PDF-Lecture14:10/27/200414-2LetparameterkdenotethesizeofW.Ifkissmall,wecan

Author : tatiana-dople | Published Date : 2015-11-18

AteachdepthwebranchintoatmosttwosubtreesandweremoveatmostnedgesfromthegraphThusthetimecomplexityofthealgorithmisO2knwhichisintheformthatwewantHencethevertexcoverproblemis xedparametertractabl

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Lecture14:10/27/200414-2LetparameterkdenotethesizeofW.Ifkissmall,wecan: Transcript

AteachdepthwebranchintoatmosttwosubtreesandweremoveatmostnedgesfromthegraphThusthetimecomplexityofthealgorithmisO2knwhichisintheformthatwewantHencethevertexcoverproblemisxedparametertractabl. arecalledtheleveragevalues.Becauseidempotent,itsrankequalsitstrace,andthustheaveragevalueofisbep/N.Valuesgreaterthan,say,3p/Nconsideredtohavehighleverageandmayhavehighin 2+"(n)8n;wheretheprobabilityistakenoverIR Gen(1n),XR DI,andthecointossesofA.2ExamplesRSAfunctionsUndertheRSAAssumption,theleastsignicantbitisahardcorebitforRSA:lsbN;e:ZN7!f0;1gGivenN;e;xemodN,wecan H(D)Pi2SDiforalli2S,whereH(`)istheharmonicnumber1+1=2++1=`.Proof.Renamethedemandpairssuchthatd(s1;t1)d(sk;tk).LetSibethesetf1;2;:::;ig.WeshowthatoneoftheseSi'swillsatisfytheconditionsoftheclai (I1)foreachproofofAinwecanndannsuchthatA(n)0isveriable,(I2)foreachproofof:AinandeachnwecanndasubstitutioninstancewhichmakesA(n)0false.Thereisalsoanobviousthirdconditionwhichrelatestheinterpretati th .Wecan’twaittosee allofourcampfriendsandgetthe2014summerseasonunderway. APRILBIRTHDAYS 4/1VIVIANFRITZ,HALEYMENIHAN4/2ETHANGROW,AUSTINMARPLE4/3ANTHONY MANCARUSO,JOSEPHMANZELLA4/4BRIANNACAIN4/6J 4M.MUSTATAu1;:::;un2O(U)formanalgebraicsystemofcoordinatesonUifdu1;:::;duntrivialize XoverU.SinceXisnonsingular,wecanndsuchasystemofcoordinatesintheneighborhoodofeverypointinX.Analgebraicsystemofco p0=T T0g0 R=1+H T0g0 RorH=T0 p p0R g01!:(1.2.1)So,basedonthepressure,wecanndthepressurealtitude.Thepressurecansimplybemeasuredusingananeroid:astaticairpressuremeter.Itshouldbenotedtha @z2=k21;(9.15)whichhassolutions1(z)/exp(kz)and1(z)/exp(kz).However,thelattersolutioncanbediscardedbecauseofboundaryconditions,sinceforz!1weneedtohaveanunperturbedstatewith1!0.Inasimilarway,wecan PartIPropositionalLogic3 xunassignediftherearenot.Is\xisaprimenumber"astatement?Answer:(todate)wecan'ttell!Butthisexampleissilly(thecontextwehavesetupishighlyartical)andquiteothepathofwhatwewillbedo Today'soutline FoundationsofstaticsPreviewofstatics.Foundations.Equivalencetheorems.Lineofaction.Poinsot'stheorem.Wrenches. Lecture14.FoundationsofStaticsFoundationsofstaticsPreviewofstatics.Foundatio

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