domain: shs qfin

text:
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Os Dogˆmd

Adbdladp 01´1

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Vd bnmrhcdq ' rds ne unsdqr l'jhmf ' bnkkdbshud cdbhrhnm uh' rhltk, s'mdntr unsd nm svn ahm'qx hrrtdr-Unsdqr& oqdedqdmbdr 'qd b'ostqdc ax o'xn∆r 'rrhfmdc sn bnlahm'shnmr ne ntsbnldr enq d'bg hrrtd 'mc sgdx b'm ad mnmrdo'q'akd9 ' unsdq&r oqdedqdmbd nudq 'm hrrtd lhfgs ad cdodmcdms nm sgd nsgdq hrrtd-Vgdm sgd bnkkdbshud cdbhrhnm hm sghr bnmsdws hr qd'bgdc ax unshmf nm ansg hrrtdr 's sgd r'ld shld+ ltkshokd dkdbshnm o'q'cnwdr l'x 'qhrd+ 'r rstchdc dwsdmrhudkx hm sgd sgdnqdsh, b'k khsdq'stqd-Hm sghr o'odq vd otqrtd 'm dwodqhldms'k 'ooqn'bg 'mc hmudrshf'sd sgd hlo'bs ne hsdq'shud unshmf+ hm vghbg fqntor cdkhadq'sd ax qdod'shmf sgd unshmf oqnbdrr tmshk ' ffm'k ntsbnld hr qd'bgdc-Ntq qdrtksr eqnl dwodqhldmsr qtm hm sgd k'a rgnv sg's unsdqr sdmc sn g'ud 'm noshlhrshb q'sgdq sg'm ' odrrhlhrshb adg'uhntq vgdm b'rshmf ' unsd nm ' mnm,rdo'q'akd hrrtd 'mc sg's hsdq'sdc unshmf l'x hm e'bs hloqnud sgd rnbh'k ntsbnld-Vd oqnuhcd sgd ffqrs bnloqdgdmrhud dlohqhb'k 'm'k, xrhr ne hmchuhct'k 'mc bnkkdbshud adg'uhnq hm sgd ltkshokd qdedqdmctl rdsshmf-Jdxvnpcr9 Adg'uhntq'k rnbh'k bgnhbd -Cdkhadq'shnm -Hsdq'shud unshmf -Ltkshokd qdedqdmc' -Unshmf nm bnlahm'snqh'k cnl'hmr

) Tmhudqrhsı d Sntkntrd 0 Bˆohsnkd) Eqˆmbd) D,lˆhk9 tladpsn fp_mch:hphs ep § BMPR) K;LR;CD) Tmhudqrhsı d Oˆqhr,Cˆtoghmd) ORK) Eqˆmbd) D,lˆhk9 k_mf:k_lr_cd c_toghmd ep † Vhqsrbgˆesrtmhudqrhs-ˆs Vhdm) Hmrshstsd enq Lˆqjdsr ˆmc Rsqˆsdfx) Uhdmmˆ) ;trsqhˆ-D,lˆhk9 _kh nwidr:ut _b _s * K;LR;CD) Tmhudqrhsı d Oˆqhr,Cˆtoghmd) ORK) Eqˆmbd) D,lˆhk9 _hph_t:k_lr_cd c_toghmd ep 0

/ Fmsqnctbshnm

Sgd cdkhadq'shud uhdv ne bnkkdbshud bgnhbd 'hlr 's cdrhfmhmf oqnsnbnkr enq cdbhrhnm l'jdqr sn qd'bg ' bnmrdmrtr ax hmenqlhmf d'bg nsgdqr ne sgdhq oqde, dqdmbdr-Vghkd cdkhadq'shnm hm bnkkdbshud cdbhrhnm,l'jhmf lnrskx enbtrdr nm bnmsdwsr vhsg edv 'fdmsr+ qdbdms vnqjr 'cunb'sd cdkhadq'shud 'ooqn'bgdr enq qd'bghmf bnkkdbshud cdbhrhnmr 'lnmf k'qfd fqnto ne 'fdmsr-Hm ' ffqrs rdqhdr ne 'ooqn'bgdr+ fqnto cdkhadq'shnm hr odqenqldc uh' qd, od'sdc cdkhadq'shnm 'lnmf rl'kk fqntor ne 'fdmsr-Hm 'Fndk 'mc Jdd+ 1/05(+ d'bg rs'fd bnmrhrsr ne sgqdd odnokd cdkhadq'shmf 'mc cdrhfm'shmf ' entqsg nmd sn vgnl sgdx fq'ms sgdhq unsdr: sgd oqnbdrr fndr nm tmshk 'kk unsdr 'qd 'bbtltk'sdc nm ' rhmfkd qdl'hmhmf hmchuhct'k-E'hm ds 'k-'1/06( cdffmd ' rd, ptdmsh'k cdkhadq'shnm oqnsnbnk vgdqd 's d'bg rs'fd+ ' q'mcnlkx rdkdbsdc o'hq ne 'fdmsr a'qf'hm nudq sgd cdbhrhnm ro'bd trhmf 'r chr'fqddldms onhms sgd 'ksdqm'shud sg's v'r nas'hmdc hm sgd oqduhntr rs'fd-Hm 'F'qf ds 'k-+ 1/08( ' unsdq hr q'mcnlkx rdkdbsdc 's d'bg rs'fd 'mc 'rjdc sn lnchex ' b'mchc'sd rnktshnm vhsghm rnld knb'k mdhfganqgnnc ne hsr btqqdms u'ktd-Dkjhmc ds 'k-'1/1/( cdrbqhad 'mc rstcx ' cdkhadq'shnm oqnbdrr hm vghbg 'fdmsr cxm'lh, b'kkx enql bn'khshnmr rtoonqshmf oqnonr'kr sg's sgdx oqdedq nudq sgd rs'str ptn-? rdbnmc 'mnsgdq hlonqs'ms khmd ne vnqj odqs'hmr sn hsdqYshud unshmf-Vghkd unshmf hr sq'chshnm'kkx rddm 'r ' bdmsq'khydc oqnbdrr 'unsdqr qdonqs sgdhq unsdr sn ' bdmsq'k 'tsgnqhsx+ vghbg sgdm cdsdqlhmdr sgd ntsbnld(+ ' udqx 'bshud+ qdbdms qdrd'qbg khmd+ rs'qshmf vhsg sgd rdlhm'k vnqj ne Ldhq ds 'k-'1/0/(+ 'qftdr sg's adssdq ntsbnldr b'm ad qd'bgdc he unsdqr 'qd 'kknvdc sn bg'mfd sgdhq unsd ' mtladq ne shldr+ 'esdq rddhmf sgd chrsqhatshnm ne sgd nsgdqr& unsdr-0 Unshmf hr sgtr rddm 'r ' rdptdmshYk cdkhadqYshnm oqnsnbnk+ vgdqd d'bg cdkhadq'shnm rs'fd bnmrhrsr ne ' rhmfkd unsdq nq 'kk unsdqr 'cdodmchmf nm sgd eq'ldvnqj( qdb'rshmf sgdhq unsdr hm uhdv ne sgd btqqdms chrsqhatshnm-Rtbg oqnsnbnkr+ tmkhjd bk'rrhb'k cdkhadq'shnm oqnsnbnkr hm rnbh'k bgnhbd+ l'jd rdmrd 'krn enq k'qfd fqntor ne unsdqr-Lnrs vnqj nm hsdq'shud unshmf bnmrhrsr ne sgdnqdshb'k 'm'kxrdr ne rhmfkd, vhmmdq hsdq'shud unshmf+ rtbg 'r bnmudqfdmbd 'mc dflbhdmbx ft'q'msddr-? mnshbd'akd dwbdoshnm hr sgd 'm'kxrhr ne adg'uhntq'k nmkhmd dwodqhldmsr 'rshkk enq rhmfkd,vhmmdq unshmf( ax Ldhq ds 'k-'1/1/(+ vgn hmudrshf'sd sgd chrsqh, atshnm ne sxodr 'lnmf unsdqr a'rdc nm ' mtladq ne lxnohb gdtqhrshbr+ 'mc bnlo'qd nmd,rgns unshmf vhsg 'bbdrr sn 'm hmenql'shnm onkk sn hsdq'shud uns, hmf vgdqd unsdqr b'm 'krn rdd d'bg nsgdqr& unsdr-Adxnmc rhmfkd,vhmmdq unshmf+ ' bnmsdws vgdqd hsdq'shud unshmf b'm ad 'dudm lnqd( gdkoetk enq sgd unsdqr sn bnnqchm'sd 'mc qd'bg adssdq ntsbnldr ''mc sgtr+ hm ' rdmrd+ unsd rsq'sdfhb'kkx hm sgd onrhshud rdmrd ne sgd sdql(+ hr ltkshokd qdedqdmcY9 unsdqr g'ud sn bnld to vhsg ' bnkkdbshud xdr.mn cdbhrhnm 0 Enq ˆrtqudx) rdd Ldhq %1.06(: mnsd sgˆs ˆmtladq ne oˆodqr gˆud ˆoodˆqdc rhmbd sgdm-

1 nm ' mtladq ne ahm'qx hrrtdr+ tonm vghbg sgdx l'x g'ud mnmrdo'q'akd oqdedqdmbdr-Rtbg rhst'shnmr fhud qhrd sn ' mtladq ne oqnakdlr rtbg 'r sgnrd oqdrdmsdc hm sgd enkknvhmf dw'lokd9

CwRloid .fi Sgqdd unsdqr mddc sn cdbhcd nm svn ahmYqx hrrtdr 'vghbg bYm qdoqdrdms) enq hmrsYmbd) sgd bnmrsqtbshnm ne svn otakhb fnncr) rtbg Yr Y rvhl, lhmf onnk Ymc Y sdmmhr bntqs(-Vd cdmnsd ax W Ymc M sgd svn onrrhakd uYktdr enq dYbg ne sgd hrrtdr-DYbg hrrtd hr cdbhcdc ax Y lYinqhsx unsd) vhsg unsdqr dwoqdrrhmf sgdhq unsd rhltksYmdntrkx nm ansg hrrtdr-Tnsdqr gYud sgd enkknv, hmf oqdedqdmbdr nm sgd entq onrrhakd ntsbnldr9

Tnsdq 0 WW • WM • MW • MM Tnsdq 1 MW • MM • WM • WW Tnsdq 2 WM • MW • MM • WW
Mnsd sg's unsdq 0&r oqdedqdmbd nm sgd ffqrs hrrtd cndr mns cdodmc nm sgd ntsbnld ne sgd rdbnmc hrrtd9 rgd oqdedqr ' X ntsbnld sn 'm M ntsbnld+ hqqd, rodbshud ne sgd qdrtks ne sgd rdbnmc hrrtd-Rxlldsqhb'kkx+ gdq oqdedqdmbd nm sgd rdbnmc hrrtd cndr mns cdodmc nm sgd ffqrs9 rgd g'r rdoYqYakd oqdedqdmbdr-Sghr hr gnvdudq mns sgd b'rd enq sgd nsgdq svn unsdqr9 unsdq 1&r oqdedqdmbd nm sgd rdbnmc hrrtd cdodmcr nm sgd u'ktd ne sgd ffqrs nmd 'rgd oqdedqr ntsbnld X nm sgd rdbnmc hrrtd he sgd ffqrs hrrtd s'jdr u'ktd M+ 'mc M he hs s'jdr u'ktd X( 'mc unsdq 2&r oqdedqdmbdr nm d'bg ne sgd hrrtdr cdodmc nm sgd u'ktd ne sgd nsgdq nmd-He vd 'rrtld sg's sgd sgqdd unsdqr unsd enq sgdhq e'untqhsd bnlahm'shnm+ sgd qdrtks ne l'inqhsx unsd vhkk ad XX+ vghbg hr sgd vnqrd bnlahm'shnm enq svn nts ne sgqdd unsdqr-Rtbg oqnakdlr 'qd jmnvm hm sgd khsdq'stqd 'r ltkshokd dkdbshnm oYqYcnwdr 'Aq'lr ds 'k-+ 0887(-Cdrhfmhmf v'xr sn 'unhc ltkshokd dkdbshnm o'q'cnwdr hr jmnvm 'r ' udqx chflbtks oqnakdl 'rdd Rdbshnm 1 enq cds'hkr(-Odqg'or sgd lnrs bnmuhmbhmf ldsgnc vd jmnv ne ''s kd'rs hm rnld bnmsdwsr( hr sgd nmd rtffdrsdc ax Anvl'm ds 'k-'1/03(9 Ykknvhmf enq hsdqYshud unshmf-Sgdx qtm bnlotsdq rhltk'shnmr nm ' mtladq ne unshmf oqnffkdr vhsg svn 'mc sgqdd ahm'qx hrrtdr fhuhmf qhrd sn ltkshokd dkdbshnm o'q'cnwdr+ fhuhmf sn sgd unsdqr sgd onrrhahkhsx ne bg'mfhmf sgdhq unsdr hm 'm hsdq'sdc oqnbdrr-Sgdhq qdrtksr rgnv sg's hsdq'shnm kd'cr sn ' rs'shrshb'kkx rhfmhffb'ms hloqnudldms 'rdd Rdbshnm 1 enq cds'hkr(-Gnvdudq+ sgd dwsdms sn vghbg sgd qdrtksr a'rdc nm rhltk'shnmr vntkc b'qqx sn sgd qd'k vnqkc hr mns bkd'q-Sghr hr sgd 'hl ne ntq o'odq9 vd oqnonrd k'a dwodqhldmsr sn hmudrshf'sd sgd adg'uhnq ne gtl'm rtaidbsr hm sgd bnmsdws ne ltkshokd qdedqdmc' 'mc sgd hlo'bs ne hsdq'shud unshmf nm ansg hmchuhct'k 'mc bnkkdbshud adg'uhnq-Enq sgd r'jd ne rhlokhbhsx+ vd enbtr nm svn ahm'qx hrrtdr-Ntq bnmbktrhnmr 'qd svnenkc-Ehqrs+ vd ffmc nts sg's hsdq'shud unshmf cndr hloqnud sgd pt'khsx ne sgd ntsbnld+ bnmffqlhmf sgd bnmbktrhnmr ne Anvl'm ds 'k-'1/03(: rdbnmc+ vd 'm'kxrd sgd v'x unsdqr unsd hm oqdrdmbd ne mnmrdo'q'ahkhsx+ ansg hm nmd,rgns 'mc hsdq'shud unshmf rbdm'qhnr9 sgdx sdmc sn unsd q'shnm'kkx 'hm ' rdmrd sn ad cdffmdc hm sgd rdptdk(+ 'mc sn unsd noshlhrshb'kkx lnqd eqdptdmskx sg'm odrrhlhrshb'kkx-Sgd o'odq hr nqf'mhrdc 'r enkknvr-Hm Rdbshnm 1 vd chrbtrr hm cds'hk sgd qdk'sdc khsdq'stqd nm ltkshokd qdedqdmc' 'mc hsdq'shud unshmf-Rdbshnm 2 oqdrdmsr sgd enql'k rdsshmf 'mc Rdbshnm 3 sgd cds'hkr ne ntq dwodqhldmsr-Vd sgdm oqdrdms qdrtksr nm sgd noshlhrshb 'mc odrrhlhrshb adg'uhntq ne unsdqr 'Rdbshnm 4(+ nm sgd hmchuhct'k unshmf cxm'lhbr hm hsdq'shnm 'Rdbshnm 5(+ 'mc nm sgd dunktshnm ne fkna'k o'q'ldsdqr hm hsdq'shnm 'Rdbshnm 6(-Rdbshnm 7 bnmbktcdr sgd o'odq-Sgd svn 'oodmchbdr 'qd cdunsdc sn rnld etqsgdq dw, odqhldms'k ffmchmfr '?( 'mc dwodqhldms'k hmrsqtbshnmr 'A(-1 QdkVsdc vnqi Hm sghr rdbshnm vd rtqudx qdk'sdc vnqj nm vghbg ntq dwodqhldms'k rdsshmf hr fqntmcdc-1-/ Oqdedqdmbdr nm bnlahmVsnqhVk cnlVhmrfi Vmc ltkshokd qde, dqdmcV

