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Monotone Classification by Function Decomposition
2005The paper focuses on the problem of classification by function decomposition within the frame of monotone classification. We propose a decomposition method for discrete functions which can be applied to monotone problems in order to generate a monotone classifier based on the extracted concept hierarchy.
Popova, V., Bioch, J.C.
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The complexity of monotone boolean functions
Mathematical Systems Theory, 1977We study the realization of monotone Boolean functions by networks. Our main result is a precise version of the following statement: the complexity of realizing a monotone Boolean function ofn arguments is less by the factor (2/πn)1/2, whereπ is the circular ratio, than the complexity of realizing an arbitrary Boolean function ofn arguments.
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Monotone Functions in Sequential Circuits
IEEE Transactions on Computers, 1973This paper is concerned with the problem of realizing an arbitrary syndconous or asynchronous sequential machine using only monotone AMR (or decreasing) switching functions. It has been found that h ion always exist, that in the asynchronous case only nomal fundamental mode flow tables are considered.
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On the Dual-Monotonicity of Threshold Functions
IEEE Transactions on Electronic Computers, 1965A necessary condition for a threshold function in terms of comparability was first reported by Paull and McCluskey [4] who have established a chain of conditions later called 1-monotonicity, 2-monotonicity, and k-monotonicity, in general. Each of these conditions entails its predecessors, and is stricter than them; the union of this denumerable set of ...
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Stochastic Monotonicity and Monotonicity of the Value Functions
2016We consider MDPs and CMs with structured state space and arbitrary transition law. We assume that the minimal assumption (MA1) holds. As in Chap. 6 we are looking for conditions under which the value functions are monotone in the initial state s. This is easy for CMs, but requires a thorough treatment of the notion of stochastic monotonicity for MDPs ...
Karl Hinderer +2 more
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On Quasi-Monotone Functions and Sequences
Computational Methods and Function Theory, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On a Singular Monotone Function
Journal of the London Mathematical Society, 1937van Kampen, E. R., Wintner, Aurel
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1990
The author defines the class of modulus monotonic functions \((MM(r,\alpha))\) as follows: \(f(z)=z+a_ 2z^ 2+a_ 3z^ 3+\cdots\) is analytic in the unit disk. There is an \(\alpha\in\left(-{\pi\over 2},{\pi\over 2}\right)\) such that \(| f(re^{i\theta})|\) decreases for \(\theta\in[\alpha,\pi-\alpha]\) and increases for \(\theta\in[\pi-\alpha,2\pi+\alpha]
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The author defines the class of modulus monotonic functions \((MM(r,\alpha))\) as follows: \(f(z)=z+a_ 2z^ 2+a_ 3z^ 3+\cdots\) is analytic in the unit disk. There is an \(\alpha\in\left(-{\pi\over 2},{\pi\over 2}\right)\) such that \(| f(re^{i\theta})|\) decreases for \(\theta\in[\alpha,\pi-\alpha]\) and increases for \(\theta\in[\pi-\alpha,2\pi+\alpha]
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The Structure of Monotone Functions
American Journal of Mathematics, 1937Hartman, Philip, Kershner, Richard
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Elements of Monotonic Analysis: Monotonic Functions
2000The theory of IPH functions defined on either the cone ℝ ++ n or the cone ℝ + n can be applied in the study of various classes of monotonic functions. One of possible approaches in this direction is to use the hypographs of decreasing functions and the epigraphs of increasing functions.
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