6,256 research outputs found
Insights into business confidence from firm-level panel data
Business confidence announcements attract widespread attention, yet relatively little is known about the series itself. What, for example, does an improvement or deterioration in business confidence mean? We consider this question using a panel of firm-level responses to a business opinion survey that includes a question on business confidence. We relate the confidence responses of the firms to microeconomic and macroeconomic variables that have a direct interpretation and, as a result, determine the variables that firms associate with business confidence. Our analysis of firm-level data reveals that what firms associate with business confidence changes over time and means different things to different firms. Consequently, it is not immediately apparent what a change in business confidence actually means
Analysis of Energy-Based Blended Quasicontinuum Approximations
The development of patch test consistent quasicontinuum energies for
multi-dimensional crystalline solids modeled by many-body potentials remains a
challenge. The original quasicontinuum energy (QCE) has been implemented for
many-body potentials in two and three space dimensions, but it is not patch
test consistent. We propose that by blending the atomistic and corresponding
Cauchy-Born continuum models of QCE in an interfacial region with thickness of
a small number of blended atoms, a general quasicontinuum energy (BQCE) can
be developed with the potential to significantly improve the accuracy of QCE
near lattice instabilities such as dislocation formation and motion. In this
paper, we give an error analysis of the blended quasicontinuum energy (BQCE)
for a periodic one-dimensional chain of atoms with next-nearest neighbor
interactions. Our analysis includes the optimization of the blending function
for an improved convergence rate. We show that the strain error for
the non-blended QCE energy (QCE), which has low order
where is the atomistic length scale, can
be reduced by a factor of for an optimized blending function where
is the number of atoms in the blending region. The QCE energy has been
further shown to suffer from a O error in the critical strain at which the
lattice loses stability. We prove that the error in the critical strain of BQCE
can be reduced by a factor of for an optimized blending function, thus
demonstrating that the BQCE energy for an optimized blending function has the
potential to give an accurate approximation of the deformation near lattice
instabilities such as crack growth.Comment: 26 pages, 1 figur
The Segal--Bargmann transform for odd-dimensional hyperbolic spaces
We develop isometry and inversion formulas for the Segal--Bargmann transform
on odd-dimensional hyperbolic spaces that are as parallel as possible to the
dual case of odd-dimensional spheres.Comment: To appear in Mathematic
Coherent states for a 2-sphere with a magnetic field
We consider a particle moving on a 2-sphere in the presence of a constant
magnetic field. Building on earlier work in the nonmagnetic case, we construct
coherent states for this system. The coherent states are labeled by points in
the associated phase space, the (co)tangent bundle of S^2. They are constructed
as eigenvectors for certain annihilation operators and expressed in terms of a
certain heat kernel. These coherent states are not of Perelomov type, but
rather are constructed according to the "complexifier" approach of T. Thiemann.
We describe the Segal--Bargmann representation associated to the coherent
states, which is equivalent to a resolution of the identity.Comment: 23 pages. To appear in Journal of Physics A, Special Issue on
Coherent State
The Segal-Bargmann transform for noncompact symmetric spaces of the complex type
We consider the generalized Segal-Bargmann transform, defined in terms of the
heat operator, for a noncompact symmetric space of the complex type. For radial
functions, we show that the Segal-Bargmann transform is a unitary map onto a
certain L^2 space of meromorphic functions. For general functions, we give an
inversion formula for the Segal-Bargmann transform, involving integration
against an "unwrapped" version of the heat kernel for the dual compact
symmetric space. Both results involve delicate cancellations of singularities.Comment: 28 pages. Minor corrections made. To appear in J. Functional Analysi
Programmatic and Direct Manipulation, Together at Last
Direct manipulation interfaces and programmatic systems have distinct and
complementary strengths. The former provide intuitive, immediate visual
feedback and enable rapid prototyping, whereas the latter enable complex,
reusable abstractions. Unfortunately, existing systems typically force users
into just one of these two interaction modes.
We present a system called Sketch-n-Sketch that integrates programmatic and
direct manipulation for the particular domain of Scalable Vector Graphics
(SVG). In Sketch-n-Sketch, the user writes a program to generate an output SVG
canvas. Then the user may directly manipulate the canvas while the system
immediately infers a program update in order to match the changes to the
output, a workflow we call live synchronization. To achieve this, we propose
(i) a technique called trace-based program synthesis that takes program
execution history into account in order to constrain the search space and (ii)
heuristics for dealing with ambiguities. Based on our experience with examples
spanning 2,000 lines of code and from the results of a preliminary user study,
we believe that Sketch-n-Sketch provides a novel workflow that can augment
traditional programming systems. Our approach may serve as the basis for live
synchronization in other application domains, as well as a starting point for
yet more ambitious ways of combining programmatic and direct manipulation.Comment: PLDI 2016 Paper + Supplementary Appendice
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