16330147
A Primal-Dual Decomposition Algorithm for Multistage Stochastic Convex Programming
This paper presents a new and high performance solution method for multistage stochastic convex programming. Stochastic programming is a quantitative tool developed in the field of optimization to cope with the problem of decision-making under uncertainty. Among others, stochastic programming has found many applications in finance, such as asset-liability and bond-portfolio management. However, many stochastic programming applications still remain computationally intractable because of their overwhelming dimensionality. In this paper we propose a new decomposition algorithm for multistage stochastic programming with a convex objective and stochastic recourse matrices, based on the path-following interior point method combined with the homogeneous self-dual embedding technique. Our preliminary numerical experiments show that this approach is very promising in many ways for solving generic multistage stochastic programming, including its superiority in terms of numerical efficiency, as well as the flexibility in testing and analyzing the model.
3196759
Low-complexity algorithms for sequencing jobs with a fixed number of job-classes
In this paper we consider the problem of scheduling n jobs such that makespan is minimized. It is assumed that the jobs can be divided into K job-classes and that the change-over time between two consecutive jobs depends on the job-classes to which the two jobs belong. In this setting, we discuss the one machine scheduling problem with arbitrary processing times and the parallel machines scheduling problem with identical processing times. In both cases it is assumed that the number of job-classes K is fixed. By using an appropriate integer programming formulation with a fixed number of variables and constraints, it is shown that these two problems are solvable in polynomial time. For the one machine scheduling case it is shown that the complexity of our algorithm is linear in the number of jobs n. Moreover, if the problem is encoded according to the high multiplicity model of Hochbaum and Shamir, the time complexity of the algorithm is shown to be a polynomial in log n. In the parallel machine scheduling case, it is shown that if the number of machines is fixed the same results hold.
96314
On the long-step path-following method for semidefinite programming
It has been shown in various recent research reports that the analysis of short-step primal-dual path following algorithms for linear programming can be nicely generalized to semidefinite programming. However, the analysis of long-step path-following algorithms for semidefinite programming appeared to be less straightforward. For such an algorithm, Monteiro (1997) obtained an O(n^1^.^5log(1/@e)) iteration bound for obtaining an @e-optimal solution, where n is the order of the semidefinite decision variable. In this paper, we propose to use a different search direction, viz. the so-called V-space direction. It is shown that this modification reduces the iteration complexity to O(nlog(1/@e)). Independently, Monteiro and Y. Zhang obtained a similar result using Nesterov-Todd directions.
5764216
Visualizing Diffusion Tensor MR Images Using Streamtubes and Streamsurfaces
We present a new method for visualizing 3D volumetric diffusion tensor MR images. We distinguish between linear anisotropy and planar anisotropy and represent values in the two regimes using streamtubes and streamsurfaces, respectively. Streamtubes represent structures with primarily linear diffusion, typically fiber tracts; streamtube direction correlates with tract orientation. The cross-sectional shape and color of each streamtube represent additional information from the diffusion tensor at each point. Streamsurfaces represent structures in which diffusion is primarily planar. Our algorithm chooses a very small representative subset of the streamtubes and streamsurfaces for display. We describe the set of metrics used for the culling process, which reduces visual clutter and improves interactivity. We also generate anatomical landmarks to identify the locations of such structures as the eyes, skull surface, and ventricles. The final models are complex surface geometries that can be imported into many interactive graphics software environments. We describe a virtual environment to interact with these models. Expert feedback from doctors studying changes in white-matter structures after gamma-knife capsulotomy and preoperative planning for brain tumor surgery shows that streamtubes correlate well with major neural structures, the 2D section and geometric landmarks are important in understanding the visualization, and the stereo and interactivity from the virtual environment aid in understanding the complex geometric models.
8339552
A sequence-based filtering method for ncRNA identification and its application to searching for riboswitch elements
MOTIVATION
Recent studies have uncovered an "RNA world", in which non coding RNA (ncRNA) sequences play a central role in the regulation of gene expression. Computational studies on ncRNA have been directed toward developing detection methods for ncRNAs. State-of-the-art methods for the problem, like covariance models, suffer from high computational cost, underscoring the need for efficient filtering approaches that can identify promising sequence segments and speedup the detection process.


RESULTS
In this paper we make several contributions toward this goal. First, we formalize the concept of a filter and provide figures of merit that allow comparison between filters. Second, we design efficient sequence based filters that dominate the current state-of-the-art HMM filters. Third, we provide a new formulation of the covariance model that allows speeding up RNA alignment. We demonstrate the power of our approach on both synthetic data and real bacterial genomes. We then apply our algorithm to the detection of novel riboswitch elements from the whole bacterial and archaeal genomes. Our results point to a number of novel riboswitch candidates, and include genomes that were not previously known to contain riboswitches.


AVAILABILITY
The program is available upon request from the authors.
1154359
Scattering number in graphs
The scattering number of a noncomplete connected graph G is defined by s(G) = max{ω(G − X) − |X|: X ⊂ V(G), ω(G − X) ≥ 2}, where ω(G − X) denotes the number of components of the graph G − X. In this paper, we show that this parameter can be used to measure the vulnerability of a graph. To some extent, it represents a trade-off between the amount of work done to damage the network and how badly the network is damaged. The relationship between the scattering number and some other parameters of a graph is discussed. Furthermore, we give the Nordhaus–Gaddum-type result for scattering number. © 2001 John Wiley & Sons, Inc.
1204298
An implicit degree condition for long cycles in 2-connected graphs
Abstract Let id ( v ) denote the implicit degree of a vertex v . In this work we prove that: If G is a 2-connected graph with max { id ( u ) , id ( v ) } ≥ c / 2 for each pair of nonadjacent vertices u and v that are vertices of an induced claw or an induced modified claw of G , then G contains either a Hamilton cycle or a cycle of length at least c . This extends several previous results on the existence of long cycles in graphs.
11213421
Consensus Folding of Unaligned RNA Sequences Revisited
As one of the earliest problems in computational biology, RNA secondary structure prediction (sometimes referred to as "RNA folding") problem has attracted attention again, thanks to the recent discoveries of many novel non-coding RNA molecules. The two common approaches to this problem are de novo prediction of RNA secondary structure based on energy minimization and the consensus folding approach (computing the common secondary structure for a set of unaligned RNA sequences). Consensus folding algorithms work well when the correct seed alignment is part of the input to the problem. However, seed alignment itself is a challenging problem for diverged RNA families. In this paper, we propose a novel framework to predict the common secondary structure for unaligned RNA sequences. By matching putative stacks in RNA sequences, we make use of both primary sequence information and thermodynamic stability for prediction at the same time. We show that our method can predict the correct common RNA secondary structures even when we are given only a limited number of unaligned RNA sequences, and it outperforms current algorithms in sensitivity and accuracy.