3,548 research outputs found
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
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 from interior Current Density Imaging data
obtainable using MRI measurements. We only require knowledge of the magnitude
of one current generated by a given voltage on the boundary
. As previously shown, the corresponding voltage potential u in
is a minimizer of the weighted least gradient problem
with . In this paper we present an
alternating split Bregman algorithm for treating such least gradient problems,
for non-negative and . 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 from knowledge of its magnitude, and of the voltage on the
boundary. We then present several numerical experiments that illustrate the
convergence behavior of the proposed algorithm
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]
Sexual selection on protamine and transition nuclear protein expression in mouse species
Post-copulatory sexual selection in the form of sperm competition is known to influence the evolution of male reproductive proteins in mammals. The relationship between sperm competition and regulatory evolution, however, remains to be explored. Protamines and transition nuclear proteins are involved in the condensation of sperm chromatin and are expected to affect the shape of the sperm head. A hydrodynamically efficient head allows for fast swimming velocity and, therefore, more competitive sperm. Previous comparative studies in rodents have documented a significant association between the level of sperm competition (as measured by relative testes mass) and DNA sequence evolution in both the coding and promoter sequences of protamine 2. Here,we investigate the influence of sexual selection on protamine and transition nuclear protein mRNA expression in the testes of eight mouse species that differ widely in levels of sperm competition.We also examined the relationship between relative gene expression levels and sperm head shape, assessed using geometric morphometrics. We found that species with higher levels of sperm competition express less protamine 2 in relation to protamine 1 and transition nuclear proteins. Moreover, therewas a significant association between relative protamine 2 expression and sperm head shape. Reduction in the relative abundance of protamine 2 may increase the competitive ability of sperm in mice, possibly by affecting sperm head shape. Changes in gene regulatory sequences thus seem to be the basis of the evolutionary response to sexual selection in these proteins. © 2014 The Author(s) Published by the Royal Society. All rights reserved.This work was supported by the Spanish Ministry of Economy and Competitiveness (grant no. CGL2011-26341)Peer Reviewe
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 . We give two basic constructions for cloaking a region
contained in a domain 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 , interpreted as a collection of sources and sinks
or an internal current.Comment: Final revision; to appear in Commun. in Math. Physic
Computationally Efficient Zero Noise Extrapolation for Quantum Gate Error Mitigation
Zero noise extrapolation (ZNE) is a widely used technique for gate error
mitigation on near term quantum computers because it can be implemented in
software and does not require knowledge of the quantum computer noise
parameters. Traditional ZNE requires a significant resource overhead in terms
of quantum operations. A recent proposal using a targeted (or random) instead
of fixed identity insertion method (RIIM versus FIIM) requires significantly
fewer quantum gates for the same formal precision. We start by showing that
RIIM can allow for ZNE to be deployed on deeper circuits than FIIM, but
requires many more measurements to maintain the same statistical uncertainty.
We develop two extensions to FIIM and RIIM. The List Identity Insertion Method
(LIIM) allows to mitigate the error from certain CNOT gates, typically those
with the largest error. Set Identity Insertion Method (SIIM) naturally
interpolates between the measurement-efficient FIIM and the gate-efficient
RIIM, allowing to trade off fewer CNOT gates for more measurements. Finally, we
investigate a way to boost the number of measurements, namely to run ZNE in
parallel, utilizing as many quantum devices as are available. We explore the
performance of RIIM in a parallel setting where there is a non-trivial spread
in noise across sets of qubits within or across quantum computers.Comment: 10 pages, 10 figure
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