Masakazu Jimbo

The Institute of Statistical Mathematics

Group testing is utilized in the case when we want to find a few defectives among large amount of items. Testing n items one by one requires n tests, but if the ratio of defectives is small, group testing is an efficient way to reduce the number of tests. Many research have been developed for group testing for a single type of defectives. In this p...

In this paper, we investigate a class of optimal circulant {0,1}-arrays other than the previously known class of optimal designs for fMRI experiments with a single type of stimulus. We suppose throughout the paper that n≡2(mod4) and discuss the asymptotic optimality and the D-efficiency of k×n circulant almost orthogonal arrays (CAOAs) with 2 level...

In 2012, Momihara et al. (2012) showed that the 2-design formed by the planes (2-flats) in AG(2n,3) can be decomposed into more subdesigns than a previously known decomposition. They restricted the group stabilizing the resulting subdesigns to the affine general linear group AGL(1,32n) and its subgroups, and then gave the best decomposition in the...

Interaction faults in component-based complex systems have been investigated from various aspects in the past few decades. The key issue is that, in a complex system, not only a single variable may cause the failure, but also the interactions among different variables. Combinatorial interaction testing has been established as one of the most fundam...

We introduce the notion of grid-block difference families (DFs) which is a generalization of DFs in combinatorial design theory. In particular, as generalizations of radical DFs, the notions of row-radical, column-radical, radical, and ([Formula presented],[Formula presented])-radical grid-block DFs are investigated. By establishing a relationship...

We introduce the concept of the asymmetry number for�finite digraphs, as a natural generalization of that for undirected graphs by Erdos and R�enyi in 1963. We prove an upper bound for the asymmetry number of finite digraphs and give a condition for equality. We show that our bound is asymptotically best for digraphs with sufficiently large order....

Let (G,+) be an abelian group. A finite multiset A over G is said to give a λ-fold factorization of G if there exists a multiset B over G such that each element of G occurs λ times in the multiset A+B:={a+b:a∈A,b∈B}. In this article, restricting G to a cyclic group, we will provide sufficient conditions on a given multiset A under which the exact v...

To determine the spectrum of Steiner quadruple systems (SQS) admitting a specific automorphism group is of great interest in design theory. We consider a strictly cyclic SQS which is invariant under the affine group, called an AsSQS. For the applications of designs of experiments, group testing, filing schemes, authentication codes, and optical ort...

A conflict-avoiding code (CAC) of length \(n\) and weight \(w\) is defined as a family \({\mathcal C}\) of \(w\) -subsets (called codewords) of \({\mathbb {Z}}_n\) , the ring of residues modulo \(n\) , such that \(\Delta (C) \cap \Delta (C') = \emptyset \) for any \(C, C' \in {\mathcal C}\) , where \(\Delta (C) = \{ j-i \pmod {n} : i, j \in C, i \n...

A t-spontaneous emission error design, called t-SEED for short, is a combinatorial design introduced by T. Beth et al. [Des. Codes Cryptography 29, No. 1–3, 51–70 (2003; Zbl 1033.94020)] in relation to a quantum jump code. In this article, firstly, it is shown that an optimal t-SEED attaining a given upper bound is a large set of Steiner t-designs....

A conflict-avoiding code (CAC) is known as a protocol sequence for transmitting data packets over a collision channel without feedback. The study of CACs has been focused on determining the size of an optimal code, i.e., the maximum size of a code, and in the past few years it has been settled by several researchers for even length and weight 3 tog...

We discuss two fundamental methods for constructing Φ p -optimal approximate designs of order 3 on the unit ball. One construction is based on the theory of harmonic polynomials invariant under the Weyl group of type B, and another uses statistical tools such as block designs and orthogonal arrays. The paper provides a systematic treatment of a gro...

There are some possibilities that the current evaluation method for a core shroud with cracks provides overly conservative results and it is recognized that the margin should be evaluated in a quantitative way. In evaluating the margin, it is difficult to evaluate the variation of factors which affect buckling and collapse loads by simple repeats o...

It is well known that for a prime power s and a positive integer m, the set of d-flats in AG(m,s)AG(m,s) forms a 2-design. In this article, it is shown that the 2-design formed by the 2-flats in AG(m,3)AG(m,3) for even m can be decomposed into more subdesigns than a previously known decomposition. Exact calculation of the number of the resulting su...

In this paper we present a construction of 3-designs by using a 3-design with resolvability. The basic construction generalizes a well-known construction of simple 3-(v,4,3) designs by Jungnickel and Vanstone (1986). We investigate the conditions under which the designs obtained by the basic construction are simple. Many infinite families of simple...

