This study investigated the effects of visual conditions associated with progressive eye disease on movement patterns and anxiety levels during gap-crossing tasks. Notably, 15 healthy young adults performed crossover platforms with a 10 cm gap at three different heights, namely equal (0 cm), raised (+15 cm), and lowered (-15 cm) levels, under four vision conditions, namely normal or corrected eyesight, 10° tunnel vision, 5° tunnel vision, and 5° tunnel vision with 0.04 occlusion. Leg movements during gap crossing were analyzed using three-dimensional motion analysis. The results highlighted a distinct motion pattern in the trajectories of participants' legs under the different visual conditions. Specifically, at the point where the gap-crossing movement began (D1), the normal or corrected eyesight conditions resulted in further separation between the steps compared with the other visual conditions. The highest point of the foot during movement (D2) did not differ between the visual conditions, except for the 0 cm step. Furthermore, anxiety levels, as quantified by the State-Trait Anxiety Inventory (STAI-S) questionnaire, were exacerbated under conditions of restricted visual information. In conclusion, visual impairments associated with progressive ocular diseases may perturb complex motor movement patterns, including those involved in gap-crossing tasks, with heightened anxiety potentially amplifying these disturbances.

Biological systems have been shown to have quantum-like behaviors by applying the adaptive dynamics view on their interaction networks. In particular, in the process of lactose–glucose metabolism, cells generate probabilistic interference patterns similarly to photons in the two-slit experiment. Such quantum-like interference patterns can be found in biological data, on all scales, from proteins to cognitive, ecological, and social systems. The adaptive dynamics approach covers both biological and physical phenomena, including the ones which are typically associated with quantum physics. We guess that the adaptive dynamics can be used for the clarification of quantum foundations, and the present paper is the first step in this direction. We suggest the use of an algorithm for the numerical simulation of the behavior of a billiard ball-like particle passing through two slits by explicitly considering the influence of the two-slit environment (experimental context). Our simulation successfully mimics the interference pattern obtained experimentally in quantum physics. The interference of photons or electrons by two slits is known as a typical quantum mechanical effect. We do not claim that the adaptive dynamics can reproduce the whole body of quantum mechanics, but we hope that this numerical simulation example will stimulate further extensive studies in this direction—the representation of quantum physical phenomena in an adaptive dynamical framework.

We present the quantum-like model of information processing by the brain's neural networks. The model does not refer to genuine quantum processes in the brain. In this model, uncertainty generated by the action potential of a neuron is represented as quantum-like superposition of the basic mental states corresponding to a neural code. Neuron's state space is described as complex Hilbert space (quantum information representation). The brain's psychological functions perform self-measurements by extracting concrete answers to questions (solutions of problems) from quantum information states. This extraction is modeled in the framework of open quantum systems theory. In this way, it is possible to proceed without appealing to the state's collapse. Dynamics of the state of psychological function F is described by the quantum master equation. Its stationary states represent classical statistical mixtures of possible outputs of F (decisions). This model can be used for justification of quantum-like modeling cognition and decision-making. The latter is supported by plenty of statistical data collected in cognitive psychology.

In this chapter, we give a mathematical representation of von Neumann's view on quantum measurement process, in which, a system to be measured interacts with infinite chain of measurement apparatus [1]. For the system, the measurement apparatus is an environment, and increase of degree of freedom in the environment is the cause of quantum decoherence of the system. We clearly represent this essential aspect in the background of quantum measurement by using lifting maps [3, 2]. A sequence of lifting maps realizes a unitary time evolution consistent with von Neumann's scheme.

In this study, we discuss a non-Kolmogorovness of the optical illusion in the human visual perception. We show subjects the ambiguous figure of "Schröeder stair", which has two different meanings [1]. We prepare 11 pictures which are inclined by different angles. The tendency to answer "left side is front" depends on the order of showing those pictures. For a mathematical treatment of such a context dependent phenomena, we propose a non-Kolmogorovian probabilistic model which is based on adaptive dynamics.

Differentiation is a universal process found in various phenomena of nature. As seen in the example of cell differentiation, the creation diversity on individual's character is caused by environmental interactions. In this paper, we try to explain its mechanism, which has been discussed mainly in Biology, by using the formalism of quantum physics. Our approach known as quantum bioinformatics shows that the temporal change of statistical state called decoherence fits to describe non-local phenomena like differentiation.

