19232033
Protein Threading by Linear Programming: Theoretical Analysis and Computational Results
In a previous paper (Xu, Li, Kim, and Xu, Journal of Bioinformatics and Computational Biology, vol. 1, no. 1, pp. 95–117, 2003), we have used an integer programming approach to implement a protein threading program RAPTOR for protein 3D structure prediction, based on the threading model treating pairwise contacts rigorously and allowing variable gaps. We have solved the integer program by the canonical branch-and-bound method. In this paper we present a branch-and-cut method, a careful theoretical analysis of our formulation and why our approach is so effective. The result of cutting plane analysis is that two types of well-known cuts for this problem are already implied in the constraint set, which provides us some intuition that our formulation would be very effective. Experimental results show that for about 99 percent of real threading instances, the linear relaxations of their integer programs solve to integral optimal solutions directly. For the rest one percent of real instances, the integral solutions can be obtained with only several branch nodes. Experimental results also show that no special template or sequence features result in more possibilities of fractional solutions. This indicates that extra effort to seek for cutting planes to strengthen the existing formulation is unnecessary.
17686330
Protein Threading by Linear Programming
Protein three-dimensional structure prediction through threading approach has been extensively studied and various models and algorithms have been proposed. In order to further explore ways to improve accuracy and efficiency of the threading process, this paper investigates the effectiveness of a new method: protein threading via linear programming. Based on the contact map model of protein 3D structure, we formulate the protein threading problem as a large scale integer programming problem, then relax to a linear programming problem, and finally solve the integer program by a branch-and-bound method. The final solution is optimal with respect to energy functions incorporating pairwise interaction and allowing variable gaps. The algorithm has been implemented as software package RAPTOR--RApid Protein Threading predictOR. Experimental results for fold recognition show that RAPTOR significantly outperforms other programs at the fold similarity level. The RAPTOR webserver is at http://www.cs.uwaterloo.ca/-j3xu/RAPTOR_form.htm.
9688726
Motion Editing in 3D Video Database
As the next generation of media, 3D video is attracting increased attention. 3D video is a sequence of three dimensional mesh models, captured and generated for a real dynamic object. In this paper, we present a simple framework of motion editing in 3D video database to re-use 3D video data. Our system is composed of two modules. In the first module, a motion database is automatically set up from original 3D video sequences off-line by analyzing the feature vectors of each frame. It is observed that our original 3D video sequences have a two-level temporal structure. A fine-to-coarse method is proposed to extract such a structure. 3D video is segmented into the fine-level structure by a three reference frame strategy and then is clustered into the coarse-level structure. In the second module, users can synthesize the motions to edit a new 3D video sequence online. A cost function is optimized to transit between two motions with the users' requirements. All the algorithms in the system are based on the analysis in feature vector space and the edited 3D video sequence is played using OpenGL.
17909513
Determining an optimal penetration among weighted regions in two and three dimensions
We present efficient algorithms for solving the problem of computing an optimal penetration (a ray or a semi-ray) among weighted regions in 2-D and 3-D spaces. This problem finds applications in several areas, such as radiation therapy, geological exploration, and environmental engineering. Our algorithms are based on a combination of geometric techniques and optimization methods. Our geometric analysis shows that the d-D (d = 2, 3) optimal penetration problem can be reduced to solving O(n2(d−1)) instances of certain special types of non-linear optimization problems, where n is the total number of vertices of the regions. We also give implementation results of our 2-D algorithms.
117096759
Determining an Optimal Penetration Among Weighted Regions in Two and Three Dimensions
We present efficient algorithms for solving the problem of computing an optimal penetration (a ray or a semi-ray) among weighted regions in 2-D and 3-D spaces. This problem finds applications in several areas, such as radiation therapy, geological exploration, and environmental engineering. Our algorithms are based on a combination of geometric techniques and optimization methods. Our geometric analysis shows that the d-D (d = 2, 3) optimal penetration problem can be reduced to solving O(n2(d−1)) instances of certain special types of non-linear optimization problems, where n is the total number of vertices of the regions. We also give implementation results of our 2-D algorithms.
14580037
An architectural framework for providing reliability and security support
This paper explores hardware-implemented error-detection and security mechanisms embedded as modules in a hardware-level framework called the reliability and security engine (RSE), which is implemented as an integral part of a modern microprocessor. The RSE interacts with the processor through an input/output interface. The CHECK instruction, a special extension of the instruction set architecture of the processor, is the interface of the application with the RSE. The detection mechanisms described here in detail are: (I) the memory layout randomization (MLR) module, which randomizes the memory layout of a process in order to foil attackers who assume a fixed system layout, (2) the data dependency tracking (DDT) module, which tracks the dependencies among threads of a process and maintains checkpoints of shared memory pages in order to rollback the threads when an offending (potentially malicious) thread is terminated, and (3) the instruction checker module (ICM), which checks an instruction for its validity or the control-flow of the program just as the instruction enters the pipeline for execution. Performance simulations for the studied modules indicate low overhead of the proposed solutions.
11486473
Circumference of Graphs with Bounded Degree
Karger, Motwani, and Ramkumar Algorithmica, 18 (1997), pp. 82--98] have shown that there is no constant approximation algorithm to find a longest cycle in a Hamiltonian graph, and they conjectured that this is the case even for graphs with bounded degree. On the other hand, Feder, Motwani, and Subi [SIAM J. Comput., 31 (2002), pp. 1596--1607] have shown that there is a polynomial time algorithm for finding a cycle of length $n^{\log_32}$ in a 3-connected cubic n-vertex graph. In this paper, we show that if G is a 3-connected n-vertex graph with maximum degree at most d, then one can find, in O(n3) time, a cycle in G of length at least $\Omega(n^{\log_b2})$, where $b=2(d-1)^2+1$.