23191981
Cycles of all lengths in arc-3-cyclic semicomplete digraphs
Abstract Let D be an arc-3-cyclic, semicomplete digraph and uv be an arc of D contained in a cycle of length r . If vu ∉ A ( D ) then the arc uv is contained in cycles of length h : 3 ⩽ h ⩽ r , or if δ + ( D ), δ − ( D ) ⩾ 3 then the arc uv is contained in cycles of length h : 6 ⩽ h ⩽ r . Also included in this paper is a very useful crossing arc theorem .
19566771
Nowhere-Zero 4-Flows and Cayley Graphs on Solvable Groups
We prove that every Cayley graph on a finite solvable group admits a nowhere-zero 4-flow. In particular, every cubic Cayley graph on a solvable group is 3-edge-colorable.
10940084
Hamiltonian Graphs with Large Neighborhood Unions
15500512
Real-time simulation of physically based on-surface flow
Although many papers have been published in the field of fluid simulation, little attention has been paid to on-surface flow involving wetting and stain transportation as well as erosion and deposition phenomena. In this paper, we introduce nonzero divergence in the mass equation of Navier–Stokes equations to simulate water penetration from on-surface flow into substrate material. Also, the volume of fluid method is adopted to track the free surface. With a computation of the actual amount of absorbed water we render the wetting effects with fully dry and fully wet texture images simultaneously. Using our model, the on-surface flow that accompanies water absorption can be simulated realistically in real time with OpenGL preview rendering. Experimental results illustrate that our model can be widely applied to solve various problems related to on-surface flow.
12158249
Bisingular maps on the sphere and the projective plane
Abstract A map is bisingular if each edge is either a loop or an isthmus (i.e., on the boundary of the same face). In this paper we study the number of rooted bisingular maps on the plane or projective plane and also we present formulae for such maps with up to three or more parameters: the root valency, the number of isthmus, the number of essential loops, and the number of planar loops.
36739594
Generating cycle spaces for graphs on surfaces with small genera
In this paper we investigate cycle base structures of a 2-(edge)-connected graph on surfaces with small genera and show that short cycles do generate the cycle spaces in the case of "small face-embeddings". Examples show that the conditions in our main results are best possible. As applications we find the exact formulae for the minimum lengths of cycle bases of some types of graphs which conclude several known results. Finally, we generalize those results for graphs embedded on general orientable surfaces.
14532857
Projecting registration error for accurate registration of overlapping range images
Abstract In this paper, we propose a novel algorithm for the automatic registration of two overlapping range images. Since it is relatively difficult to compare the registration errors of different point matches, we project them onto a virtual image plane for more accurate comparison using the classical pin-hole perspective projection camera model. While the traditional ICP algorithm is more interested in the points in the second image close to the sphere centred at the transformed point, the novel algorithm is more interested in the points in the second image as collinear as possible to the transformed point. The novel algorithm then extracts useful information from both the registration error and projected error histograms for the elimination of false matches without any feature extraction, image segmentation or the requirement of motion estimation from outliers corrupted data and, thus, has an advantage of easy implementation. A comparative study based on real images captured under typical imaging conditions has shown that the novel algorithm produces good registration results.
15077137
Modeling nonlinearity in dilution design microarray data
MOTIVATION
Dilution design (Mixed tissue RNA) has been utilized by some researchers to evaluate and assess the performance of multiple microarray platforms. Current microarray data analysis approaches assume that the quantified signal intensities are linearly related to the expression of the corresponding genes in the sample. However, there are sources of nonlinearity in microarray expression measurements. Such nonlinearity study in the expressions of the RNA mixtures provides a new way to analyze gene expression data, and we argue that the nonlinearity can reveal novel information for microarray data analysis. Therefore, we proposed a statistical model, called proportion model, which is based on the linear regression analysis. To approximately quantify the nonlinearity in the dilution design, a new calibration, beta ratio (BR) was derived from the proportion model. Furthermore, a new adjusted fold change (adj-FC) was proposed to predict the true FC without nonlinearity, in particular for large FC.


RESULTS
We applied our method to one microarray dilution dataset. The experimental results indicated that, to some extent, there are global biases comparing with the linear assumption for the significant genes. Further analysis of those highly expressed genes with significant nonlinearity revealed some promising results, e.g. 'poison' effect was discovered for some genes in RNA mixtures. The adj-FCs of those genes with 'poison' effect, indicate that the nonlinearity can be also caused by the inherent feature of the genes besides signal noise and technical variation. Moreover, when percentage of overlapping genes (POG) was used as a cross-platform consistency measure, adj-FC outperformed simple fold change to show that Affymetrix and Illumina platforms are consistent.


AVAILABILITY
The R codes which implements all described methods, and some Supplementary material, are freely available from http://www.utdallas.edu/~ying.liu/BetaRatio.htm