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.
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.
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.
1893178
An immersive virtual environment for DT-MRI volume visualization applications: a case study
We describe a virtual reality environment for visualizing tensor-valued volumetric datasets acquired with diffusion tensor magnetic resonance imaging (DT-MRI). We have prototyped a virtual environment that displays geometric representations of the volumetric second-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. Our feedback shows that compared to desktop displays, our system helps the user better interpret the large and complex geometric models, and facilitates communication among a group of users.
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.
5242506
A Model for Some Subcortical DTI Planar and Linear Anisotropy
Linear anisotropy, planar anisotropy and isotropy [1] are used as metrics for different kinds of diffusion in diffusion imaging. While linear anisotropy is reported to correlate to coherent neural fiber structures, the cause for planar anisotropy remains ambiguous. We hypothesize that overlapping linear structures and partial-volume averaging generate the planar anisotropy. We identify a subcortical region containing both linear and planar anisotropy in a human volumetric diffusion tensor image (DTI), propose a model of the anatomy and of the imaging process, and calculate simulated diffusion images of the anatomical model that qualitatively agree with the human DTI. Regions of planar anisotropy are common immediately beneath the cortex. Choosing one such region as representative, we model the anatomy with isotropic regions and linearly anisotropic structures. From the possibly overlapping model structures we simulate the diffusion imaging process, generating a series of diffusion weighted images (DWIs) of the anatomical structures. We then fit the DTI from these simulated DWIs and visualize it. The visualization agrees qualitatively with the visualization of a subcortical human DTI.
17630030
Prediction of Protein Complexes Based on Protein Interaction Data and Functional Annotation Data Using Kernel Methods
Prediction of protein complexes is a crucial problem in computational biology. The increasing amount of available genomic data can enhance the identification of protein complexes. Here we describe an approach for predicting protein complexes based on integration of protein-protein interaction (PPI) data and protein functional annotation data. The basic idea is that proteins in protein complexes often interact with each other and protein complexes exhibit high functional consistency/even multiple functional consistency. We create a protein-protein relationship network (PPRN) via a kernel-based integration of these two genomic data. Then we apply the MCODE algorithm on PPRN to detect network clusters as numerically determined protein complexes. We present the results of the approach to yeast Sacchromyces cerevisiae. Comparison with well-known experimentally derived complexes and results of other methods verifies the effectiveness of our approach.