THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

This paper presents a geometric approach to the construction of low-density parity-check (LDPC) codes. Four classes of LDPC codes are constructed based on the lines and points of Euclidean and projective geometries over finite fields. Codes of these four classes have good minimum distances and their Tanner (1981) graphs have girth 6. Finite-geometry LDPC codes can be decoded in various ways, ranging from low to high decoding complexity and from reasonably good to very good performance. They perform very well with iterative decoding. Furthermore, they can be put in either cyclic or quasi-cyclic form. Consequently, their encoding can be achieved in linear time and implemented with simple feedback shift registers. This advantage is not shared by other LDPC codes in general and is important in practice. Finite-geometry LDPC codes can be extended and shortened in various ways to obtain other good LDPC codes. Several techniques of extension and shortening are presented. Long extended finite-geometry LDPC codes have been constructed and they achieve a performance only a few tenths of a decibel away from the Shannon theoretical limit with iterative decoding.

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Low-density parity-check codes based on finite geometries: a rediscovery and new results

This chapter provides an overview of recent developments in the design and analysis of cross-over trials. We first consider the analysis of the trial that compares two treatments, A and B, over two periods and where the subjects are randomized to the treatment sequences AB and BA. We make the distinction between fixed and random effects models and show how these models can easily be fitted using modern software. Issues with fitting and testing for a difference in carry-over effects are described and the use of baseline measurements is discussed. Simple methods for testing for a treatment difference when the data are binary are also described. Various designs with two or more treatments but with three or four periods are then described and compared. These include the balanced and partially balanced designs for three or more treatments and designs for factorial treatment combinations. Also described are nearly balanced and nearly strongly balanced designs. Random subject-effects models for the designs with two or more treatments are described and methods for analysing non-normal data are also given. The chapter concludes with a description of the use of cross-over designs in the testing of bioequivalence.

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Design and Analysis of Cross-Over Trials

Introduction A fundamental objective of cryptography is to enable two persons to communicate over an insecure channel (a public channel such as the internet) in such a way that any other person is unable to recover their message (called the plaintext ) from what is sent in its place over the channel (the ciphertext ). The transformation of the plaintext into the ciphertext is called encryption , or enciphering. Encryption-decryption is the most ancient cryptographic activity (ciphers already existed four centuries b.c.), but its nature has deeply changed with the invention of computers, because the cryptanalysis (the activity of the third person, the eavesdropper, who aims at recovering the message) can use their power. The encryption algorithm takes as input the plaintext and an encryption key K E , and it outputs the ciphertext. If the encryption key is secret, then we speak of conventional cryptography , of private key cryptography , or of symmetric cryptography . In practice, the principle of conventional cryptography relies on the sharing of a private key between the sender of a message (often called Alice in cryptography) and its receiver (often called Bob). If, on the contrary, the encryption key is public, then we speak of public key cryptography . Public key cryptography appeared in the literature in the late 1970s.

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Boolean Models and Methods in Mathematics, Computer Science, and Engineering: Boolean Functions for Cryptography and Error-Correcting Codes

Exhaustive testing of computer software is intractable, but empirical studies of software failures suggest that testing can in some cases be effectively exhaustive. We show that software failures in a variety of domains were caused by combinations of relatively few conditions. These results have important implications for testing. If all faults in a system can be triggered by a combination of n or fewer parameters, then testing all n-tuples of parameters is effectively equivalent to exhaustive testing, if software behavior is not dependent on complex event sequences and variables have a small set of discrete values.

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Software fault interactions and implications for software testing

Balanced Incomplete Block Designs and t-Designs2-(v,k,l) Designs of Small OrderBIBDs with Small Block Sizet-Designs, t = 3Steiner SystemsSymmetric DesignsResolvable and Near Resolvable DesignsLatin Squares, MOLS, and Orthogonal ArraysLatin SquaresMutually Orthogonal Latin Squares (MOLS)Incomplete MOLSOrthogonal Arrays of Index More Than OneOrthogonal Arrays of Strength More Than TwoPairwise Balanced DesignsPBDs and GDDs: The BasicsPBDs: Recursive ConstructionsPBD-ClosurePairwise Balanced Designs as Linear SpacesPBDs and GDDs of Higher IndexPBDs, Frames, and ResolvabilityOther Combinatorial DesignsAssociation SchemesBalanced (Part) Ternary DesignsBalanced Tournament DesignsBhaskar Rao DesignsComplete Mappings and Sequencings of Finite GroupsConfigurationsCostas ArraysCoveringsCycle SystemsDifference FamiliesDifference MatricesDifference Sets: AbelianDifference Sets: NonabelianDifference Triangle SetsDirected DesignsD-Optimal MatricesEmbedding Partial QuasigroupsEquidistant Permutation ArraysFactorial DesignsFrequency SquaresGeneralized QuadranglesGraph Decompositions and DesignsGraphical DesignsHadamard Matrices and DesignsHall Triple SystemsHowell DesignsMaximal Sets of MOLSMendelsohn DesignsThe Oberwolfach ProblemOrdered Designs and Perpendicular ArraysOrthogonal DesignsOrthogonal Main Effect PlansPackingsPartial GeometriesPartially Balanced Incomplete Block DesignsQuasigroupsQuasi-Symmetric Designs(r,l)-DesignsRoom SquaresSelf-Orthogonal Latin Squares (SOLS)SOLS with a Symmetric Orthogonal Mate (SOLSSOM)Sequences with Zero AutocorrelationSkolem SequencesSpherical t-DesignsStartersTrades and Defining Sets(t,m,s)-NetsTuscan Squarest-Wise Balanced DesignsUniformly Resolvable DesignsVector Space DesignsWeighing Matrices and Conference MatricesWhist TournamentsYouden Designs, GeneralizedYouden SquaresApplicationsCodesComputer Science: Selected ApplicationsApplications of Designs to CryptographyDerandomizationOptimality and Efficiency: Comparing Block DesignsGroup TestingScheduling a TournamentWinning the LotteryRelated Mathematics and Computational MethodsFinite Groups and DesignsNumber Theory and Finite FieldsGraphs and MultigraphsFactorizations of GraphsStrongly Regular GraphsTwo-GraphsClassical GeometriesProjective Planes, NondesarguesianComputational Methods in Design TheoryIndex

