Designers Need End-User Software Engineering

This position paper for the End-User Software Engineering workshop outlines three systems that employ end user programming for designers: a constraint-based design environment; a sketch recognition interface for knowledge based systems, and a physical programming environment for building modular robots

The Solar Test of the Equivalence Principle

The Earth, Mars, Sun, Jupiter system allows for a sensitive test of the strong equivalence principle (SEP) which is qualitatively different from that provided by Lunar Laser Ranging. Using analytic and numerical methods we demonstrate that Earth-Mars ranging can provide a useful estimate of the SEP parameter $\eta$. Two estimates of the predicted accuracy are derived and quoted, one based on conventional covariance analysis, and another (called ``modified worst case'' analysis) which assumes that systematic errors dominate the experiment. If future Mars missions provide ranging measurements with an accuracy of $\sigma$ meters, after ten years of ranging the expected accuracy for the SEP parameter $\eta$ will be of order $(1-12)\times 10^{-4}\sigma$. These ranging measurements will also provide the most accurate determination of the mass of Jupiter, independent of the SEP effect test.Comment: 10 pages; LaTeX; three figures upon reques

Qudit versions of the qubit "pi-over-eight" gate

When visualised as an operation on the Bloch sphere, the qubit "pi-over-eight" gate corresponds to one-eighth of a complete rotation about the vertical axis. This simple gate often plays an important role in quantum information theory, typically in situations for which Pauli and Clifford gates are insufficient. Most notably, when it supplements the set of Clifford gates then universal quantum computation can be achieved. The "pi-over-eight" gate is the simplest example of an operation from the third level of the Clifford hierarchy (i.e., it maps Pauli operations to Clifford operations under conjugation). Here we derive explicit expressions for all qudit (d-level, where d is prime) versions of this gate and analyze the resulting group structure that is generated by these diagonal gates. This group structure differs depending on whether the dimensionality of the qudit is two, three or greater than three. We then discuss the geometrical relationship of these gates (and associated states) with respect to Clifford gates and stabilizer states. We present evidence that these gates are maximally robust to depolarizing and phase damping noise, in complete analogy with the qubit case. Motivated by this and other similarities we conjecture that these gates could be useful for the task of qudit magic-state distillation and, by extension, fault-tolerant quantum computing. Very recent, independent work by Campbell, Anwar and Browne confirms the correctness of this intuition, and we build upon their work to characterize noise regimes for which noisy implementations of these gates can (or provably cannot) supplement Clifford gates to enable universal quantum computation.Comment: Version 2 changed to reflect improved distillation routines in arXiv:1205.3104v2. Minor typos fixed. 12 Pages,2 Figures,3 Table

Ultra-rapid laser protein micropatterning: screening for directed polarization of single neurons

Protein micropatterning is a powerful tool for studying the effects of extracellular signals on cell development and regeneration. Laser micropatterning of proteins is the most flexible method for patterning many different geometries, protein densities, and concentration gradients. Despite these advantages, laser micropatterning remains prohibitively slow for most applications. Here, we take advantage of the rapid multi-photon induced photobleaching of fluorophores to generate sub-micron resolution patterns of full-length proteins on polymer monolayers, with sub-microsecond exposure times, i.e. one to five orders of magnitude faster than all previous laser micropatterning methods. We screened a range of different PEG monolayer coupling chemistries, chain-lengths and functional caps, and found that long-chain acrylated PEG monolayers are effective at resisting non-specific protein adhesion, while permitting efficient cross-linking of biotin-4-fluorescein to the PEG monolayers upon exposure to femtosecond laser pulses. We find evidence that the dominant photopatterning chemistry switches from a two-photon process to three- and four-photon absorption processes as the laser intensity increases, generating increasingly volatile excited triplet-state fluorophores, leading to faster patterning. Using this technology, we were able to generate over a hundred thousand protein patterns with varying geometries and protein densities to direct the polarization of hippocampal neurons with single-cell precision. We found that certain arrays of patterned triangles as small as neurite growth cones can direct polarization by impeding the elongation of reverse-projecting neurites, while permitting elongation of forward-projecting neurites. The ability to rapidly generate and screen such protein micropatterns can enable discovery of conditions necessary to create in vitro neural networks with single-neuron precision for basic discovery, drug screening, as well as for tissue scaffolding in therapeutics.Hertz Foundation (Fellowship)National Institutes of Health (U.S.) (R01 EUREKA Award 1-R01-NS066352)David & Lucile Packard Foundation (Award in Science and Engineering

On Dijkgraaf-Witten Type Invariants

We explicitly construct a series of lattice models based upon the gauge group $Z_{p}$ which have the property of subdivision invariance, when the coupling parameter is quantized and the field configurations are restricted to satisfy a type of mod-$p$ flatness condition. The simplest model of this type yields the Dijkgraaf-Witten invariant of a $3$-manifold and is based upon a single link, or $1$-simplex, field. Depending upon the manifold's dimension, other models may have more than one species of field variable, and these may be based on higher dimensional simplices.Comment: 18 page