249 research outputs found
Asymptotics for the Wiener sausage among Poissonian obstacles
We consider the Wiener sausage among Poissonian obstacles. The obstacle is
called hard if Brownian motion entering the obstacle is immediately killed, and
is called soft if it is killed at certain rate. It is known that Brownian
motion conditioned to survive among obstacles is confined in a ball near its
starting point. We show the weak law of large numbers, large deviation
principle in special cases and the moment asymptotics for the volume of the
corresponding Wiener sausage. One of the consequence of our results is that the
trajectory of Brownian motion almost fills the confinement ball.Comment: 19 pages, Major revision made for publication in J. Stat. Phy
Motility of small nematodes in disordered wet granular media
The motility of the worm nematode \textit{Caenorhabditis elegans} is
investigated in shallow, wet granular media as a function of particle size
dispersity and area density (). Surprisingly, we find that the nematode's
propulsion speed is enhanced by the presence of particles in a fluid and is
nearly independent of area density. The undulation speed, often used to
differentiate locomotion gaits, is significantly affected by the bulk material
properties of wet mono- and polydisperse granular media for .
This difference is characterized by a change in the nematode's waveform from
swimming to crawling in dense polydisperse media \textit{only}. This change
highlights the organism's adaptability to subtle differences in local structure
and response between monodisperse and polydisperse media
Cut Points and Diffusions in Random Environment
In this article we investigate the asymptotic behavior of a new class of
multi-dimensional diffusions in random environment. We introduce cut times in
the spirit of the work done by Bolthausen, Sznitman and Zeitouni, see [4], in
the discrete setting providing a decoupling effect in the process. This allows
us to take advantage of an ergodic structure to derive a strong law of large
numbers with possibly vanishing limiting velocity and a central limit theorem
under the quenched measure.Comment: 44 pages; accepted for publication in "Journal of Theoretical
Probability
Real-time 3D Tracking of Articulated Tools for Robotic Surgery
In robotic surgery, tool tracking is important for providing safe tool-tissue
interaction and facilitating surgical skills assessment. Despite recent
advances in tool tracking, existing approaches are faced with major
difficulties in real-time tracking of articulated tools. Most algorithms are
tailored for offline processing with pre-recorded videos. In this paper, we
propose a real-time 3D tracking method for articulated tools in robotic
surgery. The proposed method is based on the CAD model of the tools as well as
robot kinematics to generate online part-based templates for efficient 2D
matching and 3D pose estimation. A robust verification approach is incorporated
to reject outliers in 2D detections, which is then followed by fusing inliers
with robot kinematic readings for 3D pose estimation of the tool. The proposed
method has been validated with phantom data, as well as ex vivo and in vivo
experiments. The results derived clearly demonstrate the performance advantage
of the proposed method when compared to the state-of-the-art.Comment: This paper was presented in MICCAI 2016 conference, and a DOI was
linked to the publisher's versio
Equality of averaged and quenched large deviations for random walks in random environments in dimensions four and higher
We consider large deviations for nearest-neighbor random walk in a uniformly
elliptic i.i.d. environment. It is easy to see that the quenched and the
averaged rate functions are not identically equal. When the dimension is at
least four and Sznitman's transience condition (T) is satisfied, we prove that
these rate functions are finite and equal on a closed set whose interior
contains every nonzero velocity at which the rate functions vanish.Comment: 17 pages. Minor revision. In particular, note the change in the title
of the paper. To appear in Probability Theory and Related Fields
Random walks in random Dirichlet environment are transient in dimension
We consider random walks in random Dirichlet environment (RWDE) which is a
special type of random walks in random environment where the exit probabilities
at each site are i.i.d. Dirichlet random variables. On , RWDE are
parameterized by a -uplet of positive reals. We prove that for all values
of the parameters, RWDE are transient in dimension . We also prove that
the Green function has some finite moments and we characterize the finite
moments. Our result is more general and applies for example to finitely
generated symmetric transient Cayley graphs. In terms of reinforced random
walks it implies that directed edge reinforced random walks are transient for
.Comment: New version published at PTRF with an analytic proof of lemma
Inverting Ray-Knight identity
We provide a short proof of the Ray-Knight second generalized Theorem, using
a martingale which can be seen (on the positive quadrant) as the Radon-Nikodym
derivative of the reversed vertex-reinforced jump process measure with respect
to the Markov jump process with the same conductances. Next we show that a
variant of this process provides an inversion of that Ray-Knight identity. We
give a similar result for the Ray-Knight first generalized Theorem.Comment: 18 page
Slow movement of a random walk on the range of a random walk in the presence of an external field
In this article, a localisation result is proved for the biased random walk
on the range of a simple random walk in high dimensions (d \geq 5). This
demonstrates that, unlike in the supercritical percolation setting, a slowdown
effect occurs as soon a non-trivial bias is introduced. The proof applies a
decomposition of the underlying simple random walk path at its cut-times to
relate the associated biased random walk to a one-dimensional random walk in a
random environment in Sinai's regime
Limits and dynamics of stochastic neuronal networks with random heterogeneous delays
Realistic networks display heterogeneous transmission delays. We analyze here
the limits of large stochastic multi-populations networks with stochastic
coupling and random interconnection delays. We show that depending on the
nature of the delays distributions, a quenched or averaged propagation of chaos
takes place in these networks, and that the network equations converge towards
a delayed McKean-Vlasov equation with distributed delays. Our approach is
mostly fitted to neuroscience applications. We instantiate in particular a
classical neuronal model, the Wilson and Cowan system, and show that the
obtained limit equations have Gaussian solutions whose mean and standard
deviation satisfy a closed set of coupled delay differential equations in which
the distribution of delays and the noise levels appear as parameters. This
allows to uncover precisely the effects of noise, delays and coupling on the
dynamics of such heterogeneous networks, in particular their role in the
emergence of synchronized oscillations. We show in several examples that not
only the averaged delay, but also the dispersion, govern the dynamics of such
networks.Comment: Corrected misprint (useless stopping time) in proof of Lemma 1 and
clarified a regularity hypothesis (remark 1
Propulsive Force Measurements and Flow Behavior of Undulatory Swimmers at Low Reynolds Number
The swimming behavior of the nematode Caenorhabditis elegans is investigated in aqueous solutions of increasing viscosity. Detailed flow dynamics associated with the nematode’s swimming motion as well as propulsive force and power are obtained using particle tracking and velocimetry methods. We find that C. elegans delivers propulsive thrusts on the order of a few nanonewtons. Such findings are supported by values obtained using resistive force theory; the ratio of normal to tangential drag coefficients is estimated to be approximately 1.4. Over the range of solutions investigated here, the flow properties remain largely independent of viscosity. Velocity magnitudes of the flow away from the nematode body decay rapidly within less than a body length and collapse onto a single master curve. Overall, our findings support that C. elegans is an attractive living model to study the coupling between small-scale propulsion and low Reynolds number hydrodynamics
- …