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52
Data compression and harmonic analysis
 IEEE Trans. Inform. Theory
, 1998
"... In this paper we review some recent interactions between harmonic analysis and data compression. The story goes back of course to Shannon’s R(D) theory... ..."
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Cited by 142 (24 self)
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In this paper we review some recent interactions between harmonic analysis and data compression. The story goes back of course to Shannon’s R(D) theory...
Truth Is Beauty: Researching Embodied Conversational Agents
 In
, 2000
"... G. H. Hardy (1941) argues that the sole criterion for excellent research is that the researcher produces “beauty. ” While seemingly ineffable and frustratingly imprecise, Hardy instead suggests that creating beauty is straightforward. First, the work must be accurate: erroneous results are useless. ..."
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Cited by 53 (0 self)
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G. H. Hardy (1941) argues that the sole criterion for excellent research is that the researcher produces “beauty. ” While seemingly ineffable and frustratingly imprecise, Hardy instead suggests that creating beauty is straightforward. First, the work must be accurate: erroneous results are useless. Second, one’s peers must recognize the work to be interesting, exciting, elegant, and “cool. ” While this second criterion might seem arbitrary, there is generally good agreement between scholars in a given community about “interesting ” work (see Cole and Cole 1973 for a discussion), so one need not survey numerous researchers to ensure research is beautiful; asking a couple is equivalent to asking them all. With certain caveats, the work in embodied conversational agents (ECA) can make claims to beauty. ECAs are phenomenologically “accurate ” to the extent that the agent’s outward appearance objectively matches the appearance, language, attitudes and behavior of humans. Thus, questions that address manifestation accuracy include “Does the agent walk like a person walk? ” and “Does the agent use language and make grammatical errors the same way a person does?”
The Garden of Knowledge as a Knowledge Manifold  A Conceptual Framework for Computer Supported Subjective Education
 CID17, TRITANAD9708, DEPARTMENT OF NUMERICAL ANALYSIS AND COMPUTING SCIENCE
, 1997
"... This work presents a unied patternbased epistemological framework, called a Knowledge Manifold, for the description and extraction of knowledge from information. Within this framework it also presents the metaphor of the Garden Of Knowledge as a constructive example. Any type of KM is defined in te ..."
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Cited by 22 (14 self)
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This work presents a unied patternbased epistemological framework, called a Knowledge Manifold, for the description and extraction of knowledge from information. Within this framework it also presents the metaphor of the Garden Of Knowledge as a constructive example. Any type of KM is defined in terms of its objective calibration protocols  procedures that are implemented on top of the participating subjective knowledgepatches. They are the procedures of agreement and obedience that characterize the coherence of any type of interaction, and which are used here in order to formalize the concept of participator consciousness in terms of the inversedirect limit duality of Category Theory.
Hilbert’s twentyfourth problem
 American Mathematical Monthly
, 2001
"... 1. INTRODUCTION. For geometers, Hilbert’s influential work on the foundations of geometry is important. For analysts, Hilbert’s theory of integral equations is just as important. But the address “Mathematische Probleme ” [37] that David Hilbert (1862– 1943) delivered at the second International Cong ..."
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Cited by 9 (4 self)
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1. INTRODUCTION. For geometers, Hilbert’s influential work on the foundations of geometry is important. For analysts, Hilbert’s theory of integral equations is just as important. But the address “Mathematische Probleme ” [37] that David Hilbert (1862– 1943) delivered at the second International Congress of Mathematicians (ICM) in Paris has tremendous importance for all mathematicians. Moreover, a substantial part of
Some of My Favourite Results in Classic Process Algebra
 In Bulletin of the EATCS
, 2003
"... this paper has generated a veritable industry of results on the metatheory of SOS and process algebras. (See [10] for a mention of some of these achievements and pointers to the original literature.) The proof techniques used in these results were extremely ingenious, and have paved the way to many ..."
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Cited by 9 (4 self)
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this paper has generated a veritable industry of results on the metatheory of SOS and process algebras. (See [10] for a mention of some of these achievements and pointers to the original literature.) The proof techniques used in these results were extremely ingenious, and have paved the way to many similar developments. Again, the role played by the modal characterizations of behavioural equivalences in the proof of the characterizations of the largest congruences is remarkable
Informationtheoretic Incompleteness
 APPLIED MATHEMATICS AND COMPUTATION
, 1992
"... We propose an improved definition of the complexity of a formal axiomatic system: this is now taken to be the minimum size of a selfdelimiting program for enumerating the set of theorems of the formal system. Using this new definition, we show (a) that no formal system of complexity n can exhibit a ..."
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Cited by 6 (1 self)
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We propose an improved definition of the complexity of a formal axiomatic system: this is now taken to be the minimum size of a selfdelimiting program for enumerating the set of theorems of the formal system. Using this new definition, we show (a) that no formal system of complexity n can exhibit a specific object with complexity greater than n + c, and (b) that a formal system of complexity n can determine at most n + c scattered bits of the halting probability\Omega . We also present a short, selfcontained proof of (b).
Computably based locally compact spaces
, 2003
"... ASD (Abstract Stone Duality) is a reaxiomatisation of general topology in which the topology on a space is treated, not as an infinitary lattice, but as an exponential object of the same category as the original space, with an associated lambdacalculus. In this paper, this is shown to be equivalen ..."
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Cited by 5 (3 self)
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ASD (Abstract Stone Duality) is a reaxiomatisation of general topology in which the topology on a space is treated, not as an infinitary lattice, but as an exponential object of the same category as the original space, with an associated lambdacalculus. In this paper, this is shown to be equivalent to a notion of computable basis for locally compact sober spaces or locales, involving a family of open subspaces and accompanying family of compact ones. This generalises Smyth’s effectively given domains and Jung’s Strong proximity lattices. Part of the data for a basis is the inclusion relation of compact subspaces within open ones, which is formulated in locale theory as the waybelow relation on a continuous lattice. The finitary properties of this relation are characterised here, including the Wilker condition for the cover of a compact space by two open ones. The real line is used as a running example, being closely related to Scott’s domain of intervals. ASD does not use the category of sets, but the full subcategory of overt discrete objects plays this role; it is an arithmetic universe (pretopos with lists). In particular, we use this subcategory to translate computable bases for classical spaces into objects in the ASD calculus.
Quantum Zeno dynamics: mathematical and physical aspects
, 903
"... Abstract. If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, ..."
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Cited by 4 (0 self)
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Abstract. If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. The continuing time evolution within the projected “quantum Zeno subspace ” is called “quantum Zeno dynamics: ” for instance, if the measurements ascertain whether a quantum particle is in a given spatial region, the evolution is unitary and the generator of the Zeno dynamics is the Hamiltonian with hardwall (Dirichlet) boundary conditions. We discuss the physical and mathematical aspects of this evolution, highlighting the open mathematical problems. We then analyze some alternative strategies to obtain a Zeno dynamics and show that they are physically equivalent.
Some Practical Problems and Their Influence on Semantics
 IN PROCEEDINGS OF THE 6TH EUROPEAN SYMPOSIUM ON PROGRAMMING
, 1996
"... This paper offers an assessment of what has been achieved in three decades of work on the semantics of programming languages and pinpoints some practical problems in computing which might stimulate further research. The examples sketched in this paper come from the author's own research on concur ..."
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Cited by 3 (0 self)
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This paper offers an assessment of what has been achieved in three decades of work on the semantics of programming languages and pinpoints some practical problems in computing which might stimulate further research. The examples sketched in this paper come from the author's own research on concurrent object oriented languages, from database practice, and from more speculative research on Internet issues.