7,387 research outputs found
Betti number signatures of homogeneous Poisson point processes
The Betti numbers are fundamental topological quantities that describe the
k-dimensional connectivity of an object: B_0 is the number of connected
components and B_k effectively counts the number of k-dimensional holes.
Although they are appealing natural descriptors of shape, the higher-order
Betti numbers are more difficult to compute than other measures and so have not
previously been studied per se in the context of stochastic geometry or
statistical physics.
As a mathematically tractable model, we consider the expected Betti numbers
per unit volume of Poisson-centred spheres with radius alpha. We present
results from simulations and derive analytic expressions for the low intensity,
small radius limits of Betti numbers in one, two, and three dimensions. The
algorithms and analysis depend on alpha-shapes, a construction from
computational geometry that deserves to be more widely known in the physics
community.Comment: Submitted to PRE. 11 pages, 10 figure
Stability of continuously pumped atom lasers
A multimode model of a continuously pumped atom laser is shown to be unstable
below a critical value of the scattering length. Above the critical scattering
length, the atom laser reaches a steady state, the stability of which increases
with pumping. Below this limit the laser does not reach a steady state. This
instability results from the competition between gain and loss for the excited
states of the lasing mode. It will determine a fundamental limit for the
linewidth of an atom laser beam.Comment: 4 page
Nested Markov Properties for Acyclic Directed Mixed Graphs
Directed acyclic graph (DAG) models may be characterized in at least four
different ways: via a factorization, the d-separation criterion, the
moralization criterion, and the local Markov property. As pointed out by Robins
(1986, 1999), Verma and Pearl (1990), and Tian and Pearl (2002b), marginals of
DAG models also imply equality constraints that are not conditional
independences. The well-known `Verma constraint' is an example. Constraints of
this type were used for testing edges (Shpitser et al., 2009), and an efficient
marginalization scheme via variable elimination (Shpitser et al., 2011).
We show that equality constraints like the `Verma constraint' can be viewed
as conditional independences in kernel objects obtained from joint
distributions via a fixing operation that generalizes conditioning and
marginalization. We use these constraints to define, via Markov properties and
a factorization, a graphical model associated with acyclic directed mixed
graphs (ADMGs). We show that marginal distributions of DAG models lie in this
model, prove that a characterization of these constraints given in (Tian and
Pearl, 2002b) gives an alternative definition of the model, and finally show
that the fixing operation we used to define the model can be used to give a
particularly simple characterization of identifiable causal effects in hidden
variable graphical causal models.Comment: 67 pages (not including appendix and references), 8 figure
Tactile Interactions with a Humanoid Robot : Novel Play Scenario Implementations with Children with Autism
Acknowledgments: This work has been partially supported by the European Commission under contract number FP7-231500-ROBOSKIN. Open Access: This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.The work presented in this paper was part of our investigation in the ROBOSKIN project. The project has developed new robot capabilities based on the tactile feedback provided by novel robotic skin, with the aim to provide cognitive mechanisms to improve human-robot interaction capabilities. This article presents two novel tactile play scenarios developed for robot-assisted play for children with autism. The play scenarios were developed against specific educational and therapeutic objectives that were discussed with teachers and therapists. These objectives were classified with reference to the ICF-CY, the International Classification of Functioning – version for Children and Youth. The article presents a detailed description of the play scenarios, and case study examples of their implementation in HRI studies with children with autism and the humanoid robot KASPAR.Peer reviewedFinal Published versio
Sparse Nested Markov models with Log-linear Parameters
Hidden variables are ubiquitous in practical data analysis, and therefore
modeling marginal densities and doing inference with the resulting models is an
important problem in statistics, machine learning, and causal inference.
Recently, a new type of graphical model, called the nested Markov model, was
developed which captures equality constraints found in marginals of directed
acyclic graph (DAG) models. Some of these constraints, such as the so called
`Verma constraint', strictly generalize conditional independence. To make
modeling and inference with nested Markov models practical, it is necessary to
limit the number of parameters in the model, while still correctly capturing
the constraints in the marginal of a DAG model. Placing such limits is similar
in spirit to sparsity methods for undirected graphical models, and regression
models. In this paper, we give a log-linear parameterization which allows
sparse modeling with nested Markov models. We illustrate the advantages of this
parameterization with a simulation study.Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty
in Artificial Intelligence (UAI2013
Classical noise and flux: the limits of multi-state atom lasers
By direct comparison between experiment and theory, we show how the classical
noise on a multi-state atom laser beam increases with increasing flux. The
trade off between classical noise and flux is an important consideration in
precision interferometric measurement. We use periodic 10 microsecond
radio-frequency pulses to couple atoms out of an F=2 87Rb Bose-Einstein
condensate. The resulting atom laser beam has suprising structure which is
explained using three dimensional simulations of the five state
Gross-Pitaevskii equations.Comment: 4 pages, 3 figure
Achieving peak brightness in an atom laser
In this paper we present experimental results and theory on the first
continuous (long pulse) Raman atom laser. The brightness that can be achieved
with this system is three orders of magnitude greater than has been previously
demonstrated in any other continuously outcoupled atom laser. In addition, the
energy linewidth of a continuous atom laser can be made arbitrarily narrow
compared to the mean field energy of a trapped condensate. We analyze the flux
and brightness of the atom laser with an analytic model that shows excellent
agreement with experiment with no adjustable parameters.Comment: 4 pages, 4 black and white figures, submitted to Physical Revie
11 W narrow linewidth laser source at 780nm for laser cooling and manipulation of Rubidium
We present a narrow linewidth continuous laser source with over 11 Watts of
output power at 780nm, based on single-pass frequency doubling of an amplified
1560nm fibre laser with 36% efficiency. This source offers a combination of
high power, simplicity, mode quality and stability. Without any active
stabilization, the linewidth is measured to be below 10kHz. The fibre seed is
tunable over 60GHz, which allows access to the D2 transitions in 87Rb and 85Rb,
providing a viable high-power source for laser cooling as well as for
large-momentum-transfer beamsplitters in atom interferometry. Sources of this
type will pave the way for a new generation of high flux, high duty-cycle
degenerate quantum gas experiments.Comment: 5 pages, 3 figure
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