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Holographic reduced representations (HRR) are based on superpositions of convolution-bound n-tuples, but the n-tuples cannot be regarded as vectors since the formalism is basis dependent. This is why HRR cannot be associated with geometric structures. Replacing convolutions by geometric products one arrives at reduced representations analogous to HRR but… (More)

Modern approaches to semanic analysis if reformulated as Hilbert-space problems reveal formal structures known from quantum mechanics. Similar situation is found in distributed representations of cognitive structures developed for the purposes of neural networks. We take a closer look at similarites and differences between the above two fields and quantum… (More)

- Diederik Aerts, Marek Czachor, Liane Gabora, Maciej Kuna, Andrzej Posiewnik, Jarosław Pykacz +1 other
- Physical review. E, Statistical, nonlinear, and…
- 2003

Noncommutative propositions are characteristic of both quantum and nonquantum (sociological, biological, and psychological) situations. In a Hilbert space model, states, understood as correlations between all the possible propositions, are represented by density matrices. If systems in question interact via feedback with environment, their dynamics is… (More)

Kanerva's Binary Spatter Codes are reformulated in terms of geometric algebra. The key ingredient of the construction is the representation of XOR binding in terms of geometric product.

An abstract DNA-type system is defined by a set of nonlinear kinetic equations with polynomial nonlinearities that admit soliton solutions associated with helical geometry. The set of equations allows for two different Lax representations: A von Neumann form and a Darboux-covariant Lax pair. We explain why non-Kolmogorovian probability models occurring in… (More)

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 (GA c — "c" stands for continuous as opposed to its discrete version) of HRR is introduced – it employs role-filler binding based on geometric products.… (More)

The mathematical formalism of quantum mechanics has been successfully employed in the last years to model situations in which the use of classical structures gives rise to problematical situations, and where typically quantum effects, such as contextuality and entanglement, have been recognized. This Quantum Interaction Approach is briefly reviewed in this… (More)

- Diederik Aerts, Stan Bundervoet, Marek Czachor, Bart D 'hooghe, Liane Gabora, Philip Polk
- 2010

In this paper we suggest an alternative to standard neodarwinian evolution theory. The problem is that Darwinism, which sees evolution as a consequence of random variation and natural selection is based on a materialistic-i.e. matter-based-view of science, while matter in itself is considered to be a very complex notion in modern physics. More specifically,… (More)

The expected utility hypothesis is one of the building blocks of classical economic theory and founded on Savage's Sure-Thing Principle. It has been put forward, e.g. by situations such as the Allais and Ellsberg paradoxes, that real-life situations can violate Savage's Sure-Thing Principle and hence also expected utility. We analyze how this violation is… (More)

Population ecology is mainly based on nonlinear equations of the Lotka-Volterra type, which provide mathematical models for describing the dynamics of interacting species. However, for many interacting populations , these equations entail complex dynamical behavior and unpredictability, generating such difficulties and problematical situations as… (More)