General Theory of Music by Icosahedron 2: Analysis of musical pieces by the exceptional musical icosahedra

We propose a new way of analyzing musical pieces by using the exceptional musical icosahedra where all the major/minor triads are represented by golden triangles or golden gnomons. First, we introduce a concept of the golden neighborhood that characterizes golden triangles/gnomons that neighbor a given golden triangle or gnomon. Then, we investigate a relation between the exceptional musical icosahedra and the neo-Riemannian theory, and find that the golden neighborhoods and the icosahedron symmetry relate any major/minor triad with any major/minor triad. Second, we show how the exceptional musical icosahedra are applied to analyzing harmonies constructed by four or more tones. We introduce two concepts, golden decomposition and golden singular. The golden decomposition is a decomposition of a given harmony into the minimum number of harmonies constructing the given harmony and represented by the golden figure (a golden triangle, a golden gnomon, or a golden rectangle). A harmony is golden singular if and only if the harmony does not have golden decompositions. We show results of the golden analysis (analysis by the golden decomposition) of the tertian seventh chords and the mystic chord. While the dominant seventh chord is the only tertian seventh chord that is golden singular in the type 1[star] and the type 4[star] exceptional musical icosahedron, the half-diminished seventh chord is the only tertian seventh chord that is golden singular in the type 2 [star] and the type 3[star] exceptional musical icosahedron. Last, we apply the golden analysis to the famous prelude in C major composed by Johann Sebastian Bach (BWV 846). We found 7 combinations of the golden figures on the type 2 [star] or the type 3 [star] exceptional musical icosahedron dually represent all the measures of the BWV 846.Comment: 32 pages, 51 figure

Associative memory by virtual oscillator network based on single spin-torque oscillator

A coupled oscillator network may be able to perform an energy-efficient associative memory operation. However, its realization has been difficult because inhomogeneities unavoidably arise among the oscillators during fabrication and lead to an unreliable operation. This issue could be resolved if the oscillator network were able to be formed from a single oscillator. Here, we performed numerical simulations and theoretical analyses on an associative memory operation that uses a virtual oscillator network based on a spin-torque oscillator. The virtual network combines the concept of coupled oscillators with that of feedforward neural networks. Numerical experiments demonstrate successful associations of $60$-pixel patterns with various memorized patterns. Moreover, the origin of the associative memory is shown to be forced synchronization driven by feedforward input, where phase differences among oscillators are fixed and correspond to the colors of the pixels in the pattern.Comment: 15 pages, 4 figure

Input-driven chaotic dynamics in vortex spin-torque oscillator

A new research topic in spintronics relating to the operation principles of brain-inspired computing is input-driven magnetization dynamics in nanomagnet. In this paper, the magnetization dynamics in a vortex spin-torque oscillator (STO) driven by a series of random magnetic field are studied through a numerical simulation of the Thiele equation. It is found that input-driven synchronization occurs in the weak perturbation limit, as found recently. As well, chaotic behavior is newly found to occur in the vortex core dynamics for a wide range of parameters, where synchronized behavior is disrupted by an intermittency. Ordered and chaotic dynamical phases are examined by evaluating the Lyapunov exponent. The relation between the dynamical phase and the computational capability of physical reservoir computing is also studied.Comment: 11 pages, 4 figure

New possibilities to utilize food as a theme in a social studies lesson: From educating wise “consumer” to educating “human being” who pursues mutual agreement in a society

Many Japanese social studies teachers have utilized food as a theme in their lessons because of its student-friendly and abundant-narrative characteristics. However, there was no systemic research on why and how teachers used food as a theme in their lessons, so the value of food in social studies has not yet been clearly revealed. This study aims at reviewing social studies research that dealt with food as a theme and discovering new possibilities of food in social studies. For the aim, we collected the research that dealt with food from the three major Japanese social studies journals. After finding the similarities and differences of the research, we categorized it into four types: "Inquiring concepts and theories," "Understanding people's effort," "Analysing values," and "Regenerating one’s own region." Each type had its own positive educational vision; however, it tended to focus on an individual, instead of a society or community. In other words, food was utilized as a theme to educate an individual, wise "consumer," instead of a "human being" who could pursue a mutual agreement with others. Considering educating democratic citizens in social studies, we need to expand our usage of food from "I-focused" approach to "We-focused" approach

Surgical intervention for anomalous origin of the left coronary artery from the pulmonary artery: The Tokyo experience

AbstractBackground: Few studies after surgical repair of the anomalous origin of the left coronary artery have reported the importance of the mitral annuloplasty or the long-term results. Methods: Between January 1982 and March 2000, 29 patients with anomalous origin underwent surgical intervention at our institution (direct aortic reimplantation in 19 and Takeuchi procedure in 10). Age at the time of operation ranged from 2 months to 24 years (median, 29.3 months), and 9 patients were infants. Twenty-four patients had varying degrees of mitral incompetence. Simultaneous mitral annuloplasty at the anterolateral commissure was performed in all 24 patients with incompetence. Results: There were 2 hospital deaths among the infants, and no late deaths. Mean follow-up was 100 ± 57 months, and the actuarial survival was 93.1% at 10 years (70% confidence limits, 87-99). Cardiothoracic ratio at discharge was not decreasing significantly (P =.35); however, this value 5 years after the operation showed the significant decrease (P =.003) versus preoperative value. Preoperative mitral incompetence decreased in all but one of the operative survivors with mitral annuloplasty at the last follow-up. The left ventricular fractional shortening z-score was not normalized at discharge but was normalized in the late period. Conclusion: These data demonstrate that impaired left ventricular function normalized in the long term (even if it was below normal immediately after operation) after 2-coronary repair. We recommend that the simultaneous mitral annuloplasty should be performed at the time of operation for patients who have mitral incompetence with anomalous origin of the left coronary artery. (J Thorac Cardiovasc Surg 2001;121:792-7