Taichi Haruna

Abstract We propose a class of generalized multiplicative stochastic processes obtained by introducing an endo-perspective into one-dimensional maps with additive noise. We define an internal state for the noisy dynamics of a given one-dimensional map and study its statistical behavior. We found intermittency characterized by two power-laws in the dynamics of the internal state for the logistic map and the BZ map with noise which exhibit different noise-induced phenomena, namely, noise-induced chaos and noise-induced order, respectively. We show that the power-laws can be explained in a unified way from the theory of generalized multiplicative stochastic processes.

Abstract Human decision-making is relevant for concept formation and cognitive illusions. Cognitive illusions can be explained by quantum probability, while the reason for introducing quantum mechanics is based on ad hoc bounded rationality (BR). Concept formation can be explained in a set-theoretic way, although such explanations have not been extended to cognitive illusions. We naturally expand the idea of BR to incomplete BR and introduce the key notion of nonlocality in cognition without any attempts on quantum theory. We define incomplete bounded rationality and nonlocality as a binary relation, construct a lattice from the relation by using a rough-set technique, and define probability in concept formation. By using probability defined in concept formation, we describe various cognitive illusions, such as the guppy effect, conjunction fallacy, order effect, and so on. It implies that cognitive illusions can be explained by changes in the probability space relevant to concept formation.

Abstract We propose a growing network model that can generate dense scale-free networks with an almost neutral degree−degree correlation and a negative scaling of local clustering coefficient. The model is obtained by modifying an existing model in the literature that can also generate dense scale-free networks but with a different higher-order network structure. The modification is mediated by category theory. Category theory can identify a duality structure hidden in the previous model. The proposed model is built so that the identified duality is preserved. This work is a novel application of category theory for designing a network model focusing on a universal algebraic structure.

Burst suppression on electroencephalogram (EEG) is defined as suppression periods longer than 0.5 s during which the amplitude does not exceed 5 μV in human. The aims of this study were; 1) an attempt of creating new criteria of burst suppression in dogs; and 2) a survey on accuracy of sub-parameter of Bispectral index (BIS). Using a BIS monitor, suppression ratio (SRBIS) and raw-EEG data were recorded at 2.0%, 2.5%, 3.0%, 3.5%, 4.0%, and 5.0% end-tidal sevoflurane concentration (ETSEV) in 6 beagle dogs. The minimum ETSEV at which burst suppression was visually confirmed (ETSEVBS) was determined. By applying various duration and voltage threshold to criteria, suppression ratio was calculated (SR). Using the minimum balanced error rate (BER), new criteria consisting of the minimum duration of 0.35 s and the maximum threshold of 2.25 μV that provided SR > 0 above ETSEVBS was screened. SR was set by these criteria (SRBER) and by manual inspection (SRTRUE). The median detection rate of SRBER/SRTRUE was a statistically significant increase (p < .01) compared to that of SRBIS/SRTRUE (77% and 17% at 3.5% ETSEV, 89% and 19% at 4.0% ETSEV, and 86% and 84% at 5.0% ETSEV, respectively). In addition, between SRBER and SRTRUE evaluated by regression and Bland-Altman analyses, there was a strong correlation (r = 0.967, p < .001) and a moderate agreement (Limits of agreement: -7.14 ± 13.95). The method using BER may help to establish new criteria of burst suppression to grasp the excessive deep level of anesthesia.

Coherence of a network means that it is made up of functions of nodes glued together. In our previous work [Haruna, T., 2013. BioSystems 114, 125-148], we showed that coherence of directed networks can be captured by the lateral path which is dual to the usual directed path. In this paper, we study coherence along lateral paths emerging from random Boolean network dynamics. A s

One slogan of science of complex networks is "functionality from network topology". In order to achieve this slogan, many characteristics such as degree distributions, average path length, clustering coefficients, network motifs etc have been introduced. However, these are all based on the "real view" on networks, that is, nodes are just points and an arc or an edge between two nodes indicates existence of some interaction between the two nodes and nothing more. In this paper we introduce "dual views" on networks in contrast to the "real view" in order to promote further achievement of the slogan. In a "dual view" we interpret objects as processes. This is an abstraction from real systems in which each component has its own process. There are infinitely many "dual views", however, we can show that there is a canonical "dual view" among all possible ones. We explain mathematical idea to formulate "dual views" and discuss its application to the study of complex networks.

The aim of this paper is to investigate the discrete nature of chemically reacting systems. In order to achieve our purpose we propose a systematic method to compare the discrete stochastic model of chemically reacting systems with the continuous stochastic model. We adopt the chemical master equation (CME) as the discrete stochastic model and the chemical Fokker-Planck equation (CFPE) as the continuous stochastic model. By making use of the well-known idea of approximating diffusion processes by birth-death processes, we construct a family of master equations parameterized by the degree of discreteness. This family of master equations bridges CME and CFPE. With full degree of discreteness we obtain CME and as decreasing discreteness the family of master equations converges to CFPE. Our strategy is not to study CME directly but to distinguish the properties of CME by putting CME into the family of master equations bridging CME and CFPE. We examine the usefulness of our construction by two simple examples.