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Mathematical Reinforcement to the Minibatch of Deep Learning

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Advances in Pure Mathematics 2018年第3期8卷 307-320页

作者： Kazuyuki Fujii International College of Arts and Sciences Yokohama City University Yokohama Japan

We elucidate a practical method in Deep Learning called the minibatch which is very useful to avoid local minima. The mathematical structure of this method is, however, a bit obscure. We emphasize that a certain condition, which is not explicitly stated in ordinary expositions, is essential for the minibatch method. We present a comprehensive description Deep Learning for non-experts with the mathematical reinforcement.

关键词： Deep Learning Minibatch Error (Loss) Function Local Minima

Least Squares Method from the View Point of Deep Learning

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Advances in Pure Mathematics 2018年第5期8卷 485-493页

作者： Kazuyuki Fujii International College of Arts and Sciences Yokohama City University Yokohama Japan Department of Mathematical Sciences Shibaura Institute of Technology Saitama Japan

The least squares method is one of the most fundamental methods in Statistics to estimate correlations among various data. On the other hand, Deep Learning is the heart of Artificial Intelligence and it is a learning method based on the least squares. In this paper we reconsider the least squares method from the view point of Deep Learning and we carry out the computation thoroughly for the gradient descent sequence in a very simple setting. Depending on the values of the learning rate, an essential parameter of Deep Learning, the least squares methods of Statistics and Deep Learning reveal an interesting difference.

关键词： Least Squares Method Statistics Deep Learning Learning Rate Linear Algebra

Introduction to the Rotating Wave Approximation (RWA): Two Coherent Oscillations

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Journal of Modern Physics 2017年第12期8卷 2042-2058页

作者： Kazuyuki Fujii International College of Arts and Sciences Yokohama City University Yokohama Japan

In this note, I introduce a mysterious approximation called the rotating wave approximation (RWA) to undergraduates or non-experts who are interested in both Mathematics and Quantum Optics. In Quantum Optics, it plays a very important role in order to obtain an analytic approximate solution of some SchrÖdinger equation, while it is curious from the mathematical point of view. I explain it carefully with two coherent oscillations for them and expect that they will overcome the problem in the near future.

关键词： Quantum Optics Rabi Model Rotating Wave Approximation Coherent Oscillation

An Algebraic Proof of the Associative Law of Elliptic Curves

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Advances in Pure Mathematics 2017年第12期7卷 649-659页

作者： Kazuyuki Fujii Hiroshi Oike International College of Arts and Sciences Yokohama City University Yokohama Japan Takado Yamagata Japan

In this paper we revisit the addition of elliptic curves and give an algebraic proof to the associative law by use of MATHEMATICA. The existing proofs of the associative law are rather complicated and hard to understand for beginners. An ‘‘elementary” proof to it based on algebra has not been given as far as we know. Undergraduates or non-experts can master the addition of elliptic curves through this paper. After mastering it they should challenge the elliptic curve cryptography.

关键词： Elliptic Curve Addition Associative Law MATHEMATICA Elliptic Curve Cryptography

Gastric linitis plastica with autoimmune pancreatitis diagnosed by an endoscopic ultrasonography-guided fine-needle biopsy: A case report

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World Journal of Clinical Cases 2022年第31期10卷 11607-11616页

作者： Ryosuke Sato kazuyuki Matsumoto Hiromitsu Kanzaki Akihiro Matsumi Kazuya Miyamoto Kosaku Morimoto Hiroyuki Terasawa Yuki fujii Tatsuhiro Yamazaki Daisuke Uchida Koichiro Tsutsumi Shigeru Horiguchi Hironari Kato Gastroenterology and Hepatology Okayama University HospitalOkayama 700-8558Japan

BACKGROUND Gastric linitis plastica(GLP)is a subset of gastric cancer with a poor prognosis.It is difficult to obtain a definitive diagnosis by endoscopic mucosal biopsies,and the usefulness of an endoscopic ultrasonography-guided fine-needle biopsy(EUSFNB)for GLP has been recently reported.Meanwhile,autoimmune diseases are occasionally known to coexist with malignant tumors as paraneoplastic syndrome.We herein report the usefulness of an EUS-FNB for detecting GLP and the possibility of paraneoplastic syndrome coexisting with GLP.CASE SUMMARY An 81-year-old man was admitted to our hospital for a 1-mo history of epigastric pain that increased after eating.His laboratory data revealed high levels of serum carbohydrate antigen 19-9 and immunoglobulin-G4.Endoscopic examinations showed giant gastric folds and reddish mucosa;however,no epithelial changes were observed.The gastric lumen was not distensible by air inflation,suggesting GLP.Computed tomography showed the thickened gastric wall,the diffuse enlargement of the pancreas,and the peripancreatic rim,which suggested autoimmune pancreatitis(AIP)coexisting with GLP.Because the pathological findings of the endoscopic biopsy showed no malignancy,he underwent an EUSFNB and was diagnosed with GLP.He received chemotherapy for unresectable gastric cancer due to peritoneal metastasis,after which both the gastric wall thickening and diffuse enlargement of the pancreas were improved.CONCLUSION An EUS-FNB for GLP with a negative endoscopic biopsy is useful,and AIP may develop as a paraneoplastic syndrome.

