Identification of nonlinearity in conductivity equation via Dirichlet-to-Neumann map

We prove that the linear term and quadratic nonlinear term entering a nonlinear elliptic equation of divergence type can be uniquely identified by the Dirichlet to Neuman map. The unique identifiability is proved using the complex geometrical optics solutions and singular solutions

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

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)]

Ligand selectivity in tachykinin and natalisin neuropeptidergic systems of the honey bee parasitic mite Varroa destructor

Citation: Jiang, H., Kim, D., Dobesh, S., Evans, J. D., Nachman, R. J., Kaczmarek, K., . . . Park, Y. (2016). Ligand selectivity in tachykinin and natalisin neuropeptidergic systems of the honey bee parasitic mite Varroa destructor. Scientific Reports, 6, 8. doi:10.1038/srep19547The varroa mite, Varroa destructor, is a devastating ectoparasite of the honey bees Apis mellifera and A. cerana. Control of these mites in beehives is a challenge in part due to the lack of toxic agents that are specific to mites and not to the host honey bee. In searching for a specific toxic target of varroa mites, we investigated two closely related neuropeptidergic systems, tachykinin-related peptide (TRP) and natalisin (NTL), and their respective receptors. Honey bees lack both NTL and the NTL receptor in their genome sequences, providing the rationale for investigating these receptors to understand their specificities to various ligands. We characterized the receptors for NTL and TRP of V. destructor (VdNTL-R and VdTRP-R, respectively) and for TRP of A. mellifera (AmTRP-R) in a heterologous reporter assay system to determine the activities of various ligands including TRP/NTL peptides and peptidomimetics. Although we found that AmTRP-R is highly promiscuous, activated by various ligands including two VdNTL peptides when a total of 36 ligands were tested, we serendipitously found that peptides carrying the C-terminal motif-FWxxRamide are highly specific to VdTRP-R. This motif can serve as a seed sequence for designing a VdTRP-R-specific agonist

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 population genetics of crypsis in vertebrates: recent insights from mice, hares, and lizards

By combining well-established population genetic theory with high-throughput sequencing data from natural populations, major strides have recently been made in understanding how, why, and when vertebrate populations evolve crypsis. Here, we focus on background matching, a particular facet of crypsis that involves the ability of an organism to conceal itself through matching its color to the surrounding environment. While interesting in and of itself, the study of this phenotype has also provided fruitful population genetic insights into the interplay of strong positive selection with other evolutionary processes. Specifically, and predicated upon the findings of previous candidate gene association studies, a primary focus of this recent literature involves the realization that the inference of selection from DNA sequence data first requires a robust model of population demography in order to identify genomic regions which do not conform to neutral expectations. Moreover, these demographic estimates provide crucial information about the origin and timing of the onset of selective pressures associated with, for example, the colonization of a novel environment. Furthermore, such inference has revealed crypsis to be a particularly useful phenotype for investigating the interplay of migration and selection-with examples of gene flow constraining rates of adaptation, or alternatively providing the genetic variants that may ultimately sweep through the population. Here, we evaluate the underlying evidence, review the strengths and weaknesses of the many population genetic methodologies used in these studies, and discuss how these insights have aided our general understanding of the evolutionary process

Induction of carcinoembryonic antigen expression in a three-dimensional culture system

MIP-101 is a poorly differentiated human colon carcinoma cell line established from ascites that produces minimal amounts of carcinoembryonic antigen (CEA), a 180 kDa glycoprotein tumor marker, and nonspecific cross-reacting antigen (NCA), a related protein that has 50 and 90 kDa isoforms, in vitro in monolayer culture. MIP-101 produces CEA when implanted into the peritoneum of nude mice but not when implanted into subcutaneous tissue. We tested whether MIP-101 cells may be induced to express CEA when cultured on microcarrier beads in three-dimensional cultures, either in static cultures as non-adherent aggregates or under dynamic conditions in a NASA-designed low shear stress bioreactor. MIP- 101 cells proliferated well under all three conditions and increased CEA and NCA production 3 - 4 fold when grown in three-dimensional cultures compared to MIP-101 cells growing logarithmically in monolayers. These results suggest that three-dimensional growth in vitro simulates tumor function in vivo and that three-dimensional growth by itself may enhance production of molecules that are associated with the metastatic process