Angular-planar CMB power spectrum

Gaussianity and statistical isotropy of the Universe are modern cosmology's minimal set of hypotheses. In this work we introduce a new statistical test to detect observational deviations from this minimal set. By defining the temperature correlation function over the whole celestial sphere, we are able to independently quantify both angular and planar dependence (modulations) of the CMB temperature power spectrum over different slices of this sphere. Given that planar dependence leads to further modulations of the usual angular power spectrum $C_l$, this test can potentially reveal richer structures in the morphology of the primordial temperature field. We have also constructed an unbiased estimator for this angular-planar power spectrum which naturally generalizes the estimator for the usual $C_l$'s. With the help of a chi-square analysis, we have used this estimator to search for observational deviations of statistical isotropy in WMAP's 5 year release data set (ILC5), where we found only slight anomalies on the angular scales $l=7$ and $l=8$. Since this angular-planar statistic is model-independent, it is ideal to employ in searches of statistical anisotropy (e.g., contaminations from the galactic plane) and to characterize non-Gaussianities.Comment: Replaced to match the published version. Journal-ref: Phys.Rev. D80 063525 (2009

The Economist's Dilemma—The Relevance of Development Economics to Public Administration

Summary There is general disillusionment amongst academics concerned with development studies with the results of two decades of sustained attempts to stimulate economic development and economic planning in the developing countries. In recent literature this has been blamed partly on weaknesses in the theory of development economics and the irrelevance of much of economic theory as produced by rich countries, and partly on the failure of economists and planners to understand fully the political and social realities of the poor countries. This mood of pessimism is compared with the perceptions of generalist administrators from the developing countries participating in courses in public administration in the University of Manchester, and their understanding of the currently fashionable policies of self?reliance and a search for indigenous solutions. Resume Le dilemme de l'économiste: L'utilité de l'économique de développement pour l'administration publique Il y a un désenchantement général chez les universitaires spécialisés dans les études sur le développement devant les résultats obtenus au cours de deux décennies d'efforts soutenus pour stimuler le développement économique et la planification de l'économie dans les pays en voie de développement. Selon les ouvrages récemment publiés, la faute en incombe en partie aux faiblesses de la théorie de l'économique de développement et au manque de réalisme d'une grande partie de la théorie économique originaire des pays riches, et en partie aux économistes et planificateurs qui n'ont pas su comprendre les réalités politiques et sociales des pays pauvres. L'auteur compare cette humeur pessimiste avec les façons de voir des administrateurs généralistes des pays en vole de développement participant à des stages sur l'administration publique à l'Université de Manchester, et à leur compréhension des politiques actuellement à la mode d'auto?suffisance et de recherches de solutions indigènes. Resumen El dilema del economista: La pertinencia de los estudios económicos sobre el desarrollo para la Administración Publica Existe una desilusión general entre los académicos interesados en los estudios sobre el desarrollo hacia los resultados de dos decenios de tentativas persistentes para estimular el desarrollo económico y la planificación económica en los países en vías de desarrollo. En textos recientes, se ha acusado en parte de esto a las deficiencias de la teoría sobre economía del desarrollo y la incongruencia de bastante de lo que se considere teoría económica, según se ha producido en los países ricos, y en parte al fracaso de los economistas y planificadores en comprender completamente las realidades políticas y sociales de los países pobres. Este pesimismo se compara con las percepciones de administradores generalistas de los países en vías de desarrollo que participan en cursos de administración pública en la universidad de Manchester y su comprensión de las políticas actualmente de moda de autosuficiencia y una búsqueda de las soluciones indígenas

Imaginary in all directions: an elegant formulation of special relativity and classical electrodynamics

A suitable parameterization of space-time in terms of one complex and three quaternionic imaginary units allows Lorentz transformations to be implemented as multiplication by complex-quaternionic numbers rather than matrices. Maxwell's equations reduce to a single equation.Comment: 8 page

