Stochastic oscillations of adaptive networks: application to epidemic modelling

Adaptive-network models are typically studied using deterministic differential equations which approximately describe their dynamics. In simulations, however, the discrete nature of the network gives rise to intrinsic noise which can radically alter the system's behaviour. In this article we develop a method to predict the effects of stochasticity in adaptive networks by making use of a pair-based proxy model. The technique is developed in the context of an epidemiological model of a disease spreading over an adaptive network of infectious contact. Our analysis reveals that in this model the structure of the network exhibits stochastic oscillations in response to fluctuations in the disease dynamic.Comment: 11 pages, 4 figure

Geometric Langevin equations on submanifolds and applications to the stochastic melt-spinning process of nonwovens and biology

In this article we develop geometric versions of the classical Langevin equation on regular submanifolds in euclidean space in an easy, natural way and combine them with a bunch of applications. The equations are formulated as Stratonovich stochastic differential equations on manifolds. The first version of the geometric Langevin equation has already been detected before by Leli\`evre, Rousset and Stoltz with a different derivation. We propose an additional extension of the models, the geometric Langevin equations with velocity of constant absolute value. The latters are seemingly new and provide a galaxy of new, beautiful and powerful mathematical models. Up to the authors best knowledge there are not many mathematical papers available dealing with geometric Langevin processes. We connect the first version of the geometric Langevin equation via proving that its generator coincides with the generalized Langevin operator proposed by Soloveitchik, Jorgensen and Kolokoltsov. All our studies are strongly motivated by industrial applications in modeling the fiber lay-down dynamics in the production process of nonwovens. We light up the geometry occuring in these models and show up the connection with the spherical velocity version of the geometric Langevin process. Moreover, as a main point, we construct new smooth industrial relevant three-dimensional fiber lay-down models involving the spherical Langevin process. Finally, relations to a class of self-propelled interacting particle systems with roosting force are presented and further applications of the geometric Langevin equations are given

Sequential Decision Making with Untrustworthy Service Providers

In this paper, we deal with the sequential decision making problem of agents operating in computational economies, where there is uncertainty regarding the trustworthiness of service providers populating the environment. Specifically, we propose a generic Bayesian trust model, and formulate the optimal Bayesian solution to the exploration-exploitation problem facing the agents when repeatedly interacting with others in such environments. We then present a computationally tractable Bayesian reinforcement learning algorithm to approximate that solution by taking into account the expected value of perfect information of an agent's actions. Our algorithm is shown to dramatically outperform all previous finalists of the international Agent Reputation and Trust (ART) competition, including the winner from both years the competition has been run

A dispersive wave pattern on Jupiter's fastest retrograde jet at 20∘20^\circS

A compact wave pattern has been identified on Jupiter's fastest retrograding jet at 20S (the SEBs) on the southern edge of the South Equatorial Belt. The wave has been identified in both reflected sunlight from amateur observations between 2010 and 2015, thermal infrared imaging from the Very Large Telescope and near infrared imaging from the Infrared Telescope Facility. The wave pattern is present when the SEB is relatively quiescent and lacking large-scale disturbances, and is particularly notable when the belt has undergone a fade (whitening). It is generally not present when the SEB exhibits its usual large-scale convective activity ('rifts'). Tracking of the wave pattern and associated white ovals on its southern edge over several epochs have permitted a measure of the dispersion relationship, showing a strong correlation between the phase speed (-43.2 to -21.2 m/s) and the longitudinal wavelength, which varied from 4.4-10.0 deg. longitude over the course of the observations. Infrared imaging sensing low pressures in the upper troposphere suggest that the wave is confined to near the cloud tops. The wave is moving westward at a phase speed slower (i.e., less negative) than the peak retrograde wind speed (-62 m/s), and is therefore moving east with respect to the SEBs jet peak. Unlike the retrograde NEBn jet near 17N, which is a location of strong vertical wind shear that sometimes hosts Rossby wave activity, the SEBs jet remains retrograde throughout the upper troposphere, suggesting the SEBs pattern cannot be interpreted as a classical Rossby wave. Cassini-derived windspeeds and temperatures reveal that the vorticity gradient is dominated by the baroclinic term and becomes negative (changes sign) in a region near the cloud-top level (400-700 mbar) associated with the SEBs, suggesting a baroclinic origin for this meandering wave pattern. [Abr]Comment: 19 pages, 11 figures, article accepted for publication in Icaru

Why Do Cascade Sizes Follow a Power-Law?