In this paper, we introduce a new model of selection behavior under risk that describes an essential cognitive process for comparing values of objects and making a selection decision. This model is constructed by the quantum-like approach that employs the state representation specific to quantum theory, which has the mathematical framework beyond the classical probability theory. We show that our quantum approach can clearly explain the famous examples of anomalies for the expected utility theory, the Ellsberg paradox, the Machina paradox and the disparity between WTA and WTP. Further, we point out that our model mathematically specifies the characteristics of the probability weighting function and the value function, which are basic concepts in the prospect theory. (C) 2016 Elsevier Inc. All rights reserved.

We compare the contextual probabilistic structures of the seminal two-slit experiment (quantum interference experiment), the system of three interacting bodies and Escherichia coli lactose-glucose metabolism. We show that they have the same non-Kolmogorov probabilistic structure resulting from multi-contextuality. There are plenty of statistical data with non-Kolmogorov features; in particular, the probabilistic behaviour of neither quantum nor biological systems can be described classically. Biological systems (even cells and proteins) are macroscopic systems and one may try to present a more detailed model of interactions in such systems that lead to quantum-like probabilistic behaviour. The system of interactions between three bodies is one of the simplest metaphoric examples for such interactions. By proceeding further in this way (by playing with n-body systems) we shall be able to find metaphoric mechanical models for complex bio-interactions, e.g. signalling between cells, leading to non-Kolmogorov probabilistic data.

We compare the contextual probabilistic structures of the seminal two-slit experiment (quantum interference experiment), the system of three interacting bodies and Escherichia coli lactose-glucose metabolism. We show that they have the same non-Kolmogorov probabilistic structure resulting from multi-contextuality. There are plenty of statistical data with non-Kolmogorov features; in particular, the probabilistic behaviour of neither quantum nor biological systems can be described classically. Biological systems (even cells and proteins) are macroscopic systems and one may try to present a more detailed model of interactions in such systems that lead to quantum-like probabilistic behaviour. The system of interactions between three bodies is one of the simplest metaphoric examples for such interactions. By proceeding further in this way (by playing with n-body systems) we shall be able to find metaphoric mechanical models for complex bio-interactions, e.g. signalling between cells, leading to non-Kolmogorov probabilistic data.

We discuss foundational issues of quantum information biology (QIB)-one of the most successful applications of the quantum formalism outside of physics. QIB provides a multi-scale model of information processing in bio-systems: from proteins and cells to cognitive and social systems. This theory has to be sharply distinguished from "traditional quantum biophysics". The latter is about quantum bio-physical processes, e.g., in cells or brains. QIB models the dynamics of information states of bio-systems. We argue that the information interpretation of quantum mechanics (its various forms were elaborated by Zeilinger and Brukner, Fuchs and Mermin, and D' Ariano) is the most natural interpretation of QIB. Biologically QIB is based on two principles: (a) adaptivity; (b) openness (bio-systems are fundamentally open). These principles are mathematically represented in the framework of a novel formalism- quantum adaptive dynamics which, in particular, contains the standard theory of open quantum systems.

This chapter reviews quantum(-like) information biology (QIB). Here biology is treated widely as even covering cognition and its derivatives: psychology and decision making, sociology, and behavioral economics and finances. QIB provides an integrative description of information processing by bio-systems at all scales of life: from proteins and cells to cognition, ecological and social systems. Mathematically QIB is based on the theory of adaptive quantum systems (which covers also open quantum systems). Ideologically QIB is based on the quantum-like (QL) paradigm: complex bio-systems process information in accordance with the laws of quantum information and probability. This paradigm is supported by plenty of statistical bio-data collected at all bio-scales. QIB reflects the two fundamental principles: a) adaptivity and, b) openness (bio-systems are fundamentally open). In addition, quantum adaptive dynamics provides the most generally possible mathematical representation of these principles.

We interpret the Leggett-Garg (LG) inequality as a kind of contextual probabilistic inequality in which one combines data collected in experiments performed for three different contexts. In the original version of the inequality, these contexts have a temporal nature and they are represented by three pairs of instances of time, (t(1), t(2)), (t(2), t(3)), (t(3), t(4)), where t(1) < t(2) < t(3). We generalize LG conditions of macroscopic realism and noninvasive measurability in a general contextual framework. Our formulation is performed in purely probabilistic terms: the existence of the context-independent joint probability distribution P and the possibility of reconstructing the experimentally found marginal (two-dimensional) probability distributions from P. We derive an analog of the LG inequality, 'contextual LG inequality', and use it as a test of 'quantum-likeness' of statistical data collected in a series of experiments on the recognition of ambiguous figures. In our experimental study, the figure under recognition is the Schroder stair, which is shown with rotations for different angles. Contexts are encoded by dynamics of rotations: clockwise, anticlockwise and random. Our data demonstrated violation of the contextual LG inequality for some combinations of the aforementioned contexts. Since in quantum theory and experiments with quantum physical systems, this inequality is violated, e.g. in the form of the original LG-inequality, our result can be interpreted as a sign that the quantum-like models can provide a more adequate description of the data generated in the process of recognition of ambiguous figures.

