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j:j9{/$׋sT\8C:+eْƋCEĝ8p3)̭kǘj[+LfѨʚ .1p.yb& |ieomfxU{>m\ ;l\-'q4NG(gbh\W\5@GTE^Ohy#0p;֭3V @0q{vC|1&I0I6DceG®E7h]N7WRfN4x 3:6.쯐vNԩOΦ=HiS iz^+Dӈt(䶫N4boBUspgN|!^DSʦȎnf4<_ZXo]Z7D7f}wLs(8WhpGCߧkV(<.K?PK!drs/downrev.xmlDJ1Ef*ش`Սc]>'3_op˽˙-zۉh+ ĵӆϗ{1!k",3,;NUjDp,QA/uKy]r n;y[ip~hsK:Zf C0q\ݷw;G?Ľ܁ؿ_5DAAv˦PK-![Content_Types].xmlPK-!1_a ._rels/.relsPK-!x*. )drs/shapexml.xmlPK-!drs/downrev.xmlPKt4z | jImplementation (    (  l/z0e0e? oRjL 4"F@PK![Content_Types].xmlJ0*miG]`Hm6 Xwt?. g#Wi3E).+7 >ON ޑ1ˋz "+R RhB.} /<^ITխ%rHK4uK~I0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!dhdrs/shapexml.xmlWn6;YNb#bcm#0b/PHoP/coZoo(񺋢= 3CqH|d|vS(FG͙ԉIs g eV:vWЕ _z_[-,e!SJBxLSIEjuV!rG8J̒ܯgiiQ?~~ןYZ]IV1DCR+G60mpC{4K%*^^I+7uuwopȋS.8'_jV M1\6Œvs x@\u.9Ki/VmJp͝I;_pPs"<0vٳ@X E|`^=^WtU" Nߋcv'(y"RZ–Dl6f b=uH? :D9?[%>i>)!<ApuL POH[R-D<5ھ֗b*߅MpV7ز 3t jNV2%Ԧ'<Ҹ٩.jAghH5q5Vv |w'p0G *^5bDf!\ 讪"/yEK}~S~#P5a"q%OP6 %EE!W*w0%TNu7ͬ1Yz4޺D@iJծoQyJ/T%pc-e2@K;_,V}i/o2+:LkbKuyR٧pM&>gj+2CTz|S 'Nw~[GQ)_UD3y!J\!PS>Y!P/ $cijiJ\F?\F+<7@/I: +Щ~)mCS4ߔ^:++GPK!0`drs/downrev.xmlDJ@E0QZgZ^^,(Uv0;P1>%:.җ5kS۱:M!FWIhpʻ$yjx]syOaRdqn-"ǟ_F!@kԎ|`ݢiPK-![Content_Types].xmlPK-!1_a ._rels/.relsPK-!dh)drs/shapexml.xmlPK-!0`/drs/downrev.xmlPK5 p  | KLet x denote the list of items. For example, x = (0,0,0,0,0,0,1,0,0,0,1,0)PL )K    fp=80___PPT10.h5 WOp,7(  ,) ,  j{0e0e? jL 1    kOutcome Vectors (   ,  z{0e0e?gQ[HrbMn@S 2   The vector y is an outcome vector which is corresponding to an input x. So, yt = (1,1,0,1,1,0,0,0,1,0,0,0). If A is 1-1, then we can decode x long as we know its outcome vector. In order to get the job done with lower decoding complexity, extra properties for A is needed.  P#  $_*     , D`z?>\HrbMn@S 1`   ^(   fp=___PPT10i.@'+D=' = @B +"5 0(  0F 0  x#0e0e?Rectangle 2w7g   z,Can we find positives from the above matrix?- -(- H 0  x{0e0e?Rectangle 3  |Yes, we can if the number of positives is not too many, say at most 2, by running the 9 tests simultaneously corresponding to rows. The reason is that the union of (at most) 2 columns can not contain any other distinct column. (?)d DN;  fp=___PPT10i.E`8+D=' = @B +"5 4(  4' 4  j`$z0e0e? jL 1i   i Decoding Idea (   : 4  z{0e0e?gQ[HrbMn@S 2'g  lSince there are 12 items and the number of positives is at most 2, we have 1 + 12 + 66 possible inputs. (?) There are 29 possible distinct outcome vectors. It seems that we can use a matrix with less rows. The question is  how to construct such a matrix .: wh  4 D`{?>\HrbMn@S 1`   ^(   fp=___PPT10i.