Zhu Daming

Prediction for RNA planar pseudoknots

Abstract Based on m-stems and semi-extensible structure, a model is presented to represent RNA planar pseudoknots, and corresponding dynamic programming algorithm is designed and implemented to predict arbitrary planer pseudoknots and simple non-planar pseudoknots with O(n4) time and O(n3) space. The algorithm folds total 245 sequences in the Pseudobase database, and the test results indicate that the algorithm has good accuracy, sensitivity and specificity. *Supported by National Natural Science Foundation of China (Grant Nos. 60573024 and 60573181), the Research Project of Shandong Economic University (01610784), and NSF of Shandong Provice (2005BS01014)

Bounded Size Graph Clustering on Trees

Given an undirected graph with vertex and edge weights and a subset of vertices called terminals, the bounded size graph clustering (BSGC) problem is to partition the vertices into clusters of size at most a given budget such that each cluster contains at most one terminal and the total size of the clusters is minimized, where the size of a cluster is defined as the total vertex weight in the subset plus the total edge weight at the boundary of the cluster. For BSGC on trees, we present a pseudo-polynomial time exact algorithm, which can be modified via rounding to yield a (1+\epsilon)-approximation in polynomial time violating the given budget by a 1+\epsilon factor.

A Fixed-Parameter Tractable Algorithm for Correlation Clustering with l Clusters

Given a graph G=(V,E) with real positive edge weights, where each edge (u, v) is labeled either + or – depending on whether u and v have been deemed to be similar or dissimilar, the problem of correlation clustering with l clusters is to partition the vertices of G into at most l clusters to minimize the total weight of + edges between clusters and – edges within clusters. This problem for general graphs is APX-complete. A fixed-parameter tractable (FPT) algorithm is presented, where the parameter k is defined as the maximum, over all blocks B of the graph, of the number of vertices that must be removed from B to obtain a forest.

An approximation algorithm for the shortest cycle in an undirected unweighted graph

This paper improves Itai and Rodehs algorithm for finding a shortest cycle in an undirected unweighted graph. Given an undirected unweighted graph G with n vertices,the algorithm can determine a cycle whose length is at most k+1 where k is the length of the shortest cycle in G. The results of the experiment show that the improved algorithm runs faster than the original one when the input graph meets some special features.

Hardness and methods to solve CLIQUE

This paper briefly reviews NP-hard optimization problems and theirin approximability. The hardness of solving CLIQUE problem isspecifically discussed. A dynamic-programming algorithm and its improvedversion for CLIQUE are reviewed and some additional analysis ispresented. The analysis implies that the improved algorithm, HEWN(hierarchical edge-weighted network), only provides a heuristic oruseful method, but cannot be called a polynomial algorithm.The paper briefly reviews NP-hard optimization problems and their inapproximability. The hardness of solving CLIQUE problem is specifically discussed. A dynamic-programming algorithm and its improved version for CLIQUE are reviewed and some additional analysis is presented. The analysis implies that the improved algorithm, HEWN (hierarchical edge-weighted network), only provides a heuristic or useful method, but cannot be called a polynomial algorithm.

The new method of reducing the NMR image's ringing artifacts by wavelet transform

It is difficult to reduce an NMR images ringing artifacts and obtain better images. This paper uses the method of dyadic wavelets and self-adaptive threshold to process the images that have the ringing artifacts. The test results prove that the method is effective and it can process the NMR images ringing artifacts. Finally the paper discusses using the fuzzy method.

The upper limit of the stability of delay-type cellular neural networks

This paper gives an improved sufficient condition of ensuring the stability of delayed cellular neural networks (DCNN) by means of the analysis of a correspondent Lyapunov function. This result improved the limit given by Civalleri and gives an optional upper limit of the stability of DCNN.

Shortest paths computation of graph by neural networks in real time

A new kind of neural networks on solving shortest paths problem is presented, and the stability of the neural networks is proved. For a directed or undirected graph, the proposed neural network is always convergent to its single equilibrium, so that the shortest paths between every pair of nodes of the oriented graph are produced. This paper makes a new study on solving the optimization but not NP-hard problems by neural networks.