Ordered Algebraic Structures

Powell, Wayne B.; Tsinakis, Constantine

doi:10.1007/978-1-4757-3627-4

Cited by 26 publications

References 27 publications

(51 reference statements)

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Morphological Neural Networks with Dendrite Computation: A Geometrical Approach

Barron

Sossa

Cortés

2003

Lecture Notes in Computer Science

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Abstract. Morphological neural networks consider that the information entering a neuron is affected additively by a conductivity factor called synaptic weight. They also suppose that the input channels account with a saturation level mathematically modeled by a MAX or MIN operator. This, from a physiological point of view, appears closer to reality than the classical neural model, where the synaptic weight interacts with the input signal by means of a product; the input channel forms an average of the input signals. In this work we introduce some geometrical aspects of dendrite processing that easily allow visualizing the classification regions, providing also an intuitive perspective of the production and training of the net.

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Morphological Neural Networks with Dendrite Computation: A Geometrical Approach

Barron

Sossa

Cortés

2003

Lecture Notes in Computer Science

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Decision methods for linearly ordered Heyting algebras

Dyckhoff

Negri

2005

Arch. Math. Logic

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The Stone–Čech Compactification and the Cozero Lattice in Pointfree Topology

Banaschewski

2007

Appl Categor Struct

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In Section 2, after the account of various properties of the cozero map, it is claimed thatfor r > 0 in Q and arbitrary α, β ≥ 0 in RL. This is clearly false (although it does hold in the particular situation considered later on, where coz(α) ∨ coz(β) = e), and hence the proof of Lemma 2 as given is incomplete. It should be replaced by the following.Proof For any α, β ≥ 0 ∈ RL such that coz(α) ∨ coz(β) = e, we show (i) coz((α − β) + ) ∨ coz(β) = e, and (ii) coz((α − β) + ) ≺ ≺ coz(α).The following calculations specifically use the rules for ∨ and ∧ involving coz listed above as well as the fact that coz(sγ ) = coz(tγ ) for any γ ∈ RL and s, t > 0 in Q. Now, regarding (i)The online version of the original article can be found under

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Ordered Algebraic Structures

Cited by 26 publications

References 27 publications

Morphological Neural Networks with Dendrite Computation: A Geometrical Approach

Morphological Neural Networks with Dendrite Computation: A Geometrical Approach

Decision methods for linearly ordered Heyting algebras

The Stone–Čech Compactification and the Cozero Lattice in Pointfree Topology

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