12,075 research outputs found
Predictability of Critical Transitions
Critical transitions in multistable systems have been discussed as models for
a variety of phenomena ranging from the extinctions of species to
socio-economic changes and climate transitions between ice-ages and warm-ages.
From bifurcation theory we can expect certain critical transitions to be
preceded by a decreased recovery from external perturbations. The consequences
of this critical slowing down have been observed as an increase in variance and
autocorrelation prior to the transition. However especially in the presence of
noise it is not clear, whether these changes in observation variables are
statistically relevant such that they could be used as indicators for critical
transitions. In this contribution we investigate the predictability of critical
transitions in conceptual models. We study the quadratic integrate-and-fire
model and the van der Pol model, under the influence of external noise. We
focus especially on the statistical analysis of the success of predictions and
the overall predictability of the system. The performance of different
indicator variables turns out to be dependent on the specific model under study
and the conditions of accessing it. Furthermore, we study the influence of the
magnitude of transitions on the predictive performance
Large-Scale Kernel Methods for Independence Testing
Representations of probability measures in reproducing kernel Hilbert spaces
provide a flexible framework for fully nonparametric hypothesis tests of
independence, which can capture any type of departure from independence,
including nonlinear associations and multivariate interactions. However, these
approaches come with an at least quadratic computational cost in the number of
observations, which can be prohibitive in many applications. Arguably, it is
exactly in such large-scale datasets that capturing any type of dependence is
of interest, so striking a favourable tradeoff between computational efficiency
and test performance for kernel independence tests would have a direct impact
on their applicability in practice. In this contribution, we provide an
extensive study of the use of large-scale kernel approximations in the context
of independence testing, contrasting block-based, Nystrom and random Fourier
feature approaches. Through a variety of synthetic data experiments, it is
demonstrated that our novel large scale methods give comparable performance
with existing methods whilst using significantly less computation time and
memory.Comment: 29 pages, 6 figure
A Hybrid Segmentation and D-bar Method for Electrical Impedance Tomography
The Regularized D-bar method for Electrical Impedance Tomography provides a
rigorous mathematical approach for solving the full nonlinear inverse problem
directly, i.e. without iterations. It is based on a low-pass filtering in the
(nonlinear) frequency domain. However, the resulting D-bar reconstructions are
inherently smoothed leading to a loss of edge distinction. In this paper, a
novel approach that combines the rigor of the D-bar approach with the
edge-preserving nature of Total Variation regularization is presented. The
method also includes a data-driven contrast adjustment technique guided by the
key functions (CGO solutions) of the D-bar method. The new TV-Enhanced D-bar
Method produces reconstructions with sharper edges and improved contrast while
still solving the full nonlinear problem. This is achieved by using the
TV-induced edges to increase the truncation radius of the scattering data in
the nonlinear frequency domain thereby increasing the radius of the low pass
filter. The algorithm is tested on numerically simulated noisy EIT data and
demonstrates significant improvements in edge preservation and contrast which
can be highly valuable for absolute EIT imaging
Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials
We introduce an extended Kepler-Coulomb quantum model in spherical
coordinates. The Schr\"{o}dinger equation of this Hamiltonian is solved in
these coordinates and it is shown that the wave functions of the system can be
expressed in terms of Laguerre, Legendre and exceptional Jacobi polynomials (of
hypergeometric type). We construct ladder and shift operators based on the
corresponding wave functions and obtain their recurrence formulas. These
recurrence relations are used to construct higher-order, algebraically
independent integrals of motion to prove superintegrability of the Hamiltonian.
The integrals form a higher rank polynomial algebra. By constructing the
structure functions of the associated deformed oscillator algebras we derive
the degeneracy of energy spectrum of the superintegrable system.Comment: 20 page
Fluctuation-induced Distributed Resonances in Oscillatory Networks
Self-organized network dynamics prevails for systems across physics, biology
and engineering. How external signals generate distributed responses in
networked systems fundamentally underlies their function, yet is far from fully
understood. Here we analyze the dynamic response patterns of oscillatory
networks to fluctuating input signals. We disentangle the impact of the signal
distribution across the network, the signals' frequency contents and the
network topology. We analytically derive qualitatively different dynamic
response patterns and find three frequency regimes: homogeneous responses at
low frequencies, topology-dependent resonances at intermediate frequencies, and
localized responses at high frequencies. The theory faithfully predicts the
network-wide collective responses to regular and irregular, localized and
distributed simulated signals, as well as to real input signals to power grids
recorded from renewable-energy supplies. These results not only provide general
insights into the formation of dynamic response patterns in networked systems
but also suggest regime- and topology-specific design principles underlying
network function.Comment: 7 pages, 4 figure
Use of autologous adipose-derived mesenchymal stem cells for creation of laryngeal cartilage
OBJECTIVES/HYPOTHESIS:
Adipose-derived mesenchymal stem cells (ASCs) are an exciting potential cell source for tissue engineering because cells can be derived from the simple excision of autologous fat. This study introduces a novel approach for tissue-engineering cartilage from ASCs and a customized collagen oligomer solution, and demonstrates that the resultant cartilage can be used for laryngeal cartilage reconstruction in an animal model.
STUDY DESIGN:
Basic science experimental design.
METHODS:
ASCs were isolated from F344 rats, seeded in a customized collagen matrix, and cultured in chondrogenic differentiation medium for 1, 2, and 4 weeks until demonstrating cartilage-like characteristics in vitro. Large laryngeal cartilage defects were created in the F344 rat model, with the engineered cartilage used to replace the cartilage defects, and the rats followed for 1 to 3 months. Staining examined cellular morphology and cartilage-specific features.
RESULTS:
In vitro histological staining revealed rounded chondrocyte-appearing cells evenly residing throughout the customized collagen scaffold, with positive staining for cartilage-specific markers. The cartilage was used to successfully repair large cartilaginous defects in the rat model, with excellent functional results.
CONCLUSIONS:
This study is the first study to demonstrate, in an animal model, that ASCs cultured in a unique form of collagen oligomer can create functional cartilage-like grafts that can be successfully used for partial laryngeal cartilage replacement
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