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 ($\phi$). 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 $\phi \geq 0.55$. 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

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

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

Random walks in random Dirichlet environment are transient in dimension d≥3d\ge 3

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 $\Z^d$, RWDE are parameterized by a $2d$-uplet of positive reals. We prove that for all values of the parameters, RWDE are transient in dimension $d\ge 3$. 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 $d\ge 3$.Comment: New version published at PTRF with an analytic proof of lemma

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

Articulated Multi-Instrument 2D Pose Estimation Using Fully Convolutional Networks

Instrument detection, pose estimation and tracking in surgical videos is an important vision component for computer assisted interventions. While significant advances have been made in recent years, articulation detection is still a major challenge. In this paper, we propose a deep neural network for articulated multi-instrument 2D pose estimation, which is trained on a detailed annotations of endoscopic and microscopic datasets. Our model is formed by a fully convolutional detection-regression network. Joints and associations between joint pairs in our instrument model are located by the detection subnetwork and are subsequently refined through a regression subnetwork. Based on the output from the model, the poses of the instruments are inferred using maximum bipartite graph matching. Our estimation framework is powered by deep learning techniques without any direct kinematic information from a robot. Our framework is tested on single-instrument RMIT data, and also on multi-instrument EndoVis and in vivo data with promising results. In addition, the dataset annotations are publicly released along with our code and model

A study of blow-ups in the Keller-Segel model of chemotaxis

We study the Keller-Segel model of chemotaxis and develop a composite particle-grid numerical method with adaptive time stepping which allows us to accurately resolve singular solutions. The numerical findings (in two dimensions) are then compared with analytical predictions regarding formation and interaction of singularities obtained via analysis of the stochastic differential equations associated with the Keller-Segel model

Data-Driven Visual Tracking in Retinal Microsurgery

In the context of retinal microsurgery, visual tracking of instruments is a key component of robotics assistance. The difficulty of the task and major reason why most existing strategies fail on {\it in-vivo} image sequences lies in the fact that complex and severe changes in instrument appearance are challenging to model. This paper introduces a novel approach, that is both data-driven and complementary to existing tracking techniques. In particular, we show how to learn and integrate an accurate detector with a simple gradient-based tracker within a robust pipeline which runs at framerate. In addition, we present a fully annotated dataset of retinal instruments in {\it in-vivo} surgeries, which we use to quantitatively validate our approach. We also demonstrate an application of our method in a laparoscopy image sequence