Grand unification and enhanced quantum gravitational effects

In grand unified theories with large numbers of fields, renormalization effects significantly modify the scale at which quantum gravity becomes strong. This in turn can modify the boundary conditions for coupling constant unification, if higher dimensional operators induced by gravity are taken into consideration. We show that the generic size of these effects from gravity can be larger than the two-loop corrections typically considered in renormalization group analyses of unification. In some cases, gravitational effects of modest size can render unification impossible.Comment: 4 pages, 1 figure, revtex; minor changes in v2 (version published in Phys. Rev. Lett.

Entanglement Entropy of the Low-Lying Excited States and Critical Properties of an Exactly Solvable Two-Leg Spin Ladder with Three-Spin Interactions

In this work, we investigate an exactly solvable two-leg spin ladder with three-spin interactions. We obtain analytically the finite-size corrections of the low-lying energies and determine the central charge as well as the scaling dimensions. The model considered in this work has the same universality class of critical behavior of the XX chain with central charge c=1. By using the correlation matrix method, we also study the finite-size corrections of the Renyi entropy of the ground state and of the excited states. Our results are in agreement with the predictions of the conformal field theory.Comment: 10 pages, 6 figures, 2 table

Primary Surplus Behavior and Risks to Fiscal Sustainability in Emerging Market Countries: A "Fan-Chart" Approach

This paper proposes a probabilistic approach to public debt sustainability analy-sis (DSA) using "fan charts." These depict the magnitude of risks-upside and downside-surrounding public debt projections as a result of uncertain economic conditions and policies. We propose a simulation algorithm for the path of public debt under realistic shock configurations, combining pure economic disturbances (to growth, interest rates, and exchange rates), the endogenous policy response to these, and the possible shocks arising from fiscal policy itself. The paper empha-sizes the role of fiscal behavior, as well as the structure of disturbances facing the economy and due to fiscal policy, in shaping the risk profile of public debt. Fan charts for debt are derived from the "marriage" between the pattern of shocks on the one hand and the endogenous response of fiscal policy on the other. Applications to Argentina, Brazil, Mexico, South Africa, and Turkey are used to illustrate the approach and its limitations. Copyright 2006, International Monetary Fund

Effective Magnetic Monopoles and Universal Conductance Fluctuations

The observation of isolated positive and negative charges, but not isolated magnetic north and south poles, is an old puzzle. Instead, evidence of effective magnetic monopoles has been found in the abstract momentum space. Apart from Hall-related effects, few observable consequences of these abstract monopoles are known. Here, we show that it is possible to manipulate the monopoles by external magnetic fields and probe them by universal conductance fluctuation (UCF) measurements in ferromagnets with strong spin-orbit coupling. The observed fluctuations are not noise, but reproducible quasiperiodic oscillations as a function of magnetisation direction, a novel Berry phase fingerprint of the magnetic monopoles.Comment: Final version accepted by Physical Review Letter

EM Algorithms for Weighted-Data Clustering with Application to Audio-Visual Scene Analysis

Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical properties and to the existence of maximum-likelihood estimators based on expectation-maximization (EM). In this paper we propose a new mixture model that associates a weight with each observed point. We introduce the weighted-data Gaussian mixture and we derive two EM algorithms. The first one considers a fixed weight for each observation. The second one treats each weight as a random variable following a gamma distribution. We propose a model selection method based on a minimum message length criterion, provide a weight initialization strategy, and validate the proposed algorithms by comparing them with several state of the art parametric and non-parametric clustering techniques. We also demonstrate the effectiveness and robustness of the proposed clustering technique in the presence of heterogeneous data, namely audio-visual scene analysis.Comment: 14 pages, 4 figures, 4 table