We interpret the Leggett-Garg (LG) inequality as a kind of contextual probabilistic inequality in which one combines data collected in experiments performed for three different contexts. In the original version of the inequality, these contexts have a temporal nature and they are represented by three pairs of instances of time, (t(1), t(2)), (t(2), t(3)), (t(3), t(4)), where t(1) < t(2) < t(3). We generalize LG conditions of macroscopic realism and noninvasive measurability in a general contextual framework. Our formulation is performed in purely probabilistic terms: the existence of the context-independent joint probability distribution P and the possibility of reconstructing the experimentally found marginal (two-dimensional) probability distributions from P. We derive an analog of the LG inequality, 'contextual LG inequality', and use it as a test of 'quantum-likeness' of statistical data collected in a series of experiments on the recognition of ambiguous figures. In our experimental study, the figure under recognition is the Schroder stair, which is shown with rotations for different angles. Contexts are encoded by dynamics of rotations: clockwise, anticlockwise and random. Our data demonstrated violation of the contextual LG inequality for some combinations of the aforementioned contexts. Since in quantum theory and experiments with quantum physical systems, this inequality is violated, e.g. in the form of the original LG-inequality, our result can be interpreted as a sign that the quantum-like models can provide a more adequate description of the data generated in the process of recognition of ambiguous figures.

Recently, it has been reported that conventional probability law can be violated in the context dependent phenomena which are "adaptive" to the environment or experimental settings. Also, it has been discussed that non-Kolmogorov probability, e.g. quantum probability, is available for modeling such a context dependent phenomenon. In this study, we investigate context-dependency of human perception process for optical illusion of Schrader stair, and we propose the non-Kolmogorov probabilistic model for the illusion.

Recently, various examples of non-Kolmogorovness in contextual dependent phenomena have been reported. In this study, we introduce non-Kolmogorovness in the measurement of depth inversion for the figure of Schroder's stair. Also we propose a model of the depth inversion, based on a non-Kolmogorovian probability theory which is called adaptive dynamics.

We develop a quantum-like (QL) model of cellular evolution based on the theory of open quantum systems and entanglement between epigenetic markers in a cell. This approach is applied to modeling of epigenetic evolution of cellular populations. We point out that recently experimental genetics discovered numerous phenomena of cellular evolution adaptive to the pressure of the environment. In such phenomena epigenetic changes are fixed in one generation and, hence, the Darwinian natural selection model cannot be applied. A number of prominent genetists stress the Lamarckian character of epigenetic evolution. In quantum physics the dynamics of the state of a system (e.g. electron) contacting with an environment (bath) is described by the theory of open quantum systems. Therefore it is natural to apply this theory to model adaptive changes in the epigenome. Since evolution of the Lamarckian type is very rapid - changes in the epigenome have to be inherited in one generation - we have to find a proper mathematical description of such a speed up. In our model this is the entanglement of different epigenetic markers.

We present a very general model of epigenetic evolution unifying (neo-)Darwinian and (neo-)Lamarckian viewpoints. The evolution is represented in the form of adaptive dynamics given by the quantum(-like) master equation. This equation describes development of the information state of epigenome under the pressure of an environment. We use the formalism of quantum mechanics in the purely operational framework. (Hence, our model has no direct relation to quantum physical processes inside a cell.) Thus our model is about probabilities for observations which can be done on epigenomes and it does not provide a detailed description of cellular processes. Usage of the operational approach provides a possibility to describe by one model all known types of cellular epigenetic inheritance. © 2013 Springer Science+Business Media Dordrecht.

We provide a symmetric class of 2-qudit bound entangled states within a so-called magic simplex of Bell diagonal states. This class generalizes well-known family of 2-qutrit states introduced by Horodecki [13].

There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quantum information theory, e.g., quantum channels and liftings. In physics the basic example of the context-dependent phenomena is the famous double-slit experiment. Recently similar examples have been found in biological and psychological sciences. Our approach is an extension of traditional quantum probability theory, and it is general enough to describe aforementioned contextual phenomena outside of quantum physics.

