Generalization in Adaptation to Stable and Unstable Dynamics

Humans skillfully manipulate objects and tools despite the inherent instability. In order to succeed at these tasks, the sensorimotor control system must build an internal representation of both the force and mechanical impedance. As it is not practical to either learn or store motor commands for every possible future action, the sensorimotor control system generalizes a control strategy for a range of movements based on learning performed over a set of movements. Here, we introduce a computational model for this learning and generalization, which specifies how to learn feedforward muscle activity in a function of the state space. Specifically, by incorporating co-activation as a function of error into the feedback command, we are able to derive an algorithm from a gradient descent minimization of motion error and effort, subject to maintaining a stability margin. This algorithm can be used to learn to coordinate any of a variety of motor primitives such as force fields, muscle synergies, physical models or artificial neural networks. This model for human learning and generalization is able to adapt to both stable and unstable dynamics, and provides a controller for generating efficient adaptive motor behavior in robots. Simulation results exhibit predictions consistent with all experiments on learning of novel dynamics requiring adaptation of force and impedance, and enable us to re-examine some of the previous interpretations of experiments on generalization. © 2012 Kadiallah et al.

Motor learning of novel dynamics is not represented in a single global coordinate system: evaluation of mixed coordinate representations and local learning.

Successful motor performance requires the ability to adapt motor commands to task dynamics. A central question in movement neuroscience is how these dynamics are represented. Although it is widely assumed that dynamics (e.g., force fields) are represented in intrinsic, joint-based coordinates (Shadmehr R, Mussa-Ivaldi FA. J Neurosci 14: 3208-3224, 1994), recent evidence has questioned this proposal. Here we reexamine the representation of dynamics in two experiments. By testing generalization following changes in shoulder, elbow, or wrist configurations, the first experiment tested for extrinsic, intrinsic, or object-centered representations. No single coordinate frame accounted for the pattern of generalization. Rather, generalization patterns were better accounted for by a mixture of representations or by models that assumed local learning and graded, decaying generalization. A second experiment, in which we replicated the design of an influential study that had suggested encoding in intrinsic coordinates (Shadmehr and Mussa-Ivaldi 1994), yielded similar results. That is, we could not find evidence that dynamics are represented in a single coordinate system. Taken together, our experiments suggest that internal models do not employ a single coordinate system when generalizing and may well be represented as a mixture of coordinate systems, as a single system with local learning, or both.

NORMAL COORDINATE TREATMENT OF LEU(5)-ENKEPHALIN IN THE CRYSTAL-STATE

Vibrational studies on the neuropentapeptide Leu5-enkephalin were performed for the crystal state where different specific conformations can arise. In the present case, the peptide adopts a double fused folded conformation (beta-turn), the presence of which in the crystal state is directly related to the nature of the solvent used for its crystallization. This study completes other work relating to similar conformations of isolated molecules. It can be seen that specific interactions in the crystal state perturb to a large extent the vibrational relationships between the amide frequencies and the specific sets of dihedral angles characteristic of the particular type of turn. The tyrosyl moiety and its frequency dependence on its hydrogen bond state was especially investigated both for the Fermi resonance and the hydroxyl bending modes.

SYNTHESIS, PROPERTIES AND MOLECULAR-STRUCTURE OF 5-COORDINATE N,N-DIBENZYLDITHIOCARBAMATE COMPLEXES OF TITANOCENE, ZIRCONOCENE AND HAFNOCENE

The five complexes (RC5H4)2M(S2CNBz2)Cl (R = H, CH3; M = Ti, Zr, Hf; Bz = CH2C6H5) have been prepared by the reaction of (RC5H4)2MCl2 with anhydrous sodium salts of dibenzyldithiocarbamate in refluxing CH2Cl2. These complexes have been characterized by elemental analysis, IR and H-1 NMR. X-ray crystal structure determination of Cp2Zr(S2CNBZ2)Cl shows the molecule has a five-coordinate bent metallocene geometry in which the zirconium atom is attached to two eta-5-C5H5 groups, one bidentate dibenzyldithiocarbamate ligand and one chlorine [Zr-Cl, 2.549(1) angstrom; Zr-S, 2.734(1), 2.667(1); Cl-Zr-S, 137.6(1)-degrees and 73.3(1)-degrees; S-Zr-S, 64.3(1)-degrees]. The catalytic system Cp2Ti (S2CNBZ2)Cl-NaH exhibits high initial catalytic activity of hydrogenation of hexene-1 under mild conditions.

SYNTHESIS AND MOLECULAR-STRUCTURE OF THE 5-COORDINATE ZIRCONIUM COMPLEX (CH3C5H4)2ZRCL(ALPHA-C10H7COO)

Bis(methylcyclopentadienyl)chloro(alpha-naphthoyloxy)zirconium, (CH3C5H4)2Zr Cl(alpha-C10H7COO), has been synthesized by the reaction between (MeCp)2ZrCl2 and equimolar sodium alpha-naphthoate in toluene at room temperature. The molecular structure of the title complex was determined by X-ray diffraction. The molecules have a five-coordinate bent metallocene structure in which the alpha-naphthoxyligand is bidentate [Zr-O, 2.317(2), 2.260(2) angstrom]. The remaining distances are [Zr-Cl, 2.521(1) angstrom; Zr-C, 480-2, 565 angstrom; Zr-cent-CH3C5H4 2.217 and 2.230 angstrom].

Coordinate-Independent Computations on Differential Equations

This project investigates the computational representation of differentiable manifolds, with the primary goal of solving partial differential equations using multiple coordinate systems on general n- dimensional spaces. In the process, this abstraction is used to perform accurate integrations of ordinary differential equations using multiple coordinate systems. In the case of linear partial differential equations, however, unexpected difficulties arise even with the simplest equations.

Monitoring Activities from Multiple Video Streams: Establishing a Common Coordinate Frame

Passive monitoring of large sites typically requires coordination between multiple cameras, which in turn requires methods for automatically relating events between distributed cameras. This paper tackles the problem of self-calibration of multiple cameras which are very far apart, using feature correspondences to determine the camera geometry. The key problem is finding such correspondences. Since the camera geometry and photometric characteristics vary considerably between images, one cannot use brightness and/or proximity constraints. Instead we apply planar geometric constraints to moving objects in the scene in order to align the scene"s ground plane across multiple views. We do not assume synchronized cameras, and we show that enforcing geometric constraints enables us to align the tracking data in time. Once we have recovered the homography which aligns the planar structure in the scene, we can compute from the homography matrix the 3D position of the plane and the relative camera positions. This in turn enables us to recover a homography matrix which maps the images to an overhead view. We demonstrate this technique in two settings: a controlled lab setting where we test the effects of errors in internal camera calibration, and an uncontrolled, outdoor setting in which the full procedure is applied to external camera calibration and ground plane recovery. In spite of noise in the internal camera parameters and image data, the system successfully recovers both planar structure and relative camera positions in both settings.

Designing three-dimensional transformation optical media using quasiconformal coordinate transformations.

We introduce an approach to the design of three-dimensional transformation optical (TO) media based on a generalized quasiconformal mapping approach. The generalized quasiconformal TO (QCTO) approach enables the design of media that can, in principle, be broadband and low loss, while controlling the propagation of waves with arbitrary angles of incidence and polarization. We illustrate the method in the design of a three-dimensional carpet ground plane cloak and of a flattened Luneburg lens. Ray-trace studies provide a confirmation of the performance of the QCTO media, while also revealing the limited performance of index-only versions of these devices.