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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)

- Marek Czachor, Bart D 'hooghe, Werner Abraham, Michael Noonan
- 2004

We show the presence of genuine quantum structures in human language. The neo-Darwinian evolutionary scheme is founded on a probability structure that satisfies the Kolmogorovian axioms, and as a consequence cannot incorporate quantum-like evolutionary change. In earlier research we revealed quantum structures in processes taking place in conceptual space.… (More)

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.

- Marek Czachor, Jan Naudts
- 2002

We show that extensive thermostatistics based on Rényi entropy and Kolmogorov–Nagumo averages can be expressed in terms of Tsallis nonextensive thermostatistics. We use this correspondence to generalize thermostatistics to a large class of Kolmogorov–Nagumo means and suitably adapted definitions of entropy. As an application, we reanalyze linguistic data… (More)

- Marek Czachor
- 1991

We discuss two classical situations that lead to probabilities characteristic for systems with spin-1/2. (a) Pitowsky model: It is demonstrated that the definition of spin functions does not imply which circle (a parallel or a great circle) on the sphere should be taken as a probability space in calculation of conditional probabilities. Pitowsky's choice of… (More)

- Diederik Aerts, Marek Czachor, Bart D 'hooghe
- 2004

While some of the properties of quantum mechanics are essentially linked to the nature of the micro-world, others are connected to fundamental structures of the world at large and could therefore in principle also appear in other domains than the micro-world. The aim of this article is to show the presence of genuine quantum structures in human language.… (More)

- Diederik Aerts, Stan Bundervoet, Marek Czachor, Bart D'Hooghe, Liane Gabora, Philip Polk +1 other
- 2007

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)

- Jan L Cie´sli´nski, Marek Czachor, Nikolai V Ustinov
- 2002

Lax pairs with operator valued coefficients, which are explicitly connected by means of an additional condition, are considered. This condition is proved to be covariant with respect to the Darboux transformation of a general form. Nonlinear equations arising from the compatibility condition of the Lax pairs in the matrix case include, in particular, Nahm… (More)