Functional Dynamics I : Articulation Process

The articulation process of dynamical networks is studied with a functional map, a minimal model for the dynamic change of relationships through iteration. The model is a dynamical system of a function $f$, not of variables, having a self-reference term $f \circ f$, introduced by recalling that operation in a biological system is often applied to itself, as is typically seen in rules in the natural language or genes. Starting from an inarticulate network, two types of fixed points are formed as an invariant structure with iterations. The function is folded with time, until it has finite or infinite piecewise-flat segments of fixed points, regarded as articulation. For an initial logistic map, attracted functions are classified into step, folded step, fractal, and random phases, according to the degree of folding. Oscillatory dynamics are also found, where function values are mapped to several fixed points periodically. The significance of our results to prototype categorization in language is discussed.Comment: 48 pages, 15 figeres (5 gif files

Dynamical Networks in Function Dynamics

As a first step toward realizing a dynamical system that evolves while spontaneously determining its own rule for time evolution, function dynamics (FD) is analyzed. FD consists of a functional equation with a self-referential term, given as a dynamical system of a 1-dimensional map. Through the time evolution of this system, a dynamical graph (a network) emerges. This graph has three interesting properties: i) vertices appear as stable elements, ii) the terminals of directed edges change in time, and iii) some vertices determine the dynamics of edges, and edges determine the stability of the vertices, complementarily. Two aspects of FD are studied, the generation of a graph (network) structure and the dynamics of this graph (network) in the system.Comment: 29 pages, 10 figure

CP violation in modified bipair neutrino mixing and leptogenesis

We study effects of CP violation in a modified bipair neutrino mixing scheme predicting $\sin^2\theta_{23}$ near both 0.4 and 0.6 currently consistent with experimentally allowed values. The source of CP violation is supplied by charged lepton mixing accompanied by a single phase, whose mixing size is assumed to be less than that of the Wolfenstein parameter for the quark mixing. Including results of leptogenesis, which is based on the minimal seesaw model, we obtain the allowed region of CP-violating Dirac and Majorana phases, which provides the observed baryon asymmetry of the universe in the case of the Dirac neutrino mass matrix subject to one zero texture.Comment: 5 pages, 30 figures, accepted for publication in Physics Letters

Higher-continuity s-version of finite element method with B-spline functions

This paper proposes a strategy to solve the problems of the conventional s-version of finite element method (SFEM) fundamentally. Because SFEM can reasonably model an analytical domain by superimposing meshes with different spatial resolutions, it has intrinsic advantages of local high accuracy, low computation time, and simple meshing procedure. However, it has disadvantages such as accuracy of numerical integration and matrix singularity. Although several additional techniques have been proposed to mitigate these limitations, they are computationally expensive or ad-hoc, and detract from its strengths. To solve these issues, we propose a novel strategy called B-spline based SFEM. To improve the accuracy of numerical integration, we employed cubic B-spline basis functions with $C^2$-continuity across element boundaries as the global basis functions. To avoid matrix singularity, we applied different basis functions to different meshes. Specifically, we employed the Lagrange basis functions as local basis functions. The numerical results indicate that using the proposed method, numerical integration can be calculated with sufficient accuracy without any additional techniques used in conventional SFEM. Furthermore, the proposed method avoids matrix singularity and is superior to conventional methods in terms of convergence for solving linear equations. Therefore, the proposed method has the potential to reduce computation time while maintaining a comparable accuracy to conventional SFEM.Comment: 40 pages, 15 figures and 2 table

DeepSaucer: Unified Environment for Verifying Deep Neural Networks

In recent years, a number of methods for verifying DNNs have been developed. Because the approaches of the methods differ and have their own limitations, we think that a number of verification methods should be applied to a developed DNN. To apply a number of methods to the DNN, it is necessary to translate either the implementation of the DNN or the verification method so that one runs in the same environment as the other. Since those translations are time-consuming, a utility tool, named DeepSaucer, which helps to retain and reuse implementations of DNNs, verification methods, and their environments, is proposed. In DeepSaucer, code snippets of loading DNNs, running verification methods, and creating their environments are retained and reused as software assets in order to reduce cost of verifying DNNs. The feasibility of DeepSaucer is confirmed by implementing it on the basis of Anaconda, which provides virtual environment for loading a DNN and running a verification method. In addition, the effectiveness of DeepSaucer is demonstrated by usecase examples

