• Title, Summary, Keyword: P-polynomial scheme

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EXPLICIT EXPRESSION OF THE KRAWTCHOUK POLYNOMIAL VIA A DISCRETE GREEN'S FUNCTION

  • Kim, Gil Chun;Lee, Yoonjin
    • Journal of the Korean Mathematical Society
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    • v.50 no.3
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    • pp.509-527
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    • 2013
  • A Krawtchouk polynomial is introduced as the classical Mac-Williams identity, which can be expressed in weight-enumerator-free form of a linear code and its dual code over a Hamming scheme. In this paper we find a new explicit expression for the $p$-number and the $q$-number, which are more generalized notions of the Krawtchouk polynomial in the P-polynomial schemes by using an extended version of a discrete Green's function. As corollaries, we obtain a new expression of the Krawtchouk polynomial over the Hamming scheme and the Eberlein polynomial over the Johnson scheme. Furthermore, we find another version of the MacWilliams identity over a Hamming scheme.

An Adaptive Maximum Power Point Tracking Scheme Based on a Variable Scaling Factor for Photovoltaic Systems (태양광 시스템을 위한 가변 조정계수 기반의 적응형 MPPT 제어 기법)

  • Lee, Kui-Jun;Kim, Rae-Young;Hyun, Dong-Seok;Lim, Chun-Ho;Kim, Woo-Chull
    • The Transactions of the Korean Institute of Power Electronics
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    • v.17 no.5
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    • pp.423-430
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    • 2012
  • An adaptive maximum power point tracking (MPPT) scheme employing a variable scaling factor is presented. A MPPT control loop was constructed analytically and the magnitude variation in the MPPT loop gain according to the operating point of the PV array was identified due to the nonlinear characteristics of the PV array output. To make the crossover frequency of the MPPT loop gain consistent, the variable scaling factor was determined using an approximate curve-fitted polynomial equation about linear expression of the error. Therefore, a desirable dynamic response and the stability of the MPPT scheme were maintained across the entire MPPT voltage range. The simulation and experimental results obtained from a 3 KW rated prototype demonstrated the effectiveness of the proposed MPPT scheme.

Cluster-based Pairwise Key Establishment in Wireless Sensor Networks (센서 네트워크에서의 안전한 통신을 위한 클러스터 기반 키 분배 구조)

  • Chun Eunmi;Doh Inshil;Oh Hayoung;Park Soyoung;Lee Jooyoung;Chae Kijoon;Lee Sang-Ho;Nah Jaehoon
    • The KIPS Transactions:PartC
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    • v.12C no.4
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    • pp.473-480
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    • 2005
  • We can obtain useful information by deploying large scale sensor networks in various situations. Security is also a major concern in sensor networks, and we need to establish pairwise keys between sensor nodes for secure communication. In this paper, we propose new pairwise key establishment mechanism based on clustering and polynomial sharing. In the mechanism, we divide the network field into clusters, and based on the polynomial-based key distribution mechanism we create bivariate Polynomials and assign unique polynomial to each cluster. Each pair of sensor nodes located in the same cluster can compute their own pairwise keys through assigned polynomial shares from the same polynomial. Also, in our proposed scheme, sensors, which are in each other's transmission range and located in different clusters, can establish path key through their clusterheads. However, path key establishment can increase the network overhead. The number of the path keys and tine for path key establishment of our scheme depend on the number of sensors, cluster size, sensor density and sensor transmission range. The simulation result indicates that these schemes can achieve better performance if suitable conditions are met.

Classification Rule for Optimal Blocking for Nonregular Factorial Designs

  • Park, Dong-Kwon;Kim, Hyoung-Soon;Kang, Hee-Kyoung
    • Communications for Statistical Applications and Methods
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    • v.14 no.3
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    • pp.483-495
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    • 2007
  • In a general fractional factorial design, the n-levels of a factor are coded by the $n^{th}$ roots of the unity. Pistone and Rogantin (2007) gave a full generalization to mixed-level designs of the theory of the polynomial indicator function using this device. This article discusses the optimal blocking scheme for nonregular designs. According to hierarchical principle, the minimum aberration (MA) has been used as an important criterion for selecting blocked regular fractional factorial designs. MA criterion is mainly based on the defining contrast groups, which only exist for regular designs but not for nonregular designs. Recently, Cheng et al. (2004) adapted the generalized (G)-MA criterion discussed by Tang and Deng (1999) in studying $2^p$ optimal blocking scheme for nonregular factorial designs. The approach is based on the method of replacement by assigning $2^p$ blocks the distinct level combinations in the column with different blocks. However, when blocking level is not a power of two, we have no clue yet in any sense. As an example, suppose we experiment during 3 days for 12-run Plackett-Burman design. How can we arrange the 12-runs into the three blocks? To solve the problem, we apply G-MA criterion to nonregular mixed-level blocked scheme via the mixed-level indicator function and give an answer for the question.

Private Wildcard Query over FHE-Encrypted Databases (동형암호기반의 안전한 와일드카드 쿼리)

  • Kim, Myungsun
    • Journal of Security Engineering
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    • v.14 no.2
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    • pp.115-130
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    • 2017
  • In this paper, we deal with a method to securely process a query to a database outsourced to a remote server. In particular we are interested in a wildcard query in which a database query statement contains a wildcard character. Moreover, we consider a setting where users' data are very sensitive (e.g., medical information) so that they should be handled very carefully in the light of security. To this end, we use a fully homomorphic encryption scheme as a baseline encryption. Together with this encryption scheme, our basic idea to the wildcard query problem is to segment an input string as ${\tau}$-gram and to represent the ${\tau}$-gram into the correspnong polynomial $Q_{\tau}(x)$. Later a user sends a wildcard pattern including p, then the server evaluate the polynomial as $Q_{\tau}(p)$, and so if the evaluation result is equal to 0, then it implies that the string involves the pattern p as a substring. All computations are performed on encryptions so that we can guarantee that it is as secure as the baseline encryption scheme applied to the protocol. Finally our construction only requires multiplicative depth $O(log_2k)$ where k is the maximum length of strings.

AN UPPER BOUND ON THE CHEEGER CONSTANT OF A DISTANCE-REGULAR GRAPH

  • Kim, Gil Chun;Lee, Yoonjin
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.2
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    • pp.507-519
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    • 2017
  • We present an upper bound on the Cheeger constant of a distance-regular graph. Recently, the authors found an upper bound on the Cheeger constant of distance-regular graph under a certain restriction in their previous work. Our new bound in the current paper is much better than the previous bound, and it is a general bound with no restriction. We point out that our bound is explicitly computable by using the valencies and the intersection matrix of a distance-regular graph. As a major tool, we use the discrete Green's function, which is defined as the inverse of ${\beta}$-Laplacian for some positive real number ${\beta}$. We present some examples of distance-regular graphs, where we compute our upper bound on their Cheeger constants.