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%%Creator: %!PS-Adobe-2.0 dvips(k) 5.90a Copyright 2002 Radical Eye Software %%Title: main.dvi %%Pages: 21 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: Times-Roman Times-Bold Times-Italic Courier %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips main.dvi -o %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2004.12.14:0139 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse
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FJ(G)g FK(has)h(a)f(v)o(erte)o(x)g(co)o(v)o(er)h(of)f(size)h(at)f(most) g FJ(b)g FK(if)g(and)g(only)h(if)f FJ(G)3573 171 y FP(0)3627 204 y FK(has)g(an)83 317 y(independent)d(set)d(of)f(size)h(at)g(least)g FJ(b)1253 284 y FP(0)1276 317 y FK(.)224 430 y(Notice)30 b(that)h(if)e FJ(S)42 b FH(\022)37 b FJ(V)20 b FI(\()p FJ(G)p FI(\))30 b FK(is)g(a)f(v)o(erte)o(x)h(co)o(v)o(er)l(,)i(then)f (clearly)g FJ(V)20 b FI(\()p FJ(G)p FI(\))26 b FH(\000)f FJ(S)34 b FK(is)29 b(an)h(independent)j(set)d(and)h(vice)83 543 y(v)o(ersa.)e(Hence,)24 b(letting)h FJ(G)928 510 y FP(0)977 543 y FI(=)g FJ(G)e FK(and)h FJ(b)1360 510 y FP(0)1409 543 y FI(=)h FH(j)p FJ(V)20 b FI(\()p FJ(G)p FI(\))p FH(j)i(\000)e FJ(b)j FK(completes)i(the)f(reduction.)p 3797 543 4 62 v 3801 485 55 4 v 3801 543 V 3855 543 4 62 v 83 731 a Ft(Example)f(3.2.)42 b FK(IS)23 b FH(\024)802 745 y FC(p)866 731 y FK(C)t FE(L)t(I)t(Q)s(U)t(E)r FK(.)83 918 y FF(Pr)l(oof)o(.)46 b FK(Gi)n(v)o(en)29 b(a)g(graph)h FJ(G)37 b FI(=)f(\()p FJ(V)5 b(;)15 b(E)5 b FI(\))p FK(,)31 b(the)e(complement)i(graph)2287 895 y FI(\026)2266 918 y FJ(G)e FK(of)g FJ(G)g FK(is)g(a)g(graph)i(with)e(the)h(same)f(v)o (erte)o(x)h(set)83 1031 y(as)f FJ(G)g FK(and)g(the)g(edge)h(set)f FJ(E)5 b FI(\()p FJ(G)1092 998 y FP(0)1117 1031 y FI(\))28 b FK(the)h(complement)i(of)e FJ(E)5 b FI(\()p FJ(G)p FI(\))p FK(;)32 b(namely)e FI(\()p FJ(u;)15 b(v)s FI(\))37 b FH(2)e FJ(E)2881 998 y FP(0)2933 1031 y FK(if)n(f)28 b FI(\()p FJ(u;)15 b(v)s FI(\))47 b FJ(=)-55 b FH(2)35 b FJ(E)5 b FK(.)44 b(W)l(ith)30 b(this)83 1144 y(construction,)d(an)c (independent)k(set)d(of)f FJ(G)h FK(is)f(a)g(clique)i(of)1980 1121 y FI(\026)1959 1144 y FJ(G)e FK(and)h(vice)g(v)o(ersa.)30 b(Thus,)23 b FJ(G)g FK(has)h(an)g(independent)j(set)c(of)83 1257 y(size)h(at)f(least)i FJ(b)e FK(if)g(and)h(only)g(if)1102 1234 y FI(\026)1081 1257 y FJ(G)g FK(has)g(a)f(clique)i(of)e(size)h(at) f(least)i FJ(b)p FK(.)p 3797 1257 V 3801 1199 55 4 v 3801 1257 V 3855 1257 4 62 v 224 1445 a(The)d(follo)n(wing)i(lemmas)f (are)g(tri)n(vial)g(to)g(sho)n(w)-6 b(,)22 b(yet)h(are)g(important)h (properties)h(of)e(the)g(polynomial)h(time)f(reduc-)83 1557 y(tion.)83 1745 y Ft(Lemma)g(3.3.)42 b FF(If)23 b FI(\005)728 1712 y FP(0)777 1745 y FH(2)h Fo(P)p FF(,)f(and)h FI(\005)i FH(\024)1303 1759 y FC(p)1367 1745 y FI(\005)1435 1712 y FP(0)1459 1745 y FF(,)c(then)j FI(\005)g FH(2)g Fo(P)p FF(.)83 1933 y Ft(Lemma)e(3.4.)42 b FF(If)23 b FI(\005)728 1900 y FP(0)777 1933 y FH(2)h Fo(NP)q FF(,)e(and)i FI(\005)i FH(\024)1385 1947 y FC(p)1449 1933 y FI(\005)1517 1900 y FP(0)1541 1933 y FF(,)c(then)i FI(\005)i FH(2)f Fo(NP)p FF(.)83 2120 y Ft(Lemma)e(3.5.)42 b FF(If)23 b FI(\005)728 2134 y FG(1)793 2120 y FH(\024)864 2134 y FC(p)928 2120 y FI(\005)996 2134 y FG(2)1059 2120 y FF(,)f(and)i FI(\005)1331 2134 y FG(2)1396 2120 y FH(\024)1467 2134 y FC(p)1532 2120 y FI(\005)1600 2134 y FG(3)1639 2120 y FF(,)f(then)h FI(\005)1932 2134 y FG(1)1997 2120 y FH(\024)2068 2134 y FC(p)2133 2120 y FI(\005)2201 2134 y FG(3)2240 2120 y FF(.)224 2308 y FK(Finally)-6 b(,)24 b(we)f(are)h(ready)h(to)e(formally)i(de\002ne)f(the)g Fo(NPC)f FK(class.)30 b(A)22 b(problem)j FI(\005)e FK(is)h Fo(NP)p FF(-har)m(d)h FK(if)e(e)n(v)o(ery)h(problem)83 2421 y(in)f Fo(NP)g FK(is)h(polynomial-time)j(reducible)f(to)d FI(\005)p FK(.)p 878 2552 2191 4 v 876 2665 4 113 v 927 2631 a(A)g(problem)h FI(\005)f FK(is)h Fo(NP)p FF(-complete)h FK(\(or)f FH(2)h Fo(NPC)p FK(\))e(if)g(and)h(only)g(if)p 3067 2665 V 876 2778 V 1433 2744 a FI(\005)i FH(2)f Fo(NP)e