An MEP.1 plan for a 2m factorial experiment is able to search and estimate one possible nonzero interaction effect along with estimating the general mean and main effects. Construction of such a plan has been tackled by several authors. Some of these works are developed for all m, in which are focused on m=2h−1 or m=4λ−1 for positive integers h>2 a...

Quantum jump codes were introduced by Alber et al. (2001). Quantum jump codes have a close connection with combinatorial designs called t-SEED (t-spontaneaus emission error design). In this paper, we give a brief survey of a quantum jump code together with some new results. Firstly, fundamental properties of a t-error correcting quantum jump code a...

We study the group test for DNA library screening based on probabilistic approach. Group test is a method of detecting a few positive items from among a large number of items, and has wide range of applications. In DNA library screening, positive item corresponds to the clone having a specified DNA segment, and it is necessary to identify and isola...

The study of gene functions requires high-quality DNA libraries. However, a large number of tests and screenings are necessary for compiling such libraries. We describe an algorithm for extracting as much information as possible from pooling experiments for library screening. Collections of clones are called pools, and a pooling experiment is a gro...

It is well known that the extended binary Golay [24,12,8] code yields 5-designs. In particular, the supports of all the weight 8 codewords in the code form a Steiner system S(5,8,24). In this paper, we give a construction of mutually disjoint Steiner systems S(5,8,24) by constructing isomorphic Golay codes. As a consequence, we show that there exis...

We describe an algorithm for extracting as much information as possible from pooling experiments for library screening based on the concave-convex procedure (CCCP). Called the CCCP pool result decoder (CCPD), it is a positive clone de-tecting algorithm. Its performance is compared, by simulation, with the Bayesian network pool result decoder (BNPD)...

Frequency hopping spread spectrum and direct sequence spread spectrum are two main spread coding technologies in communication systems. Frequency hopping sequences are needed in frequency hopping code-division multiple-access (FH-CDMA) systems. In this paper, four algebraic and a combinatorial constructions of optimal sets of frequency hopping sequ...

In this paper, we investigate a set-sequence containing k-subsets of a v-set as elements such that the collection of all involved k-subsets and unions of all two consecutive k-subsets of this sequence forms an error correcting code with minimum distance d. Such a sequence is called a cyclic sequence with error correcting consecutive unions, and sai...

We consider the diallel cross experiments with control and test lines. The purpose is to study A-optimal diallel cross experiments relative to comparison between control lines and test lines with respect to their general combining ability effects.

In the case of s=2, Seiden and Zemach [1966. On orthogonal arrays. Ann. Math. Statist. 37, 1355–1370] classified all OA(2tλ,t+1,2,t) for any λ. Fujii et al. [1989. Classification of two symbol orthogonal arrays of strength t, t+3 constraints and index 4, II. SUT J. Math. 25, 161–177] classified OA(2t+1,t+2,2,t) and OA(2t+2,t+3,2,t). Recently, Stufk...

In this article, we investigate a block sequence of a Steiner quadruple system which contains the blocks exactly once such that the collection of all blocks together with all unions of two consecutive blocks of the sequence forms an error correcting code with minimum distance four. In particular, we give two recursive constructions and obtain infin...

In this paper, we investigate cyclic sequences which contain as elements all k-subsets of {0,1,...,n-1} exactly once such that the unions of any two consecutive k-subsets of this sequences are pairwise distinct. Furthermore, if Y is some prescribed subset of the power set of {0,1,...,n-1}, we require that all unions are in Y. In particular, we are...

In this paper, several constructions are presented for balanced incomplete block designs with nested rows and columns. Some of them refine theorems due to Hishida and Jimbo [6] and Uddin and Morgan [17], and some of them give parameters which have not been available before.

New improved upper and lower bounds on the maximum size of a symmetric or arbitrary conflict-avoiding code of length n = 4 m for three active users are proved. Furthermore, direct constructions for optimal conflict-avoiding codes of length n = 4 m and m equiv 2 (mod 4) for three active users are provided.

A conflict-avoiding code (CAC) C of length n with weight k is a family of binary sequences of length n and weight k satisfying ¿0¿t¿n-1 xitxj,t+s ¿ ¿ for any distinct codewords xi = (xi0, xi1,...,xi,n-1) and xj = (xj0, xj1,...,xj,n-1) in C and for any integer s, where the subscripts are taken modulo n. A CAC with maximal code size for given n and k...

A conflict-avoiding code (CAC) C of length n with weight k is a family of binary sequences of length n and weight k satisfying Sigma(0 <= t <= n-1) x(it)x(j,t+s) <=lambda for any distinct codewords x(i) = (x(i0), x(i1),..., x(i,n-1)) and x(j) = (x(j0), x(j1),..., x(j,n-1)) in C and for any integer s, where the subscripts are taken modulo n. A CAC w...

