Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets

We generalize an efficient exact synthesis algorithm for single-qubit unitaries over the Clifford+T gate set which was presented by Kliuchnikov, Maslov and Mosca. Their algorithm takes as input an exactly synthesizable single-qubit unitary--one which can be expressed without error as a product of Clifford and T gates--and outputs a sequence of gates which implements it. The algorithm is optimal in the sense that the length of the sequence, measured by the number of T gates, is smallest possible. In this paper, for each positive even integer $n$ we consider the "Clifford-cyclotomic" gate set consisting of the Clifford group plus a z-rotation by $\frac{\pi}{n}$. We present an efficient exact synthesis algorithm which outputs a decomposition using the minimum number of $\frac{\pi}{n}$ z-rotations. For the Clifford+T case $n=4$ the group of exactly synthesizable unitaries was shown to be equal to the group of unitaries with entries over the ring $\mathbb{Z}[e^{i\frac{\pi}{n}},1/2]$. We prove that this characterization holds for a handful of other small values of $n$ but the fraction of positive even integers for which it fails to hold is 100%.Comment: v2: published versio

Automated pebble mosaic stylization of images

Digital mosaics have usually used regular tiles, simulating the historical "tessellated" mosaics. In this paper, we present a method for synthesizing pebble mosaics, a historical mosaic style in which the tiles are rounded pebbles. We address both the tiling problem, where pebbles are distributed over the image plane so as to approximate the input image content, and the problem of geometry, creating a smooth rounded shape for each pebble. We adapt SLIC, simple linear iterative clustering, to obtain elongated tiles conforming to image content, and smooth the resulting irregular shapes into shapes resembling pebble cross-sections. Then, we create an interior and exterior contour for each pebble and solve a Laplace equation over the region between them to obtain height-field geometry. The resulting pebble set approximates the input image while presenting full geometry that can be rendered and textured for a highly detailed representation of a pebble mosaic

Evolution of Subjective Hurricane Risk Perceptions: A Bayesian Approach

This paper studies how individuals update subjective risk perceptions in response to hurricane track forecast information, using a unique data set from an event market, the Hurricane Futures Market (HFM). We derive a theoretical Bayesian framework which predicts how traders update their perceptions of the probability of a hurricane making landfall in a certain range of coastline. Our results suggest that traders behave in a way consistent with Bayesian updating but this behavior is based on the perceived quality of the information received.risk perceptions, learning, Bayesian learning, event markets, prediction markets, favorite-longshot bias, hurricanes

Identification of vortexes obstructing the dynamo mechanism in laboratory experiments

The magnetohydrodynamic dynamo effect explains the generation of self-sustained magnetic fields in electrically conducting flows, especially in geo- and astrophysical environments. Yet the details of this mechanism are still unknown, e.g., how and to which extent the geometry, the fluid topology, the forcing mechanism and the turbulence can have a negative effect on this process. We report on numerical simulations carried out in spherical geometry, analyzing the predicted velocity flow with the so-called Singular Value Decomposition, a powerful technique that allows us to precisely identify vortexes in the flow which would be difficult to characterize with conventional spectral methods. We then quantify the contribution of these vortexes to the growth rate of the magnetic energy in the system. We identify an axisymmetric vortex, whose rotational direction changes periodically in time, and whose dynamics are decoupled from those of the large scale background flow, is detrimental for the dynamo effect. A comparison with experiments is carried out, showing that similar dynamics were observed in cylindrical geometry. These previously unexpected eddies, which impede the dynamo effect, offer an explanation for the experimental difficulties in attaining a dynamo in spherical geometry.Comment: 25 pages, 12 figures, submitted to Physics of Fluid

The Quantitative Strategic Planning Matrix (QSPM) Applied to a Retail Computer Store

This article presents the Quantitative Strategic Planning Matrix (QSPM), an analytical tool used in formulating strategies. First introduced in a Long Range Planning (3), the QSPM has become widely used among strategic management professors and students for two decades. However, the QSPM has not been widely adopted by strategic planning consultants and organizations. This paper discusses how and why the QSPM should be used by businesses for strategic planning. An example QSPM for a retail computer store is provided and the benefits and limitations of this important strategic planning analytical tool are addressed. Specific guidelines are provided for preparing a QSPM

Assessing the Impact of Retreat Mechanisms in a Simple Antarctic Ice Sheet Model Using Bayesian Calibration

The response of the Antarctic ice sheet (AIS) to changing climate forcings is an important driver of sea-level changes. Anthropogenic climate change may drive a sizeable AIS tipping point response with subsequent increases in coastal flooding risks. Many studies analyzing flood risks use simple models to project the future responses of AIS and its sea-level contributions. These analyses have provided important new insights, but they are often silent on the effects of potentially important processes such as Marine Ice Sheet Instability (MISI) or Marine Ice Cliff Instability (MICI). These approximations can be well justified and result in more parsimonious and transparent model structures. This raises the question of how this approximation impacts hindcasts and projections. Here, we calibrate a previously published and relatively simple AIS model, which neglects the effects of MICI and regional characteristics, using a combination of observational constraints and a Bayesian inversion method. Specifically, we approximate the effects of missing MICI by comparing our results to those from expert assessments with more realistic models and quantify the bias during the last interglacial when MICI may have been triggered. Our results suggest that the model can approximate the process of MISI and reproduce the projected median melt from some previous expert assessments in the year 2100. Yet, our mean hindcast is roughly 3/4 of the observed data during the last interglacial period and our mean projection is roughly 1/6 and 1/10 of the mean from a model accounting for MICI in the year 2100. These results suggest that missing MICI and/or regional characteristics can lead to a low-bias during warming period AIS melting and hence a potential low-bias in projected sea levels and flood risks.Comment: v1: 16 pages, 4 figures, 7 supplementary files; v2: 15 pages, 4 figures, 7 supplementary files, corrected typos, revised title, updated according to revisions made through publication proces

Spherical single-roll dynamos at large magnetic Reynolds numbers

This paper concerns kinematic helical dynamos in a spherical fluid body surrounded by an insulator. In particular, we examine their behaviour in the regime of large magnetic Reynolds number \Rm, for which dynamo action is usually concentrated upon a simple resonant stream-surface. The dynamo eigensolutions are computed numerically for two representative single-roll flows using a compact spherical harmonic decomposition and fourth-order finite-differences in radius. These solutions are then compared with the growth rates and eigenfunctions of the Gilbert and Ponty (2000) large \Rm asymptotic theory. We find good agreement between the growth rates when \Rm>10^4, and between the eigenfunctions when \Rm>10^5.Comment: 36 pages, 8 figures. V2: incorrect labels in Fig3 corrected. The article appears in Physics of Fluids, 22, 066601, and may be found at http://pof.aip.org/phfle6/v22/i6/p066601_s1 . (Copyright 2010 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics

Futurologie et transitologie : les think tanks face à la "société de l’information"

Liés à l’étude des stratégies militaires, les think thanks jouent rapidement un rôle important dans le façonne-ment, l’évolution et la diffusion des méthodes de la futurologie. Ils se sont également investis de la mission, d’une part, de « penser » la société « post-industrielle » devenue « société de l¹information » et, d’autre part, d’accompagner la transition d’un type de société à un autre sur fond de « fin des idéologies » et de révolution technique permanente.In relation with military strategies, think tanks are quickly playing an important role regarding the shap­ing, evolution and diffusion of the futurology meth­odology. They have also taken part in the mission, on one hand, to think the “post-industrial” society which became the “information” society, and on the other hand, they have participated to the transition of one type of society to the other in the context of the end of ideologies and permanent technical revolution