1,442 research outputs found
Experimenters' guide to colocalization studies: finding a way through indicators and quantifiers, in practice
International audienceMulticolor fluorescence microscopy helps to define the local interplay of subcellular components in cell biological experiments. The analysis of spatial coincidence of two or more markers is a first step in investigating the potential interactions of molecular actors. Colocalization studies rely on image preprocessing and further analysis; however, they are limited by optical resolution. Once those limitations are taken into account, characterization might be performed. In this review, we discuss two types of parameters that are aimed at evaluating colocalization, which are indicators and quantifiers. Indicators evaluate signal coincidence over a predefined scale, while quantifiers provide an absolute measurement. As the image is both a collection of intensities and a collection of objects, both approaches are applicable. Most of the available image processing software include various colocalization options; however, guidance for the choice of the appropriate method is rarely proposed. In this review, we provide the reader with a basic description of the available colocalization approaches, proposing a guideline for their use, either alone or in combination
Spectral Statistics for the Dirac Operator on Graphs
We determine conditions for the quantisation of graphs using the Dirac
operator for both two and four component spinors. According to the
Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry
the energy level statistics are expected, in the semiclassical limit, to
correspond to those of random matrices from the Gaussian symplectic ensemble.
This is confirmed by numerical investigation. The scattering matrix used to
formulate the quantisation condition is found to be independent of the type of
spinor. We derive an exact trace formula for the spectrum and use this to
investigate the form factor in the diagonal approximation
Quantum graphs with singular two-particle interactions
We construct quantum models of two particles on a compact metric graph with
singular two-particle interactions. The Hamiltonians are self-adjoint
realisations of Laplacians acting on functions defined on pairs of edges in
such a way that the interaction is provided by boundary conditions. In order to
find such Hamiltonians closed and semi-bounded quadratic forms are constructed,
from which the associated self-adjoint operators are extracted. We provide a
general characterisation of such operators and, furthermore, produce certain
classes of examples. We then consider identical particles and project to the
bosonic and fermionic subspaces. Finally, we show that the operators possess
purely discrete spectra and that the eigenvalues are distributed following an
appropriate Weyl asymptotic law
Semiclassical Approach to Parametric Spectral Correlation with Spin 1/2
The spectral correlation of a chaotic system with spin 1/2 is universally
described by the GSE (Gaussian Symplectic Ensemble) of random matrices in the
semiclassical limit. In semiclassical theory, the spectral form factor is
expressed in terms of the periodic orbits and the spin state is simulated by
the uniform distribution on a sphere. In this paper, instead of the uniform
distribution, we introduce Brownian motion on a sphere to yield the parametric
motion of the energy levels. As a result, the small time expansion of the form
factor is obtained and found to be in agreement with the prediction of
parametric random matrices in the transition within the GSE universality class.
Moreover, by starting the Brownian motion from a point distribution on the
sphere, we gradually increase the effect of the spin and calculate the form
factor describing the transition from the GOE (Gaussian Orthogonal Ensemble)
class to the GSE class.Comment: 25 pages, 2 figure
From error bounds to the complexity of first-order descent methods for convex functions
This paper shows that error bounds can be used as effective tools for
deriving complexity results for first-order descent methods in convex
minimization. In a first stage, this objective led us to revisit the interplay
between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can
show the equivalence between the two concepts for convex functions having a
moderately flat profile near the set of minimizers (as those of functions with
H\"olderian growth). A counterexample shows that the equivalence is no longer
true for extremely flat functions. This fact reveals the relevance of an
approach based on KL inequality. In a second stage, we show how KL inequalities
can in turn be employed to compute new complexity bounds for a wealth of
descent methods for convex problems. Our approach is completely original and
makes use of a one-dimensional worst-case proximal sequence in the spirit of
the famous majorant method of Kantorovich. Our result applies to a very simple
abstract scheme that covers a wide class of descent methods. As a byproduct of
our study, we also provide new results for the globalization of KL inequalities
in the convex framework.
