1,725,260 research outputs found
A model of adaptive invariance
No full textThis thesis is about adaptive invariance, and a new model of it: the Group Representation Network. We begin by discussing the concept of adaptive invariance. We then present standard background material, mostly from the fields of group theory and neural networks. Following this we introduce the problem of invariant pattern recognition and describe a number of methods for solving various instances of it. Next, we define the Symmetry Network, a connectionist model of permutation invariance, and we develop some new theory of this model. We also extend the applicability of the Symmetry Network to arbitrary finite group actions. We then introduce the Group Representation Network (GRN) as an abstract model, with which in principle we can construct concomitants between arbitrary group representations. We show that the GRN can be regarded as a neural network model, and that it includes the Symmetry Network as a submodel. We apply group representation theory to the analysis of GRNs. This yields general characterizations of the allowable activation functions in a GRN and of their weight matrix structure. We examine various generalizations and restricted cases of the GRN model, and in particular look at the construction of GRNs over infinite groups. We then consider the issue of a GRN's discriminability, which relates to the problem of graph isomorphism. We look next at the computational abilities of the GRN, and postulate that it is capable of approximately computing any group concomitant. We show constructively that any polynomial concomitant can be computed by a GRN. We also prove that a variety of standard models for invariant pattern recognition can be viewed as special instances of the GRN model. Finally, we propose that the GRN model may be biologically plausible and give suggestions for further research
Modules and behaviours in nD systems theory
No full textThis paper is intended both as an introduction to the behavioural theory of nD systems, in particular the duality of Oberst and its applications, and also as a bridge between the behavioural theory and the module-theoretic approach of Fliess, Pommaret and others. Our presentation centres on the notion of a system observable, first formally introduced by Pommaret, and uses this concept to provide new interpretations of known behavioural results. We discuss among other subjects autonomous systems, controllable systems, observability, transfer matrices, computation of trajectories, and system complexity
Invariant pattern recognition: a review
No full textIn this document we review and compare some of the classical and modern techniques for solving the problem of invariant pattern recognition. Such techniques include integral transforms, construction of algebraic moments and the use of structured neural networks. In all cases we assume that the nature of the invariance group is known a priori. Many of the methods described apply to specific geometrical transformation groups; however some of the techniques are highly general and applicable to large classes of invariance groups. We also review some results regarding the existence and structure of invariants under certain kinds of groups
Poles and zeros – examples of the behavioral approach applied to discrete linear repetitive processes
No full textIn this paper the behavorial approach is applied to discrete linear repetitive processes, which are class of 2D systems of both systems theoretic and applications interest. The main results are on poles and zeros for these processes, which have exponential trajectory interpretations
Wood, J F, 424549
No full textThis record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/426945Surname: WOOD. Given Name(s) or Initials: J F. Military Service Number or Last Known Location: 424549. Missing, Wounded and Prisoner of War Enquiry Card Index Number: 53537.248960
Item: [2016.0049.59206] "Wood, J F, 424549
Wood, J K, 403540
No full textThis record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/426936Surname: WOOD. Given Name(s) or Initials: J K. Military Service Number or Last Known Location: 403540. Missing, Wounded and Prisoner of War Enquiry Card Index Number: 45134.248951
Item: [2016.0049.59197] "Wood, J K, 403540
Wood, J, NX33270
No full textThis record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/426974Surname: WOOD. Given Name(s) or Initials: J. Military Service Number or Last Known Location: NX33270. Missing, Wounded and Prisoner of War Enquiry Card Index Number: 1959.248989
Item: [2016.0049.59235] "Wood, J, NX33270
Wood, J L, SX13645
No full textThis record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/426995Surname: WOOD. Given Name(s) or Initials: J L. Military Service Number or Last Known Location: SX13645. Missing, Wounded and Prisoner of War Enquiry Card Index Number: 33540.249010
Item: [2016.0049.59256] "Wood, J L, SX13645
Wood, J W, 410280
No full textThis record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/426940Surname: WOOD. Given Name(s) or Initials: J W. Military Service Number or Last Known Location: 410280. Missing, Wounded and Prisoner of War Enquiry Card Index Number: 53435.248955
Item: [2016.0049.59201] "Wood, J W, 410280
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