Visuomotor Transformation in the Fly Gaze Stabilization System

For sensory signals to control an animal's behavior, they must first be transformed into a format appropriate for use by its motor systems. This fundamental problem is faced by all animals, including humans. Beyond simple reflexes, little is known about how such sensorimotor transformations take place. Here we describe how the outputs of a well-characterized population of fly visual interneurons, lobula plate tangential cells (LPTCs), are used by the animal's gaze-stabilizing neck motor system. The LPTCs respond to visual input arising from both self-rotations and translations of the fly. The neck motor system however is involved in gaze stabilization and thus mainly controls compensatory head rotations. We investigated how the neck motor system is able to selectively extract rotation information from the mixed responses of the LPTCs. We recorded extracellularly from fly neck motor neurons (NMNs) and mapped the directional preferences across their extended visual receptive fields. Our results suggest that—like the tangential cells—NMNs are tuned to panoramic retinal image shifts, or optic flow fields, which occur when the fly rotates about particular body axes. In many cases, tangential cells and motor neurons appear to be tuned to similar axes of rotation, resulting in a correlation between the coordinate systems the two neural populations employ. However, in contrast to the primarily monocular receptive fields of the tangential cells, most NMNs are sensitive to visual motion presented to either eye. This results in the NMNs being more selective for rotation than the LPTCs. Thus, the neck motor system increases its rotation selectivity by a comparatively simple mechanism: the integration of binocular visual motion information

Computational Techniques for Efficient Conversion of Image Files from Area Detectors

Area detectors are used in many scientific and technological applications such as particle and radiation physics. Thanks to the recent technological developments, the radiation sources are becoming increasingly brighter and the detectors become faster and more efficient. The result is a sharp increase in the size of data collected in a typical experiment. This situation imposes a bottleneck on data processing capabilities, and could pose a real challenge to scientific research in certain areas. This article proposes a number of simple techniques to facilitate rapid and efficient extraction of data obtained from these detectors. These techniques are successfully implemented and tested in a computer program to deal with the extraction of X-ray diffraction patterns from EDF image files obtained from CCD detectors.Comment: 16 pages, 6 figure

When Can You Fold a Map?

We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds; the simplest one-layer simple fold rotates a portion of paper about a crease in the paper by +-180 degrees. We first consider the analogous questions in one dimension lower -- bending a segment into a flat object -- which lead to interesting problems on strings. We develop efficient algorithms for the recognition of simply foldable 1D crease patterns, and reconstruction of a sequence of simple folds. Indeed, we prove that a 1D crease pattern is flat-foldable by any means precisely if it is by a sequence of one-layer simple folds. Next we explore simple foldability in two dimensions, and find a surprising contrast: ``map'' folding and variants are polynomial, but slight generalizations are NP-complete. Specifically, we develop a linear-time algorithm for deciding foldability of an orthogonal crease pattern on a rectangular piece of paper, and prove that it is (weakly) NP-complete to decide foldability of (1) an orthogonal crease pattern on a orthogonal piece of paper, (2) a crease pattern of axis-parallel and diagonal (45-degree) creases on a square piece of paper, and (3) crease patterns without a mountain/valley assignment.Comment: 24 pages, 19 figures. Version 3 includes several improvements thanks to referees, including formal definitions of simple folds, more figures, table summarizing results, new open problems, and additional reference

Planar shape manipulation using approximate geometric primitives

We present robust algorithms for set operations and Euclidean transformations of curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is \bigo(n\log n+k) for an input of size $n$ with k=\bigo(n^2) consistency violations. The output is as accurate as the geometric primitives. We validate our algorithms in floating point using sequences of six set operations and Euclidean transforms on shapes bounded by curves of algebraic degree~1 to~6. We test generic and degenerate inputs. Keywords: robust computational geometry, plane subdivisions, set operations

An averaging principle for diffusions in foliated spaces

Consider an SDE on a foliated manifold whose trajectories lay on compact leaves. We investigate the effective behavior of a small transversal perturbation of order $\varepsilon$. An average principle is shown to hold such that the component transversal to the leaves converges to the solution of a deterministic ODE, according to the average of the perturbing vector field with respect to invariant measures on the leaves, as $\varepsilon$ goes to zero. An estimate of the rate of convergence is given. These results generalize the geometrical scope of previous approaches, including completely integrable stochastic Hamiltonian system.Comment: Published at http://dx.doi.org/10.1214/14-AOP982 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Image processing for grazing incidence fast atom diffraction

Grazing incidence fast atom diffraction (GIFAD, or FAD) has developed as a surface sensitive technique. GIFAD is less sensitive to thermal decoherence but more demanding in terms of surface coherence, the mean distance between defects. Such high quality surfaces can be obtained from freshly cleaved crystals or in a molecular beam epitaxy (MBE) chamber where a GIFAD setup has been installed allowing in situ operation. Based on recent publications by Atkinson et al. and Debiossac et al, the paper describes in detail the basic steps needed to measure the relative intensities of the diffraction spots. Care is taken to outline the underlying physical assumptions.Comment: IISC-21 International Workshop on Inelastic Ion-Surface Collisions, Dosnostia Sept. 2015. Elsevier, NIM-B (2016