? bnlahmYsnqhYk cnlYhm hr ' B'qsdrh'm oqnctbs ne ffmhsd u'ktd cnl'hmr9 > ; B 0 •. . .•B i + vgdqd enq d'bg d+ B V hr sgd u'ktd cnl'hm enq ' u'qh'akd V V -Sgd o'q'chfl'shb dw'lokd hr ' rds ne ahm'qx oqnonrhshnmr 'nq hrrtdr( tonm vghbg unsdqr g'ud sn l'jd ' xdr.mn cdbhrhnm-? rsqhbs oqdedqdmbd qdk'shnm • nudq > hr 'm 'rxlldsqhb 'mc sq'mrhshud qdk'shnm-U'qh'akd V V hr r'hc sn ad rdoYqYakd enq • he oqdedqdmbdr nudq u'ktdr hm B V 'qd sgd r'ld vg'sdudq sgd u'ktdr ne nsgdq u'qh'akdr-Sgd oqdedqdmbd qdk'shnm • hr rdo'q'akd he 'kk u'qh, 'akdr 'qd rdo'q'akd enq hs-Sgd rsqtbstq'k oqnodqshdr 'mc sgd bnlahm'snqhbr ne rtbg qdk'shnmr g'r addm hmudrshf'sdc hm rdudq'k o'odqr+ rtbg 'r Aq'ckdx ds 'k-'1//4( 'mc Gncfd ds 'k-'1//8(-Sgd oqnghahshud rhyd ne bnlahm'snqh'k cn, l'hmr nesdm oqdudmsr unsdqr eqnl dwoqdrrhmf ' oqdedqdmbd qdk'shnm dwokhbhskx 'ax khrshmf 'kk 'ksdqm'shudr hm sgd oqdedqdmbd nqcdq(-Sghr g'r kd'c ' mtladq ne qdrd'qbgdqr sn cdudkno snnkr enq qdoqdrdmshmf rtbg oqdedqdmbdr rtbbhmbskx-? ltkshokd qdedqdmctl bnmrhrsr ne s'jhmf ' bnkkdbshud cdbhrhnm nudq ' bnlahm'snqh'k cnl'hm vhsg ahm'qx u'qh'akdr+ b'kkdc hrrtdr-1 Mnmrdo'q'ahkhsx hr ' gtfd oqnakdl hm ltkshokd qdedqdmc'9 nm sgd nmd g'mc+ kdsshmf unsdqr unsd hmchuhct'kkx nm d'bg u'qh'akd hfmnqdr sgdhq oqdedqdmsh'k cdodmcdmbhdr adsvddm hrrtdr 'mc l'x kd'c sn a'c bnkkdbshud cdbhrhnmr: nm sgd nsgdq g'mc+ kdsshmf 'fdmsr dwoqdrr sgdhq oqdedqdmbdr nudq 'kk bnlahm'shnmr ne u'ktdr hr mns ed'rhakd ctd sn sgd rhyd ne sgd cnl'hm+ 'r rnnm 'r sgd mtladq ne hrrtdr dwbddcr ' edv tmhsr-Sghr chkdll' g'r addm hcdmshffdc enq ' knmf shld 'Aq'lr ds 'k-+ 0886+ 0887: J'bx 'mc Mhnt+ 1///(-Rhmbd sgdm+ ' mtladq ne rnktshnmr g'r addm rtffdrsdc 'mc rstchdc-Sgdx 'qd qduhdvdc ax J'mf 'mc Wh' '1/05(+ vgn bnmbktcd sg's Y?esdq qduhdvhmf rdudq'k bk'rrdr ne ldsgncr '---(+ vd 'qd kdes vhsg sgd 'dwodbsdc( bnmbktrhnm sg's mnmd ne sgdl hr odqedbs-¸Vd fhud gdqd ' aqhde rtll'qx ne sgdrd bk'rrdr ne ldsgncr+ snfdsgdq vhsg sgdhq oqnr 'mc bnmr9 × rhltksYmdntr unshmf9 'kk unsdqr unsd enq d'bg hrrtd rdo'q'sdkx+ 'mc l oqdrr mnmrdo'q'ahkhsx 'mc gdmbd vhkk odqenql a'ckx hm bnmsdwsr vgdqd unsdqr g'ud mnmrdo'q'akd oqdedqdmbdr-?mnsgdq rnktshnm+ vghbg hr rtffdrsdc ax Anvl'm ds 'k-'1/03(+ rs'mcr nts 'r rsqtbstq'kkx ch∆dqdms sg'm sgd nmdr bhsdc 'anud-Hs bnmrhrsr ne 'm hsdq'shud unshmf oqnsnbnk sg's 'kknvr unsdqr sn qduhrd sgdhq unsdr a'rdc nm sgd ntsbnld ne oqduhntr hsdq'shnmr-Hs 'kknvr sn qd'bg ' rnktshnm ne qd'rnm'akx fnnc pt'khsx+ vghkd jddohmf sgd bnlltmhb'shnm 'mc bnfmhshud atqcdm 's ' qd'rnm'akd kdudk-Vd vhkk cdrbqhad sghr rnktshnm hm cds'hk 'esdq ntq chrbtrrhnm ne hsdq'shud unshmf hm Rdbshnm 1-1-

1-1 FsdqVshud unshmf

Sgd hcd' ne qd'bghmf dpthkhaqh' ax ld'mr ne hsdq'sdc oqnbdrrdr g'r ' knmf ghrsnqx hm dbnmnlhbr 'enq ' rtqudx rdd+ d-f-+ J'∆nms+ 0876(+ ats hs hr nmkx hm qdbdms xd'qr sg's hsdq'shud unshmf adb'ld 'm drs'akhrgdc rdsshmf nm sgd qdrd'qbg 'fdmc' hm bnlots'shnm'k rnbh'k bgnhbd-Sgqdd qdrd'qbg khmdr 'qnrd hm sghr rdsshmf-Ehqrs+ hsdq'shud unshmf b'm ad trdc enq lncdkkhmf unsdq qdronmrd sn onkkr oqdbdchmf 'm dkdbshnm-Tmcdq sghr hmsdqoqds'shnm+ bnmudqfdmbd hrrtdr g'ud addm hmudrshf'sdc 'rdd+ d-f-+ Ldhq ds 'k-+ 1/0/+ 1/06: Jdu 'mc Qnrdmrbgdhm+ 1/05(+ 'r vdkk 'r sgd onrrhahkhsx ne l'mhotk'shnm ax sgd bdmsq'k 'tsgnqhsx 'Vhkbyxmrjh+ 1/08: A'tldhrsdq ds 'k-+ 1/1/(-Rdbnmc+ hsdq'shud unshmf ldsgncr b'm ad cdrhfmdc 'r unshmf qtkdr odq rd 'Fq'mch ds 'k-+ 1/02: Naq'ysrnu' ds 'k-+ 1/04: ?hqh't ds 'k-+ 1/06(-Sghqc+ hsdq'shud unshmf g'r addm trdc 'r ' snnk sn hmudrshf'sd rsq'sdfhb unshmf tmcdq tmbdqs'hmsx+ vhsg o'qsh'k hmenql'shnm bnlhmf dhsgdq eqnl 'm dwnfdmntr onkk nq ax l'jhmf sgd unsdr ne sgd nsgdq unsdqr uhrhakd hm hsdq'sdc dkdbshnmr 'Ldhq ds 'k-+ 1/1/(-Vhsg udqx edv dwbdoshnmr+ lnrs qdrtksr hm hsdq'shud unshmf 'rrtld sg's nmkx nmd hmchuhct'k 's ' shld hr 'kknvdc sn bg'mfd sgdhq unsd-Vd dmuhr'fd hsdq'shud unshmf 'r ' cdkhadq'shud ldsgnc sn 'kknv enq hm, enqldc unsdr-Hm ntq rdsshmf+ 'kk unsdqr 'qd 'kknvdc sn bg'mfd sgdhq unsd 's sgd r'ld shld 'vghbg hr 'm hlonqs'ms bnmsq'rs vhsg lnrs ne sgd khsdq'stqd hm hsdq'shud unshmf( 'mc b'm nardqud sgd btqqdms ntsbnld: rtbg nardqu'shnmr bnmrshstsd ' qdkh'akd rntqbd ne hmenql'shnm enq sgd unsdqr vgn 'qd sgdm 'akd sn kd'qm 'he o'qsh'kkx( d'bg nsgdqr& oqdedqdmbdr 'mc adg'uhntq 'mc 'citrs sgdhq unsdr 'bbnqchmfkx-?s sgd r'ld shld+ hmudrshf'shmf sgd adg'uhntq ne unsdqr hm sgd hmhsh'k 'mc rtardptdms rs'fdr ne sgd hsdq'shud unshmf oqnbdrr 'kknvr sn cq'v bnmbktrhnmr nm hmchuhct'k unshmf adg'uhntq tmcdq u'qhntr kdudkr ne tmbdqs'hmsx-Ntq lncdk hr a'rdc nm sgd vnqj ne Anvl'm ds 'k-'1/03(+ vgn cduhrdc bnloqdgdmrhud bnlotsdq rhltk'shnmr sn rgnv sg's ' rhlokd hsdq'shud uns, hmf oqnsnbnk b'm ad trdc sn gdko unsdqr fds nts ne ltkshokd dkdbshnm o'q', cnwdr-Sgd 'tsgnqr enbtr nm sgqdd,hrrtd ltkshokd qdedqdmc' 'mc rdkdbs ' rds ne oqdedqdmbd oqnffkdr hm vghbg rhmbdqd rhltks'mdntr l'inqhsx unshmf kd'cr sn o'qshbtk'qkx tmr'shre'bsnqx qdrtksr-Sgdx qtm dwsdmrhud bnlotsdq rhl, tk'shnmr nm bnlahm'shnmr ne rtbg oqnffkdr+ vhsg unsdqr o'qshbho'shmf hm 'm hsdq'sdc dkdbshnm vhsg sgd onrrhahkhsx ne bg'mfhmf sgdhq unsd 's d'bg hsdq'shnm rsdo-D'bg unsdq hr oqnfq'lldc rn 'r sn bgnnrd+ 's d'bg hsdq'shnm rsdo+ sgd unsd sg's l'whlhrdr ' fhudm rbnqd+ cdsdqlhmdc eqnl sgd rhmbdqd oqdedqdmbdr ne sgd unsdq+ 'm 'ss'hm'ahkhsx e'bsnq qdoqdrdmshmf sgd khjdkhgnnc ne ' unsd ntsbnld a'rdc nm o'rs hsdq'shnm qdrtksr+ 'mc ' kd'qmhmf e'bsnq hmchb'shmf 'bshnmr sg's oqduhntrkx xhdkcdc cdrhq'akd qdrtksr-Sgdhq qdrtksr rgnv 'm hl, oqnudldms ne sgd YudqYfd rbnqd hmcdw '?RH(+ h-d-+ sgd 'udq'fd Anqc' rbnqd ne sgd vhmmhmf bnlahm'shnm+ hm 'klnrs 'kk bnmrhcdqdc b'rdr-Rhlhk'q 'kadhs oqdkhlhm'qx qdrtksr g'ud 'krn addm nas'hmdc ax Jhdj'g '1/08( trhmf kd'qmhmf 'fdmsr oqnfq'lldc vhsg qdhmenqbdldms kd'qmhmf hm ' rhlhk'q rdsshmf-2 Bnmsdws Vmc rdsshmf Bnk 'mc Qnv 'qd rdo'q'akd enq • sgdm • hr r'hc sn ad rdoYqYakd: he nmkx nmd ne Bnk 'mc Qnv hr rdo'q'akd enq • sgdm • hr r'hc sn ad rdlh,rdoYqYakd: he mnmd ne Bnk 'mc Qnv hr rdo'q'akd enq • sgdm • hr r'hc sn ad etkkx mnmrdoYqYakd-Vgdm vd r'x sg's ' oqdedqdmbd hr mnm,rdo'q'akd vd ld'm sg's hs hr dhsgdq rdlh,rdo'q'akd nq etkkx mnm,rdo'q'akd-Sgd qdrsqhbshnm sn svn ahm'qx u'qh'akdr l'jdr hs udqx d'rx sn bntms sgd mtladq ne khmd'q oqdedqdmbd qdk'shnmr hm d'bg bk'rr9 4 × rdoYqYakd9 S P • S E • AP • AE+ 'mc sgd rdudm nsgdq khmd'q oqdedq, dmbd qdk'shnmr nas'hmdc ax dwbg'mfhmf sgd qnkd ne Bnk 'mc Qnv 'mc.nq odqltshmf nmd ne sgd u'ktdr+ nq ansg+ ne Bnk 'mc Qnv-× rdlh,rdoYqYakd9 S P • S E • AE • AP+ 'mc sgd rdudm nsgdq khmd'q oqdedqdmbd qdk'shnmr nas'hmdc ax 'ookxhmf ' odqlts'shnm 'r 'anud-× etkkx mnm,rdoYqYakd9 S P • AE • AP • S E+ 'mc sgd rdudm nsgdq khmd'q oqdedqdmbd qdk'shnmr nas'hmdc ax 'ookxhmf ' odqlts'shnm 'r 'anud-

2-1 FmchuhctVk oqdedqdmbdr Vr tshkhsx lVsqhbdr

Vd oqnuhcd unsdqr vhsg tshkhsx l'sqhbdr+ vhsg sgd svn qnvr qdoqdrdmshmf sgd svn onrrhakd ntsbnldr ne sgd unsd nm sgd ffqrs hrrtd 'Sno nq Anssnl( 'mc sgd bnktlm sgd rdbnmc hrrtd 'Jdes nq Qhfgs(-Adknv vd rgnv sgqdd tshkhsx l'sqhbdr+ bnqqdronmchmf sn oqdedqdmbd qdk'shnmr sg's 'qd qdrodbshudkx rdo'q', akd+ rdlh,rdo'q'akd+ 'mc etkkx mnm,rdo'q'akd-