FK(and)h FI(\005)e FK(is)i Fo(NP)p FK(-hard.)p 3067 2778 V 878 2781 2191 4 v 83 2959 a Ft(Lemma)f(3.6.)42 b FF(Suppose)25 b FI(\005)h FH(2)f Fo(NP)p FF(,)d(and)i FI(\005)1512 2926 y FP(0)1561 2959 y FH(\024)1632 2973 y FC(p)1697 2959 y FI(\005)f FF(wher)m(e)g FI(\005)2097 2926 y FP(0)2143 2959 y FF(is)h Fo(NP)p FF(-complete)o(,)h(then)f FI(\005)f FF(is)h Fo(NP)p FF(-complete)o(.)83 3146 y(Pr)l(oof)o(.)46 b FK(This)23 b(follo)n(ws)h(tri)n(vially)i(from)d(Lemma)g(3.5,)g(which) h(says)g(that)g(the)g(relation)h FH(\024)2886 3160 y FC(p)2948 3146 y FK(is)f(transiti)n(v)o(e.)p 3797 3146 4 62 v 3801 3088 55 4 v 3801 3146 V 3855 3146 4 62 v 83 3439 a FM(4)119 b(Cook')l(s)29 b(theor)n(em)83 3646 y FK(No)n(w)d(that)i(the)f(intuiti)n(v)o(e)i(notion)g(of)e(an)g (algorithm)i(has)f(been)g(formalized)h(by)f(the)f(concept)i(of)f(a)e(T) l(uring)i(machine,)83 3759 y(we)e(are)h(ready)h(to)e(pro)o(v)o(e)h (Cook')-5 b(s)28 b(theorem)g(that)f(the)g(set)g(of)f Fo(NP)q FK(-complete)i(\(NPC\))d(problems)j(is)f(not)g(empty)-6 b(.)39 b(The)83 3872 y(\002rst)23 b(problem)i(which)f(has)g(been)g(sho) n(wn)g(to)f(be)h(in)f(NPC)f(is)h(the)j(S)t FE(A)l(T)t(I)t(S)t(FI)t(A)t (B)t(I)t(L)t(I)t(T)5 b(Y)31 b FK(\(SA)-10 b(T\))22 b(problem.)224 3985 y(Let)31 b FJ(X)48 b FI(=)40 b FH(f)p FJ(x)707 3999 y FG(1)747 3985 y FJ(;)15 b(:)g(:)g(:)i(;)e(x)1001 3999 y FC(n)1048 3985 y FH(g)32 b FK(be)f(a)h(set)g(of)f(boolean)j(v)n (ariables.)55 b(A)31 b FF(truth)i(assignment)i FK(for)d FJ(X)39 b FK(is)31 b(a)h(function)h FJ(t)41 b FI(:)83 4098 y FJ(X)33 b FH(!)25 b(f)r FE(T)t(R)q(U)t(E)5 b FJ(;)17 b FE(F)o(A)t(L)t(S)t(E)5 b FH(g)p FK(.)29 b(Basically)-6 b(,)25 b FJ(t)e FK(assigns)i(to)f(each)g(v)n(ariable)i(in)d FJ(X)31 b FK(a)23 b(v)n(alue)h(of)g(either)j FE(T)t(R)q(U)t(E)g FK(or)e FE(F)o(A)t(L)t(S)t(E)6 b FK(.)28 b(F)o(or)23 b(a)83 4211 y(v)n(ariable)i FJ(x)p FK(,)e(we)f(use)30 b FI(\026)-51 b FJ(x)23 b FK(to)g(denote)j(the)d(ne)o(gation)i(of)f FJ(x)p FK(.)k(If)23 b FJ(x)g FK(is)g(a)g(v)n(ariable,)i FJ(x)e FK(and)30 b FI(\026)-51 b FJ(x)22 b FK(are)i(called)h FF(liter)o(als)p FK(.)224 4324 y(A)d(set)h FJ(C)29 b FK(of)22 b(literals)j(o)o(v)o(er)e FJ(X)30 b FK(is)22 b(called)i(a)f FF(clause)h FK(o)o(v)o(er)f FJ(X)7 b FK(,)23 b(e.g.)28 b FJ(C)k FI(=)25 b FH(f)p FJ(x)2578 4338 y FG(1)2617 4324 y FJ(;)d FI(\026)-52 b FJ(x)2709 4338 y FG(3)2749 4324 y FJ(;)15 b(x)2841 4338 y FG(4)2881 4324 y FH(g)23 b FK(is)f(a)h(clause.)30 b(A)22 b(clause)i FJ(C)k FK(is)83 4436 y FF(satis\002ed)i FK(by)25 b(a)g(truth)i (assignment)g FJ(t)e FK(if)n(f)g(at)g(least)h(one)g(of)f(its)h(members) g(is)h FE(T)t(R)q(U)t(E)h FK(under)f FJ(t)p FK(.)33 b(One)25 b(thinks)i(of)e(a)g(clause,)83 4549 y(say)h FJ(C)36 b FI(=)30 b FH(f)p FJ(x)528 4563 y FG(1)567 4549 y FJ(;)22 b FI(\026)-52 b FJ(x)659 4563 y FG(3)699 4549 y FJ(;)15 b(x)791 4563 y FG(4)831 4549 y FH(g)p FK(,)26 b(as)g(the)i FE(O)t(R)f FK(of)f(the)g(literal)h(members)f(of)g(the)g(clause.)37 b(In)26 b(ef)n(fect,)h(one)f(can)h(think)g(of)e FJ(C)32 b FK(as)26 b(a)83 4662 y(boolean)g(formula:)1591 4775 y FJ(C)31 b FI(=)25 b(\()p FJ(x)1870 4789 y FG(1)1930 4775 y FH(_)h FI(\026)-51 b FJ(x)2063 4789 y FG(3)2123 4775 y FH(_)19 b FJ(x)2255 4789 y FG(4)2295 4775 y FI(\))p FJ(:)85 5000 y FK(S)t FE(A)l(T)t(I)t(S)t(FI)t(A)t(B)t(I)t(L)t(I)t(T)5 b(Y)31 b FK(\(SA)-10 b(T\))312 5130 y FE(I)t(N)t(S)t(T)m(A)t(N)t(C)t(E) r FK(:)32 b(A)23 b(set)h FJ(X)30 b FK(of)23 b(v)n(ariables)j(and)e(a)f (collection)j FH(C)31 b FI(=)25 b FH(f)p FJ(C)2400 5144 y FG(1)2439 5130 y FJ(;)15 b(:)g(:)g(:)i(;)e(C)2706 5144