+D=' = @B +"5 8(  8/ 8  xz0e0e?Rectangle 2gW   cSet Notation (Design) ( T 8  x z0e0e?Rectangle 3   "Let M = [mi,j] be a txn matrix mentioned above. Then we can use n sets (ordered) Si s to represent the matrix where Sk = {i : mi,k = 1, i = 1, 2, & , t}, k = 1, 2, & , n. The following sets represent the (0,1)-matrix of the last 9x12 matrix: {1,2,3}, {4,5,6}, {7,8,9}, {1,4,7}, {2,5,8}, {3,6,9}, {1,5,9}, ({2,6,7}, {3,4,8}, {1,6,8}, {2,4,9}, {3,5,7}. (Projective plane of order 3.) 4u 8 G    E C$ GG  fp=___PPT10i.?y+D=' = @B +"5 <(  <L <  x#0e0e?Rectangle 2`P   2d-separable and d-disjunct matrices3 3(3 , <  xz0e0e?Rectangle 3  `A matrix is d-separable if D D for any two distinct d-sets D and D (columns), i.e. no two unions of d columns are the same. A matrix is d-disjunct if no column is contained in the union of any other d columns. ~  $F A  fp=___PPT10i.+D=' = @B +"5 @(  @) @  x-z0e0e?Rectangle 2   ]Important Facts ( 5 @  x 0e0e?Rectangle 3   igA d-disjunct matrix is also a d-separable matrix. A d-separable matrix can be applied to find exactly d positives. Proof. The union of d columns corresponds to distinct outcome vector. d-disjunct matrices have a simple decoding algorithm, namely, a column is positive if and only if it does not appear in a negative row. (The above matrix is 2-disjunct.) s ZI Z Z Z24 "h  fp=___PPT10i. p+D=' = @B +"5 D(  D( D  j {0e0e? jL 19 )   jVarious Models (   D  z{0e0e?gQ[HrbMn@S 2   Errors occurred. There are inhibitors. There is a threshold. Defective items are sets: complex model. Competitive model: the number of defectives is unknown. The defectives are mutually obscuring.      @   D D@{?>\HrbMn@S 1`   ^(   fp=80___PPT10. "5 H(  H) H  j`{0e0e? jL 1    kDisjunct Matrices (   H  z{0e0e?gQ[HrbMn@S 2zz   "Disjunct matrices can be considered as special designs or special codes. Extra constrains are needed in order to handle various models in group testing. We are aiming at finding all the defectives with comparatively easier decoding algorithms. Of course, also minimize the number of tests.^# I"   fp=80___PPT10."5 g_LG(  L% L  j`^}0e0e? jL 1   g(d; z)-disjunct(   L  zP0e0e?gQ[HrbMn@S 3   Let A be a tn (0, 1)-matrix in which the rows are indexed by [1, t] and the columns are indexed with the supports of columns. (Columns are subsets of [1, t].) A is (d; z)-disjunct if for any d+1 columns C0, C1, & , Cd, |C0/(C1C2& Cd)| e" z. If z e" 2e + 1, then this matrix can be applied to find d defectives with e errors in outcome vectors.&X -eW   fp=80___PPT10.