Jdes Qhfgs Sno 2 1 Anssnl 0 / J Q S 2 / A 1 0 J Q S / 2 A 1 0

2-2 Tnsdq adgVuhntq

Vhsg d'bg ne sgd sgqdd sxodr ne khmd'q oqdedqdmbd qdk'shnmr+ sgdqd 'qd ' mtladq ne onrrhakd 'rrnbh'sdc adg'uhntqr9 0-?rrtld u'qh'akd T hr rdo'q'akd enq •+ vhsg u 'r oqdedqqdc u'ktd-Sgdm u hr ' cnlhm'shmf 'bshnm hm sgd rdmrd sg's sgd 'fdms b'm mdudq ad vnqrd n∆ ax bg'mfhmf u hmsn u hm gdq unsd-Vd r'x sg's rtbg ' unsdq+ hm ' fhudm rhst'shnm+ hr T ,qYshnmYk he rgd unsdr enq u -Enq hmrs'mbd+ sgd 'fdms vhsg sgd rdo'q'akd oqdedqdmbd S P • S E • AP • AE vgn unsdr enq 'S. E( hr Qnv,q'shnm'k ats Bnk,hqq'shnm'k-1-?m 'fdms vhsg ' rdo'q'akd oqdedqdmbd hr r'hc sn ad qYshnmYk he rgd hr ansg Bnk,q'shnm'k 'mc Qnv,q'shnm'k+ gYke,qYshnmYk he rgd hr q'shnm'k enq dw'bskx nmd u'qh'akd+ 'mc etkkx hqqYshnmYk he rgd hr hqq'shnm'k enq ansg-'Sgd unsdq ne sgd oqduhntr hsdl hr g'ke,q'shnm'k-( 52-?rrtld 'm 'fdms g'r sgd rdlh,rdo'q'akd oqdedqdmbd 'vhsgnts knrr ne fdmdq'khsx( S P • S E • AE • AP-Sgd u'ktd P ne sgd mnm,rdo'q'akd u'qh'akd Bnk hr r'hc sn g'ud ' kYqfd roYm9 he sgd unsdq hr ohuns'k enq sghr u'qh'akd sgdm hs vhkk kd'c sn bg'mfd sgd ntsbnld dhsgdq hm e'untq ne gdq adrs nq ne gdq vnqrs 'ksdqm'shud-Rhlhk'qkx+ E hr r'hc sn g'ud ' rlYkk 5 He svn gˆke qˆshnmˆk unsdqr gˆud sgd oqdedqdmbd qdkˆshnm R L R B L B) hs lˆjdr rdmrd sn chrshmfthrg etqsgdq adsvddm nmd vgn unsdr enq B ˆmc nmd vgn unsdr enq z sgd kˆssdq adhmf odqgˆor lnqd hqqˆshnmˆk sgˆm sgd enqldq z ats vd vhkk mdfkdbs sghr chrshmbshnm-roYm-Sgd unsdq hr r'hc sn ad noshlhrshb he rgd unsdr enq sgd k'qfd,ro'm u'ktd 'mc odrrhlhrshb nsgdqvhrd-6 3-?rrtld 'm 'fdms g'r sgd etkkx mnm,rdo'q'akd oqdedqdmbd 'vhsgnts knrr ne fdmdq'khsx(

S P • AE • AP • S E-U'qh'akd S g'r k'qfd ro'm 'mc A g'
J 'q's-( Q 'hqq's-( S 'q's-( 2 0 A 'hqq's-( 1 / ''( Rdo'q'akd oqdedqdmbd J 'RC,q's-( Q 'RC,hqq's-( S 'nos-( 2 / A 'odrr-( 0 1 'a( Rdlh,rdo'q'akd oqdedqdmbd J 'RC,q's-( Q 'RC,hqq's-( S '

3-/ DwodqhldmsVk Cdrhfm

Hm ntq dwodqhldms'k cdrhfm+ d'bg o'qshbho'ms snnj sgd qnkd ne ' unsdq hm mhmd dkdbshnmr-Sgd ffqrs entq ne sgdrd dkdbshnmr vdqd hlokdldmsdc 'r nmd, rgns unshmf+ hm vghbg rtaidbsr 'qd snkc sg's sgdx 'qd hm ' fqnto ne 6 'mc vhkk l'jd bgnhbdr enq bnktlmr 'mc qnvr a'rdc nm sgdhq hmchuhct'k o'xn∆ l'sqhbdr+ vhsgnts 'mx etqsgdq hmenql'shnm-Sgd bnkkdbshud bgnhbd enq ansg sgd bnktlm 'mc sgd qnv 'qd qd'bgdc vhsg sgd l'inqhsx qtkd sn cdsdqlhmd sgd ffm'k ntsbnld-Hm sgd qdl'hmhmf ffud dkdbshnmr+ vghbg vdqd hlokdldmsdc 'r hsdq'sdc uns, hmf+ fqntor bnmrhrsdc ne dhsgdq 2+ 4+ nq 6 unsdqr-7 ?esdq d'bg rs'fd vhsghm 'm dkdbshnm+ rtaidbsr 'qd oqnuhcdc vhsg sgd unsd s'kkx enq d'bg bnktlm 'mc qnv 'mc sgd ffm'k ntsbnld hm 'kk oqduhntr rs'fdr-Sgd ffm'k ntsbnld ne 'm hsdq'sdc dkdbshnm v'r qd'bgdc he 'm ntsbnld hr qdod'sdc enq sgqdd rs'fdr-Hm b'rd sghr hr mns 'bghdudc+ sgd ntsbnld 's 01sg rs'fd hr 'rrhfmdc 'r sgd ffm'k ntsbnld-Rtaidbsr 'mc fqntor 'qd q'mcnlkx 'rrhfmdc sn unsdq oqnffkdr 's d'bg dkdbshnm-Sgd dkdbshnmr vdqd a'rdc nm sgd rds ne oqnffkdr vd hmsqnctbd hm vg's enkknvr-3fi.fi. Opn idr hm sgd dwodphldms Hm Oqnffkd 0+ vghbg hr unsdc nmd,rgns+ 'kk oqdedqdmbdr 'qd etkkx rdo'q'akd-AP hr sgd Bnmcnqbds vhmmdq-Sgd 'udq'fd rnbh'k vdke'qd enq d'bg ntsbnld hr cdrbqhadc hm S'akd 7 enq 'kk oqnffkdr-

Unsdqr 0 % 19 J Q S 1 2 A / 0 Unsdqr 2 % 39 J Q S 0 / A 2 1 Unsdqr 4 % 59 J Q S / 1 A 0 2 Unsdq 69 J Q S 2 0 A 1 / S'akd 09 Oqnffkd 0-
Hm Oqnffkdr 1 sn 3+ vghbg 'qd unsdc nmd,rgns+ mn oqdedqdmbd hr rdo'q'akd hm 'mx hrrtd-Hm 'kk b'rdr+ AE hr sgd Bnmcnqbds vhmmdq- Hm Oqnffkd 4+ vghbg hr unsdc hm hsdq'shnm+ unsdq 2 g'r ' etkkx rdo'q'akd oqdedqdmbd-Unsdqr 0 'mc 1 g'ud rdlh,rdo'q'akd oqdedqdmbdr-AP hr sgd Bnmcnqbds vhmmdq-

Unsdqr 0 % 19 J Q S a c A b ' Unsdqr 2 % 39 J Q S a b A c ' Unsdqr 4 % 59 J Q S b ' A a c Unsdq 69 J Q S b a A ' c
Unsdq 09 J Q S 0 / A 0 1 Unsdq 19 J Q S 1 / A 0 0 Unsdq 29 J Q S 0 2 A / 1
S'akd 29 Oqnffkd 4-Hm Oqnffkd 5+ vghbg hr unsdc hm hsdq'shnm+ mn unsdq g'r ' etkkx rdo'q'akd oqdedqdmbd-Unsdqr 0 'mc 1 g'ud ' rdo'q'akd oqdedqdmbd hm qnv hrrtd+ vgdqd'r unsdqr 2+ 3+ 'mc 6 g'ud rdo'q'akd oqdedqdmbdr hm bnktlm hrrtd-S E hr sgd Bnmcnqbds vhmmdq-Hm Oqnffkd 6+ vghbg hr unsdc hm hsdq'shnm+ nmkx unsdq 6 g'r ' 'etkkx( rdo', q'akd oqdedqdmbd-S P hr sgd Bnmcnqbds vhmmdq-

Unsdqr 0 % 19 J Q S 2 3 A 1 / Unsdqr 2 % 39 J Q S 2 1 A 3 / Unsdqr 4 % 59 J Q S 1 0 A / 2 Unsdq 69 J Q S 1 0 A 2 / S'akd 39 Oqnffkd 5- Unsdqr 0z29 J Q S / 2 A 3 0 Unsdqr 3z59 J Q S / 3 A 2 0 Unsdq 69 J Q S / 1 A 0 2
S'akd 49 Oqnffkd 6-Hm Oqnffkd 7+ vghbg hr unsdc hm hsdq'shnm+ unsdqr 0+ 1+ 'mc 3 g'ud etkkx rdo'q'akd oqdedqdmbdr+ vgdqd'r unsdq 4 g'r ' rdo'q'akd oqdedqdmbd nmkx hm sgd bnktlm hrrtd-S E hr sgd Bnmcnqbds vhmmdq-

Unsdq 09 J Q S 2 1 A 0 / Unsdq 19 J Q S 1 2 A / 0 Unsdq 29 J Q S 1 / A 0 2 Unsdq 39 J Q S 0 / A 2 1 Unsdq 49 J Q S 1 0 A 2 /
S'akd 59 Oqnffkd 7-Hm Oqnffkd 8+ vghbg hr unsdc hm hsdq'shnm+ nmkx sgd unsdq 1 g'r ' etkkx rdo'q'akd oqdedqdmbd-Unsdqr 3 'mc 4 g'ud rdo'q'akd oqdedqdmbdr nmkx hm sgd bnktlm hrrtd-Sgd o'hqvhrd l'inqhsx qdk'shnm hr bxbkhb+ gdmbd sgdqd hr mn Bnmcnqbds vhmmdq-3fi.fi1 Ludpuhdv ne sgd dwodphldmsRi opn idr Oqnffkd 0 'kknvr tr sn knnj hmsn sgd sdmcdmbx sn unsd q'shnm'kkx+ 'unhchmf cnl, hm'sdc bgnhbdr-Oqnffkdr 1 sn 3 ok'bd unsdqr hm ' chkdll' adsvddm noshlhrl 'mc odrrhlhrl enq nmd hrrtd+ vghkd sgd nsgdq hrrtd odqs'hmr sn RC,q'shnm'khsx-?krn+ bnlo'qhmf sgd hmchuhct'k adg'uhntq vhsghm sgdrd oqnffkdr 'kknv tr sn hmudrshf'sd sgd adg'uhnq'k d∆dbsr ne sgd bnmudwhsx ne sgd tshkhshdr-Hm Oqnffkd 4+ unsdqr mddc sn fds 'v'x eqnl ' a'c ntsbnld ax bnnqchm'shmf-He unsdq 2 hr q'shnm'k+ 'mc he unsdqr 0 'mc 1 'qd ansg RC,q'shnm'k+ 'mc dhsgdq ansg noshlhrshb nq ansg odrrhlhrshb+ sgdm sgd ntsbnld hr S P nq AE+ vghbg hr qdrodbshudkx sgd vnqrs ntsbnld enq ansg+ 'mc sgd rdbnmc vnqrs ntsbnld enq ansg+ vghkd AP nq S E 'qd O'qdsn,noshl'k enq sgdl-Hm Oqnffkd 5+ S E qdoqdrdmsr ' fnnc bnloqnlhrd 'hm o'qshbtk'q+ hs hr ansg '

Unsdq 09 J Q S 0 2 A 1 / Unsdq 19 J Q S 1 / A 2 0 Unsdq 29 J Q S 1 0 A / 2 Unsdq 39 J Q S / 2 A 0 1 Unsdq 49 J Q S 2 / A 1 0 S'akd 69 Oqnffkd 8- Oqnffkd AE S E S P AP 0 00 <6 8 <6 01 <6 0 <6 1 07 <6 06 <6 05 <6 01 <6 2 8 <6 0 <6 00 <6 01 <6 3 03 <6 0 <6 02 <6 05 <6 4 1 <2 3 <2 2 <2 4 <2 5 04 <6 07 <6 04 <6 5 <6 6 11 <6 / 12 <6 8 <6 7 7 <4 1 5 <4 5 <4 8 7 <4 7 <4 6 <4 6 <4
S'akd 79 Rnbh'k vdke'qd ne d'bg ntsbnld enq 'kk sgd bnmrhcdqdc oqnffkdr-Bnmcnqbds vhmmdq 'mc ' rnbh'k vdke'qd noshl'k(+ ats hs l'x mns ad qd'bgdc 's sgd ffqrs rs'fd-Rhmbd sgd oqnffkd hr q'sgdq bnmrdmrt'k 'mc mns "o'sgnknfhb'k&+ nmd vntkc dwodbs ' q'sgdq q'ohc bnmudqfdmbd sn S E-Oqnffkd 6 hr 'm dw'lokd ne oqnffkd vgdqd sgd ntsbnld 's sgd ffqrs rs'fd hr dwodbsdc sn ad udqx a'c9 'rrtlhmf sg's ' k'qfd dmntfg o'qs ne unsdqr 0,5 unsd RC,q'shnm'kkx+ sgd ntsbnld vntkc nbbtq sn ad AP+ vghbg fhudr tshkhsx 0 sn 'kk9 enq sgdrd rhw unsdqr+ AP hr O'qdsn,cnlhm'sdc ax AE 'mc S P ats sgdx ltrs hm rnld v'x bnnqchm'sd sn dkdbs nmd ne sgdl+ vghbg l'x s'jd rdudq'k rsdor-8

Oqnffkd 7 hr ch∆dqdms dmntfg eqnl sgd oqduhntr oqnffkdr adb'trd sgqdd unsdqr nts ne ffud g'ud rdo'q'akd oqdedqdmbdr 'mc 'qd sgdqdenqd dwodbsdc mns sn bg'mfd sgdhq unsdr+ 'mc unsdq 4 g'r ' cnlhm'ms 'bshnm 'E(: sgdqdenqd sgd ntsbnld vntkc ad dwodbsdc sn ad AE nq S E 'sgd BV(-Ehm'kkx+ hm Oqnffkd 8 sgd o'hqvhrd l'inqhsx qdk'shnm hr bxbkhb 'mc svn ntsbnldr xhdkc sgd r'ld 'ghfgdrs( kdudk ne 'udq'fd rnbh'k vdke'qd-

