Mei Kobayashi - Academia.edu (original) (raw)

Papers by Mei Kobayashi

Research paper thumbnail of Eigenvalues of discontinuous Sturm-Liouville problems with symmetric potentials

Computers & mathematics with applications, 1989

Alam'aet-In this paper we consider three examples of discontinuous Sturm-Liouville problems with ... more Alam'aet-In this paper we consider three examples of discontinuous Sturm-Liouville problems with symmetric potentials. The ¢igcnvalues of the systems were determined using the classical fourth order Runge-Kutta method. These eigenvalues are used to reconstruct the potential function using an algorithm presented in Kobayashi [1, 2]. The results of our numerical experiments are discussed.

Research paper thumbnail of An algorithm for discontinuous inverse Sturm-Liouville problems with symmetric potentials

Computers & Mathematics with Applications, 1989

Almtriet-In this paper we consider two Sturm-Liouville problems with symmetric potentials and sym... more Almtriet-In this paper we consider two Sturm-Liouville problems with symmetric potentials and symmetric discontinuities satisfying symmetric boundary and jump conditions. In the first section we derive a simple expression for the difference of potentials when only a finite number of eigenvalues differ. In the second section this result is used to construct an algorithm for solving the discontinuous inverse Sturm-Liouville problem numerically.

Research paper thumbnail of Discontinuous Inverse Sturm-Liouville Problems with Symmetric Potentials

In this paper we study the Inverse Sturm-Liouville problem on a finite interval with a symmetric ... more In this paper we study the Inverse Sturm-Liouville problem on a finite interval with a symmetric potential function with two interior discontinuities. In the introductory chapter we survey previous results on the existence and uniqueness of solutions to inverse Sturm-Liouville problems and discuss earlier numerical methods. In chapter 1 we present a uniqueness proof for the inverse Sturm-Liouville problem on a finite interval with a symmetric potential having two interior jump discontinuities. In chapter 2 we show that any absolutely continuous function can be expanded in terms of the eigenfunctions of a Sturm-Liouville problem with two discontinuities. In chapter 3 we consider two Sturm-Liouville problems with different symmetric potentials with two discontinuities satisfying symmetric boundary conditions and symmetric jump conditions. We find that if only a finite number of eigenvalues differ then a simple expression for the difference of the potentials can be established. In addition, the locations of the discontinuities are uniquely determined. Finally, in chapter 4 we derive an algorithm for solving the discontinuous inverse Sturm-Liouville problem numerically and present the results of numerical experiments.

Research paper thumbnail of An algorithm for discontinuous inverse Sturm-Liouville problems with symmetric potentials

Computers & mathematics with applications, 1989

Almtriet-In this paper we consider two Sturm-Liouville problems with symmetric potentials and sym... more Almtriet-In this paper we consider two Sturm-Liouville problems with symmetric potentials and symmetric discontinuities satisfying symmetric boundary and jump conditions. In the first section we derive a simple expression for the difference of potentials when only a finite number of eigenvalues differ. In the second section this result is used to construct an algorithm for solving the discontinuous inverse Sturm-Liouville problem numerically.

Research paper thumbnail of 大規模デ-タベ-スの主要クラスタ・二次クラスタの探索 (微分方程式の数値解法と線形計算)

We present anovel search and cluster mining system based on vector space modeling that addresses ... more We present anovel search and cluster mining system based on vector space modeling that addresses some issues that have been neglected by conventional systems for database analysis. Novel features of our search and cluster mining engine are: discovery of both major and minor clusters, accommodation of cluster overlap, automatic labeling of clusters based on their document contents, and advanced visualization of search and mining results. Implementation studies using adata set with over 100,000 news articles demonstrate the effectiveness of our system.

Research paper thumbnail of Webコミュニティマイニング

Research paper thumbnail of Book review: Math girls

Research paper thumbnail of A Direct Inversion of Chemical Kinetics Problems(The State of the Art of Scientific Computing and Its Prospect II)

Research paper thumbnail of Wavelets and Digitized Images

Research paper thumbnail of Cultural Differences in Social Media: Trust and Authority

Roles, Trust, and Reputation in Social Media Knowledge Markets, 2014

Sociologists and psychologists study how humans evaluate trust and reputation of people, document... more Sociologists and psychologists study how humans evaluate trust and reputation of people, documents, institutions, etc. in the real-world. Their studies of interactions between people from different cultures have contributed to the appreciation of diverse viewpoints. While the sudden emergence and proliferation of the internet has altered the landscape of relationships and social interactions, there has not been sufficient time to revisit and study cultural and demographic differences in perceptions of trust and reputation in the cyberspace domain on a grand scale. Studies that have been conducted to-date have been limited in scope with respect to number of countries, types of behavior, and size of data sets. This chapter reviews studies on cultural differences in behavior in cyberspace, with particular attention to the concepts of expertise, quality, and trust. It discusses applications that can benefit from these studies, such as: targeted marketing, crowd sourcing applications, and enhancement of security systems. It concludes with a discussion on open data and how Wikipedia data provides an opportunity to examine behavioral differences in different communities.

