Marek Czachor

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when one moves downwards starting from the first row. Now let us define the functions F and G by F (a) = F (d) = F (e) = F (h) = F (i) = F (l) = F (m) = F (p) = +1, F (b) = F (c) = F (f) = F (g) = F (j) = F (k) = F (n) = F (o) = −1, G(x1x2x3x4) = F (x1) + F (x2) + F (x3) − F (x4). On each four-character string of the regrouped part of the text we evaluate(More)
Holographic reduced representations (HRR) are based on superpositions of convolution-bound ntuples, 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)
Nonlinear operator equations one encounters in quantum optics and quantum field theory are typically solved by techniques which are either perturbative or semiclassical (cf. [1,2]). The situation is caused by the fact that analytic methods of dealing with “non-Abelian” nonlinearites are still at a rather preliminary stage of development. An important step(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)
Diederik Aerts 1 and Marek Czachor 1,2 1 Centrum Leo Apostel (CLEA) and Foundations of the Exact Sciences (FUND) Vrije Universiteit Brussel, 1050 Brussels, Belgium 2 Katedra Fizyki Teoretycznej i Informatyki Kwantowej Politechnika Gdańska, 80-952 Gdańsk, Poland Abstract We present a computational framework based on geometric structures. No quantum mechanics(More)
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)
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)
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)