The Effect of Inverse Document Frequency Weights on Retrieval of Genomic Sequences: Towards a vector space approach

1
The Effect of Inverse Document Frequency Weights
on Retrieval of Genomic SequencesTowards a
vector space approach

• Kevin C. O'Kane
• Department of Computer Science
• The University of Northern Iowa
• Cedar Falls, Iowa 50613

2
The area of natural language text indexing and
retrieval has been studied since the mid-50's.
In text retrieval, the problem is to locate
documents related to a natural language query.
To this purpose, natural language text indexing
programs have employed many techniques to
identify terms in a document most likely to be
content descriptors as opposed to terms that are
poor content descriptors. By eliminating poor
descriptors and pre-indexing documents by
descriptors more likely to be good
discriminators, the speed of selection and
precision of document relevance ranking can be
improved. The vector space model, developed
by G. Salton, views the problem as an
n-dimensional hyperspace in which documents and
queries.
3
Overview

• In text retrieval, the problem is to locate
  documents related to a natural language query.
• Natural language text indexing programs identify
  terms in a document most likely to be content
  descriptors.
• The goal of these experiments is to apply text
  indexing techniques to genomic data bases.

4
Natural Language Indexing

• Natural language text indexing and retrieval has
  been studied since the mid-50's. In text
  retrieval, the problem is to locate documents
  related to a natural language query.
• Natural language text indexing programs employ
  techniques to identify terms in a document most
  likely to be content descriptors.
• By eliminating poor descriptors and pre-indexing
  documents by descriptors likely to be good
  discriminators, the speed of selection and
  precision of document relevance ranking can be
  improved.
• The vector space model, developed by G. Salton,
  views the problem as an n-dimensional hyperspace
  of documents and queries.

5
Document Hyperspace
6
Hyperspace Queries
7
Clustering Objects by Feature
8
Cosine Similarity Coefficient
9
Genomic Data Bases

• EMBL (http//www.embl.org)
• SWISS-PROT (http//www.expasy.org/sprot/sprot-top
  .html)
• PROSITE (http//www.expasy.org/prosite/)
• PIR (http//pir.georgetown.edu/home.shtml)
• NCBI/NLM GenBank (http//www.ncbi.nih.gov/)
• MGD The Mouse Genome Database (http//www.informa
  tics.jax.org/)
• OMIM - Online Mendelian Inheritance in Man
  (http//www.ncbi.nlm.nih.gov/entrez/query.fcgi?db
  OMIM)

10
nt Sequence Data Base

• NCBI nt data base 12 billion bytes in length
  comprising 2,584,440 sequences in FASTA format
  (Sept 2004).
• Example sequence
• gt gi2695852embY13263.1ABY13263 Acipenser
  baeri mRNA for immunoglobulin heavy chain, clone
  CAAGAACCACAATACTGCAGTACAATGGGGATTTTAACAGCTCTCTGTAT
  AATAATGACAGCTCTATCAAGTGTCCGGTCTGATGTAGTGTTGACTGAGT
  CCGGACCAGCAGTTATAAAGCCTGGAGAGTCCCATAAACTGTCCTGTAAA
  GCCTCTGGATTCACATTCAGCAGCAACAACATGGGCTGGGTTCGACAAGC
  TCCTGGAAAGGGTCTGGAATGGGTGTCTACTATAAGCTATAGTGTAAATG
  CATACTATGCCCAGTCTGTCCAGGGAAGATTCACCATCTCCAGAGACGAT
  TCCAACAGCATGCTGTATTTACAAATGAACAGCCTGAAGACTGAAGACTC
  TGCCGTGTATTACTGTGCTCGAGAGTCTAACTTCAACCGCTTTGACTACT
  GGGGATCCGGGACTATGGTGACCGTAACAAATGCTACGCCATCACCACCG
  ACAGTGTTTCCGCTTATGCAGGCATGTTGTTCGGTCGATGTCACGGGTCC
  TAGCGCTACGGGCTGCTTAGCAACCGAATTC

