Partially metric association schemes with a multiplicity three

van Dam, Edwin R.,Koolen, Jack H.,Park, Jongyook Elsevier 2018 Journal of combinatorial theory. Series B Vol.130 No.-

<P><B>Abstract</B></P> <P>An association scheme is called partially metric if it has a connected relation whose distance-two relation is also a relation of the scheme. In this paper we determine the symmetric partially metric association schemes with a multiplicity three. Besides the association schemes related to regular complete 4-partite graphs, we obtain the association schemes related to the Platonic solids, the bipartite double scheme of the dodecahedron, and three association schemes that are related to well-known 2-arc-transitive covers of the cube: the Möbius–Kantor graph, the Nauru graph, and the Foster graph F048A. In order to obtain this result, we also determine the symmetric association schemes with a multiplicity three and a connected relation with valency three. Moreover, we construct an infinite family of cubic arc-transitive 2-walk-regular graphs with an eigenvalue with multiplicity three that give rise to non-commutative association schemes with a symmetric relation of valency three and an eigenvalue with multiplicity three.</P>

CLASSIFICATION OF ASSOCIATION SCHEMES WITH 18 AND 19 VERTICES

Hanaki, A.,Miyamoto, I. 한국전산응용수학회 1998 Journal of applied mathematics & informatics Vol.5 No.3

The isomorphism classes of association schemes with 18 and 19 vertices are classified. We obtain 95 isomorphism classes of association schemes with 18 vertices and denote the representatives of the isomorphism classes as subschemes of 7 association schemes. We obtain 7 isomorphism classes of association schemes with 19 vertices and six of them are cyclotomic schemes.

Duality of translation association schemes coming from certain actions

김대산,H. K. Kim 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.2

Translation association schemes are constructed from ac-tions of ¯nite groups on ¯nite abelian groups satisfying certain natural conditions. It is also shown that the mere existence of maps from ¯-nite groups to themselves sending each element in their groups to its `adjoint' entails the self-duality of the constructed association schemes. Many examples of these, including Hamming scheme and sesquilinear forms schemes, are provided. This construction is further generalized to show the duality of the association schemes coming from actions of two ¯nite groups on the same ¯nite abelian group. An example of this is supplied with weak Hamming schemes.

Schemes and Performance Evaluation Criteria of Korean Association of External Quality Assessment (KEQAS) for Improving Laboratory Testing

Kim Sollip,Lee Kyunghoon,Park Hyung-Doo,Lee Yong-Wha,Chun Sail,Min Won-Ki 대한진단검사의학회 2021 Annals of Laboratory Medicine Vol.41 No.2

External quality assessment (EQA) is important for evaluating clinical laboratories and enhancing their testing quality. EQA schemes are variable; thus, it is crucial that the EQA organizers share their experiences to continuously improve the EQA scheme. The Korean Association of External Quality Assessment Service (KEQAS) has been the leading, authorized EQA institute for the standardization and quality management of laboratory testing in Korean medical institutions since 1976. The EQA scheme underwent a major change in 2016, and the number of EQA programs increased significantly since then. The key changes implemented in EQA scheme include a fully computerized assessment to accelerate feedback and unification of the testing and reporting methods. We provide an overview of the EQA schemes and performance evaluation criteria of the KEQAS and suggest directions for achieving the global harmonization of EQA.

프라이버시 보장형 연관성 분석을 위한 동형암호 기반 지지도 계산

박윤수,숙쿤리닌,이문규 한국정보과학회 2024 정보과학회논문지 Vol.51 No.3

Homomorphic encryption is a cryptographic scheme that enables computation on ciphertexts without decryption. Homomorphic encryption is attracting attention as a cryptographic technology that can solve the issue of user privacy invasion in machine learning and cloud services. A representative scheme of homomorphic encryption is the CKKS scheme. CKKS is an approximate homomorphic encryption scheme that supports real and complex number operations. In this paper, we propose a method to efficiently compute support among evaluation metrics of association analysis using CKKS scheme, and a method to compute supports in parallel using matrix multiplication for multiple itemsets. We implemented and evaluated the proposed method to compute supports using the HEaaN library. According to evaluation results, the support value calculated by the proposed method was almost identical to that calculated without encryption, confirming that the proposed method could effectively calculate the support value while protecting user data privacy.

