4,085 research outputs found
Trace anomaly of the conformal gauge field
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
The hidden burden of adult allergic rhinitis : UK healthcare resource utilisation survey
Funding Funding for this survey was provided by Meda Pharma.Peer reviewedPublisher PD
Non collinear magnetism and single ion anisotropy in multiferroic perovskites
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 BiFeO and LaFeO 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 electronic configuration of Fe, the SIA is
very large in some structures and is surprisingly strongly sensitive to the
chemistry of the -site cation of the BO perovskite. In the ground
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
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
Given an undirected graph , a collection of
pairs of vertices, and an integer , the Edge Multicut problem ask if there
is a set of at most edges such that the removal of disconnects
every from the corresponding . Vertex Multicut is the analogous
problem where is a set of at most vertices. Our main result is that
both problems can be solved in time , i.e.,
fixed-parameter tractable parameterized by the size of the cutset in the
solution. By contrast, it is unlikely that an algorithm with running time of
the form 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
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
We study the inflated phase of two dimensional lattice polygons with fixed
perimeter and variable area, associating a weight to a
polygon with area and bends. For convex and column-convex polygons, we
show that , where , and . The
constant 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 . 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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