Automated synthesis of multiple analog circuits using evolutionary computation for redundancy-based fault-tolerance

Analog circuits are one of the most important parts of modern electronic systems and the failure of electronic hardware presents a critical threat to the completion of modern aircraft, spacecraft, and robot missions. Compared to digital circuits, designing fault-tolerant analog circuits is a difficult and knowledge-intensive task. A simple but powerful method for robustness is a redundancy approach to use multiple circuits instead of single one. For example, if component failures occur, other redundant components can replace the functions of broken parts and the system can still work. However, there are several research issues to make the redundant system automatically. In this paper, we used evolutionary computation to generate multiple analog circuits automatically and then we combined the solutions to generate robust outputs. Evolutionary computation is a natural way to produce multiple redundant solutions because it is a population-based search. Experimental results on the evolution of the low-pass, high-pass and band-stop filters show that the combination of multiple evolved analog circuits produces results that are more robust than those of the best single circuit.     

Two new characteristic parameters for runoff computation

A method capable of estimating the hydrograph from a prescribed storm for a practical mild slope upstream catchment is proposed. This method makes use of two new characteristic parameters, andS, in conjunction with the kinematic wave equation to compute lateral inflows of the main stream of the catchment. The depth profile of overland flow at any instant within the catchment and hydrograph at any location can be easily found. Lag times for individual lateral inflows are then considered and are linearly combined to obtain the hydrograph at the outlet of the catchment or depth profile of the main stream at any instant. The validity of the excess rainfall-surface runoff linear relationship in this study has also been verified with Tatsunokuchiyama catchment, and it shows good results for this computed runoff.     

Some efficient solutions to the affine scheduling problem. Part II. Multidimensional time

This paper extends the algorithms which were developed in Part I to cases in which there is no affine schedule, i.e. to problems whose parallel complexity is polynomial but not linear. The natural generalization is to multidimensional schedules with lexicographic ordering as temporal succession. Multidimensional affine schedules, are, in a sense, equivalent to polynomial schedules, and are much easier to handle automatically. Furthermore, there is a strong connection between multidimensional schedules and loop nests, which allows one to prove that a static control program always has a multidimensional schedule. Roughly, a larger dimension indicates less parallelism. In the algorithm which is presented here, this dimension is computed dynamically, and is just sufficient for scheduling the source program. The algorithm lends itself to a divide and conquer strategy. The paper gives some experimental evidence for the applicability, performances and limitations of the algorithm.     

On problem transformability in VLSI

The two basic performance parameters that capture the complexity of any VLSI chip are the area of the chip,A, and the computation time,T. A systematic approach for establishing lower bounds onA is presented. This approach relatesA to the bisection flow, . A theory of problem transformation based on , which captures bothAT ² andA complexity, is developed. A fundamental problem, namely, element uniqueness, is chosen as a computational prototype. It is shown under general input/output protocol assumptions that any chip that decides ifn elements (each with (1+)lognbits) are unique must have =(nlogn), and thus, AT²=(n ²log² n), andA= (nlogn). A theory of VLSI transformability reveals the inherentAT ² andA complexity of a large class of related problems.This work was supported in part by the Semiconductor Research Corporation under contract RSCH 84-06-049-6.     

轴流式转轮三元粘性流动数值计算

为进一步提高轴流式转轮的设计精度与性能,采用时均Navier-Stokes控制方程,标准k-ε湍流模型及SIMPLEC算法,对一轴流定浆式水轮机转轮内三元粘性流动进行了数值模拟。提出了水力损失计算方法,获得了转轮的预测效率。分析了转轮内部流场分布规律,建立了叶片表面压力在包角范围内的变化曲线,有助于认识转轮内真实流动现象,为改善设计提供可视化数据支持。     

FracSym: Automated symbolic computation of Lie symmetries of fractional differential equations

In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n$n$ independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented.     

Computer Algebra Derivation of the Bias of Linear Estimators of Autoregressive Models

Abstract. A symbolic method which can be used to obtain the asymptotic bias and variance coefficients to order O(1/n) for estimators in stationary time series is discussed. Using this method, the large‐sample bias of the Burg estimator in the AR(p) for p = 1, 2, 3 is shown to be equal to that of the least squares estimators in both the known and unknown mean cases. Previous researchers have only been able to obtain simulation results for the Burg estimator's bias because this problem is too intractable without using computer algebra. The asymptotic bias coefficient to O(1/n) of Yule–Walker as well as least squares estimates is also derived in AR(3) models. Our asymptotic results show that for the AR(3), just as in the AR(2), the Yule–Walker estimates have a large bias when the parameters are near the nonstationary boundary. The least squares and Burg estimates are much better in this situation. Simulation results confirm our findings.     

Holographic algorithms on bases of rank 2

An essential problem in the design of holographic algorithms is to decide whether the required signatures can be realized under a suitable basis transformation (SRP). For holographic algorithms with matchgates on domain size 2, , ,  and  have built a systematical theory. In this paper, we reduce SRP on domain size k≥3$k\ge 3$ to SRP on domain size 2 for holographic algorithms with matchgates on bases of rank 2. Furthermore, we generalize the collapse theorem of [3] to domain size k≥3$k\ge 3$.     

基于GPU-CUDA的共轭斜量法实现及性能对比

偏微分方程数值解法(包括有限差分法、有限元法)以及大量的数学物理方程数值解法最终都会演变成求解大型线性方程组。因此,探讨快速、稳定、精确的大型线性方程组解法一直是数值计算领域不断深入研究的课题且具有特别重要的意义。在迭代法中,共轭斜量法(又称共轭梯度法)被公认为最好的方法之一。但是,该方法最大缺点是仅适用于线性方程组系数矩阵为对称正定矩阵的情况,而且常规的CPU算法实现非常耗时。为此,通过将线性方程组系数矩阵作转换成对称矩阵后实施基于GPU-CUDA的快速共轭斜量法来解决一般性大型线性方程组的求解问题。试验结果表明:在求解效率方面,基于GPU-CUDA的共轭斜量法运行效率高,当线性方程组阶数超过3000时,其加速比将超过14;在解的精确性与求解过程的稳定性方面,与高斯列主元消去法相当。基于GPU-CUDA的快速共轭斜量法是求解一般性大型线性方程组快速而非常有效的方法。     

基于宇宙计算的图形处理器算法实现

下一代观测望远镜将会产生数以亿计的星系测量数据值,这将导致使用中央处理器处理数据时效率低下、成本较高。为了解决这一问题,提出了基于宇宙计算的图形处理器算法。研究了两点式角相关函数以及孔径质量统计这两种宇宙学的计算方法,构建算法代码,并使用统一计算设备架构在图形处理器上实现了这两种算法;比较了算法在中央处理器和图形处理器上使用的运行速度。实验结果表明,与中央处理器相比,使用图形处理器的计算速度得到了显著提高。