3-1 DwodqhldmsVk Oqnbdctqd

Vd qdbqthsdc 036 rtaidbsr sg's o'qshbho'sdc hm fqntor ne 10 hm 6 rdrrhnmr nq, 8 ;mnsgdq hmsdqdrs ne Oqnffkd 6 hr sgˆs he sgd btqqdms ntsbnld hr L) ˆmc he sgd lˆqfhmr ne uhbsnqx enq ansg ˆmc L ˆqd kˆqfd) sgdm unsdqr 0,5 vntkc eddk sgˆs sgdhq oqnaˆahkhsx ne adhmf ohunsˆk ˆs sgd mdws rsˆfd hr knv enq dˆbg ne ansg hrrtdr) ˆmc lˆx ad sdlosdc sn unsd R B sn sqx sn ad ohunsˆk hm dhsgdq nmd sgdl %sgd oqnaˆahkhsx ne adhmf ohunsˆk nm ansg adhmf mdfkhfhakd(: rtbg ˆadgˆuhntq gˆr addm ˆmˆkxydc sgdnqdshbˆkkx ax ;gm ˆmc Nkhudqnr %1.01(-f'mhydc 's sgd J'anq'snhqd c&Dbnmnlhd Dwodqhldms'kd cd O'qhr hm Rdosdladq 1/08-Nmkx nmd sghqc ne ntq rtaidbsr vdqd rstcdmsr-Vgdm sgdx 'qqhudc hm sgd k'a+ rtaidbsr vdqd q'mcnlkx 'rrhfmdc sn ' bnlotsdq sdqlhm'k-Fdmdq'k hmrsqtbshnmr vdqd qd'c 'kntc 'mc chrsqhatsdc hm oqhms 's sgd sdqlhm'kr-Sgdrd hmrsqtbshnmr b'm ad entmc hm sgd ?oodmchw A-Rtaidbsr vdqd hmenqldc sg's sgd dwodqhldms bnmrhrsdc ne ' rds ne mhmd dkdbshnmr-Hs hr l'cd dwokhbhs sg's rtaidbsr vntkc ad o'hc hm b'rg 's sgd dmc ne sgd dwodqhldms 'vhsg bnmudq, rhnm q'sd ne 0 dwodqhldms'k onhms ; 0 Dtqn(+ a'rdc nm sgdhq 'mc sgd nsgdq o'qshbho'msr& bgnhbdr hm dkdbshnmr-Ptdrshnmr 'qd s'jdm adenqd sgd rs'qs ne sgd qntmcr 'mc mn ptdrshnmr vdqd 'kknvdc ctqhmf sgd dwodqhldms-Sgd dwodqh, ldmsr rs'qsdc enkknvhmf rodbhffb hmrsqtbshnmr 'ants gnv sn qd'c sgd rbqddmr-Sgd dwodqhldmsr vdqd bnlotsdqhydc vhsg erj 'Onvdkk+ 1/08( 'mc vd 'qd fq'sdetk sn sgd rtoonqs vd qdbdhudc eqnl Nvdm Onvdkk-Adenqd d'bg dkdbshnm qntmc+ hs hr rodbhffdc he sgd dkdbshnm vhkk ad hlokd, ldmsdc 'r nmd,rgns nq hm hsdq'shnm-Hm dkdbshnmr vhsg hsdq'shnm+ h-d-) oqnffkdr 4 sn 8+ hs hr dwok'hmdc sg's sgd dkdbshnmr vntkc bnmbktcd he sgd ntsbnld qd, od'sr enq sgqdd qntmcr-Hm b'rd sgqdd qntmcr ne qdodshshnm chc mns nbbtq+ sgd dkdbshnm vntkc dmc 's sgd 01sg qntmc-?s sgd dmc ne sgd dwodqhldms+ vd bnmctbsdc ' rgnqs ptdrshnmm'hqd nm cdlnfq'oghbr 'mc rtaidbsr& odqbdoshnmr 'ants hsdq'sdc dkdbshnmr+ vghbg b'm ad entmc hm sgd ?oodmchw-?udq'fd o'xldms odq rtaidbs v'r 05 Dtqnr 'q'mfhmf eqnl 3 sn 15(-Hm 'cchshnm sn sg's+ vd o'hc 4 Dtqnr o'qshbho'shnm edd sn dudqx rtaidbs+ hmbktchmf sgnrd vgn 'qqhudc ats bntkc mns o'qshbho'sd 'r 'kk sgd rknsr vdqd ffkkdc+ 'r vdkk-Nm 'udq'fd+ sgd vgnkd dwodqhldms eqnl hmrsqtbshnmr sn sgd o'xldmsr k'rsdc 34 lhmtsdr-

QVshnmVkhyVahkhsx Vmc noshlhrshb adgVuhnq

Hm sghr rdbshnm vd enbtr nm sgd hmchuhct'k adg'uhnq ne rtaidbsr vhsg qdf'qc sn q'shnm'khy'ahkhsx 'mc noshlhrl ur-odrrhlhrl-Vd enbtr lnrskx nm bgnhbdr l'cd hm sgd nmd,rgns unsdr 'mc ffqrs rs'fdr ne hsdq'shud unsdr+ 'r kd'qmhmf hm qdf'qc sn nsgdqr& oqdedqdmbdr hr mns 'm hrrtd hm sgdrd b'rdr-Vd ffqrs knnj 's sgd oqdu'kdmbd ne cduh'shnmr eqnl q'shnm'khsx+ s'jdm 'r bgnnrhmf ' cnlhm'sdc 'bshnm-Sgdm+ vd knnj 's sgd RC,q'shnm'khy'ahkhsx hm sgd b'rd ne etkkx mnm, rdo'q'akd oqdedqdmbdr-Ehm'kkx+ vd knnj 's sgd oqdu'kdmbd ne noshlhrl 'mc odrrhlhrl hm sgd b'rdr ne etkkx mnm,rdo'q'akd 'mc rdlh,rdo'q'akd oqdedqdmbdr-

4-/ CnlhmVsdc bgnhbdr

Exonsgdrhr . Tnsdqr Yunhc cnlhmYsdc bgnhbdr-Hm S'akd 8 vd oqdrdms sgd mtladq ne hmrs'mbdr 'o'hqr ne unsdq 'mc oqnffkd( hm vghbg rtaidbsr l'cd ' cnlhm'sdc bgnhbd nm ansg hrrtdr 'fhudm rdo'q'akd oqdedqdmbdr(+ ' cnlhm'sdc bgnhbd nm nmd hrrtd g'uhmf rdo'q'akd oqdedqdmbdr+ 'ssq'bsdc lnqd ax sgd adrs 'ksdqm'shud hm Oqnffkd 3 rhmbd hs kd'cr sn fqd'sdq qdk'shud f'hm 'gdmbd sdmc sn ad lnqd noshlhrshb+ 'krn 'r sgd rl'kk ro'm 'bshnm o'xr kdrr(-Vd nardqud sg's bgnhbdr 'qd rhfmhffb'mskx lnqd noshlhrshb fnhmf eqnl Oqnffkd 1 sn 2 'mc.nq sn Oqnffkd 3+ rtoonqshmf Gxonsgdrhr 3-Sgd Ehrgdq dw'bs sdrs rs'shrshb u'ktdr 'qd /-513 enq bnlo'qhmf Oqnffkdr 1 'mc 2+ /-/66 enq bnlo'qhmf Oqnffkdr 1 'mc 3+ 'mc /-137 enq bnlo'qhmf Oqnffkdr 2 'mc 3- Mdws+ vd knnj vgdsgdq sgd odqbdms'fd ne nardqudc noshlhrshb bgnhbdr cd, odmc nm sgd oqdrdmbd ne hsdq'shnm-Sgtr+ hm vg's enkknvr+ vd bnlo'qd bgnhbdr hm nmd,rgns dkdbshnmr 'mc sgd ffqrs rs'fdr hm hsdq'shud dkdbshnmr-Gnvdudq+ vd mddc sn enbtr nm bnlo'q'akd b'rdr+ h-d-) 'kk unsdqr hm Oqnffkd 2 'mc unsdqr 4 'mc 5 hm Oqnffkd 5+ unsdq 2 hm Oqnffkd 7 'mc unsdqr 0 'mc 2 hm Oqnffkd 8-00 Sgdrd unsdqr g'ud etkkx mnm,rdo'q'akd oqdedqdmbdr 'mc tshkhshdr 'qd ne sgd enql 210/-Vd ffmc sg's sgdqd hr mn rs'shrshb'kkx rhfmhffb'ms ch∆dqdmbd ad, svddm sgd nmd,rgns oqnffkdr 'mc sgd ffqrs rs'fdr ne hsdq'sdc oqnffkdr hm sdqlr ne sgd nardqudc odqbdms'fdr ne noshlhrshb bgnhbdr 'ch∆dqdmbdr adsvddm Oqnffkd 2 'mc nsgdqr 'qd mns rhfmhffb'ms 's 0/" 'bbnqchmf sn Ehrgdq&r dw'bs sdrs+ rdd S'akd 03(+ hmchb'shmf mn rs'shrshb'k rtoonqs enq sgd 'qftldms sg's hsdq'shnm kd'cr sn lnqd noshlhrshb bgnhbdr-Gxonsgdrhr 4+ sgtr+ cndr mns ffmc rtoonqs hm ntq dwodqhldms'k c's'-

FmchuhctVk Tnshmf CxmVlhbr

Hm sghr rdbshnm vd enbtr nm hsdq'shud dkdbshnmr 'mc hmudrshf'sd gnv rtaidbsr& bgnhbdr dunkud hm qdk'shnm sn sgd rdo'q'ahkhsx ne sgdhq oqdedqdmbdr 'mc sn sgd ntsbnldr 'mc sgdhq ohuns'khsx hm oqduhntr qntmcr- S'akd 049 Mtladq ne rtaidbsr vhsg rdo'q'akd 'mc mnm,rdo'q'akd oqdedqdmbdr vgn bg'mfd sgdhq unsdr 's kd'rs nmbd 'mc vgn cn mns bg'mfd 's 'kk-?r ' ffqrs kdudk 'm'kxrhr+ vd bnlo'qd sgd mtladq ne rtaidbsr vgn bg'mfd sgdhq unsdr 's kd'rs nmbd 'mc sgnrd vgn mdudq bg'mfd+ a'rdc nm vgdsgdq sgdhq oqdedqdmbdr 'qd rdo'q'akd nq mns+ fhudm hm S'akd 04-?bbnqchmf sn Ehrgdq&r dw'bs sdrs+ sgd ch∆dqdmbd hr rs'shrshb'kkx rhfmhffb'ms 'bnlo'qhmf 037 nts ne 141 'mc 75 nts ne 071+ sdrs rs'shrshb u'ktd hr /-/08( 's 4"+ gdmbd vd hmcddc nardqud ' ghfgdq sdmcdmbx sn bg'mfd vgdm oqdedqdmbdr 'qd mnm,rdo'q'akd+ hm sgd khmd ne Gxonsgdrhr 5-Vd mdws drshl'sdc sgd enkknvhmf khmd'q oqna'ahkhsx lncdk sn cdsdbs sgd d∆dbs ne rdo'q'ahkhsx nm sgd unsd bg'mfhmf adg'uhnq9

u Vp ; ) 0 RDN Vp ) t Vp .
'0( vgdqd u Vp dpt'kr 0 he unsdq d bg'mfdc gdq unsd enq dhsgdq ne sgd hrrtdr eqnl rs'fd p 0 sn p 'mc / nsgdqvhrd+ RDN Vp dpt'kr 0 he sgd oqdedqdmbd hr rdo'q'akd 'mc / he mnm,rdo'q'akd+ 'mc t Vp cdmnsd sgd dqqnq sdql-01 ?r b'm ad rddm hm sgd S'akd 05 adknv+ vghbg rgnvr sgd drshl'shnm qdrtksr vgdqd rs'mc'qc dqqnqr 'qd bktrsdqdc 's sgd rtaidbs kdudk+ 'ksgntfg sgd d∆dbs hr mns k'qfd ''ants 6" ghfgdq oqna'ahkhsx ne bg'mfhmf ' unsd hm b'rd ne mnm,rdo'q'akd oqdedqdmbdr bnlo'qdc sn rdo'q'akd oqdedqdmbdr(+ vd nardqud sg's mnm,rdo'q'ahkhsx kd'cr sn lnqd bg'mfd- S'akd 069 Mtladq ne rtaidbsr vhsg rdlh,rdo'q'akd oqdedqdmbdr vgn bg'mfd 'mc vgn cn mns bg'mfd sgdhq unsdr 'bqnrr oqnffkdr-Vd mnv knnj 's gnv rtaidbsr qdronmc sn sgd ntsbnldr ne oqduhntr qntmcr-Vd 'rrtld sg's rtaidbsr vntkc v'ms sn hloqnud sgd ntsbnld enq sgdlrdkudr-Vd r'x sg's ' unsdq hr ohuns'k vgdm sgd ntsbnld ne sgd oqduhntr qntmc g'r ' l'qfhm ne uhbsnqx ne nmd nm 'mx ne sgd svn hrrtdr-Sgtr+ oqnuhcdc sg's 'kk nsgdq unsdqr jddo sgd r'ld unsd+ sgd unsdq b'm rvhsbg sgd ntsbnld ax tmhk'sdq'k cduh'shnm-Exonsgdrhr 6 Tnsdqr bgYmfd sgdhq unsdr lnqd nesdm he sgdx vdqd ohunsYk hm sgd oqduhntr qntmc-S'akd 07 adknv rgnvr sgd mtladq ne rtaidbsr vgn bg'mfd sgdhq unsdr eqnl qntmc p 0 sn p+ a'rdc nm he sgdx vdqd ohuns'k hm qntmc p 0+ fhudm sg's sgdx chc mns unsd enq sgdhq noshl'k bgnhbd hm qntmc p 0 'mc sg's sgdhq noshl'k bgnhbd v'r mns bgnrdm-Vd nardqud mn rs'shrshb'kkx rhfmhffb'ms ch∆dqdmbd 'Ehrgdq&r dw'bs sdrs xhdkcr n / /.0(-S'akd 08 adknv rgnvr sgd mtladq ne rtaidbsr vgn bg'mfd sgdhq unsdr eqnl qntmc p 0 sn p+ a'rdc nm he sgdx vdqd ohuns'k hm qntmc p 0+ fhudm Vd 'krn b'kbtk'sdc sgd odqbdms'fd ne adrs qdronmrdr 'h-d-+ unsd enq sgdhq e'untqhsd bdkk( 'lnmf sgd unsd bg'mfdr hmctbdc ax ohuns'khsx 'rdd S'akd 1/(+ ffmchmf sg's hm ' l'inqhsx ne sgd b'rdr rtaidbsr adrs qdronmc vgdm ohuns'k nm ansg hrrtdr-03 02 Vgdm sgd ntsbnld ne sgd kˆrs odqhnc hr mns sgd vnqrs) 16-.´ne sgd %0128( shldr sgd rtaidbsr bgˆmfd sgdhq unsdr vgdm sgdx vdqd ohunsˆk) bnloˆqdc sn 2.-6´%nts ne 550 bˆrdr( vgdm sgdx vdqd mns ohunsˆk-03 Vd gˆud ˆkrn bgdbjdc vgdsgdq unsdqr vhsg etkkx mnmrdoˆqˆakd oqdedqdmbdr vntkc unsd enq sgd noonrhsd ne sgdhq eˆuntqhsd bdkkr) vgdm sgd odqbdhudc oqnaˆahkhsx ne adhmf ohunsˆk nm ansg hrrtdr hr udqx knv) hm khmd vhsg sgd ˆmˆkxrhr ax ;gm ˆmc Nkhudqnr %1.01(-Hmrsˆmbdr ne rtbg ˆogdmnldmnm nbbtq hm sgd enkknvhmf bhqbtlrsˆmbdr) %0( etkkx mnm rdoˆqˆakd oqdedq, dmbdr) rtbg ˆr unsdqr 0,5 hm Oqnffkd 6: %1( sgd btqqdms ntsbnld hr sgd rdbnmc vnqrs ntsbnld % L enq sgdrd 5 unsdqr(: %2( sgd lˆqfhm ne uhbsnqx enq ansg hrrtdr hr kˆqfd %. e ) vhsgnts bntmshmf sgd unsdq) 4,0 nq 5,.(: %3( ˆs sgd mdws qntmc) sgd unsdq bgˆmfdr sgdhq unsd nm ansg hrrtdr %R B enq sgd kˆssdq 5 unsdqr(-Fnvdudq) vd bˆmmns rˆx ltbg9 ˆlnmf entq nbbtqqdmbdr ne %0( ˆmc %1() sgdqd ˆqd svn sgˆs bnlokx vhsg ntq ˆqftldms-Sghr bntkc ad vnqsg khmd ne hmpthqx sn otqrtd hm etstqd qdrdˆqbg vhsg ˆm dwodqhldmsˆk cdrhfm sgˆs hr ˆhldc sn enbtr nm sghr ogdmnldmnm-1/ ?r enq sgd d∆dbsr ne hsdq'shnm nm Bnmcnqbds dflbhdmbx+ sgdqd hr mn bkd'q hmchb'shnm ne hmbqd'rd nq cdbqd'rd-Hm 'kk oqnffkdr ok'xdc hm hsdq'shnm+ sgd Bnmcnqbds vhmmdq hr 'krn sgd rnbh'k vdke'qd noshltl: sghr hr mns ' ft'q'msdd ne sghr ntsbnld sn ad dkdbsdc9 hm Oqnffkd 7+ S E hr dkdbsdc hm kdrr sg'm 4/" ne sgd b'rdr-Fhudm ntq ffmchmfr+ sgd nardqudc hmbqd'rd hm rnbh'k vdke'qd hr ctd lnqd sn unsdqr 'unhchmf a'c ntsbnldr sg'm hloqnuhmf fnnc nmdr-Sghr hr bnqqnanq'sdc ax ntq qdrtksr nm ohuns'khsx sg's rgnv sg's unsdqr sdmc sn bg'mfd sgdhq unsd nmkx he sgdx fds ' o'qshbtk'qkx a'c ntsbnld-

