Abstract:
Consider a complete communication network of $n$ nodes, where the nodes receive a common clock pulse. We study the synchronous $c$-counting problem: given any starting state and up to $f$ faulty nodes with arbitrary behaviour, the task is to eventually have all correct nodes counting modulo $c$ in agreement. Thus, we are considering algorithms that are self-stabilizing despite Byzantine failures. In this work, we give new algorithms for the synchronous counting problem that (1) are deterministic, (2) have linear stabilisation time in $f$, (3) use a small number of states, and (4) achieve almost-optimal resilience. Prior algorithms either resort to randomisation, use a large number of states, or have poor resilience. In particular, we achieve an exponential improvement in the space complexity of deterministic algorithms, while still achieving linear stabilisation time and almost-linear resilience.

Abstract:
Counting the solution number of combinational optimization problems is an important topic in the study of computational complexity, especially on the #P-complete complexity class. In this paper, we first investigate some organizations of Vertex-Cover unfrozen subgraphs by the underlying connectivity and connected components of unfrozen vertices. Then, a Vertex-Cover Solution Number Counting Algorithm is proposed and its complexity analysis is provided, the results of which fit very well with the simulations and have better performance than those by 1-RSB in a neighborhood of c = e for random graphs. Base on the algorithm, variation and fluctuation on the solution number statistics are studied to reveal the evolution mechanism of the solution numbers. Besides, marginal probability distributions on the solution space are investigated on both random graph and scale-free graph to illustrate different evolution characteristics of their solution spaces. Thus, doing solution number counting based on graph expression of solution space should be an alternative and meaningful way to study the hardness of NP-complete and #P-complete problems, and appropriate algorithm design can help to achieve better approximations of solving combinational optimization problems and the corresponding counting problems.

Abstract:
量子遗传算法具有种群规模小而不影响算法性能、收敛速度快和全局搜索能力强等优点。为了获得高功率密度和低成本的电动车用轮毂电机，基于量子遗传算法，针对研究设计的一种外转子永磁同步轮毂电机，以电机有效质量、材料成本和功率损耗为优化目标，建立了包含8个设计变量和5个约束的数学模型，对电机进行优化设计。研究结果表明：永磁同步轮毂电机有效质量、材料成本和功率损耗降低，效率特性提升，有限元分析结果与量子遗传算法计算结果接近，能满足电动车对驱动轮毂电机的使用要求，因此，量子遗传算法对于轮毂电机优化设计是有效可行的。 Quantum genetic algorithm (QGA) has advantages of small population size with good algorithm performance, fast convergent rate and powerful ability of global search. In order to acquire high power density and low cost in-wheel motor of electric vehicle,based on the quantum genetic algorithm, a designed outer-rotor permanent magnet synchronous in-wheel motor model with 8 designed variables and 5 constraints was built to optimize the effective quality, material cost and power consumption. The results show that the effective quality, material cost and power consumption of the motor are decreased and the efficiency of the motor is improved. The results of finite element analysis are close to those calculated by quantum genetic algorithm,which can satisfy the using requirements of driving in-wheel motor electric vehicle. Therefore, the QGA is an effective and feasible algorithm in optimization design of in-wheel motor

Abstract:
We show that for sets with the Hausdorff--Besicovitch dimension equal zero the box counting algorithm commonly used to calculate Renyi exponents ($d_q$) can exhibit perfect scaling suggesting non zero $d_q$'s. Properties of these pathological sets ({\it pseudofractals}) are investigated. Numerical, as well as analytical estimates for $d_q$'s are obtained. A simple indicator is given to distinguish pseudofractals and fractals in practical applications of the box counting method. Histograms made of pseudofractal sets are shown to have Pareto tails.

Abstract:
Accuracy of the box-counting algorithm for numerical computation of the fractal exponents is investigated. To this end several sample mathematical fractal sets are analyzed. It is shown that the standard deviation obtained for the fit of the fractal scaling in the log-log plot strongly underestimates the actual error. The real computational error was found to have power scaling with respect to the number of data points in the sample ($n_{tot}$). For fractals embedded in two-dimensional space the error is larger than for those embedded in one-dimensional space. For fractal functions the error is even larger. Obtained formula can give more realistic estimates for the computed generalized fractal exponents' accuracy.

Abstract:
A message-passing algorithm for counting short cycles in a graph is presented. For bipartite graphs, which are of particular interest in coding, the algorithm is capable of counting cycles of length g, g +2,..., 2g - 2, where g is the girth of the graph. For a general (non-bipartite) graph, cycles of length g; g + 1, ..., 2g - 1 can be counted. The algorithm is based on performing integer additions and subtractions in the nodes of the graph and passing extrinsic messages to adjacent nodes. The complexity of the proposed algorithm grows as $O(g|E|^2)$, where $|E|$ is the number of edges in the graph. For sparse graphs, the proposed algorithm significantly outperforms the existing algorithms in terms of computational complexity and memory requirements.

Abstract:
We derive a Belief-Propagation algorithm for counting large loops in a directed network. We evaluate the distribution of the number of small loops in a directed random network with given degree sequence. We apply the algorithm to a few characteristic directed networks of various network sizes and loop structures and compare the algorithm with exhaustive counting results when possible. The algorithm is adequate in estimating loop counts for large directed networks and can be used to compare the loop structure of directed networks and their randomized counterparts.

Abstract:
Custom memory organization are challenging task in the area of VLSI design. This study aims to design high speed and low power consumption memory for embedded system. Synchronous SRAM has been proposed and analyzed using various simulators. Xilinx simulator simulates the Synchronous SRAM memories which can perform efficient read/write capability for embedded systems. Xinix tool also provide the access time that required selecting a word and reading it. Synchronous Static RAM which has easily read /writes capability and performs scheduled read /writes operation in efficient manner.

Abstract:
Permanent Magnet Synchronous Motors (PMSMs) have been widely used in many industrial applications. In This paper a new method for multi objective optimal design of a permanent magnet synchronous motor (PMSMs) with surface mounted permanent magnet rotor is presented to achieve maximum efficiency and power density using a Bees algorithm for industrial applications. The objective function is a combination of power density and efficiency to be maximized simultaneously. A particular optimal machine is chosen and its performances are validated with FE analysis. The design optimization results in a motor with great improvement regarding the original motor.

Abstract:
This paper proposes a coarse-to-fine two-level synchronous data acquisition and transmission system for binocular stereo vision, which satisfies strict synchronous requirement of stereo vision. Specifically, this synchronization system design contains: coarse level synchronous based on hardware circuit design and the fine level synchronous based on hardware description language (HDL) design. The former includes the synchronization design of clock and external trigger. The latter utilizes a multi-level synchronous control strategy from field-level to pixel-level, which consists of field-synchronous acquisition of the two-channel video inputs, two-channel Ping-pong buffers switch control module, and pixel-synchronous bit-splicing and PCI transmission module. The experiments of synchronous acquisition and display demonstrate the high reliability and great performance of this synchronous system.