@0G"5 @8P (  P% P  jP0e0e? jL 1gW   g(d, r]-disjunct(   P  z@Q0e0e?gQ[HrbMn@S 2   9A is (d, r]-disjunct if the union of any d columns does not contain the intersection of any other r columns. If the defectives are r-subsets instead of items (complex model), this matrix can be utilized to find d defective complexes. In case of errors occurred, we define a (d, r; z]-disjunct matrix accordingly.t:' K g9   fp=80___PPT10.HL"m5 T(  T% T  jU0e0e? jL 1gW   g(d, h)-disjunct(  0 T  zQ0e0e?gQ[HrbMn@S 2   bA is called (d, h)-disjunct if the union of any d columns does not contain the union of the other h columns. A can be applied to find d defectives in an inhibitor model with h inhibitors. We need extra effort to handle this model with errors!0;7   fp=80___PPT10.Pai~" 5   X (  X. X  jR0e0e? jL 1   p(d, s out of r]-disjunct(  u  X  z S0e0e?gQ[HrbMn@S 2"|PK![Content_Types].xmlJ0*miG]`Hm6 Xwt?. g#Wi3E).+7 >ON ޑ1ˋz "+R RhB.} /<^ITխ%rHK4uK~I0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!udrs/shapexml.xmlYO7Ww|,YCEV(LmNDj[9TZE=΢VR+F`lg9L[HcLA3,N4/ά:*2+iߝ3 ֶ|\i6m4\j&ICLVj'JUj=j"Ѽb բа$ib7]?󛷟>~y/ 3Ȣ_"Tl+8P(X)h@?=ǻ&r ʿvd*?SVrjbq*C[fB1B1g]ψz̙2gi͘~7In]Co&9nsQŭx@}](s_Y |zBX\>^ka 񬰽"9־2RCanbH^,Vb$w(TmPK!Ǚ4drs/downrev.xmlLMk@EnNZi+HAR R<`M;t!]^\lћZ|eY8A[]q_=LAL a10ն-Pa2&%ch+vESHLJz/)?.F/MvW=R~"P1[ & Uz>Sݢi9PK-![Content_Types].xmlPK-!1_a ._rels/.relsPK-!u)drs/shapexml.xmlPK-!Ǚ4mdrs/downrev.xmlPKq  ^V___PPT980 A is (d, s out of r]-disjunct if for any d columns and any other r columns, there exists a row (index) in which none of the d columns appear and at least s of r columns do. If s = 1, then A is (d, r)-disjunct and if s = r, then A is (d, r]-disjunct.^%,#  8  #   fp=80___PPT10.Pv"5  0\(  \( \  j!z0e0e? jL 1gW   j(k, m, n)-selector(   \  z%z0e0e?gQ[HrbMn@S 2   PFor m d" k, A is a (k, m, n)-selector if any tk submatrix of A contains at least m rows of the identity matrix Ik. A (k, m, n)-selector corresponds to well-known combinatorial objects such as superimposed code and k-selectors. Superimposed codes and k-selectors are very basic combinatorial structures and find application in a variety of areas such as cryptography, data security, computational molecular biology etc. $cC O$f<   fp=80___PPT10.d"5 :2@`(  `7 `  j{0e0e? jL 1`P   y!Construction of disjunct-matrices""(!  9 `  z{0e0e?gQ[HrbMn@S 2   kThere are known constructions, deterministic and probabilistic. Here, we shall use the well-known Lovsz Local Lemma to construct such matrices. We shall present one of them and the others are similar in some sense.Tbgc  b ` :A?? WGr 4s  p fp=80___PPT10.`!"[5 Pd(  dN d  j@{0e0e? jL 1   Lovsz Local Lemma>(g((   d  z{0e0e?gQ[HrbMn@S 2" Ý PK![Content_Types].xmlJ0*miG]`Hm6 Xwt?. g#Wi3E).+7 >ON ޑ1ˋz "+R RhB.