1,613 research outputs found
Retraction-based random walk for Itô diffusions on the torus
No full textMathematica notebook demonstrating the retraction-based random walk for Itô diffusions on Riemannian manifolds, as introduced in the related publication, on the example of the toru
Predicting opioid overdose locations using the INLA-SPDE method for fast Bayesian inference in point process models
No full textEfficient Itô diffusions on Riemannian manifolds
No full textA generalization of Donsker’s theorem states that, under mild conditions, Itô diffusions
on complete Riemannian manifolds can be approximated by geodesic random walks. Generally,
this does not provide an efficient way of simulating Itô diffusions on Riemannian
manifolds, since a non-linear differential equation must be solved at every step. In the
special case of Brownian motion on a compact manifold, approximate geodesic random
walks based on approximations of the exponential map called retractions have been proposed
and shown to be efficiently computable and convergent to Brownian motion. Using
the theory of Feller processes, we generalize the method of retraction-based random walks
and its convergence results to Itô diffusions on compact Riemannian manifolds under mild
assumptions on the drift and diffusion terms
Sub-Riemannian Random Walks: From Connections to Retractions
No full textWe study random walks on sub-Riemannian manifolds using the framework of retractions, i.e., approximations of normal geodesics. We show that such walks converge to the correct horizontal Brownian motion if normal geodesics are approximated to at least second order. In particular, we (i) provide conditions for convergence of geodesic random walks defined with respect to normal, compatible, and partial connections and (ii) provide examples of computationally efficient retractions, e.g., for simulating anisotropic Brownian motion on Riemannian manifolds
Efficient Itô diffusions on Riemannian manifolds
No full textA generalization of Donsker’s theorem states that, under mild conditions, Itô diffusions
on complete Riemannian manifolds can be approximated by geodesic random walks. Generally,
this does not provide an efficient way of simulating Itô diffusions on Riemannian
manifolds, since a non-linear differential equation must be solved at every step. In the
special case of Brownian motion on a compact manifold, approximate geodesic random
walks based on approximations of the exponential map called retractions have been proposed
and shown to be efficiently computable and convergent to Brownian motion. Using
the theory of Feller processes, we generalize the method of retraction-based random walks
and its convergence results to Itô diffusions on compact Riemannian manifolds under mild
assumptions on the drift and diffusion terms
Sub-Riemannian Random Walks: From Connections to Retractions
No full textWe study random walks on sub-Riemannian manifolds using the framework of retractions, i.e., approximations of normal geodesics. We show that such walks converge to the correct horizontal Brownian motion if normal geodesics are approximated to at least second order. In particular, we (i) provide conditions for convergence of geodesic random walks defined with respect to normal, compatible, and partial connections and (ii) provide examples of computationally efficient retractions, e.g., for simulating anisotropic Brownian motion on Riemannian manifolds
Preliminary studies developing methods for the control of Chrysomya putoria, the African latrine fly, in pit latrines in The Gambia.
