11005224
A phase transition for avoiding a giant component
Let c be a constant and (e1, f1), (e2, f2), . . . , (ecn, fcn) be a sequence of ordered pairs of edges from the complete graph Kn chosen uniformly and independently at random. We prove that there exists a constant c2 such that if c > c2 then whp every graph which contains at least one edge from each ordered pair (ei, fi) has a component of size Ω(n) and if c < c2 then whp there is a graph containing at least one edge from each pair that has no component with more than O ( n1−2 ) vertices, where 2 is a constant that depends on c2− c. The constant c2 is roughly 0.97677.
15935373
Random Matchings Which Induce Hamilton Cycles and Hamiltonian Decompositions of Random Regular Graphs
Select four perfect matchings of 2n vertices, independently at random. We find the asymptotic probability that each of the first and second matchings forms a Hamilton cycle with each of the third and fourth. This is generalised to embrace any fixed number of perfect matchings, where a prescribed set of pairs of matchings must each produce Hamilton cycles (with suitable restrictions on the prescribed set of pairs). We also show how the result with four matchings implies that a random d-regular graph for fixed even d?4 asymptotically almost surely decomposes into d/2 Hamilton cycles. This completes a general result on the edge-decomposition of a random regular graph into regular spanning subgraphs of given degrees together with Hamilton cycles and verifies conjectures of Janson and of Robinson and Wormald.
18486242
Perfect matchings in random uniform hypergraphs
Let ℋk(n, p) be the random k-uniform hypergraph on V = [n] with edge probability p. Motivated by a theorem of Erdős and Renyi 7 regarding when a random graph G(n, p) = ℋ2(n, p) has a perfect matching, the following conjecture may be raised. (See J. Schmidt and E. Shamir 16 for a weaker version.) Conjecture. Let k|n for fixed k ≥ 3, and the expected degree d(n, p) = p(). Then 
 
 
 
 
 
 
(Erdős and Renyi 7 proved this for G(n, p).) Assuming d(n, p)/n1/2 ∞, Schmidt and Shamir 16 were able to prove that ℋk(n, p) contains a perfect matching with probability 1 − o(1). Frieze and Janson 8 showed that a weaker condition d(n, p)/n1/3 ∞ was enough. In this paper, we further weaken the condition to 
 
 
 
 
 
 
A condition for a similar problem about a perfect triangle packing of G(n, p) is also obtained. A perfect triangle packing of a graph is a collection of vertex disjoint triangles whose union is the entire vertex set. Improving a condition p ≥ cn−2/3+1/15 of Krivelevich 12, it is shown that if 3|n and p ≫ n−2/3+1/18, then 
 
 
 
 
 
 
© 2003 Wiley Periodicals, Inc. Random Struct. Alg., 23: 111–132, 2003
14570877
Genetic Elevator Group Control
In a tall building with multiple elevators, it is a notoriously di cult task to control the elevators in the most e cient manner [1].The system proposed in this paper contains two key ideas. First, it continuously generates dispatch functions by adaptation to changes in passenger tra c. Second, it tries to reduce passengers' waiting time by multiple elevator allocation when it is expected that one elevator cannot serve all the passengers for a hall call at a oor.
10981925
Geometrical Learning Algorithm for Multilayer Neural Networks in a Binary Field
A geometrical expansion learning algorithm for multilayer neural networks using unipolar binary neurons with integer connection weights, which guarantees convergence for any Boolean function, is introduced. Neurons in the hidden layer develop as necessary without supervision. In addition, the computational amount is much less than that of the backpropagation algorithm. >
1278377
A Tree Obscured By Vines: Horizontal Gene Transfer and the Median Tree Method of Estimating Species Phylogeny
A phylogeny is a tree graph representation of genealogical relationships between biological objects. It is of general interest to estimate the phylogeny of whole organisms (species trees) using bio-molecular sequences. When multiple sequences are available for each organism such as with whole genome data, individual phylogenies estimated by each molecule (gene trees) may not be concordant. The lack of concordance may be due to actual biological mechanisms such as horizontal transfer of the molecules. Here, we present a new phylogeny estimation method designed to estimate the species tree despite such horizontal transfer. It uses the idea that horizontal transfer distorts distance relationships between pairs of species but a median estimate of the distances is robust to such distortions. We demonstrate the utility of our method using a simulation study.
3197241
Explicit construction of families of LDPC codes with no 4-cycles
Low-density parity-check (LDPC) codes are serious contenders to turbo codes in terms of decoding performance. One of the main problems is to give an explicit construction of such codes whose Tanner graphs have known girth. For a prime power q and m/spl ges/2, Lazebnik and Ustimenko construct a q-regular bipartite graph D(m,q) on 2q/sup m/ vertices, which has girth at least 2/spl lceil/m/2/spl rceil/+4. We regard these graphs as Tanner graphs of binary codes LU(m,q). We can determine the dimension and minimum weight of LU(2,q), and show that the weight of its minimum stopping set is at least q+2 for q odd and exactly q+2 for q even. We know that D(2,q) has girth 6 and diameter 4, whereas D(3,q) has girth 8 and diameter 6. We prove that for an odd prime p, LU(3,p) is a [p/sup 3/,k] code with k/spl ges/(p/sup 3/-2p/sup 2/+3p-2)/2. We show that the minimum weight and the weight of the minimum stopping set of LU(3,q) are at least 2q and they are exactly 2q for many LU(3,q) codes. We find some interesting LDPC codes by our partial row construction. We also give simulation results for some of our codes.
701944
Simulation-Based Security Testing for Continuity of Essential Service
One of the most important characteristic of essential service in the computer network is its continuity. If the continuity of essential service is not guaranteed, it causes a big problem in normal operation of computer network. In our research, we suggest the simulation-based security testing for the continuity of essential service. Especially, the security testing sequence and Experimental Frame is designed to get indexes related to the continuity of essential service. We choose three testing indexes that represent the degree of service continuity and testing methods to get those indexes. Also, to explain the indexes and the testing methods, two testing examples are presented.