is 75 and fi...