On the dynamics of WKB wave functions whose phase are weak KAM solutions of H-J equation

In the framework of toroidal Pseudodifferential operators on the flat torus $\Bbb T^n := (\Bbb R / 2\pi \Bbb Z)^n$ we begin by proving the closure under composition for the class of Weyl operators $\mathrm{Op}^w_\hbar(b)$ with simbols $b \in S^m (\mathbb{T}^n \times \mathbb{R}^n)$. Subsequently, we consider $\mathrm{Op}^w_\hbar(H)$ when $H=\frac{1}{2} |\eta|^2 + V(x)$ where $V \in C^\infty (\Bbb T^n;\Bbb R)$ and we exhibit the toroidal version of the equation for the Wigner transform of the solution of the Schr\"odinger equation. Moreover, we prove the convergence (in a weak sense) of the Wigner transform of the solution of the Schr\"odinger equation to the solution of the Liouville equation on $\Bbb T^n \times \Bbb R^n$ written in the measure sense. These results are applied to the study of some WKB type wave functions in the Sobolev space $H^{1} (\mathbb{T}^n; \Bbb C)$ with phase functions in the class of Lipschitz continuous weak KAM solutions (of positive and negative type) of the Hamilton-Jacobi equation $\frac{1}{2} |P+ \nabla_x v_\pm (P,x)|^2 + V(x) = \bar{H}(P)$ for $P \in \ell \Bbb Z^n$ with $\ell >0$, and to the study of the backward and forward time propagation of the related Wigner measures supported on the graph of $P+ \nabla_x v_\pm$

Tightness for a stochastic Allen--Cahn equation

We study an Allen-Cahn equation perturbed by a multiplicative stochastic noise which is white in time and correlated in space. Formally this equation approximates a stochastically forced mean curvature flow. We derive uniform energy bounds and prove tightness of of solutions in the sharp interface limit, and show convergence to phase-indicator functions.Comment: 27 pages, final Version to appear in "Stochastic Partial Differential Equations: Analysis and Computations". In Version 4, Proposition 6.3 is new. It replaces and simplifies the old propositions 6.4-6.

Telemedicine in Primary Health: The Virtual Doctor Project Zambia

This paper is a commentary on a project application of telemedicine to alleviate primary health care problems in Lundazi district in the Eastern province of Zambia. The project dubbed 'The Virtual Doctor Project' will use hard body vehicles fitted with satellite communication devices and modern medical equipment to deliver primary health care services to some of the neediest areas of the country. The relevance and importance of the project lies in the fact that these areas are hard-to-reach due to rugged natural terrain and have very limited telecommunications infrastructure. The lack of these and other basic services makes it difficult for medical personnel to settle in these areas, which leads to an acute shortage of medical personnel. We comment on this problem and how it is addressed by 'The Virtual Doctor Project', emphasizing that while the telemedicine concept is not new in sub-Saharan Africa, the combination of mobility and connectivity to service a number of villages 'on the go' is an important variation in the shift back to the 1978 Alma Ata principles of the United Nations World Health Organization [WHO]

Shocks and Universal Statistics in (1+1)-Dimensional Relativistic Turbulence

We propose that statistical averages in relativistic turbulence exhibit universal properties. We consider analytically the velocity and temperature differences structure functions in the (1+1)-dimensional relativistic turbulence in which shock waves provide the main contribution to the structure functions in the inertial range. We study shock scattering, demonstrate the stability of the shock waves, and calculate the anomalous exponents. We comment on the possibility of finite time blowup singularities.Comment: 37 pages, 7 figure

Novel Characteristics of Valveless Pumping

This study investigates the occurrence of valveless pumping in a fluidfilled system consisting of two open tanks connected by an elastic tube. We show that directional flow can be achieved by introducing a periodic pinching applied at an asymmetrical location along the tube, and that the flow direction depends on the pumping frequency. We propose a relation between wave propagation velocity, tube length, and resonance frequencies associated with shifts in the pumping direction using numerical simulations. The eigenfrequencies of the system are estimated from the linearized system, and we show that these eigenfrequencies constitute the resonance frequencies and the horizontal slope frequencies of the system; 'horizontal slope frequency' being a new concept. A simple model is suggested, explaining the effect of the gravity driven part of the oscillation observed in response to the tank and tube diameter changes. Results are partly compared with experimental findings.Art. no. 22450

