Fixed Parameter Undecidability for Wang Tilesets

Deciding if a given set of Wang tiles admits a tiling of the plane is decidable if the number of Wang tiles (or the number of colors) is bounded, for a trivial reason, as there are only finitely many such tilesets. We prove however that the tiling problem remains undecidable if the difference between the number of tiles and the number of colors is bounded by 43. One of the main new tool is the concept of Wang bars, which are equivalently inflated Wang tiles or thin polyominoes.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

Uniqueness of asymptotic cones of complete noncompact shrinking gradient Ricci solitons with Ricci curvature decay

We discuss an elementary consequence of the works of (1) Brett Kotschwar and Lu Wang and (2) Ovidiu Munteanu and Jiaping Wang

A note on QUBO instances defined on Chimera graphs

McGeoch and Wang (2013) recently obtained optimal or near-optimal solutions to some quadratic unconstrained boolean optimization (QUBO) problem instances using a 439 qubit D-Wave Two quantum computing system in much less time than with the IBM ILOG CPLEX mixed-integer quadratic programming (MIQP) solver. The problems studied by McGeoch and Wang are defined on subgraphs -- with up to 439 nodes -- of Chimera graphs. We observe that after a standard reformulation of the QUBO problem as a mixed-integer linear program (MILP), the specific instances used by McGeoch and Wang can be solved to optimality with the CPLEX MILP solver in much less time than the time reported in McGeoch and Wang for the CPLEX MIQP solver. However, the solution time is still more than the time taken by the D-Wave computer in the McGeoch-Wang tests.Comment: Version 1 discussed computational results with random QUBO instances. McGeoch and Wang made an error in describing the instances they used; they did not use random QUBO instances but rather random Ising Model instances with fields (mapped to QUBO instances). The current version of the note reports on tests with the precise instances used by McGeoch and Wan

The Berger-Wang formula for the Markovian joint spectral radius

The Berger-Wang formula establishes equality between the joint and generalized spectral radii of a set of matrices. For matrix products whose multipliers are applied not arbitrarily but in accordance with some Markovian law, there are also known analogs of the joint and generalized spectral radii. However, the known proofs of the Berger-Wang formula hardly can be directly applied in the case of Markovian products of matrices since they essentially rely on the arbitrariness of appearance of different matrices in the related matrix products. Nevertheless, as has been shown by X. Dai the Berger-Wang formula is valid for the case of Markovian analogs of the joint and the generalized spectral radii too, although the proof in this case heavily exploits the more involved techniques of multiplicative ergodic theory. In the paper we propose a matrix theory construction allowing to deduce the Markovian analog of the Berger-Wang formula from the classical Berger-Wang formula.Comment: 13 pages, 29 bibliography references; minor corrections; accepted for publication in Linear Algebra and its Application

Jing Wang. High culture fever : politics, aesthetics, and ideology in Deng\u27s China; Jing Wang, ed. China\u27s avant-garde fiction : an anthology

This article reviews the books High Culture Fever: Politics, Aesthetics, and Ideology in Deng\u27s China written by Jing Wang and China\u27s Avant-Garde Fiction: An Anthology edited by Jing Wang

Wang Li (1900-1986)

Wang Li (Wang Liaoyi) was one of the three most prominent linguists in China in the 20th century. He was born August 10, 1900, in what is now Bobai County of the Guangxi Zhuang Autonomous Area