There exist several phenomena breaking the classical probability laws. The systems related to such phenomena are context-dependent, so that they are adaptive to other systems. In this paper, we present a new mathematical formalism to compute the joint probability distribution for two event-systems by using concepts of the adaptive dynamics and quantum information theory, e.g., quantum channels and liftings. In physics the basic example of the context-dependent phenomena is the famous double-slit experiment. Recently similar examples have been found in biological and psychological sciences. Our approach is an extension of traditional quantum probability theory, and it is general enough to describe aforementioned contextual phenomena outside of quantum physics.

We will show the necessary and sufficient condition of separability for a sub-class of circulant states in the 3 ⊗ 3 system. This sub-class includes the models proposed by several authors as special cases. Moreover, it will be proved that our separability condition equals to the failure condition of quasi-distillation of entanglement. © 2013 World Scientific Publishing Company.

We develop a quantum-like (QL) model of cellular evolution based on the theory of open quantum systems and entanglement between epigenetic markers in a cell. This approach is applied to modeling of epigenetic evolution of cellular populations. We point out that recently experimental genetics discovered numerous phenomena of cellular evolution adaptive to the pressure of the environment. In such phenomena epigenetic changes are fixed in one generation and, hence, the Darwinian natural selection model cannot be applied. A number of prominent genetists stress the Lamarckian character of epigenetic evolution. In quantum physics the dynamics of the state of a system (e.g. electron) contacting with an environment (bath) is described by the theory of open quantum systems. Therefore it is natural to apply this theory to model adaptive changes in the epigenome. Since evolution of the Lamarckian type is very rapid - changes in the epigenome have to be inherited in one generation - we have to find a proper mathematical description of such a speed up. In our model this is the entanglement of different epigenetic markers.

Recently, various examples of non-Kolmogorovness in contextual dependent phenomena have been reported. In this study, we introduce non-Kolmogorovness in the measurement of depth inversion for the figure of Schroder's stair. Also we propose a model of the depth inversion, based on a non-Kolmogorovian probability theory which is called adaptive dynamics.

We provide a symmetric class of 2-qudit bound entangled states within a so-called magic simplex of Bell diagonal states. This class generalizes well-known family of 2-qutrit states introduced by Horodecki [13].

In this paper we apply the quantum-like (QL) approach to microbiology to present an operational description of the complex process of diauxie in Escherichia coli. We take as guaranteed that dynamics in cells is adaptive, i.e., it depends crucially on the microbiological context. This very general assumption is sufficient to appeal to quantum and more general QL probabilistic models. The next step is to find the operational representation - by operators in complex Hilbert space (as in quantum physics). To determine QL operators, we used the statistical data from Inada et al. (1996). To improve the QL-representation, we needed better experimental data. Corresponding experiments were recently done by two of the authors and in this paper we use these new data. In these data we found that biochemical context of precultivation of populations of E. coli plays a crucial role in E. coli preferences with respect to sugars. Hence, the form of the QL operator representing lactose operon activation also depends crucially on precultivation. One of our results is decomposition of the lactose operon activation operator to extract the factor determined by precultivation. The QL operational approach developed in this paper can be used not only for description of the process of diauxie in E. coli, but also other processes of gene expression. However, new experimental statistical data are demanded. (C) 2012 Elsevier Ltd. All rights reserved.

In this paper we apply the quantum-like (QL) approach to microbiology to present an operational description of the complex process of diauxie in Escherichia coli. We take as guaranteed that dynamics in cells is adaptive, i.e., it depends crucially on the microbiological context. This very general assumption is sufficient to appeal to quantum and more general QL probabilistic models. The next step is to find the operational representation - by operators in complex Hilbert space (as in quantum physics). To determine QL operators, we used the statistical data from Inada et al. (1996). To improve the QL-representation, we needed better experimental data. Corresponding experiments were recently done by two of the authors and in this paper we use these new data. In these data we found that biochemical context of precultivation of populations of E. coli plays a crucial role in E. coli preferences with respect to sugars. Hence, the form of the QL operator representing lactose operon activation also depends crucially on precultivation. One of our results is decomposition of the lactose operon activation operator to extract the factor determined by precultivation. The QL operational approach developed in this paper can be used not only for description of the process of diauxie in E. coli, but also other processes of gene expression. However, new experimental statistical data are demanded. (C) 2012 Elsevier Ltd. All rights reserved.