y FC(m)2773 5130 y FH(g)23 b FK(of)h(clauses)h(o)o(v)o(er)e FJ(X)7 b FK(.)312 5280 y FE(Q)s(U)t(E)t(S)t(T)t(I)t(O)t(N)r FK(:)32 b(Is)24 b(there)g(a)f(truth)i(assignment)h(which)e(satis\002es) g(all)g(clauses)h(in)f FH(C)5 b FK(.)1928 5782 y(10)p eop end %%Page: 11 11 TeXDict begin 11 10 bop 224 91 a FK(In)34 b(other)g(w)o(ords,)j(we)32 b(w)o(ant)i(to)f(kno)n(w)h(if)f(there)i(is)e(a)g(truth)i(assignment)g (for)f(which)g FJ(\036)p FI(\()p FJ(t)p FI(\()p FJ(x)3233 105 y FG(1)3273 91 y FI(\))p FJ(;)15 b(:)g(:)g(:)i(;)e(t)p FI(\()p FJ(x)3630 105 y FC(n)3678 91 y FI(\)\))44 b(=)85 204 y FE(T)t(R)q(U)t(E)t FK(,)22 b(gi)n(v)o(en)i(a)g(boolean)h(formula) g FJ(\036)e FK(under)h FF(conjunctive)j(normal)d(form)g FK(\(CNF\).)e(F)o(or)g(instance,)816 403 y FJ(\036)p FI(\()p FJ(x)957 417 y FG(1)997 403 y FJ(;)15 b(:)g(:)g(:)i(;)e(x)1251 417 y FC(n)1298 403 y FI(\))25 b(=)g(\()p FJ(x)1541 417 y FG(1)1601 403 y FH(_)h FI(\026)-51 b FJ(x)1734 417 y FG(3)1794 403 y FH(_)20 b FJ(x)1927 417 y FG(4)1966 403 y FI(\))h FH(^)e FI(\()p FJ(x)2189 417 y FG(2)2249 403 y FH(_)h FJ(x)2382 417 y FG(3)2422 403 y FI(\))g FH(^)g FI(\()6 b(\026)-51 b FJ(x)2645 417 y FG(1)2705 403 y FH(_)20 b FJ(x)2838 417 y FG(2)2897 403 y FH(_)26 b FI(\026)-51 b FJ(x)3030 417 y FG(3)3069 403 y FI(\))p FJ(:)83 602 y Ft(Theor)n(em)24 b(4.1)f(\(Cook)g(-)g(1971\).)43 b FF(SA)m(T)22 b(is)i Fo(NP)p FF(-complete)o(.)83 785 y(Pr)l(oof)o(.)46 b Ft(TBD)p FK(.)p 3797 785 4 62 v 3801 727 55 4 v 3801 785 V 3855 785 4 62 v 83 1077 a FM(5)119 b(Pr)n(o)o(ving)30 b FL(NP)p FM(-completeness)f(r)n(esults)83 1284 y FK(Gi)n(v)o(en)e(SA)-10 b(T)26 b(as)h(a)g(basis,)j(Lemma)c(3.6)i (helps)g(sho)n(w)g(man)o(y)f(other)i(problems)g(are)f Fo(NP)p FK(-complete.)43 b(T)-7 b(o)26 b(sho)n(w)i(that)g(a)83 1397 y(problem)i FI(\005)e FK(is)h Fo(NP)p FK(-complete,)i(we)d (\002rst)h(ha)n(v)o(e)g(to)g(sho)n(w)f(that)i FI(\005)35 b FH(2)f Fo(NP)p FK(,)29 b(which)g(in)g(most)g(cases)h(is)e(tri)n (vial;)33 b(then,)83 1509 y(we)26 b(\002nd)h(another)h(problem)g FI(\005)1078 1476 y FP(0)1128 1509 y FK(which)f(has)g(been)h(sho)n(wn)f (to)g(be)g Fo(NP)p FK(-complete,)i(and)e(sho)n(w)g(that)h FI(\005)3361 1476 y FP(0)3415 1509 y FH(\024)3486 1523 y FC(p)3557 1509 y FI(\005)p FK(.)38 b(Note)83 1622 y(the)22 b(direction)j(of)c(reduction)k(here.)k(Man)o(y)22 b(students)i(ha)n(v)o (e)e(done)h(the)f(reduction)j(in)d(the)g(wrong)g(direction,)j(due)d(to) g(the)83 1735 y(some)n(what)i(confusing)i(nature)f(of)f(the)g(w)o(ord)f (\223reducible\224)k(in)c(this)h(conte)o(xt.)224 1848 y(Another)32 b(point)f(w)o(orth)g(noticing)h(is)f(that)f(\002nding)i(a) e(reduction)i(often)g(helps)f(us)g(understand)i(the)e(structure)h(of)83 1961 y(the)24 b(problem)g(at)f(hand)i(much)e(better)-5 b(.)30 b(In)23 b(ef)n(fect,)h(we)f(sho)n(w)g(that)h(our)g(problem)g(is) f(a)g(special)i(case)f(of)g(another)h(kno)n(wn)83 2074 y(problem.)31 b(If)23 b(there)i(w)o(as)e(a)h(good)h(approximation)i (algorithm)e(to)f(solv)o(e)h(the)f(other)g(problem,)h(then)g(our)f (problem)h(can)83 2187 