This paper addresses the natural question: “How should frames be compared?” We answer this question by quantifying the overcompleteness of all frames with the same index set. We introduce the concept of a frame measure function: a function which maps each frame to a continuous function. The comparison of these functions induces an equivalence and partial order that allows for a meaningful compa...

We state the fractional Fourier transform and the continuous fractional wave packet transform as ways for analyzing persistent signals such as almost periodic functions and strong limit power signals. We construct frame decompositions for almost periodic functions using these two transforms. Also a norm equality of this signal is given using the continuous fractional wave packet transform.

Based on original work in [TV03], this paper gives a representation theorem for the Scott continuous maps between frames in terms of natural transformations between functors indexed by frames. The result specializes to frame homomorphisms, thereby giving a representation theorem for all locale maps (i.e. continuous maps as defined in locale theory).

Temporal integration of equations possessing continuous symmetries (e.g. systems with translational invariance associated with traveling solutions and scale invariance associated with self-similar solutions) in a “co-evolving” frame (i.e. a frame which is co-traveling, co-collapsing or co-exploding with the evolving solution) leads to improved accuracy because of the smaller time derivative in ...

Many applications in biology, such as long-term functional imaging of neural and cardiac systems, require continuous high-speed imaging. This is typically not possible, however, using commercially available systems. The frame rate and the recording time of high-speed cameras are limited by the digitization rate and the capacity of on-camera memory. Further restrictions are often imposed by the ...

In this paper, equivalent stiffness and mass matrices of a beam to a frame with repeated lattice structure are obtained to permute a frame to an equivalent continuous beam. Static and dynamic results of the permutated beam are obtained and compared to ANSYS’s results for the original frames with good agreements. The technique can be usefully employed for analyzing the global behavior of a frame...

We introduce an algorithm for the automatic computation of global parameterizations on arbitrary simplicial 2manifolds, whose parameter lines are guided by a given frame field, for example, by principal curvature frames. The parameter lines are globally continuous and allow a remeshing of the surface into quadrilaterals. The algorithm converts a given frame field into a single vector field on a...

Recent advances in web-based geospatial tools (the Geoweb) show promise as low-cost and easy-to-use methods to support citizen participation. This research presents two case studies of Geoweb implementation set in community-based organizations in rural Quebec, Canada. When comparing the development and sustainability of each Geoweb tool, the implementation time frame plays a key role. Two imple...

This paper studies the problem of sequence-to-sequence alignment, namely establishing correspondences in time and in space between two di erent video sequences of the same dynamic scene. The sequences are recorded by uncalibrated video cameras, which are either stationary or jointly moving, with xed (but unknown) internal parameters and relative inter-camera external parameters. Temporal variat...