11
GenBank

• LOCUS AAB2MCG1 289 bp
  DNA linear PRI 23-AUG-2002
• DEFINITION Aotus azarai beta-2-microglobulin
  precursor exon 1.
• ACCESSION AF032092
• VERSION AF032092.1 GI3265027
• KEYWORDS .
• SEGMENT 1 of 2
• SOURCE Aotus azarai (Azara's night monkey)
• ORGANISM Aotus azarai
• Eukaryota Metazoa Chordata
  Craniata Vertebrata Euteleostomi
• Mammalia Eutheria Primates
  Platyrrhini Cebidae Aotinae Aotus.
• REFERENCE 1 (bases 1 to 289)
• AUTHORS Canavez,F.C., Ladasky,J.J.,
  Muniz,J.A., Seuanez,H.N., Parham,P. and
• Cavanez,C.
• TITLE beta2-Microglobulin in neotropical
  primates (Platyrrhini)
• JOURNAL Immunogenetics 48 (2), 133-140 (1998)
• MEDLINE 98298008
• PUBMED 9634477
• REFERENCE 2 (bases 1 to 289)
• AUTHORS Canavez,F.C., Ladasky,J.J.,
  Seuanez,H.N. and Parham,P.

• JOURNAL Submitted (31-OCT-1997) Structural
  Biology, Stanford University,
• Fairchild Building Campus West Dr.
  Room D-100, Stanford, CA
• 94305-5126, USA
• FEATURES Location/Qualifiers
• source 1..289
• /organism"Aotus azarai"
• /mol_type"genomic DNA"
• /db_xref"taxon30591"
• sig_peptide 134..193
• exon lt134..200
• /number1
• intron 201..gt289
• /number1
• ORIGIN
• 1 gtccccgcgg gccttgtcct gattggctgt
  ccctgcgggc cttgtcctga ttggctgtgc
• 61 ccgactccgt ataacataaa tagaggcgtc
  gagtcgcgcg ggcattactg cagcggacta
• 121 cacttgggtc gagatggctc gcttcgtggt
  ggtggccctg ctcgtgctac tctctctgtc
• 181 tggcctggag gctatccagc gtaagtctct
  cctcccgtcc ggcgctggtc cttcccctcc

12
Sequence Matching

• Currrent access to sequence databases mainly by
  heuristic-assisted pattern matching on flat or
  nearly flat files using programs such as BLAST
  and FASTA.
• Underlying data bases growing rapidly with
  consequent deterioration of search times even on
  large, multiprocessor systems as current software
  tools reach design limits.
• BLAST systems index data base sequences according
  to short code letter words (usually, 3 letters
  for amino acids and 11 for nucleotide data
  bases) scoring matrices.
• Queries also decomposed to similar short code
  words. The data base is scanned sequences with
  words in common with the query are processed to
  extend the initial code word match.

13
Example BLAST Output

• 
  Score E
• Sequences producing significant alignments
  (bits) Value
• embBX015832.1CNS08KDO Single read from an
  extremity of a ... 918 0.0
• embBX032891.1CNS08XJJ Single read from an
  extremity of a ... 902 0.0
• embBX065445.1CNS09MNT Single read from an
  extremity of a ... 894 0.0
• embBX052703.1CNS09CTV Single read from an
  extremity of a ... 894 0.0
• embBX030708.1CNS08VUW Single read from an
  extremity of a ... 894 0.0
• embBX030663.1CNS08VTN Single read from an
  extremity of a ... 894 0.0
• ..................................................
  ...........................
• gtembBX015832.1CNS08KDO Single read from an
  extremity of a full-length cDNA clone made from
  Anopheles gambiae total adult females. 3-PRIME
  end of clone FK0AAA23DA12
• Length 866
• Score 918 bits (463), Expect 0.0
• Identities 535/559 (95)
• Strand Plus / Plus
• 
  

14
Developing A Vector Space Approach to Sequence
Indexing

• This work attempts to explore natural language
  indexing techniques applied genomic data bases
  through
• Weight based indexing of k-tuples derived from
  NCBI nt sequence data base.
• Text terms used in genomic sequence data banks
  and literature
• Both applications are implemented for Linux and
  written in Mumps and MDH, a Mumps related C
  toolkit capable of indexing data sets of up to
  256 terabytes using a B-tree based
  multidimensional data model, that includes many
  retrieval and sequence matching functions.