y(bene\002t)f(from)g(it)f(via)h(the)g (reduction.)224 2300 y(Beside)30 b(the)f(problems)h(de\002ned)g (earlier)g(lik)o(e)g(VC,)f(C)t FE(L)t(I)t(Q)s(U)t(E)r FK(,)j(IS,)27 b(...,)i(we)f(de\002ne)h(a)f(fe)n(w)g(more)h(problems)i (here)83 2413 y(and)i(sho)n(w)f(that)h(the)o(y)g(are)f(also)h Fo(NP)q FK(-complete.)57 b(The)31 b(proofs)j(shall)g(also)f(illustrate) h(se)n(v)o(eral)g Fo(NP)p FK(-completeness)83 2526 y(proof)29 b(techniques.)45 b(More)28 b(e)o(xamples)h(and)f(a)g(classi\002cation)j (of)c(techniques)k(can)e(be)e(found)j(in)d(the)i(classic)g(te)o(xt)f
(by)83 2639 y(Gare)o(y)23 b(and)h(Johnson)i([13].)83 2810 y FI(3)r FK(-)t(S)t(A)-6 b(T)312 2935 y FE(I)t(N)t(S)t(T)m(A)t(N)t (C)t(E)r FK(:)43 b(A)27 b(collection)32 b FH(C)h FK(of)28 b(clauses)j FH(f)p FJ(C)1828 2949 y FG(1)1868 2935 y FJ(;)15 b(:)g(:)g(:)h(;)f(C)2134 2949 y FC(m)2201 2935 y FH(g)29 b FK(o)o(v)o(er)f FJ(X)43 b FI(=)34 b FH(f)p FJ(x)2781 2949 y FG(1)2821 2935 y FJ(;)15 b(:)g(:)g(:)i(;)e(x)3075 2949 y FC(n)3122 2935 y FH(g)p FK(,)29 b(where)g(each)310 3047 y(clause)c FJ(C)625 3061 y FC(i)676 3047 y FK(consists)h(of)d(e)o (xactly)i FI(3)e FK(literals.)312 3197 y FE(Q)s(U)t(E)t(S)t(T)t(I)t(O)t (N)r FK(:)32 b(Is)24 b(there)g(a)f(truth)i(assignment)h(satisfying)g (all)e(clauses)h(in)e FH(C)5 b FK(.)85 3380 y(S)t FE(E)t(T)29 b FK(C)t FE(OV)t(E)t(R)d FK(\(SC\))312 3505 y FE(I)t(N)t(S)t(T)m(A)t(N) t(C)t(E)r FK(:)48 b(A)29 b(f)o(amily)j FH(S)37 b FK(of)31 b(subsets)i FH(f)p FJ(S)1722 3519 y FG(1)1762 3505 y FJ(;)15 b(:)g(:)g(:)h(;)f(S)2019 3519 y FC(m)2086 3505 y FH(g)31 b FK(of)g(a)f(\002nite)h(uni)n(v)o(erse)i FJ(U)40 b FK(\()p FH(j)p FJ(U)10 b FH(j)40 b FI(=)f FJ(n)p FK(\),)32 b(and)f(a)310 3618 y(bound)25 b FJ(b)h FH(2)e FB(Z)775 3585 y FG(+)830 3618 y FK(.)312 3767 y FE(Q)s(U)t(E)t(S)t(T)t(I)t(O)t (N)r FK(:)32 b(Is)24 b(there)g FJ(I)33 b FH(\022)25 b(f)p FI(1)p FJ(;)15 b(:)g(:)g(:)i(;)e(m)p FH(g)p FK(,)23 b FH(j)p FJ(I)7 b FH(j)26 b(\024)f FJ(b)p FK(,)e(such)h(that)1761 3980 y FJ(U)35 b FI(=)1957 3893 y Fj([)1954 4090 y FC(i)p FP(2)p FC(I)2076 3980 y FJ(S)2132 3994 y FC(i)2160 3980 y FJ(:)310 4266 y FK(The)23 b(collection)k FH(f)p FJ(S)957 4280 y FC(i)1008 4266 y FH(j)c FJ(i)i FH(2)g FJ(I)7 b FH(g)23 b FK(satisfying)k(the)d(abo)o(v)o(e)g(condition)i(is)d(called)i (a)e FF(set)h(co)o(ver)h FK(of)e FJ(U)10 b FK(.)85 4449 y(D)t FE(O)t(M)t(I)t(N)r(A)l(T)t(I)t(N)t(G)29 b FK(S)t FE(E)t(T)e FK(\(DS\))312 4574 y FE(I)t(N)t(S)t(T)m(A)t(N)t(C)t(E)r FK(:)32 b(A)23 b(graph)i FJ(G)g FI(=)g(\()p FJ(V)5 b(;)15 b(E)5 b FI(\))p FK(,)24 b(a)f(bound)i FJ(b)h FH(2)e FB(Z)2078 4541 y FG(+)2133 4574 y FK(.)312 4723 y FE(Q)s(U)t(E)t(S)t(T)t(I)t(O)t (N)r FK(:)38 b(Is)26 b(there)i(a)d(subset)j FJ(S)36 b FH(\022)30 b FJ(V)20 b FK(,)26 b FH(j)p FJ(S)5 b FH(j)31 b(\024)f FJ(b)p FK(,)c(such)i(that)e(e)n(v)o(ery)h(v)o(erte)o(x)g FJ(v)i FK(not)e(in)f FJ(S)31 b FK(is)26 b(incident)310 4836 y(to)e(some)f(v)o(erte)o(x)i(in)e FJ(S)5 b FK(.)28 b(The)23 b(v)o(ertices)i(in)f FJ(S)j FF(dominates)f FK(all)d(v)o (ertices)i(in)f FJ(V)c FK(.)83 5019 y FI(3)r FK(-)t FE(C)t(O)t(L)t(O)t (R)t(A)t(B)t(I)t(L)t(I)t(T)t(Y)312 5144 y(I)t(N)t(S)t(T)m(A)t(N)t(C)t (E)r FK(:)32 b(A)23 b(graph)i FJ(G)g FI(=)g(\()p FJ(V)5 b(;)15 b(E)5 b FI(\))p FK(.)312 5294 y FE(Q)s(U)t(E)t(S)t(T)t(I)t(O)t (N)r FK(:)37 b(Is)25 b FJ(G)g FI(3)p FF(-color)o(able)p FK(,)k(i.e.)35 b(is)25 b(there)h(a)g(w)o(ay)f(to)g(assign)i(each)g(v)o (erte)o(x)f(of)g FJ(G)f FK(one)h(of)f FI(3)h FK(colors)310 5406 y(such)f(that)f(tw)o(o)f(adjacent)j(v)o(ertices)f(ha)n(v)o(e)f (dif)n(ferent)h(colors.)83 