Our main results inaugurate a simple methodology: derive an error bound,
compute the desingularizing function whenever possible, identify essential
constants in the descent method and finally compute the complexity using the
one-dimensional worst case proximal sequence. Our method is illustrated through
projection methods for feasibility problems, and through the famous iterative
shrinkage thresholding algorithm (ISTA), for which we show that the complexity
bound is of the form where the constituents of the bound only depend
on error bound constants obtained for an arbitrary least squares objective with
regularization
Semiclassical Approach to Chaotic Quantum Transport
We describe a semiclassical method to calculate universal transport
properties of chaotic cavities. While the energy-averaged conductance turns out
governed by pairs of entrance-to-exit trajectories, the conductance variance,
shot noise and other related quantities require trajectory quadruplets; simple
diagrammatic rules allow to find the contributions of these pairs and
quadruplets. Both pure symmetry classes and the crossover due to an external
magnetic field are considered.Comment: 33 pages, 11 figures (appendices B-D not included in journal version
Chemical Abundances For Evolved Stars In M5: Lithium Through Thorium
We present analysis of high-resolution spectra of a sample of stars in the globular cluster M5 (NGC 5904). The sample includes stars from the red giant branch (RGB; seven stars), the red horizontal branch (two stars), and the asymptotic giant branch (AGB; eight stars), with effective temperatures ranging from 4000 K to 6100 K. Spectra were obtained with the HIRES spectrometer on the Keck I telescope, with a wavelength coverage from 3700 angstrom to 7950 angstrom for the HB and AGB sample, and 5300 angstrom to 7600 angstrom for the majority of the RGB sample. We find offsets of some abundance ratios between the AGB and the RGB branches. However, these discrepancies appear to be due to analysis effects, and indicate that caution must be exerted when directly comparing abundance ratios between different evolutionary branches. We find the expected signatures of pollution from material enriched in the products of the hot hydrogen burning cycles such as the CNO, Ne-Na, and Mg-Al cycles, but no significant differences within these signatures among the three stellar evolutionary branches especially when considering the analysis offsets. We are also able to measure an assortment of neutron-capture element abundances, from Sr to Th, in the cluster. We find that the neutron-capture signature for all stars is the same, and shows a predominately r-process origin. However, we also see evidence of a small but consistent extra s-process signature that is not tied to the light-element variations, pointing to a pre-enrichment of this material in the protocluster gas.National Science Foundation AST-0802292NSF AST-0406988, AST-0607770, AST-0607482DFGW. M. Keck FoundationAstronom
Trace Formulae for quantum graphs with edge potentials
This work explores the spectra of quantum graphs where the Schr\"odinger
operator on the edges is equipped with a potential. The scattering approach,
which was originally introduced for the potential free case, is extended to
this case and used to derive a secular function whose zeros coincide with the
eigenvalue spectrum. Exact trace formulas for both smooth and
-potentials are derived, and an asymptotic semiclassical trace formula
(for smooth potentials) is presented and discussed
Photometry of the Globular Cluster NGC 5466: Red Giants and Blue Stragglers
We present wide-field BVI photometry for about 11,500 stars in the
low-metallicity cluster NGC 5466. We have detected the red giant branch bump
for the first time, although it is at least 0.2 mag fainter than expected
relative to the turnoff. The number of red giants (relative to main sequence
turnoff stars) is in excellent agreement with stellar models from the
Yonsei-Yale and Teramo groups, and slightly high compared to Victoria-Regina
models. This adds to evidence that an abnormally large ratio of red giant to
main-sequence stars is not correlated with cluster metallicity. We discuss
theoretical predictions from different research groups and find that the
inclusion or exclusion of helium diffusion and strong limit Coulomb
interactions may be partly responsible.
We also examine indicators of dynamical history: the mass function exponent
and the blue straggler frequency. NGC 5466 has a very shallow mass function,
consistent with large mass loss and recently-discovered tidal tails. The blue
straggler sample is significantly more centrally concentrated than the HB or
RGB stars. We see no evidence of an upturn in the blue straggler frequency at
large distances from the center. Dynamical friction timescales indicate that
the stragglers should be more concentrated if the cluster's present density
structure has existed for most of its history. NGC 5466 also has an unusually
low central density compared to clusters of similar luminosity. In spite of
this, the specific frequency of blue stragglers that puts it right on the
frequency -- cluster M_V relation observed for other clusters.Comment: 51 pages, 21 figures, 1 electronic table, accepted to Ap
Semiclassical analysis of the lowest-order multipole deformations of simple metal clusters
We use a perturbative semiclassical trace formula to calculate the three
lowest-order multipole (quadrupole \eps_2, octupole \eps_3, and
hexadecapole \eps_4) deformations of simple metal clusters with atoms in their ground states. The self-consistent mean field of the
valence electrons is modeled by an axially deformed cavity and the oscillating
part of the total energy is calculated semiclassically using the shortest
periodic orbits. The average energy is obtained from a liquid-drop model
adjusted to the empirical bulk and surface properties of the sodium metal. We
obtain good qualitative agreement with the results of quantum-mechanical
calculations using Strutinsky's shell-correction method.Comment: LaTeX file (v2) 6 figures, to be published in Phys. Lett.
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