Abstract. We show a large time behavior result for class of weakly coupled systems of first-order Hamilton-Jacobi equations in the periodic setting. We use a PDE approach to extend the convergence result proved by Namah and Roquejoffre (Commun. Partial. Differ. Equ. 24(5-6):883-893, 1999) in the scalar case. Our proof is based on new comparison, existence and regularity results for systems. An interpretation of the solution of the system in terms of an optimal control problem with switching is given. Mathematics Subject Classification (2000). Primary 49L25; Secondary 35F30 and 35B25 and 58J37.
BackgroundMaternal and Child Health (MCH) Handbook, an integrated MCH home-based record, was piloted in four provinces of Vietnam (Dien Bien, Hoa Binh, Thanh Hoa and An Giang). The study is aimed at assessing the changes in pregnant women’s behavior towards the frequencies of their antenatal care service utilizations and their subsequent breastfeeding practices up to six months of age, through the MCH Handbook intervention. This is because the levels of pregnant women’s knowledge, attitude and practices (KAP) towards their antenatal care service utilizations and exclusive breastfeeding practices have been previously neither analyzed nor reported in relation to MCH home-based records in the country.MethodsTo compare pre-intervention baseline in 2011, post-intervention data were collected in 2013. Structured interviews were conducted with randomly selected 810 mothers of children 6-18 months of age in the four provinces. A focus group discussion among mothers in each of four provinces was conducted.ResultsThere was no significant difference in pregnant women’s knowledge about the need for ≥3 antenatal care visits between pre- and post-interventions. Yet, the proportion of pregnant women who made ≥3 antenatal care visits in post-intervention was significantly higher than in pre-intervention. Thus, MCH Handbook is likely to have contributed to practicing ≥3 antenatal care visits, by changing their attitude. The proportion of mothers who know the need for exclusive breastfeeding necessary during the initial six months significantly increased between pre- and post-interventions. The proportion of those practicing exclusive breastfeeding significantly increased between pre- and post-interventions, too. Thus, MCH Handbook is likely to have contributed to the increase in both knowledge about and practices of exclusive breastfeeding.ConclusionThe results of study imply that MCH Handbook contributed to the increase in pregnant women’s practices of ≥3 antenatal care visits and in their knowledge about and practice of exclusive breastfeeding. While there is room for improvement in the level of its data recording, the study confirmed that MCH Handbook plays a catalytic role in ensuring a continuum of maternal, newborn and child care. Note that this study is the first study that attempted to estimate pregnant women’s behavioral changes through MCH Handbook intervention in Vietnam.
Abstract-Recent research has shown that machine learning systems, including state-of-the-art deep neural networks, are vulnerable to adversarial attacks. By adding to the input object an imperceptible amount of adversarial noise, it is highly likely that the classifier can be tricked into assigning the modified object to any desired class. It has also been observed that these adversarial samples generalize well across models. A complete understanding of the nature of adversarial samples has not yet emerged. Towards this goal, we present a novel theoretical result formally linking the adversarial vulnerability of learning to the intrinsic dimensionality of the data. In particular, our investigation establishes that as the local intrinsic dimensionality (LID) increases, 1-NN classifiers become increasingly prone to being subverted. We show that in expectation, a k-nearest neighbor of a test point can be transformed into its 1-nearest neighbor by adding an amount of noise that diminishes as the LID increases. We also provide an experimental validation of the impact of LID on adversarial perturbation for both synthetic and real data, and discuss the implications of our result for general classifiers.
The two-dimensional Mandel-type problem geometry is well-known to bio-geomechanicians for testing rocks, cartilages, and bones with solutions in Cartesian coordinates for rectangular specimens or polar coordinates for cylindrical and disk samples. To date, all existing solutions are only applicable to single-porosity and single-permeability models, which could fall short when the porous material exhibits multiporosity and/or multipermeability characteristics, such as secondary porosity or fracture. This paper extends the plane strain and axisymmetric Mandel-type solutions from single-to dual-porosity and dual-permeability poromechanics. The solutions are presented in explicit analytical forms and account for arbitrary time-dependent external loading conditions, e.g., cyclic and ramping. The derived analytical solutions and results exhibit general behaviors characterized by two time scales. Stresses, pore pressures, and displacements are plotted for various time scale ratios to illustrate the interplaying effects of permeability and stiffness contrast of both porous regions, in addition to the interporosity exchange, on the overall responses of the system. Also, examples with realistic loading conditions for laboratory testing or field simulation such as cyclic and ramping are provided to demonstrate the engineering applications of the presented dual-poroelastic formulation and solutions.
