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D___PPT10$b___PPT9D< PAntnio Morgado - ajrm@soton.ac.uk Dr. Joo Marques Silva - jpms@ecs.soton.ac.ukHQ          T0"T0<P__r 2 C JA2ECS Logo - UOS 4 Col Posef{6 6 NČ;dudu"`GX H bThis work is being supported by Microsoft Research through its European PhD Scholarship Programmecc__R < s *3I1 ? B;dudu"`y @3tl___PPTMac11  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.      hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   D___PPT10$b___PPT9D< 5SAT is a well known problem and a area of intensive research SAT and SAT extensions provide compact models and efficient algorithms Efficient solvers are available for both SAT and SAT extensions:>H/  %%__~" K HC(d" `#r! &O4 N B=dudu"`H 0/.V+___PPTMac110+(+  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. 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Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.      hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   <___PPT10         R___PPT94,           eProblem Description: Given a set G of n genotypes, find a set H of 2n haplotypes (not necessarily distinct), such that for each genotype gi in G there is at least one pair of haplotypes (hj,hk), with hk and hj in H such that the pair (hj,hk) explains gi Technology used: SAT and Pseudo Boolean Optimization Reference: J. Marques-Silva & I. 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Co., Ltd.   ___PPT10tl     ___PPT9      r,Problem Description: Given a sequence of amino acids of a protein, determine the structure to which the protein folds Technology used: Pseudo Boolean Optimization (PBO) Current stage: currently a first attempt to directly translate the HP Lattice Model to PBO has been done Given the sequence  PHPPHPHP the energy of the conformation in the right is -2 Expected future steps: Inclusion of lower bounds that are able to efficiently reduce the search space Introduction of techniques to break and remove symmetries Ev3  jE  O$$$$ <((,,0044%__. V BX(=dudu"`:!?A@ 8  ___PPTMac11     hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.      hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   l___PPT10LD___PPT9 fBesides SAT itself, other extensions of SAT might be used to solve problems of BioInformatics: Pseudo Boolean Optimization Satisfiability Module Theories SAT Enumeration Counting SAT Quantified Boolean Formulas & _vo_     %YY__r2  <Y3d" `b q~. \ B 3Odudu"`6*1L,D,V+___PPTMAC110+(+  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. 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Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.      hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   T___PPT104,___PPT9d\ Problem Description: Compute the exact genomic distance between two genomes in the presence of duplications, namely, determining the maximum number of common intervals between the genomes Technology used: Pseudo Boolean Optimization Reference: check this on the internet??06 vCC-)  C%%__R ^ C *Aexample16*9/e;H  02uF[ ? 33___PPT10i.s+D=' == @B +0 ~v@( rG X  C vj   =v  # `= @  = " H  0޽h ? 3380___PPT10.s,0r@.D  1<(4J / 0DArialngsdwritiLL8Ԗ0ԖD-3 00000dwritiLL8ԖOh+'0dR hp    ,4(What SAT can do for Bioinformatics ? 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Co., Ltd.   ( ʚ;&)ʚ;dd0___PPT10 pp2___PPT9/ 0? %%What SAT can do for BioInformatics ? D&KC`C`C` /d 0 og $_ ( vaC'zBCB  r" 0 <ud" u2    <u " `2    " M NGH" `/$ DB6x" H Byd @" 7aBx" G Byd @" X'a3~" F HGuyd @" &.2Cr" E <yd" ` P1" C  fHduduyd @#" ` P2m%v___PPTMac11PH  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   0___PPT106___PPT9 ZC  __2 B # l?x 0<<P"` ]$f" A 0y" `4 1  NlH!@H!@?3"``` ,!80r___PPTMac11LD   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography D___PPT10$b___PPT9D< SAT & SAT ExtensionsZG6 G6G6 G 6BBB   T#H!@H!@?"`7 9 lOther& ?$((BBB   Ht#H!@H!@?"`&Y1N___PPTMac11(    hnamd` Arial&Monotype Typography 4___PPT10 B___PPT9$ yChecking Pedigree Consistency"(MBBB   H#H!@H!@?"` @+@  oHaplotype Inference"(MBBB    T,$#H!@H!@?"`') {Genome Rearrangement Distance$(MBBB   T2#H!@H!@?"`'*)N___PPTMac11(    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, Protein Folding<C.C.(BBB x"  B" `!  N07#H!@H!@?#" `d  N___PPTMac11(    hnamd` Arial&Monotype Typography 4___PPT10 B___PPT9$ 'Compact Models and Efficient Algorithms"('%MBBB "  # lD#H!@H!@d#" ` `,lf___PPTMac11@8  hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography  0___PPT106___PPT9 \M  BBB "  c X#H!@H!@GHd1#" ` `> S(f___PPTMac11@8  hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography  0___PPT106___PPT9 \M  BBB R ! s *A?gGQq I . C bAJMSR Logo with transparent backgroundEa$2H / Bd#dudu"`\DF|___PPTMac11  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.    pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.    pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.    pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.  D___PPT10$b___PPT9D< PAntnio Morgado - ajrm@soton.ac.uk Dr. Joo Marques Silva - jpms@ecs.soton.ac.ukHQ          T0"T0<P__r 2 C JA2ECS Logo - UOS 4 Col Posef{6 6 Nu#dudu"`GX H bThis work is being supported by Microsoft Research through its European PhD Scholarship Programmecc__R < s *3I1 ? B #dudu"`y @3tl___PPTMac11  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.      hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   D___PPT10$b___PPT9D< 5SAT is a well known problem and a area of intensive research SAT and SAT extensions provide compact models and efficient algorithms Efficient solvers are available for both SAT and SAT extensions:>H/  %%__~" K HC(d" `#r! &O4 N B#dudu"`H 0/.V+___PPTMac110+(+  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.      hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   <___PPT10         R___PPT94,           eProblem Description: Given a set G of n genotypes, find a set H of 2n haplotypes (not necessarily distinct), such that for each genotype gi in G there is at least one pair of haplotypes (hj,hk), with hk and hj in H such that the pair (hj,hk) explains gi Technology used: SAT and Pseudo Boolean Optimization Reference: J. Marques-Silva & I. Lynce, AAAI 06 f CC C CCC    D    $ $((,C,0C0)44448 8<<< <   CCC    $ $((, ,00 00004 48C88C8588<</C0 Y %%__6 R B#dudu"`*j0E<4___PPTMac11`X  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.      hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   ___PPT10tl     ___PPT9      r,Problem Description: Given a sequence of amino acids of a protein, determine the structure to which the protein folds Technology used: Pseudo Boolean Optimization (PBO) Current stage: currently a first attempt to directly translate the HP Lattice Model to PBO has been done Given the sequence  PHPPHPHP the energy of the conformation in the right is -2 Expected future steps: Inclusion of lower bounds that are able to efficiently reduce the search space Introduction of techniques to break and remove symmetries Ev3  jE  O$$$$ <((,,0044%__. V B@%dudu"`:!?A@ 8  ___PPTMac11     hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.      hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   l___PPT10LD___PPT9 fBesides SAT itself, other extensions of SAT might be used to solve problems of BioInformatics: Pseudo Boolean Optimization Satisfiability Module Theories SAT Enumeration Counting SAT Quantified Boolean Formulas & _vo_     %YY__r2  <Y3d" `b q~. \ B %dudu"`6*1L,D,V+___PPTMAC110+(+  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.      hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   T___PPT104,___PPT9d\ Problem Description: Compute the exact genomic distance between two genomes in the presence of duplications, namely, determining the maximum number of common intervals between the genomes Technology used: Pseudo Boolean Optimization Reference: check this on the internet??06 vCC-)  C%%__R ^ C *Aexample16*9/e;. _ B%dudu"`0;#L,D,V+___PPTMAC110+(+  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.      hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   T___PPT104,___PPT9d\ Problem Description: Given a pedigree check if it is consistent with the Mendelian laws of inheritance, i.e., check if every individual inherits exactly one allele from each of its parents Technology used: SAT by translation into CNF Reference: check this on the internet??06 vCC-)  CI %%__H  02uF[ ? 33___PPT10i.s+D=' #= @B +r"f 1<(4J / 0DArialngsdwritiLL8Ԗ0ԖD-3 00000dwritiLL8Ԗ0Ԗ0 DArial BlackritiLL8Ԗ0Ԗ"0DTimes New RomanLL8Ԗ0Ԗ@DLucida Handwriting8Ԗ0ԖBPDWingdings ՜.+,04     CustomOffice 2004 Test Drive User\; ArialMS Pゴシック Arial BlackTimes New RomanLucida Handwriting WingdingsBlank Presentation&What SAT can do for BioInformatics ?  Fonts UsedDesign Template Slide Titles_8  a3~" F HGuyd @" &.2Cr" E <yd" ` P1" C  f,duduyd @#" ` P2m%v___PPTMac11PH  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   0___PPT106___PPT9 ZC  __2 B # l?x 0<<P"` ]$f" A 0y" `4 1  N0H!@H!@?3"``` ,!80r___PPTMac11LD   hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography D___PPT10$b___PPT9D< SAT & SAT ExtensionsZG6 G6G6 G 6BBB   T$H!@H!@?"`7 9 lOther& ?$((BBB   Ht$H!@H!@?"`&Y1N___PPTMac11(    hnamd` Arial&Monotype Typography 4___PPT10 B___PPT9$ yChecking Pedigree Consistency"(MBBB   H0$H!@H!@?"` @+@  oHaplotype Inference"(MBBB    T $H!@H!@?"