The mu-way intersection problem for m-cycle systems

An m-cycle system of order upsilon is a partition of the edge-set of a complete graph of order upsilon into m-cycles. The mu -way intersection problem for m-cycle systems involves taking mu systems, based on the same vertex set, and determining the possible number of cycles which can be common to all mu systems. General results for arbitrary m are obtained, and detailed intersection values for (mu, m) = (3, 4), (4, 5),(4, 6), (4, 7), (8, 8), (8, 9). (For the case (mu, m)= (2, m), see Billington (J. Combin. Des. 1 (1993) 435); for the case (Cc,m)=(3,3), see Milici and Quattrochi (Ars Combin. A 24 (1987) 175. (C) 2001 Elsevier Science B.V. All rights reserved.

The metamorphosis of lambda-fold 4-wheel systems into lambda-fold 4-cycle systems

A 4-wheel is a simple graph on 5 vertices with 8 edges, formed by taking a 4-cycle and joining a fifth vertex (the centre of the 4-wheel) to each of the other four vertices. A lambda -fold 4-wheel system of order n is an edge-disjoint decomposition of the complete multigraph lambdaK(n) into 4-wheels. Here, with five isolated possible exceptions when lambda = 2, we give necessary and sufficient conditions for a lambda -fold 4-wheel system of order n to be transformed into a lambda -fold Ccyde system of order n by removing the centre vertex from each 4-wheel, and its four adjacent edges (retaining the 4-cycle wheel rim), and reassembling these edges adjacent to wheel centres into 4-cycles.

Quantitative and qualitative influences of tapasin on the class I peptide repertoire

Tapasin is critical for efficient loading and surface expression of most HLA class I molecules. The high level surface expression of HLA-B*2705 on tapasin-deficient 721.220 cells allowed the influence of this chaperone on peptide repertoire to be examined. Comparison of peptides bound to HLA-B*2705 expressed on tapasin-deficient and -proficient cells by mass spectrometry revealed an overall reduction in the recovery of B*2705-bound peptides isolated from tapasin-deficient cells despite similar yields of B27 heavy chain and beta (2)-microglobulin. This indicated that a proportion of suboptimal ligands were associated with B27, and they were lost during the purification process. Notwithstanding this failure to recover these suboptimal peptides, there was substantial overlap in the repertoire and biochemical properties of peptides recovered from B27 complexes derived from tapasin-positive and -negative cells. Although many peptides were preferentially or uniquely isolated from B*2705 in tapasin-positive cells, a number of species were preferentially recovered in the absence of tapasin, and some of these peptide ligands have been sequenced. In general, these ligands did not exhibit exceptional binding affinity, and we invoke an argument based on lumenal availability and affinity to explain their tapasin independence. The differential display of peptides in tapasin-negative and -positive cells was also apparent in the reactivity of peptide-sensitive alloreactive CTL raised against tapasin-positive and -negative targets, demonstrating the functional relevance of the biochemical observation of changes in peptide repertoire in the tapasin-deficient APC. Overall, the data reveal that tapasin quantitatively and qualitatively influences ligand selection by class I molecules.

Fitting mixtures of Kent distributions to aid in joint set identification

When examining a rock mass, joint sets and their orientations can play a significant role with regard to how the rock mass will behave. To identify joint sets present in the rock mass, the orientation of individual fracture planer can be measured on exposed rock faces and the resulting data can be examined for heterogeneity. In this article, the expectation-maximization algorithm is used to lit mixtures of Kent component distributions to the fracture data to aid in the identification of joint sets. An additional uniform component is also included in the model to accommodate the noise present in the data.

Step size control for efficient discrete element simulation

The step size determines the accuracy of a discrete element simulation. The position and velocity updating calculation uses a pre-calculated table and hence the control of step size can not use the integration formulas for step size control. A step size control scheme for use with the table driven velocity and position calculation uses the difference between the calculation result from one big step and that from two small steps. This variable time step size method chooses the suitable time step size for each particle at each step automatically according to the conditions. Simulation using fixed time step method is compared with that of using variable time step method. The difference in computation time for the same accuracy using a variable step size (compared to the fixed step) depends on the particular problem. For a simple test case the times are roughly similar. However, the variable step size gives the required accuracy on the first run. A fixed step size may require several runs to check the simulation accuracy or a conservative step size that results in longer run times. (C) 2001 Elsevier Science Ltd. All rights reserved.

Theory of pseudomodes in quantum optical processes

This paper deals with non-Markovian behavior in atomic systems coupled to a structured reservoir of quantum electromagnetic field modes, with particular relevance to atoms interacting with the field in high-Q cavities or photonic band-gap materials. In cases such as the former, we show that the pseudomode theory for single-quantum reservoir excitations can be obtained by applying the Fano diagonalization method to a system in which the atomic transitions are coupled to a discrete set of (cavity) quasimodes, which in turn are coupled to a continuum set of (external) quasimodes with slowly varying coupling constants and continuum mode density. Each pseudomode can be identified with a discrete quasimode, which gives structure to the actual reservoir of true modes via the expressions for the equivalent atom-true mode coupling constants. The quasimode theory enables cases of multiple excitation of the reservoir to now be treated via Markovian master equations for the atom-discrete quasimode system. Applications of the theory to one, two, and many discrete quasimodes are made. For a simple photonic band-gap model, where the reservoir structure is associated with the true mode density rather than the coupling constants, the single quantum excitation case appears to be equivalent to a case with two discrete quasimodes.

Non-Markovian quantum optical processes and pseudomodes

Non-Markovian behaviour in atomic systems coupled to a structured reservoir of quantum EM field modes, such as in high Q cavities, is treated using a quasimode description, and the pseudo mode theory for single quantum reservoir excitations is obtained via Fano diagonalisation. The atomic transitions are coupled to a discrete set of (cavity) quasimodes, which are also coupled to a continuum set of (external) quasimodes with slowly varying coupling constants. Each pseudomode corresponds to a cavity quasimode, and the original reservoir structure is obtained in expressions for the equivalent atom-true mode coupling constants. Cases of multiple excitation of the reservoir are now treatable via Markovian master equations for the atom-discrete quasimode system.

Demography of bridled nailtail wallabies translocated to the edge of their former range from captive and wild stock

Despite numerous, generally unsuccessful attempts to reintroduce threatened Australian mammals, the factors leading to their failure have not been fully clarified, although predator control would appear to be of paramount importance. An experimental approach was taken in attempting to establish a population of bridled nailtail wallabies ih an area of apparently suitable habitat and low fox density, but on the edge of the species' former range. The 133 wallabies released since late 1996 comprised four groups captive-bred animals, wild caught from the single remaining wild population, animals that were captive bred and acclimatised at the translocation site in a 10 ha predator-proof enclosure, and animals which had been bred in the enclosure. Survival was highest in those bred in the enclosure and highly variable among captive-bred animals. Survival estimates for wild recruits suggested the population would maintain a positive rate of increase under prevailing environmental conditions. Spotlighting surveys suggested the population had increased to approximately 400 animals by late 1999. Above average rainfall during 1996-1999 and no apparent predation suggests caution in describing the translocation as a success. Ongoing monitoring is critical, because it A uncertain ho v the population will cope with drought and inevitable predation events, and whether the population will expand and persist outside of limited preferred habitat. (C) 2001 Elsevier Science Ltd. All rights reserved.