5590 y FJ(k)5 b FK(-)t FE(C)t(O)t(L)t(O)t(R) t(A)t(B)t(I)t(L)t(I)t(T)t(Y)1928 5782 y FK(11)p eop end %%Page: 12 12 TeXDict begin 12 11 bop 312 91 a FE(I)t(N)t(S)t(T)m(A)t(N)t(C)t(E)r FK(:)32 b(A)23 b(graph)i FJ(G)g FI(=)g(\()p FJ(V)5 b(;)15 b(E)5 b FI(\))p FK(,)24 b FJ(k)29 b FH(\025)c FI(3)p FK(.)312 241 y FE(Q)s(U)t(E)t(S)t(T)t(I)t(O)t(N)r FK(:)36 b(Is)25 b FJ(G)f(k)s FF(-color)o(able)p FK(,)k(i.e.)34 b(is)25 b(there)h(a)e(w)o(ay)h(to)g(assign)i(each)f(v)o(erte)o(x)g(of)f FJ(G)f FK(one)i(of)f FJ(k)j FK(colors)310 354 y FH(f)p FI(1)p FJ(;)15 b(:)g(:)g(:)j(;)d(k)s FH(g)24 b FK(such)g(that)g(tw)o(o)
f(adjacent)j(v)o(ertices)f(ha)n(v)o(e)f(dif)n(ferent)i(colors.)85 540 y(H)t FE(A)t(M)t(I)t(L)m(T)s(O)t(N)t(I)t(A)t(N)k(C)t(Y)t(C)t(L)t(E) d FK(\(HC\))312 667 y FE(I)t(N)t(S)t(T)m(A)t(N)t(C)t(E)r FK(:)32 b(A)23 b(graph)i FJ(G)g FI(=)g(\()p FJ(V)5 b(;)15 b(E)5 b FI(\))p FK(.)312 817 y FE(Q)s(U)t(E)t(S)t(T)t(I)t(O)t(N)r FK(:)33 b(Does)24 b FJ(G)g FK(contain)h(a)f(Hamiltonian)h(c)o(ycle?)31 b(\(An)24 b(HC)e(is)i(a)f(c)o(ycle)i(containing)h(all)e(v)o(ertices)310 930 y(of)g FJ(G)p FK(.\))85 1116 y(T)t FE(R)t(A)-6 b(V)t(E)t(L)t(I)t(N) t(G)30 b FK(S)t FE(A)t(L)t(E)t(S)t(M)t(A)t(N)f FK(P)t FE(R)q(O)t(B)t(L)t(E)t(M)e FK(\()r(T)t(S)t(P)r(\))312 1243 y FE(I)t(N)t(S)t(T)m(A)t(N)t(C)t(E)r FK(:)52 b(A)32 b(complete)j(graph)g FJ(G)44 b FI(=)f(\()p FJ(V)5 b(;)15 b(E)5 b FI(\))p FK(,)37 b(a)c(cost)h(function)h FJ(c)44 b FI(:)g FJ(E)49 b FH(!)43 b FB(Z)3059 1210 y FG(+)3114 1243 y FK(,)35 b(and)f(a)e(bound)310 1356 y FJ(b)26 b FH(2)e FB(Z)525 1323 y FG(+)580 1356 y FK(.)312 1506 y FE(Q)s(U)t(E)t(S)t(T)t(I)t(O)t(N)r FK(:)32 b(Is)24 b(there)g(a)f(TSP)f(tour)i(with)f(total)i(cost)f(at)f(most)h FJ(b)p FK(?)85 1691 y(E)t FE(U)t(C)t(L)t(I)t(D)t(E)t(A)t(N)29 b FK(T)t FE(R)t(A)-6 b(V)t(E)t(L)t(I)t(N)t(G)30 b FK(S)t FE(A)t(L)t(E)t(S)t(M)t(A)t(N)e FK(\()r(E)t FE(U)t(C)t(L)t(I)t(D)t(E)t (A)t(N)h FK(T)t(S)t(P)r(\))312 1819 y FE(I)t(N)t(S)t(T)m(A)t(N)t(C)t(E) r FK(:)39 b(A)25 b(set)i FJ(C)37 b FI(=)31 b FH(f)p FJ(p)1272 1833 y FG(1)1311 1819 y FJ(;)15 b(:)g(:)g(:)i(;)e(p)1559 1833 y FC(n)1606 1819 y FH(g)26 b FK(of)h FJ(n)e FK(points)j(on)f(a)f (plane)i(gi)n(v)o(en)f(by)g(their)g FJ(x;)15 b(y)s FK(-coordinates)310 1932 y FJ(p)356 1946 y FC(i)409 1932 y FI(=)25 b(\()p FJ(x)592 1946 y FC(i)621 1932 y FJ(;)15 b(y)706 1946 y FC(i)734 1932 y FI(\))26 b FH(2)f FB(Z)15 b FH(\002)20 b FB(Z)p FK(,)e(a)23 b(bound)i FJ(b)h FH(2)f FB(Z)1687 1899 y FG(+)1741 1932 y FK(.)312 2082 y FE(Q)s(U)t(E)t(S)t(T)t(I)t(O)t (N)r FK(:)32 b(Is)24 b(there)g(a)f(TSP)f(tour)i(with)f(total)i(length)g (at)e(most)h FJ(b)p FK(?)85 2267 y(S)t FE(U)t(B)t(S)t(E)t(T)30 b FK(S)t FE(U)t(M)d FK(\()t(S)t(S)t(\))312 2395 y FE(I)t(N)t(S)t(T)m(A) t(N)t(C)t(E)r FK(:)32 b(A)23 b(\002nite)g(set)h FJ(S)k FK(of)23 b(natural)j(numbers,)e(and)g(a)f(tar)n(get)i FJ(t)g FH(2)g FB(N)7 b FK(.)312 2545 y FE(Q)s(U)t(E)t(S)t(T)t(I)t(O)t (N)r FK(:)32 b(Is)24 b(there)g(a)f(subset)i FJ(S)1429 2512 y FP(0)1478 2545 y FH(\022)g FJ(S)5 b FK(,)22 b(whose)i(elements)h (sum)e(up)h(to)g FJ(t)p FK(?)85 2730 y(K)t FE(N)r(A)t(P)t(S)t(A)q(C)t (K)312 2858 y(I)t(N)t(S)t(T)m(A)t(N)t(C)t(E)r FK(:)38 b FJ(n)25 b FK(items,)i(their)g(v)n(alues)g FJ(v)1575 2872 y FC(i)1634 2858 y FH(2)j FB(Z)1790 2825 y FG(+)1845 2858 y FK(,)25 b(their)j(corresponding)i(weights)d FJ(w)3004 2872 y FC(i)3063 2858 y FH(2)j FB(Z)3219 2825 y FG(+)3274 2858 y FK(,)25 b(a)h(weight)310 2971 y(limit)e FJ(W)38 b FH(2)24 b FB(Z)779 2938 y FG(+)834 2971 y FK(,)f(and)h(a)f(v)n(alue)h (limit)...
