A Neural Model of Visually Guided Steering, Obstacle Avoidance, and Route Selection

A neural model is developed to explain how humans can approach a goal object on foot while steering around obstacles to avoid collisions in a cluttered environment. The model uses optic flow from a 3D virtual reality environment to determine the position of objects based on motion discotinuities, and computes heading direction, or the direction of self-motion, from global optic flow. The cortical representation of heading interacts with the representations of a goal and obstacles such that the goal acts as an attractor of heading, while obstacles act as repellers. In addition the model maintains fixation on the goal object by generating smooth pursuit eye movements. Eye rotations can distort the optic flow field, complicating heading perception, and the model uses extraretinal signals to correct for this distortion and accurately represent heading. The model explains how motion processing mechanisms in cortical areas MT, MST, and VIP can be used to guide steering. The model quantitatively simulates human psychophysical data about visually-guided steering, obstacle avoidance, and route selection.Air Force Office of Scientific Research (F4960-01-1-0397); National Geospatial-Intelligence Agency (NMA201-01-1-2016); National Science Foundation (NSF SBE-0354378); Office of Naval Research (N00014-01-1-0624

Generating Functionals for Spin Foam Amplitudes

We construct a generating functional for the exact evalutation of a coherent representation of spin network amplitudes. This generating functional is defined for arbitrary graphs and depends only on a pair of spinors for each edge. The generating functional is a meromorphic polynomial in the spinor invariants which is determined by the cycle structure of the graph. The expansion of the spin network generating function is given in terms of a newly recognized basis of SU(2) intertwiners consisting of the monomials of the holomorphic spinor invariants. This basis is labelled by the degrees of the monomials and is thus discrete. It is also overcomplete, but contains the precise amount of data to specify points in the classical space of closed polyhedra, and is in this sense coherent. We call this new basis the discrete-coherent basis. We focus our study on the 4-valent basis, which is the first non-trivial dimension, and is also the case of interest for Quantum Gravity. We find simple relations between the new basis, the orthonormal basis, and the coherent basis. Finally we discuss the process of coarse graining moves at the level of the generating functionals and give a general prescription for arbitrary graphs. A direct relation between the polynomial of cycles in the spin network generating functional and the high temperature loop expansion of the 2d Ising model is found.Comment: PhD Thesis, 128 page

Frame to frame interpolation for high-dimensional data visualisation using the woylier package

The woylier package implements tour interpolation paths between frames using Givens rotations. This provides an alternative to the geodesic interpolation between planes currently available in the tourr package. Tours are used to visualise high-dimensional data and models, to detect clustering, anomalies and non-linear relationships. Frame-to-frame interpolation can be useful for projection pursuit guided tours when the index is not rotationally invariant. It also provides a way to specifically reach a given target frame. We demonstrate the method for exploring non-linear relationships between currency cross-rates