**Abstract: **In this paper, we consider several variants of the pattern matching with mismatches problem. In particular, given a text \(T=t_1 t_2\cdots t_n\) and a pattern \(P=p_1p_2\cdots p_m\), we investigate the following problems: (1) pattern matching with mismatches: for every \(i, 1\leq i \leq n-m+1\) output, the distance between \(P\) and \(t_i t_{i+1}\cdots t_{i+m-1}\); and (2) pattern matching with \(k\) mismatches: output those positions \(i\) where the distance between \(P\) and \(t_i t_{i+1}\cdots t_{i+m-1}\) is less than a given threshold \(k\). The distance metric used is the Hamming distance. We present some novel algorithms and techniques for solving these problems. We offer deterministic, randomized and approximation algorithms. We consider variants of these problems where there could be wild cards in either the text or the pattern or both. We also present an experimental evaluation of these algorithms. The source code is available at http://www.engr.uconn.edu/\(\sim\)man09004/kmis.zip.

**Abstract: **We introduce a multi-feature optimization clustering algorithm for color image segmentation. The local binary pattern, the mean of the min-max difference, and the color components are combined as feature vectors to describe the magnitude change of grey value and the contrastive information of neighbor pixels. In clustering stage, it gets the initial clustering center and avoids getting into local optimization by adding mutation operator of genetic algorithm to particle swarm optimization. Compared with well-known methods, the proposed method has an overall better segmentation performance and can segment image more accurately by evaluating the ratio of misclassification.

**Abstract: **In this work we generate the numerical solutions of Burgers’ equation by applying the Crank-Nicholson method and different schemes for solving nonlinear systems, instead of using Hopf-Cole transformation to reduce Burgers’ equation into the linear heat equation. The method is analyzed on two test problems in order to check its efficiency on different kinds of initial conditions. Numerical solutions as well as exact solutions for different values of viscosity are calculated, concluding that the numerical results are very close to the exact solution.

**Abstract: **In this paper, we propose a detection method of pulmonary nodules in X-ray computed tomography (CT) scans by use of three image filters and appearance-based k-means clustering. First, voxel values are suppressed in radial directions so as to eliminate extra regions in the volumes of interest (VOIs). Globular regions are enhanced by moment-of-inertia tensors where the voxel values in the VOIs are regarded as mass. Excessively enhanced voxels are reduced based on displacement between the VOI centers and the gravity points of the voxel values in the VOIs. Initial nodule candidates are determined by these filtering processings. False positives are reduced by, first, normalizing the directions of intensity distributions in the VOIs by rotating the VOIs based on the eigenvectors of the moment-of-inertia tensors, and then applying an appearance-based two-step k-means clustering technique to the rotated VOIs. The proposed method is applied to actual CT scans and experimental results are shown.

**Abstract: **We propose a linear time algorithm, called **G2DLP**, for generating 2D lattice *L*(*n*_{1}, *n*_{2}) paths, equivalent to two-item multiset permutations, with a given number of *turns*. The usage of *turn* has three meanings: in the context of multiset permutations, it means that two consecutive elements of a permutation belong to two different items; in lattice path enumerations, it means that the path changes its direction, either from eastward to northward or from northward to eastward; in open shop scheduling, it means that we transfer a job from one type of machine to another. The strategy of **G2DLP** is divide-and-combine; the division is based on the enumeration results of a previous study and is achieved by aid of an integer partition algorithm and a multiset permutation algorithm; the combination is accomplished by a concatenation algorithm that constructs the paths we require. The advantage of **G2DLP** is twofold. First, it is optimal in the sense that it directly generates all feasible paths without visiting an infeasible one. Second, it can generate all paths in any specified order of *turns*, for example, a decreasing order or an increasing order. In practice, two applications, scheduling and cryptography, are discussed.

**Abstract: **The construction of a similarity matrix is one significant step for the spectral clustering algorithm; while the Gaussian kernel function is one of the most common measures for constructing the similarity matrix. However, with a fixed scaling parameter, the similarity between two data points is not adaptive and appropriate for multi-scale datasets. In this paper, through quantitating the value of the importance for each vertex of the similarity graph, the Gaussian kernel function is scaled, and an adaptive Gaussian kernel similarity measure is proposed. Then, an adaptive spectral clustering algorithm is gotten based on the importance of shared nearest neighbors. The idea is that the greater the importance of the shared neighbors between two vertexes, the more possible it is that these two vertexes belong to the same cluster; and the importance value of the shared neighbors is obtained with an iterative method, which considers both the local structural information and the distance similarity information, so as to improve the algorithm’s performance. Experimental results on different datasets show that our spectral clustering algorithm outperforms the other spectral clustering algorithms, such as the self-tuning spectral clustering and the adaptive spectral clustering based on shared nearest neighbors in clustering accuracy on most datasets.