An informal argument shows that common knowledge of rationality implies the iterative elimination of strongly dominated strategies. Rationality here means that players do not play strategies that are strongly dominated relative to their knowledge. We formalize and prove this claim. When by rationality we mean that players do not play strategies that are weakly dominated relative to their knowle...

In this paper we develop a general and very simple construction for complete orthonormal bases for system identiication. This construction provides a unifying formulation of all known orthonormal bases since the common FIR and recently popular Laguerre and Kautz model structures are restrictive special cases of our construction as is another construction method based on balanced realisations of...

It is instructive to see how the use of Gröbner bases [2] can clarify certain computational and theoretic aspects of various topics. Here the choice of topics come from association schemes and fusion of flag algebras arising from generalized n-gons and 2-(v, k, 1) designs [6]. Three different ways of using concepts related to Gröbner bases are given as a guide for using such concepts in similar...

This paper investigates the use of general bases with fixed poles for the purposes of robust estimation. These bases, which generalise the common FIR, Laguerre and two–parameter Kautz ones, are shown to be fundamental in the disc algebra provided a very mild condition on the choice of poles is satisfied. It is also shown, that by using a min–max criterion, these bases lead to robust estimators ...

g-frames in hilbert spaces are a redundant set of operators which yield a repre-sentation for each vector in the space. in this paper we investigate the connection betweeng-frames, g-orthonormal bases and g-riesz bases. we show that a family of bounded opera-tors is a g-bessel sequences if and only if the gram matrix associated to its denes a boundedoperator.

Symmetry adapted bases in quantum chemistry and bases adapted to quantum information share a common characteristics: both of them are constructed from subspaces of the representation space of the group SO(3) or its double group (i.e., spinor group) SU(2). We exploit this fact for generating spin bases of relevance for quantum systems with cyclic symmetry and equally well for quantum information...

In many deep learning/sparse coding papers involving images, it is a common trend that patterns resembling Gabor filters/edge filters are usually present in the learnt bases. In this project, we investigate whether various sparse learning models are able to learn edge filter bases for sparse representation of both natural and non-natural images. Experiments are also conducted for each of the th...