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Search results for: GEOMETRIC ANALOGUES
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A comparison of geometric analogues of holographic reduced representations, original holographic reduced representations and binary spatter codes
PublicationGeometric Analogues of Holographic Reduced Representations (GA HRR) employ role-filler binding based on geometric products. Atomic objects are real-valued vectors in n-dimensional Euclidean space and complex statements belong to a hierarchy of multivectors. The paper reports a battery of tests aimed at comparison of GA HRR with Holographic Reduced Representation (HRR) and Binary Spatter Codes (BSC). Firstly, we perform a test of...
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Geometric analogue of holographic reduced representation
PublicationHolographic reduced representations (HRRs) are distributed representations of cognitive structuresbased on superpositions of convolution-bound n-tuples. Restricting HRRs to n-tuples consisting of 1,one reinterprets the variable binding as a representation of the additive group of binary n-tupleswith addition modulo 2. Since convolutions are not defined for vectors, the HRRs cannot be directlyassociated with geometric structures....
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Experiments on Preserving Pieces of Information in a Given Order in Holographic Reduced Representations and the Continuous Geometric Algebra Model
PublicationGeometric Analogues of Holographic Reduced Representations (GAc, which is the continuous version of the previously developed discrete GA model) employ role-filler binding based on geometric products.Atomic objects are real-valued vectors in n-dimensional Euclidean space and complex statements belong to a hierarchy of multivectors. The property of GAc and HRR studied here is the ability to store pieces of information in a given...
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(CsX)Cu5O2(PO4)2 (X = Cl, Br, I): A Family of Cu2+ S = 1/2 Compounds with Capped-Kagomé Networks Composed of OCu4 Units
PublicationThree new salt inclusion compounds (CsX)Cu5O2(PO4)2 (X = Cl, Br, I), phosphate analogues of the kagomé mineral averievite, are reported. Their crystal structures are composed of trigonal networks of corner-sharing OCu4 anion-centered tetrahedra, forming capped-kagomé planes, which can also be regarded as two-dimensional slices along the [111] direction of a pyrochlore lattice. Magnetization and heat capacity measurements reveal...
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Marek Czachor prof. dr hab.
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