The porochemoelectroelastic analytical models and solutions have been used to describe the response of chemically active and electrically charged saturated porous media such as clays, shales, and biological tissues. However, these attempts have been restricted to one-dimensional consolidation problems, which are very limited in practice and not general enough to serve as benchmark solutions for numerical validation. This work summarizes the general linear porochemoelectroelastic formulation and presents the solution of an inclined wellbore drilled in a fluid-saturated chemically active and ionized formation, such as shale, and subjected to a three-dimensional in-situ state of stress. The analytical solution to this geometry incorporates the coupled solid deformation and simultaneous fluid/ion flows induced by the combined influences of pore pressure, chemical potential, and electrical potential gradients under isothermal conditions. The formation pore fluid is modeled as an electrolyte solution comprised of a solvent and one type of dissolved cation and anion. The analytical approach also integrates into the solution the quantitative use of the cation exchange capacity (CEC) commonly obtained from laboratory measurements on shale samples. The results for stresses and pore pressure distributions due to the coupled electrochemical effects are illustrated and plotted in the vicinity of the inclined wellbore and compared with the classical porochemoelastic and poroelastic solutions.
Abstract. We are interested in the study of parabolic equations on a multi-dimensional junction, i.e. the union of a finite number of copies of a half-hyperplane of dimension d + 1 whose boundaries are identified. The common boundary is referred to as the junction hyperplane. The parabolic equations on the half-hyperplanes are in non-divergence form, fully non-linear and possibly degenerate, and they do degenerate and are quasi-convex along the junction hyperplane. More precisely, along the junction hyperplane the nonlinearities do not depend on second order derivatives and their sublevel sets with respect to the gradient variable are convex. The parabolic equations are supplemented with a non-linear boundary condition of Neumann type, referred to as a generalized junction condition, which is compatible with the maximum principle. Our main result asserts that imposing a generalized junction condition in a weak sense reduces to imposing an effective one in a strong sense. This result extends the one obtained by Imbert and Monneau for Hamilton-Jacobi equations on networks and multi-dimensional junctions. We give two applications of this result. On the one hand, we give the first complete answer to an open question about these equations: we prove in the two-domain case that the vanishing viscosity limit associated with quasi-convex Hamilton-Jacobi equations coincides with the maximal Ishii solution identified by Barles, Briani and Chasseigne (2012). On the other hand, we give a short and simple PDE proof of a large deviation result of Boué, Dupuis and Ellis (2000).
Fragility fracture is a serious public health problem in the world. The risk of fracture is determined by genetic and nongenetic clinical risk factors. This study sought to quantify the contribution of genetic profiling to fracture prognosis. The study was built on the ongoing Dubbo Osteoporosis Epidemiology Study, in which fracture and risk factors of 858 men and 1358 women had been monitored continuously from 1989 and 2008. Fragility fracture was ascertained by radiologic reports. Bone mineral density at the femoral neck was measured by dual-energy X-ray absorptiometry (DXA). Fifty independent genes with allele frequencies ranging from 0.01 to 0.60 and relative risks (RRs) ranging from 1.01 to 3.0 were simulated. Three predictive models were fitted to the data in which fracture was a function of (1) clinical risk factors only, (2) genes only, and (3) clinical risk factors and 50 genes. The area under the curve (AUC) for model 1 was 0.77, which was lower than that of model II (AUC ¼ 0.82). Adding genes into the clinical risk factors model (model 3) increased the AUC to 0.88 and improved the accuracy of fracture classification by 45%, with most (41%) improvement in specificity. In the presence of clinical risk factors, the number of genes required to achieve an AUC of 0.85 was around 25. These results suggest that genetic profiling could enhance the predictive accuracy of fracture prognosis and help to identify high-risk individuals for appropriate management of osteoporosis or intervention. ß
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