Efficacy of species-specific protein antibiotics in a murine model of acute Pseudomonas aeruginosa lung infection

Protein antibiotics, known as bacteriocins, are widely produced by bacteria for intraspecies competition. The potency and targeted action of bacteriocins suggests that they could be developed into clinically useful antibiotics against highly drug resistant Gram-negative pathogens for which there are few therapeutic options. Here we show that Pseudomonas aeruginosa specific bacteriocins, known as pyocins, show strong efficacy in a murine model of P. aeruginosa lung infection, with the concentration of pyocin S5 required to afford protection from a lethal infection at least 100-fold lower than the most commonly used inhaled antibiotic tobramycin. Additionally, pyocins are stable in the lung, poorly immunogenic at high concentrations and efficacy is maintained in the presence of pyocin specific antibodies after repeated pyocin administration. Bacteriocin encoding genes are frequently found in microbial genomes and could therefore offer a ready supply of highly targeted and potent antibiotics active against problematic Gram-negative pathogens

Local Volatility Calibration by Optimal Transport

The calibration of volatility models from observable option prices is a fundamental problem in quantitative finance. The most common approach among industry practitioners is based on the celebrated Dupire's formula [6], which requires the knowledge of vanilla option prices for a continuum of strikes and maturities that can only be obtained via some form of price interpolation. In this paper, we propose a new local volatility calibration technique using the theory of optimal transport. We formulate a time continuous martingale optimal transport problem, which seeks a martingale diffusion process that matches the known densities of an asset price at two different dates, while minimizing a chosen cost function. Inspired by the seminal work of Benamou and Brenier [1], we formulate the problem as a convex optimization problem, derive its dual formulation, and solve it numerically via an augmented Lagrangian method and the alternative direction method of multipliers (ADMM) algorithm. The solution effectively reconstructs the dynamic of the asset price between the two dates by recovering the optimal local volatility function, without requiring any time interpolation of the option prices

A predicted astrometric microlensing event by a nearby white dwarf

We used the Tycho-Gaia Astrometric Solution catalogue, part of the Gaia Data Release 1, to search for candidate astrometric microlensing events expected to occur within the remaining lifetime of the Gaia satellite. Our search yielded one promising candidate. We predict that the nearby DQ type white dwarf LAWD 37 (WD 1142-645) will lens a background star and will reach closest approach on November 11th 2019 ($\pm$ 4 days) with impact parameter $380\pm10$ mas. This will produce an apparent maximum deviation of the source position of $2.8\pm0.1$ mas. In the most propitious circumstance, Gaia will be able to determine the mass of LAWD 37 to $\sim3\%$. This mass determination will provide an independent check on atmospheric models of white dwarfs with helium rich atmospheres, as well as tests of white dwarf mass radius relationships and evolutionary theory

Mapping vulnerability to multiple hazards in the Savanna Ecosystem in Ghana

The interior savannah ecosystem in Ghana is subjected to a number of hazards, including droughts, windstorms, high temperatures and heavy rainfall, the frequency and intensity of which are projected to increase during the 21st century as a result of climate variability and change. Vulnerabilities to these hazards vary, both spatially and temporally, due to differences in susceptibilities and adaptive capacities. Many mapping exercises in Ghana have considered the impacts of single hazards on single sectors, particularly agriculture. But the hazards often occur concurrently or alternately, and have varying degrees of impacts on different sectors. The impacts also interact. These interactions make mapping of the vulnerabilities of multiple sectors to multiple hazards imperative. This paper presents an analysis of the spatial dimension of vulnerabilities by mapping vulnerability of sectors that support livelihood activities at a single point in time, using the Upper East Region of Ghana as a case study. Data colected to develop the maps were largely quantitative and from secondary sources. Other data drew on fieldwork undertaken in the region from July - September 2013. Quantitative values were assigned to qualitative categorical data as the mapping process is necessarily quantitative. Data were divided into susceptibility and adaptive capacity indicators and mapped in ArcGIS 10.2 using weighted linear sum aggregation. Agriculture was found to be the most vulnerable sector in all districts of the Upper East Region and experienced the greatest shocks from all hazards. Although all districts were vulnerable, the Talensi, Nabdam, Garu-Temapane and Kassena-Nankana West Districts were most vulnerable. Findings highlight the need for more targeted interventions to build adaptive capacity in light of the spatial distributions of vulnerabilities to hazards across sectors