关于控制临界数(英)

本文给出控制临界数的一系列上界，且刻划了控制临界数为△＋1的图的特征．     

Discrepancy of Certain Kronecker Sequences Concerning Transcendental Numbers

Let ω1,..., ωs be a set of real transcendental numbers satisfying a certain Diophantine inequality. The upper bound for the discrepancy of the Kronecker sequence （{nω1},..., {nωs}）（1 ≤ n ≤ N） is given. In particular, some low-discrepancy sequences are constructed.     

Overall values of conventional discrepancy indices for related and unrelated models of a non-centrosymmetric crystal with a centrosymmetric group

Theoretical expressions for the overall values of the conventional discrepancy indicesR(F) andR(I) are derived for a non-centrosymmetric crystal with a centrosymmetric group by taking the centrosymmetric group and a part of the other atoms in the unit cell as the trial structure. These results are used to obtain tables of values of these indices in terms of the parameter σ _1c ² and σ ₁ ² which define the fractional contribution to the local mean intensity from the centrosymmetric group and all the known atoms respectively. Contribution No. 561     

Lattice points in bodies of revolution II

In [3] it was shown that when a three-dimensional smooth convex body has rotational symmetry around a coordinate axis one can find better bounds for the lattice point discrepancy than what is known for more general convex bodies. To accomplish this, however, it was necessary to assume a non-vanishing condition on the third derivative of the generatrix. In this article we drop this condition, showing that the aforementioned bound holds for a wider family of revolution bodies, which includes those with analytic boundary. A novelty in our approach is that, besides the usual analytic methods, it requires studying some Diophantine properties of the Taylor coefficients of the phase on the Fourier transform side.     

Efficient algorithms for discrepancy minimization in convex sets

A result of Spencer states that every collection of n sets over a universe of size n has a coloring of the ground set with of discrepancy . A geometric generalization of this result was given by Gluskin (see also Giannopoulos) who showed that every symmetric convex body with Gaussian measure at least , for a small , contains a point where a constant fraction of coordinates of y are in . This is often called a partial coloring result. While the proofs of both these results were inherently non‐algorithmic, recently Bansal (see also Lovett‐Meka) gave a polynomial time algorithm for Spencer's setting and Rothvoß gave a randomized polynomial time algorithm obtaining the same guarantee as the result of Gluskin and Giannopoulos. This paper contains several related results which combine techniques from convex geometry to analyze simple and efficient algorithms for discrepancy minimization. First, we prove another constructive version of the result of Gluskin and Giannopoulos, in which the coloring is attained via the optimization of a linear function. This implies a linear programming based algorithm for combinatorial discrepancy obtaining the same result as Spencer. Our second result suggests a new approach to obtain partial colorings, which is also valid for the non‐symmetric case. It shows that every (possibly non‐symmetric) convex body , with Gaussian measure at least , for a small , contains a point where a constant fraction of coordinates of y are in . Finally, we give a simple proof that shows that for any there exists a constant c > 0 such that given a body K with , a uniformly random x from is in cK with constant probability. This gives an algorithmic version of a special case of the result of Banaszczyk.     

Intercalates and discrepancy in random Latin squares

An intercalate in a Latin square is a 2 × 2 Latin subsquare. Let be the number of intercalates in a uniformly random n × n Latin square. We prove that asymptotically almost surely , and that (therefore asymptotically almost surely for any ). This significantly improves the previous best lower and upper bounds. We also give an upper tail bound for the number of intercalates in 2 fixed rows of a random Latin square. In addition, we discuss a problem of Linial and Luria on low‐discrepancy Latin squares.     

一种寻找星图光斑质心的高精度算法及在成像畸变矫正中的应用

首先讨论星图识别中的质心寻找问题,提出了一种改进的匹配算法.使用高斯分布对光斑内像素点的强度分布进行近似模拟, 并采用最小二乘法中的法方程法对光斑图像质心坐标进行优化计算.算例表明该算法可以得到更为精确的结果, 在噪声小于最大像素值的$5\%$时,质心坐标计算精度高于0.04个像素, 优于以往的匹配算法的结果.最后讨论了算法在望远镜光学成像畸变矫正中的应用, 设计了矫正算法, 并通过算例验证了算法的合理性.     

Deterministic random walks on regular trees

Jim Propp's rotor–router model is a deterministic analog of a random walk on a graph. Instead of distributing chips randomly, each vertex serves its neighbors in a fixed order. Cooper and Spencer (Comb Probab Comput 15 (2006) 815–822) show a remarkable similarity of both models. If an (almost) arbitrary population of chips is placed on the vertices of a grid ?^d and does a simultaneous walk in the Propp model, then at all times and on each vertex, the number of chips on this vertex deviates from the expected number the random walk would have gotten there by at most a constant. This constant is independent of the starting configuration and the order in which each vertex serves its neighbors. This result raises the question if all graphs do have this property. With quite some effort, we are now able to answer this question negatively. For the graph being an infinite k‐ary tree (k ≥ 3), we show that for any deviation D there is an initial configuration of chips such that after running the Propp model for a certain time there is a vertex with at least D more chips than expected in the random walk model. However, to achieve a deviation of D it is necessary that at least exp(Ω(D²)) vertices contribute by being occupied by a number of chips not divisible by k at a certain time. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

Cycle embedding in star graphs with conditional edge faults

Among the various interconnection networks, the star graph has been an attractive one. In this paper, we consider the cycle embedding problem in star graphs with conditional edge faults. We show that there exist cycles of all even lengths from 6 to n! in an n-dimensional star graph with ?2n-7 edge faults in which each vertex is incident with at least two healthy edges for n?4.     

基于迁移学习的GH159螺栓热镦后头部缺陷识别

为准确进行GH159螺栓热镦后头部缺陷识别,提出了基于迁移学习的缺陷识别方法,其中,不同场景亮度下的数据集分别设置为迁移学习的源域,目标域.首先,考虑域条件分布的多簇特点,使用K-means算法对同类缺陷数据进行簇划分,确定簇中心,并基于其构造新的分布差异度量;其次,为有效提升迁移学习计算效率,使用簇中心间距离以及各簇...