Bnmbktrhnmr

Ntq dwodqhldmsr 'kknvdc tr sn udqhex rnld ne ntq gxonsgdrdr+ 'mc sn bnmffql 'mnsgdq nmd sg's g'c addm udqhffdc nmkx hm rhltk'shnmr-Hm rtll'qx9 × hm oqdrdmbd ne rdo'q'ahkhsx+ rtaidbsr sdmc sn unsd q'shnm'kkx-× hm oqdrdmbd ne mnm,rdo'q'ahkhsx+ rtaidbsr sdmc sn ok'x ' rsnbg'rshb ' ?m hlonqs'ms b'ud's ne ntq qdrtksr hr sgd qdrsqhbshnm sn svn 'ahm'qx( hrrtdr-Sghr bgnhbd v'r bkd'qkx lnshu'sdc ax ed'rhahkhsx9 hlokdldmshmf 'm dwodqhldms vhsg sgqdd hrrtdr nq lnqd l'jdr hs chflbtks sn vqhsd sgd o'xn∆ l'sqhbdr hm ' trdq,eqhdmckx v'x+ sgd dwodqhldms vntkc g'ud addm lnqd bnfmh, shudkx bnlokdw 'mc sgd qhrj vntkc sgdm g'ud addm sg's ' rhfmhffb'ms mtladq ne unsdqr cn mns tmcdqrs'mc hs vdkk nq sg's sgdx ffmc hs snn cdl'mchmf 'mc dmc to ok'xhmf q'mcnlkx-?r ' bnmrdptdmbd+ hs l'jdr hs chflbtks sn bnlo'qd chqdbskx vhsg sgd rhltk'shnm qdrtksr hm Anvl'm ds 'k-'1/03(+ vgn bnmrhcdqdc sgqdd ahm'qx hrrtdr-Sghr kd'cr tr sn sgd enkknvhmf hlonqs'ms ptdrshnm9 vghbg ne ntq bnmbkt, rhnmr vntkc rshkk gnkc enq lnqd sg'm svn hrrtdr= Enq rnld ne sgdl+ vghkd hs hr hlonrrhakd sn g'ud ' ft'q'msdd sg's sgdx hmcddc vntkc gnkc mns g'uhmf l'cd 'mx etqsgdq dwodqhldms+ hs b'm rshkk ad qd'rnm'akd sn 'rrtld sg's sgdx vntkc bnmshmtd sn gnkc-Sghr hr sgd b'rd enq gxonsgdrdr 0+ 1+ 5 'mc 7: sghr hr 'krn sgd b'rd enq gxonsgdrdr 2,4 ats hs hr lnqd chflbtks sn cdffmd noshlhrl 'mc odrrhlhrl adb'trd sgdrd mnshnmr adbnld fq'ct'k 'r rnnm 'r vd g'ud lnqd sg'm svn u'qh'akdr-Hs hr rkhfgskx lnqd chflbtks sn l'jd bnmidbstqdr enq gxonsgdrdr 6 'mc 8+ 'ksgntfg vd cn mns rdd ' bkd'q qd'rnm vgx sgdx vntkc mns gnkc enq lnqd sg'm svn hrrtdr-Hm 'mx b'rd+ dudm he ntq qdrtksr gdkc enq nmkx svn hrrtdr+ sgdx vntkc rshkk ad ld'mhmfetk9 hm lnrs oq'bshb'k b'rdr+ unsdqr& oqdedqdmsh'k cdodmcdmbhdr adsvddm hrrtdr hm ltkshokd qdedqdmc' b'm ad qdrsqhbsdc sn rdsr ne hrrtdr ne rhyd svn ''ksgntfg vd 'bjmnvkdcfd sg's rhst'shnmr vgdqd lnqd sg'm svn hrrtdr hmsdq'bs cn nbbtq+ drodbh'kkx enq etmchmf otakhb oqnidbsr vhsg atcfds bnmrsq'hmsr(-Sgd l'hm oq'bshb'k hlo'bs ne ntq rstcx hr ' bnmffql'shnm sg's hsdq'shud unshmf hr ' uh'akd v'x ne g'mckhmf mnmrdo'q'ahkhsx hm ltkshokd qdedqdmc'+ bnmffqlhmf sgd rhltk'shnm,a'rdc qdrtksr ne 'Anvl'm ds 'k-+ 1/03(-Sn otrg etqsgdq sgd hmbktrhnm ne cdkhadq'shud snnkr hm sgd hsdq'shud unshmf oqnsnbnk+ hm etstqd vnqj vd vhkk 'kknv Ybgd'o s'kj¸'lnmf unsdqr hm adsvddm sgd hsdq', shnmr nm d'bg unsd+ sdrshmf vgdsgdq sghr kd'cr sn ' cdbqd'rd hm sgd mtladq ne hsdq'shnmr nq he hs lnchffdr sgdhq hmchuhct'k unshmf adg'uhntq-

:bimnvkdcfdldmsr

Vd 'qd udqx ltbg hmcdasdc sn Id'm,Eq'mbnhr Anmmdenm vgn v'r sgd ffqrs sn g'ud sgd hcd' ne sghr dwodqhldms 'ants ' cdb'cd 'fn 'mc vgn g'c rs'qsdc sn cdrhfm nmd-Vd 'krn sg'mj Id'm,Eq'mbnhr J'rkhdq enq trdetk rtffdrshnmr 'ants sgd oqnsnbnk-J'rs ats mns kd'rs+ vd sg'mj L'whl Eqnknu 'mc Nvdm Onvdkk enq sgdhq gtfd rtoonqs adenqd 'mc ctqhmf sgd k'a rdrrhnmr-Vd sg'mj sgd o'qshbho'msr ne sgd C'frstgk rdlhm'q 08270 nm Y?ookhb'shnm,Nqhdmsdc Bnlots'shnm'k Rnbh'k Bgnhbd+¸'r vdkk 'r ntq bnkkd'ftdr 's sgd Hmrshsts cd Qdbgdqbgd dm Hmenql'shptd cd Sntkntrd 'HQHS( enq o'qshbho'shmf sn u'qhntr ohkns udqrhnmr ne ntq k'a dwodqhldms-A :oodmchw8 DwodqhldmsVk Fmrsqtbshnmr

  S'akd 19 Oqnffkdr 1+2+ 'mc 3+ vgdqd enq Oqnffkd 1 sgd tshkhsx udbsnq 'X. a. b. c( ; '/. 1. 2. 3( enq Oqnffkd 29 'X. a. b. c( ; '/. 0. 1. 2( 'mc enq Oqnffkd 3 'X. a. b. c( ; '/. 0. 1. 3(

:

  tsgnqrfi mnsd9 Hm d'bg rdrrhnm+ sgd dwodqhldms bnmrhrsdc ne 8 l'hm o'qsr+ enkknvdc ax ' ptdrshnmm'hqd 'mc ' qdb'o ne d'qmhmfr-Sgd ffqrs entq o'qsr bnmrhrsdc ne 3 nmd,rgns unsdr+ vgdqd'r d'bg ne sgd qdl'hmhmf 4 o'qsr bnmrhrsdc ne hsdq'sdc unsdr-Sgd hmrsqtbshnmr+ vghbg vdqd oqhmsdc nm rbqddmr 'r vdkk+ vdqd qd'c 'kntc hm sgd adfhmmhmf ne sgd ffqrs 'mc ffesg o'qsr-Sgd enkknvhmf hr sgd Dmfkhrg sq'mrk'shnmr ne sgd nqhfhm'k hmrsqtbshnmr hm Eqdmbg 'r 'ood'qdc nm rtaidbsr& rbqddmr-Hmrsptbshnmr ORps . Xnt vhkk o'qshbho'sd hm 'm dwodqhldms sg's s'jdr ok'bd hm rdudq'k o'qsr-Sgd dwodqhldms g'r 8 o'qsr-Sgd ffqrs entq o'qsr bnmrhrs ne rhmfkd stqmr-Sgd enkknvhmf o'qsr bnmrhrs ne rdudq'k stqmr-Hm d'bg f'ld+ xnt vhkk rdd ' s'akd khjd 's hr rgnvm hm d'bg ne sgd anwdr hr vg's xnt d'qm he sg's anw vhmr vgdm sgd f'ld dmcr-Enq dw'lokd+ he sgd vhmmhmf anw vgdm sgd f'ld dmcr hr TO,QHFGS+ sgdm enq sg's f'ld xnt d'qm B1-Sgd mtladqr vhkk 'kv'xr ad 's kd'rs 'r k'qfd 'r /9 xnt vhkk mdudq knrd 'mxsghmf-Xntq ffm'k d'qmhmf vhkk ad sgd rtl ne xntq d'qmhmfr hm sgd 5 f'ldr-Vd vhkk mnv dwok'hm vg's cdsdqlhmdr sg's ' anw hr ' vhmmdq-Xnt vhkk unsd enq ' qnv 'TO nq CNVM( 'mc enq ' bnktlm 'JDES nq QHFGS(-Hm d'bg f'ld+ sgdqd vhkk ad ' mtladq ne nsgdq ok'xdqr vgn vhkk 'krn unsd enq ' qnv 'mc enq ' bnktlm-Nsgdq ok'xdqr l'x g'ud ch∆dqdms 'qq'xr eqnl xntqr+ 'mc xnt b'mmns jmnv sgd u'ktdr ne sgdhq 'qq'xr-Gnvdudq+ xnt vhkk jmnv sgd mtladq ne ok'xdqr 'vghbg+ cdodmchmf nm sgd b'rd+ vhkk ad 2+ 4 nq 6(-He ' l'inqhsx ne ok'xdqr unsdc JDES+ sgdm sgd vhmmhmf qnv hr JDES-He ' l'inqhsx ne ok'xdqr unsdc enq QHFGS+ sgdm sgd vhmmhmf qnv hr QHFGS-He ' l'inqhsx ne ok'xdqr unsdc TO+ sgdm sgd vhmmhmf bnktlm hr TO-He ' l'inqhsx ne ok'xdqr unsdc CNVM+ sgdm sgd vhmmhmf bnktlm hr CNVM-Sgd vhmmhmf anw hr 's sgd hmsdqrdbshnm ne sgd vhmmhmf qnv 'mc sgd vhmmhmf bnktlm-He enq dw'lokd sgdqd 'qd 4 ok'xdqr+ sgqdd unsd TO 'mc svn unsd CNVM+ sgdm sgd vhmmhmf qnv hr TO-He entq ok'xdqr unsd enq QHFGS 'mc nmd enq JDES+ sgdm sgd vhmmhmf bnktlm hr QHFGS+ 'mc sgd vhmmhmf anw hr TO, QHFGS-2/ Ctqhmf sgd ffqrs entq dkdbshnmr+ sgdqd vhkk ad nmkx nmd qntmc9 xnt vhkk unsd enq ' qnv 'mc ' bnktlm+ sgd nsgdq ok'xdqr snn+ 'mc xnt vhkk vhm sgd rtl sg's bnqqdronmcr sn sgd vhmmhmf anw hm sgd s'akd-ORps 1 O'qs vhsg nmkx nmd qntmc-ORps 2 O'qs vhsg nmkx nmd qntmc-ORps 3 O'qs vhsg nmkx nmd qntmc-ORps 4 Sgd enkknvhmf o'qsr vhkk bnmrhrs ne rdudq'k qntmcr-Hm d'bg qntmc xnt vhkk unsd enq ' qnv 'mc ' bnktlm-Sgdm hs vhkk ad sgd rdbnmc qntmc9 xnt vhkk unsd 'f'hm+ 'mc 's sgd dmc ne sgd rdbnmc qntmc+ 'f'hm xnt vhkk jmnv sgd vhmmhmf anw 'mc sgd mtladq ne unsdr enq TO+ enq JNV+ enq JDES+ 'mc enq QHFGS-?mc rn nm+ tmshk sgd dkdbshnm dmcr-Sgd dkdbshnm vhkk dmc vgdm sgd vhmmhmf anw hr sgd r'ld sgqdd shldr hm ' qnv nq vgdm 01 stqmr g'ud addm ok'xdc-Enq dw'lokd9 × ffqrs qntmc9 TO 2+ CNVM 1+ JDES 0+ QHFGS 3-Vhmmhmf anw9 TO, QHFGS × rdbnmc qntmc9 TO 1+ CNVM 2+ JDES 1+ QHFGS 2-Vhmmhmf anw9 CNVM,QHFGS × sghqc qntmc9 TO 1+ CNVM 2+ JDES 2+ QHFGS 1-Vhmmhmf anw9 CNVM,JDES × entqsg qntmc9 TO 0+ CNVM 3+ JDES 1+ QHFGS 2-Vhmmhmf anw9 ANSSNL,QHFGS × ffesg qntmc9 TO /+ CNVM 4+ JDES 1+ QHFGS 2-Vhmmhmf anw9 ANSSNL,QHFGS × rhwsg qntmc9 TO 0+ CNVM 3+ JDES 1+ QHFGS 2-Vhmmhmf anw9 ANSSNL,QHFGS-Sgd CNVM,QHFGS anw g'r vnm sgqdd shldr hm ' qnv9 sgd f'ld hr nudq+ 'mc xnt vhm sgd 'lntms sg's bnqqdronmcr sn sgd CNVM,QHFGS anw-OidRrd mnsd9 Sgd mtladq ne o'qshbho'msr l'x u'qx enq d'bg o'qs 'f'ldr vhsg 2+ 4 nq 6 o'qshbho'msr(-Vgdm sgd mtladq ne o'qshbho'msr hm ' f'ld hr 4+ nmd odqrnm hm sgd qnnl vhkk mns ok'x sg's f'ld-Okd'rd qd'c sgdrd hmrsqtbshnmr b'qdetkkx-He xnt g'ud ptdrshnmr mnv hr sgd shld sn 'rj sgdl-ORps 5 O'qs vhsg rdudq'k qntmcrxnt g'ud 'mx bnlldmsr nm sgd ldsgncr+ nq rtffdrshnmr nm gnv sn nqf'mhyd rtbg bgnhbdr nm rdudq'k hrrtdr= 2-Vg's hr xntq 'fd q'mfd= 's hr sgd ghfgdrs cdfqdd xnt g'ud nas'hmdc=× Mn 'mrvdq × Onrsfq'ct'sd cdfqdd+ cnbsnq'sd+ fq'mcd dbnkd+ dmfhmddq × Fq'ct'sd cdfqdd × Tmcdqfq'ct'sd cdfqdd+ ASR+ CTS+ nq dpthu'kdms+ A'b ) 1 kdudk × Fdmdq'k+ sdbgmnknfhb'k+ oqnedrrhnm'k nq dpthu'kdms a'bb'k'tqd'sd × B?O+ ADO nq choknl' ne sgd r'ld kdudk × Bnkkdfd choknl'+ ADOB × Oqhl'qx rbgnnk bdqshffb'sd+ mn choknl' 5-G'ud xnt dudq s'jdm ' bntqrd hm dbnmnlhbr= × Mn 'mrvdq × Xdr+ sghr hr lx l'hm sq'hmhmf × Xdr+ ats sghr hr mns lx l'hm sq'hmhmf × Mn 6-G'ud xnt dudq o'qshbho'sdc hm 'm dbnmnlhb k'anq'snqx rtqudx= × Mn 'mrvdq × Xdr × Mn hs&r sgd ffqrs shld 7-Xnt g'ud sdrsdc svn bgnhbd ldsgncr nm ltkshokd ptdrshnmr9 nmd vgdqd xnt unsd nmkx nmbd enq d'bg ne sgd svn ptdrshnmr+ 'mc nmd vgdqd xnt unsd hm rdudq'k rs'fdr-Vghbg cn xnt sghmj hr sgd lnrs d∆dbshud= × Mn 'mrvdq × Sgd nmd,rsdo ldsgnc × Sgd ltksh,rsdo ldsgnc × Ansg ldsgncr 'qd dpt'kkx d∆dbshud × H cnm&s jmnv . H oqdedq mns sn 'mrvdq 8-Cndr sgd nmd,rsdo ldsgnc rddl d'rx sn tmcdqrs'mc 'mc trd= × Mn 'mrvdq × D'rx × Q'sgdq d'rx × Q'sgdq chflbtks × Chflbtks × H cnm&s jmnv . H oqdedq mns sn 'mrvdq 0/-Cndr sgd ltksh,rsdo ldsgnc rddl d'rx sn tmcdqrs'mc 'mc trd= × Mn 'mrvdq × D'rx × Q'sgdq d'rx × Q'sgdq chflbtks × Chflbtks × H cnm&s jmnv . H oqdedq mns sn 'mrvdq

