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We derive conditions for a nonholonomic system subject to nonlinear constraints (obeying Chetaev's rule) to preserve a smooth volume form. When applied to affine constraints, these conditions dictate that a basic invariant density exists if and only if a certain 1-form is exact and a certain function vanishes (this function automatically vanishes for linear constraints). Moreover, this result can be extended to geodesic flows for arbitrary metric connections and the sufficient condition manifests as integrability of the torsion. As a consequence, volume-preservation of a nonholonomic system is closely related to the torsion of the nonholonomic connection. Examples of nonlinear/affine/linear constraints are considered.

 

Muscle tissue drives nearly all movement in the animal kingdom, providing power, mobility, and dexterity. Technologies for measuring muscle tissue motion, such as sonomicrometry, fluoromicrometry, and ultrasound, have significantly advanced our understanding of biomechanics. Yet, the field lacks the ability to monitor muscle tissue motion for animal behavior outside the lab. Towards addressing this issue, we previously introduced magnetomicrometry, a method that uses magnetic beads to wirelessly monitor muscle tissue length changes, and we validated magnetomicrometry via tightly-controlled in situ testing. In this study we validate the accuracy of magnetomicrometry against fluoromicrometry during untethered running in an in vivo turkey model. We demonstrate real-time muscle tissue length tracking of the freely-moving turkeys executing various motor activities, including ramp ascent and descent, vertical ascent and descent, and free roaming movement. Given the demonstrated capacity of magnetomicrometry to track muscle movement in untethered animals, we feel that this technique will enable new scientific explorations and an improved understanding of muscle function. 

Human movement is accomplished through muscle contraction, yet there does not exist a portable system capable of monitoring muscle length changes in real time. To address this limitation, we previously introduced magnetomicrometry, a minimally-invasive tracking technique comprising two implanted magnetic beads in muscle and a magnetic field sensor array positioned on the body’s surface adjacent the implanted beads. The implant system comprises a pair of spherical magnetic beads, each with a first coating of nickel-copper-nickel and an outer coating of Parylene C. In parallel work, we demonstrate submillimeter accuracy of magnetic bead tracking for muscle contractions in an untethered freely-roaming avian model. Here, we address the clinical viability of magnetomicrometry. Using a specialized device to insert magnetic beads into muscle in avian and lagomorph models, we collect data to assess gait metrics, bead migration, and bead biocompatibility. For these animal models, we find no gait differences post-versus pre-implantation, and bead migration towards one another within muscle does not occur for initial bead separation distances greater than 3 cm. Further, using extensive biocompatibility testing, the implants are shown to be non-irritant, non-cytotoxic, non-allergenic, and non-irritating. Our cumulative results lend support for the viability of these magnetic bead implants for implantation in human muscle. We thus anticipate their imminent use in human-machine interfaces, such as in control of prostheses and exoskeletons and in closed-loop neuroprosthetics to aid recovery from neurological disorders. 

In this paper, we extend the recently developed continuous visual odometry framework for RGB-D cameras to an adaptive framework via online hyperparameter learning. We focus on the case of isotropic kernels with a scalar as the length-scale. In practice and as expected, the length-scale has remarkable impacts on the performance of the original framework. Previously it was handled using a fixed set of conditions within the solver to reduce the length-scale as the algorithm reaches a local minimum. We automate this process by a greedy gradient descent step at each iteration to find the next-best length-scale. Furthermore, to handle failure cases in the gradient descent step where the gradient is not wellbehaved, such as the absence of structure or texture in the scene, we use a search interval for the length-scale and guide it gradually toward the smaller values. This latter strategy reverts the adaptive framework to the original setup. The experimental evaluations using publicly available RGB-D benchmarks show the proposed adaptive continuous visual odometry outperforms the original framework and the current state-of-the-art. We also make the software for the developed algorithm publicly available. 

Quantum cryptography provides absolute security against an all-powerful eavesdropper (Eve). However, in practice Eve's resources may be restricted to a limited aperture size so that she cannot collect all paraxial light without alerting the communicating parties (Alice and Bob). In this paper we study a quantum wiretap channel in which the connection from Alice to Eve is lossy, so that some of the transmitted quantum information is inaccessible to both Bob and Eve. For a pureloss channel under such restricted eavesdropping, we show that the key rates achievable with a two-mode squeezed vacuum state, heterodyne detection, and public classical communication assistance-given by the Hashing inequality-can exceed the secret key distillation capacity of the channel against an omnipotent eavesdropper. We report upper bounds on the key rates under the restricted eavesdropping model based on the relative entropy of entanglement, which closely match the achievable rates. For the pure-loss channel under restricted eavesdropping, we compare the secret-key rates of continuous-variable (CV) quantum key distribution (QKD) based on Gaussian-modulated coherent states and heterodyne detection with the discrete variable (DV) decoystate BB84 QKD protocol based on polarization qubits encoded in weak coherent laser pulses.