Exact Controllability of the Time Discrete Wave Equation: A Multiplier Approach

In this paper we summarize our recent results on the exact boundary controllability of a trapezoidal time discrete wave equation in a bounded domain. It is shown that the projection of the solution in an appropriate space in which the high frequencies have been filtered is exactly controllable with uniformly bounded controls (with respect to the time-step). By classical duality arguments, the problem is reduced to a boundary observability inequality for a time-discrete wave equation. Using multiplier techniques the uniform observability property is proved in a class of filtered initial data. The optimality of the filtering parameter is also analyzed

Phenotypic features effectively stratify risk for advanced colorectal neoplasia in asymptomatic adults

poster abstractBackground: While colorectal cancer (CRC) screening is effective and cost-effective for reducing CRC incidence and mortality, it is underutilized (nearly 40% of U.S. adults are either not current with or have never been screened), inefficient (low-risk persons undergo colonoscopy), and costly to the U.S. health care system. A simple and effective way of stratifying risk for advanced neoplasia (AN – CRC and advanced, precancerous polyps) could improve the efficiency and uptake of screening by tailoring colonoscopy toward persons at highrisk and giving low-risk persons less-invasive options. Although several risk factors for AN have been identified, they are not used in clinical practice in part because of inability to integrate the factors to produce a risk estimate. Objective: To derive and validate a risk index for AN (CRC, advanced adenomas, serrated polyps >= 1 cm) anywhere in the colorectum. Methods: We measured socio-demographic features, medical and family history, lifestyle factors, and physical features in 50-80 year old persons who underwent first-time screening colonoscopy between December 2004 and September 2011, and linked these factors to endoscopic and histologic findings. Using logistic regression, we derived a risk equation on a randomly selected 2/3s of the sample. A 12-variable model was selected based on optimal statistical metrics. Based on model coefficients, we assigned points to each variable to create a risk score, which ranged from -13 to 8. Scores with comparable magnitudes of risk were collapsed into 3 risk categories. The model was tested on the remaining third of the sample. Results: Among 3025 subjects in the derivation set (mean age 57.3 ± 6.5 years; 52% women), the prevalence of AN was 9.4% (including 26 CRCs). Model variables include age, sex, smoking, ethanol use, marital status, NSAID and aspirin use, physical activity, education level, and metabolic syndrome (P-value for fit = 0.09; cstatistic=0.78). Respective risks of AN in the low- (scores of -13 to -5), intermediate- (scores of -4 to 2) and high- (scores of 3 to 12) were 1.52% (95%, 0.07-2.8%), 6.86%, and 26.8% (P-value for trend < 0.001), with respective cohort proportions of 23%, 59% and 18%. Ten low-risk subjects had AN (0 CRCs, 6 distal). Based on finding a distal sentinel polyp, sigmoidoscopy to the descending colon would have detected 7(70%) ANs. Among the 1475 subjects in the test set (mean age 57.2 ± 6.5 years; 52% women), AN prevalence was 8.4%. Risk of AN in the low-risk subgroup was 2.73% (CI, 1.25-5.11%) and was 5.57% and 25.4% in the intermediate- and high-risk subgroups, respectively (P<0.001), with cohort proportions of 23%, 59%, and 18%. Nine low-risk subjects had AN (0 CRCs, 5 distal, 6 detectable by sigmoidoscopy. Conclusion: This new risk index effectively stratifies the risk for AN among asymptomatic adults, identifying a low-risk subgroup of 23% that may be screened effectively and efficiently with tests other than colonoscopy and a high-risk subgroup of 18% in which colonoscopy may be preferable. If validated in other settings, this index could increase both the efficiency and uptake of CRC screening

Continuum viscoplastic simulation of a granular column collapse on large slopes: μ(I) rheology and lateral wall effects

We simulate here dry granular flows resulting from the collapse of granular columns on an inclined channel (up to 22°) and compare precisely the results with laboratory experiments. Incompressibility is assumed despite the dilatancy observed in the experiments (up to 10%). The 2-D model is based on the so-called μ(I) rheology that induces a Drucker-Prager yield stress and a variable viscosity. A nonlinear Coulomb friction term, representing the friction on the lateral walls of the channel, is added to the model. We demonstrate that this term is crucial to accurately reproduce granular collapses on slopes ≳10°, whereas it remains of little effect on the horizontal slope. Quantitative comparison between the experimental and numerical changes with time of the thickness profiles and front velocity makes it possible to strongly constrain the rheology. In particular, we show that the use of a variable or a constant viscosity does not change significantly the results provided that these viscosities are of the same order. However, only a fine tuning of the constant viscosity (η=1 Pa s) makes it possible to predict the slow propagation phase observed experimentally at large slopes. Finally, we observed that small-scale instabilities develop when refining the mesh (also called ill-posed behavior, characterized in the work of Barker et al. [“Well-posed and ill-posed behaviour of the μ(I)-rheology for granular flow,” J. Fluid Mech. 779, 794–818 (2015)] and in the present work) associated with the mechanical model. The velocity field becomes stratified and the bands of high velocity gradient appear. These model instabilities are not avoided by using variable viscosity models such as the μ(I) rheology. However we show that the velocity range, the static-flowing transition, and the thickness profiles are almost not affected by them

An alternating descent method for the optimal control of the inviscid Burgers equation in the presence of shocks.