Research paper thumbnail of Wavelets and their Applications to Image Processing : dedicated to my father for his 60th birthday(Numerical Analysis and their Algorithms)

Research paper thumbnail of An Information Retrieval System using a Principal Component Analysis

Research paper thumbnail of 4. Wavelet Analysis for a Text-to-Speech (TTS) System

Wavelets and Their Applications: Case Studies, 1998

Research paper thumbnail of Wavelet Analysis: Applications in Industry

Wavelet Analysis and Multiresolution Methods

Research paper thumbnail of Data Stream Mining: selected tools & algorithms (Numerical Analysis and New Information Technology)

Research paper thumbnail of Exploring overlapping clusters using dynamic re-scaling and sampling

Knowledge and Information Systems, 2006

Until recently, the aim of most text-mining work has been to understand major topics and clusters... more Until recently, the aim of most text-mining work has been to understand major topics and clusters. Minor topics and clusters have been relatively neglected even though they may represent important information on rare events. We present a novel method for exploring overlapping clusters of heterogeneous sizes, which is based on vector space modeling, covariance matrix analysis, random sampling, and dynamic

Research paper thumbnail of Speech synthesis using glottal closure instants determined from adaptively-threshold wavelet transforms

The Journal of the Acoustical Society of America, 1998

A speech synthesis system making use of a pitch-synchronous waveform overlap method to realize st... more A speech synthesis system making use of a pitch-synchronous waveform overlap method to realize stable speech synthesis processing in which pitch shaking is negligible. The present invention is characterized in that glottal closure instants are used as reference points (pitch marks) for overlapping. Since the glottal closure instants can be extracted stably and accurately by using dyadic Wavelet conversion, speech in which pitch shaking is negligible and rumbling sounds are minimized can be synthesized stably. In addition, more flexible waveform separation becomes possible by setting the reference point for overlapping and the reference point for waveform separation to different positions. The extraction of glottal closure instants is performed by searching the local peaks of the dyadic Wavelet conversion, but preferably a threshold value for searching for the local peaks of the dyadic Wavelet conversion is adaptively controlled each time dyadic Wavelet conversion is obtained.

Research paper thumbnail of Matrix computations for information retrieval and major and outlier cluster detection

Journal of Computational and Applied Mathematics, 2002

In this paper we introduce COV, a novel information retrieval (IR) algorithm for massive database... more In this paper we introduce COV, a novel information retrieval (IR) algorithm for massive databases based on vector space modeling and spectral analysis of the covariance matrix, for the document vectors, to reduce the scale of the problem. Since the dimension of the covariance matrix depends on the attribute space and is independent of the number of documents, COV can be applied to databases that are too massive for methods based on the singular value decomposition of the document-attribute matrix, such as latent semantic indexing (LSI). In addition to improved scalability, theoretical considerations indicate that results from our algorithm tend to be more accurate than those from LSI, particularly in detecting subtle differences in document vectors. We demonstrate the power and accuracy of COV through an important topic in data mining, known as outlier cluster detection. We propose two new algorithms for detecting major and outlier clusters in databases—the first is based on LSI, and the second on COV. Our implementation studies indicate that our cluster detection algorithms outperform the basic LSI and COV algorithm in detecting outlier clusters.

Research paper thumbnail of Estimation of singular values of very large matrices using random sampling

Computers & Mathematics with Applications, 2001

Research paper thumbnail of Efficient estimation of singular values for searching very large and dynamic web databases

ABSTRACT The singular value decomposition (SVD) has enjoyed a long and rich history. Recently, it... more ABSTRACT The singular value decomposition (SVD) has enjoyed a long and rich history. Recently, it is being used in data mining applications and by search engines to rank documents in very large databases, including the Web. The dimensions of matrices which appear in these applications are becoming so large that classical algorithms for computing the SVD cannot always be used. We present a new method to determine the largest 10%{25% of the singular values of matrices which are so enormous that use of standard algorithms and computational packages will strain computational resources available to most users. In our method, rows from the matrix are randomly selected, and a smaller matrix is constructed from the selected rows. Next, we compute the singular values of the smaller matrix. This process of random sampling and computing singular values is repeated as many times as necessary (usually a few hundred times) to generate a set of training data for neural net analysis. We demonstrate t...