15
Inverse Document Frequency Wgt.

• The IDF weight yields higher values for words
  whose distribution is more concentrated and lower
  values for words whose use is more widespread.
• Thus, words of broad context are weighted lower
  than words of narrow context.
• Words of low weight are hypothesized to be poor
  indexing terms while words with high weights are
  hypothesized to be good indexing terms.
• The bulk of the words, as is the case in natural
  language text, reside in the middle range.

16
Natural Language Example

• Word Freq(i,j) TotFreq DocFreq
  Wgt1 Wgt2 Wgt3 MCA
• 1 Death of a cult. (Apple Computer needs to
  alter its strategy) (column)
• apple 4 261 112
  1.716 9.757 17 -1.1625
• computer 4 706 358
  2.028 5.109 10 -19.4405
• mac 2 146 71
  0.973 6.290 6 -0.0256
• macintosh 4 210 107
  2.038 9.940 20 -0.5855
• strategy 2 79 67
  1.696 6.406 11 -0.0592
• 3 WordPerfect. (WordPerfect for the
  Macintosh 2.0) (evaluation) Taub, Eric.
• edit 2 111 77
  1.387 6.128 8 -0.0961
• frame 2 9 7
  1.556 10.924 17 0.0131
• import 2 29 19
  1.310 8.927 12 0.0998
• macintosh 3 210 107
  1.529 7.705 12 -0.5855
• macro 3 38 24
  1.895 12.189 23 0.1075
• outstand 1 10 9
  0.900 5.711 5 0.0168
• user 4 861 435
  2.021 4.330 9 -26.8094

17
Indexing Experiment

• Sequences from the NCBI "nt" (non-redundant
  nucleotide) data base were used.
• The nt data base is approximately 12 billion
  bytes in length comprising 2,584,440 sequences in
  FASTA format (Sept 2004).
• A word size of 11 was used throughout. A total
  of 4,194,299 words were identified, slightly less
  than the theoretical maximum of 4,194,304.

18
Calculating the IDF Weight

• The overall frequencies of occurrence of all
  possible 11 character words from each sequence
  were determined along with the number of
  sequences in which each unique word was found.
• A weight Wgti for each word i was calculated by
  taking the Log10, multiplied by 10 and truncated
  to the nearest integer, of the total number of
  sequences (N) divided by the number of sequences
  in which the word occurred (DocFreqi).
• Wgti (int) 10 Log10 ( N
  / DocFreqi )
• In natural language indexing, this is referred to
  as the inverse document frequency (IDF) weight.

19
File Sizes

• Initial file analysis produces about 110
  intermediate files of about 440 million bytes
  each from the input data base (12 GB).
• out.table is a large (40 billion byte)
  word-sequence file.
• freq.bin contains the inverse document frequency
  weight for each word (53 million bytes)
• index (76 million bytes) gives for each word the
  eight byte offset of the word's entry in
  out.table.
• index and freq.bin are merged into ITABLE (112
  million bytes) which contains for each word its
  weight, offset, and a pointer to a list of
  aliases (not used with the nt data base).