Rectangular designs are constructed from symmetric balanced nested designs. The constructions are new but they generalize previously known results. A table of parameter sets for new rectangular designs obtained from our constructions is given.

Colbourn (1999) developed some strategy for nonadaptive group testing when the items are linearly ordered and the positive items form a consecutive subset of all items.Müller and Jimbo (2004) improved his strategy by introducing the concept of 2-consecutive positive detectable matrices (2CPD-matrix) requiring that all columns and bitwise OR-sum of...

To minimize the access cost in large disk arrays (RAID) Cohen et al. (5-7) introduced (d, f)-cluttered orderings of various set systems, d, f ∈ N. In case of a graph this amounts to an ordering of the edge set such that the number of points contained in any d consecutive edges is bounded by the number f. For the complete graph, Cohen et al. gave so...

A method for constructing some new incomplete split-block designs with desirable properties is given. The new class of the designs is characterized with respect to the general balance property. Moreover, the efficiency factors of the designs proposed are given. Copyright Springer-Verlag 2005

For a v-set V, let A be a collection of r × c arrays with elements in V. A pair (V, A) is called an r × c grid-block packing if every two distinct points i and j in V occur together at most once in the same row or in the same column of arrays in A. And an r × c grid-block packing (V, A) is said to be resolvable if the collection of arrays A can be...

In this paper, we investigate erasure-resilient codes coming from Steiner 2-designs with block size k which can correct up to any k erasures. In view of applications it is desirable that such a code can also correct as many erasures of higher order as possible. Our main result is that the erasure-resilient code constructed from an affine space with...

In the paper, we propose new incomplete split-plot designs. The designs proposed are obtained by some modified Kronecker product of two components designs, one for whole-plot treatments and second for subplot treatments. The new designs are characterized with respect to general balance property. Moreover, the efficiency factors of the design with r...

Colbourn (1999) developed some strategy for nonadaptive group test- ing when the items are linearly ordered and the positives items form a consecutive subset of all items. We improve his strategy by introducing the concept of 2-consecutive positive detectable matrices (2CPD-matrix) requiring that all columns and bitwise OR-sum of each two consecuti...

We consider the problem of decomposing a complete graph into the Cartesian product of two complete graphs Kr and Kc. This problem originated from the clone library screening. We give a general method of constructing such decompositions using various sorts of combinatorial designs. In particular, for r=3 and c=3, we show that such a decomposition ex...

In the case where errors are correlated depending on the closeness of the experiments, the optimality of multilevel orthogonal arrays is discussed and some advantages of linear orthogonal arrays are also given.

It is known that group divisible designs (GDDs) with r = gimel(1) + 1 are regular and symmetric, and that the combinatorial structure of these designs is characterized in terms of Hadamard tournaments and strongly regular graphs. In this paper, it is shown that GDDs without alpha-resolution classes in each group are also specified by Hadamard tourn...

Fu, Hwang, Jimbo, Mutoh, and Shiue [J. Statist. Plann. Inference, to appear] introduced the concept of a grid-block design, which is defined as follows: For a v- set V, let A be a collection of r x c arrays with elements in V. A pair ( V, A) is called an r x c grid-block design if every two distinct points i and j in V occur exactly once in the sam...

A sufficient condition for an incomplete split-block design to be universally optimal is given. Optimal properties are examined under two linear models, i.e., with interaction effects and without these effects. Furthermore, some methods of constructing universally optimal incomplete split-block designs are presented.

In this paper, a balanced incomplete split-block design (BISBD) is shown to be universally optimum for the estimation of the interaction effects with respect to each of the intra-plot stratum estimation and the GLSE. Furthermore, the efficiency factor of an optimal design is investigated.

A special type of balanced bipartite block designs is defined and a lower bound of the number of superblocks of the design is given. Furthermore, some constructions are provided for the balanced bipartite block design attaining the lower bound.

It is well known that a two-level orthogonal array of strength 2 is universally optimum for the estimation of main effects for uncorrelated errors. In this paper, the property of orthogonal arrays which are also optimum even for correlated errors is discussed and a construction for such optimal designs is presented. Furthermore, in case when there...

In this paper, we will extend a semiframe to a more general notion ‘quasiframe’ and discuss a recursive construction for a quasiframe with cyclic property. Furthermore, as an application of a cyclic quasiframe, another recursive construction for a cyclically resolvable cyclic Steiner 2-design will be provided, which cannot be supplied by a recursiv...

In this paper, an explicit solution of the optimum requirement spanning tree (ORST), studied by Hu, is obtained in the case when a weight is assigned to each node and when maximum-degree conditions are given. Further, the solution is shown to minimize the probability of communication failure in the situation where one node or line is broken down. ©...