No full textOBJECTIVE: To explore ways of controlling Chrysomya putoria, the African latrine fly, in pit latrines. As pit latrines are a major source of these flies, eliminating these important breeding sites is likely to reduce village fly populations, and may reduce the spread of diarrhoeal pathogens. METHODS: We treated 24 latrines in a Gambian village: six each with (i) pyriproxyfen, an insect juvenile hormone mimic formulated as Sumilarv(®) 0.5 G, a 0.5% pyriproxyfen granule, (ii) expanded polystyrene beads (EPB), (iii) local soap or (iv) no treatment as controls. Flies were collected using exit traps placed over the drop holes, weekly for five weeks. In a separate study, we tested whether latrines also function as efficient flytraps using the faecal odours as attractants. We constructed six pit latrines each with a built-in flytrap and tested their catching efficiency compared to six fish-baited box traps positioned 10 m from the latrine. Focus group discussions conducted afterwards assessed the acceptability of the flytrap latrines. RESULTS: Numbers of emerging C. putoria were reduced by 96.0% (95% CIs: 94.5-97.2%) 4-5 weeks after treatment with pyriproxyfen; by 64.2% (95% CIs: 51.8-73.5%) after treatment with local soap; by 41.3% (95% CIs = 24.0-54.7%) after treatment with EPB 3-5 weeks after treatment. Flytraps placed on latrines collected C. putoria and were deemed acceptable to local communities. CONCLUSIONS: Sumilarv 0.5 G shows promise as a chemical control agent, whilst odour-baited latrine traps may prove a useful method of non-chemical fly control. Both methods warrant further development to reduce fly production from pit latrines. A combination of interventions may prove effective for the control of latrine flies and the diseases they transmit
Undrained stability of pit-in-pit braced excavations under hydraulic uplift
No full textPit-in-pit (PIP) excavations in an aquifer–aquitard system likely undergo catastrophic failures under the hydraulic uplift, the associated undrained stability problem, however, has not been well analyzed in the past. To this end, a hypothetical model of PIP braced excavation in typical soil layers of Shanghai, China is developed using the finite element limit analysis (FELA) tool. The FELA solutions of safety factors (FSs) against hydraulic uplift are verified with the results from the finite element analysis with strength reduction technique (SRFEA) and existing design approaches. Subsequently, FELA is employed to identify the triggering and failure mechanisms of PIP braced excavations subjected to hydraulic uplift. A series of parametric studies considering the various geometric configurations of the PIP excavation, undrained shear strengths of aquitard, and artesian pressures are carried out. The sensitivities of relevant design parameters are further assessed using a multivariate adaptive regression splines (MARS) model that is capable of accurately capturing the nonlinear relationships between a set of input variables and output variables in multi-dimensions. A MARS-based design equation used for predicting FS is finally presented using the artificial dataset from FELA for practical design uses.Geo-engineerin
Modelling the Effects of Gate Pit-Stops on Apron Congestion
No full textDemand for air traffic is growing worldwide. In order to accommodate this growth, existing infrastructure such as gates should be used more efficiently. One technique to increase gate utilization is by introducing gate pit-stops. Introducing gate pit-stops leads to additional towing movements which can potentially interfere with other traffic on the apron. This in turn will lead to delays, which is undesirable. Currently, gate pit-stops are only performed for flights with a turnaround time of three hours or more. In order to investigate whether pit-stops can be effectively introduced on a broader scale, a model has been created that simulates gate assignments and apron movements. This model provides insight in the effect of gate pit-stops on gate utilization and apron congestion for different airport scenarios. Results show that introducing pit-stops for flights with a turnaround time of less than 180 minutes leads to an increase in flights that can be handled at a gate instead of a remote stand, at a small delay penalty. Airlines and airports can benefit from these findings as they will be able to handle more flights at a gate using existing infrastructure.Aerospace Engineerin
Homoplastic occurrence of perforated pit membranes and torus-bearing pit membranes in ancestral angiosperms as observed by field-emission scanning electron microscopy
No full textRecent studies demonstrated that perforated pit membranes (i.e., pit membranes with a large opening in their central portion) are commonly present between wood fibers in core eudicots. It is unclear whether this type of pit membranes might also occur in ancestral angiosperms. Therefore, structure of interfiber pit membranes was examined by field-emission scanning electron microscopy in nine species representing seven families that are located at more ancestral position than core eudicots. We found perforated pit membranes in three of the nine species. Our observations indicate that perforated pit membranes are relatively common even in ancestral groups of angiosperms. In the non-perforated pit membranes of the other six species, we found a range of structural variations. Thin-walled pit membranes without apparent intercellular layers were always found in three of the six species and the porosity of sheet-like pit membranes differed among the three species. Unlike the thin-walled pit membranes, interfiber pit membranes of Buxus microphylla var. japonica were thick-walled with obvious intercellular layers, and in Schisandra chinensis, we often observed torus-bearing pit membranes. Such variations in layered structure of pit membranes and homoplastic occurrence of torus-bearing pit membranes have not yet been reported for ancestral angiosperms. Our observations indicate that the structure of interfiber pit membranes might be more complicated than previous studies might suggest
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