20
Data Base

• W ( w1, w2, w3, ... wM) vector of M weights
• F ( f1,1 f1,2 f1,3 ... f1,N )
• ( f2,1 f2,2 f2,3 ... f2,N )
• ( f3,1 f3,2 f3,3 ... f3,N )
• ... word-sequence matrix
• ( fM,1 fM,2 fM,3 ... fM,N )
• 
  

21
Number of Words at each Weight

• for i 1 to 120
• zi ? 0
• for j 1 to M
• if wj i then zi ? zi 1

22
Number of Words at Each IDF Wgt.
23
Sum of all Instances of Each Weight

• for i 1 to 120
  // for each weight
• xi ? 0
• for j 1 to M
  // for each word
• for k 1 to N //
  for each sequence
• if fj, k i then xi ? xi 1

24
Number of Occurrences at Each IDF Level
25
Sequence Retrieval

• For retrieval, a query sequence is read and
  decomposed into 11 character words. These words
  are reduced to a numeric equivalent which is used
  as an index into the word-sequence table.
  Entries in a master vector corresponding to
  sequences are incremented by the weight of the
  word if the word occurs in the sequence if the
  weight of the word lies within a specified range.
  When all words have been processed, entries in
  the master sequence vector are normalized
  according to the length of the underlying
  sequence in respect to the length of the query.
  Finally, the master sequence vector is sorted and
  the top scoring entries printed or submitted to a
  Smith-Waterman alignment, sorted and then
  printed. Optionally, the Smith-Waterman
  alignments themselves can be printed and the
  selected sequences can be extracted from the nt
  data base and stored in a separate output file
  for additional processing. FASTA post-processing
  is an option.

26
Unweighted Result for 500 Random Queries
27
Result for 500 Random Queries Weight Range 65-120
28
Overall Results for 500 Random Queries
29
Index Scoring Results

• Query gtgi19911940dbjAB072098.1 Hepatitis C
  virus type 1b gene for polyprotein, NS3 region,
  partial cds, isolate71
• Query string has 289 letters
• Searching ...
• 68224 gtgi19911940dbjAB072098.1 Hepatitis C
  virus type 1b gene for polyprotein, NS3 region, p
• 31420 gtgi29467317dbjAB089555.1 Hepatitis C
  virus NS3 gene for polyprotein, partial cds, isol
• 30508 gtgi19911912dbjAB072084.1 Hepatitis C
  virus type 1b gene for polyprotein, NS3 region, p
• 30296 gtgi29467668dbjAB100815.1 Hepatitis C
  virus NS3 gene for polyprotein, partial cds, isol
• 29800 gtgi14150634gbAF369255.1 Hepatitis C
  virus Pt.2F NS3 protease gene, partial cds
• 29444 gtgi19911960dbjAB072108.1 Hepatitis C
  virus type 1b gene for polyprotein, NS3 region, p
• 29240 gtgi19911888dbjAB072072.1 Hepatitis C
  virus type 1b gene for polyprotein, NS3 region, p
• 29196 gtgi14150646gbAF369261.1 Hepatitis C
  virus Pt.6A NS3 protease gene, partial cds
• 29120 gtgi19911862dbjAB072059.1 Hepatitis C
  virus type 1b gene for polyprotein, NS3 region, p
• 28896 gtgi14150628gbAF369252.1 Hepatitis C
  virus Pt.128 NS3 protease gene, partial cds
• 28116 gtgi2731651gbU81612.1HCU81612 Hepatitis
  C virus polyprotein gene, partial cds
• 28116 gtgi3157741dbjAB013621.1 Hepatitis C
  virus RNA for polyprotein (NS3 proteinase
  region),
• 27700 gtgi14150620gbAF369248.1 Hepatitis C
  virus Pt.1 NS3 protease gene, partial cds
• ..................................................
  ...........................................

30
Smith-Waterman Result Scoring

• Query gtgi19911940dbjAB072098.1 Hepatitis C
  virus type 1b gene for polyprotein, NS3 region,
  partial cds, isolate71
• Query string has 289 letters
• top gtgi19911940dbjAB072098.1 Hepatitis C
  virus type 1b gene for polyprotein, NS3 region,
  partial cds, isolate71
• 166 TTCCACGGTGCCGGCTCAAAGACCCTAGCCGGCCCGAAGGGCCA
  AATCACCCAGATGTACACCAATGTAGACCAGGACCT 245
• 
  