A directed BIB design DB(k, λ; v) is a BIB design B(k, 2λ; v) in which the blocks are transitively ordered k-tuples and each ordered pair of elements occurs in exactly λ blocks. A nested directed BIB design NDB(k, λ; v) of form ∏2≤n≤k-1(njn, λn)in is a DB(k, λ; v) where each block contains Σ2≤n≤k-1 injn mutually disjoint subblocks, injn subblocks o...

The incidence relation between points and lines in PG(n,q), which is n-dimensional projective geometry over GF(q), is a BIB design with v=q n+1 -1 q-1, k=q+1, λ=1. It is known that the design is resolvable when n is odd. Recently, Sarmiento showed that the BIB design associated with PG(5,2) is cyclically resolvable and she classified them into ineq...

In this article, direct and recursive constructions for a cyclically resolvable cyclic Steiner 2-design are given. © 1997 John Wiley & Sons, Inc. J Combin Designs 5: 177–187, 1997

In this paper, a series of identities concerned with inverse matrices of a linear combination of association matrices on Hamming schemes is given, which is useful in the field of statistical design of experiments.

An explicit solution of the optimum requirement spanning tree, studied by T. C. Hu [SIAM J. Comput. 3, 188-195 (1974; Zbl 0269.90010)], is obtained in case when a weight is assigned to each node and when maximum degree conditions are given. Further the solution is shown to minimize the probability of communication failure in the situation where one...

この論文は国立情報学研究所の電子図書館事業により電子化されました。

In this paper, recursive constructions for cyclic BIB designs and for BIB designs with more general automorphism groups are discussed. First, a brief survey of cyclic BIB designs and 1-rotational BIB designs is given along with two types of recursive constructions for them. Secondly, it is shown that the recursive construction method can be applied...

A construction method of semi-regular group divisible designs is proposed, which is based on a product technique of a kind of “q-ary BIB designs” and (r,λ)-designs. Furthermore, a combinatorial problem related to the present method is discussed.

The concept of balanced arrays is related to factorial designs, orthogonal arrays, (r, λ)-designs, and t-designs. In this paper the concept of resolvability of block designs is generalized to (r0, r1,…, rs-1)-resolvability of balanced arrays. A method of extending the constraints of resolvable balanced arrays with gradually increasing size (experim...

In 1982, G.J. Simmons introduced a mathematical model of authentication theory. Recently, E.F. Brickell (1984) and D.R. Stinson (1988) have shown some combinatorial constructions for optimal authentication systems. In the present work, game-theoretical models are proposed for authentication systems that have multilevel costs on sources, and lower b...

Vanstone has shown a procedure, called r-complementation, to construct a regular pairwise balanced design from an existing regular pairwise balanced design. In this paper, we give a generalization of r-complementation, called balanced complementation. Necessary and sufficient conditions for balanced complementation which gives a regular t-wise bala...

A balanced incomplete block design with nested rows and columns, denoted by (balanced incomplete block design with nested rows and columns) BIBRC(v,b,r,k1,k2,λ), is a block design in which the plots of the blocks are arranged in arrays of size k1×k2 such thatis a constant not depending on the choice of points i,j, where λR(i,j), λC(i,j), λB(i,j) ar...

The concept of balanced arrays is related to combinatorial structures of factorial designs, orthogonal arrays, t-designs, partially balanced incomplete block (PBIB) designs, (r,λ)-designs and error- correcting codes. In this paper Wilson’s recursive construction of transversal designs is generalized to construct balanced arrays with higher values o...

A graph design, which is a generalization of a path design, a circuit design or a bipartite design, has been studied by many authors (see, for example, Hell and Rosa [4] and Bermond and Sotteau [l]). In this paper, a product method for cyclic graph designs is given.

A CB(v,k,λ) means a cyclic 2-design of block size k coincidence number λ, and with v points. In this paper, a recursive construction of a CB(v,k,λ) from two or three cyclic 2-designs is given.

In this paper, the necessary and sufficient condition for the existence of a 1-rotational Sλ (2, 3, ν) design is obtained, and it is shown that an Sλ (2, 3, ν) design, if it exists, can be always constructed cyclically.

It is known that there are close relations between cyclic neofields and cyclic 2-designs with block size 3. In this paper it is shown that every cyclic Steiner 2-design with block size 4 is algebraically equivalent to a cyclic neofield with a suitable property.

A Steiner 2-design S(2,k, v) is said to be 1-rotational if it admits an automorphism whose cycle structure is a (v – 1)-cycle and a fixed point. In this paper, a recursive construction of 1-rotational Steiner 2-designs is given.

An iteration method is given for computing the relative capacity of a discrete memoryless channel, i.e., the maximum of the information transmission rate per cost. The algorithm is simpler and more tractable than that of B. Meister and W. Oettli (1967,Inform. Contr.11, 341–351). Also it contains Arimoto and Blahut's method for computing the capacit...