1,204 research outputs found
A Metric for genus-zero surfaces
We present a new method to compare the shapes of genus-zero surfaces. We
introduce a measure of mutual stretching, the symmetric distortion energy, and
establish the existence of a conformal diffeomorphism between any two
genus-zero surfaces that minimizes this energy. We then prove that the energies
of the minimizing diffeomorphisms give a metric on the space of genus-zero
Riemannian surfaces. This metric and the corresponding optimal diffeomorphisms
are shown to have properties that are highly desirable for applications.Comment: 33 pages, 8 figure
Managing Interacting Criteria: Application to Environmental Evaluation Practices
The need for organizations to evaluate their environmental practices has been recently increasing. This fact has led to the development of many approaches to appraise such practices. In this paper, a novel decision model to evaluate company’s environmental practices is proposed to improve traditional evaluation process in different facets. Firstly, different reviewers’ collectives related to the company’s activity are taken into account in the process to increase company internal efficiency and external legitimacy. Secondly, following the standard ISO 14031, two general categories of environmental performance indicators, management and operational, are considered. Thirdly, since the assumption of independence among environmental indicators is rarely verified in environmental context, an aggregation operator to bear in mind the relationship among such indicators in the evaluation results is proposed. Finally, this new model integrates quantitative and qualitative information with different scales using a multi-granular linguistic model that allows to adapt diverse evaluation scales according to appraisers’ knowledge
M\"obius Invariants of Shapes and Images
Identifying when different images are of the same object despite changes
caused by imaging technologies, or processes such as growth, has many
applications in fields such as computer vision and biological image analysis.
One approach to this problem is to identify the group of possible
transformations of the object and to find invariants to the action of that
group, meaning that the object has the same values of the invariants despite
the action of the group. In this paper we study the invariants of planar shapes
and images under the M\"obius group , which arises
in the conformal camera model of vision and may also correspond to neurological
aspects of vision, such as grouping of lines and circles. We survey properties
of invariants that are important in applications, and the known M\"obius
invariants, and then develop an algorithm by which shapes can be recognised
that is M\"obius- and reparametrization-invariant, numerically stable, and
robust to noise. We demonstrate the efficacy of this new invariant approach on
sets of curves, and then develop a M\"obius-invariant signature of grey-scale
images
Gauge Invariant Action for the Open Bosonic String: Tachyon Action
A gauge invariant action for the open bosonic string has been proposed in an
earlier paper. We work out the consequences of this proposal for the lowest
mode, viz. the tachyon. The action can be calculated for generic momenta,
perturbatively, order by order in the tachyon field. For on shell tachyons we
explicitly calculate the cubic action and show that it reproduces the correct
equations of motion and coincides wih the function to the required
order. The calculation is done in terms of bare fields with a finite cutoff,
which is the original prescription. We also show that it is possible in some
momentum regions to renormalize the theory and eliminate the cutoff dependence
so that the continuum limit can be taken. After renormalization, the parameter
is replaced by where is an IR cutoff, is the UV
cutoff and is some renormalization scale. There is also some arbitrariness
in the overall normalization due to the choice of regularization scheme - this
does not affect on-shell quantities. We also rederive within this scheme, the
action in the region of zero momentum, which gives the exact (tree level)
tachyon potential. The tachyon potential is consistent with Sen's conjecture
that the height of the potential is the same as the tension of the brane.Comment: 31 pages, Late
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