Distance-Regular Graphs with c i = b d-i and Antipodal Double Covers

Let be a distance-regular graph of diameter d and valency k > 2. Suppose there exists an integer s with d 2s such that c _i = b _d-i for all 1 i s. Then is an antipodal double cover.     

Distinguishing embedded curves in rational complex surfaces

We construct many pairs of smoothly embedded complex curves with the same genus and self-intersection number in the rational complex surfaces with the property that no self-diffeomorphism of sends one to the other. In particular, as a special case we answer a question originally posed by R. Gompf (1995) concerning genus two curves of self-intersection number 0 in .

     

Compact Manifolds Covered by a Torus

Let X be a compact complex manifold which is the image of a complex torus by a holomorphic surjective map A→X. We prove that X is Kähler and that up to a finite étale cover, X is a product of projective spaces by a torus.     

A list heuristic for vertex cover

We analyze a list heuristic for the vertex cover problem that handles the vertices in a given static order based on the degree sequence. We prove an approximation ratio of at most for a nonincreasing degree sequence, and show that no ordering can achieve an approximation ratio of less than .     

On finding a large number of 3D points with a small diameter

Given a set S of n points in R³, we wish to decide whether S has a subset of size at least k with Euclidean diameter at most r. It is unknown whether this decision problem is NP-hard. The two closely related optimization problems, (i) finding a largest subset of diameter at most r, and (ii) finding a subset of the smallest diameter of size at least k, were recently considered by Afshani and Chan. For maximizing the size, they presented several polynomial-time algorithms with constant approximation factors, the best of which has a factor of . For maximizing the diameter, they presented a polynomial-time approximation scheme. In this paper, we present improved approximation algorithms for both optimization problems. For maximizing the size, we present two algorithms: the first one improves the approximation factor to 2.5 and the running time by an O(n) factor; the second one improves the approximation factor to 2 and the running time by an O(n²) factor. For minimizing the diameter, we improve the running time of the PTAS from O(nlogn+2^O(1/ε3)n) to O(nlogn+2^{O(1/(ε1.5logε))}n).     

平面上的近似连续积分

近似连续Ｐｅｒｒｏｎ 积分首先由Ｂｕｒｋｉｌｌ提出,称之为ＡＰ积分,由于近似复盖具有划分性质,因而可以给出ＡＰ积分的Ｒｉｅｍ ａｎｎ型定义． 但是,在平面上近似复盖是否具有划分性质还不知道． 本文给出了一种方法,用这种方法可以在平面上给出ＡＰ积分的Ｒｉｅｍ ａｎｎ型定义而不需要证明划分的存在性．     

给定度序列图的覆盖成本和反向覆盖成本的研究

具有n个顶点且度序列为(m,2,…,2,1,…,1)(1的重数为m)的连通图不止一个(这些图均为树),而每个树对应唯一一个段序列(l1,l2,…,lm).通过对任意一树移动最长段的悬挂点到最短段悬挂点的方式得到另一树,比较前后两树的覆盖成本和反向覆盖成本,给出了具有最小覆盖成本和反向覆盖成本的极树,并且进一步给出了取得...     

Statistical and Visual Analysis of Audio,Text, and Image Features for Multi-Modal Music Genre Recognition

We present a multi-modal genre recognition framework that considers the modalities audio, text, and image by features extracted from audio signals, album cover images, and lyrics of music tracks. In contrast to pure learning of features by a neural network as done in the related work, handcrafted features designed for a respective modality are also integrated, allowing for higher interpretability of created models and further theoretical analysis of the impact of individual features on genre prediction. Genre recognition is performed by binary classification of a music track with respect to each genre based on combinations of elementary features. For feature combination a two-level technique is used, which combines aggregation into fixed-length feature vectors with confidence-based fusion of classification results. Extensive experiments have been conducted for three classifier models (Naïve Bayes, Support Vector Machine, and Random Forest) and numerous feature combinations. The results are presented visually, with data reduction for improved perceptibility achieved by multi-objective analysis and restriction to non-dominated data. Feature- and classifier-related hypotheses are formulated based on the data, and their statistical significance is formally analyzed. The statistical analysis shows that the combination of two modalities almost always leads to a significant increase of performance and the combination of three modalities in several cases.     

逻辑函数高阶布尔e偏导数求解算法的实现

针对已有方法在求解布尔e偏导数时只能解决小规模电路的问题,提出了一种基于逻辑函数不相交运算的大函数高阶布尔e偏导数的求解算法.该方法将逻辑函数转化为不相交乘积项的集合,用逻辑函数的不相交运算替代布尔e导数运算中的逻辑“与”运算;并将不包含待求导变量的乘积项拆分出来,不参与布尔e导数运算,以达到降低算法复杂度、提高算法速度的目的.提出的算法用C语言编程实现,并用MCNC测试电路进行了测试.实验结果显示,本算法能快速实现大函数高阶布尔e偏导数的求解,求解效率与参与不相交运算的乘积项数量有关,但对输入变量的数量不敏感.     

直线阵光学综合孔径成像中的子孔径尺寸效应

光学综合孔径阵列中的子孔径的位置和直径的大小对成像质量有着重要的影响。详细分析了几种不同优化排列的光学综合孔径直线阵列的无像差点扩展函数、光学传递函数和衍射成像特性．结果表明,子孔径的位置不同．光学传递函数的空间频率覆盖有很大的差异。增大子孔径的直径可以增大空间频率覆盖程度．但子孔径直径过大时义会产生空间频率冗余度和增加制造成本。直线阵光学综合孔径的衍射成像是多重像,子孔径直径的增大还可以减小重影的程度,提高成像质量。结果说明,在进行光学综合孔径阵列优化排列时必须考虑子孔径的直径大小这个重耍的因素。