In this paper we develop a general quantum-like model of decision making. Here updating of probability is based on linear algebra, the von Neumann-Luders projection postulate, Born's rule, and the quantum representation of the state space of a composite system by the tensor product. This quantum-like model generalizes the classical Bayesian inference in a natural way. In our approach the latter appears as a special case corresponding to the absence of relative phases in the mental state. By taking into account a possibility of the existence of correlations which are encoded in relative phases we developed a more general scheme of decision making. We discuss natural situations inducing deviations from the classical Bayesian scheme in the process of decision making by cognitive systems: in situations that can be characterized as objective and subjective mental uncertainties. Further, we discuss the problem of base rare fallacy. In our formalism, these "irrational" (non-Bayesian) inferences are represented by quantum-like bias operations acting on the mental state. (C) 2012 Elsevier Inc. All rights reserved.

We developed a quantum-like model describing the gene regulation of glucose/lactose metabolism in a bacterium, Escherichia coli. Our quantum-like model can be considered as a kind of the operational formalism for microbiology and genetics. Instead of trying to describe processes in a cell in the very detail, we propose a formal operator description. Such a description may be very useful in situation in which the detailed description of processes is impossible or extremely complicated. We analyze statistical data obtained from experiments, and we compute the degree of E. coli's preference within adaptive dynamics. It is known that there are several types of E. coli characterized by the metabolic system. We demonstrate that the same type of E. coli can be described by the well determined operators we find invariant operator quantities characterizing each type. Such invariant quantities can be calculated from the obtained statistical data. © 2012 Springer Science+Business Media B.V.

In this paper we develop a general quantum-like model of decision making. Here updating of probability is based on linear algebra, the von Neumann-Luders projection postulate, Born's rule, and the quantum representation of the state space of a composite system by the tensor product. This quantum-like model generalizes the classical Bayesian inference in a natural way. In our approach the latter appears as a special case corresponding to the absence of relative phases in the mental state. By taking into account a possibility of the existence of correlations which are encoded in relative phases we developed a more general scheme of decision making. We discuss natural situations inducing deviations from the classical Bayesian scheme in the process of decision making by cognitive systems: in situations that can be characterized as objective and subjective mental uncertainties. Further, we discuss the problem of base rare fallacy. In our formalism, these "irrational" (non-Bayesian) inferences are represented by quantum-like bias operations acting on the mental state. (C) 2012 Elsevier Inc. All rights reserved.

In this paper we develop a general quantum-like model of decision making. Here updating of probability is based on linear algebra, the von Neumann-Luders projection postulate, Born's rule, and the quantum representation of the state space of a composite system by the tensor product. This quantum-like model generalizes the classical Bayesian inference in a natural way. In our approach the latter appears as a special case corresponding to the absence of relative phases in the mental state. By taking into account a possibility of the existence of correlations which are encoded in relative phases we developed a more general scheme of decision making. We discuss natural situations inducing deviations from the classical Bayesian scheme in the process of decision making by cognitive systems: in situations that can be characterized as objective and subjective mental uncertainties. Further, we discuss the problem of base rare fallacy. In our formalism, these "irrational" (non-Bayesian) inferences are represented by quantum-like bias operations acting on the mental state. (C) 2012 Elsevier Inc. All rights reserved.

In cognitive psychology, some experiments for games were reported, and they demonstrated that real players did not use the "rational strategy" provided by classical game theory and based on the notion of the Nasch equilibrium. This psychological phenomenon was called the disjunction effect. Recently, we proposed a model of decision making which can explain this effect ("irrationality" of players) Asano et al. (2010, 2011) [23,24]. Our model is based on the mathematical formalism of quantum mechanics, because psychological fluctuations inducing the irrationality are formally represented as quantum fluctuations Asano et al. (2011)[55]. In this paper, we reconsider the process of quantum-like decision-making more closely and redefine it as a well-defined quantum dynamics by using the concept of lifting channel, which is an important concept in quantum information theory. We also present numerical simulation for this quantum-like mental dynamics. It is non-Markovian by its nature. Stabilization to the steady state solution (determining subjective probabilities for decision making) is based on the collective effect of mental fluctuations collected in the working memory of a decision maker. (C) 2011 Elsevier B.V. All rights reserved.

In this paper, we construct a teleportation model with nonmaximal entangled state. This model, called the m-level teleportation, is discussed on the basis of the Kossakowski and Ohya teleportation scheme. For this study, we define a generalized Bell state in terms of Latin square, by which we derive a general form of appropriate nonmaximal entangled state for a perfect m-level teleportation.

In this paper we develop a general quantum-like representation of decision making. Here quantum-like representation is based on linear algebra, the von Neumann-Lüders projection postulate, Born's rule, and the quantum representation of the state space of a composite system by the tensor product. Our approach generalizes in a natural way the classical Bayesian inference and explains irrational (non-Bayesian) inference biased by psychological factors. For the mathematical description of irrational inference, we use the lifting map, which is important concept to discuss a general quantum dynamics called adaptive dynamics. © 2012 Springer-Verlag.