Japan's ODA assistance scheme and Central Asian engagement: Determinants, trends, expectations

Timur Dadabaev 한양대학교 아태지역연구센터 2016 Journal of Eurasian Studies Vol.7 No.1

As demonstrated in this paper, Japan over the years has grown to become the leading ODA provider in Central Asia (CA). ODA has served as a foreign policy tool and as the most significant tool for maintaining cooperation ties. Although the focus of Japan's ODA assistance over the years has been on East Asian countries, CA is growing to become another frontier for more proactive Japanese policies. The Japan-supported initiatives of recent years tend to favor more pragmatic cooperation schemes. As is exemplified by water-related assistance in Uzbekistan and support for local capacity building in Kyrgyzstan, Japanese assistance of a more focused character can better contribute to development both in these societies and in the region in general. These types of initiatives can successfully complement government-to-government assistance schemes and Japanese investments into large scale projects. The focus on local communities will also ensure that beneficiaries of the Japanese assistance projects will include not only governmental institutions but also the general public at large. As demonstrated in this paper, Japan over the years has grown to become the leading ODA provider in Central Asia (CA). ODA has served as a foreign policy tool and as the most significant tool for maintaining cooperation ties. Although the focus of Japan's ODA assistance over the years has been on East Asian countries, CA is growing to become another frontier for more proactive Japanese policies. The Japan-supported initiatives of recent years tend to favor more pragmatic cooperation schemes. As is exemplified by water-related assistance in Uzbekistan and support for local capacity building in Kyrgyzstan, Japanese assistance of a more focused character can better contribute to development both in these societies and in the region in general. These types of initiatives can successfully complement government-to-government assistance schemes and Japanese investments into large scale projects. The focus on local communities will also ensure that beneficiaries of the Japanese assistance projects will include not only governmental institutions but also the general public at large.

Terwilliger algebras of direct and wreath products of association schemes

Hanaki, Akihide,Kim, Kijung,Maekawa, Yu Elsevier 2011 Journal of algebra Vol.343 No.1

<P><B>Abstract</B></P><P>We will consider structures of Terwilliger algebras of direct and wreath products of association schemes. In general, it is difficult to determine the structure of the Terwilliger algebras though they are known to be semisimple C-algebras. But, we get the structure of Terwilliger algebras of these cases under some assumptions.</P>

COMMUTATIVITY OF ASSOCIATION SCHEMES OF ORDER pq

Hanaki, Akihide,Hirasaka, Mitsugu The Youngnam Mathematical Society 2013 East Asian mathematical journal Vol.29 No.1

Let (X, S) be an association scheme where X is a finite set and S is a partition of $X{\times}X$. The size of X is called the order of (X, S). We define $\mathcal{C}$ to be the set of positive integers m such that each association scheme of order $m$ is commutative. It is known that each prime is belonged to $\mathcal{C}$ and it is conjectured that each prime square is belonged to $\mathcal{C}$. In this article we give a sufficient condition for a scheme of order pq to be commutative where $p$ and $q$ are primes, and obtain a partial answer for the conjecture in case where $p=q$.

COMMUTATIVITY OF ASSOCIATION SCHEMES OF ORDER pq

Akihide Hanaki,히라사카 영남수학회 2013 East Asian mathematical journal Vol.29 No.1

Let (X; S) be an association scheme where X is a nite set and S is a partition of X X. The size of X is called the order of (X; S). We de ne C to be the set of positive integers m such that each association scheme of order m is commutative. It is known that each prime is belonged to C and it is conjectured that each prime square is belonged to C. In this article we give a su cient condition for a scheme of order pq to be commutative where p and q are primes, and obtain a partial answer for the conjecture in case where p = q.

Investigations on association schemes with elementary abelian thin residue

Kim, Kijung,Song, Sung-Yell,Xu, Bangteng North-Holland Pub. Co 2017 Discrete mathematics Vol.340 No.12

<P><B>Abstract</B></P> <P>In this paper, we give a new class of association schemes whose thin residues are isomorphic to an elementary abelian p -group of order <SUP> p 2 </SUP> . We then study the automorphism groups of these schemes and determine whether these schemes are schurian.</P>