• 1 TTCCACGGTGCCGGCTCAAAGACCCTAGCCGGCCCGAAGGGCCA
  AGTCACCCAGATGTACACCAATGTAGACCAGGTCCT 80
• 246 CGTCGGCTGGCCGGCGCCCCCCGGAGCGCGTTCCTTGACACCAT
  GCACCTGCGGCAGCTCGGACCTTTATTTGGTCACGA 325
• 
  
• 81 CGTCGGCTGGCCGGCGCCGCCCGGAGCGCGTTCCTTGAGACCAT
  GCACCTGCGGCAGCTCGGACCTTTATTTGGTCACGA 160
• 326 GACATGCTGACGTCATCCCGGTGCGCCGGCGGGGCGACAGCAGG
  GGGAGCTTGCTTTCTCCTAGGCCCATCTCTTACTTA 405
• 
  
• 161 GACATGCTGACGTCATCCCGGTGCGCCGGCGGGGCGACAGCAGG
  GGGAGCTTGCTTTCTCCTAGGCCCATCTCTTACTTA 240
• 406 AAGGGCTCTTCGGGCGGTCCACTGCTTTGCCCCTCGGGGCACGC
  TGTGG 454
• 
  

31
S-W Scores

• 566 gtgi19911940dbjAB072098.1 Hepatitis C
  virus type 1b gene for polyprotein, NS3 region, p
• 505 gtgi29467668dbjAB100815.1 Hepatitis C
  virus NS3 gene for polyprotein, partial cds, isol
• 504 gtgi29467317dbjAB089555.1 Hepatitis C
  virus NS3 gene for polyprotein, partial cds, isol
• 503 gtgi19911914dbjAB072085.1 Hepatitis C
  virus type 1b gene for polyprotein, NS3 region, p
• 503 gtgi14150628gbAF369252.1 Hepatitis C virus
  Pt.128 NS3 protease gene, partial cds
• 502 gtgi29467247dbjAB089520.1 Hepatitis C
  virus NS3 gene for polyprotein, partial cds, isol
• 502 gtgi3157741dbjAB013621.1 Hepatitis C virus
  RNA for polyprotein (NS3 proteinase region),
• 501 gtgi19911862dbjAB072059.1 Hepatitis C
  virus type 1b gene for polyprotein, NS3 region, p
• 499 gtgi29467670dbjAB100816.1 Hepatitis C
  virus NS3 gene for polyprotein, partial cds, isol
• 498 gtgi3157753dbjAB013627.1 Hepatitis C virus
  RNA for polyprotein (NS3 proteinase region),
• 498 gtgi14150634gbAF369255.1 Hepatitis C virus
  Pt.2F NS3 protease gene, partial cds
• 497 gtgi29467311dbjAB089552.1 Hepatitis C
  virus NS3 gene for polyprotein, partial cds, isol
• 497 gtgi19911934dbjAB072095.1 Hepatitis C
  virus type 1b gene for polyprotein, NS3 region, p
• 497 gtgi19911912dbjAB072084.1 Hepatitis C
  virus type 1b gene for polyprotein, NS3 region, p
• 496 gtgi19911900dbjAB072078.1 Hepatitis C
  virus type 1b gene for polyprotein, NS3 region, p
• 495 gtgi14150638gbAF369257.1 Hepatitis C virus
  Pt.3O NS3 protease gene, partial cds
• 495 gtgi14150616gbAF369246.1 Hepatitis C virus
  Pt.1A NS3 protease gene, partial cds
• 495 gtgi14150646gbAF369261.1 Hepatitis C virus
  Pt.6A NS3 protease gene, partial cds
• 494 gtgi14150620gbAF369248.1 Hepatitis C virus
  Pt.1 NS3 protease gene, partial cds

32
Larger Sequences

• On larger query sequences (5,000 to 6,000
  letters), the IDF method performed slightly
  better than BLAST. On 25 sequences randomly
  generated, the IDF method correctly ranked the
  original sequence first 24 times and once at rank
  3. BLAST, on the other hand, ranked the
  original sequence first 21 times while the
  remaining 4 were ranked 2, 2, 3 and 4. Average
  time per query for the IDF method was 47.4
  seconds and the average time for BLAST was 122.8
  seconds.

