Following results of Bourgain and Gorelik we show that the spaces lp, 1 < p < ∞, as well as some related spaces have the following uniqueness property: If X is a Banach space uniformly homeomorphic to one of these spaces then it is linearly isomorphic to the same space. We also prove that if a C(K) space is uniformly homeomorphic to c0, then it is isomorphic to c0. We show also that there are B...

This paper establishes the equality of the observation spaces defined by means of piecewise constant controls with those defined in terms of differentiable controls. This research was supported in part by US Air Force Grant AFOSR-88-0235. keywords: Observation space, shuffle product, input-output system, generating series.

This chapter focuses on the World Wide Web (Web) as a provider of shared information landscapes. It reviews our work to design 3D spaces for information navigation and social interaction, and suggests an approach to such design based on an experiential theory of meaning. The increasing use of virtual 3D space in information environments is noted, and Personal Spaces are contrasted with Public P...

Group equivariant and steerable convolutional neural networks (regular and steerable G-CNNs) have recently emerged as a very effective model class for learning from signal data such as 2D and 3D images, video, and other data where symmetries are present. In geometrical terms, regular G-CNNs represent data in terms of scalar fields (“feature channels”), whereas the steerable G-CNN can also use v...

In essence, designing a perfect-reconstruction (PR) biorthogonal cosine-modulated filter bank (BCM) is a non-convex constrained optimization problem that can be solved in principle using general optimization solvers. However, when the number of channels is large and the order of the prototype filter (PF) is high, numerical difficulties in using those optimization solvers often occur, and the co...

TV White Spaces have recently been proposed as an alternative to alleviate the spectrum crunch, characterised by the need to reallocate frequency bands to accommodate the ever-growing demand for wireless communications. In this paper, we discuss the motivations and challenges for collecting spectrum measurements in developing regions and discuss a scalable system for communities to gather and p...