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SUNY Buffalo - CSE - 620
Welcome toCSE 620 Advanced Networking Concepts Time: MWF 16:00-16:50 Place: PARK 250 Fall 2005SUNY at Buffalo; Computer Science; CSE620 Advanced Networking Concepts; Fall 2005; Instructor: Hung Q. Ngo1Today's AgendaAdministrative aspects o
SUNY Buffalo - CSE - 620
Today's AgendaGroup division (random?)You can form your own group, NOW. Size at most 3.Internet:Service perspective Component perspective Basic architectureInternet Philosophy & Design Principles"end-to-end" argument: then and nowSUNY at Bu
SUNY Buffalo - CSE - 620
Today's AgendaA proposal for a new Internet architecture The NewArch ProjectSUNY at Buffalo; Computer Science; CSE620 Advanced Networking Concepts; Fall 2005; Instructor: Hung Q. Ngo1The NewArch Project Main question:If we could design the
SUNY Buffalo - CSE - 620
Today's AgendaReview of Internet routing algorithms Shortest path algorithmso oDijkstra algorithm Bellman-Ford algorithm Link-state routing Distance vector routing Intra-AS routing: OSPF, RIP, IS-IS, Static Inter-AS routing: BGP1Routing alg
SUNY Buffalo - CSE - 620
Today's AgendaBGP Overview Note: it takes years to really master BGP Many slides stolen from Prof. Zhi-Li Zhang at Minnesota and from Avi Freedman's slides There'll be some openresearch topics hereAS Relationship InferenceSUNY at Buffal
SUNY Buffalo - CSE - 620
Today's AgendaAS relationship inferenceWhy is it important ? Why is it difficult ? Some algorithms proposed in the literature Evaluating inference algorithms Some open problems.SUNY at Buffalo; Computer Science; CSE620 Advanced Networking Concep
SUNY Buffalo - CSE - 620
AgendaLast time: finished brief overview of bufferoverflow attacks Today: IP TracebackSUNY at Buffalo; Computer Science; CSE620 Advanced Networking Concepts; Fall 2005; Instructor: Hung Q. Ngo1What and WhyIP Traceback: Why is th
SUNY Buffalo - CSE - 594
CSE 594: Combinatorial and Graph Algorithms SUNY at Buffalo, Fall 2006Lecturer: Hung Q. Ngo Scribe: Hung Q. NgoA Linear Algebra PrimerStandard texts on Linear Algebra and Algebra are [1, 8].11.1PreliminariesVectors and matricesWe shall u
SUNY Buffalo - CSE - 594
%!PS-Adobe-2.0 %Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %Title: main.dvi %Pages: 21 %PageOrder: Ascend %BoundingBox: 0 0 596 842 %DocumentFonts: Times-Roman CMBX12 CMSY8 Times-Bold CMMI10 CMR10 CMSY10 %+ CMR8 Times-Italic CMMI8 MS
University of Medicine and Dentistry of New Jersey - LECT - 5220
vti_encoding:SR|utf8-nl vti_timelastmodified:TR|17 Feb 2006 02:56:00 -0000 vti_extenderversion:SR|4.0.2.7802 vti_filesize:IR|688128 vti_title:SR|CYGWIN vti_backlinkinfo:VX| vti_cacheddtm:TX|17 Feb 2006 02:56:00 -0000 vti_cachedlinkinfo:VX| vti_cached
University of Medicine and Dentistry of New Jersey - LECT - 5220
vti_encoding:SR|utf8-nl vti_timelastmodified:TR|17 Feb 2006 02:54:44 -0000 vti_extenderversion:SR|4.0.2.7802 vti_filesize:IR|472064 vti_title:SR| Announcements vti_assignedto:SR| vti_approvallevel:SR| vti_backlinkinfo:VX| vti_cacheddtm:TX|17 Feb 2006
University of Medicine and Dentistry of New Jersey - LECT - 5220
vti_encoding:SR|utf8-nl vti_timelastmodified:TR|17 Feb 2006 02:53:31 -0000 vti_extenderversion:SR|4.0.2.7802 vti_filesize:IR|492032 vti_title:SR|ACS:SGI Remote Usage vti_assignedto:SR| vti_approvallevel:SR| vti_backlinkinfo:VX| vti_cacheddtm:TX|17 Fe
University of Medicine and Dentistry of New Jersey - LECT - 5220
vti_encoding:SR|utf8-nl vti_timelastmodified:TR|17 Feb 2006 02:52:12 -0000 vti_extenderversion:SR|4.0.2.7802 vti_filesize:IR|1103872 vti_title:SR| VNC vti_backlinkinfo:VX| vti_cacheddtm:TX|17 Feb 2006 02:52:12 -0000 vti_cachedlinkinfo:VX| vti_cacheds
University of Medicine and Dentistry of New Jersey - LECT - 5220
vti_encoding:SR|utf8-nl vti_timelastmodified:TR|17 Feb 2006 02:50:46 -0000 vti_extenderversion:SR|4.0.2.7802 vti_filesize:IR|219136 vti_title:SR| Announcements vti_assignedto:SR| vti_approvallevel:SR| vti_backlinkinfo:VX| vti_cacheddtm:TX|17 Feb 2006
Penn State - MATH - 513
Syllabus for M513PDE: Partial Differential Equations Instructor: Yuxi Zheng (August 25, 2008, updated Sept 9.)Lecture Schedule: MWF 9:05-9:55AM, 106MB Contact info: yzheng@math.psu.edu, 8650361; McAllister 229 Web address: http:/www.math.psu.edu/y
Penn State - MATH - 513
Homework #10 Assigned Wed Nov 19, due Wed Dec 3Section 4.7: Problems 4, 9.=Homework #9 Assigned Monday Nov 10, due Wed Nov. 19Section 4.7: Problems 3.==Homework #8 Assigned Friday Oct 31, due Monday Nov. 10Section 3.5: Problems 4,
Penn State - MATH - 513
M 513. Fall, 2008 Homework 10 1. Solve the characteristic boundary value problem: uyy - uxx = 0, (x, y) {(x, y) R2 | y > |x| }; u(x, x) = f (x) u(x, -x) = g(x) Assume that f (0) = g(0) and both f and g are C 2 smooth. (x > 0), (x < 0).
