Search results for: geometric algebra

• Geometric Algebra Model of Distributed Representations

  Publication

  • A. Patyk-Łońska

  - Year 2010

  Formalism based on GA is an alternative to distributed representation models developed so far-Smolensky's tensor product, Holographic Reduced Representations (HRR) and Binary Spatter Code (BSC). Convolutions are replaced by geometric products, interpretable in terms of geometry which seems to be the most natural language for visualization of higher concepts. This paper recalls the main ideas behind the GA model and investigates...

• Distributed Representations Based on Geometric Algebra: the Continuous Model

  Publication

  • A. Patyk-Łońska
  • M. Czachor
  • D. Aerts

  - Informatica - Year 2011

  Authors revise the concept of a distributed representation of data as well as two previously developed models: Holographic Reduced Representation (HRR) and Binary Spatter Codes (BSC). A Geometric Analogue (GAc - ''c'' stands for continuous as opposed to its discrete version) of HRR is introduced - it employs role-filler binding based on geometric products. Atomic objects are real-valued vectors in n-dimensional Euclidean space...

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• Beitrage zur Algebra und Geometrie-Contributions to Algebra and Geometry

  Journals

  ISSN: 0138-4821 , eISSN: 2191-0383

• Algebraic and Geometric Topology

  Journals

  ISSN: 1472-2739

• Experiments on Preserving Pieces of Information in a Given Order in Holographic Reduced Representations and the Continuous Geometric Algebra Model

  Publication

  • A. Patyk-Łońska

  - Informatica - Year 2011

  Geometric 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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• Algebraic Geometry

  Journals

  ISSN: 2313-1691 , eISSN: 2214-2584

• Algebra modułów ontologicznych

  Publication

  • K. Goczyła
  • A. Waloszek
  • W. Waloszek

  - Year 2013

  Bardzo ważnym problemem w środowisku Semantic Web jest efektywne korzystanie z rożnych baz wiedzy rozproszonych w Internecie. Niniejsze opracowanie rozpatruje możliwość zaadaptowania do tego celu elastycznego i potężnego aparatu, jakim jest algebra relacji. W tym celu przedstawiono różnice i podobieństwa między bazami danych i bazami wiedzy oraz leżącymi u ich podstaw modelami odwzorowywania dziedziny problemu. Zaproponowana została...

• JOURNAL OF ALGEBRAIC GEOMETRY

  Journals

  ISSN: 1056-3911 , eISSN: 1534-7486

• SIAM Journal on Applied Algebra and Geometry

  Journals

  ISSN: 2470-6566

• A New Geodetic Method of Examination of Geometrical Conditions of a Crane Bridge

  Publication

  • D. Filipiak-Kowszyk
  • W. Kamiński
  • K. Makowska-Jarosik

  - Geosciences - Year 2019

  Safety is one of the key aspects related to crane-based material transport. In order to ensure safe crane operation and material transport, it is necessary to meet certain geometrical conditions. The authors addressed the geometrical conditions of a crane bridge, a substantial crane component. The paper presents the method to compute displacement components of points on the top of a bridge crane relative to their design position....

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