Particle based gPC methods for mean-field models of swarming with uncertainty

In this work we focus on the construction of numerical schemes for the approximation of stochastic mean--field equations which preserve the nonnegativity of the solution. The method here developed makes use of a mean-field Monte Carlo method in the physical variables combined with a generalized Polynomial Chaos (gPC) expansion in the random space. In contrast to a direct application of stochastic-Galerkin methods, which are highly accurate but lead to the loss of positivity, the proposed schemes are capable to achieve high accuracy in the random space without loosing nonnegativity of the solution. Several applications of the schemes to mean-field models of collective behavior are reported.Comment: Communications in Computational Physics, to appea

Zoology of a non-local cross-diffusion model for two species

We study a non-local two species cross-interaction model with cross-diffusion. We propose a positivity preserving finite volume scheme based on the numerical method introduced in Ref. [15] and explore this new model numerically in terms of its long-time behaviours. Using the so gained insights, we compute analytical stationary states and travelling pulse solutions for a particular model in the case of attractive-attractive/attractive-repulsive cross-interactions. We show that, as the strength of the cross-diffusivity decreases, there is a transition from adjacent solutions to completely segregated densities, and we compute the threshold analytically for attractive-repulsive cross-interactions. Other bifurcating stationary states with various coexistence components of the support are analysed in the attractive-attractive case. We find a strong agreement between the numerically and the analytically computed steady states in these particular cases, whose main qualitative features are also present for more general potentials

Public Information and Household Expectations in Developing Countries: Evidence From a Natural Experiment

Governments provide public information about economic conditions to reduce information imperfections and facilitate efficient allocation of resources. Do households in developing countries rely on public signals to inform themselves about market conditions? To identify the importance of public information in households’ price expectations, we take advantage of a unique natural experiment in Ecuador where the published inflation rate had been different from the true rate over a period of 14 months due to a software error. We find that the public signal about prices plays an important role in households’ price expectations; the effect is stronger for better educated families, older people and men.Public Information, Price Expectations, Developing Countries, Natural Experiment, Heterogeneity

Local well-posedness of the generalized Cucker-Smale model

In this paper, we study the local well-posedness of two types of generalized Cucker-Smale (in short C-S) flocking models. We consider two different communication weights, singular and regular ones, with nonlinear coupling velocities $v|v|^{\beta-2}$ for $\beta > \frac{3-d}{2}$. For the singular communication weight, we choose $\psi^1(x) = 1/|x|^{\alpha}$ with $\alpha \in (0,d-1)$ and $\beta \geq 2$ in dimension $d > 1$. For the regular case, we select $\psi^2(x) \geq 0$ belonging to (L_{loc}^\infty \cap \mbox{Lip}_{loc})(\mathbb{R}^d) and $\beta \in (\frac{3-d}{2},2)$. We also remark the various dynamics of C-S particle system for these communication weights when $\beta \in (0,3)$

Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, co-operads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretations of known constructions in a large common framework, which is presented step-by-step with examples throughout. In this first part of two papers, we concentrate on the simplicial and operadic aspects.Comment: This replacement is part I of the final version of the paper, which has been split into two parts. The second part is available from the arXiv under the title "Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation" arXiv:2001.0872

Planning and implementation of effective collaboration in construction projects

The 21st century is now seen as the time for the construction industry to embrace new ways of working if it is to continue to be competitive and meet the needs of its ever demanding clients. Collaborative working is considered by many to be essential if design and construction teams are to consider the whole lifecycle of the construction product. Much of the recent work on collaborative working has focused on the delivery of technological solutions with a focus on web (extranets), CAD (visualisation), and knowledge management technologies. However, it is now recognised that good collaboration does not result from the implementation of information technology solutions alone. The organisational and people issues, which are not readily solved by pure technical systems, need to be resolved. However, approaches that exclusively focus on organisational and people issues will not reap the benefits derived from the use of technology, especially in the context of distributed teams which are the norm in construction. Work currently being undertaken at Loughborough University aims to bring together the benefits enabled by the technology, with the organisational, and its people issues to provide a framework enabling high level strategic decisions to be made to implement effective collaboration. This paper reports on the initial stages of the project: the background to the project, the methodology used, and findings from the literature survey and the requirements capture survey conducted as part of the project