  ', inqhsx qtkd hr trdc sn cdbhcd nm d'bg hrrtd hmcdodmcdmskx-Sghr hr sgd rhlokdrs rnktshnm+ 'r hs hr udqx bgd'o hm bnlltmhb'shnm 'mc 'sn ' kdrrdq dwsdms( bnfmhshud d∆nqs: hs hr trdc hm lnrs nbbtqqdmbdr ne ltkshokd qde, dqdmc'+ rtbg 'r hm Rvhsydqk'mc nq B'khenqmh'-Gnvdudq+ sghr rhlokd rds,

shmf hr udqx ltbg oqnmd sn rdudqd o'q'cnwdr 'Aq'lr ds 'k-+ 0887: J'bx 'mc Mhnt+ 1///(+ 'mc sgd ntsbnld l'x ad e'q eqnl sgd noshltl-2 Sgd dwhrsdmbd 'mc bg'q'bsdqhy'shnm ne dpthkhaqh' enq rhltks'mdntr uns, hmf+ enqltk'sdc 'r ' A'xdrh'm f'ld+ hr rstchdc ax ?gm 'mc Nkhudqnr '1/01(-

×

rdptdmshYk unshmf9 unsdqr unsd nm hmchuhct'k hrrtdr hm rdptdmbd: sgdx b'm rdd sgd ntsbnld nm d'qkhdq hrrtdr vgdm sgdx unsd nm ' k'sdq hrrtd-Rdptdmsh'k unshmf o'qskx qdrnkudr rnld ne sgd oqnakdlr ne rhltks'mdntr unshmf+ 'mc qdl'hmr qdk'shudkx bgd'o hm bnlltmhb'shnm+ ats hs hr rshkk oqnmd sn o'q'cnwdr 'J'mf 'mc Wh'+ 1//8: Bnqmdkhn ds 'k-+ 1/08(-× dwoqdrrhmf oqdedqdmbdr hm Y bnloYbs kYmftYfd9 unsdqr dwoqdrr sgdhq oqde, dqdmbdr hm ' rnoghrshb'sdc k'mft'fd vgnrd 'hl hr sn n∆dq ' sq'cd,n∆ adsvddm rtbbhmbsmdrr 'mc dwoqdrrhudmdrr+ rtbg 'r BO,mdsr 'Bnmhsydq ds 'k-+ 1/00(+ bnmchshnm'kkx kdwhbnfq'oghb oqdedqdmbd sqddr 'J'mf ds 'k-+ 1/07(+ nq fq'oghb'k k'mft'fdr enq b'qchm'k oqdedqdmbdr 'Fnmy'kdr ds 'k-+ 1//7(-Sghr 'kknvr ' udqx dwoqdrrhud dwoqdrrhnm ne oqdedqdmbdr+ gdmbd, enqsg sn 'm ntsbnld ne qd'rnm'akx fnnc pt'khsx+ ats tmenqstm'sdkx hs bnldr vhsg 'm hlonqs'ms atqcdm nm sgd unsdqr hm sdqlr ne bnlltmh, b'shnm 'mc bnfmhshud d∆nqs-× dwoqdrrhmf oqdedqdmbd Yr chrsYmbd sn sgd sno YksdqmYshud9 unsdqr dwoqdrr nmkx sgdhq lnrs oqdedqqdc 'ksdqm'shud+ 'mc sgdhq vgnkd oqdedqdmbd qdk', shnm hr sgdm hmctbdc eqnl ' oqdcdffmdc chrs'mbd adsvddm 'ksdqm'shudr+ rtbg 'r sgd G'llhmf chrs'mbd 'Aq'lr ds 'k-+ 1//6: B ˘tg'c'qnfkt 'mc J'hmd+ 1/01(-Vghkd sghr hr qd'rnm'akd hm rnld bnmsdwsr+ hs e'hkr sn dw,

  r rl'kk ro'm+ sgdqdenqd vd 'krn r'x sg's rtbg ' unsdq hr noshlhrshb 'qdro-odrrhlhrshb( he rgd unsdr enq S 'qdro-A(-Enq Bnk+ sghr hr ch∆dqdms9 sgd u'ktd P kd'cr sn dhsgdq sgd adrs nq sgd rdbnmc vnqrs 'ksdqm'shud hm b'rd sgd unsdq hr ohuns'k enq Bnk+ vghkd E kd'cr sn dhsgdq sgd rdbnmc adrs nq sgd rdbnmc vnqrs 'ksdqm'shud-Vd r'x sg's P hr rsnbgYrshbYkkx cnlhmYms-Sgd unsdq hr r'hc sn ad RC,qYshnmYk he rgd unsdr

enq sgd rsnbg'rshb'kkx cnlhm'ms u'qh'akd+ 'mc RC,hqq'shnm'k nsgdqvhrd-?m dw'lokd ne d'bg unsdq adg'uhntq cdrbqhadc 'anud b'm ad entmc hm Ehftqd 0 trhmf sgd qdoqdrdms'shnm vhsg tshkhsx l'sqhbdr-

  HsdqYshud unshmf enq ltkshokd qdedqdmc' hr cdffmdc 'r ' rdqhdr ne rhltks', mdntr unshmf rs'fdr: 's d'bg rs'fd+ unsdqr nardqud sgd chrsqhatshnm ne unsdr qdf'qchmf d'bg hrrtd 's sgd oqduhntr rs'fd-Sgtr+ 's rs'fd 0+ unsdqr cn mns nardqud 'mxsghmf: 's rs'fd 1+ sgdx jmnv sgd mtladq ne unsdr enq E+ P+ S 'mc A enq rs'fd 0: 's rs'fd 2+ sgdx jmnv sgd mtladq ne unsdr enq E+ P+ S 'mc A enq rs'fdr 0 'mc 1+ 'mc rn nm-Sgd rsnoohmf bqhsdqhnm hr cdffmdc dwnfdmdntrkx-Hm nqcdq sn du'kt'sd sgd pt'khsx ne sgd ntsbnld+ vd enbtr nm sgd 'udq'fd rnbh'k vdke'qd ne sgd rnbh'k ntsbnld 'sgd 'udq'fd o'xn∆ unsdqr fds( 'mc sgd eqdptdmbx ne Bnmcnqbds vhmmdqr adhmf dkdbsdc ''m ntsbnld u hr ' Bnmcnqbds vhmmdq 'BV( he enq 'mx nsgdq ntsbnld x+ u fhudr ' ghfgdq o'xn∆ sg'm x sn ' l'inqhsx ne unsdqr(-Ntq dwodqhldms'k cdrhfm hr athks nm sgd l'hm lnshu'shnm ne sgd o'odq+ sg's hr+ rstcxhmf sgd adg'uhntq ne unsdqr hm rhltks'mdntr 'mc hsdq'shud unshmf enq ltkshokd qdedqdmc' 'mc+ hm o'qshbtk'q+ hmudrshf'shmf sgd hlo'bs ne hsdq', shud unshmf nm hmchuhct'k 'mc bnkkdbshud adg'uhnq-Adknv vd rtll'qhyd sgd dwodqhldms'k oqnbdctqd sg's vd hlokdldmsdc-

	3 Sgd dwodqhldmsr
	noshlhrshb(	2	/
	A 'odrrhlhrshb(	0	1
			Vgdm
	' unsdq b'rsr ' unsd qdf'qchmf 'm hrrtd+ rgd cndr mns jmnv sgd nsgdq unsdr
	qdf'qchmf sghr hrrtd+ mnq sgd unsdr qdf'qchmf sgd nsgdq hrrtd-Enq d'bg hrrtd+
	sgd bnkkdbshud cdbhrhnm hr l'cd uh' l'inqhsx qtkd: eqnl mnv nm vd 'rrtld i
	sn ad ncc rn sg's shdr b'mmns nbbtq-

'b( Etkkx mnm,rdo'q'akd oqdedqdmbd Ehftqd 09 Uhrt'k dwok'm'shnm ne unsdq adg'uhntq vhsg sgqdd sxodr ne oqdedq, dmbdr nudq svn hrrtdr-2-3 RhltksVmdntr Vmc hsdqVshud unshmf enq ltkshokd qdedqdmcV ? ltkshokd qdedqdmctl bnmrhrsr ne ' rds ne n ahm'qx hrrtdr+ 'mc ' rds L ne i unsdqr+ d'bg ne vgnl g'r oqhu'sd oqdedqdmbdr nudq 'kk bnlahm'shnmr ne hrrtdr-RhltksYmdntr unshmf bnmrhrsr ne 'rjhmf d'bg unsdq sn b'rs ' unsd qdf'qchmf d'bg hrrtd-Sgtr+ enq sgd svn,hrrtd b'rd 'n ; 1(+ d'bg ne sgd i unsdqr g'r sn unsd svhbd9 nmd enq sgd bnktlm hrrtd 'sg's hr+ rgd g'r sn unsd enq E nq enq P( 'mc nmd enq sgd qnv hrrtd 'sg's hr+ rgd g'r sn unsd enq S nq enq A(-

  Hm sghr rdbshnm vd 'm'kxyd sgd bnkkdbshud adg'uhnq ne sgd unsdqr hm sgd hsdq'sdc dkdbshnmr 'h-d-) Oqnffkdr 4 sn 8( 'mc du'kt'sd sgd dkdbshnm ntsbnldr hm sdqlr ne rnbh'k vdke'qd 'mc sgd eqdptdmbx ne dkdbshmf ' Bnmcnqbds vhmmdq-Qdb'kk sg's sgd sdqlhm'shnm qtkd otsr 'm dmc sn sgd hsdq'shnm vgdm sgd ntsbnld cndr mns bg'mfd enq sgqdd qntmcr-?r b'm ad rddm hm Ehftqd 1 l'mx fqntor bnmbktcdc sgdhq hsdq'shud unshmf oqnbdrr 's sgd dmc ne sgd sghqc rs'fd+ sgd d'qkhdrs onrrhakd-Nmkx 42+ 18+ 32+ 25+ 'mc 35 " ne fqntor qdl'hm hm hsdq'shnm adxnmc sgd sghqc rs'fd hm oqnffkdr 4 sn 8 qdrodbshudkx-?kk fqntor hm Oqnffkd 6 bnmbktcd ax rs'fd 5-Ehftqd 19 Mtladq ne fqntor hm sgd hsdq'sdc unsdr ax hsdq'shnm rs'fd-Vd chuhcd sgd fqntor ne unsdqr hmsn svn b'sdfnqhdr hm sdqlr ne sgd dun, ktshnm ne dkdbshnm ntsbnldr-Sgd rsYshb 'qd sgnrd fqntor vgn sdqlhm'sd 's sgd sghqc hsdq'shnm rs'fd+ 'mc sgd cxmYlhb fqntor 'qd sgnrd vgn fn etqsgdq-Vd nardqud sg's enq ansg sxodr ne fqntor sgdqd 'qd rhfmhffb'ms mtladqr ne rtaidbsr vgn bg'mfd sgdhq unsdr-Lnqd oqdbhrdkx+ sgd odqbdms'fd ne rtaidbsr hm cxm'lhb fqntor vgn toc'sd sgdhq unsd hm sgd ffqrs sgqdd qntmcr hr hm sgd hloqnud hs sn ' bnlo'q'akd kdudk hm sgd k'rs rs'fd ne hsdq'shnm-05 Hmsdqdrshmfkx+ sgdrd qdrtksr bnmsq'rs vhsg sgd ffmchmfr ne Ldhq ds 'k-'1/1/( hm nmkhmd hsdq'sdc dkdbshnmr+ vgn cn mns ffmc 'mx rs'shrshb'kkx rhfmhffb'ms hl, oqnudldms hm rnbh'k vdke'qd sgqntfg hsdq'shnm-Sghr rtffdrsr sg's ltksh,hrrtd dkdbshnmr 'qd lnqd khjdkx sn oqnffs eqnl 'm hsdq'shud unshmf rbgdld sg'm bk'r, rhb'k oktq'khsx dkdbshnmr nudq ' rds ne b'mchc'sdr-Vd sgdm hmudrshf'sdc sgd hlo'bs ne hsdq'shud unshmf nm sgd Bnmcnqbds dflbhdmbx+ h-d-+ sgd oqna'ahkhsx ne dkdbshmf ' Bnmcnqbds vhmmdq vgdm sgdqd hr nmd-Hm 'kk ntq oqnffkdr ats sgd k'rs nmd '8( sgdqd hr ' Bnmcnqbds vhmmdq-S'akd 11 adknv rgnvr sgd eqdptdmbx ne Bnmcnqbds vhmmdqr adhmf bgnrdm hm nmd,rgns unsdr 'Oqnffkdr 0z3( 'mc S'akd 12 sgnrd hm sgd ffqrs rs'fd ne hsdq'sdc dkdbshnmr 'Oqnffkdr 4z7(-Sgd nardqudc kdudk ne Bnmcnqbds dflbhdmbx hr pthsd knv-Gnvdudq+ hs hr mns bnlokdsdkx bkd'q vg's bnmbktrhnmr b'm ad cq'vm eqnl sgdrd mtladqr+ 'r lnrs ne ntq oqnffkdr vdqd bgnrdm rn 'r sn ad 's kd'rs rnldvg's o'sgnknfhb'k hm sgd ffqrs ok'bd 'mc mns ffs enq sghr o'qshbtk'q ptdrshnm-

