The theory of partial inductive definitions is a mathematical formalism which has proved to be useful in a number of different applications. The fundamentals of the theory is shortly described. Partial inductive definitions and their associated calculi are essentially infinitary. To implement them on a computer, they must be given a formal finitary representation. We present such a finitary rep...

Many data representation structures, such as web site categories and domain ontologies, have been established for semantic-based information search and retrieval on the web. These structures consist of concepts and their interrelationships. Approaches to determine the similarity in semantics among concepts in data representation structures have been developed in order to facilitate information ...

We present the extension of the Lagrangian loop gauge invariant representation in such a way to include matter fields. The partition function of lattice compact U (1)-Higgs model is expressed as a sum over closed as much as open surfaces. These surfaces correspond to world sheets of loop-like pure electric flux excitations and open electric flux tubes carrying matter fields at their ends. This ...

Graphical games introduce a compact representation, where agents’ outcomes depend only on their neighbors. A distributed search algorithm for pure Nash equilibria of graphical games is presented. The algorithm uses the analogy of graphical games with asymmetric distributed constraints optimization problems (ADCOPs). The proposed algorithm includes three components an admissible pruning heuristi...

Many data representation structures, such as web site categories and domain ontologies, have been established for semantic-based information search and retrieval on the web. These structures consist of concepts and their interrelationships. Approaches to determine the similarity in semantics among concepts in data representation structures have been developed in order to facilitate information ...

We present two different representations of (1, 1)-knots and study some connections between them. The first representation is algebraic: every (1, 1)-knot is represented by an element of the pure mapping class group of the twice punctured torus PMCG2(T ). Moreover, there is a surjective map from the kernel of the natural homomorphism Ω : PMCG2(T ) → MCG(T ) ∼= SL(2, Z), which is a free group of...

Starting from the observation that in Yang-Mills theory the Schroedinger state functional in the momentum representation is not gauge invariant, we investigate the reversed question: Which are the representations for the operators of a gauge theory that lead to an invariant wave functional once the quantum constraints have been imposed upon it? Stated otherwise: Which representation do we have ...

We propose an amplitude-phase representation of the dual-tree complex wavelet transform (DT-CWT) which provides an intuitive interpretation of the associated complex wavelet coefficients. The representation, in particular, is based on the shifting action of the group of fractional Hilbert transforms (fHT) which allow us to extend the notion of arbitrary phase-shifts beyond pure sinusoids. We ex...

A fundamental feature of auditory perception is the constancy of sound recognition over a large range of intensities. Although this invariance has been described in behavioral studies, the underlying neural mechanism is essentially unknown. Here we show a putative level-invariant representation of sounds by populations of neurons in primary auditory cortex (A1) that may provide a neural basis f...