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J. DAEMEN AND V. RIJMEN, Annex to AES Proposal: 5, Propagation and Correlation (1999a). Available at http://crsc.nist.gov.encryption/aes/rijndael/. O. S. ROTHHAUS. On Bent Functions , Journal of Combinatorial Theory, 20A, pp. 300 305 (1976). J. SEBERRY AND XIAN-MO ZHENG, Highly Nonlinear 0-1 Balanced Boolean Functions Satisfying Strict Avalanche Criterion , in Advances in Cryptology AUSCRYPT 92, Springer-Verlag (New York, NY), 1993, pp. 145 155. J. SEBERRY, XIAN-MO ZHANG, AND Y. ZHENG, Improving the Strict Avalanche Characteristics of Cryptographic Functions , Information Processing Letters, 50, 1994, pp. 37 41. J. SEBERRY, XIAN-MO ZHANG, AND Y. ZHENG, Relationships Among Nonlinearity Criteria , in Advances in Cryptology EUROCRYPT 94, Springer-Verlag (New York, NY), 1995, pp. 376 386. J. L. SMITH, The Design of Lucifer, A Cryptographic Device for Data Communications , IBM Research Report RC3326, Yorktown Heights, New York, 1971. A. SORKIN, Lucifer, A Cryptographic Algorithm , Cryptologia, 8, pp. 22 41 (1984); with addendum Cryptologia, 84, 260 261 (1984). M. WIENER, Ef cient DES Key Search , reprinted in Practical Cryptography for Data Internetworks, William Stallings (ed.), IEEE Computer Society Press (New York, NY), 1996, pp. 31 79. Bruce Schneier Applied Cryptography (2nd edn), John Wiley, 1993, p. 296.



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Essential Nuclear Medicine Physics, Second Edition Rachel A. Powsner, Edward R. Powsner Copyright 2006 Rachel A. Powsner and Edward R. Powsner

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The combination of 2D gel electrophoresis and mass spectrometry is a traditional approach towards proteomics. 2D gel electrophoresis separates proteins according to orthogonal properties; gels are stained, then spots cut from the gel and identi ed by mass spectrometry using sequence information from gene databases coupled with peptide mass ngerprinting (Figure 9.20). The use of these techniques alone has allowed types of cataloguing experiments to be performed wherein patterns on 2D gels can be examined and spots on gel identi ed. These approaches have had most impact when examining systems somewhat simpler than the whole cell situation, for instance the compositions of subcellular organelles or multi-protein complexes. Alternatively, comparative experiments may be performed using pattern-matching algorithms to compare 2D gel electrophoresis results in an attempt to make out the differences, for example in protein pro les between diseased and normal tissues thereby uncovering disease biomarkers. However, there are signi cant problems with using the combination of 2D electrophoresis and mass spectrometry. First, only the high abundance proteins are identi ed on 2D gels it has been estimated that the number of genes expressed at any one time in a human cell type could exceed 10 000. If post-translational modi cation were also considered then the numbers of distinct polypeptides even within a single cell could run into the millions. On

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SELECT COUNT(*) as numhh, SUM(CASE WHEN minfname = maxfname AND mingender = maxgender THEN 1 ELSE 0 END) as allsame FROM (SELECT householdid, COUNT (*) as cnt, MIN(firstname) as minfname, MAX(firstname) as maxfname, MIN(gender) as mingender, MAX(gender) as maxgender FROM customer GROUP BY householdid) hh WHERE numcustomers > 1

11.1 Show how the principle of inclusion exclusion can be used to derive the formula of Proposition 11.6 for the Euler totient function. 11.2 Prove that Vm v : 1 gcd{v, m} is a group; that is, 11.2a v1, v2 [ Vm ) v1v2 [ Vm; 11.2b 1 [ Vm; 11.2c If v [ Vm, then v 21 [ Vm. 11.3 Prove that the cardinality of jVmj is the value of the Euler totient functjon f(m). 11.4 Calculate the cardinality of Gm(s) {vs : v [ Vm}. Problems 11.5 to 11.8 provide examples of Merkle Hellman knapsack encipherment. They require two programs: the rst to encipher ASCII character plaintext, and the second to decipher ciphertext. The Merkle Hellman encipherment program takes as parameters

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Parallel and distributed computing systems are now widely availabli . A parullel system consists of multiple processors that communicate with each otl er using shared memory. As the number of transistors on a chip increases, miiltipro essor chips will become fairly common. With enough parallelism available in applicE :ions, such systerns will easily beat sequential systems in performance. Figure 1.1 lows a parallel system with multiple processors. These processors communicate ith each other using the shared memory. Each processor may also have local mem Iry that is not shared with other processors. We define distributed systems as those computer syst.ems that co kain mult.iple processors connected by a communication network. In these syste 1 s processors 1 communicate with each other using messages that are sent over the I 2twork. Such systems are increasingly available because of decrease in prices of c o a iuter processors and the high-bandwidth links t o connect them. Figure 1.2 shows distributed system. The communication network in the figure could be a local ,rea network such as an Ethernet, or a wide area network such the Internet. Programming parallel and distributed systems requires a different set of tools and techniques than that required by the traditional sequential software. The focus of this book is on these techniques,.

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