关键词： Endoscopic ultrasound-guided fine needle aspiration Linitis plastica Autoimmune pancreatitis Paraneoplastic syndromes Case report

A Proposal of Reliable Control Plane Establishment Method for Ring Networks

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A Proposal of Reliable Control Plane Establishment Method fo...

Mobility-Reduction-Free Low-Distortion OTA using Backgate-Bias Technique

2005'第四届光互联网国际学术会议

作者： Shoichiro Seno Teruko fujii Eiichi Horiuchi Motofumi Tanabe kazuyuki Kashima Yoshimasa Baba Tetsuo Ideguchi Information Technology R＆D Center Mitsubishi Electric CorporationKamakuraKanagawa247-8501 Japan Information Technology R＆D Center Mitsubishi Electric CorporationKamakuraKanagawa247-8501 Japan Information Technology R＆D Center Mitsubishi Electric CorporationKamakuraKanagawa247-8501 Japan Information Technology R＆D Center Mitsubishi Electric CorporationKamakuraKanagawa247-8501 Japan Information Technology R＆D Center Mitsubishi Electric CorporationKamakuraKanagawa247-8501 Japan Information Technology R＆D Center Mitsubishi Electric CorporationKamakuraKanagawa247-8501 Japan Faculty of Information Science and Technology Aichi Prefectural UniversityNagakute-choAichi-gunAichi480-1198 Japan

＜正＞In the next generation photonic networks controlled by the GMPLS （Generalized Multi-Protocol Label Switching） protocols, reliability of the control plane is a mandate requirement. This paper discusses requirements of a control plane over a ring network and examines several schemes to support it, considering failure recovery and easiness of administration. It also proposes a simple method to establish the control plane over a ring network based upon VLAN （Virtual LAN） technology.

关键词： Control Plane GMPLS Optical Networks VLAN

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Mobility-Reduction-Free Low-Distortion OTA using Backgate-Bi...

Integrating the effect of abutments in estimating the average vertical stress of elastic hard rock pillars by combining numerical modelling and artificial neural networks

Electronic Communication Systems--The 2000 IEEE Asia-Pacific Conference on Circuits and Systems

作者： Takahide Sato Mamoru Nakamura Shigetaka Takagi kazuyuki Wada Nobuo fujii Tokyo Institute of Technology 2-12-1 O-okayama Meguro-kuTokyo 152-8552Japan

＜正＞This paper proposes a low-distortion CMOS operational transconductance amplifier（OTA） based on backgate-bias technique especially for an OTA using four MOSFET’s operating in the non-saturation region as a voltage controlled current source（VCCS）.In the VCCS two input signals are applied to two drain terminals of the four MOSFET’s respectively and their gate-to-source voltages are kept constant. Therefore the VCCS is free from mobility reduction. To make backgate-to-source voltages of two MOSFET’s in the VCCS equal to DC shift of input signals will reduce output current distortion of the OTA drastically.In addition to these features the proposed OTA is free from body effect even when it is realized by single well process.Simulation results confirm the theory and the effectiveness of the proposed method.

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Underground Space 2023年第6期13卷 121-135页

作者： Nevaid Dzimunya Yoshiaki fujii Youhei Kawamura Faculty of Engineering Hokkaido UniversitySapporo N13W8Japan

Estimating average vertical pillar stresses is a critical step in designing room-and-pillar mines.Several analytical methods can be used to estimate the vertical stresses acting on the pillars.However,the present analytical methods fail to adequately account for the influence of abutments on the distribution of vertical stresses,especially when applied to narrow panel widths and pillar layouts comprising evenly spaced barriers.In this study,a multi-layer perceptron neural network(MLPNN)was applied to predict the vertical loads of regular pillars more accurately.Hundreds of room-and-pillar mine layouts were modeled using a displacement discontinuity method(DDM),and a database of 2355 sampled pillar cases was compiled.The MLPNN was trained based on this database,and its prediction capabilities were further validated using simulations by a finite difference code(i.e.,FLAC3D).The model predictions and the FLAC3D simulations reasonably agreed with a regression coefficient of 0.99.The model was also adapted for mine cases with evenly spaced barrier pillars,and its application to a real case study mine has shown to provide accurate pillar stress estimations;hence,this model is suitable for practical use at mines.Even though the MLPNN model cannot be applied universally to all mine situations,it seems as a significant improvement over existing analytical techniques in terms of accounting for the influence of abutments on pillar stresses.

关键词： Pillar stress Abutments Multi-layer perceptron neural network Numerical simulation Room-and-pillar mine

An MAPK Pathway in Papilla Cells for Successful Pollination in Arabidopsis

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Molecular Plant 2020年第11期13卷 1539-1541页

作者： Yoshinobu Kato Sota fujii Laboratory of Bioorganic Chemistry Graduate School of Agriculture and Life SciencesThe University of Tokyo1-1-1 YayoiBunkyo-kuTokyo 113-8657Japan

During the pollination process in Brassicaceae,pollen and papilla cells at the tip of the pistil communicate with each other and trigger various physiological responses such as pollen hydration/germination and self-incompatibility.It was thought that papilla cells drastically change their cellular environment to conduct water and calciumion release and to provide an energy source for pollen germination and pollen-tube elongation(Doucet et al.,2016).

关键词： Arabidopsis hydration release