17,049 research outputs found
Cramer-Rao Lower Bound for Point Based Image Registration with Heteroscedastic Error Model for Application in Single Molecule Microscopy
The Cramer-Rao lower bound for the estimation of the affine transformation
parameters in a multivariate heteroscedastic errors-in-variables model is
derived. The model is suitable for feature-based image registration in which
both sets of control points are localized with errors whose covariance matrices
vary from point to point. With focus given to the registration of fluorescence
microscopy images, the Cramer-Rao lower bound for the estimation of a feature's
position (e.g. of a single molecule) in a registered image is also derived. In
the particular case where all covariance matrices for the localization errors
are scalar multiples of a common positive definite matrix (e.g. the identity
matrix), as can be assumed in fluorescence microscopy, then simplified
expressions for the Cramer-Rao lower bound are given. Under certain simplifying
assumptions these expressions are shown to match asymptotic distributions for a
previously presented set of estimators. Theoretical results are verified with
simulations and experimental data
Phase space interference and the WKB approximation for squeezed number states
Squeezed number states for a single mode Hamiltonian are investigated from
two complementary points of view. Firstly the more relevant features of their
photon distribution are discussed using the WKB wave functions. In particular
the oscillations of the distribution and the parity behavior are derived and
compared with the exact results. The accuracy is verified and it is shown that
for high photon number it fails to reproduce the true distribution. This is
contrasted with the fact that for moderate squeezing the WKB approximation
gives the analytical justification to the interpretation of the oscillations as
the result of the interference of areas with definite phases in phase space. It
is shown with a computation at high squeezing using a modified prescription for
the phase space representation which is based on Wigner-Cohen distributions
that the failure of the WKB approximation does not invalidate the area overlap
picture.Comment: 9 pages, 4 figure
Accurate determination of the scattering length of metastable Helium atoms using dark resonances between atoms and exotic molecules
We present a new measurement of the s-wave scattering length a of
spin-polarized helium atoms in the 2^3S_1 metastable state. Using two-photon
photoassociation spectroscopy and dark resonances we measure the energy
E_{v=14}= -91.35 +/- 0.06 MHz of the least bound state v=14 in the interaction
potential of the two atoms. We deduce a value of a = 7.512 +/- 0.005 nm, which
is at least one hundred times more precise than the best previous
determinations and is in disagreement with some of them. This experiment also
demonstrates the possibility to create exotic molecules binding two metastable
atoms with a lifetime of the order of 1 microsecond.Comment: 4 pages, 4 figure
Surface characterization data for tethered polyacrylic acid layers synthesized on polysulfone surfaces.
The data presented are supplementary to an article [Kim et al., 2019] on synthesis and surface characterization of tethered polyacrylic acid (PAA) layers on polysulfone (PSf) film/membrane surfaces via atmospheric pressure plasma-induced graft polymerization (APPIGP). Data on surface characterization of the synthesized tethered PAA layers includes: AFM topographic surface images and height distributions of surface features, dry layer thickness, chain rupture length distributions determined via AFM based force spectroscopy (AFM-FS), in addition to measurements of water contact angles. Fouling propensity data for ultrafiltration of alginic acid as a model foulant are also provided for native and PAA grafted PSf ultrafiltration (UF) membranes
Complex collective states in a one-dimensional two-atom system
We consider a pair of identical two-level atoms interacting with a scalar
field in one dimension, separated by a distance . We restrict our
attention to states where one atom is excited and the other is in the ground
state, in symmetric or anti-symmetric combinations. We obtain exact collective
decaying states, belonging to a complex spectral representation of the
Hamiltonian. The imaginary parts of the eigenvalues give the decay rates, and
the real parts give the average energy of the collective states. In one
dimension there is strong interference between the fields emitted by the atoms,
leading to long-range cooperative effects. The decay rates and the energy
oscillate with the distance . Depending on , the decay rates
will either decrease, vanish or increase as compared with the one-atom decay
rate. We have sub- and super-radiance at periodic intervals. Our model may be
used to study two-cavity electron wave-guides. The vanishing of the collective
decay rates then suggests the possibility of obtaining stable configurations,
where an electron is trapped inside the two cavities.Comment: 14 pages, 14 figures, submitted to Phys. Rev.
The Kaon B-parameter in Mixed Action Chiral Perturbation Theory
We calculate the kaon B-parameter, B_K, in chiral perturbation theory for a
partially quenched, mixed action theory with Ginsparg-Wilson valence quarks and
staggered sea quarks. We find that the resulting expression is similar to that
in the continuum, and in fact has only two additional unknown parameters. At
one-loop order, taste-symmetry violations in the staggered sea sector only
contribute to flavor-disconnected diagrams by generating an O(a^2) shift to the
masses of taste-singlet sea-sea mesons. Lattice discretization errors also give
rise to an analytic term which shifts the tree-level value of B_K by an amount
of O(a^2). This term, however, is not strictly due to taste-breaking, and is
therefore also present in the expression for B_K for pure G-W lattice fermions.
We also present a numerical study of the mixed B_K expression in order to
demonstrate that both discretization errors and finite volume effects are small
and under control on the MILC improved staggered lattices.Comment: 29 pages, 4 figures; Expanded spurion discussion, other discussions
clarified, version to appear in PR
Fermion and Anti-Fermion Effective Masses in High Temperature Gauge Theories in -Asymmetric Background
We calculate the splitting between fermion and anti-fermion effective masses
in high temperature gauge theories in the presence of a non-vanishing chemical
potential due to the -asymmetric fermionic background. In particular we
consider the case of left-handed leptons in the theory when
the temperature is above GeV and the gauge symmetry is restored.Comment: 13 pages, TIPAC-93001
orbifold compactifications in with Gauss-Bonnet term
We present a general setup for junctions of semi-infinite 4-branes in
with the Gauss-Bonnet term. The 3-brane tension at the junction of 4-branes can
be nonzero. Using the brane junctions as the origin of the discrete
rotation symmetry, we identify 3-brane tensions at three fixed points of the
orbifold in terms of the 4-brane tensions. As a result, the three
3-brane tensions can be simultaneously positive, which enables us to explain
the mass hierarchy by taking one of two branes apart from the hidden brane as
the visible brane, and hence does not introduce a severe cosmological problem.Comment: Latex file of 20 pages including 2 figure
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