} /<^ITխ%rHK4uK~I0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!B5Bdrs/shapexml.xml\Ao6 x-\;6F" muZc5kKПK/C̀{$;4J "G|#X)W:Jd@7(2L< N%09d"q繛\J^!W!FHu]uܾzNJvb[)2WxSl/SM&/sZS. ~p+ lddO/ {;W£?|6P5-s7WY?n;2 2sN^6Z6Mީ^0kG RyĔT0t6}[ .v1]Y.]kmfGZIVlbm|rw󕝋ÑSI+`2899$-}Vח\Hi"+\.=|ȼRn}ceRrbY+S^pi;[t?PK!cdrs/downrev.xmlDKK@ab'Z|{[D%MB3gI\p݊}hA8g ؔV5Bجn@HFQk #8|v|4\,[J$ 9!1\P֬)cbSຕYv%55&=rkѦXwOޟ\ٍ'-C|'WĶ8|F-)D-&KPK-![Content_Types].xmlPK-!1_a ._rels/.relsPK-!B5B)drs/shapexml.xmlPK-!cdrs/downrev.xmlPK  jb___PPT9D< (Symmetric Case) Let A1, A2, & , Am be events in an arbitrary probability space. Suppose that each event Ai is mutually independent of a set of other events Aj but at most of them, and that Pr(Ai) is at most 0 < p < 1 for all 1 d" I d" m. If eepe( +1) d" 1, then the product of m probabilities Pr(Bi) is larger than 0 where Bi is the complement of the event Ai.\   G 3   "  * + " ; &  .  &  . ! &  .  & p      s   fp=80___PPT10.`"5 +#`h (  h3 h  j{0e0e? jL 1   u (d, r]-disjunct Case (    h  z0e0e?gQ[HrbMn@S 2"  PK![Content_Types].xmlJ0*miG]`Hm6 Xwt?. g#Wi3E).+7 >ON ޑ1ˋz "+R RhB.} /<^ITխ%rHK4uK~I0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!7( drs/shapexml.xmlYO7Ww|,aaA;DHPQ LmCS.Cz\zɥJQ/Sioa`Q+%,.YfW<{?g,dʕcѣJA(}mN(цsMտ4@ckGG$|^#1 N V3U|0DX( %CWrI Si[pчH'/^v˟~իחxi>wMӊNb@0k`HGh4yTJz:hcYV?e8||R*DsPR(`e5>3ćJZ)AaR ibGTKjfvغu{a>?V J^(`&LqJR{zT*jfJǕ"dzMFNF,¤z, 9e%̴d'Qǒ(mgL%ywF,VM[8HV!v"阹7r~"Z*L?drO,b (AA(`i-%q J<~gR׆9ML#i`rU=brFӞH>RX DӉ 2$O:%y) s5>Vgٔ]v rim;('ElPLcѿ_sbXVpU:!Yͽ$ yhg.o4]4J {؛-w>K'fipH7k-6orm+͇?>||` n ָ2~~^(> !G]kWn2o\dg$tC/(:S!nd 8;0nͭnndvxwt5F-\L1+;~r#ޣY!`//!?PK!drs/downrev.xmlDMK0E!ON ޑ1ˋz "+R RhB.} /<^ITխ%rHK4uK~I0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!jxPdrs/shapexml.xml\Ko8/uqh(E Q1d:VMQZvz){OK/{뽇bg(Y~Iڊ@!Ň8rF:x:sXztQ.K>??=D&{LĒ{t5}zOIK'KJ<:0&i:Gq%c1YuYO\fA7zBI+9&lQ$yEd4('no5wih4ّqܛa)>N@$cuE+`SHl5!K9Nb&LЫG,yb 8Jin`EK9`*!F|b%V`6Hź6;tTOo/'brgb ThmVK`#AIϙ߽ @ gmy}?6FЀ=x%,H𐆥@ttC k.@Bc_ W>5fK'{'Oa*yd _qa~ X r.d'J/@( ehWx.Ca65m>A\ {yTB!wm!WQZDQ%+""Dg:*6 b -$^e| .EÛXle"PI*T`y`feFv f> `hD/k¤l@8K RlXED UsB&V9 @[nLs֢T7 =D1Η0 pZI*.\:L1 gB8*gBE[ٸ j $Ggtyy8Y\VeXan8Φ#"p4 F1f`KZYn_VRon4r18k@eS w1| V&v,6tmSb*XRgsWg%zGVR~ ==]tF{z~i*VYmC"7c3y"AǍpV復7):XvTge_E9˪u0gTՋnzMRsfSfNPK!ݣPdrs/downrev.xmlDMK@Eaxb'iA"/kygI_B{9X 9_[V0' k.w/w |@X&gZ^_-0Ӷ uPa*6c`+vGi4If`–+*ۓQ0Gۧh"ҥEj,8/W @NAPK-![Content_Types].xmlPK-!1_a ._rels/.relsPK-!jxP)drs/shapexml.xmlPK-!ݣPdrs/downrev.xmlPK  ___PPT9 t(n, d, r] d" (1 + d/r)r(1 + r/d)d e {1 + ln[((n, d))((n-d, r))  ((n-d-r, d))e ((n-2d-r, r))]}. Proof. (Sketch) Let M be a tn (0, 1)-matrix with Pr(mi,j = 1) = p and Pr(mi,j = 0) = 1  p. Note that all entries are chosen independently. $  "* "*"* * *+"""& "" "   "  *  " $"$$*$$"$("(,",80"04c48c8<<  !    ,    #  9     8     fp=___PPT10i.pݬc+D=' = @B +"45 #p(  p p  j`)z0e0e? jL 1   "  p  z@{0e0e?gQ[HrbMn@S 2" PK![Content_Types].xmlJ0*miG]`Hm6 Xwt?. g#Wi3E).+7 >ON ޑ1ˋz "+R RhB.} /<^ITխ%rHK4uK~I0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!Tidrs/shapexml.xml]OoHakE Ti$vWB*z37;(KC?^z[{/RT[{c $!f`Pp޼7Ȑ m^Yq'ʶ^4 G$]֘E֫:QHdCK֋3F/q§ 1.^W- \aK`9qoN}o?z#)[Ť}|*4:J:ETW0ҙ"`H%AQ(M>pd[rRkI۸4PF룞۵cZz=J#f Zt=u6āj $ Ux⎨= r:Ǩ>0$P?7 (2}@lVTkRe*eȈlM'[Y!rj[2MI(?ۡ q,!$9}2ՀI2m(/E-{,I6)ů]5 = m1^xۆyɦ @Vqĥ >Q d*ek&h $pCG7WE8<k tJ#_y+ÂY;^`:VƊa;YeØyN`t}Bт'3QEqnoboߪح|ܦwd.)Oq& (c= Cmc m孥dX'w'd2{"j$"Y1S Xyi VU;` _6fK4ɖyU6te̞iZ"H37X>(^cW%Q;Bjt>A׸5K\mpw[TPx;?/<^׮xӵǛNQs$ORLO :“PK!4drs/downrev.xmlDKK@ab'6 "BOm3$.ty8MnD ܎l jS"o7 | a>RlomB)"LJ_Tɏm&v4])>u#'Ir/5&>TKqs]==W}Gu"Nj}:+Q !q_VkBtPK-![Content_Types].xmlPK-!1_a ._rels/.relsPK-!Ti)drs/shapexml.xmlPK-!4drs/downrev.xmlPK q  ___PPT9tl fLet D (([n], d)), R (([n], r)), DR = and AD,R be the event such that R D. Hence, the complement of AD,R says that R is not contained in D. Pr(AD,R) = (1  pr(1-p)d)t. ( +1) = ((n, d)) e ((n-d, r)) - ((n d-r, d)) e ((n-2d-r, r)). Hence, e e (1  pr(1-p)d)te[((n, d)) e ((n-d, r)) - ((n d-r, d)) e ((n-2d-r, r))] d" 1 is required to make sure that the intersection of the complements of all events AD,R does have nonnegative probability and hence we have a (d, r]-disjunct matrix. z%vM,#& &?&&&      <&P&M&                     fp=___PPT10i.+D=' = @B +"5 nftN(  t t  j&z0e0e? jL 1`P   " . t  z -z0e0e?gQ[HrbMn@S 2" PK![Content_Types].xmlJ0*miG]`Hm6 Xwt?. g#Wi3E).+7 >ON ޑ1ˋz "+R RhB.} /<^ITխ%rHK4uK~I0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!6mc^drs/shapexml.xml\n8/@Z׉8E Q1e:V-QZNz)=zþAѷR6Zrh2)R9gq8ˡ{&B5"~w5M=wjPRޡYzyOgA5 \jPzR|>{̣s?`ʺ𨄬K*A/uu)0e_7q:5"z=~ۇO_=)ZB{FUt=RW-ǡmР-֬RROQ]].w(TaWx6Vn˅BAC rD5VPOʕ2"68.8)C;[zTmkX7 ' ŃE P,ÚU)J42'EȈɒd xWmk͒qJB{{ l} D(oo&"͵р J-q]%!-ʖl[cEEh0aȽRBpAJpдkP۵HuohAbFR] uI(-(i 9RtQؼ0$;O4&k\l]IUǸEW֍o 7C%$Е$sգpYUIz*USDV$xu(tA5CW6Ty[QZ"GR{s5S<Ǩ.Ù;/4ܪDIH,5'p`vo ݅eF@5 CԬR)u1f3GȎ)WЎ_A{f¡Q9ZJEN8DHZ*G+d.dNdt)L93Eأ~;OGF9]A[6 pFA@۔3׏~ܑ7Hm?yܘ'>,{5n1 p c2O/UwR3r%].7w>xN/ΩHtb(LDuA:'TDq9CuPuTLzV*֚kXb&* %2&%k۰:M!FWH娏p]i  2 & &"&  & $&$$&$((,,0044N4&48888888888<<<u<<         K           fp=___PPT10i.Ƙ+D=' = @B +"5 xv(  x x  j`0e0e? jL 1`P   " V x  z0e0e?gQ[HrbMn@S 2    I would like to express my gratitude to Professor Frank K. Hwang and all my former students who are working on Group Testing especially Kuo-An Yu, Drs. Hong-Bin Chen, Huilan Chang and Chih-Huai Shih. Without their help, presenting this talk is an impossible mission.