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The photophysical properties of solutions of dansyl [5-(dimethylamino)naphthalenyl-lsulfonyl] labeled poly(iV-isopropylacrylamide) (PNIPAM-Da; Mv 220 000; label content, 0.06 molar %) were examined in mixtures of water and methanol in order to investigate the phenomenon of cononsolvency exhibited by the PNIPAM/water/methanol ternary system. They were compared to the photophysical properties of dansyl-labeled polyUV-isopropylacrylamide) gels (cross-linker, N,/V'-methylenebis(acrylamide); cross-linker content, 1.2 molar %; probe content, 0.06 molar %) equilibrated in mixtures of methanol and water. The swelling of these gels decreases abruptly in aqueous solutions containing 7-25 mol % methanol and increases gradually in systems with a higher methanol concentration. Steady-state emission and excitation spectra, fluorescence decays, and fluorescence polarization were recorded at 20 °C from polymer solutions and from equilibrated gels. Shifts in the wavelength of maximum emission and changes in the fluorescence lifetimes and in the rotational diffusion coefficients of the probe were correlated to the macroscopic changes in swelling volume.

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We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in a complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices (representing mental states). This equilibrium state determines Alice's mixed (i.e., probabilistic) strategy. We use a master equation which in quantum physics describes the process of decoherence as the result of interaction with environment. Thus our model is a model of thinking through decoherence of the initially pure mental state. Decoherence is induced by the interaction with memory and the external mental environment. We study (numerically) the dynamics of quantum entropy of Alice's mental state in the process of decision making. We also consider classical entropy corresponding to Alice's choices. We introduce a measure of Alice's diffidence as the difference between classical and quantum entropies of Alice's mental state. We see that (at least in our model example) diffidence decreases (approaching zero) in the process of decision making. Finally, we discuss the problem of neuronal realization of quantum-like dynamics of in the brain; especially roles played by lateral prefrontal cortex or and orbitofrontal cortex.

In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics was pointed out that statistics collected in such the experiments have "quantum-like" properties, which can not be explained in classical probability theory. In this paper, we design a simple quantum-like model describing a decision-making process in a two-players game and try to explain a mechanism of the irrational behavior of players. Finally we discuss a mathematical frame of non-Kolmogorovian system in terms of liftings (Accardi and Ohya, in Appl. Math. Optim. 39:33-59, 1999).