		Oqnffkd 4 Oqnffkd 5 Oqnffkd 6 Oqnffkd 7 Oqnffkd 8
		51"	44"		60"		53"	6/"
	S'akd 1/9 Sgd odqbdms'fd ne adrs,qdronmrd bgnhbdr vgdm rtaidbsr 'qd ohuns'k
	nm ansg hrrtdr-
	6 Bnkkdbshud cxmVlhbr Vmc ptVkhsx ne sgd mVk nts,
	bnld
				Oqnffkd Eqdptdmbx ne bgnrdm BVr
				0		13 "
	49			1		08 "
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	39			3			4 "
	19 29 S'akd 119 Eqdptdmbx ne bgnrdm Bnmcnqbds vhmmdqr ax oqnffkd hm nmd,rgns unsdr-btlaNp6ne6spntor :kk CxmYlhb RsYshb
	09	Oqnffkd Ehqrs J'rs Ehqrs J'rs Ehqrs ; J'rs
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	9		5 13 " 13 " 06 " 06 "	16 "
	0	1	2 6 41 " 18 " 67 " 11 " 3 4 5 m 7 uGNpIGgn 6rGIPN 7 18 " 07 " 2/ " / "	8	09 22 " 17 "	00	01
				fpnegiN	4	5	m	7	8
	S'akd 129 Eqdptdmbx ne dkdbshnm ne sgd Bnmcnqbds vhmmdq hm hsdq'sdc oqnffkdr
	hm sgd ffqrs 'mc k'rs hsdq'shnm-Sgd bnktlm Y?kk¸hmbktcdr 'kk fqntor+ Ycx,
	m'lhb¸nmkx sgnrd fqntor fnhmf adxnmc sgqdd hsdq'shnmr+ 'mc Yrs'shb¸sgnrd
	vgn rsnoodc 'esdq sgqdd hsdq'shnmr-

  kkx cnlhm'ms 'bshnm vgdm sgdx g'ud nmd+ 'mc nsgdqvhrd sdmc sn unsd nosh, lhrshb'kkx lnqd nesdm sg'm odrrhlhrshb'kkx: sgd eqdptdmbx ne noshlhrl hmbqd'rdr vhsg sgd bnmudwhsx ne o'xn∆r 'ats cndr mns hmbqd'rd vhsg shld hm hsdq'sdc unshmf(-× hm hsdq'sdc dkdbshnmr rtaidbsr vhsg mnm,rdo'q'akd oqdedqdmbdr sdmc sn bg'mfd sgdhq bgnhbdr lnqd nesdm sg'm unsdqr vhsg rdo'q'akd oqdedqdmbdr-

	× hm hsdq'sdc dkdbshnmr rtaidbsr sdmc sn bg'mfd sgdhq unsdr lnqd nesdm he sgdx vdqd ohuns'k hm sgd oqduhntr qntmc+ oqnuhcdc sgdx fns ' a'c nts,
	bnld hm sg's qntmc 'hm nsgdq b'rdr sgdqd hr mn duhcdmbd sg's ohuns'khsx
	g'r 'm hmfitdmbd nm bg'mfhmf unsdr(-
	× hsdq'shud unshmf hmbqd'rdr rnbh'k vdke'qd+ vghbg bnmffqlr sgd ffmchmfr ax Anvl'm ds 'k-'1/03(+ nas'hmdc eqnl rhltk'shnmr-Nm sgd nsgdq
	g'mc+ ntq dwodqhldmsr cn mns 'kknv tr sn cq'v 'mx bnmbktrhnm 'ants
	vgdsgdq hsdq'shud unshmf hmbqd'rdr Bnmcnqbds,dflbhdmbx-

Dwˆlokdr eqnl sgd qdˆk vnqkc ˆqd tahpthsntr) hmbktchmf sgd bnllnmkx bhsdc cdbhrhnm, lˆjhmf oqnbdrrdr hm Rvhsydqkˆmc ˆmc Bˆkhenqmhˆ-Enq sgd kˆssdq) enq hmrsˆmbd) rdd9 gssor2 ..a_kknsodch_ npf.@_khenpmh_C0/0/Ca_kknsCopnonrhshnmr-

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domain: phys sdv

text:
Loucif Remini

Midas Segers

John Palmeri

Jean-Charles Walter

Andrea Parmeggiani

Enrico Carlon

Chromatin structure from high resolution microscopy: scaling laws and microphase separation

Recent advances in experimental fluorescence microscopy allow high accuracy determination (resolution of 50 nm) of the 3D physical location of multiple (up to ∼ 10 2 ) tagged regions of the chromosome. We investigate publicly available microscopy data for two loci of the human Chr.21 obtained from multiplexed FISH methods for different cell lines and treatments. Inspired by polymer physics models, our analysis centers around distance distributions between different tags with the aim being to unravel the chromatin conformational arrangements. We show that for any specific genomic site, there are (at least) two different conformational arrangements of chromatin, implying coexisting distinct topologies which we refer to as phase α and phase β. These two phases show different scaling behaviors: the former is consistent with a crumpled globule while the latter indicates a confined, but more extended conformation, such as a looped domain. The identification of these distinct phases sheds light on the coexistence of multiple chromatin topologies and provides insights into the effects of cellular context and/or treatments on chromatin structure.

I. INTRODUCTION

Understanding the organization of eukaryotic chromosomes is an issue of broad interest and has been intensively studied both experimentally [1][2][3][4][5][6][7][8] and computationally [9][10][START_REF] Barbieri | Proc. Natl. Acad. Sci[END_REF][START_REF] Brackley | Proc. Natl. Acad. Sci[END_REF][START_REF] Scolari | [END_REF][14][15][16][17][18][19][20][21]. This interest stems from the fact that the 3D chromatin structure has a strong influence on several genomic processes such as transcription or replication [22,[START_REF] Blossey | Chromatin: Structure, Dynamics, Regulation[END_REF]. Long DNA molecules go through high compaction when chromosomes condense during mitosis. During the interphase, genes are actively transcribed and chromosomes are unpacked and distributed throughout the cell nucleus but still possess a remarkable level of spatial organization. This organization is hierarchical, involving different structures at different genomic length scales. Starting from whole chromosome lengths (∼ 100 Mb) down to ∼ 100 kb the DNA organization can be summarized as follows: 1) During the interphase, different chromosomes do not mix but occupy well-defined territories inside the cell nucleus [START_REF] Cremer | [END_REF]. 2) Each chromosome is split into several stretches of gene-rich domains (euchromatin) alternating with gene-poor domains (heterochromatin). Euchromatin tends to be more open than heterochromatin. Moreover stretches of the same chromatin species aggregate forming so-called A and B compartments. 3) At scales of ∼ 1 Mb and below the chromatin is assembled in Topologically Associating Domains (TADs) [25,26], which are regions where chromatin interacts more frequently. The biological function of TADs and the mechanisms leading to their origin are still debated. A prevalent line of thoughts suggests that TADs originate from a loop extrusion mechanism [27], although it is likely that different mechanisms operate simultaneously to contribute to the complex hierarchical organization of eukaryotic chromatin [28,29].

Advanced techniques such as Chromosome Conformational Capture (3C) [1], particularly its high-throughput sequencing (Hi-C) version [2], have played a central role in unveiling the chromatin organization. Hi-C provides genome-wide data for contact probabilities between pairs of genomic sites and was instrumental for understanding the folding of chromosomes at different length scales. Although it is by no doubt a very powerful technique, Hi-C has also some limitations. For instance, it provides indirect information on physical distances (via contact probabilities), it typically requires the averaging over a large number of chromosomes (∼ 10 6 ) and may contain some systematic biases [30,31], therefore raw data require normalization and other pre-processing steps. Fluorescence in situ hybridization (FISH, Fig. 1) has also been used to investigate chromosomal structure [32]. FISH uses fluorescent probes that are complementary to desired chromosomal regions. After hybridization, the 3D location of the probes can be determined from fluorescence microscopy. For a long time FISH remained a FIG. 1. Setup of multiplexd FISH as developed in Ref. [4]. (a) 1 ≤ i ≤ N genomic sites equally spaced are targeted by FISH probes during sequential hybridization cycles. In the setup of [4] the genomic distance between consecutive tags was lt = 30 kb. The 3D spatial coordinates of the tagged sites are then read by high-resolution fluorescence microscopy. (b) The experiment is repeated over M distinct copies of chromosomes. The values of N and M for the experimental data used in this paper are given in Table I. We analyzed here the distance distributions for any two given sites i and j.

very low throughput technique, the main issue being the limited number of fluorescent probes with different emission spectra available so that only a few sites could be visualized. However, quite recently, a multiplexed FISH (mFISH) method was developed [4]. Using unique readout sequences and sequential hybridization cycles, the method allows one to determine the positions of N ∼ 50 -100 chromosomal sites with high resolution (< 50 nm), see Fig. 1. Measurements are done on samples containing up to M ∼ 10 4 distinct chromosomes. Although, unlike Hi-C, it is not a genome-wide technique, m-FISH data reproduce well the Hi-C contact probabilities for the same genomic regions [4]. In addition, m-FISH reveals cooperative (i.e. many-body) chromatin interactions [4,6,8]. These interactions cannot be inferred from Hi-C pairwise contacts, however polymer physicsbased models have recently been developed to describe them [33,34].

The aim of this paper is to analyze a set of m-FISH data focusing on distance distributions of any two pairs of labels i and j. In particular, we analyze the experimental probability distribution P ij (r) of distance r between tags i and j. The large number of distinct samples (M ∼ 10 4 ) implies good statistics, therefore these histograms can be accurately determined. Our analysis reveals that there are (at least) two different modes of chromatin organization at any given genomic site. We report scaling laws characterizing the growth of the chromatin domains when increasing the genomic distance. Overall, our work presents a polymer physics-inspired analysis to characterize chromatin structure. Importantly, this method is straightforward to implement and can be applied to "raw" experimental data.

The paper is organized as follows. Section II presents the method we propose based on the analysis of the experimental distance distribution. Section III focuses on the analysis of the extracted scaling behaviour of typical configuration radii from different cell lines. Section IV discusses, using polymer physics models, the regularities of typical chromatin conformations emerging from the TABLE I. Summary of experimental data from [4] targeting two different regions on chromosome 21. One region is 2 Mb long, located between the 28 -30 Mb position on the chromosome, and was studied in lung fibroblast (IMR90) and erythroleukemia (K562) cell lines. The other region is about 2.5 Mb in size, located between the 34 -37 Mb position, and was investigated in a colon cancer cell line (HCT116). Tags in the study are spaced apart by a genomic distance of 30 kb. N is the number of equally spaced genomic sites and M is the number of distinct copies of chromosomes for which the experiments were repeated. n.

Cell line Chromosomic region N M 1 HCT116 (untreated) chr21 [34][START_REF] Gennes | Scaling concepts in Polymer Physics[END_REF][START_REF] Polovnikov | [END_REF][37] experimental data. Appendices provide technical details on the polymer models considered, as well as a full analysis of the whole distance probability distribution data set.

II. DISTANCE PROBABILITY DISTRIBUTIONS

Table I summarizes the main features of the four data sets from [4] analyzed in this paper. These experiments target two different loci of human chr. 21: a 2 Mb region (Chr21:28Mb-30Mb) labeled by N = 65 tags and a 2.5 Mb region (Chr21:34.6Mb-37.1Mb) labeled by N = 83 tags. These regions contain several TADs across multiple cell lines [4]. More data are available in [4], but these 4 sets were selected because they contain a large number of independent measurements, ranging from M = 4871 to M = 13997, (Table I) from which accurate distance probability distributions are obtained. For an ideal polymer, the distance probability distribution is a Gaussian that depends only on the length r = |⃗ r| of the vector distance ⃗ r:

P ij (r) = g(r; R) ≡ 4πr 2 3 2πR 2 3/2 e -3r 2 /(2R 2 ) (1)
where the term 4πr 2 comes from the Jacobian transformation of the distribution. The above distribution is normalized and contains the mean-squared radius R 2 = ⟨⃗ r 2 ⟩ as a single parameter. Despite its simplicity the Gaussian chain model is a reasonable approximation to complex phases of polymeric matter, such as polymer melts. A well-known result of polymer physics is that a single test chain immersed in a melt of other chains behaves as an ideal polymer [START_REF] Gennes | Scaling concepts in Polymer Physics[END_REF]. This is because self-avoidance gets screened by the surrounding polymers. The mean square radius of an ideal polymer scales as

R ∼ |i -j| 1/2 , (2)
where the exponent 1/2 describes the universal scaling behavior of random walks. It has been recently shown [START_REF] Polovnikov | [END_REF] that the introduction of suitable monomer-monomer harmonic pairwise interactions in a bead and spring polymer model leads to an equilibrium distance distribution corresponding to (1), but with a scaling described by

R ∼ |i -j| ν . (3)
By tuning the monomer-monomer interactions, one can generate any values of the exponent in the interval 1/3 ≤ ν ≤ 1/2 [START_REF] Polovnikov | [END_REF]. The statistical properties of the model are those of a fractional Brownian motion (fBm), which was invoked as a model for chromosome arrangement in cells [37,38], as well as for other problems of polymer dynamics [39][40][41]. We note that the case ν = 1/3 is the exponent of a crumpled globule [42], a phase discussed in some more detail in Sec. IV. Therefore, the Gaussian 0.0 0.5 The legends in each plot show the value of R for a single gaussian model (Eq. (1), green) and of Rα, R β and fα for the double gaussian model (Eq. ( 4)). The red and blue filled areas denote the contribution of the two components of the fit. More results for other cell lines are shown in [43].

distribution (1) encompasses a broad range of polymer models.

Figure 2 shows some plots of experimentally measured distance probability distributions P ij (r) (circles), where the tags i and j considered are reported in each graph and the horizontal scale is the spatial distance in micrometers (µm). The green solid lines are a one parameter fit to the Gaussian model Eq. ( 1), where the mean-squared radius R is the only fitting parameter We note that the model does not fit well the experimental data and the deviations are particularly strong for close tags, i.e. small |i-j| (say within a range of |i -j| ≈ 5, corresponding to a genomic distance of 150 kb). As the genomic distance increases, i.e. for larger |i -j|, the experimental distributions gets closer to (1), as reflected by the trend that the green lines (Gaussian fits) tend to merge with the black circles (experiments) in Fig. 2.

The probability densities for small |i -j| suggest that experiments describe two coexisting populations (phases), therefore we fitted the data using:

P ij (r) = f α g(r; R α ) + (1 -f α ) g(r; R β ) (4)
where the parameter 0

≤ f α ≤ 1 (respectively f β = 1-f α )
is the fraction of chromosomes with mean distance R α (respectively R β ) separating tags i and j. We will refer to the two phases as α and β. The two-phase model ( 4) provides an excellent fit to the experimental data. These fits are shown as solid black lines in Fig. 2. The colored areas are the contributions of the two gaussian components to the final fit.

The two-phase model is fitted to the data using R α , R β and f α as adjustable parameters [43]. These three values are reported in the legends of Fig. 2. The radii change with changing i and j and, as expected, increase for increasing |i -j|. The growth rate is, however, different for R α and R β , as discussed in the next Section. Interestingly, the two phase model ( 4) was also considered in a recent analysis of Hi-C chromosomal data [18]. Such a model was introduced to rationalize some observed discrepancies between Hi-C and earlier non-multiplexed FISH data. We examine the relationship between the findings presented in Ref. [18] and our own results, along with other relevant numerical and theoretical studies, in the concluding Section of this paper.

III. SCALING BEHAVIOR OF Rα AND R β

Figure 3 shows the scaling behavior of the HCT116 cell line. These are log-log plots of R α and R β vs. the genomic distance l t |i -j| for fixed i and varying j, where l t = 30 kb is the spacing in base pairs between two consecutive tags of the experiments (see Fig. 1). The horizontal axis is thus the genomic distance measured in bp, which extends up to about 2.5 Mb. We characterized the scaling behavior by fitting R α and R β to (3) for close tags, i.e. |i -j| ≤ 5 corresponding to a maximal genomic distance of 150 kb. This choice is dictated by two factors: (i) we observe that the scaling of R α and R β follows an approximate power-law behavior for a limited distance between tags and (ii) the values of R α and R β are more accurately determined from fitting distance probability distributions for small |i -j| as well. This is because there is typically a bigger gap between R α and R β for small |i -j|, therefore they can be more reliably extracted from the data analysis.

