808 research outputs found
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
Equine Welfare: A Study of Dermatophilosis and the Management of Data Relevant to the Health and Wellbeing of Horses
This thesis considers aspects of equine welfare which have received little attention in the U.K. Skin disease, particularly bacterial skin disease, was highlighted as an area giving rise to concern with respect to equine welfare. Dermatophilosis was examined in detail as one of the commoner bacterial skin conditions responsible for animal suffering, and one for which management is often difficult. Essential fatty acids (EFAs) were evaluated as a dietary supplement in an alternative approach to the management of equine dermatophilosis. The pharmacokinetics of EFAs in the horse were investigated, with EFAs supplemented as evening primrose oil (EPO), containing linoleic acid (LA) and gamma-linolenic acid (GLA). A very slow conversion of LA to its active metabolites was found in the horse compared to other species. A daily dose regime of 20g of 80% EPO and 20% fish oil and vitamin E was adopted for the consequent treatment and prophylactic studies. In a placebo-controlled, double blind treatment study no significant effect was seen on severity or extent of distribution of lesions of dermatophilosis when horses received EFAs orally. When EFAs were supplemented over the traditional autumn high dermatophilosis risk period in a controlled prophylactic study, they did not prevent development of lesions or reduce incidence of infection. No significant improvement was afforded by EFAs on the condition of the coat, mane, tail or hooves, nor on general body condition. EFAs were not harmful and exerted no effect, adverse or beneficial, on haematological or biochemical parameters. The characteristics of D. congolensis were examined in relation to the site and severity of lesions of dermatophilosis, but no correlation was found. All isolates were different when examined by differential bacteriological growth characteristics and sodium dodecyl sulphate polyacrylamide gel electrophoresis (SDS-PAGE). Proteolytic enzyme production by D. congolensis was investigated with regard to the virulence of the organism, and several isolates demonstrated extracellular protease activity. The clinical and haematological consequences of bleeding horses at regular intervals were monitored in a group of animals maintained for commercial blood production. No adverse effect was recorded on clinical, protein or haematological profiles when 8 litres of blood were removed every three weeks. Thoroughbred animals supported regular bleeding better than non-Thoroughbred animals. A relational database system was created as a management tool for the manager of the horse herd. The information contained within the system, regarding horse details, bloodroom records and farm laboratory records, could be constantly updated. Rapid detection of poor performers or anaemic animals could permit prompt instigation of corrective action, avoiding undue animal distress. It is hoped that some of the work within this thesis has made a worthwhile contribution to the extension of knowledge concerning the welfare of horses in the U.K
Competing epidemics on complex networks
Human diseases spread over networks of contacts between individuals and a
substantial body of recent research has focused on the dynamics of the
spreading process. Here we examine a model of two competing diseases spreading
over the same network at the same time, where infection with either disease
gives an individual subsequent immunity to both. Using a combination of
analytic and numerical methods, we derive the phase diagram of the system and
estimates of the expected final numbers of individuals infected with each
disease. The system shows an unusual dynamical transition between dominance of
one disease and dominance of the other as a function of their relative rates of
growth. Close to this transition the final outcomes show strong dependence on
stochastic fluctuations in the early stages of growth, dependence that
decreases with increasing network size, but does so sufficiently slowly as
still to be easily visible in systems with millions or billions of individuals.
