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A quantum geometric model of similarity
No other study has had as great an impact on the development of the similarity literature as that of Tversky (1977), which provided compelling demonstrations against all the fundamental assumptions of the popular, and extensively employed, geometric similarity models. Notably, similarity judgments were shown to violate symmetry and the triangle inequality, and also be subject to context effects, so that the same pair of items would be rated differently, depending on the presence of other items. Quantum theory provides a generalized geometric approach to similarity and can address several of Tversky’s (1997) main findings. Similarity is modeled as quantum probability, so that asymmetries emerge as order effects, and the triangle equality violations and the diagnosticity effect can be related to the context-dependent properties of quantum probability. We so demonstrate the promise of the quantum approach for similarity and discuss the implications for representation theory in general
VoroCrust: Voronoi Meshing Without Clipping
Polyhedral meshes are increasingly becoming an attractive option with
particular advantages over traditional meshes for certain applications. What
has been missing is a robust polyhedral meshing algorithm that can handle broad
classes of domains exhibiting arbitrarily curved boundaries and sharp features.
In addition, the power of primal-dual mesh pairs, exemplified by
Voronoi-Delaunay meshes, has been recognized as an important ingredient in
numerous formulations. The VoroCrust algorithm is the first provably-correct
algorithm for conforming polyhedral Voronoi meshing for non-convex and
non-manifold domains with guarantees on the quality of both surface and volume
elements. A robust refinement process estimates a suitable sizing field that
enables the careful placement of Voronoi seeds across the surface circumventing
the need for clipping and avoiding its many drawbacks. The algorithm has the
flexibility of filling the interior by either structured or random samples,
while preserving all sharp features in the output mesh. We demonstrate the
capabilities of the algorithm on a variety of models and compare against
state-of-the-art polyhedral meshing methods based on clipped Voronoi cells
establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed
images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf.
Supplemental materials available on
https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd
Putting a cap on causality violations in CDT
The formalism of causal dynamical triangulations (CDT) provides us with a
non-perturbatively defined model of quantum gravity, where the sum over
histories includes only causal space-time histories. Path integrals of CDT and
their continuum limits have been studied in two, three and four dimensions.
Here we investigate a generalization of the two-dimensional CDT model, where
the causality constraint is partially lifted by introducing weighted branching
points, and demonstrate that the system can be solved analytically in the
genus-zero sector.Comment: 17 pages, 4 figure
Bell's Inequalities, Superquantum Correlations, and String Theory
We offer an interpretation of super-quantum correlations in terms of a
"doubly" quantum theory. We argue that string theory, viewed as a quantum
theory with two deformation parameters, the string tension \alpha' and the
string coupling constant g_s, is such a super-quantum theory, one that
transgresses the usual quantum violations of Bell's inequalities. We also
discuss the \hbar\to\infty limit of quantum mechanics in this context. As a
super-quantum theory, string theory should display distinct experimentally
observable super-correlations of entangled stringy states.Comment: 7 pages, revtex
Building Engineering Feasibility Study: Herreshoff Marine Museum
Our design team was supplied with a dozen architectural designs from the students of the Roger Williams University Architectural School. After discussing the strengths and weaknesses of each our team was able to narrow our choices down to one base design to conduct our feasibility and structural integrity analysis. Currently, the structural integrity of the proposed building addition has been examined by determining the wind and the snow loads, the green roof requirements, and the column and beam loads. The feasibility of the chosen design was assessed by researching Bristol zoning regulations and developing a path through the required zoning variances, which will help in the construction phase
Deformed General Relativity and Torsion
We argue that the natural framework for embedding the ideas of deformed, or
doubly, special relativity (DSR) into a curved spacetime is a generalisation of
Einstein-Cartan theory, considered by Stelle and West. Instead of interpreting
the noncommuting "spacetime coordinates" of the Snyder algebra as endowing
spacetime with a fundamentally noncommutative structure, we are led to consider
a connection with torsion in this framework. This may lead to the usual
ambiguities in minimal coupling. We note that observable violations of charge
conservation induced by torsion should happen on a time scale of 10^3 s, which
seems to rule out these modifications as a serious theory. Our considerations
show, however, that the noncommutativity of translations in the Snyder algebra
need not correspond to noncommutative spacetime in the usual sense.Comment: 20 pages, 1 figure, revtex; expanded sections 3 and 4 for clarity,
moved material to appendix B, corrected a few minor error
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