On the expected uniform error of geometric Brownian motion approximated by the L\'evy-Ciesielski construction

It is known that the Brownian bridge or L\'evy-Ciesielski construction of Brownian paths almost surely converges uniformly to the true Brownian path. In the present article the focus is on the error. In particular, we show for geometric Brownian motion that at level $N$, at which there are $d=2^N$ points evaluated on the Brownian path, the expected uniform error has an upper bound of order $\mathcal{O}(\sqrt{N/2^N})$, or equivalently, $\mathcal{O}(\sqrt{\ln d/d})$. This upper bound matches the known order for the expected uniform error of the standard Brownian motion. We apply the result to an option pricing example

Iodine status of young Burkinabe children receiving small-quantity lipid-based nutrient supplements and iodised salt : a cluster-randomised trial

The objective of the present study was to assess the impact of providing small-quantity lipid-based nutrient supplements (SQ-LNS) on the I status of young Burkinabe children. In total, thirty-four communities were assigned to intervention (IC) or non-intervention cohorts (NIC). IC children were randomly assigned to receive 20 g lipid-based nutrient supplements (LNS)/d containing 90 mu g I with 0 or 10 mg Zn from 9 to 18 months of age, and NIC children received no SQ-LNS. All the children were exposed to iodised salt through the national salt iodization programme. Spot urinary iodine (UI), thyroid-stimulating hormone (TSH) and total thyroxine (T-4) in dried blood spots as well as plasma thyroglobulin (Tg) concentrations were assessed at 9 and 18 months of age among 123 IC and fifty-six NIC children. At baseline and at 18 months, UI, TSH and T-4 did not differ between cohorts. Tg concentration was higher in the NIC v. IC at baseline, but this difference did not persist at 18 months of age. In both cohorts combined, the geometric mean of UI was 339.2 (95 % CI 298.6, 385.2) mu g/l, TSH 0.8 (95 % CI 0.7, 0.8) mU/l, T-4 118 (95 % CI 114, 122) nmol/l and Tg 26.0 (95 % CI 24.3, 27.7) mu g/l at 18 months of age. None of the children had elevated TSH at 18 months of age. Marginally more children in NIC (8.9 %) had low T-4 (15 ppm). A reduction of SQ-LNS I content could be considered in settings with similarly successful salt iodisation programmes

Numerical Calculation of Convection with Reduced Speed of Sound Technique

Context. The anelastic approximation is often adopted in numerical calculation with low Mach number, such as stellar internal convection. This approximation requires frequent global communication, because of an elliptic partial differential equation. Frequent global communication is negative factor for the parallel computing with a large number of CPUs. Aims. The main purpose of this paper is to test the validity of a method that artificially reduces the speed of sound for the compressible fluid equations in the context of stellar internal convection. The reduction of speed of sound allows for larger time steps in spite of low Mach number, while the numerical scheme remains fully explicit and the mathematical system is hyperbolic and thus does not require frequent global communication. Methods. Two and three dimensional compressible hydrodynamic equations are solved numerically. Some statistical quantities of solutions computed with different effective Mach numbers (due to reduction of speed of sound) are compared to test the validity of our approach. Results. Numerical simulations with artificially reduced speed of sound are a valid approach as long as the effective Mach number (based on the reduced speed of sound) remains less than 0.7.Comment: 16 pages, 10 figures, accepted to A&

Finding evolved stars in the inner Galactic disk with Gaia

The Bulge Asymmetries and Dynamical Evolution (BAaDE) survey will provide positions and line-of-sight velocities of ~20,000 evolved, maser bearing stars in the Galactic plane. Although this Galactic region is affected by optical extinction, BAaDE targets may have Gaia cross-matches, eventually providing additional stellar information. In an initial attempt to cross-match BAaDE targets with Gaia, we have found more than 5,000 candidates. Of these, we may expect half to show SiO emission, which will allow us to obtain velocity information. The cross-match is being refined to avoid false positives using different criteria based on distance analysis, flux variability, and color assessment in the mid- and near-IR. Once the cross-matches can be confirmed, we will have a unique sample to characterize the stellar population of evolved stars in the Galactic bulge, which can be considered fossils of the Milky Way formation.Comment: To appear in the Proceedings of the IAU Symposium No. 330: "Astrometry and Astrophysics in the Gaia sky

