A new approach to hyperbolic inverse problems

We present a modification of the BC-method in the inverse hyperbolic problems. The main novelty is the study of the restrictions of the solutions to the characteristic surfaces instead of the fixed time hyperplanes. The main result is that the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the self-adjoint hyperbolic operator up to a diffeomorphism and a gauge transformation. In this paper we prove the crucial local step. The global step of the proof will be presented in the forthcoming paper.Comment: We corrected the proof of the main Lemma 2.1 by assuming that potentials A(x),V(x) are real value

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

A penalty approach to the numerical simulation of a constrained wave motion

The main goal of this article is to investigate the numerical solution of a vector-valued nonlinear wave equation, the nonlinearity being of the Ginzburg-Landau type, namely (|u|2-1)u. This equation is obtained when treating by penalty a constrained wave-motion, where the displacement vector is of constant length (1 here, after rescaling). An important step of the approximation process is the construction of a time discretization scheme preserving-in some sense-the energy conservation property of the continuous model. The stability properties of the above scheme are discussed. The authors discuss also the finite element approximation and the quasi-Newton solution of the nonlinear elliptic system obtained at each time step from the time discretization. The results of numerical experiments are presented; they show that for the constraint of the original wave problem to be accurately verified we need to use a small value of the penalty parameter

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

Salivary melatonin onset in youth at familial risk for bipolar disorder

Melatonin secretion and polysomnography (PSG) were compared among a group of healthy adolescents who were at high familial risk for bipolar disorder (HR) and a second group at low familial risk (LR). Adolescent participants (n = 12) were a mean age 14 ± 2.3 years and included 8 females and 4 males. Saliva samples were collected under standardized condition light (red light) and following a 200 lux light exposure over two consecutive nights in a sleep laboratory. Red Light Melatonin onset (RLMO) was defined as saliva melatonin level exceeding the mean of the first 3 readings plus 2 standard deviations. Polysomnography was also completed during each night. HR youth, relative to LR, experienced a significantly earlier melatonin onset following 200 lux light exposure. Polysomnography revealed that LR youth, relative to HR, spent significantly more time in combined stages 3 and 4 (deep sleep) following red light exposure. Additionally, regardless of the group status (HR or LR), there was no significant difference in Red Light Melatonin Onset recorded at home or in the laboratory, implying its feasibility and reliability

On discretization in time in simulations of particulate flows

We propose a time discretization scheme for a class of ordinary differential equations arising in simulations of fluid/particle flows. The scheme is intended to work robustly in the lubrication regime when the distance between two particles immersed in the fluid or between a particle and the wall tends to zero. The idea consists in introducing a small threshold for the particle-wall distance below which the real trajectory of the particle is replaced by an approximated one where the distance is kept equal to the threshold value. The error of this approximation is estimated both theoretically and by numerical experiments. Our time marching scheme can be easily incorporated into a full simulation method where the velocity of the fluid is obtained by a numerical solution to Stokes or Navier-Stokes equations. We also provide a derivation of the asymptotic expansion for the lubrication force (used in our numerical experiments) acting on a disk immersed in a Newtonian fluid and approaching the wall. The method of this derivation is new and can be easily adapted to other cases