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Quantum Bio-Informatics

THE PROBLEM OF QUANTUM-LIKE REPRESENTATION IN ECONOMY COGNITIVE SCIENCE, AND GENETICS

Luigi Accardi, Andrei Yu. Khrennikov, Makoto Ohya

Published Feb 1, 2009• 17 citations
Publisher

Abstract

We outline our programme to create quantum-like representations in economy, cognitive science, psychology, genetics,....
DOI
10.1142/9789814273756_0001

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The Problems of Quantum-Like Representation in Economy Cognitive Science, and Genetics (L Accardi et al.) The Compound Fock Space and Its Application in Brain Models (K H Fichtner & W Freudenberg) On Quantum Algorithm for Multiple Alignment of Amino Acid Sequences (S Iriyama & M Ohya) Theory of Proton-Induced Superionic Conduction in Hydrogen-Bonded Systems (H Kamimurai) Quantum-Like Models for Decision Making in Psychology and Cognitive Science (A Khrennikov) On Completely Positive Non-Markovian Evolution of A d-Level System (A Kossakowski & R Rebolledo) Perspective from Micro-Macro Duality - Towards Non-Pertubative Renormalization Scheme (I Ojima) Some Aspects of Quadratic Generalized White Noise Functionals (Si Si & T Hida) Time in Physics and Life Science (I V Volovich) Note on Entropies in Quantum Processes (N Watanabe) Massive Collection of Full-Length Complementary DNA Clones and Microarray Analyses: Keys to Rice Transcriptome Analysis (S Kikuchi) A Basic Introduction to Gene Expression Studies Using Microarray Expression Data Analysis (D Wanke & J Kilian) and other papers.
Recently the mathematical formalism of quantum mechanics, especially methods of quantum probability theory, started to be widely used in a variety of applications outside of physics, e.g., cognition and psychology as well as economy and finances. To distinguish such models from genuine quantum physical models, they often called quantum-like (although often people simply speak about, e.g., "quantum cognition"). These novel applications generate a number of foundational questions. Nowadays we can speak about a new science - foundations of quantum-like modeling. At the first stage this science was mainly about comparison of classical and quantum models, mainly in the probabilistic setting. It was found that statistical data from cognitive psychology violate some basic constraints posed on data by classical probability theory (Kolmogorov, 1933); in particular, the constraints given by the formula of total probability and Bell's type inequalities. Recently another question attracted some attention. In spite of real success in applications, there are no reason to believe that the quantum probability would cover completely all problems of, e.g., cognition. May be more general probability models have to be explored. A similar problem attracted a lot of attention in foundations of quantum physics culminating in a series of experiments to check Sorkin's equality for the triple-slit experiment by Weihs' group. In this note we present a similar test in the cognitive experimental setting. Performance of this test would either give further confirmation of the adequacy of the quantum probability model to cognitive applications or rejection of the conventional quantum model. Thus this note opens the door for a series of exciting experimental tests for the quantum-like model of cognition.
Starting with 2003 some authors performed a number of experiments with the finality to ascertain if quantum mechanics has a role during the perception and cognition in Humans. The arising quantum cognitive model was repeatedly confirmed. In the present paper we perform for the first time a similar experiment but executed this time on the single subject. The finality is to establish if also in these conditions we are able to estimate the quantum interference effects. Since the results of the experimentation are positive we conclude that we may start using the quantum cognitive model not only as basic theoretical framework for understanding cognition in humans but also to apply the new methodology in clinical cases of interest as in investigation of psychological disorders and psychiatric diseases.