2,201 research outputs found
Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging
Locally adaptive differential frames (gauge frames) are a well-known
effective tool in image analysis, used in differential invariants and
PDE-flows. However, at complex structures such as crossings or junctions, these
frames are not well-defined. Therefore, we generalize the notion of gauge
frames on images to gauge frames on data representations defined on the extended space of positions and
orientations, which we relate to data on the roto-translation group ,
. This allows to define multiple frames per position, one per
orientation. We compute these frames via exponential curve fits in the extended
data representations in . These curve fits minimize first or second
order variational problems which are solved by spectral decomposition of,
respectively, a structure tensor or Hessian of data on . We include
these gauge frames in differential invariants and crossing preserving PDE-flows
acting on extended data representation and we show their advantage compared
to the standard left-invariant frame on . Applications include
crossing-preserving filtering and improved segmentations of the vascular tree
in retinal images, and new 3D extensions of coherence-enhancing diffusion via
invertible orientation scores
A PDE Approach to Data-driven Sub-Riemannian Geodesics in SE(2)
We present a new flexible wavefront propagation algorithm for the boundary
value problem for sub-Riemannian (SR) geodesics in the roto-translation group
with a metric tensor depending on a smooth
external cost , , computed from
image data. The method consists of a first step where a SR-distance map is
computed as a viscosity solution of a Hamilton-Jacobi-Bellman (HJB) system
derived via Pontryagin's Maximum Principle (PMP). Subsequent backward
integration, again relying on PMP, gives the SR-geodesics. For
we show that our method produces the global minimizers. Comparison with exact
solutions shows a remarkable accuracy of the SR-spheres and the SR-geodesics.
We present numerical computations of Maxwell points and cusp points, which we
again verify for the uniform cost case . Regarding image
analysis applications, tracking of elongated structures in retinal and
synthetic images show that our line tracking generically deals with crossings.
We show the benefits of including the sub-Riemannian geometry.Comment: Extended version of SSVM 2015 conference article "Data-driven
Sub-Riemannian Geodesics in SE(2)
Narrowband Photon Pair Source for Quantum Networks
We demonstrate a compact photon pair source based on a periodically poled
lithium niobate nonlinear crystal in a cavity. The cavity parameters are chosen
such that the emitted photon pair modes can be matched in the region of telecom
ultra dense wavelength division multiplexing (U-DWDM) channel spacings. This
approach provides efficient, low-loss, mode selection that is compatible with
standard telecommunication networks. Photons with a coherence time of 8.6 ns
(116 MHz) are produced and their purity is demonstrated. A source brightness of
134 pairs(s.mW.MHz) is reported. The high level of purity and
compatibility with standard telecom networks is of great importance for complex
quantum communication networks
Quantum random number generation for 1.25 GHz quantum key distribution systems
Security proofs of quantum key distribution (QKD) systems usually assume that
the users have access to source of perfect randomness. State-of-the-art QKD
systems run at frequencies in the GHz range, requiring a sustained GHz rate of
generation and acquisition of quantum random numbers. In this paper we
demonstrate such a high speed random number generator. The entropy source is
based on amplified spontaneous emission from an erbium-doped fibre, which is
directly acquired using a standard small form-factor pluggable (SFP) module.
