A Nonlinear Plancherel Theorem with Applications to Global Well-Posedness for the Defocusing Davey-Stewartson Equation and to the Inverse Boundary Value Problem of Calderón

We prove a Plancherel theorem for a nonlinear Fourier transform in two dimensions arising in the Inverse Scattering method for the defocusing Davey-Stewartson II equation. We then use it to prove global well-posedness and scattering in $L^2$ for defocusing DSII. This Plancherel theorem also implies global uniqueness in the inverse boundary value problem of Calder\'on in dimension $2$, for conductivities \sigma>0 with $\log \sigma \in \dot H^1$. The proof of the nonlinear Plancherel theorem includes new estimates on classical fractional integrals, as well as a new result on $L^2$-boundedness of pseudo-differential operators with non-smooth symbols, valid in all dimensions

Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential

For the Schrodinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential. For the case of zero background potential these results were obtained in [R.G.Novikov, Multidimensional inverse spectral problem for the equation -\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22, (1988)]

A convergent algorithm for the hybrid problem of reconstructing conductivity from minimal interior data

We consider the hybrid problem of reconstructing the isotropic electric conductivity of a body $\Omega$ from interior Current Density Imaging data obtainable using MRI measurements. We only require knowledge of the magnitude $|J|$ of one current generated by a given voltage $f$ on the boundary $\partial\Omega$. As previously shown, the corresponding voltage potential u in $\Omega$ is a minimizer of the weighted least gradient problem $$u=\hbox{argmin} \{\int_{\Omega}a(x)|\nabla u|: u \in H^{1}(\Omega), \ \ u|_{\partial \Omega}=f\},$$ with $a(x)= |J(x)|$. In this paper we present an alternating split Bregman algorithm for treating such least gradient problems, for $a\in L^2(\Omega)$ non-negative and $f\in H^{1/2}(\partial \Omega)$. We give a detailed convergence proof by focusing to a large extent on the dual problem. This leads naturally to the alternating split Bregman algorithm. The dual problem also turns out to yield a novel method to recover the full vector field $J$ from knowledge of its magnitude, and of the voltage $f$ on the boundary. We then present several numerical experiments that illustrate the convergence behavior of the proposed algorithm

A comparative study of allowable pesticide residue levels on produce in the United States

Background: The U.S. imports a substantial and increasing portion of its fruits and vegetables. The U.S. Food and Drug Administration currently inspects less than one percent of import shipments. While countries exporting to the U.S. are expected to comply with U.S. tolerances, including allowable pesticide residue levels, there is a low rate of import inspections and few other incentives for compliance. Methods: This analysis estimates the quantity of excess pesticide residue that could enter the U.S. if exporters followed originating country requirements but not U.S. pesticide tolerances, for the top 20 imported produce items based on quantities imported and U.S. consumption levels. Pesticide health effects data are also shown. Results: The model estimates that for the identified items, 120 439 kg of pesticides in excess of U.S. tolerances could potentially be imported to the U.S., in cases where U.S. regulations are more protective than those of originating countries. This figure is in addition to residues allowed on domestic produce. In the modeling, the top produce item, market, and pesticide of concern were oranges, Chile, and Zeta-Cypermethrin. Pesticides in this review are associated with health effects on 13 body systems, and some are associated with carcinogenic effects. Conclusions: There is a critical information gap regarding pesticide residues on produce imported to the U.S. Without a more thorough sampling program, it is not possible accurately to characterize risks introduced by produce importation. The scenario presented herein relies on assumptions, and should be considered illustrative. The analysis highlights the need for additional investigation and resources for monitoring, enforcement, and other interventions, to improve import food safety and reduce pesticide exposures in originating countries

New global stability estimates for the Gel'fand-Calderon inverse problem

We prove new global stability estimates for the Gel'fand-Calderon inverse problem in 3D. For sufficiently regular potentials this result of the present work is a principal improvement of the result of [G. Alessandrini, Stable determination of conductivity by boundary measurements, Appl. Anal. 27 (1988), 153-172]

ADMAN: an Alarm-based mobile Diabetes MANagement system for mobile geriatric teams

In this article, we introduce ADMAN an alarm-based diabetes management system for the disposal of Mobile Geriatric Teams MGT. The system aims at providing a form of remote monitoring in order to control the diabetes rate for elder patients. The system is multidimensional in a way that it resides at the patient mobile machine from a side, the doctor’s mobile machine from another side and can be connected to any other entity related to the MGT that is handling his case (e.g. dietitian)

Full-wave invisibility of active devices at all frequencies

There has recently been considerable interest in the possibility, both theoretical and practical, of invisibility (or "cloaking") from observation by electromagnetic (EM) waves. Here, we prove invisibility, with respect to solutions of the Helmholtz and Maxwell's equations, for several constructions of cloaking devices. Previous results have either been on the level of ray tracing [Le,PSS] or at zero frequency [GLU2,GLU3], but recent numerical [CPSSP] and experimental [SMJCPSS] work has provided evidence for invisibility at frequency $k\ne 0$. We give two basic constructions for cloaking a region $D$ contained in a domain $\Omega$ from measurements of Cauchy data of waves at \p \Omega; we pay particular attention to cloaking not just a passive object, but an active device within $D$, interpreted as a collection of sources and sinks or an internal current.Comment: Final revision; to appear in Commun. in Math. Physic

The role of mutation rate variation and genetic diversity in the architecture of human disease

Background We have investigated the role that the mutation rate and the structure of genetic variation at a locus play in determining whether a gene is involved in disease. We predict that the mutation rate and its genetic diversity should be higher in genes associated with disease, unless all genes that could cause disease have already been identified. Results Consistent with our predictions we find that genes associated with Mendelian and complex disease are substantially longer than non-disease genes. However, we find that both Mendelian and complex disease genes are found in regions of the genome with relatively low mutation rates, as inferred from intron divergence between humans and chimpanzees, and they are predicted to have similar rates of non-synonymous mutation as other genes. Finally, we find that disease genes are in regions of significantly elevated genetic diversity, even when variation in the rate of mutation is controlled for. The effect is small nevertheless. Conclusions Our results suggest that gene length contributes to whether a gene is associated with disease. However, the mutation rate and the genetic architecture of the locus appear to play only a minor role in determining whether a gene is associated with disease

Emergence and patterning dynamics of mouse-definitive endoderm

The segregation of definitive endoderm (DE) from bipotent mesendoderm progenitors leads to the formation of two distinct germ layers. Dissecting DE commitment and onset has been challenging as it occurs within a narrow spatiotemporal window in the embryo. Here, we employ a dual Bra/Sox17 reporter cell line to study DE onset dynamics. We find Sox17 expression initiates in vivo in isolated cells within a temporally restricted window. In 2D and 3D in vitro models, DE cells emerge from mesendoderm progenitors at a temporally regular, but spatially stochastic pattern, which is subsequently arranged by self-sorting of Sox17 + cells. A subpopulation of Bra-high cells commits to a Sox17+ fate independent of external Wnt signal. Self-sorting coincides with upregulation of E-cadherin but is not necessary for DE differentiation or proliferation. Our in vivo and in vitro results highlight basic rules governing DE onset and patterning through the commonalities and differences between these systems