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CRC Handbook of Combinatorial Designs

PREFACE INTRODUCTION NEW! Opening the Door NEW! Design Theory: Antiquity to 1950 BLOCK DESIGNS 2-(v, k, ?) Designs of Small Order NEW! Triple Systems BIBDs with Small Block Size t-Designs with t = 3 Steiner Systems Symmetric Designs Resolvable and Near-Resolvable Designs LATIN SQUARES Latin Squares Quasigroups Mutually Orthogonal Latin Squares (MOLS) Incomplete MOLS Self-Orthogonal Latin Squares (SOLS) Orthogonal Arrays of Index More Than One Orthogonal Arrays of Strength More Than Two PAIRWISE BALANCED DESIGNS PBDs and GDDs: The Basics PBDs: Recursive Constructions PBD-Closure NEW! Group Divisible Designs PBDs, Frames, and Resolvability Pairwise Balanced Designs as Linear Spaces HADAMARD MATRICES AND RELATED DESIGNS Hadamard Matrices and Hadamard Designs Orthogonal Designs D-Optimal Matrices Bhaskar Rao Designs Generalized Hadamard Matrices Balanced Generalized Weighing Matrices and Conference Matrices Sequence Correlation Complementary, Base and Turyn Sequences NEW! Optical Orthogonal Codes OTHER COMBINATORIAL DESIGNS Association Schemes Balanced Ternary Designs Balanced Tournament Designs NEW! Bent Functions NEW! Block-Transitive Designs Complete Mappings and Sequencings of Finite Groups Configurations Correlation-Immune and Resilient Functions Costas Arrays NEW! Covering Arrays Coverings Cycle Decompositions Defining Sets NEW! Deletion-Correcting Codes Derandomization Difference Families Difference Matrices Difference Sets Difference Triangle Sets Directed Designs Factorial Designs Frequency Squares and Hypercubes Generalized Quadrangles Graph Decompositions NEW! Graph Embeddings and Designs Graphical Designs NEW! Grooming Hall Triple Systems Howell Designs NEW! Infinite Designs Linear Spaces: Geometric Aspects Lotto Designs NEW! Low Density Parity Check Codes NEW! Magic Squares Mendelsohn Designs NEW! Nested Designs Optimality and Efficiency: Comparing Block Designs Ordered Designs, Perpendicular Arrays and Permutation Sets Orthogonal Main Effect Plans Packings Partial Geometries Partially Balanced Incomplete Block Designs NEW! Perfect Hash Families NEW! Permutation Codes and Arrays NEW! Permutation Polynomials NEW! Pooling Designs NEW! Quasi-3 Designs Quasi-Symmetric Designs (r, ?)-designs Room Squares Scheduling a Tournament Secrecy and Authentication Codes Skolem and Langford Sequences Spherical Designs Starters Superimposed Codes and Combinatorial Group Testing NEW! Supersimple Designs Threshold and Ramp Schemes (t,m,s)-Nets Trades NEW! Turan Systems Tuscan Squares t-Wise Balanced Designs Whist Tournaments Youden Squares and Generalized Youden Designs RELATED MATHEMATICS Codes Finite Geometry NEW! Divisible Semiplanes Graphs and Multigraphs Factorizations of Graphs Computational Methods in Design Theory NEW! Linear Algebra and Designs Number Theory and Finite Fields Finite Groups and Designs NEW! Designs and Matroids Strongly Regular Graphs NEW! Directed Strongly Regular Graphs Two-Graphs BIBLIOGRAPHY INDEX

Handbook of Combinatorial Designs

Orthogonal Factorizations of Graphs (B. Alspach, et al.). Conjugate--Orthogonal Latin Squares and Related Structures (F. Bennett & L. Zhu). Directed and Mendelsohn Triple Systems (C. Colbourn & A. Rosa). Room Squares and Related Designs (J. Dinitz & D. Stinson). Steiner Quadruple Systems (A. Hartman & K. Phelps). Difference Sets (D. Jungnickel). Decomposition Into Cycles II: Cycle Systems (C. Lindner & C. Rodger). Coverings and Packings (W. Mills & R. Mullin). Colorings of Block Designs (A. Rosa & C. Colbourn). Hadamard Matrices, Sequences, and Block Designs (J. Seberry & M. Yamada). Large Sets of Disjoint Designs and Related Structures (L. Teirlinck). One--Factorizations of Complete Graphs (W. Wallis). Index.

Jeffrey H. Dinitz

Papers

CRC Handbook of Combinatorial Designs

Handbook of Combinatorial Designs

Contemporary design theory : a collection of surveys

Mutually orthogonal latin squares (MOLS)

Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)