The module connects to the Field Programmable Gate Array (FPGA) of a QKD
system. A real-time randomness extractor is implemented in the FPGA and
achieves a sustained rate of 1.25 Gbps of provably random bits.Comment: 6 pages, 8 figure
High efficiency coupling of photon pairs in practice
Multi-photon and quantum communication experiments such as loophole-free Bell
tests and device independent quantum key distribution require entangled photon
sources which display high coupling efficiency. In this paper we put forward a
simple quantum theoretical model which allows the experimenter to design a
source with high pair coupling efficiency. In particular we apply this approach
to a situation where high coupling has not been previously obtained: we
demonstrate a symmetric coupling efficiency of more than 80% in a highly
frequency non-degenerate configuration. Furthermore, we demonstrate this
technique in a broad range of configurations, i.e. in continuous wave and
pulsed pump regimes, and for different nonlinear crystals
Improving Fiber Alignment in HARDI by Combining Contextual PDE Flow with Constrained Spherical Deconvolution
We propose two strategies to improve the quality of tractography results
computed from diffusion weighted magnetic resonance imaging (DW-MRI) data. Both
methods are based on the same PDE framework, defined in the coupled space of
positions and orientations, associated with a stochastic process describing the
enhancement of elongated structures while preserving crossing structures. In
the first method we use the enhancement PDE for contextual regularization of a
fiber orientation distribution (FOD) that is obtained on individual voxels from
high angular resolution diffusion imaging (HARDI) data via constrained
spherical deconvolution (CSD). Thereby we improve the FOD as input for
subsequent tractography. Secondly, we introduce the fiber to bundle coherence
(FBC), a measure for quantification of fiber alignment. The FBC is computed
from a tractography result using the same PDE framework and provides a
criterion for removing the spurious fibers. We validate the proposed
combination of CSD and enhancement on phantom data and on human data, acquired
with different scanning protocols. On the phantom data we find that PDE
enhancements improve both local metrics and global metrics of tractography
results, compared to CSD without enhancements. On the human data we show that
the enhancements allow for a better reconstruction of crossing fiber bundles
and they reduce the variability of the tractography output with respect to the
acquisition parameters. Finally, we show that both the enhancement of the FODs
and the use of the FBC measure on the tractography improve the stability with
respect to different stochastic realizations of probabilistic tractography.
This is shown in a clinical application: the reconstruction of the optic
radiation for epilepsy surgery planning
Approximation and inference methods for stochastic biochemical kinetics-a tutorial review
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the chemical master equation. Despite its simple structure, no analytic solutions to the chemical master equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics
Model Reduction for the Chemical Master Equation: an Information-Theoretic Approach
The complexity of mathematical models in biology has rendered model reduction
an essential tool in the quantitative biologist's toolkit. For stochastic
reaction networks described using the Chemical Master Equation, commonly used
methods include time-scale separation, the Linear Mapping Approximation and
state-space lumping. Despite the success of these techniques, they appear to be
rather disparate and at present no general-purpose approach to model reduction
for stochastic reaction networks is known. In this paper we show that most
common model reduction approaches for the Chemical Master Equation can be seen
as minimising a well-known information-theoretic quantity between the full
model and its reduction, the Kullback-Leibler divergence defined on the space
of trajectories. This allows us to recast the task of model reduction as a
variational problem that can be tackled using standard numerical optimisation
approaches. In addition we derive general expressions for the propensities of a
reduced system that generalise those found using classical methods. We show
that the Kullback-Leibler divergence is a useful metric to assess model
discrepancy and to compare different model reduction techniques using three
examples from the literature: an autoregulatory feedback loop, the
Michaelis-Menten enzyme system and a genetic oscillator
Enhancement of K+ conductance improves in vitro the contraction force of skeletal muscle in hypokalemic periodic paralysis
An abnormal ratio between Na+ and K+ conductances seems to be the cause for the depolarization and paralysis of skeletal muscle in primary hypokalemic periodic paralysis. Recently we have shown that the k+ channel opener cromakalim hyperpolarizes mammalian skeletal muscle fibers. Now we have studied the effects of this drug on the twitch force of muscle biopsies from normal and diseased human skeletal muscle. Cromakalim had little effect on the twitch force of normal muscle whereas it strongly improved the contraction force of fibers from patients suffering from hypokalemic periodic paralysis. Recordings of intracellular K+ and Cl- activities in human muscle and isolated rat soleus muscle support the view that cromakalim enhances the membrane K+ conductance (gK+). These data indicate that K+ channel openers may have a beneficial effect in primary hypokalemic periodic paralysis
Comparison of Bond Character in Hydrocarbons and Fullerenes
We present a comparison of the bond polarizabilities for carbon-carbon bonds
in hydrocarbons and fullerenes, using two different models for the fullerene
Raman spectrum and the results of Raman measurements on ethane and ethylene. We
find that the polarizabilities for single bonds in fullerenes and hydrocarbons
compare well, while the double bonds in fullerenes have greater polarizability
than in ethylene.Comment: 7 pages, no figures, uses RevTeX. (To appear in Phys. Rev. B.
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