Computational Power of Asynchronously Tuned Automata Enhancing the Unfolded Edge of Chaos

Asynchronously tuned elementary cellular automata (AT-ECA) are described with respect to the relationship between active and passive updating, and that spells out the relationship between synchronous and asynchronous updating. Mutual tuning between synchronous and asynchronous updating can be interpreted as the model for dissipative structure, and that can reveal the critical property in the phase transition from order to chaos. Since asynchronous tuning easily makes behavior at the edge of chaos, the property of AT-ECA is called the unfolded edge of chaos. The computational power of AT-ECA is evaluated by the quantitative measure of computational universality and efficiency. It shows that the computational efficiency of AT-ECA is much higher than that of synchronous ECA and asynchronous ECA.

Asynchronous cellular automata that hide some of the configurations during evolution

In the light of recent developments in the theory of reversibility for asynchronous cellular automata, we attempt to explore the dynamics of recurrent rules under fully asynchronous updating scheme. Depending on the reachability of the configurations for a communication class during the evolution of the system, we classify the recurrent rules into two classes — partially exposed recurrent system and fully exposed recurrent system.

Point-block incomplete LU preconditioning with asynchronous iterations on GPU for multiphysics problems

Point-block matrices arise naturally in multiphysics problems when all variables associated with a mesh point are ordered together, and are different from the general block matrices since the sizes of the blocks are so small one can often invert some of the diagonal blocks explicitly. Motivated by the recent works of Chow and Patel and Chow et al., we propose an efficient incomplete LU (ILU) preconditioner for point-block matrices targeting applications on GPU. The construction of the preconditioner involves two critical steps: (1) the initial guessing of values for the lower and upper triangular matrices; and (2) several sweeps of asynchronous updating of the triangular matrices. Three representative problems are studied to show the advantage of the proposed point-block approach over the standard point-wise approach in terms of the number of GMRES iterations and also the total compute time. Moreover, we compare the proposed algorithm with the level-scheduling based parallel algorithm employed in NVIDIA’s cuSPARSE library as well as the serial method implemented in Intel MKL library, and the experiments show that a 2×–5× speedup can be achieved over the block-based ILU( p) factorizations from the cuSPARSE library.

Breaking of the Trade-Off Principle between Computational Universality and Efficiency by Asynchronous Updating

Although natural and bioinspired computing has developed significantly, the relationship between the computational universality and efficiency beyond the Turing machine has not been studied in detail. Here, we investigate how asynchronous updating can contribute to the universal and efficient computation in cellular automata (CA). First, we define the computational universality and efficiency in CA and show that there is a trade-off relation between the universality and efficiency in CA implemented in synchronous updating. Second, we introduce asynchronous updating in CA and show that asynchronous updating can break the trade-off found in synchronous updating. Our finding spells out the significance of asynchronous updating or the timing of computation in robust and efficient computation.

Asynchronous Algorithms for Computing Equilibrium Prices in a Capital Asset Pricing Model

In this paper, we extend the work of [Tong, J, J Hu and J Hu (2017). Computing equilibrium prices for a capital asset pricing model with heterogeneous beliefs and margin-requirement constraints. European Journal of Operational Research, 256(1), 24–34] and develop various asynchronous algorithms to calculate the equilibrium asset prices in a heterogeneous capital asset pricing model. These asynchronous algorithms are based on different asynchronous updating schemes such as delayed updating, cyclic updating, fixed-length updating and random updating. In addition to potential benefits of improving computational efficiency, these asynchronous updating schemes also reflect several scenarios in financial markets in which investors may receive asset pricing information with various degrees of delays and their preferences on how and when to rebalance their portfolios may also be different. The proofs for the convergence of these algorithms are given. Numerical experiments are also provided to compare these algorithms and they show that these asynchronous algorithms work quite well.