> (FAC    fp=___PPT10i.Ș++D=' = @B +"5 |(  |  |  jV0e0e? jL 1    b References    q |  z@V0e0e?gQ[HrbMn@S 2" PK![Content_Types].xmlJ0*miG]`Hm6 Xwt?. g#Wi3E).+7 >ON ޑ1ˋz "+R RhB.} /<^ITխ%rHK4uK~I0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!:bli9drs/shapexml.xml[n8/@pN(Ec Q1e*VCQZvz){#쥗C_f[ )?ȡ[+Ѐ% )r>~pD<]$̹T.t˫8Qk&'LtsN^(,^ЩY^)OX$͸(U UWLK4<(AXSJGPa(|>*Ojt]J$K౷_~w|x-izQgЦA^Eط4lFLUЭ>nZ(}l \@s]Gl ΰ"l ˌG,v mUFqf3|+#1*eaЧ\^^AT1a͞c%b}dOI}^?B*if(fD$!Ϧ!\!6+N@{q6Ǻ!P N槷jB (([/comzWY;^žڀhBUEċ$UUmyعvT[_ j+#nUǪ@byqMX#eZ#r2d.Oq{0`o-}kV'J;N.f{Yy_y_w/ yy0&`39LFĈ޶Hv}s ~g#cc G4Ko\Vb\:-{U/cY\ ,D"oKVbK|r#@AVot䲛 ;4y oIz0+l4 wȟsrs+<+RYZK2= ~R1[A?PK!Ldrs/downrev.xmlDMK@Eaxb'j$(Ag5 ęi{˹jԭ46%~ru2ZkVef6"B ˤEŚvlbwNSѕR9"\:Ić:~hG0cڬw=|~F@8f&qO_VBPK-![Content_Types].xmlPK-!1_a ._rels/.relsPK-!:bli9)drs/shapexml.xmlPK-!Ldrs/downrev.xmlPKMM   oA new construction of 3-bar-separable matrices via improved decoding of Macula construction (with F. K. Hwang), Discrete Optim., 5(2008), 700-704. An upper bound of the number of tests in pooling designs for the error-tolerant complex model (with Hong-Bin. Chen and F. K. Hwang), Optimization Letters, 2(2008), no. 3, 425-431. The minimum number of e-vertex-cover among hypergraphs with e edges of given rank (with F. H. Chang, F. K. Hwang and B. C. Lin), Discrete Applied Math., 157(2009), 164-169. Non-adaptive algorithms for threshold group testing (with Hong-Bin Chen), Discrete Applied Math., 157(2009), 1581-1585. p KU'G J3 $TG %    fp=___PPT10i.ɘ`+D=' = @B +"5 x(     j0e0e? jL 19)   a Continued       z ]0e0e?gQ[HrbMn@S 2" PK![Content_Types].xmlJ0*miG]`Hm6 Xwt?. g#Wi3E).+7 >ON ޑ1ˋz "+R RhB.} /<^ITխ%rHK4uK~I0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!(_|ǟIdrs/shapexml.xml\Oo6w x\'c'F1mQuZb5KЏK/þ̀{$,'vJdR{z(<%Lq*l.t˫8Q #&Rz5}~w'YGg.tlL֩u8 ҌKhR0UuU\fF7ZŒPr: Ki_xЃFOd wۯ_/}4h=]΀^^0vF.Ddi ꖪ@ M1P9 hqhXţ֤'sNpl 17Xt XRqBjlU \.|ehpa kEmAu#Dl9Bh5+ND+P OZQzYccN%<䅪 V8+)XOU|syVHo 23Sf=EtS杲܍{8eU?<-w˲ևs"!Kj}FF3a-'gv>VQNj"Zipz:+ XmeecT@!7./+Vp^ kC(9GGkmJ~'o999Sr%Ƨ+r*EPK!hdrs/downrev.xmlDMK@Eaxb'mh초 /]?3IhM&wp˽˙/ӈ-+ą5 {> kl,3yX../im(EPABI鋊 mcw`ѕR;#4r$w`–+*ۓQ0Sz\+=x{onVjxzhχEjiN@} Eh rPK-![Content_Types].xmlPK-!1_a ._rels/.relsPK-!(_|ǟI)drs/shapexml.xmlPK-!hdrs/downrev.xmlPK   4Identification and classification problem on pooling designs for inhibitor models (with Huilan Chang and Hong-Bin Chen), J. Computational Biology, 17(2010), No. 7, 927-941. Reconstruction of hidden graphs and threshold group testing (with Huilan Chang, Hong-Bin Chen and Chih-Huai Shih), J. Combin. Optimization, 22(2011), no. 2, 270  281. Group testing with multiple mutually-obscuring positives (with Hong-Bin Chen), Lecture Notes Computer Science, 7777(2013), 557  568. Threshold group testing on inhibitor model (Huilan Chang and Chih-Huai Shih), J. Computational Biology, Vol. 20, No. 6, 2013, 1  7. aA /.E:   * bT     fp=___PPT10i.