University of Medicine and Dentistry of New Jersey - LECT - 5220
vti_encoding:SR|utf8-nl vti_timelastmodified:TR|01 Mar 2006 01:33:31 -0000 vti_extenderversion:SR|4.0.2.7802 vti_cacheddtm:TX|01 Mar 2006 01:33:31 -0000 vti_filesize:IR|5913088 vti_cachedlinkinfo:VX|H|http:/cmm.info.nih.gov/modeling/gateway.html H| h
Knox College - CS - 262
CS262Info MgmtBlahetaHomework 5Due: 12 Oct 2007Problem 5.1Consider the situation where you know your opponent is running a strict minimax strategy. Would it be to your advantage to, at least sometimes, pick your move randomly instead of obey
University of Medicine and Dentistry of New Jersey - LECT - 5220
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UCSD - CHEM - 165
Buzz Words (Transmission Electron Microscopy)Abbe's Law Airy disk amplitude (scattering/aperture) contrast angular aperture anticontaminator astigmatism barrel distortion BFEM (Bright Field EM) binning blind imaging Cc (chromatic aberration coeffici
UCSD - CHEM - 165
CHEM 165, 265/BI M M 1 62/BG GN 2623D EL ECTR O N MI CROS COPY OF MA CRO M OLECUL ESLECT URE NOT ES T ABLE OF CONTENTSI. THE MICROSCOPE .A. PRINC IPLES OF THE T RA NSM ISS IO N E LE C TRO N MIC ROS CO PE (TE M) 1. Origin of the Electron Microsc
UCSD - CHEM - 165
CHEM 165,265/BIMM 162/BGGN 262TEXTBOOK/PERIODICALS LISTMost of the references listed here are in the Science & Engineering Library (S&E) on the Main Floor, East Wing of Geisel, and several have been put on reserve (see list on page 6). Those mark
UCSD - CHEM - 165
CHEM 165,265/BIMM 162/BGGN 2623D ELECTRON MICROSCOPY OF MACROMOLECULESBASIC INFO AND SYLLABUSLECTURER: Tim S. Baker, Natural Sciences NSB 4-105, 4-5845, tsb@ucsd.eduADMIN. ASSIST.: Robyn Swanland: Pacific Hall 6223, 4-4466, rswanlan@chem.ucsd.
UCSD - CHEM - 219
Buzz Words (Transmission Electron Microscopy)Airy disk amplitude contrast angular aperture anticontaminator astigmatism barrel distortion BFEM (Bright Field EM) blind imaging Cc (chromatic aberration coefficient) CCD (charge coupled device) chromati
UCSD - CHEM - 219
Buzz Words (Transmission Electron Microscopy)Airy disk amplitude contrast angular aperture anticontaminator astigmatism barrel distortion BFEM (Bright Field EM) blind imaging Cc (chromatic aberration coefficient) CCD (charge coupled device) chromati
UCSD - CHEM - 219
Buzz Words (Transmission Electron Microscopy)Airy disk amplitude contrast angular aperture anticontaminator aperture contrast astigmatism barrel distortion BFEM (Bright Field EM) blind imaging Bragg reflection Cc (chromatic aberration coefficient) c
UCSD - CHEM - 219
CHE M 21 9C3D E LE CTR O N M IC RO S COPY OF M AC RO MOLE CU LE S PRA CT IC E EXAM QU ES TIO NSHere are several questions to give you a flavor of the types of questions to expect on the upcoming Mideterm Exam. Questions that are not multiple choi
UCSD - CHEM - 219
CHE M 21 9C3D E LE CTR O N M IC RO S COPY OF M AC RO MOLE CU LE SLECT URE NOT ES T ABLE OF CONTENTSI. THE MICROSCOPE .A. PRINC IPLES OF THE T RA NSM ISS IO N E LE C TRO N MIC ROS CO PE (TE M) 1. Origin of the Electron Microscope . 2. Comparison
UCSD - CHEM - 219
CHE M 21 9C /B IMM 162 /B G GN 26 2TEXTBOOK /PE RIO D IC A LS LISTMost of the references listed here are in the Biomedical Library (BML) in the 1st Floor, West Wing of the Geisel Library or the Science & Engineering Library (S&E) on the Main Floo
UCSD - CHEM - 219
CHE M 21 9C /B IMM 162 /B G GN 26 2RE FE RE NCE LIST SThe lecture notes provide a fairly complete introduction to the principles and practice of transmission electron microscopy and to image reconstruction, BUT they are NOT comprehensive. The fol
UCSD - CHEM - 219
CHEM 219C/BIMM 162/BGGN 2623D ELECTRON MICROSCOPY OF MACROMOLECULESBASIC INFO AND SYLLABUSLECTURER: WHERE & WHEN: Tim S. Baker, Natural Sciences NSB 4-105, 4-5845, tsb@ucsd.edu HSS 1305; Tue & Thu 3:30-4:50PM->? (demos) ADMIN. ASSISTANT: Robyn S
UCSD - CHEM - 165
CHEM 165, 265/BI M M 1 62/BG GN 2623D EL ECTR O N MI CROS COPY OF MA CRO M OLECUL ESLECT URE NOT ES T ABLE OF CONTENTSI. THE MICROSCOPE .A. PRINC IPLES OF THE T RA NSM ISS IO N E LE C TRO N MIC ROS CO PE (TE M) 1. Origin of the Electron Microsc
North Texas - LTEC - 0145
LTEC 3440.020: Inro to Instructional Technology Project B: Lesson plan for a face-to-face lesson with instructional technology Kelsey R. CampbellStates of MatterCourse Time: 60 min. 1) Learner Outcome: Learning Goals: The learner will grasp th
Carnegie Mellon - STAT - 462
Indirect Inference C. Gourieroux; A. Monfort; E. Renault Journal of Applied Econometrics, Vol. 8, Supplement: Special Issue on Econometric Inference Using Simulation Techniques. (Dec., 1993), pp. S85-S118.Stable URL: http:/links.jstor.org/sici?sici=
Carnegie Mellon - STAT - 462