Quantum computing with nearest neighbor interactions and error rates over 1%

Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure that requires only a 2-D square lattice of qubits that can interact with their nearest neighbors, yet can tolerate quantum gate error rates over 1%. The precise maximum tolerable error rate depends on the error model, and we calculate values in the range 1.1--1.4% for various physically reasonable models. Even the lowest value represents the highest threshold error rate calculated to date in a geometrically constrained setting, and a 50% improvement over the previous record.Comment: 4 pages, 8 figure

Hierarchical mean-field approach to the J1J_1-J2J_2 Heisenberg model on a square lattice

We study the quantum phase diagram and excitation spectrum of the frustrated $J_1$-$J_2$ spin-1/2 Heisenberg Hamiltonian. A hierarchical mean-field approach, at the heart of which lies the idea of identifying {\it relevant} degrees of freedom, is developed. Thus, by performing educated, manifestly symmetry preserving mean-field approximations, we unveil fundamental properties of the system. We then compare various coverings of the square lattice with plaquettes, dimers and other degrees of freedom, and show that only the {\it symmetric plaquette} covering, which reproduces the original Bravais lattice, leads to the known phase diagram. The intermediate quantum paramagnetic phase is shown to be a (singlet) {\it plaquette crystal}, connected with the neighboring N\'eel phase by a continuous phase transition. We also introduce fluctuations around the hierarchical mean-field solutions, and demonstrate that in the paramagnetic phase the ground and first excited states are separated by a finite gap, which closes in the N\'eel and columnar phases. Our results suggest that the quantum phase transition between N\'eel and paramagnetic phases can be properly described within the Ginzburg-Landau-Wilson paradigm.Comment: LaTeX 2e, 14 pages, 17 figure

Maximum weight cycle packing in directed graphs, with application to kidney exchange programs

Centralized matching programs have been established in several countries to organize kidney exchanges between incompatible patient-donor pairs. At the heart of these programs are algorithms to solve kidney exchange problems, which can be modelled as cycle packing problems in a directed graph, involving cycles of length 2, 3, or even longer. Usually, the goal is to maximize the number of transplants, but sometimes the total benefit is maximized by considering the differences between suitable kidneys. These problems correspond to computing cycle packings of maximum size or maximum weight in directed graphs. Here we prove the APX-completeness of the problem of finding a maximum size exchange involving only 2-cycles and 3-cycles. We also present an approximation algorithm and an exact algorithm for the problem of finding a maximum weight exchange involving cycles of bounded length. The exact algorithm has been used to provide optimal solutions to real kidney exchange problems arising from the National Matching Scheme for Paired Donation run by NHS Blood and Transplant, and we describe practical experience based on this collaboration

Towards practical classical processing for the surface code

The surface code is unarguably the leading quantum error correction code for 2-D nearest neighbor architectures, featuring a high threshold error rate of approximately 1%, low overhead implementations of the entire Clifford group, and flexible, arbitrarily long-range logical gates. These highly desirable features come at the cost of significant classical processing complexity. We show how to perform the processing associated with an nxn lattice of qubits, each being manipulated in a realistic, fault-tolerant manner, in O(n^2) average time per round of error correction. We also describe how to parallelize the algorithm to achieve O(1) average processing per round, using only constant computing resources per unit area and local communication. Both of these complexities are optimal.Comment: 5 pages, 6 figures, published version with some additional tex

Deuteron Dipole Polarizabilities and Sum Rules

The scalar, vector, and tensor components of the (generalized) deuteron electric polarizability are calculated, as well as their logarithmic modifications. Several of these quantities arise in the treatment of the nuclear corrections to the deuterium Lamb shift and the deuterium hyperfine structure. A variety of second-generation potential models are used and a (subjective) error is assigned to the calculations. The zero-range approximation is used to analyze a subset of the results, and a simple relativistic version of this approximation is developed.Comment: 14 pages, LaTex - submitted to Physical Review

Tripartite to Bipartite Entanglement Transformations and Polynomial Identity Testing

We consider the problem of deciding if a given three-party entangled pure state can be converted, with a non-zero success probability, into a given two-party pure state through local quantum operations and classical communication. We show that this question is equivalent to the well-known computational problem of deciding if a multivariate polynomial is identically zero. Efficient randomized algorithms developed to study the latter can thus be applied to the question of tripartite to bipartite entanglement transformations