Recently connections between the wavelet transform and lter banks have been established. We show that similar relations exist between the Gabor expansion and DFT lter banks. We introduce the \z-Zak transform" by suitably extending the discrete-time Zak transform and show its equivalence to the polyphase representation. A systematic discussion of parallels between DFT lter banks and Weyl-Heisenb...

We propose that the “magic number 4” puzzle of argument structure in semantic frames across most human languages is explained by selection pressures given inherent computational efficiency properties naturally arising from fundamental combinatorial mathematics of compositionality. Irrespective of language, school, or theoretical bias, linguists have long observed that what are now generally cal...

We use principal component analysis (PCA) to reduce the dimensionality of features of video frames for the purpose of content description. This low dimensional description makes practical the direct use of all the frames of a video sequence in later analysis. The PCA representation circumvents or eliminates several of the stumbling blocks in current analysis methods, and makes new analyses feas...

Using object-concepts as a matching framework, we provide guidelines for identifying what types of problems are best served by which knowledge representation technique. We find that production rules are best for hierarchical classification problems, because they support classification/instantiation of data. Frames are best for data retrieval and inference problems, because, using data abstracti...

The objective of this study is to compare description logics (DLs) and frames for representing large-scale biomedical ontologies and reasoning with them. The ontology under investigation is the Foundational Model of Anatomy (FMA). We converted it from its frame-based representation in Protégé into OWL DL. The OWL reasoner Racer helped identify unsatisfiable classes in the FMA. Support for consi...

In many areas of mathematics, orthonormal bases are a standard tool for representing vectors or operators. For certain problems, however, it is preferable to use an overcomplete, non-orthogonal set of vectors instead of an orthonormal basis, and thereby incorporate redundancy in the representation. Frames are overcomplete sets which are associated with redundant linear representations that have...

This paper presents an approach for human action recognition by finding the discriminative key frames from a video sequence and representing them with the distribution of local motion features and their spatiotemporal arrangements. In this approach, the key frames of the video sequence are selected by their discriminative power and represented by the local motion features detected in them and i...

A symmetry extension of Maxwell’s rule for rigidity of frames shows that every fully triangulated torus has at least six states of self stress with a well defined set of symmetries related to rotational and translational representations in the point group. In contrast, in trivalent polyhedral toroidal frames, i.e. the duals of the deltahedra, the rigid body motions plus the mechanisms are at le...

In this paper, a class of rational spatial curves that have a rational binormal is introduced. Such curves (called PB curves) play an important role in the derivation of rational rotation-minimizing conformal frames. The PB curve construction proposed is based upon the dual curve representation and the Euler-Rodrigues frame obtained from quaternion polynomials. The construction significantly si...

We summarize recent developments in our platform for symbolically representing and reasoning over human narratives. The expressive range of the system is bolstered by the infusion of a large library of knowledge frames, including verbs, adjectives, nouns and adverbs, from external linguistic resources. Extensions to the model itself include alternate timelines (imagined states for goals, plans,...