3,107 research outputs found
The circular SiZer, inferred persistence of shape parameters and application to early stem cell differentiation
We generalize the SiZer of Chaudhuri and Marron (J. Amer. Statist. Assoc. 94
(1999) 807-823, Ann. Statist. 28 (2000) 408-428) for the detection of shape
parameters of densities on the real line to the case of circular data. It turns
out that only the wrapped Gaussian kernel gives a symmetric, strongly Lipschitz
semi-group satisfying "circular" causality, that is, not introducing possibly
artificial modes with increasing levels of smoothing. Some notable differences
between Euclidean and circular scale space theory are highlighted. Based on
this, we provide an asymptotic theory to make inference about the persistence
of shape features. The resulting circular mode persistence diagram is applied
to the analysis of early mechanically-induced differentiation in adult human
stem cells from their actin-myosin filament structure. As a consequence, the
circular SiZer based on the wrapped Gaussian kernel (WiZer) allows the
verification at a controlled error level of the observation reported by Zemel
et al. (Nat. Phys. 6 (2010) 468-473): Within early stem cell differentiation,
polarizations of stem cells exhibit preferred directions in three different
micro-environments.Comment: Published at http://dx.doi.org/10.3150/15-BEJ722 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Shear thickening in densely packed suspensions of spheres and rods confined to few layers
We investigate confined shear thickening suspensions for which the sample
thickness is comparable to the particle dimensions. Rheometry measurements are
presented for densely packed suspensions of spheres and rods with aspect ratios
6 and 9. By varying the suspension thickness in the direction of the shear
gradient at constant shear rate, we find pronounced oscillations in the stress.
These oscillations become stronger as the gap size is decreased, and the stress
is minimized when the sample thickness becomes commensurate with an integer
number of particle layers. Despite this confinement-induced effect, viscosity
curves show shear thickening that retains bulk behavior down to samples as thin
as two particle diameters for spheres, below which the suspension is jammed.
Rods exhibit similar behavior commensurate with the particle width, but they
show additional effects when the thickness is reduced below about a particle
length as they are forced to align; the stress increases for decreasing gap
size at fixed shear rate while the shear thickening regime gradually
transitions to a Newtonian scaling regime. This weakening of shear thickening
as an ordered configuration is approached contrasts with the strengthening of
shear thickening when the packing fraction is increased in the disordered bulk
limit, despite the fact that both types of confinement eventually lead to
jamming.Comment: 21 pages, 14 figures. submitted to the Journal of Rheolog
Frequency-Aware Model Predictive Control
Transferring solutions found by trajectory optimization to robotic hardware
remains a challenging task. When the optimization fully exploits the provided
model to perform dynamic tasks, the presence of unmodeled dynamics renders the
motion infeasible on the real system. Model errors can be a result of model
simplifications, but also naturally arise when deploying the robot in
unstructured and nondeterministic environments. Predominantly, compliant
contacts and actuator dynamics lead to bandwidth limitations. While classical
control methods provide tools to synthesize controllers that are robust to a
class of model errors, such a notion is missing in modern trajectory
optimization, which is solved in the time domain. We propose frequency-shaped
cost functions to achieve robust solutions in the context of optimal control
for legged robots. Through simulation and hardware experiments we show that
motion plans can be made compatible with bandwidth limits set by actuators and
contact dynamics. The smoothness of the model predictive solutions can be
continuously tuned without compromising the feasibility of the problem.
Experiments with the quadrupedal robot ANYmal, which is driven by
highly-compliant series elastic actuators, showed significantly improved
tracking performance of the planned motion, torque, and force trajectories and
enabled the machine to walk robustly on terrain with unmodeled compliance
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