117 research outputs found
Using Automatic Differentiation as a General Framework for Ptychographic Reconstruction
Coherent diffraction imaging methods enable imaging beyond lens-imposed
resolution limits. In these methods, the object can be recovered by minimizing
an error metric that quantifies the difference between diffraction patterns as
observed, and those calculated from a present guess of the object. Efficient
minimization methods require analytical calculation of the derivatives of the
error metric, which is not always straightforward. This limits our ability to
explore variations of basic imaging approaches. In this paper, we propose to
substitute analytical derivative expressions with the automatic differentiation
method, whereby we can achieve object reconstruction by specifying only the
physics-based experimental forward model. We demonstrate the generality of the
proposed method through straightforward object reconstruction for a variety of
complex ptychographic experimental models.Comment: 23 pages (including references and supplemental material), 19
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Teleparallel Energy-Momentum Distribution of Static Axially Symmetric Spacetimes
This paper is devoted to discuss the energy-momentum for static axially
symmetric spacetimes in the framework of teleparallel theory of gravity. For
this purpose, we use the teleparallel versions of Einstein, Landau-Lifshitz,
Bergmann and Mller prescriptions. A comparison of the results shows
that the energy density is different but the momentum turns out to be constant
in each prescription. This is exactly similar to the results available in
literature using the framework of General Relativity. It is mentioned here that
Mller energy-momentum distribution is independent of the coupling
constant . Finally, we calculate energy-momentum distribution for the
Curzon metric, a special case of the above mentioned spacetime.Comment: 14 pages, accepted for publication in Mod. Phys. Lett.
Teleparallel Energy-Momentum Distribution of Spatially Homogeneous Rotating Spacetimes
The energy-momentum distribution of spatially homogeneous rotating spacetimes
in the context of teleparallel theory of gravity is investigated. For this
purpose, we use the teleparallel version of Moller prescription. It is found
that the components of energy-momentum density are finite and well-defined but
are different from General Relativity. However, the energy-momentum density
components become the same in both theories under certain assumptions. We also
analyse these quantities for some special solutions of the spatially
homogeneous rotating spacetimes.Comment: 12 pages, accepted for publication in Int. J. Theor. Phy
Antidepressant Activity of Pharmacological and Genetic Deactivation of the Small-Conductance Calcium-Activated Potassium Channel Subtype-3
Funding and Disclosure This research was supported by awards from the Neuroscience Catalyst program (Toronto) (FRB and JNN), the Canadian Institutes of Health Research (FRB and JN) and the National Science and Engineering Research Council of Canada (FRB). M.N. was additionally supported by a CAMH Discovery Fund Post-doctoral Fellowship. Conflict of Interest: None declared. Acknowledgments We thank J. Li, U. Mumtaz, S. Khan, S. Sivaruban, M. Billyard, E. Hauck, D. Oleinichenko, Michael Coombs and Lucas Francis Fowler for technical assistance at different stages of the work.Peer reviewedPostprin
The Energy of Regular Black Hole in General Relativity Coupled to Nonlinear Electrodynamics
According to the Einstein, Weinberg, and M{\o}ller energy-momentum complexes,
we evaluate the energy distribution of the singularity-free solution of the
Einstein field equations coupled to a suitable nonlinear electrodynamics
suggested by Ay\'{o}n-Beato and Garc\'{i}a. The results show that the energy
associated with the definitions of Einstein and Weinberg are the same, but
M{\o}ller not. Using the power series expansion, we find out that the first two
terms in the expression are the same as the energy distributions of the
Reissner-Nordstr\"{o}m solution, and the third term could be used to survey the
factualness between numerous solutions of the Einstein field eqautions coupled
to a nonlinear electrodynamics.Comment: 11 page
A differentiable forward model for the concurrent, multi-peak Bragg coherent x-ray diffraction imaging problem
We present a general analytic approach to spatially resolve the nano-scale
lattice distortion field of strained and defected compact crystals with Bragg
coherent x-ray diffraction imaging (BCDI). Our approach relies on fitting a
differentiable forward model simultaneously to multiple BCDI datasets
corresponding to independent Bragg reflections from the same single crystal. It
is designed to be faithful to heterogeneities that potentially manifest as
phase discontinuities in the coherently diffracted wave, such as lattice
dislocations in an imperfect crystal. We retain fidelity to such small features
in the reconstruction process through a Fourier transform -based resampling
algorithm designed to largely avoid the point spread tendencies of commonly
employed interpolation methods. The reconstruction model defined in this manner
brings BCDI reconstruction into the scope of explicit optimization driven by
automatic differentiation. With results from simulations and experimental
diffraction data, we demonstrate significant improvement in the final image
quality compared to conventional phase retrieval, enabled by explicitly
coupling multiple BCDI datasets into the reconstruction loss function.Comment: 30 pages, 23 figure
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