33
The Next Step

• Future work
• Weighted Term Vectors.
• Other weighting schemes such as the Modified
  Centroid Algorithm.
• Sequence-Sequence and Term-Term Correlations.
• Sequence clustering.

34
References

• Altschul SF, Gish W, Miller W, Myers EW, Lipman
  DJ. (1990) Basic local alignment search tool. J.
  Mol. Biol. 215403-10.
• O'Kane, K.C. and Lockner, M. J. (2004) Indexing
  genomic sequence libraries, Information
  Processing and Management, 41265-274.
• O'Kane, K.C. (2004) The Effect of Inverse
  Document Frequency Weights on Indexed Sequence
  Retrieval, submitted.
• Pearson, W. R. (2000) Flexible sequence
  similarity searching with the FASTA3 program
  package. Methods Mol. Biol. 132185-219.
• Salton, G. (1983), Introduction to Modern
  Information Retrieval, McGraw-Hill (New York
  1983).
• Smith, T.F. Waterman, M.S. (1981)
  Identification of common molecular subsequences.
  J. Mol. Biol. 147195-197

35
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36
Hierarchical Data Base
37
Bioinformatics

• Sloan Report on Bioinformatics from June 2004.
• Number of graduates
• There were only 26 new PhD's produced...
• 102 masters degrees awarded...
• Only 17 Bachelor's degrees produced...
• The data is for January 2002 until March
  2003.
• "... in the next few years the number of
  graduates is expected to increase by two or three
  times."
• Average program enrollment
• 103 Bachelors
• 435 Masters
• 296 Phd

38
B.S. in Bioinformtics at UNI

• Mathematics 800060 800061 800064 800152
  800164 (17 hours)
• Computer Science 810061 810062 810065
  810066
• 810080 810114
  810115 810180 (24 hours)
• Biology 840051 840052 840130 840140
  840153 (19 hours)
• Chemistry 860070 or both 860044 and 860048
  860063 (9-12 hours)
• Elective One course from the following
  (3 hours)
• Computer Science 810143 810147 810153
  810155
• 810161 810172
  810181
• 
  Total 73-75 hours

39
Courses

• 800060. Calculus I . The derivatives and
  integrals of elementary functions and their
  applications.
• 800061. Calculus II. Continuation of 800060
• 800064. Elementary Probability and Statistics
  for Bioinformatics. Descriptive statistics, basic
  probability concepts, confidence intervals,
  hypothesis testing, correlation and regression,
  elementary concepts of survival analysis
• 800152. Introduction to Probability. Axioms of
  probability, sample spaces having equally likely
  outcomes, conditional probability and
  independence, random variables, expectation,
  moment generating functions, jointly distributed
  random variables, weak law of large numbers,
  central limit theorem

40
Courses

• 800164. Statistical Methods in Bioinformatics.
  Analysis of a DNA sequence, analysis of multiple
  DNA and protein sequences, BLAST.
• 810061. Computer Science I. Introduction to
  computer programming in the context of a modern
  object-oriented programming language. Emphasis on
  good programming techniques, object-oriented
  design, and style through extensive practice in
  designing, coding, and debugging programs.
• 810062. Computer Science II. Intermediate
  programming in an object-oriented environment.
  Topics include object-oriented design,
  implementation of classes and methods, dynamic
  polymorphism, frameworks, patterns, software
  reuses, limitations, exceptions, and threads.

41
Courses

• 810065. Computing for Bioinformatics I.
  Intermediate programming with emphasis on
  bioinformatics. Includes file handling, memory
  management, multi-threading, B-trees,
  introduction to dynamic programming including
  Wunsch-Neddleman and Smith-Waterman algorithms
  for optimal alignments, exploration of BLAST,
  FASTA and gapped alignment, substitution
  matrices.
• 810066. Computing for Bioinformatics II.
  Advanced bioinformatics computing Perl and CGI
  programming data base facilities for
  bioinformatics pattern matching with regular
  expressions advanced dynamic programming
  optimal versus local alignment, multiple
  alignments data base mining tools, Entrez, SRS,
  BLAST, FASTA, CLUSTAL graphical 3-D
  representation of proteins phylogenic trees.

