Information-theoretic Sensorimotor Foundations of Fitts' Law

© 2019 ACM. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published is accessible via https://doi.org/10.1145/3290607.3313053We propose a novel, biologically plausible cost/fitness function for sensorimotor control, formalized with the information-theoretic principle of empowerment, a task-independent universal utility. Empowerment captures uncertainty in the perception-action loop of different nature (e.g. noise, delays, etc.) in a single quantity. We present the formalism in a Fitts' law type goal-directed arm movement task and suggest that empowerment is one potential underlying determinant of movement trajectory planning in the presence of signal-dependent sensorimotor noise. Simulation results demonstrate the temporal relation of empowerment and various plausible control strategies for this specific task

One-way quantum computing with arbitrarily large time-frequency continuous-variable cluster states from a single optical parametric oscillator

One-way quantum computing is experimentally appealing because it requires only local measurements on an entangled resource called a cluster state. Record-size, but non-universal, continuous-variable cluster states were recently demonstrated separately in the time and frequency domains. We propose to combine these approaches into a scalable architecture in which a single optical parametric oscillator and simple interferometer entangle up to ($3\times 10^3$ frequencies) $\times$ (unlimited number of temporal modes) into a new and computationally universal continuous-variable cluster state. We introduce a generalized measurement protocol to enable improved computational performance on this new entanglement resource.Comment: (v4) Consistent with published version; (v3) Fixed typo in arXiv abstract, 14 pages, 8 figures; (v2) Supplemental material incorporated into main text, additional explanations added, results unchanged, 14 pages, 8 figures; (v1) 5 pages (3 figures) + 6 pages (5 figures) of supplemental material; submitted for publicatio

A Primal-Dual Method for Optimal Control and Trajectory Generation in High-Dimensional Systems

Presented is a method for efficient computation of the Hamilton-Jacobi (HJ) equation for time-optimal control problems using the generalized Hopf formula. Typically, numerical methods to solve the HJ equation rely on a discrete grid of the solution space and exhibit exponential scaling with dimension. The generalized Hopf formula avoids the use of grids and numerical gradients by formulating an unconstrained convex optimization problem. The solution at each point is completely independent, and allows a massively parallel implementation if solutions at multiple points are desired. This work presents a primal-dual method for efficient numeric solution and presents how the resulting optimal trajectory can be generated directly from the solution of the Hopf formula, without further optimization. Examples presented have execution times on the order of milliseconds and experiments show computation scales approximately polynomial in dimension with very small high-order coefficients.Comment: Updated references and funding sources. To appear in the proceedings of the 2018 IEEE Conference on Control Technology and Application

Directional optical switching and transistor functionality using optical parametric oscillation in a spinor polariton fluid

Over the past decade, spontaneously emerging patterns in the density of polaritons in semiconductor microcavities were found to be a promising candidate for all-optical switching. But recent approaches were mostly restricted to scalar fields, did not benefit from the polariton's unique spin-dependent properties, and utilized switching based on hexagon far-field patterns with 60{\deg} beam switching (i.e. in the far field the beam propagation direction is switched by 60{\deg}). Since hexagon far-field patterns are challenging, we present here an approach for a linearly polarized spinor field, that allows for a transistor-like (e.g., crucial for cascadability) orthogonal beam switching, i.e. in the far field the beam is switched by 90{\deg}. We show that switching specifications such as amplification and speed can be adjusted using only optical means

Reduced-order Description of Transient Instabilities and Computation of Finite-Time Lyapunov Exponents

High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have finite-time duration. Because of the finite-time character of these transient events, their detection through infinite-time methods, e.g. long term averages, Lyapunov exponents or information about the statistical steady-state, is not possible. Here we utilize a recently developed framework, the Optimally Time-Dependent (OTD) modes, to extract a time-dependent subspace that spans the modes associated with transient features associated with finite-time instabilities. As the main result, we prove that the OTD modes, under appropriate conditions, converge exponentially fast to the eigendirections of the Cauchy--Green tensor associated with the most intense finite-time instabilities. Based on this observation, we develop a reduced-order method for the computation of finite-time Lyapunov exponents (FTLE) and vectors. In high-dimensional systems, the computational cost of the reduced-order method is orders of magnitude lower than the full FTLE computation. We demonstrate the validity of the theoretical findings on two numerical examples