There exist several phenomena (systems) breaking the classical probability laws. In this report, we present a new mathematical formula to compute the probability in those context dependent systems by using the concepts of the adaptive dynamics and the lifting. © 2012 Springer-Verlag.

Recently it is pointed out that there exists the experimental data in Escherichia coli's metabolism which violate the law of total probability in classical probability. In this report, we propose a model which describes such phenomenon based on adaptive dynamics. © 2012 Springer-Verlag.

We apply theory of open quantum systems to modeling of epigenetic evolution. This is an attempt to unify Darwinian and Lamarckian viewpoints on evolution on the basis of a quantum-like model. The state of uncertainty of cell's epigenome is resolved to a stable and inherited epigenetic configuration. This process of evolution and stabilization is described by the quantum master equation (the Gorini-Kossakowski-Sudarshan-Lindblad equation). The initial state of epigenome starting interaction with a new environment is represented as a pure quantum state. It evolves to a steady state solution of the quantum master equation given by a diagonal density matrix. The latter represents the state resulting from a series of epimutations induced by the environment. We use the information interpretation of the wave function which was elaborated by C. Fuchs and A. Zeilinger.

In cognitive psychology, some experiments of games were reported [1, 2, 3, 4], and these demonstrated that real players did not use the "rational strategy" provided by classical game theory. To discuss probabilities of such "irrational choice", recently, we proposed a decision-making model which is based on the formalism of quantum mechanics [5, 6, 7, 8]. In this paper, we briefly explain the above model and calculate the probability of irrational choice in several prisoner's dilemma (PD) games.

Recently, we proposed a new method to compute probabilities which do not satisfy basic law in classical probability theory. In this note, we analyze glucose effect in Escherichia coli's growth with the method, and we show an invariant quantity which Escherichia coli has.

There exist several phenomena (systems) breaking the classical probability laws. In this report, we present a new mathematical formula to compute the probability in those context dependent systems by using the concepts of the adaptive dynamics and the lifting. © 2012 Springer-Verlag.

In this paper we develop a general quantum-like representation of decision making. Here quantum-like representation is based on linear algebra, the von Neumann-Lüders projection postulate, Born's rule, and the quantum representation of the state space of a composite system by the tensor product. Our approach generalizes in a natural way the classical Bayesian inference and explains irrational (non-Bayesian) inference biased by psychological factors. For the mathematical description of irrational inference, we use the lifting map, which is important concept to discuss a general quantum dynamics called adaptive dynamics. © 2012 Springer-Verlag.

Recently it is pointed out that there exists the experimental data in Escherichia coli's metabolism which violate the law of total probability in classical probability. In this report, we propose a model which describes such phenomenon based on adaptive dynamics. © 2012 Springer-Verlag.

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 in which 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 in the brain; especially roles played by lateral prefrontal cortex or/and orbitofrontal cortex. (C) 2011 Elsevier Ltd. All rights reserved.

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 in which 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 in the brain; especially roles played by lateral prefrontal cortex or/and orbitofrontal cortex. (C) 2011 Elsevier Ltd. All rights reserved.

We proceed towards an application of the mathematical formalism of quantum mechanics to cognitive psychology - the problem of decision-making in games of the Prisoners Dilemma type. These games were used as tests of rationality of players. Experiments performed in cognitive psychology by Shafir and Tversky [1,2], Croson [3], Hofstader [4,5] demonstrated that in general real players do not use "rational strategy" provided by classical game theory; this psychological phenomenon was called the disjunction effect. We elaborate a model of quantum-like decision making which can explain this effect ("irrationality" of plays). Our model is based on quantum information theory. The main result of this paper is the derivation of Gorini-Kossakowski-Sudarshan-Lindblad equation whose equilibrium solution gives the quantum state used for decision making. It is the first application of this equation in cognitive psychology.

In experiments of games, players frequently make choices which are regarded as irrational in game theory. In papers of Khrennikov (Information Dynamics in Cognitive, Psychological and Anomalous Phenomena. Fundamental Theories of Physics, Kluwer Academic, Norwell, 2004; Fuzzy Sets Syst. 155:4-17, 2005; Biosystems 84:225-241, 2006; Found. Phys. 35(10):1655-1693, 2005; in QP-PQ Quantum Probability and White Noise Analysis, vol. XXIV, pp. 105-117, 2009), it 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).

