Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression

We investigated the effects of synaptic depression on the macroscopic behavior of stochastic neural networks. Dynamical mean field equations were derived for such networks by taking the average of two stochastic variables: a firing state variable and a synaptic variable. In these equations, their average product is decoupled as the product of averaged them because the two stochastic variables are independent. We proved the independence of these two stochastic variables assuming that the synaptic weight is of the order of 1/N with respect to the number of neurons N. Using these equations, we derived macroscopic steady state equations for a network with uniform connections and a ring attractor network with Mexican hat type connectivity and investigated the stability of the steady state solutions. An oscillatory uniform state was observed in the network with uniform connections due to a Hopf instability. With the ring network, high-frequency perturbations were shown not to affect system stability. Two mechanisms destabilize the inhomogeneous steady state, leading two oscillatory states. A Turing instability leads to a rotating bump state, while a Hopf instability leads to an oscillatory bump state, which was previous unreported. Various oscillatory states take place in a network with synaptic depression depending on the strength of the interneuron connections.Comment: 26 pages, 13 figures. Preliminary results for the present work have been published elsewhere (Y Igarashi et al., 2009. http://www.iop.org/EJ/abstract/1742-6596/197/1/012018

Numerical experiments on tsunami flow depth prediction for clustered areas using regression and machine learning models

Emergency responses during a massive tsunami disaster require information on the flow depth of land for rescue operations. This study aims to predict tsunami flow depth distribution in real time using regression and machine learning. Training data of 3480 earthquake-induced tsunamis in the Nankai Trough were constructed by numerical simulations. Initially, the k-means method was used to discriminate the areas with approximately the same flow depth. The number of clustered areas was 18, and the standard deviation of the flow depth data in a cluster was 0.46 m on average. The objective variables were the mean and standard deviation of the flow depth in the clustered areas. The explanatory variables were the maximum deviation of the water pressure at the seafloor observation points of the DONET observatory. We generated multiple regression equations for a power law using these datasets and the conjugate gradient method. Further, we employed the multilayer perceptron method, a machine learning technique, to evaluate the prediction performance. Both methods accurately predicted the tsunami flow depth calculated by testing 11 earthquake scenarios in the cabinet office of the government of Japan. The RMSE between the predicted and the true (via forward tsunami calculations) values of the mean flow depth ranged from 0.34–1.08 m. In addition to large-scale tsunami prediction systems, prediction methods with a robust and light computational load as used in this study are essential to prepare for unforeseen situations during large-scale earthquakes and tsunami disasters

Maximum tsunami height prediction using pressure gauge data by a Gaussian process at Owase in the Kii Peninsula, Japan

We constructed a model to predict the maximum tsunami height by a Gaussian process (GP) that uses pressure gauge data from the Dense Oceanfloor Network System for Earthquakes and Tsunamis (DONET) in the Nankai trough. We found a greatly improved generalization error of the maximum tsunami height by our prediction model. The error is about one third of that by a previous method, which tends to make larger predictions, especially for large tsunami heights (>10 m). These results indicate that GP enables us to get a more accurate prediction of tsunami height by using pressure gauge data

A nonlinear parametric model based on a power law relationship for predicting the coastal tsunami height

When a subduction-zone earthquake occurs, the tsunami height must be predicted to cope with the damage generated by the tsunami. Therefore, tsunami height prediction methods have been studied using simulation data acquired by large-scale calculations. In this research, we consider the existence of a nonlinear power law relationship between the water pressure gauge data observed by the Dense Oceanfloor Network System for Earthquakes and Tsunamis (DONET) and the coastal tsunami height. Using this relationship, we propose a nonlinear parametric model and conduct a prediction experiment to compare the accuracy of the proposed method with those of previous methods and implement particular improvements to the extrapolation accuracy

中学校音楽における効果的・効率的な箏の授業の手立て ―教育学部と附属中学校連携授業から見る一考察―

中学校で和楽器の授業が必修化されて早10年が過ぎ、授業実践は広がりつつある。しかし実際の現場では、調達可能な楽器数の不足、調絃等の物理的準備の大変さに加え、授業時数が少ないために内容が充実しない等未だに問題が多い。本論は、平成22年度と23年度に教育学部と附属中学校で行った箏の連携授業の実践から、中学校音楽の限られた時数の中でより効果的・効率的な箏の授業を行う手立てを探るものである。連携授業は附属中学校第１・第２学年各４クラスにおいて各２時間行い、学部教員は授業者として、教育学部音楽教育専攻生は授業支援者として参加した。この実践をもとに本稿では、具体的な教材・手立てとして①３人１面での活動の利点、 ②基礎技能習得のための「親指AB練習シート」、③「わらべうた」「名前呼びリレー」「俳句de創作」などの五音音階を用いた創作活動、④琉球民謡「てぃんさぐぬ花」の手立て⑤表現とリンクする鑑賞活動、の５つの視点から述べる。これらを踏まえた考察としては、中学生の「仮面性」に対し、「創作的要素が強い３人一組での活動」が主となる箏アンサンブルでは、箏の有効な「道具性」が見て取れた。同時に「生徒の音楽的創造のプロセス」を評価する指導・支援の在り方も、これらの手立てを有効にする重要な視点であるといえる

Locality Properties of a New Class of Lattice Dirac Operators

A new class of lattice Dirac operators $D$ which satisfy the index theorem have been recently proposed on the basis of the algebraic relation $\gamma_{5}(\gamma_{5}D) + (\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$. Here $k$ stands for a non-negative integer and $k=0$ corresponds to the ordinary Ginsparg-Wilson relation. We analyze the locality properties of Dirac operators which solve the above algebraic relation. We first show that the free fermion operator is analytic in the entire Brillouin zone for a suitable choice of parameters $m_{0}$ and $r$, and there exists a well-defined ``mass gap'' in momentum space, which in turn leads to the exponential decay of the operator in coordinate space for any finite $k$. This mass gap in the free fermion operator suggests that the operator is local for sufficiently weak background gauge fields. We in fact establish a finite locality domain of gauge field strength for $\Gamma_{5}=\gamma_{5}-(a\gamma_{5}D)^{2k+1}$ for any finite $k$, which is sufficient for the cohomological analyses of chiral gauge theory. We also present a crude estimate of the localization length defined by an exponential decay of the Dirac operator, which turns out to be much shorter than the one given by the general Legendre expansion.Comment: Some clarifying comments are added, and a misprint was corrected. Nuclear Physics B(in press