25,127 research outputs found
Neural network image reconstruction for magnetic particle imaging
We investigate neural network image reconstruction for magnetic particle
imaging. The network performance depends strongly on the convolution effects of
the spectrum input data. The larger convolution effect appearing at a
relatively smaller nanoparticle size obstructs the network training. The
trained single-layer network reveals the weighting matrix consisted of a basis
vector in the form of Chebyshev polynomials of the second kind. The weighting
matrix corresponds to an inverse system matrix, where an incoherency of basis
vectors due to a low convolution effects as well as a nonlinear activation
function plays a crucial role in retrieving the matrix elements. Test images
are well reconstructed through trained networks having an inverse kernel
matrix. We also confirm that a multi-layer network with one hidden layer
improves the performance. The architecture of a neural network overcoming the
low incoherence of the inverse kernel through the classification property will
become a better tool for image reconstruction.Comment: 9 pages, 11 figure
Quantizations of some Poisson-Lie groups: The bicrossed product construction
By working with several specific Poisson-Lie groups arising from Heisenberg
Lie bialgebras and by carrying out their quantizations, a case is made for a
useful but simple method of constructing locally compact quantum groups. The
strategy is to analyze and collect enough information from a Poisson-Lie group,
and using it to carry out a ``cocycle bicrossed product construction''.
Constructions are done using multiplicative unitary operators, obtaining
C*-algebraic, locally compact quantum (semi-)groups.Comment: 26 page
Eigenfunctions for Liouville Operators, Classical Collision Operators, and Collision Bracket Integrals in Kinetic Theory
In the kinetic theory of dense fluids the many-particle collision bracket
integral is given in terms of a classical collision operator defined in the
phase space. To find an algorithm to compute the collision bracket integrals,
we revisit the eigenvalue problem of the Liouville operator and re-examine the
method previously reported[Chem. Phys. 20, 93(1977)]. Then we apply the notion
and concept of the eigenfunctions of the Liouville operator and knowledge
acquired in the study of the eigenfunctions to obtain alternative forms for
collision integrals. One of the alternative forms is given in the form of time
correlation function. This form, on an additional approximation, assumes a form
reminiscent of the Chapman-Enskog collision bracket integral for dilute gases.
It indeed gives rise to the latter in the case of two particles. The
alternative forms obtained are more readily amenable to numerical simulation
methods than the collision bracket integras expressed in terms of a classical
collision operator, which requires solution of classical Lippmann-Schwinger
integral equations. This way, the aforementioned kinetic theory of dense fluids
is made more accessible by numerical computation/simulation methods than
before.Comment: 34 pages, no figure, original pape
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