40360391
On the number of rooted c-nets
36530209
Determination of the star valency of a graph
The star valency of a graph G is the minimum, over all star decompositions π, of the maximum number of elements in π incident with a vertex. The maximum average degree of G, denoted by dmax-ave(G), is the maximum average degree of all subgraphs of G. In this paper, we prove that the star valency of G is either ⌈dmax-ave(G)/2⌉ or ⌈dmax-ave(G)/2⌉ + 1, and provide a polynomial time algorithm for determining the star valency of a graph.
43124802
On the Isomorphisms of Cayley Graphs of Abelian Groups
Let G be a finite group, S a subset of G\{1}, and let Cay (G, S) denote the Cayley digraph of G with respect to S. If, for any subset T of G\{1}, Cay(G, S) ≅ Cay(G, T) implies that Sα = T for some α ∈ Aut(G), then S is called a CI-subset. The group G is called a CIM-group if for any minimal generating subset S of G, S ∪ S-1 is a CI-subset. In this paper, CIM-abelian groups are characterized.
27650319
Generalized Bicycles
Let G = (V,E) be a graph with IZ vertices, and let A4 be a (left) module over a principal ideal domain D. Let Wo(A4) and WI(M) denote the modules of all vertex and edge weightings over M, respectively. An incidence weighting q of G is a weighting of each incident vertex-edge pair (u,e) with an element of D. Now consider an orientation of the edges of G. Let 6, denote the linear operator from We(M) to WI(M) given by 6,(w)(e) = q(u,e)w(u) yl(a,e)w(a), where e E E and u and 1: denote the tail and head of e, respectively. An v-cocycle is a weighting c E WI(M), such that c = 6(w) for some w c We(M). An q-bicycle is an q-cocycle that is also a cycle (ordinary bicycles are obtained when q E 1). Let B,(M) denote the module of all vertex weightings b E We(M), such that 6,(b) is an q-bicycle. For T a spanning tree rooted at vertex c, let q(T) denote the product of q(u,e) over all the edges e of T, where u denotes the end vertex of e that is further from u in T. The q-complexity Z~ of G is the vertex weighting over D, such that 74(c’) is the sum of q(T) over all spanning trees T rooted at t’. In this paper, we show that B,(M) ” M if, and only if 7,,m is nonzero for every nonzero m t M. Further if B,(M) 2 M then B,(M) = { z,,m : m E M}. As special cases of this formula, we obtain results about bicycles, balanced vertex weightings, resistive and leaky electrical networks, handicap ranking of tournaments, and Markov chains. The gcd q-complexity t,, is the greatest common divisor of (7411) : u E V}. We show that t, has a factorization t, = tl t2 t+l, unique up to multiplication by units of D, such that t,+l divides t, and such that for every module M over D, B,(M) is isomorphic to the direct sum of M and the submodules M(t,) = {m E A4 : t,m = 0}, i = 1,. , n 1. The latter formula generalizes the bicycle isomorphism formula given in Berman (1986).
43519756
The Number of Loopless 4-Regular Maps on the Projective Plane
In this paper rooted loopless (near) 4-regular maps on surfaces such as the sphere and the projective plane are counted and exact formulae with up to three or four parameters for such maps are given. Several classical results on regular maps and one-faced maps are deduced.
39617215
Counting rooted near-triangulations on the sphere
This paper provides the results on the enumerations of rooted simple outerplanar maps, rooted outerplanar near-triangulations, rooted 2-connected near-triangulations, rooted strict 2-connected near-triangulations and rooted simple 2-connected near-triangulations. The answer to an open problem proposed by one of the authors is also provided.
34451404
The enumeration of near-perfect matchings of factor-critical graphs
Abstract A matching of a graph is a near-perfect matching if it covers all but one vertex. A connected graph G is said to be factor-critical if G − v has perfect matchings for every vertex v of G. In this paper, the enumeration problems for near-perfect matchings in special factor-critical graphs are solved. From this, the exact values of the number of perfect matchings in special bicritical graphs are obtained.
737114
Building a Scalable Bipartite P2P Overlay Network
The peer-to-peer (P2P) model, being widely adopted in today's Internet computing, suffers from the problem of topology mismatch between the overlay networks and the underlying physical network. Traditional topology optimization techniques identify physically closer nodes to connect as overlay neighbors, but could significantly shrink the search scope. Efforts have been made to address the mismatch problem without sacrificing the search scope, but they either need time synchronization among peers or have a low convergent speed. In this paper, we propose a scalable bipartite overlay (SBO) scheme to optimize the overlay topology by identifying and replacing the mismatched connections. In SBO, we employ an efficient strategy for distributing optimization tasks in peers with different colors. We conducted comprehensive simulations to evaluate this design. The results show that SBO achieves approximately 85 percent of reduction on traffic cost and about 60 percent of reduction on query response time. Our comparisons with previous approaches to address the topology mismatch problem have shown that SBO can achieve a fast convergent speed, without the need of time synchronization among peers.
6732585
Systematic Derivation of Incremental Programs
A systematic approach is given for deriving incremental programs from non-incremental programs written in a standard functional programming language. We exploit a number of program analysis and transformation techniques and domain-specific knowledge, centered around effective utilization of caching, in order to provide a degree of incrementality not otherwise achievable by a generic incremental evaluator.
37420469
Getting most out of evolutionary approaches
Evolutionary algorithms (EAs) have been widely used in evolvable hardware. The very term, evolvable hardware, reflects the importance and omnitude of EAs in this field. However, EAs have primarily been used as an optimisation or search tool, which can explore a large and complex space. While success has been demonstrated by EAs in exploring unconventional designs that are hard to reach by human experts, it is interesting to ask the question whether we have fully used all the potentialities of EAs. We argue in this paper that there is rich information in a population which can and should be exploited. The classical approach of evolving the best individual in a population may not be the best one. A truly population-based approach that emphasizes population rather than the best individual can often bring in several important benefits to evolvable hardware, including efficiency, accuracy, adaptiveness, and fault-tolerance.
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