We introduce random directed acyclic graph and use it to model the information diffusion network. Subsequently, we analyze the cascade generation model (CGM) introduced by Leskovec et al. [19]. Until now only empirical studies of this model were done. In this paper, we present the first theoretical proof that the sizes of cascades generated by the CGM follow the power-law distribution, which is consistent with multiple empirical analysis of the large social networks. We compared the assumptions of our model with the Twitter social network and tested the goodness of approximation.Comment: 8 pages, 7 figures, accepted to WWW 201

Bulk spectral function sum rule in QCD-like theories with a holographic dual

We derive the sum rule for the spectral function of the stress-energy tensor in the bulk (uniform dilatation) channel in a general class of strongly coupled field theories. This class includes theories holographically dual to a theory of gravity coupled to a single scalar field, representing the operator of the scale anomaly. In the limit when the operator becomes marginal, the sum rule coincides with that in QCD. Using the holographic model, we verify explicitly the cancellation between large and small frequency contributions to the spectral integral required to satisfy the sum rule in such QCD-like theories.Comment: 16 pages, 2 figure

The Euler-Maruyama approximation for the absorption time of the CEV diffusion

A standard convergence analysis of the simulation schemes for the hitting times of diffusions typically requires non-degeneracy of their coefficients on the boundary, which excludes the possibility of absorption. In this paper we consider the CEV diffusion from the mathematical finance and show how a weakly consistent approximation for the absorption time can be constructed, using the Euler-Maruyama scheme

Product renovation and shared ownership: sustainable routes to satisfying the world's growing demand for goods

It has been estimated that by 2030 the number of people who are wealthy enough to be considered as middle class consumers will have tripled. This will have a dramatic impact on the demands for primary materials and energy. Much work has been carried out on sustainable ways of meeting the World’s energy demands and some work has been carried out on the sustainable production and consumption of goods. It has been estimated that with improvements in design and manufacturing it is possible to reduce the primary material requirements by 30% to produce the current demand for goods. Whilst this is a crucial step on the production side, there will still be a doubling of primary material requirements by the end of the century because of an absolute rise in demand for goods and services. It is therefore clear that the consumption of products must also be explored. This is a key areas of research for the UK INDEMAND centre, which is investigating ways of reducing the UK’s industrial energy demand and demand for energy intensive materials. Our ongoing work shows that two strategies would result in considerable reductions in the demand for primary materials: product longevity and using goods more intensively (which may requires increased durability). Product longevity and durability are not new ideas, but ones that can be applied across a raft of goods as methods of reducing the consumption of materials. With long life products there is a potential risk of outdated design and obsolescence, consequently there is a need to ensure upgradability and adaptability are incorporated at the design stage. If products last longer, then the production of new products can be diverted to emerging markets rather than the market for replacement goods. There are many goods which are only used occasionally; these goods do not normally wear out. The total demand for such could be drastically reduced if they were shared with other people. Sharing of goods has traditionally been conducted between friends or by hiring equipment. The use of modern communication systems and social media could enable the development of sharing co-ops and swap spaces that will increase the utilisation of goods and hence reduce the demand for new goods. This could also increase access to a range of goods for those on low incomes. From a series of workshops it has been found that the principal challenges are sociological rather than technological. This paper contains a discussion of these challenges and explores possible futures where these two strategies have been adopted. In addition, the barriers and opportunities that these strategies offer for consumers and businesses are identified, and areas where government policy could be instigated to bring about change are highlighted

Primary health eye care knowledge among general practitioners working in the Cape Town metropole

Aim: The main purpose of this study was to determine whether general practitioners (GPs) in the Cape Town metropole have sufficient knowledge to diagnose and treat primary care ophthalmic conditions correctly, and to assess their own perceptions of their levels of knowledge. Secondary objectives included identifying the need for courses to improve the ophthalmic knowledge of GPs and assessing whether there is a need to revise the undergraduate curriculum in ophthalmology in general.Method: A cross-sectional survey was done. A questionnaire of 10 primary care level ophthalmology questions, including a self-assessment section, was sent to each of 140 randomly chosen GPs in Cape Town.Results: A response rate of 79.2% was obtained. Respondents included graduates from all eight medical schools in South Africa. Most of the responding GPs were practising for more than 10 years (78.2%). The mean test score was 52.5% (standard deviation [SD]: 22.2). The mean self-rating was 51.9% (SD: 14.5). There was no statistically significant difference between the test score and the self-rating score (p = 0.5840). Responding GPs felt that there is a need for ophthalmology up-skilling courses and 99.9% of them would attend such courses. Also, 82% of GPs felt that primary care doctors, not optometrists, should deliver primary eye care. Conclusion: GPs appear to lack sufficient knowledge to manage primary health eye care problems, presumably due to a lack of adequate training in the field. Clinical up-skilling courses are needed to improve core knowledge in ophthalmology.Keywords: survey; ophthalmology; general practitioner