Fractional Stochastic Partial Differential Equation for Random Tangent Fields on the Sphere

This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of a random tangent vector field on the unit sphere. The SPDE is governed by a fractional diffusion operator to model the L\'{e}vy-type behaviour of the spatial solution, a fractional derivative in time to depict the intermittency of its temporal solution, and is driven by vector-valued fractional Brownian motion on the unit sphere to characterize its temporal long-range dependence. The solution to the SPDE is presented in the form of the Karhunen-Lo\`{e}ve expansion in terms of vector spherical harmonics. Its covariance matrix function is established as a tensor field on the unit sphere that is an expansion of Legendre tensor kernels. The variance of the increments and approximations to the solutions are studied and convergence rates of the approximation errors are given. It is demonstrated how these convergence rates depend on the decay of the power spectrum and variances of the fractional Brownian motion.Comment: 20 page

Multifractal scaling of products of birth--death processes

We investigate the scaling properties of products of the exponential of birth--death processes with certain given marginal discrete distributions and covariance structures. The conditions on the mean, variance and covariance functions of the resulting cumulative processes are interpreted in terms of the moment generating functions. We provide four illustrative examples of Poisson, Pascal, binomial and hypergeometric distributions. We establish the corresponding log-Poisson, log-Pascal, log-binomial and log-hypergeometric scenarios for the limiting processes, including their R\'{e}nyi functions and dependence properties.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ156 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Fractional-in-time and multifracational-in-space stochastic partial differential equations

This paper derives the weak-sense Gaussian solution to a family of fractional-in-time and multifractional-in-space stochastic partial differential equations, driven by fractional-integrated-in-time spatiotemporal white noise. Some fundamental results on the theory of pseudodifferential operators of variable order, and on the Mittag-Leffler function are applied to obtain the temporal, spatial and spatiotemporal H¨older continuity, in the mean-square sense, of the derived solution

Brief communication: immunogenicity of measles vaccine when co-administered with 10-valent pneumococcal conjugate vaccine.

This brief communication describes the findings from a randomised controlled trial in Vietnam that co-administration of measles vaccine (MV) with 10-valent pneumococcal conjugate vaccine (PCV10, Synflorix®, GSK) does not affect the immunogenicity of MV. These findings are most relevant for low- and middle-income countries (LMICs) in Asia considering PCV introduction

Identification of the population density of a species model with nonlocal diffusion and nonlinear reaction

The identification of the population density of a logistic equation backwards in time associated with nonlocal diffusion and nonlinear reaction, motivated by biology and ecology fields, is investigated. The diffusion depends on an integral average of the population density whilst the reaction term is a global or local Lipschitz function of the population density. After discussing the ill-posedness of the problem, we apply the quasi-reversibility method to construct stable approximation problems. It is shown that the regularized solutions stemming from such method not only depend continuously on the final data, but also strongly converge to the exact solution in L²-norm. New error estimates together with stability results are obtained. Furthermore, numerical examples are provided to illustrate the theoretical results

Experience in Using Mobile Laboratory for Monitoring and Diagnostics in the Socialist Republic of Vietnam

The aim was to present the experience of using mobile laboratory for monitoring and diagnostics (MLMD) during the epizootiological monitoring of the northern provinces of Vietnam. MLMD was transferred by Federal Service for Surveillance in the Sphere of Consumers Rights Protection and Human Welfare to the Socialist Republic of Vietnam as part of implementation of cooperation programs on combating infectious diseases. The use of MLMD made it possible to obtain new information on the circulation of pathogens of natural-focal infectious diseases on the territory of Vietnam. It also provided the necessary conditions for conducting research using methods of express diagnostics, bacteriological analysis, performing a full cycle of work – from the receipt of samples to the disinfection and destruction of infected material in compliance with the requirements of biological safety in the field. The effectiveness of using mobile laboratories in response to the emergencies of sanitary and epidemiological nature, both to strengthen stationary laboratory bases and to organize diagnostic studies in remote regions, has been shown. The use of MLMD for the diagnosis of COVID‑19 has been an effective component of countering the new coronavirus infection in Vietnam and significantly increased the volume of testing in the country