Threshold effects for two pathogens spreading on a network

Diseases spread through host populations over the networks of contacts between individuals, and a number of results about this process have been derived in recent years by exploiting connections between epidemic processes and bond percolation on networks. Here we investigate the case of two pathogens in a single population, which has been the subject of recent interest among epidemiologists. We demonstrate that two pathogens competing for the same hosts can both spread through a population only for intermediate values of the bond occupation probability that lie above the classic epidemic threshold and below a second higher value, which we call the coexistence threshold, corresponding to a distinct topological phase transition in networked systems.Comment: 5 pages, 2 figure

Percolation in the Sherrington-Kirkpatrick Spin Glass

We present extended versions and give detailed proofs of results concerning percolation (using various sets of two-replica bond occupation variables) in Sherrington-Kirkpatrick spin glasses (with zero external field) that were first given in an earlier paper by the same authors. We also explain how ultrametricity is manifested by the densities of large percolating clusters. Our main theorems concern the connection between these densities and the usual spin overlap distribution. Their corollaries are that the ordered spin glass phase is characterized by a unique percolating cluster of maximal density (normally coexisting with a second cluster of nonzero but lower density). The proofs involve comparison inequalities between SK multireplica bond occupation variables and the independent variables of standard Erdos-Renyi random graphs.Comment: 18 page

Random graphs with clustering

We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be neighbors of one another. We show how standard random graph models can be generalized to incorporate clustering and give exact solutions for various properties of the resulting networks, including sizes of network components, size of the giant component if there is one, position of the phase transition at which the giant component forms, and position of the phase transition for percolation on the network.Comment: 5 pages, 2 figure

Identity and Search in Social Networks

Social networks have the surprising property of being "searchable": Ordinary people are capable of directing messages through their network of acquaintances to reach a specific but distant target person in only a few steps. We present a model that offers an explanation of social network searchability in terms of recognizable personal identities: sets of characteristics measured along a number of social dimensions. Our model defines a class of searchable networks and a method for searching them that may be applicable to many network search problems, including the location of data files in peer-to-peer networks, pages on the World Wide Web, and information in distributed databases.Comment: 4 page, 3 figures, revte

Efficient configurational-bias Monte-Carlo simulations of chain molecules with `swarms' of trial configurations

Proposed here is a dynamic Monte-Carlo algorithm that is efficient in simulating dense systems of long flexible chain molecules. It expands on the configurational-bias Monte-Carlo method through the simultaneous generation of a large set of trial configurations. This process is directed by attempting to terminate unfinished chains with a low statistical weight, and replacing these chains with clones (enrichments) of stronger chains. The efficiency of the resulting method is explored by simulating dense polymer brushes. A gain in efficiency of at least three orders of magnitude is observed with respect to the configurational-bias approach, and almost one order of magnitude with respect to recoil-growth Monte-Carlo. Furthermore, the inclusion of `waste recycling' is observed to be a powerful method for extracting meaningful statistics from the discarded configurations

Hand pollination to increase seed-set of red helleborine Cephalanthera rubra in the Chiltern Hills, Buckinghamshire, England

In 2007 and in previous years, as part of ongoing attempts to improve red helleborine Cephalanthera rubra seed-set, hand pollination of florets has been undertaken at a small colony of this species in Buckinghamshire, southern England. Natural pollination rarely occurs (one mature pod recorded in 10 years) at this site. In 2007, hand pollination resulted in the production of four seed pods, of which one withered and died. Upon ripening, the three remaining pods were removed for attempted micropropagation of the seeds. Ongoing conservation management has probably benefited the solitary bee Chelostoma campanularum which now appears fairly plentiful at the site, but despite the presence of this red helleborine flower visitor, natural pollination remains virtually unrecorded at this locality; field observations suggest that C.campanularum is in fact probably not large enough to act as an effective red helleborine pollinator as it can slip in and out of the flowers without removing the pollinia, unlike it larger relative C.fuliginosum, absent from the UK but which is a known pollinator of red helleborine in continental Europe

Variability in spawning frequency and reproductive development of the narrow-barred Spanish mackerel (Scomberomorus commerson) along the west coast of Australia

The narrow-barred Spanish mackerel (Scomberomorus commerson) is widespread throughout the Indo-West Pacific region. This study describes the reproductive biology of S. commerson along the west coast of Australia, where it is targeted for food consumption and sports fishing. Development of testes occurred at a smaller body size than for ovaries, and more than 90% of males were sexually mature by the minimum legal length of 900 mm TL compared to 50% of females. Females dominated overall catches although sex ratios within daily catches vary considerably and females were rarely caught when spaw n ing. Scomberomorus commerson are seasonally abundant in coastal waters and most of the commercial catch is taken prior to the reproductive season. Spawning occurs between about August and November in the Kimberley region and between October and January in the Pilbara region. No spawning activity was recorded in the more southerly West Coast region, and only in the north Kimberley region were large numbers of fish with spawning gonads collected. Catches dropped to a minimum when spawning began in the Pilbara region, when fish became less abundant in inshore waters and inclement weather conditions limited fishing on still productive offshore reefs. Final maturation and ovulation of oocytes took place within a 24-hour period, and females spawned in the afternoon-evening every three days. A third of these spawning females released batches of eggs on consecutive days. Relationships between length, weight, and batch fecundity are presented

Comment on ``Capacity of the Hopfield model''

In a recent paper ``The capacity of the Hopfield model, J. Feng and B. Tirozzi claim to prove rigorous results on the storage capacity that are in conflict with the predictions of the replica approach. We show that their results are in error and that their approach, even when the worst mistakes are corrected, is not giving any mathematically rigorous results.Comment: 4pp, Plain Te

Spectral densities of scale-free networks

The spectral densities of the weighted Laplacian, random walk and weighted adjacency matrices associated with a random complex network are studied using the replica method. The link weights are parametrized by a weight exponent $\beta$. Explicit results are obtained for scale-free networks in the limit of large mean degree after the thermodynamic limit, for arbitrary degree exponent and $\beta$.Comment: 14 pages, two figure