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

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

FINITE-ELEMENT APPROXIMATION OF THE PARABOLIC P-LAPLACIAN

Published versio

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

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

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

Simulating (electro)hydrodynamic effects in colloidal dispersions: smoothed profile method

Previously, we have proposed a direct simulation scheme for colloidal dispersions in a Newtonian solvent [Phys.Rev.E 71,036707 (2005)]. An improved formulation called the ``Smoothed Profile (SP) method'' is presented here in which simultaneous time-marching is used for the host fluid and colloids. The SP method is a direct numerical simulation of particulate flows and provides a coupling scheme between the continuum fluid dynamics and rigid-body dynamics through utilization of a smoothed profile for the colloidal particles. Moreover, the improved formulation includes an extension to incorporate multi-component fluids, allowing systems such as charged colloids in electrolyte solutions to be studied. The dynamics of the colloidal dispersions are solved with the same computational cost as required for solving non-particulate flows. Numerical results which assess the hydrodynamic interactions of colloidal dispersions are presented to validate the SP method. The SP method is not restricted to particular constitutive models of the host fluids and can hence be applied to colloidal dispersions in complex fluids