39027321
A Fan Type Condition For Heavy Cycles in Weighted Graphs
Abstract. A weighted graph is a graph in which each edge e is assigned a non-negative number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges. The weighted degree dw(v) of a vertex v is the sum of the weights of the edges incident with v. In this paper, we prove the following result: Suppose G is a 2-connected weighted graph which satisfies the following conditions: 1. max{dw(x),dw(y)∣d(x,y)=2}≥c/2; 2. w(xz)=w(yz) for every vertex z∈N(x)∩N(y) with d(x,y)=2; 3. In every triangle T of G, either all edges of T have different weights or all edges of T have the same weight. Then G contains either a Hamilton cycle or a cycle of weight at least c. This generalizes a theorem of Fan on the existence of long cycles in unweighted graphs to weighted graphs. We also show we cannot omit Condition 2 or 3 in the above result.
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.
31017610
Structural Alignment of Pseudoknotted RNA
In this paper, we address the problem of discovering novel non-coding RNA (ncRNA) using primary sequence, and secondary structure conservation, focusing on ncRNA families with pseudo-knotted structures. Our main technical result is an efficient algorithm for computing an optimum structural alignment of an RNA sequence against a genomic substring. This algorithm finds two applications. First, by scanning a genome, we can identify novel (homologous) pseudoknotted ncRNA, and second, we can infer the secondary structure of the target aligned sequence. We test an implementation of our algorithm (Pal), and show that it has near-perfect behavior for predicting the structure of many known pseudoknots. Additionally, it can detect the true homologs with high sensitivity and specificity in controlled tests. We also use Pal to search entire viral genome and mouse genome for novel homologs of some viral, and eukaryotic pseudoknots respectively. In each case, we have found strong support for novel homologs.
5623352
Toward Application of Virtual Reality to Visualization of DT-MRI Volumes
We describe a virtual reality application for visualizing tensor-valued volume data acquired with diffusion tensor magnetic resonance imaging (DT-MRI). We have prototyped a virtual environment that displays geometric representations of the volumetric 2nd-order diffusion tensor data and are developing interaction and visualization techniques for two application areas: studying changes in white-matter structures after gamma-knife capsulotomy and pre-operative planning for brain tumor surgery.
17355776
A deep cut ellipsoid algorithm for convex programming: Theory and applications
This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided. Moreover, for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed. Finally some computational results of the deep and central cut version of the algorithm applied to a min—max stochastic queue location problem are reported.
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.
30170890
A new algorithm for generalized fractional programs
A new dual problem for convex generalized fractional programs with no duality gap is presented and it is shown how this dual problem can be efficiently solved using a parametric approach. The resulting algorithm can be seen as “dual” to the Dinkelbach-type algorithm for generalized fractional programs since it approximates the optimal objective value of the dual (primal) problem from below. Convergence results for this algorithm are derived and an easy condition to achieve superlinear convergence is also established. Moreover, under some additional assumptions the algorithm also recovers at the same time an optimal solution of the primal problem. We also consider a variant of this new algorithm, based on scaling the “dual” parametric function. The numerical results, in case of quadratic-linear ratios and linear constraints, show that the performance of the new algorithm and its scaled version is superior to that of the Dinkelbach-type algorithms. From the computational results it also appears that contrary to the primal approach, the “dual” approach is less influenced by scaling.