We introduce a new optimization strategy to compute numerical approximations of minimizers for optimal control problems governed by scalar conservation laws in the presence of shocks. We focus on the 1 − d inviscid Burgers equation. We first prove the existence of minimizers and, by a -convergence argument, the convergence of discrete minima obtained by means of numerical approximation schemes satisfying the so called onesided Lipschitz condition (OSLC). Then we address the problem of developing efficient descent algorithms. We first consider and compare the existing two possible approaches: the so-called discrete approach, based on a direct computation of gradients in the discrete problem and the so-called continuous one, where the discrete descent direction is obtained as a discrete copy of the continuous one. When optimal solutions have shock discontinuities, both approaches produce highly oscillating minimizing sequences and the effective descent rate is very weak. As a solution we propose a new method, that we shall call alternating descent method, that uses the recent developments of generalized tangent vectors and the linearization around discontinuous solutions. This method distinguishes and alternates the descent directions that move the shock and those that perturb the profile of the solution away of it producing very efficient and fast descent algorithms

Augmented Lagrangian Method for Constrained Nuclear Density Functional Theory

The augmented Lagrangiam method (ALM), widely used in quantum chemistry constrained optimization problems, is applied in the context of the nuclear Density Functional Theory (DFT) in the self-consistent constrained Skyrme Hartree-Fock-Bogoliubov (CHFB) variant. The ALM allows precise calculations of multidimensional energy surfaces in the space of collective coordinates that are needed to, e.g., determine fission pathways and saddle points; it improves accuracy of computed derivatives with respect to collective variables that are used to determine collective inertia; and is well adapted to supercomputer applications.Comment: 6 pages, 3 figures; to appear in Eur. Phys. J.

High-temperature magnetodielectric Bi(Fe0.5Mn0.5)O3 thin films with checkerboard-ordered oxygen vacancies and low magnetic damping

The possibility of affecting the magnetic properties of a material by dielectric means, and vice versa, remains an attractive perspective for modern electronics and spintronics. Here, we report on epitaxial Bi(Fe0.5Mn0.5)O3 thin films with exceptionally low Gilbert damping and magnetoelectric coupling above room temperature (<400 K). The ferromagnetic order, not observed in bulk, has been detected with a total magnetization of 0.44 μB/formula units with low Gilbert damping parameter (0.0034), both at room temperature. Additionally, a previously overlooked check-board ordering of oxygen vacancies is observed, providing insights on the magnetic and dielectric origin of the multifunctional properties of the films. Finally, intrinsic magnetodielectric behavior is observed as revealed by the variation of dielectric permittivity well above room temperature. These findings show the possibility of electric-field-controlled magnetic properties, in low Gilbert-damping-based spintronic devices, using single-phase multiferroic material

Genetic and environmental risk for major depression in African-American and European-American women

It is unknown whether there are racial differences in the heritability of major depressive disorder (MDD) because most psychiatric genetic studies have been conducted in samples comprised largely of white non-Hispanics. To examine potential differences between African-American (AA) and European-American (EA) young adult women in (1) DSM-IV MDD prevalence, symptomatology and risk factors and (2) genetic and/or environmental liability to MDD, we analyzed data from a large, population representative sample of twins ascertained from birth records (n= 550 AA and n=3226 EA female twins) aged 18–28 years at the time of MDD assessment by semi-structured psychiatric interview. AA women were more likely to have MDD risk factors; however, there were no significant differences in lifetime MDD prevalence between AA and EA women after adjusting for covariates (Odds Ratio = 0.88, 95% confidence interval: 0.67–1.15 ). Most MDD risk factors identified among AAs were also associated with MDD at similar magnitudes among EAs. Although the MDD heritability point estimate was higher among AA than EA women in a model with paths estimated separately by race (56%, 95% CI: 29%–78% vs. 41%, 95% CI: 29%–52%), the best-fitting model was one in which additive genetic and nonshared environmental paths for AA and EA women were constrained to be equal (A = 43%, 33%–53% and E = 57%, 47%–67%). Despite a marked elevation in the prevalence of environmental risk exposures related to MDD among AA women, there were no significant differences in lifetime prevalence or heritability of MDD between AA and EA young women

Derivation and Validation of a Scoring System to Stratify Risk for Advanced Colorectal Neoplasia in Asymptomatic Adults: A Cross-sectional Study

Several methods are recommended equally strongly for colorectal cancer screening in average-risk persons. Risk stratification would enable tailoring of screening within this group, with less invasive tests (sigmoidoscopy or occult blood tests) for lower-risk persons and colonoscopy for higher-risk persons

Boundary stabilization of numerical approximations of the 1-D variable coefficients wave equation: A numerical viscosity approach

In this paper, we consider the boundary stabilization problem associated to the 1- d wave equation with both variable density and diffusion coefficients and to its finite difference semi-discretizations. It is well-known that, for the finite difference semi-discretization of the constant coefficients wave equation on uniform meshes (Tébou and Zuazua, Adv. Comput. Math. 26:337–365, 2007) or on somenon-uniform meshes (Marica and Zuazua, BCAM, 2013, preprint), the discrete decay rate fails to be uniform with respect to the mesh-size parameter. We prove that, under suitable regularity assumptions on the coefficients and after adding an appropriate artificial viscosity to the numerical scheme, the decay rate is uniform as the mesh-size tends to zero. This extends previous results in Tébou and Zuazua (Adv. Comput.Math. 26:337–365, 2007) on the constant coefficient wave equation. The methodology of proof consists in applying the classical multiplier technique at the discrete level, with a multiplier adapted to the variable coefficients