42
Courses

• 810080. Discrete Structures. Topics include
  propositional and first-order logic proofs and
  inference mathematical induction sets,
  relations, and functions and graphs, lattices,
  and Boolean algebra, all in the context of
  computer science.
• 810114. Database Systems. Storage of, and access
  to, physical databases data models, query
  languages, transaction processing, and recovery
  techniques object-oriented and distributed
  database systems and database design.
• 810115. Information Storage and Retrieval.
  Natural language processing analysis of textual
  material by statistical, syntactic, and logical
  methods retrieval systems models, dictionary
  construction, query processing, file structures,
  content analysis automatic retrieval systems and
  question-answering systems and evaluation of
  retrieval effectiveness.

43
Courses

• 810180. Undergraduate Research in Computer
  Science
• 840051. General Biology Organismal Diversity.
  Study of organismic biology emphasizing
  evolutionary patterns and diversity of organisms
  and interdependency of structure and function in
  living systems.
• 840052. General Biology Cell Structure and
  Function. Study of cells, genetics, and DNA
  technology emphasizing the chemical basis of life
  and flow of information.
• 840130. Molecular Biology of the Cell.
  Introduction to the molecular, biochemical, and
  cellular structure and function of cells, DNA
  structure and functions, and the translation of
  genetic information into functional structures of
  living cells. DNA replication, transcription of
  genes, and synthesis and processing of proteins
  will be emphasized.

44
Courses

• 840140. Genetics. Analytical approach to
  classical, molecular, and population genetics
• 840153. Recombinant DNA Techniques. Study of
  techniques for manipulating and analyzing DNA,
  including genomic library construction,
  polymerase chain reaction, oligonucleotide
  synthesis, genomic analysis with computers, and
  DNA and RNA isolation.
• 860070. General Chemistry I-II. Accelerated
  course for well-prepared students. Content
  similar to 860044 and 860048 but covered in one
  semester. Completion satisfies General Chemistry
  requirement of any chemistry major.

45
Courses

• 860063. Applied Organic and Biochemistry. Basic
  concepts in organic chemistry and biochemistry,
  including nomenclature, functional groups,
  reactivity, and macromolecules.
• Elective from
• 810143(g). Operating Systems. History and
  evolution of operating systems process and
  processor management primary and auxiliary
  storage management performance evaluation,
  security, and distributed systems issues and
  case studies of modern operating systems.

46
Courses

• 810147. Networking. Network architectures and
  communication protocol standards. Topics include
  communication of digital data, data-link
  protocols, local-area networks, network-layer
  protocols, transport-layer protocols,
  applications, network security, and management.
• 810153. Design and Analysis of Algorithms.
  Algorithm design techniques such as dynamic
  programming and greedy algorithms complexity
  analysis of algorithms efficient algorithms for
  classical problems intractable problems and
  techniques for addressing them and algorithms
  for parallel machines.
• 810155. Translation of Programming Languages.
  Introduction to analysis of programming languages
  and construction of translators.

47
Courses

• 810161. Artificial Intelligence. Models of
  intelligent behavior and problem solving
  knowledge representation and search methods
  learning topics such as knowledge-based systems,
  language understanding, and vision optional
  1-hour lab in symbolic programming techniques
  heuristic programming symbolic representations
  and algorithms and applications to search,
  parsing, and high-level problem-solving tasks.
• 810172. Software Engineering. Study of software
  life cycle models and their phases--planning,
  requirements, specifications, design,
  implementation, testing, and maintenance.
  Emphasis on tools, documentation, and
  applications.
• 810181. Theory of Computation. Topics include
  regular languages and grammars finite state
  automata context-free languages and grammars
  language recognition and parsing and turing
  computability and undecidability.