INDIRECT INFERENCE (prepared for: The New Palgrave Dictionary of Economics, Second Edition)Abstract Indirect inference is a simulation-based method for estimating the parameters of economic models. Its hallmark is the use of an auxiliary model to c
Washington - ET - 510
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Carnegie Mellon - STAT - 462
SELF-ORGANIZATION OF RANDOM CELLULAR AUTOMATA: FOUR SNAPSHOTSDAVID GRIFFEATH Department of Mathematics University of Wisconsin Madison, WI 53706 U.S.A.Abstract. We discuss four very simple random cellular automaton (CA) systems that self-organize
Carnegie Mellon - STAT - 462
[Statistics, Probability and Chaos]: Comment Colleen D. Cutler Statistical Science, Vol. 7, No. 1. (Feb., 1992), pp. 91-94.Stable URL: http:/links.jstor.org/sici?sici=0883-4237%28199202%297%3A1%3C91%3A%5BPACC%3E2.0.CO%3B2-J Statistical Science is cu
Carnegie Mellon - STAT - 462
[Statistics, Probability and Chaos]: Comment: Inference and Prediction in the Presence of Uncertainty and Determinism John Geweke Statistical Science, Vol. 7, No. 1. (Feb., 1992), pp. 94-101.Stable URL: http:/links.jstor.org/sici?sici=0883-4237%2819
Carnegie Mellon - STAT - 462
[Statistics, Probability and Chaos]: Comment Clive W. J. Granger Statistical Science, Vol. 7, No. 1. (Feb., 1992), pp. 102-104.Stable URL: http:/links.jstor.org/sici?sici=0883-4237%28199202%297%3A1%3C102%3A%5BPACC%3E2.0.CO%3B2-T Statistical Science
Maple Springs - ECON - 2400
Econ 2400MW, 2009, Midterm 2 MarksStudent # 80249 94720 804 2461 57408 40017 26196 52794 75290 46968 94762 11103 31499 87747 92697 20745 64628 43471 88021 20699 87748 89595 10425 44390 97141 3592 26189 55261 86191 94955 8763 59832 61341 42974 11068
Maple Springs - ECON - 2400
ECON2400MW - Midterm Marks - 2009Student No. 80249 94720 804 2461 57408 40017 26196 52794 75290 46968 94762 11103 31499 87747 92697 20745 64628 43471 88021 20699 87748 89595 10425 44390 97141 3592 26189 55261 86191 94955 8763 59832 61341 42974 11068
North Texas - CECS - 0079
Script 1. Intro Screen/Music comes on first 2. Explanation Screen/Music displays secondMrs. Naragon What is Rule Number that begins a sentence even with the other numbers are shown as figure?Students/Visual All Students: Are looking at the page t
North Texas - CECS - 0079
North Texas - CECS - 0079
North Texas - CECS - 0079
North Texas - CECS - 0079
North Texas - CECS - 0079
North Texas - CECS - 0079
Penn State - STAT - 511
Statistics 511Homework 1c dueFri. Sept. 9, 2:005Fall 2005All about plots: We are going to use a lot of plots in this course. I would like you to be familiar with: histograms boxplots Normal Probability Plots These are not well described in the
Penn State - STAT - 511
Statistics 511Homework 4a Due: Wednesday Oct. 4Fall 2006On the plots below, sketch the estimated fitted regression line. Which plot will have the largest R2? (Hint: The slope on plot A is zero. The slopes on the other 3 plots is positive.)
Maple Springs - ECON - 2400
Answers to Practice Questions For Chapter 3October 25, 2004Question 1We have to see what happens in each of the two models in the long run (steady state) and in the short run (transition dynamics). Solow Model Long Run A rise in the depreciation
USC - CSCI - 410
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USC - CSCI - 410
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USC - CSCI - 410
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USC - CSCI - 410
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USC - CSCI - 410
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Maple Springs - ECON - 2400
Answers to Practice Exercises for Chapter 41. Answers to Analytical Exercises from textbook Exercise 2: A move to zero population growth would raise the steady-state capital output ratio and raise the level of output per worker along the steady-stat
USC - CSCI - 410
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USC - CSCI - 410
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Flashcards
| Cognitive Neuroscience | |
| Term | Definition |
| Amygdala | Emotion |
| Medulla | Heart Rate... |
| EEG has ______... | Great |
| dysarthria | impaired... |
| Psych test . 6a | |
| Term | Definition |
| Mesokurtic | Normal |
| Behaviorist Perspective | -Skinner... |
| Morpheme | Smallest... |
| Resistance | Largely,... |
| I understand why accountants are alcoholics . .... | |
| Term | Definition |
| What are typical... | Revnue Cycle... |
| What are typical... | Production... |
| Source Document | Contain the... |
| Turn-around Document | Records of... |
| SJSU - Bus 111 Ch 1-6 | |
| Term | Definition |
| YR-Phone Invented | 1876 |
| YR-First... | 1915 |
| YR-Rotary Phones | 1919 |
| YR-Microwave trunk lines | 1948 |
| 3S251 1-1 | |
| Term | Definition |
| 001. How do you... | Determine... |
| 001. What does... | Information... |
| 001. What does a... | An overall... |
| 001. What are the... | Purpose,... |