Research paper thumbnail of Eigenvalues of discontinuous Sturm-Liouville problems with symmetric potentials

Computers & mathematics with applications, 1989

Alam'aet-In this paper we consider three examples of discontinuous Sturm-Liouville problems with ... more Alam'aet-In this paper we consider three examples of discontinuous Sturm-Liouville problems with symmetric potentials. The ¢igcnvalues of the systems were determined using the classical fourth order Runge-Kutta method. These eigenvalues are used to reconstruct the potential function using an algorithm presented in Kobayashi [1, 2]. The results of our numerical experiments are discussed.

Research paper thumbnail of An algorithm for discontinuous inverse Sturm-Liouville problems with symmetric potentials

Computers & Mathematics with Applications, 1989

Almtriet-In this paper we consider two Sturm-Liouville problems with symmetric potentials and sym... more Almtriet-In this paper we consider two Sturm-Liouville problems with symmetric potentials and symmetric discontinuities satisfying symmetric boundary and jump conditions. In the first section we derive a simple expression for the difference of potentials when only a finite number of eigenvalues differ. In the second section this result is used to construct an algorithm for solving the discontinuous inverse Sturm-Liouville problem numerically.

Research paper thumbnail of Discontinuous Inverse Sturm-Liouville Problems with Symmetric Potentials

In this paper we study the Inverse Sturm-Liouville problem on a finite interval with a symmetric ... more In this paper we study the Inverse Sturm-Liouville problem on a finite interval with a symmetric potential function with two interior discontinuities. In the introductory chapter we survey previous results on the existence and uniqueness of solutions to inverse Sturm-Liouville problems and discuss earlier numerical methods. In chapter 1 we present a uniqueness proof for the inverse Sturm-Liouville problem on a finite interval with a symmetric potential having two interior jump discontinuities. In chapter 2 we show that any absolutely continuous function can be expanded in terms of the eigenfunctions of a Sturm-Liouville problem with two discontinuities. In chapter 3 we consider two Sturm-Liouville problems with different symmetric potentials with two discontinuities satisfying symmetric boundary conditions and symmetric jump conditions. We find that if only a finite number of eigenvalues differ then a simple expression for the difference of the potentials can be established. In addition, the locations of the discontinuities are uniquely determined. Finally, in chapter 4 we derive an algorithm for solving the discontinuous inverse Sturm-Liouville problem numerically and present the results of numerical experiments.

Research paper thumbnail of An algorithm for discontinuous inverse Sturm-Liouville problems with symmetric potentials

Computers & mathematics with applications, 1989

Almtriet-In this paper we consider two Sturm-Liouville problems with symmetric potentials and sym... more Almtriet-In this paper we consider two Sturm-Liouville problems with symmetric potentials and symmetric discontinuities satisfying symmetric boundary and jump conditions. In the first section we derive a simple expression for the difference of potentials when only a finite number of eigenvalues differ. In the second section this result is used to construct an algorithm for solving the discontinuous inverse Sturm-Liouville problem numerically.

Research paper thumbnail of 大規模デ-タベ-スの主要クラスタ・二次クラスタの探索 (微分方程式の数値解法と線形計算)

We present anovel search and cluster mining system based on vector space modeling that addresses ... more We present anovel search and cluster mining system based on vector space modeling that addresses some issues that have been neglected by conventional systems for database analysis. Novel features of our search and cluster mining engine are: discovery of both major and minor clusters, accommodation of cluster overlap, automatic labeling of clusters based on their document contents, and advanced visualization of search and mining results. Implementation studies using adata set with over 100,000 news articles demonstrate the effectiveness of our system.

Research paper thumbnail of Webコミュニティマイニング

Research paper thumbnail of Book review: Math girls

Research paper thumbnail of A Direct Inversion of Chemical Kinetics Problems(The State of the Art of Scientific Computing and Its Prospect II)

Research paper thumbnail of Wavelets and Digitized Images

Research paper thumbnail of Cultural Differences in Social Media: Trust and Authority

Roles, Trust, and Reputation in Social Media Knowledge Markets, 2014

Sociologists and psychologists study how humans evaluate trust and reputation of people, document... more Sociologists and psychologists study how humans evaluate trust and reputation of people, documents, institutions, etc. in the real-world. Their studies of interactions between people from different cultures have contributed to the appreciation of diverse viewpoints. While the sudden emergence and proliferation of the internet has altered the landscape of relationships and social interactions, there has not been sufficient time to revisit and study cultural and demographic differences in perceptions of trust and reputation in the cyberspace domain on a grand scale. Studies that have been conducted to-date have been limited in scope with respect to number of countries, types of behavior, and size of data sets. This chapter reviews studies on cultural differences in behavior in cyberspace, with particular attention to the concepts of expertise, quality, and trust. It discusses applications that can benefit from these studies, such as: targeted marketing, crowd sourcing applications, and enhancement of security systems. It concludes with a discussion on open data and how Wikipedia data provides an opportunity to examine behavioral differences in different communities.