Spatially Continuous Non-Contact Cold Sensation Presentation Based on Low-Temperature Airflows

Our perception of cold enriches our understanding of the world and allows us to interact with it. Therefore, the presentation of cold sensations will be beneficial in improving the sense of immersion and presence in virtual reality and the metaverse. This study proposed a novel method for spatially continuous cold sensation presentation based on low-temperature airflows. We defined the shortest distance between two airflows perceived as different cold stimuli as a local cold stimulus group discrimination threshold (LCSGDT). By setting the distance between airflows within the LCSGDT, spatially continuous cold sensations can be achieved with an optimal number of cold airflows. We hypothesized that the LCSGDTs are related to the heat-transfer capability of airflows and developed a model to relate them. We investigated the LCSGDTs at a flow rate of 25 L/min and presentation distances ranging from 10 to 50 mm. The results showed that under these conditions, the LCSGDTs are 131.4 $\pm$ 1.9 mm, and the heat-transfer capacity of the airflow corresponding to these LCSGDTs is an almost constant value, that is, 0.92.Comment: 7 page

Thermal Conductivity in the Bose-Einstein Condensed State of Triplons in the Bond-Alternating Spin-Chain System Pb2V3O9

In order to clarify the origin of the enhancement of the thermal conductivity in the Bose-Einstein Condensed (BEC) state of field-induced triplons, we have measured the thermal conductivity along the [101] direction parallel to spin-chains, $kappa_{\|[101]}$, and perpendicular to spin-chains, $kappa_{\perp[101]}$, of the S=1/2 bond-alternating spin-chain system Pb2V3O9 in magnetic fields up to 14 T. With increasing field at 3 K, it has been found that both $kappa_{\|[101]}$ and $kappa_{\perp[101]}$ are suppressed in the gapped normal state in low fields. In the BEC state of field-induced triplons in high fields, on the other hand, $kappa_{\|[101]}$ is enhanced with increasing field, while $kappa_{\perp[101]}$ is suppressed. That is, the thermal conductivity along the direction, where the magnetic interaction is strong, is markedly enhanced in the BEC state. Accordingly, our results suggest that the enhancement of $kappa_{\|[101]}$ in the BEC state is caused by the enhancement of the thermal conductivity due to triplons on the basis of the two-fluid model, as in the case of the superfluid state of liquid 4He.Comment: 5 pages, 3 figure

Oxidation of CuSn alloy nanotree and application for gas sensors

The CuSn alloy nanotree formed by DC electroplating is a true three-dimensional (3D) structure with many branches that separate the trunk perpendicularly. We carried out the oxidation of CuSn nanotrees in atmosphere in order to study the possibility of such nanotrees for application to sensors. It was confirmed that the oxygen concentration in the CuSn nanotree oxide increased with temperature and reached 40 at. % at 350 °C. The optical reflectance spectra of the CuSn nanotree oxide formed at 250 °C showed a 3–4% reflectance in the wavelength range between 400 and 900 nm, and its behavior differed from those of Cu and Sn oxides formed at 250 °C. The temperature dependence of electrical resistivity for the CuSn nanotree oxide showed a typical semiconductor behavior. By the introduction of H2, O2, N2, and CO gases into the chamber, the resistance of the CuSn nanotree oxide responded against H2 most sensitively, as well as against O2 and CO gases. From the resistance change tendency, it is strongly suggested that the CuSn nanotree oxide is a p-type semiconductor, because it shows an increase in conductivity caused by the adsorption of a negative charge such as O−. However, the conductivity decreases with the adsorption of a positive charge such as H+. The present study suggests the high potential of the CuSn nanotree oxide as a gas sensor, since it has a very high surface-to-volume ratio