• KIPS Transactions on Software and Data Engineering
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• v.10 no.11
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• pp.483-490
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• 2021

In order to learn an existing song and create a new song using an artificial neural network, it is necessary to convert the song into numerical data that the neural network can recognize as a preprocessing process, and one-hot encoding has been used until now. In this paper, we proposed a note embedding method using notes as a basic unit and a bar embedding method that uses the bar as the basic unit, and compared the performance with the existing one-hot encoding. The performance comparison was conducted based on quantitative evaluation to determine which method produced a song more similar to the song composed by the composer, and quantitative evaluation methods used in the field of natural language processing were used as the evaluation method. As a result of the evaluation, the song created with bar embedding was the best, followed by note embedding. This is significant in that the note embedding and bar embedding proposed in this paper create a song that is more similar to the song composed by the composer than the existing one-hot encoding.

• East Asian mathematical journal
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• v.39 no.5
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• pp.515-522
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• 2023

In the case that the set of sorts is countable, we will prove that any sorted profinite group has the unique SEP-cover using the notion of prime model in model theory.

• Bulletin of the Korean Mathematical Society
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• v.39 no.2
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• pp.289-297
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• 2002

It was shown by L. Polterovich ([3]) that if L is a totally real submanifold of a symplectic manifold $(M,\omega)$ and L is parallelizable then L is normal. So we try to find an answer to the question of whether there is a compatible almost complex structure J on the symplectic vector bundle $TM$\mid$_{L}$ such that $TL{\cap}JTL=0$ assuming L is normal and parallelizable. Although we could not reach an answer, we observed that the claim holds at the vector space level. And related to the question, we showed that for a symplectic vector bundle $(M,\omega)$ of rank 2n and $E=E_1{\bigoplus}E_2$, where $E=E_1,E_2$are Lagrangian subbundles of E, there is an almost complex structure J on E compatible with ${\omega}$ and $JE_1=E_2$. And finally we provide a necessary and sufficient condition for a given embedding into a symplectic manifold to be normal.

• East Asian mathematical journal
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• v.36 no.3
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• pp.377-387
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• 2020

In this paper, we provide detailed proof of the Sawyer type characterization of the two weight estimate for the dyadic paraproduct. Although the dyadic paraproduct is known to be a well localized operators and the testing conditions obtained from checking boundedness of the given localized operator on a collection of test functions are provided by many authors. The main purpose of this paper is to present the necessary and sufficient conditions on the weights to ensure boundedness of the dyadic paraproduct directly.

• Communications of the Korean Mathematical Society
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• v.15 no.3
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• pp.511-519
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• 2000

If G is a strict generalized orthomodular lattice and H={I｜I=[0, $\chi$, $\chi$$\in$G}, then H is prime ideal of the Janowitz's hull J(G) of G. If f is the janowitz's embedding, then the set of all commutatiors of f(G) equals the set of all commutators of the Janowitz's hull J(G) of G. Let L be an OML. Then L J(G) for a strict GOML G if and only if ther exists a proper nonprincipal prime ideal G in L.

• Journal of Information Processing Systems
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• v.13 no.5
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• pp.1382-1396
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• 2017

In this paper, we analyze a recently proposed semi-fragile watermarking scheme based on local binary pattern (LBP) operators, and note that it has a fundamental flaw in the design. In this work, a binary watermark is embedded into image blocks by modifying the neighborhood pixels according to the LBP pattern. However, different image blocks might have the same LBP pattern, which can lead to false detection in watermark extraction process. In other words, one can modify the host image intentionally without affecting its watermark message. In addition, there is no encryption process before watermark embedding, which brings another potential security problem. To illustrate its weakness, two special copy-paste attacks are proposed in this paper, and several experiments are conducted to prove the effectiveness of these attacks. To solve these problems, an improved semi-fragile watermarking based on LBP operators is presented. In watermark embedding process, the central pixel value of each block is taken into account and Arnold transform is adopted to guarantee the security of watermark. Experimental results show that the improved watermarking scheme can overcome the above defects and locate the tampered region effectively.

• Communications of the Korean Mathematical Society
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• v.34 no.1
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• pp.279-286
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• 2019

Complex Grassmann manifolds $G_{n,k}$ are a generalization of complex projective spaces and have many important features some of which are captured by the $Pl{\ddot{u}}cker$ embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$ where $N=\(^n_k\)$. The problem of existence of cross sections of fibrations can be studied using the Gottlieb group. In a more generalized context one can use the relative evaluation subgroup of a map to describe the cohomology of smooth fiber bundles with fiber the (complex) Grassmann manifold $G_{n,k}$. Our interest lies in making use of techniques of rational homotopy theory to address problems and questions involving applications of Gottlieb groups in general. In this paper, we construct the Sullivan minimal model of the (complex) Grassmann manifold $G_{n,k}$ for $2{\leq}k<n$, and we compute the rational evaluation subgroup of the embedding $f:G_{n,k}{\rightarrow}{\mathbb{C}}P^{N-1}$. We show that, for the Sullivan model ${\phi}:A{\rightarrow}B$, where A and B are the Sullivan minimal models of ${\mathbb{C}}P^{N-1}$ and $G_{n,k}$ respectively, the evaluation subgroup $G_n(A,B;{\phi})$ of ${\phi}$ is generated by a single element and the relative evaluation subgroup $G^{rel}_n(A,B;{\phi})$ is zero. The triviality of the relative evaluation subgroup has its application in studying fibrations with fibre the (complex) Grassmann manifold.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.771-790
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• 1997

By using the method of equivalence of E. Cartan we calculate the local scalar invariants for Riemannian 2-maniolds. We define also a notion of local invariants for submanifolds in $R^{n + d}, n \geq 2, d \geq 1$, in terms of the symmetry of the local isometric embedding equations of Riemannian n-manifolds into $R^{n + d}$. We show that the local invariants obtained by the Cartan's method are the intrinsic expressions of the local invariants in our sense in the casees of surfaces in $R^3$.

• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.715-720
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• 2004

Suppose X is a closed subspace of Z = ${({{\Sigma}^{\infty}}_{n=1}Z_{n})}_{p}$ (1 < p < ${\infty}$, dim $Z_{n}$ < ${\infty}$). We investigate an isometrically isomorphic embedding of L(X)/K(X) into L(X, Z)/K(X, Z), where L(X, Z) (resp. L(X)) is the space of the bounded linear operators from X to Z (resp. from X to X) and K(X, Z) (resp. K(X)) is the space of the compact linear operators from X to Z (resp. from X to X).

• The Journal of the Acoustical Society of Korea
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• v.15 no.1
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• pp.54-60
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• 1996

In most pattern recognition and image understanding applications, images are degraded by noise and other distortions. Therefore, it is more relevant to decide how similar two objects are rather than to decide whether the two are exactly the same. In this paper, we propose a method for recognizing degraded symbols using a distance measure between two graphs representing the symbols. a symbol is represented as a graph consisting of nodes and edges based on the run graph concept. The graph is then transformed into a reference model graph with production rule containing the embedding transform. The symbols are recognized by using the distance measure which is estimated by using the number of production rules used and the structural homomorphism between a transformed graph and a model graph. the proposed approach is applies to the recognition of non-note musical symbols and the result are given.