We present the quantum-like paradigm for biology, cognitive psychology, and modeling of brain's functioning. By this paradigm contextuality of biological processes induces violation of laws of classical (Kolmogorovian) probability, starting with the fundamental law of total probability. New nonclassical models have to be used for mathematical modeling of contextual phenomena.

We present the quantum-like paradigm for biology, cognitive psychology, and modeling of brain's functioning. By this paradigm contextuality of biological processes induces violation of laws of classical (Kolmogorovian) probability, starting with the fundamental law of total probability. New nonclassical models have to be used for mathematical modeling of contextual phenomena.

Recently, applications of quantum mechanics to coginitive psychology have been discussed, see [1]-[11]. It was known that statistical data obtained in some experiments of cognitive psychology cannot be described by classical probability model (Kolmogorov's model) [12]-[15]. Quantum probability is one of the most advanced mathematical models for non-classical probability. In the paper of [11], we proposed a quantum-like model describing decision-making process in a two-player game, where we used the generalized quantum formalism based on lifting of density operators [16]. In this paper, we discuss the quantum-like representation of Bayesian inference, which has been used to calculate probabilities for decision making under uncertainty. The uncertainty is described in the form of quantum superposition, and Bayesian updating is explained as a reduction of state by quantum measurement.

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 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. By using this equilibrium point Alice determines her mixed (i.e., probabilistic) strategy with respect to Bob. Thus our model is a model of thinking through decoherence of initially pure mental state. Decoherence is induced by interaction with memory and external environment. In this paper we study (numerically) dynamics of quantum entropy of Alice's state in the process of decision making. Our analysis demonstrates that this dynamics depends nontrivially on the initial state of Alice's mind on her own actions and her prediction state (for possible actions of Bob.)

It has been considered that a maximal entangled state is needed for complete quantum teleportation. However, Kossakowski and Ohya proposed a scheme of complete teleportation for nonmaximal entangled state [1]. Basing on their scheme, we proposed a teleportation model of 2-level state with a non-maximal entangled state [2]. In the present study, we construct its expanded model, in which Alice can teleport m-level state even if non-maximal entangled state is used.

We proceed towards an application of the mathematical formalism of quantum mechanics to cognitive psychology - the problem of decision-making in games of the Prisoners Dilemma type. These games were used as tests of rationality of players. Experiments performed in cognitive psychology by Shafir and Tversky [1,2], Croson [3], Hofstader [4,5] demonstrated that in general real players do not use "rational strategy" provided by classical game theory; this psychological phenomenon was called the disjunction effect. We elaborate a model of quantum-like decision making which can explain this effect ("irrationality" of plays). Our model is based on quantum information theory. The main result of this paper is the derivation of Gorini-Kossakowski-Sudarshan-Lindblad equation whose equilibrium solution gives the quantum state used for decision making. It is the first application of this equation in cognitive psychology.

Recently, Kossakowski and Ohya (K-O) proposed a new teleportation scheme which enables perfect teleportation even for a nonmaximal entangled state [A. Kossakowski and M. Ohya, Infinite Dimensional Analysis Quantum Probability and Related Topics 10, 411 (2007)]. To discuss a physical realization of the K-O scheme, we propose a model based on quantum optics. In our model, we take a superposition of Schrodinger's cat states as an input state being sent from Alice to Bob, and their entangled state is generated by a photon number state through a beam splitter. When the average photon number for our input states is equal to half the number of photons into the beam splitter, our model has high fidelity.

In many models of perfect quantum teleportation, maximal entangled states are postulated between Alice and Bob. Recently, Kossakowski and Ohya proposed a new scheme of perfect teleportation where a non-maximal entangled state is used 3. In this paper, we introduce a concrete teleportation model of K-O scheme, called a m-level teleportation. A non-maximal entangled state in this model is realizable in optical techniques. Moreover, we propose another teleportation model designed by using a mathematical formalism of K-O theory. In the second model, a new operation is added to a conventional teleportation process, which is called a filtering and implemented before Alice's measurement. We show effects of the filtering for success probabilities of teleportation.

The quantum teleportation has been discussed by several articles, and in most of models, perfect quantum teleportation can be occurred if the entangled state between Alice and Bob is maximal. Recently, Kossakowski and Ohya reformulated the teleportation process and proposed a new scheme of perfect teleportation where a non-maximal entangled state is used [3]. In this paper, we introduce two models designed according to the K-O formalism. The first one is called m-level perfect teleportation. We show that a non-maximal entangled state used in this model is realizable in optical techniques. In the second model, a new operation is added to a conventional teleportation process, which is called "filtering" and implemented before Alice's measurement. We show availabilities of the filtering for success probabilities of teleportation.