`') {Genome Rearrangement Distance$(MBBB   T'$H!@H!@?"`'*)N___PPTMac11(    hnamd` Arial&Monotype Typography <___PPT10R___PPT94, Protein Folding<C.C.(BBB x"  B" `!  N?$H!@H!@?#" `d  N___PPTMac11(    hnamd` Arial&Monotype Typography 4___PPT10 B___PPT9$ 'Compact Models and Efficient Algorithms"('%MBBB "  # lI$H!@H!@d#" ` `,lf___PPTMac11@8  hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography  0___PPT106___PPT9 \M  BBB "  c ,K$H!@H!@GHd1#" ` `> S(f___PPTMac11@8  hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography  0___PPT106___PPT9 \M  BBB R ! s *A?gGQq I . C bAJMSR Logo with transparent backgroundEa$2H / B+$dudu"`\DF|___PPTMac11  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.    pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.    pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.    pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.  D___PPT10$b___PPT9D< PAntnio Morgado - ajrm@soton.ac.uk Dr. Joo Marques Silva - jpms@ecs.soton.ac.ukHQ          T0"T0<P__r 2 C JA2ECS Logo - UOS 4 Col Posef{6 6 Nd{$dudu"`GX H bThis work is being supported by Microsoft Research through its European PhD Scholarship Programmecc__R < s *3I1 ? B$dudu"`y @3tl___PPTMac11  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.      hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   D___PPT10$b___PPT9D< 5SAT is a well known problem and a area of intensive research SAT and SAT extensions provide compact models and efficient algorithms Efficient solvers are available for both SAT and SAT extensions:>H/  %%__~" K HC(d" `#r! &Q4 N B$dudu"`H 0/.V+___PPTMac110+(+  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.      hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   <___PPT10         R___PPT94,           gProblem Description: Given a set G of n genotypes, find a set H of 2n haplotypes (not necessarily distinct), such that for each genotype gi in G there is at least one pair of haplotypes (hj,hk), with hk and hj in H such that the pair (hj,hk) explains gi Technology used: SAT and Pseudo Boolean Optimization Reference: J. Marques-Silva and I. Lynce, AAAI 06 h CC C CCC    D    $ $((,C,0C0)44448 8<<< <   CCC    $ $((, ,00 00004 48C88C8588<<1C0 [ %%__6 R B $dudu"`*j0E<4___PPTMac11`X  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.      hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   ___PPT10tl     ___PPT9      r,Problem Description: Given a sequence of amino acids of a protein, determine the structure to which the protein folds Technology used: Pseudo Boolean Optimization (PBO) Current stage: currently a first attempt to directly translate the HP Lattice Model to PBO has been done Given the sequence  PHPPHPHP the energy of the conformation in the right is -2 Expected future steps: Inclusion of lower bounds that are able to efficiently reduce the search space Introduction of techniques to break and remove symmetries Ev3  jE  O$$$$ <((,,0044%__. V Bl^$dudu"`:!?A@ 8  ___PPTMac11     hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.      hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   l___PPT10LD___PPT9 fBesides SAT itself, other extensions of SAT might be used to solve problems of BioInformatics: Pseudo Boolean Optimization Satisfiability Module Theories SAT Enumeration Counting SAT Quantified Boolean Formulas & _vo_     %YY__r2  <Y3d" `b q~/ \ B&dudu"`6*2L,D,V+___PPTMAC110+(+  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.       !"#    pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.      hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   T___PPT104,___PPT9d\ 40Problem Description: Compute the exact genomic distance between two genomes in the presence of duplications, namely, determining the maximum number of common intervals between the genomes Technology used: Pseudo Boolean Optimization Reference: S.Angibaud, G.Fertin, I.Rusu and S.Vialette, RECOMB-CG 06 v1CC-D  CP  %%__R ^ C *Aexample16*9/e;// _ B<$&dudu"`0+$L,D,V+___PPTMAC110+(+  pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.     pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.      hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography    hnamd` Arial&Monotype Typography   pnamdhHiragino Kaku Gothic Pro W3Dainippon Screen Mfg. Co., Ltd.   T___PPT104,___PPT9d\ [3Problem Description: Given a pedigree check if it is consistent with the Mendelian laws of inheritance, i.e., check if every individual inherits exactly one allele from each of its parents Technology used: SAT by translation into CNF Reference: P. Manolios, M. Galceran Oms and S. Oliva Valls, TACAS 07 v4CC-D  CtI  %%__H  02uF[ ? 33___PPT10i.s+D=' $= @B +rb  1