5,599 research outputs found
Edge-reinforced random walk on a ladder
We prove that the edge-reinforced random walk on the ladder
with initial weights is recurrent. The
proof uses a known representation of the edge-reinforced random walk on a
finite piece of the ladder as a random walk in a random environment. This
environment is given by a marginal of a multicomponent Gibbsian process. A
transfer operator technique and entropy estimates from statistical mechanics
are used to analyze this Gibbsian process. Furthermore, we prove spatially
exponentially fast decreasing bounds for normalized local times of the
edge-reinforced random walk on a finite piece of the ladder, uniformly in the
size of the finite piece.Comment: Published at http://dx.doi.org/10.1214/009117905000000396 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Asymptotic behavior of edge-reinforced random walks
In this article, we study linearly edge-reinforced random walk on general
multi-level ladders for large initial edge weights. For infinite ladders, we
show that the process can be represented as a random walk in a random
environment, given by random weights on the edges. The edge weights decay
exponentially in space. The process converges to a stationary process. We
provide asymptotic bounds for the range of the random walker up to a given
time, showing that it localizes much more than an ordinary random walker. The
random environment is described in terms of an infinite-volume Gibbs measure.Comment: Published at http://dx.doi.org/10.1214/009117906000000674 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Bayesian analysis for reversible Markov chains
We introduce a natural conjugate prior for the transition matrix of a
reversible Markov chain. This allows estimation and testing. The prior arises
from random walk with reinforcement in the same way the Dirichlet prior arises
from P\'{o}lya's urn. We give closed form normalizing constants, a simple
method of simulation from the posterior and a characterization along the lines
of W. E. Johnson's characterization of the Dirichlet prior.Comment: Published at http://dx.doi.org/10.1214/009053606000000290 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Linearly edge-reinforced random walks
We review results on linearly edge-reinforced random walks. On finite graphs,
the process has the same distribution as a mixture of reversible Markov chains.
This has applications in Bayesian statistics and it has been used in studying
the random walk on infinite graphs. On trees, one has a representation as a
random walk in an independent random environment. We review recent results for
the random walk on ladders: recurrence, a representation as a random walk in a
random environment, and estimates for the position of the random walker.Comment: Published at http://dx.doi.org/10.1214/074921706000000103 in the IMS
Lecture Notes--Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
How Vertex reinforced jump process arises naturally
We prove that the only nearest neighbor jump process with local dependence on
the occupation times satisfying the partial exchangeability property is the
vertex reinforced jump process, under some technical conditions. This result
gives a counterpart to the characterization of edge reinforced random walk
given by Rolles.Comment: 14 pages, 3 figures, version
Characterizing gas flow from aerosol particle injectors
A novel methodology for measuring gas flow from small orifices or nozzles
into vacuum is presented. It utilizes a high-intensity femtosecond laser pulse
to create a plasma within the gas plume produced by the nozzle, which is imaged
by a microscope. Calibration of the imaging system allows for the extraction of
absolute number densities. We show detection down to helium densities of
~cm with a spatial resolution of a few micrometer. The
technique is used to characterize the gas flow from a convergent-nozzle aerosol
injector [Struct.\ Dyn.~2, 041717 (2015)] as used in single-particle
diffractive imaging experiments at free-electron laser sources. Based on the
measured gas-density profile we estimate the scattering background signal under
typical operating conditions of single-particle imaging experiments and
estimate that fewer than 50 photons per shot can be expected on the detector
High-repetition-rate and high-photon-flux 70 eV high-harmonic source for coincidence ion imaging of gas-phase molecules
Unraveling and controlling chemical dynamics requires techniques to image
structural changes of molecules with femtosecond temporal and picometer spatial
resolution. Ultrashort-pulse x-ray free-electron lasers have significantly
advanced the field by enabling advanced pump-probe schemes. There is an
increasing interest in using table-top photon sources enabled by high-harmonic
generation of ultrashort-pulse lasers for such studies. We present a novel
high-harmonic source driven by a 100 kHz fiber laser system, which delivers
10 photons/s in a single 1.3 eV bandwidth harmonic at 68.6 eV. The
combination of record-high photon flux and high repetition rate paves the way
for time-resolved studies of the dissociation dynamics of inner-shell ionized
molecules in a coincidence detection scheme. First coincidence measurements on
CHI are shown and it is outlined how the anticipated advancement of fiber
laser technology and improved sample delivery will, in the next step, allow
pump-probe studies of ultrafast molecular dynamics with table-top XUV-photon
sources. These table-top sources can provide significantly higher repetition
rates than the currently operating free-electron lasers and they offer very
high temporal resolution due to the intrinsically small timing jitter between
pump and probe pulses
Imaging Molecular Structure through Femtosecond Photoelectron Diffraction on Aligned and Oriented Gas-Phase Molecules
This paper gives an account of our progress towards performing femtosecond
time-resolved photoelectron diffraction on gas-phase molecules in a pump-probe
setup combining optical lasers and an X-ray Free-Electron Laser. We present
results of two experiments aimed at measuring photoelectron angular
distributions of laser-aligned 1-ethynyl-4-fluorobenzene (C8H5F) and
dissociating, laseraligned 1,4-dibromobenzene (C6H4Br2) molecules and discuss
them in the larger context of photoelectron diffraction on gas-phase molecules.
We also show how the strong nanosecond laser pulse used for adiabatically
laser-aligning the molecules influences the measured electron and ion spectra
and angular distributions, and discuss how this may affect the outcome of
future time-resolved photoelectron diffraction experiments.Comment: 24 pages, 10 figures, Faraday Discussions 17
Steps in immunosuppression for renal transplantation
The authors provide a historical survey of the immunosuppressive agents that have been used to prevent allograft rejection. Attention is given to the expected effect of cyclosporin in kidney translations
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