ɘŲ+D=' = @B +"5 |(     j{0e0e? jL 1    a Continued       z{0e0e?gQ[HrbMn@S 2" PK![Content_Types].xmlJ0*miG]`Hm6 Xwt?. g#Wi3E).+7 >ON ޑ1ˋz "+R RhB.} /<^ITխ%rHK4uK~I0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!K2ϡvDdrs/shapexml.xml\Oo6w x-\'$F"1mQu Zb5KЏK/CL{d;^kgMHߏ?=ѳI"Ș+2Ow(2L%09`"jmgYMX,1J{YWa(|>*ZQ"Yy翿盏HVg dcEbod"2EAvU+U!Q;l6k 2CBi[8֚D*YV#Jn+mPCBHo6AϔoBtؒ9Ѳ+|WA{ B2T]SV1P}D&u@w Hco5ҟO 0[j`@ K&3B̈eɔ6WLey lƩdjȩ_"+UŦ̽k$LuU~0^X%1h nrl h\P29sP=YGK|Jsb3q,y;!|dRQ<А1Cvk|S-慺: 8b═/OBO4xEFCH~}ŰyUy@;/GIob[ ( \V^ ӱa4\, %}=* TŗШɴgC\r@j $6"(!blmZWidÃX9Չi BYghNEITqVpBjLJ91y~p`SR`Á˚.SH)%X'kSȔ3 Qmô8!pmJR dO]Y <-kπŽ ,ѣ^^=.S ~ Gvb~lh:GQ>$+wپcGˏYA>o4р(=#NALo,6*Y9Jaw5aEvޫ9yo/o,+o3{4ɯxUQ;-08*=Lls5βpg U aM[p5pz{o."g3)~. &53\{]~CzbS1=,,^913 ;A4[XvP`']3%h%+陼 4$Ww8"LXrF9xQ )Cc~v-ûG#׮J>מ!Pa/APK!drs/downrev.xmlD]K0.eN1Q}yڼkJ&Y{zy8,׃nXGWM`d ++S 8w|@#\z5Yb&moB" ڌs_(觶%uCaI5V&>(lEQQ.Z/zd'x< 4q=VW) MOs`*G ~6_PK-![Content_Types].xmlPK-!1_a ._rels/.relsPK-!K2ϡvD)drs/shapexml.xmlPK-!drs/downrev.xmlPK MM   6New bound on 2-bar-separable codes of length 2 (with Minquan Cheng, J. Jiang, Yuan-Hsun Lo and Ying Miao), Des. Code Cryptography, to appear. Learning a hidden graph (with Huilan Chang and Chie-Huai Shih), under review of Optimization Letters. Expanded separable codes (with Minquan Cheng, J. Jiang, Yuan-Hsun Lo and Ying Miao), under review of IEEE Transaction of Information Theory. Applications of the Lovsz Local Lemma to pooling designs, M.S. thesis, 2007, National Chiao Tung University.  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   l如螢幕大小 (4:3) &Comic Sans MS 新細明體Arial 標楷體SymbolCrayons 1_Crayons!Pooling Designs in Group TestingGroup TestingFormal Definitions'Adaptive (Sequential) and Non-adaptiveDeterministic AlgorithmsNon-adaptive Algorithm Incidence MatrixImplementationOutcome Vectors-Can we find positives from the above matrix?Decoding IdeaSet Notation (Design)3d-separable and d-disjunct matricesImportant FactsVarious ModelsDisjunct Matrices(d; z)-disjunct(d, r]-disjunct(d, h)-disjunct(d, s out of r]-disjunct(k, m, n)-selector"Construction of disjunct-matricesLovász Local Lemma (d, r]-disjunct Case Upper BoundPowerPoint 簡報PowerPoint 簡報PowerPoint 簡報 References Continued Continued  使用字型 佈景主題投影片標題_㳟mUSERUSER  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      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