4,085 research outputs found

    Trace anomaly of the conformal gauge field

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    The proposed by Bastianelli and van Nieuwenhuizen new method of calculations of trace anomalies is applied in the conformal gauge field case. The result is then reproduced by the heat equation method. An error in previous calculation is corrected. It is pointed out that the introducing gauge symmetries into a given system by a field-enlarging transformation can result in unexpected quantum effects even for trivial configurations.Comment: 9 pages, LaTeX file, BI-TP 93/3

    Non collinear magnetism and single ion anisotropy in multiferroic perovskites

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    The link between the crystal distortions of the perovskite structure and the magnetic exchange interaction, the single-ion anisotropy (SIA) and the Dzyaloshinsky-Moriya (DM) interaction are investigated by means of density-functional calculations. Using BiFeO3_3 and LaFeO3_3 as model systems, we quantify the relationship between the oxygen octahedra rotations, the ferroelectricity and the weak ferromagnetism (wFM). We recover the fact that the wFM is due to the DM interaction induced by the oxygen octahedra rotations. We find a simple relationship between the wFM, the oxygen rotation amplitude and the ratio between the DM vector and the exchange parameter such as the wFM increases with the oxygen octahedra rotation when the SIA does not compete with the DM forces induced on the spins. Unexpectedly, we also find that, in spite of the d5d^5 electronic configuration of Fe3+^{3+}, the SIA is very large in some structures and is surprisingly strongly sensitive to the chemistry of the AA-site cation of the AABO3_3 perovskite. In the ground R3cR3c state phase we show that the SIA shape induced by the ferroelectricity and the oxygen octahedra rotations are in competition such as it is possible to tune the wFM "on" and "off" through the relative size of the two types of distortion

    First-principles study of the ferroelectric Aurivillius phase Bi2WO6

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    In order to better understand the reconstructive ferroelectric-paraelectric transition of Bi2WO6, which is unusual within the Aurivillius family of compounds, we performed first principles calculations of the dielectric and dynamical properties on two possible high-temperature paraelectic structures: the monoclinic phase of A2/m symmetry observed experimentally and the tetragonal phase of I4/mmm symmetry, common to most Aurivillius phase components. Both paraelectric structures exhibits various unstable modes, which after their condensation bring the system toward more stable structures of lower symmetry. The calculations confirms that, starting from the paraelectric A2/m phase at high temperature, the system must undergo a reconstructive transition to reach the P2_1ab ferroelectric ground state.Comment: added Appendix and two table

    Fixed-parameter tractability of multicut parameterized by the size of the cutset

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    Given an undirected graph GG, a collection {(s1,t1),...,(sk,tk)}\{(s_1,t_1),..., (s_k,t_k)\} of pairs of vertices, and an integer pp, the Edge Multicut problem ask if there is a set SS of at most pp edges such that the removal of SS disconnects every sis_i from the corresponding tit_i. Vertex Multicut is the analogous problem where SS is a set of at most pp vertices. Our main result is that both problems can be solved in time 2O(p3)...nO(1)2^{O(p^3)}... n^{O(1)}, i.e., fixed-parameter tractable parameterized by the size pp of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form f(p)...nO(1)f(p)... n^{O(1)} exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset

    A Cost-based Optimizer for Gradient Descent Optimization

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    As the use of machine learning (ML) permeates into diverse application domains, there is an urgent need to support a declarative framework for ML. Ideally, a user will specify an ML task in a high-level and easy-to-use language and the framework will invoke the appropriate algorithms and system configurations to execute it. An important observation towards designing such a framework is that many ML tasks can be expressed as mathematical optimization problems, which take a specific form. Furthermore, these optimization problems can be efficiently solved using variations of the gradient descent (GD) algorithm. Thus, to decouple a user specification of an ML task from its execution, a key component is a GD optimizer. We propose a cost-based GD optimizer that selects the best GD plan for a given ML task. To build our optimizer, we introduce a set of abstract operators for expressing GD algorithms and propose a novel approach to estimate the number of iterations a GD algorithm requires to converge. Extensive experiments on real and synthetic datasets show that our optimizer not only chooses the best GD plan but also allows for optimizations that achieve orders of magnitude performance speed-up.Comment: Accepted at SIGMOD 201

    Asymptotic Behavior of Inflated Lattice Polygons

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    We study the inflated phase of two dimensional lattice polygons with fixed perimeter NN and variable area, associating a weight exp[pAJb]\exp[pA - Jb ] to a polygon with area AA and bb bends. For convex and column-convex polygons, we show that /Amax=1K(J)/p~2+O(ρp~)/A_{max} = 1 - K(J)/\tilde{p}^2 + \mathcal{O}(\rho^{-\tilde{p}}), where p~=pN1\tilde{p}=pN \gg 1, and ρ<1\rho<1. The constant K(J)K(J) is found to be the same for both types of polygons. We argue that self-avoiding polygons should exhibit the same asymptotic behavior. For self-avoiding polygons, our predictions are in good agreement with exact enumeration data for J=0 and Monte Carlo simulations for J0J \neq 0. We also study polygons where self-intersections are allowed, verifying numerically that the asymptotic behavior described above continues to hold.Comment: 7 page
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