Multiqubit logical gates are proposed as implementations of logical operations on N qubits realized physically by the local manipulation of qubits before and after the one-time evolution of an Ising chain. This construction avoids complicated tuning of the interactions between qubits. The general rules of the action of multiqubit logical gates are derived by decomposing the process into the product of two-qubit logical operations. The formalism is demonstrated by the construction of a special type of multiqubit logical gate that is simulated by a quantum circuit composed of controlled-NOT gates.

本研究課題は（１）認識論的意思決定理論の構築（２）認識論的意思決定理論を用いた社会モデルの提案を目的としている。現在、社会科学における認識論的意思決定理論の重要性とその構築に必要な数学的枠組みに関する検討を、現代の思想潮流である「新しい実在論」の視座からおこなっている。新しい実在論は存在の概念を「何らかの対象が何らかの特定の仕方（意味）で現象すること」と捉え、現象の領域（意味の場と呼ばれる）の多元的実在を認める。存在論的（自然科学的）に客観的な事実は自然という意味の場に現象し、人間の体験といった認識論的に客観的な事実は（自然とは別の）信念や志向性を象徴する意味の場に現象する。一般に、これらの場は部分的に重なりがあるにせよ、包摂の関係にはないとされる。つまり認識論的事実は必ずしも存在論的、自然科学的事実に還元されるとは言えない。意思決定の背後には多様な体験で構成された文脈があるが、その内容を脳内、または身体外部に観察される事実のみで説明することは不可能であるかもしれない。新しい実在論が与えるこのような示唆は文脈を直接の記述対象とする認識論的意思決定理論の重要性を示すうえで不可欠である。また、期待効用仮設を前提として構成されている既存の意思決定理論（ゲーム理論とその周辺理論）との対比についても論じられた。期待効用仮設は確率論に則した合理的意思決定のあり方、すなわち確率論が重視する存在論的客観性と認識論的客観性の重なりに現象する体験と解釈できる。（行動経済学は存在論的客観性からの逸脱、非合理性を現象論的に説明する試みと位置付けられる。）対して認識論的意思決定理論は合理性と非合理性の区別を超えたメタな視点を有さなければならない。当理論が確率論を包含する枠組み(非可換確率論の枠組み)に構成されることはこの点において必然である。以上の論点を精査した内容は今後報告される予定である。

本研究は外来癌化学療法（以下、化療）中の患者を対象に有害事象である発熱性好中球減少症（以下、FN）の早期発見とセルフモニタリング機能を有するタブレット端末利用の通信システムを開発した。本システムは（1）先行研究によるFN発症リスク因子等の病歴データ収集（2）対象者は化療期間3週間の体温、酸素飽和度、息切れ感などのデータを連日送信（3）1および2の両データに基づくFN発症リスク者へアラートを発信する、というシステムである。セルフケア・アドヒアランス率はほぼ100％であり、システムの有用性が確認でき、対象者のうち2名が発熱し、システムにより自動アラートが表示され、これにより早期受診につながった。

乳癌化学療法（以下、化療）中の患者で筋肉量が少なく抑うつ状態にある者は身体活動量が低かった。化療中の発熱性好中球減少症（FN）の発症予測は患者の身体活動性や生活の質の維持のために重要である。そこで肺癌、乳癌、大腸癌の化療患者の病歴調査よりFNのリスク因子を抽出した。続いて化療中で在宅期の患者がTablet PCを用いて体温、倦怠感等の身体状況を自己モニタリングし、これらのデータを送信しFN発症のリスクが高まった場合にはアラートを発信するシステムを開発した。過去の化療で敗血症既往があり、G-CSF（顆粒球コロニー刺激因子）の投与歴がある者はFN発症リスクが有意に高かった。

We design quantum gates feasible with multiple interactions between qubits, and discuss the utility. Also, we propose the realization method of realistic quantum teleportations using non-maximum entangled-states.

本研究の目的は、いくつかの具体的な問題を通して量子（非可換）確率論の基礎を検討することにある。現在の量子情報に関わる様々な理論は量子確率論をベースにしているが、そこに存在するいくつかの問題点を明らかにし、その解決を試みる。そこで、本研究では以下の順に研究を遂行した。（１）量子情報理論、特に、量子エントロピー論、量子テレポーテーション理論、量子アルゴリズム論に存在するいくつかの問題点を取り上げ、それらを整理した。（２）（１）で掲げた問題はどこまで従来の量子確率論の公理系で議論できるか検討した。（３）（２）の検討の下に、量子確率論の新たな数理を考えた。