23,785 research outputs found
Reentrant stability of BEC standing wave patterns
We describe standing wave patterns induced by an attractive finite-ranged
external potential inside a large Bose-Einstein Condensate (BEC). As the
potential depth increases, the time independent Gross-Pitaevskii equation
develops pairs of solutions that have nodes in their wavefunction. We elucidate
the nature of these states and study their dynamical stability. Although we
study the problem in a two-dimensional BEC subject to a cylindrically symmetric
square-well potential of a radius that is comparable to the coherence length of
the BEC, our analysis reveals general trends, valid in two and three
dimensions, independent of the symmetry of the localized potential well, and
suggestive of the behavior in general, short- and large-range potentials. One
set of nodal BEC wavefunctions resembles the single particle n node bound state
wavefunction of the potential well, the other wavefunctions resemble the n-1
node bound-state wavefunction with a kink state pinned by the potential. The
second state, though corresponding to the lower free energy value of the pair
of n node BEC states, is always unstable, whereas the first can be dynamically
stable in intervals of the potential well depth, implying that the standing
wave BEC can evolve from a dynamically unstable to stable, and back to unstable
status as the potential well is adiabatically deepened, a phenomenon that we
refer to as "reentrant dynamical stability".Comment: 13 pages, 9 figures; revised discussion in Sec.
On the "Poisson Trick" and its Extensions for Fitting Multinomial Regression Models
This article is concerned with the fitting of multinomial regression models
using the so-called "Poisson Trick". The work is motivated by Chen & Kuo (2001)
and Malchow-M{\o}ller & Svarer (2003) which have been criticized for being
computationally inefficient and sometimes producing nonsense results. We first
discuss the case of independent data and offer a parsimonious fitting strategy
when all covariates are categorical. We then propose a new approach for
modelling correlated responses based on an extension of the Gamma-Poisson
model, where the likelihood can be expressed in closed-form. The parameters are
estimated via an Expectation/Conditional Maximization (ECM) algorithm, which
can be implemented using functions for fitting generalized linear models
readily available in standard statistical software packages. Compared to
existing methods, our approach avoids the need to approximate the intractable
integrals and thus the inference is exact with respect to the approximating
Gamma-Poisson model. The proposed method is illustrated via a reanalysis of the
yogurt data discussed by Chen & Kuo (2001)
A Proof of Entropy Minimization for Outputs in Deletion Channels via Hidden Word Statistics
From the output produced by a memoryless deletion channel from a uniformly
random input of known length , one obtains a posterior distribution on the
channel input. The difference between the Shannon entropy of this distribution
and that of the uniform prior measures the amount of information about the
channel input which is conveyed by the output of length , and it is natural
to ask for which outputs this is extremized. This question was posed in a
previous work, where it was conjectured on the basis of experimental data that
the entropy of the posterior is minimized and maximized by the constant strings
and and the alternating strings
and respectively. In the present
work we confirm the minimization conjecture in the asymptotic limit using
results from hidden word statistics. We show how the analytic-combinatorial
methods of Flajolet, Szpankowski and Vall\'ee for dealing with the hidden
pattern matching problem can be applied to resolve the case of fixed output
length and , by obtaining estimates for the entropy in
terms of the moments of the posterior distribution and establishing its
minimization via a measure of autocorrelation.Comment: 11 pages, 2 figure
The Digital Age: Reminder and Confirmation Preference in Blood Donation
Introduction:
It is widely accepted that individuals are more likely to comply and follow through with responsibilities when reminded and asked to confirm their commitments. With the American Red Cross’ access to fast and affordable communication and this notion in mind, there is potential to develop new recruitment strategies and better methods of ensuring blood donation commitments.
In particular, understanding modes of communication with the donor population can have significant implications: avoiding loss of follow up, improving donor experience, and ensuring appropriate use of resources and staff; therefore, the American Red Cross is interested in understanding demographic differences among those who prefer different modes of communication for blood donor appointment reminders and confirmations.https://scholarworks.uvm.edu/comphp_gallery/1223/thumbnail.jp
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