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Countable functionals and the projective hierarchy
Journal of Symbolic Logic, 1981Kleene [7] and Kreisel [8] defined independently the countable (continuous) functionals. Kleene [7] defined the countable functionals of type k to be total functionals of type k acting in a continuous way when restricted to countable arguments of type k − 1. He also defined the associates for countable functionals.
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A topological hierarchy for functions on triangulated surfaces
IEEE Transactions on Visualization and Computer Graphics, 2004We combine topological and geometric methods to construct a multiresolution representation for a function over a two-dimensional domain. In a preprocessing stage, we create the Morse-Smale complex of the function and progressively simplify its topology by cancelling pairs of critical points.
Peer-Timo Bremer +3 more
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1992
The impact of covariant perturbation theory and the analysis of the consequences of the axioms lead in the fifties to a description of quantum field theory in terms of infinite hierarchies of functions.1 Different choices of hierarchies were considered; the properties of the functions and their interrelation were studied, using as an input the general ...
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The impact of covariant perturbation theory and the analysis of the consequences of the axioms lead in the fifties to a description of quantum field theory in terms of infinite hierarchies of functions.1 Different choices of hierarchies were considered; the properties of the functions and their interrelation were studied, using as an input the general ...
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1968
As Frege set about to carry out the logical construction of arithmetic in a strictly ideographic way in the Basic Laws of Arithmetic, his logical views had significantly progressed over those of the Begriffsschrift and Foundations. The change is so decisive that commentators — like Bierich, Papst, Scholz, etc.
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As Frege set about to carry out the logical construction of arithmetic in a strictly ideographic way in the Basic Laws of Arithmetic, his logical views had significantly progressed over those of the Begriffsschrift and Foundations. The change is so decisive that commentators — like Bierich, Papst, Scholz, etc.
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A continuous functional with noncollapsing hierarchy
Journal of Symbolic Logic, 1978In [5] S. S. Wainer introduces a hierarchy for arbitrary type-2-functionals. Given F, he defines a set of ordinal notations OF, and for each a ∈ OF, a function fa recursive in F and an ordinal ∣a∣F < For any f recursive in F there is an a ∈ OF such that f is primitive recursive in fa.Let ρF be the least ordinal α such that for any f recursive in F ...
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The functions and dysfunctions of hierarchy
Research in Organizational Behavior, 2010Abstract Functionalist accounts of hierarchy, longstanding in the social sciences, have gained recent prominence in studies of leadership, power, and status. This chapter takes a critical look at a core implication of the functionalist perspective – namely, that steeper hierarchies help groups and organizations perform better than do flatter ...
Cameron Anderson, Courtney E. Brown
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The polynomial hierarchy of functions and its levels
Theoretical Computer Science, 2022In the paper under review the author gives purely recursion-theoretic characterizations of all levels of the polynomial-time analogue of the arithmetical hierarchy and of the hierarchy itself. Namely, the class of functions computable in polynomial time by deterministic Turing machines with \(\Sigma_n^{\mathrm P}\)-oracles and the class of Boolean ...
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Functional constraint hierarchies in CLP
1996HCLP extend CLP to include constraint hierarchies. We present an algorithm based on our previous work and on the extended notion of comparators for comparisons between the hierarchies that arise from alternate rule choices in the program.
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Functional Hierarchies in the Brain
1978One of the greatest challenges of brain research is to relate the anatomical (substratum-) structure of the brain to its functional performance. The behaviour of biological organisms is goal-oriented, with the basic aim of surviving and optimizing its performance in a given environment. The brain performs the control functions in this activity, as well
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Determination of the Functional Hierarchy in Multifocal Epilepsy
1976An averaging technique of epileptic spikes, carried out on human stereoelectroencephalographic explorations, allowed the detection of morphological alterations of spikes peculiar to a given structure, associated with variations of temporal relations among spikes simultaneously recorded in different structures.
B, Cavazza +3 more
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