Propagation of chaos for rank-based interacting diffusions and long time behaviour of a scalar quasilinear parabolic equation

We study a quasilinear parabolic Cauchy problem with a cumulative distribution function on the real line as an initial condition. We call 'probabilistic solution' a weak solution which remains a cumulative distribution function at all times. We prove the uniqueness of such a solution and we deduce the existence from a propagation of chaos result on a system of scalar diffusion processes, the interactions of which only depend on their ranking. We then investigate the long time behaviour of the solution. Using a probabilistic argument and under weak assumptions, we show that the flow of the Wasserstein distance between two solutions is contractive. Under more stringent conditions ensuring the regularity of the probabilistic solutions, we finally derive an explicit formula for the time derivative of the flow and we deduce the convergence of solutions to equilibrium.Comment: Stochastic partial differential equations: analysis and computations (2013) http://dx.doi.org/10.1007/s40072-013-0014-

Last passage percolation and traveling fronts

We consider a system of N particles with a stochastic dynamics introduced by Brunet and Derrida. The particles can be interpreted as last passage times in directed percolation on {1,...,N} of mean-field type. The particles remain grouped and move like a traveling wave, subject to discretization and driven by a random noise. As N increases, we obtain estimates for the speed of the front and its profile, for different laws of the driving noise. The Gumbel distribution plays a central role for the particle jumps, and we show that the scaling limit is a L\'evy process in this case. The case of bounded jumps yields a completely different behavior

Future Imaginings: Organizing in Response to Climate Change

Climate change has rapidly emerged as a major threat to our future. Indeed the increasingly dire projections of increasing global average temperatures and escalating extreme weather events highlight the existential challenge that climate change presents for humanity. In this editorial article we outline how climate change not only presents real, physical threats but also challenges the way we conceive of the broader economic, political and social order. We asked ourselves (and the contributors to this special issue) how we can imagine alternatives to our current path of ever escalating greenhouse gas emissions and economic growth. Through reference to the contributions that make up this special issue, we suggest that critically engaging with the concept of social, economic and political imaginaries can assist in tackling the conceptual and organizational challenges climate change poses. Only by questioning current sanitised and market-oriented interpretations of the environment, and embracing the catharsis and loss that climate change will bring, can we open up space for new future imaginings

Pushed traveling fronts in monostable equations with monotone delayed reaction

We study the existence and uniqueness of wavefronts to the scalar reaction-diffusion equations $u_{t}(t,x) = \Delta u(t,x) - u(t,x) + g(u(t-h,x)),$ with monotone delayed reaction term $g: \R_+ \to \R_+$ and $h >0$. We are mostly interested in the situation when the graph of $g$ is not dominated by its tangent line at zero, i.e. when the condition $g(x) \leq g'(0)x,$ $x \geq 0$, is not satisfied. It is well known that, in such a case, a special type of rapidly decreasing wavefronts (pushed fronts) can appear in non-delayed equations (i.e. with $h=0$). One of our main goals here is to establish a similar result for $h>0$. We prove the existence of the minimal speed of propagation, the uniqueness of wavefronts (up to a translation) and describe their asymptotics at $-\infty$. We also present a new uniqueness result for a class of nonlocal lattice equations.Comment: 17 pages, submitte

Enhancement of immune response of HBsAg loaded poly(L-lactic acid) microspheres against Hepatitis B through incorporation of alum and chitosan

Purpose: Poly (L-lactic acid) (PLA) microparticles encapsulating Hepatitis B surface antigen (HBsAg) with alum and chitosan were investigated for their potential as a vaccine delivery system. Methods: The microparticles, prepared using a water-in-oil-in-water (w/o/w) double emulsion solvent evaporation method with polyvinyl alcohol (PVA) or chitosan as the external phase stabilising agent showed a significant increase in the encapsulation efficiency of the antigen. Results: PLA-Alum and PLA-chitosan microparticles induced HBsAg serum specific IgG antibody responses significantly higher than PLA only microparticles and free antigen following subcutaneous administration. Chitosan not only imparted a positive charge to the surface of the microparticles but was also able to increase the serum specific IgG antibody responses significantly. Conclusions: The cytokine assays showed that the serum IgG antibody response induced is different according to the formulation, indicated by the differential levels of interleukin 4 (IL-4), interleukin 6 (IL-6) and interferon gamma (IFN-γ). The microparticles eliciting the highest IgG antibody response did not necessarily elicit the highest levels of the cytokines IL-4, IL-6 and IFN-γ