Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization

A versatile method is described for the practical computation of the discrete Fourier transforms (DFT) of a continuous function $g(t)$ given by its values $g_{j}$ at the points of a uniform grid $F_{N}$ generated by conjugacy classes of elements of finite adjoint order $N$ in the fundamental region $F$ of compact semisimple Lie groups. The present implementation of the method is for the groups SU(2), when $F$ is reduced to a one-dimensional segment, and for $SU(2)\times ... \times SU(2)$ in multidimensional cases. This simplest case turns out to result in a transform known as discrete cosine transform (DCT), which is often considered to be simply a specific type of the standard DFT. Here we show that the DCT is very different from the standard DFT when the properties of the continuous extensions of these two discrete transforms from the discrete grid points $t_j; j=0,1, ... N$ to all points $t \in F$ are considered. (A) Unlike the continuous extension of the DFT, the continuous extension of (the inverse) DCT, called CEDCT, closely approximates $g(t)$ between the grid points $t_j$. (B) For increasing $N$, the derivative of CEDCT converges to the derivative of $g(t)$. And (C), for CEDCT the principle of locality is valid. Finally, we use the continuous extension of 2-dimensional DCT to illustrate its potential for interpolation, as well as for the data compression of 2D images.Comment: submitted to JMP on April 3, 2003; still waiting for the referee's Repor

Digital Quantum Simulation of the Statistical Mechanics of a Frustrated Magnet

Many interesting problems in physics, chemistry, and computer science are equivalent to problems of interacting spins. However, most of these problems require computational resources that are out of reach by classical computers. A promising solution to overcome this challenge is to exploit the laws of quantum mechanics to perform simulation. Several "analog" quantum simulations of interacting spin systems have been realized experimentally. However, relying on adiabatic techniques, these simulations are limited to preparing ground states only. Here we report the first experimental results on a "digital" quantum simulation on thermal states; we simulated a three-spin frustrated magnet, a building block of spin ice, with an NMR quantum information processor, and we are able to explore the phase diagram of the system at any simulated temperature and external field. These results serve as a guide for identifying the challenges for performing quantum simulation on physical systems at finite temperatures, and pave the way towards large scale experimental simulations of open quantum systems in condensed matter physics and chemistry.Comment: 7 pages for the main text plus 6 pages for the supplementary material

An Action-Based Approach to Presence: Foundations and Methods

This chapter presents an action-based approach to presence. It starts by briefly describing the theoretical and empirical foundations of this approach, formalized into three key notions of place/space, action and mediation. In the light of these notions, some common assumptions about presence are then questioned: assuming a neat distinction between virtual and real environments, taking for granted the contours of the mediated environment and considering presence as a purely personal state. Some possible research topics opened up by adopting action as a unit of analysis are illustrated. Finally, a case study on driving as a form of mediated presence is discussed, to provocatively illustrate the flexibility of this approach as a unified framework for presence in digital and physical environment

Single-cell analysis: visualizing pharmaceutical and metabolite uptake in cells with label-free 3D mass spectrometry imaging

Detecting metabolites and parent compound within a cell type is now a priority for pharmaceutical development. In this context, three-dimensional secondary ion mass spectrometry (SIMS) imaging was used to investigate the cellular uptake of the antiarrhythmic agent amiodarone, a phospholipidosis-inducing pharmaceutical compound. The high lateral resolution and 3D imaging capabilities of SIMS combined with the multiplex capabilities of ToF mass spectrometric detection allows for the visualization of pharmaceutical compound and metabolites in single cells. The intact, unlabeled drug compound was successfully detected at therapeutic dosages in macrophages (cell line: NR8383). Chemical information from endogenous biomolecules was used to correlate drug distributions with morphological features. From this spatial analysis, amiodarone was detected throughout the cell with the majority of the compound found in the membrane and subsurface regions and absent in the nuclear regions. Similar results were obtained when the macrophages were doped with amiodarone metabolite, desethylamiodarone. The FWHM lateral resolution measured across an intracellular interface in a high lateral resolution ion images was approximately 550 nm. Overall, this approach provides the basis for studying cellular uptake of pharmaceutical compounds and their metabolites on the single cell level

Broadband Coupling into a Single-Mode, Electroactive Integrated Optical Waveguide for Spectroelectrochemical Analysis of Surface-Confined Redox Couples

Pushing the sensitivity of spectroelectrochemical techniques to routinely monitor changes in spectral properties of thin molecular films (i.e., monolayer or submonolayer) adsorbed on an electrode surface has been a goal of many investigators since the earliest developments in this field. 1 It was initially recognized that exploiting the evanescent field generated by total internal reflection at the interface of an optically transparent electrode (such as a thin film of tin oxide or indium tin oxide (ITO) on glass or quartz) has the inherent advantage of selectively probing only the near-surface region, as opposed to bulk sampling with transmission based techniques. Furthermore, by utilizing the multiple reflections in an attenuated total reflectance (ATR) geometry, an enhancement in sensitivity can be realized, and as the thickness of the ATR element is decreased, the number of reflections increases, yielding a substantial sensitivity enhancement. [2][3][4][5][6] Itoh and Fujishima were the first to show the advantages of reducing the thickness of an ATR element overcoated with a transparent conductive oxide to the integrated optical waveguide (IOW) regime. Using a four-mode, gradient index waveguide coated with a transparent, conductive tin oxide layer, they demonstrated large sensitivity enhancements, relative to a single pass transmission experiment, for spectroelectrochemical measurements of methylene blue. 7,8 Other research groups subsequently described similar gradient index, multilayer, electroactive waveguide structures, but they did not make use of the technology to explore the spectroelectrochemistry of (sub)monolayer coverage films. [9][10][11][12][13] We recently described a single-mode, electroactive planar IOW (the EA-IOW) having a step refractive index profile. It was fabricated by sputtering a Corning 7059 glass layer (400 nm) over soda lime glass or quartz, followed by a 200-nm layer of SiO 2

Grassroots Agency: Participation and Conflict in Buenos Aires Shantytowns seen through the Pilot Plan for Villa 7 (1971–1975)

open access articleIn 1971, after more than a decade of national and municipal policies aimed at the top-down removal of shantytowns, the Buenos Aires City Council approved the Plan Piloto para la Relocalización de Villa 7 (Pilot Plan for the Relocation of Shantytown 7; 1971–1975, referred to as the Pilot Plan hereinafter). This particular plan, which resulted in the construction of the housing complex, Barrio Justo Suárez, endures in the collective memory of Argentines as a landmark project regarding grassroots participation in state housing initiatives addressed at shantytowns. Emerging from a context of a housing shortage for the growing urban poor and intense popular mobilizations during the transition to democracy, the authors of the Pilot Plan sought to empower shantytown residents in novel ways by: 1) maintaining the shantytown’s location as opposed to eradication schemes that relocated the residents elsewhere, 2) formally employing some of the residents for the stage of construction, as opposed to “self-help” housing projects in which the residents contributed with unpaid labor, and 3) including them in the urban and architectural design of the of the new housing. This paper will examine the context in which the Pilot Plan was conceived of as a way of re-assessing the roles of the state, the user, and housing-related professionals, often seen as antagonistic. The paper argues that residents’ fair participation and state intervention in housing schemes are not necessarily incompatible, and can function in specific social and political contexts through multiactor proposals backed by a political will that prioritizes grassroots agency