In most regions of the phase diagram we find that one disease eventually
dominates while the other reaches only a vanishing fraction of the network, but
the system also displays a significant coexistence regime in which both
diseases reach epidemic proportions and infect an extensive fraction of the
network.Comment: 14 pages, 5 figure
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
Directed percolation with incubation times
We introduce a model for directed percolation with a long-range temporal
diffusion, while the spatial diffusion is kept short ranged. In an
interpretation of directed percolation as an epidemic process, this
non-Markovian modification can be understood as incubation times, which are
distributed accordingly to a Levy distribution. We argue that the best approach
to find the effective action for this problem is through a generalization of
the Cardy-Sugar method, adding the non-Markovian features into the geometrical
properties of the lattice. We formulate a field theory for this problem and
renormalize it up to one loop in a perturbative expansion. We solve the various
technical difficulties that the integrations possess by means of an asymptotic
analysis of the divergences. We show the absence of field renormalization at
one-loop order, and we argue that this would be the case to all orders in
perturbation theory. Consequently, in addition to the characteristic scaling
relations of directed percolation, we find a scaling relation valid for the
critical exponents of this theory. In this universality class, the critical
exponents vary continuously with the Levy parameter.Comment: 17 pages, 7 figures. v.2: minor correction
Random graphs containing arbitrary distributions of subgraphs
Traditional random graph models of networks generate networks that are
locally tree-like, meaning that all local neighborhoods take the form of trees.
In this respect such models are highly unrealistic, most real networks having
strongly non-tree-like neighborhoods that contain short loops, cliques, or
other biconnected subgraphs. In this paper we propose and analyze a new class
of random graph models that incorporates general subgraphs, allowing for
non-tree-like neighborhoods while still remaining solvable for many fundamental
network properties. Among other things we give solutions for the size of the
giant component, the position of the phase transition at which the giant
component appears, and percolation properties for both site and bond
percolation on networks generated by the model.Comment: 12 pages, 6 figures, 1 tabl
Chaotic synchronizations of spatially extended systems as non-equilibrium phase transitions
Two replicas of spatially extended chaotic systems synchronize to a common
spatio-temporal chaotic state when coupled above a critical strength. As a
prototype of each single spatio-temporal chaotic system a lattice of maps
interacting via power-law coupling is considered. The synchronization
transition is studied as a non-equilibrium phase transition, and its critical
properties are analyzed at varying the spatial interaction range as well as the
nonlinearity of the dynamical units composing each system. In particular,
continuous and discontinuous local maps are considered. In both cases the
transitions are of the second order with critical indexes varying with the
exponent characterizing the interaction range. For discontinuous maps it is
numerically shown that the transition belongs to the {\it anomalous directed
percolation} (ADP) family of universality classes, previously identified for
L{\'e}vy-flight spreading of epidemic processes. For continuous maps, the
critical exponents are different from those characterizing ADP, but apart from
the nearest-neighbor case, the identification of the corresponding universality
classes remains an open problem. Finally, to test the influence of
deterministic correlations for the studied synchronization transitions, the
chaotic dynamical evolutions are substituted by suitable stochastic models. In
this framework and for the discontinuous case, it is possible to derive an
effective Langevin description that corresponds to that proposed for ADP.Comment: 12 pages, 5 figures Comments are welcom
Validation and Calibration of Models for Reaction-Diffusion Systems
Space and time scales are not independent in diffusion. In fact, numerical
simulations show that different patterns are obtained when space and time steps
( and ) are varied independently. On the other hand,
anisotropy effects due to the symmetries of the discretization lattice prevent
the quantitative calibration of models. We introduce a new class of explicit
difference methods for numerical integration of diffusion and
reaction-diffusion equations, where the dependence on space and time scales
occurs naturally. Numerical solutions approach the exact solution of the
continuous diffusion equation for finite and , if the
parameter assumes a fixed constant value,
where is an odd positive integer parametrizing the alghorithm. The error
between the solutions of the discrete and the continuous equations goes to zero
as and the values of are dimension
independent. With these new integration methods, anisotropy effects resulting
from the finite differences are minimized, defining a standard for validation
and calibration of numerical solutions of diffusion and reaction-diffusion
equations. Comparison between numerical and analytical solutions of
reaction-diffusion equations give global discretization errors of the order of
in the sup norm. Circular patterns of travelling waves have a maximum
relative random deviation from the spherical symmetry of the order of 0.2%, and
the standard deviation of the fluctuations around the mean circular wave front
is of the order of .Comment: 33 pages, 8 figures, to appear in Int. J. Bifurcation and Chao
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