Learning and Acting in Peripersonal Space: Moving, Reaching, and Grasping

The young infant explores its body, its sensorimotor system, and the immediately accessible parts of its environment, over the course of a few months creating a model of peripersonal space useful for reaching and grasping objects around it. Drawing on constraints from the empirical literature on infant behavior, we present a preliminary computational model of this learning process, implemented and evaluated on a physical robot. The learning agent explores the relationship between the configuration space of the arm, sensing joint angles through proprioception, and its visual perceptions of the hand and grippers. The resulting knowledge is represented as the peripersonal space (PPS) graph, where nodes represent states of the arm, edges represent safe movements, and paths represent safe trajectories from one pose to another. In our model, the learning process is driven by intrinsic motivation. When repeatedly performing an action, the agent learns the typical result, but also detects unusual outcomes, and is motivated to learn how to make those unusual results reliable. Arm motions typically leave the static background unchanged, but occasionally bump an object, changing its static position. The reach action is learned as a reliable way to bump and move an object in the environment. Similarly, once a reliable reach action is learned, it typically makes a quasi-static change in the environment, moving an object from one static position to another. The unusual outcome is that the object is accidentally grasped (thanks to the innate Palmar reflex), and thereafter moves dynamically with the hand. Learning to make grasps reliable is more complex than for reaches, but we demonstrate significant progress. Our current results are steps toward autonomous sensorimotor learning of motion, reaching, and grasping in peripersonal space, based on unguided exploration and intrinsic motivation.Comment: 35 pages, 13 figure

The semiclassical relation between open trajectories and periodic orbits for the Wigner time delay

The Wigner time delay of a classically chaotic quantum system can be expressed semiclassically either in terms of pairs of scattering trajectories that enter and leave the system or in terms of the periodic orbits trapped inside the system. We show how these two pictures are related on the semiclassical level. We start from the semiclassical formula with the scattering trajectories and derive from it all terms in the periodic orbit formula for the time delay. The main ingredient in this calculation is a new type of correlation between scattering trajectories which is due to trajectories that approach the trapped periodic orbits closely. The equivalence between the two pictures is also demonstrated by considering correlation functions of the time delay. A corresponding calculation for the conductance gives no periodic orbit contributions in leading order.Comment: 21 pages, 5 figure

Quantum graphs whose spectra mimic the zeros of the Riemann zeta function

One of the most famous problems in mathematics is the Riemann hypothesis: that the non-trivial zeros of the Riemann zeta function lie on a line in the complex plane. One way to prove the hypothesis would be to identify the zeros as eigenvalues of a Hermitian operator, many of whose properties can be derived through the analogy to quantum chaos. Using this, we construct a set of quantum graphs that have the same oscillating part of the density of states as the Riemann zeros, offering an explanation of the overall minus sign. The smooth part is completely different, and hence also the spectrum, but the graphs pick out the low-lying zeros.Comment: 8 pages, 8 pdf figure