Research paper thumbnail of Wavelets and their Applications to Image Processing : dedicated to my father for his 60th birthday(Numerical Analysis and their Algorithms)

Research paper thumbnail of An Information Retrieval System using a Principal Component Analysis

Research paper thumbnail of 4. Wavelet Analysis for a Text-to-Speech (TTS) System

Wavelets and Their Applications: Case Studies, 1998

Research paper thumbnail of Wavelet Analysis: Applications in Industry

Wavelet Analysis and Multiresolution Methods

Research paper thumbnail of Data Stream Mining: selected tools & algorithms (Numerical Analysis and New Information Technology)

Research paper thumbnail of Exploring overlapping clusters using dynamic re-scaling and sampling

Knowledge and Information Systems, 2006

Until recently, the aim of most text-mining work has been to understand major topics and clusters... more Until recently, the aim of most text-mining work has been to understand major topics and clusters. Minor topics and clusters have been relatively neglected even though they may represent important information on rare events. We present a novel method for exploring overlapping clusters of heterogeneous sizes, which is based on vector space modeling, covariance matrix analysis, random sampling, and dynamic

Research paper thumbnail of Speech synthesis using glottal closure instants determined from adaptively-threshold wavelet transforms

The Journal of the Acoustical Society of America, 1998

A speech synthesis system making use of a pitch-synchronous waveform overlap method to realize st... more A speech synthesis system making use of a pitch-synchronous waveform overlap method to realize stable speech synthesis processing in which pitch shaking is negligible. The present invention is characterized in that glottal closure instants are used as reference points (pitch marks) for overlapping. Since the glottal closure instants can be extracted stably and accurately by using dyadic Wavelet conversion, speech in which pitch shaking is negligible and rumbling sounds are minimized can be synthesized stably. In addition, more flexible waveform separation becomes possible by setting the reference point for overlapping and the reference point for waveform separation to different positions. The extraction of glottal closure instants is performed by searching the local peaks of the dyadic Wavelet conversion, but preferably a threshold value for searching for the local peaks of the dyadic Wavelet conversion is adaptively controlled each time dyadic Wavelet conversion is obtained.

Research paper thumbnail of Matrix computations for information retrieval and major and outlier cluster detection

Journal of Computational and Applied Mathematics, 2002

In this paper we introduce COV, a novel information retrieval (IR) algorithm for massive database... more In this paper we introduce COV, a novel information retrieval (IR) algorithm for massive databases based on vector space modeling and spectral analysis of the covariance matrix, for the document vectors, to reduce the scale of the problem. Since the dimension of the covariance matrix depends on the attribute space and is independent of the number of documents, COV can be applied to databases that are too massive for methods based on the singular value decomposition of the document-attribute matrix, such as latent semantic indexing (LSI). In addition to improved scalability, theoretical considerations indicate that results from our algorithm tend to be more accurate than those from LSI, particularly in detecting subtle differences in document vectors. We demonstrate the power and accuracy of COV through an important topic in data mining, known as outlier cluster detection. We propose two new algorithms for detecting major and outlier clusters in databases—the first is based on LSI, and the second on COV. Our implementation studies indicate that our cluster detection algorithms outperform the basic LSI and COV algorithm in detecting outlier clusters.

Research paper thumbnail of Estimation of singular values of very large matrices using random sampling

Computers & Mathematics with Applications, 2001

Research paper thumbnail of Efficient estimation of singular values for searching very large and dynamic web databases

ABSTRACT The singular value decomposition (SVD) has enjoyed a long and rich history. Recently, it... more ABSTRACT The singular value decomposition (SVD) has enjoyed a long and rich history. Recently, it is being used in data mining applications and by search engines to rank documents in very large databases, including the Web. The dimensions of matrices which appear in these applications are becoming so large that classical algorithms for computing the SVD cannot always be used. We present a new method to determine the largest 10%{25% of the singular values of matrices which are so enormous that use of standard algorithms and computational packages will strain computational resources available to most users. In our method, rows from the matrix are randomly selected, and a smaller matrix is constructed from the selected rows. Next, we compute the singular values of the smaller matrix. This process of random sampling and computing singular values is repeated as many times as necessary (usually a few hundred times) to generate a set of training data for neural net analysis. We demonstrate t...