Molecular weight effects on chain pull-out fracture of reinforced polymeric interfaces

Using Brownian dynamics, we simulate the fracture of polymer interfaces reinforced by diblock connector chains. We find that for short chains the interface fracture toughness depends linearly on the degree of polymerization $N$ of the connector chains, while for longer chains the dependence becomes $N^{3/2}$. Based on the geometry of initial chain configuration, we propose a scaling argument that accounts for both short and long chain limits and crossover between them.Comment: 5 pages, 3 figure

Two-photon interference with thermal light

The study of entangled states has greatly improved the basic understanding about two-photon interferometry. Two-photon interference is not the interference of two photons but the result of superposition among indistinguishable two-photon amplitudes. The concept of two-photon amplitude, however, has generally been restricted to the case of entangled photons. In this letter we report an experimental study that may extend this concept to the general case of independent photons. The experiment also shows interesting practical applications regarding the possibility of obtaining high resolution interference patterns with thermal sources.Comment: Added reference 1

Small-quantity lipid-based nutrient supplements containing different amounts of zinc along with diarrhea and malaria treatment increase iron and vitamin A status and reduce anemia prevalence, but do not affect zinc status in young Burkinabe children : a cluster-randomized trial

Background: We assessed the effects of providing a package of interventions including small-quantity lipid-based nutrient supplements (SQ-LNS) containing 0, 5 or 10 mg zinc and illness treatment to Burkinabe children from 9 to 18 months of age, on biomarkers of zinc, iron and vitamin A status at 18 months and compared with a non-intervention cohort (NIC). Methods: Using a two-stage cluster randomized trial design, communities were randomly assigned to the intervention cohort (IC) or NIC, and extended family compounds within the IC were randomly assigned to different treatment groups. IC children (n = 2435) were provided with 20 g SQ-LNS/d containing 0, 5 or 10 mg zinc, 6 mg of iron and 400 mu g of vitamin A along with malaria and diarrhea treatment. NIC children (n = 785) did not receive the intervention package. At 9 and 18 months, hemoglobin (Hb), zinc, iron and vitamin A status were assessed in a sub-group (n = 404). Plasma concentrations of zinc (pZC), ferritin (pF), soluble transferrin receptor (sTfR) and retinol-binding protein (RBP) were adjusted for inflammation. Results: At baseline, 35% of children had low adjusted pZC ( 8.3 mg/L) and 47% had low adjusted RBP (< 0.94 mu mol/L), with no group-wise differences. Compared with the NIC, at 18 months IC children had significantly lower anemia prevalence (74 vs. 92%, p = 0.001) and lower iron deficiency prevalence (13% vs. 32% low adjusted pF and 41% vs. 71% high adjusted sTfR, p < 0.001), but no difference in pZC. Mean adjusted RBP was greater at 18 months in IC vs. NIC (0.94 mu mol/L vs. 0.86 mu mol/L, p = 0.015), but the prevalence of low RBP remained high in both cohorts. Within the IC, different amounts of zinc had no effect on the prevalence of low pZC or indicators of vitamin A deficiency, whereas children who received SQ-LNS with 10 mg zinc had a significantly lower mean pF at 18 months compared to children who received SQ-LNS with 5 mg zinc (p = 0.034). Conclusions: SQ-LNS regardless of zinc amount and source provided along with illness treatment improved indicators of iron and vitamin A status, but not pZC

Filling a silo with a mixture of grains: Friction-induced segregation

We study the filling process of a two-dimensional silo with inelastic particles by simulation of a granular media lattice gas (GMLG) model. We calculate the surface shape and flow profiles for a monodisperse system and we introduce a novel generalization of the GMLG model for a binary mixture of particles of different friction properties where, for the first time, we measure the segregation process on the surface. The results are in good agreement with a recent theory, and we explain the observed small deviations by the nonuniform velocity profile.Comment: 10 pages, 5 figures, to be appear in Europhys. Let