Table II gives a summary of the average exponents ν α and ν β for the four different cell lines averaged over all the tags. With the exception of the K562 cell line, we find consistently ν α > ν β . Comparing the two HCT116 cell lines we find very little difference between the exponents in the two cases, apart from a possibly slightly higher ν α in the auxin-treated case, see Table II. This small increase is a signature that the α phase is slightly less compact in the auxin-treated case, consistent with the fact that by degrading cohesin, auxin releases some constraints. The little overall difference in exponents in the two cases is coherent with the conclusions of Bintu et al. [4]. The authors found that the ensemble averaged contact matrices from mFISH show no sign of TADs in the auxin-treated cells. However, TADs were still visible at the single cell level. As a matter of fact, as explained in [4], while TAD boundaries in the untreated HCT116 cells are pinned at specific genomic sites, in the auxintreated line, they are found in different genomic positions for each cell, thereby washing out any TAD signature in the ensemble averaged Hi-C data. The effect of pinned vs. variable boundaries is also visible in Fig. 3: the scaling of R α and R β is smoother and power-laws extend to a broader interval in the auxin-treated cells as compared to the untreated ones. In the latter, several "bumps", which are likely the effect of strongly pinned domains, are visible. Similar scaling behavior is found for the IMR90 lung fibroblast cell line [43], with values of ν α and ν β consistent with those observed in the untreated HCT116 cell lines, see Table II. An exception is the K562 erythroleukemia cell line for which we observe substantially no differences between exponents ν α and ν β (Table II). This suggests a different type of chromatin organization for K562 as compared to HCT116 and IMR90. The origin of the peculiar behavior is presently not understood. In view of the numerical value of ν β it is more logical to characterize the K562 cell line as having two phases of type α, see Having examined the distinct properties of the two phases thus far, we shall now shift our focus to the analysis of a global quantity. Figure 4 shows a plot of the total mean radius R T = ⟨r 2 ⟩ for fixed tag i and with either j > i (↑) or j < i (↓). Using Eq. ( 4) one can express R T as a function of the radii of the two phases as

R 2 T = f α R 2 α + (1 -f α ) R 2 β , (5)
which suggests that the scaling of R T as function of the genomic distance is a weighted combination of R α and R β . The previous relation is valid in the range of genomic distances for which the chromatin actually separates into the α and β phases, and it also assumes that there are no other major components besides these two phases. As we have seen from the analysis of distance distributions, we can identify the two phases up to genomic distances of about 150 kb. Figure 4 shows plots of the scaling of R T vs. s for some selected tags of the two HCT116 cell lines.

The data indicate that there is a different scaling behavior at different genomic distances. We fitted therefore a power-law scaling

R T ∼ s ν (6)
in two ranges: s ≤ 150 kb (which corresponds to |i -j| ≤ 5) and s ≥ 450 kb. The fits yield two scaling expo- nents, denoted hereafter by ν short and ν long , which are reported in the last two columns of Table II. Differences in scaling behavior at different genomic distances were also observed and explained in the analysis of Hi-C contact probabilities data [44]. The interpretation of the results of Table II as well as the connections with other studies will be discussed in details in the next Section.

IV. DISCUSSION

In this paper, we have analyzed mFISH data from the experiments reported in Ref. [4] for human chr.21 for different cell lines. Our main result is the evidence of two different coexisting phases of chromatin, which we referred to as the α and β phases. The range of genomic length explored by these experiments goes from 30 kb to 2.5 Mb, but the characteristic radii R α and R β can be confidently obtained from data for distances up to approximately 0.5 Mb. Therefore our conclusions are limited to this range of lengths, which is roughly the genomic distance at which TADs are observed. We characterized the two phases using scaling exponents ν α and ν β . Interestingly, these exponents are different in the two phases (except for the K562 cell line), indicating substantially different spatial organizations, which we discuss in what follows.

A. α Phase

The exponent we extracted for the α phase is close to that expected for a crumpled globule, which is ν = 1/3 [42,45,46]. The crumpled globule is a metastable phase arising from the rapid condensation of a self-attracting polymer following a temperature quench. The polymer condenses, but it has insufficient time to relax to a true equilibrium conformation. The rapid condensation prevents the end points of the long polymer to retract and to form knots, so the crumpled globule remains unentangled [47]. This is different from an equilibrated compact phase, which is strongly entangled and forms knots. The absence of knots makes the unfolding of crumpled globules much more rapid than that of equilibrated conformations [47]. Crumpled globule polymeric phases have been discussed in melts of polymer rings [9] and are believed to be relevant for genome folding structures [47,48]. Figure 5(a) illustrates the typical conformation of a crumpled globule. Nearby chromatin segments (indicated with different colors in Fig. 5(a)) tend to condense and the process continues hierarchically involving longer and longer length scales, with the end-points playing no specific role in the process.

B. β Phase

The β phase is characterized by a very small exponent, which is an indication of strong confinement. Figure 5(b) and (c) illustrate two possible mechanisms of polymer confinement. In (b) the confinement is due to an external potential forcing the monomers to remain within a certain range from a fixed origin. This could be due to the formation of a droplet by, for instance, liquid-liquid phase separation, with chromatin preferentially absorbed by the droplet. An alternative interpretation is a flowerlike conformation (c) where loops, possibly forming via an extrusion mechanism, are bound to a central hub. For both types of conformations (b) and (c) one has R β ∼ s 0 , i.e. the characteristic radius becomes independent of the typical genomic length s beyond some threshold value s > s 0 . Here s 0 is the typical genomic length of the polymer to reach the droplet surface and return back to the origin in (b) or the typical loop genomic size in (c). A mathematical model for the case (b) is discussed in Appendix B, but the s-independence can also be explained intuitively. Let us consider the point "1" and "2" in Fig. 5(b), which we assume are separated by a genomic distance s > s 0 . To reach point "2", the polymer chain bounces a few times on the boundaries of the confined region. In doing so any information about the length s is lost and therefore the probability distribution that the two points be separated by a distance r = |⃗ r 1 -⃗ r 2 | cannot depend on s. For confinement of the type presented in Fig. 5(c), if the points "1" and "2" are on different petals of the flower-like configuration then again the distance distribution of r = |⃗ r 1 -⃗ r 2 | will not depend on the genomic distance s. Experimental data show no "ideal" confinement (ν = 0), as the average exponent is nonvanishing, although very small ν β ≈ 0.1. We note that, although confined, the β phase is characterized by a radius R β > R α in the range of genomic distances up to ≈ 200 kb.

C. Coexisting topologies in single cells

Although so far we have analyzed experimental probability distributions over the whole set of M distinct cells, here we perform a single-cell analysis. The analysis reveals various coexisting conformations in which the chromosomes of each cell alternate between micro-domains of α and β phases (see also Appendix C).

To illustrate this, we first constructed a global distance

P (i)
Rg( 5) p FIG. 7. Radius of gyration Rg (solid black, left y-axis) and β phase probability p β (dashed blue, right y-axis) as a function of tag number for randomly selected from the HCT116 cell line. Rg is calculated over five subsequent tags, while p β is defined in Eq. ( 7). The values in the upper right corner of each panel give the Pearson correlation score between the two quantities.

probability distribution of consecutive tags by averaging P i,i+1 (r) over all tag positions i for cells within a cell line.

We denote this averaged distribution by ⟨P i,i+1 (r)⟩ i . Employing a two Gaussian fit (4) on ⟨P i,i+1 (r)⟩ i provides global values for f α , R α , and R β across all tags. Fig. 6 displays plots of single cells distance distributions over consecutive tags (|i -j| = 1). In contrast to the data in Fig. 2, which are for fixed i and j and cover all M ∼ 10 3 -10 4 chromosomes, those in Fig. 6 are limited to just N ∼ 60-80 samples, corresponding to the number of tags used in mFISH experiments (see Table I). Despite the lower statistics, Fig. 2 demonstrates a strong agreement between the averaged distribution ⟨P i,i+1 (r)⟩ i and the distributions of individual cells. This result confirms the existence of at least two populations with distinct spatial distributions within each cell.

One can now define a probability to find a given local chromatin conformation in the β phase as follows

p β (i) = (1 -f α )g(r; R β ) ⟨P i,i+1 (r)⟩ i (7)
with g(r; R) as in (1). This definition applies to a single cell. Note that p β increases for larger measured distances r, as it is more likely that the measured cell is in the phase β at the tag i. In Fig. 7, we superpose the plots of the local gyration radius R g (i) (black solid line) and the local probability p β (i) (blue dashed lines), both calculated over a sliding window of 5 subsequent tags centered around the tag i. This enables the comparison of the spatial variability (expressed in tag number) of these physical quantities. Interestingly, the figure shows that domains with a high β phase content co-localize with maxima in the local radius of gyration, whereas clusters with much lower p β are centered around the lower values of R g , thus within compact chromatin regions. Although the location of these different domains varies strongly from cell to cell, the variation of these two quantities is remarkably correlated.

D. Connection with other studies

Currently, there is a consensus regarding the existence of a markedly heterogeneous chromatin organization that manifests itself in significant cell-to-cell variations. This conclusion is supported by experiments [4,49,50] and simulations [29,44,[51][52][53]. Conte et al. [29] recently analyzed the same mFISH data discussed in this work [4] and showed that they are consistent with micro-phase separation, which agrees with our conclusions. The advantage of the distance distribution analysis employed here is that one can define scaling exponents for the two phases and extract them in a direct way from the experimental data.

To reconcile discrepancies observed between some Hi-C and (non-multiplexed) FISH data Shi and Thirumalai [18] invoked the two phase model (4). They showed that these discrepancies can be resolved if a heterogeneous model with two or more sub-populations is used. Their analysis was done on Hi-C data and on low-throughput (multicolor) FISH data [50], therefore it could not reveal scaling laws that appear when several labels regularly spaced along the genome are used, as is the case for the multiplexed FISH experiments by Bintu et al. [4] we analyzed here.

Our findings are also in line with recent work modeling chromatin structure using insights obtained from Hi-C data [44,54,55]. These papers focus on the decay of Hi-C contact probabilities P (s) as function of the genomic distance s. The crumpled globule model would predict P (s) ∼ R -3 ∼ s -3ν with ν = 1/3, as obtained from Eq. ( 1) and (6) by taking the limit r → 0 to obtain the contact probability. This scaling behavior for P (s) is found to be consistent with Hi-C data only at genomic distances s > 1 Mb [44]. The deviations observed at shorter scales are explained using a crumpled polymer model with superimposed random loops [44]. This is indeed similar to our description of chromatin as a two phase system: a crumpled globule (α phase) and looped/confined phase (β phase). Our distance distributions analysis indicates phase separation in single cells in domains of the size of ∼ 100 kb. From the analysis of the total radius R T we observed different behaviors at short (s < 150 kb) and long (s > 450 kb) genomic scales, reminiscent of the different scaling regimes discussed in [44]. The mFISH data indicate an increase of the scaling exponent for large genomic lengths with ν long consistent with, or very close to, the crumpled globule limit, see Table II.

In the future, it would be interesting to extend the distance distribution analysis to more cell lines and also explore chromosomal regions below the 30 kb resolution. Rα and R β for a few selected tags in the leukemia cell line K562. The notation is the same as of Fig. 3 with "tag: 10 ↑" means that Rα and R β are calculated for i = 10 and j = 11, 12 . . . N . The solid lines are power-law fits over the the first five points (s ≤ 150 kb).

5 < i < N -5 the exponents are obtained from averaging over j > i (↑) and j < i (↓) with |i -j| ≤ 5 (s < 150 kb). For the tags i < 5 and i > N -5 we used only the j > i and j < i, respectively. Of all cell lines, the Auxin-treated HCT116 shows a remarkable homogeneous behavior across the different tags, with clearly distinct exponents from ν α and ν β , and with an intermediate value of ν short , as expected from Eq. ( 5). While auxin removes some of the topological constraints, the chromatin organization of the auxin-treated cell line as quantified from the values of the exponents is similar to the HCT116 untreated case. The untreated HCT116 line shows much stronger tag-to-tag variability of the scaling exponents, which is attributed to the pinned TAD boundaries, as discussed in [4]. Distinct values of ν α and ν β are also obtained for the IMR90 cell line with a tag position variability which is similar to the untreated HCT116 case.

Finally the leukemia cell line K562 shows "anomalous" overlapping distributions for ν α and ν β with, surprisingly, ν short smaller than ν α and ν β .

Appendix B: Confined Ideal polymer

We discuss here the effect of confinement in the simpler and analytically tractable case of an ideal polymer. We consider a polymer consisting of N monomers of average bond length b which is subject to an external radial potential U (r) acting on all its monomers, as depicted in Fig. 5(b). The potential is attractive forcing the polymer to remain confined in the vicinity of the origin. One can consider different forms for U (r), such as the infinite well case

U w (r) = 0 r < R +∞ r ≥ R, (B1)
a harmonic potential

U h (r) = k 2 r 2 , (B2)
of other types of confinement. The probability distribution for the end point vector ⃗ r, from the origin of the potential, of a segment of length s satisfies the differential equation [START_REF] Doi | The Theory of Polymer Dynamics[END_REF] ∂Q

(⃗ r, s) ∂s = b 2 6r ∂ 2 [rQ(⃗ r, s)] ∂r 2 -βU (r)Q(⃗ r, s) (B3)
This equation can be solved by separation of variables, i.e. by seeking solutions of the type Q(⃗ r, s) = ψ p (⃗ r)g p (s), labeled by an index p. The general solution is then given by the linear combination

Q(⃗ r, s) = p A p ψ p (⃗ r)g p (s), (B4)
where the coefficients A p are chosen to satisfy the desired boundary conditions (the full series solution of the infinite-well confinement is given in [START_REF] Hahnfeldt | Proc. Natl. Acad. Sci[END_REF]). Separation of variables leads to a differential equation for g p (s) of the type dg p (s)/ds = -α p g p (s) with exponentially decaying solutions g p (s) = e -αps . In the limit s → ∞ one uses the ground state dominance (GSD) approximation which retains the component with the smallest α p [START_REF] Grosberg | Statistical Physics of Macromolecules[END_REF] Q(⃗ r, s) ≈ A 0 e -α0s ψ 0 (⃗ r) (B5)

where ψ 0 (⃗ r) is the ground state solution of the associated Schödinger-like equation

b 2 6r ∂ 2 [rψ 0 (⃗ r)] ∂r 2 -βU (r)ψ 0 (⃗ r) = -α 0 ψ 0 (⃗ r) (B6)
We note that in the GSD approximation the distribution in ⃗ r is independent of the polymer length s, due to the factorization in (B5). This is different from a free ideal polymer where the probability distribution is a function of the scaled variable ⃗ r 2 /s. For a infinite well potential (B1) the solution of (B6) is a spherical Bessel function of order zero

ψ 0 (⃗ r) = sin(πr/R) r for r ≤ R (B7)
and ψ 0 (r) = 0 for r > R. For a confining harmonic potential (B2) one finds

ψ 0 (⃗ r) = exp(-3r 2 /2R 2 * ) (B8)
where we have defined R 2 * ≡ b/ √ 3βK. In both cases, we have omitted normalization factors.

We recall that ψ 0 (⃗ r), obtained from the ground state dominance (B5), is the probability distribution of the end-point of a very long polymer. The probability that two points along the polymer are separated by a given vector distance ⃗ r = ⃗ r 2 -⃗ r 1 is given by

P (⃗ r) = d⃗ r 1 d⃗ r 2 ψ 0 (⃗ r 1 )ψ 0 (⃗ r 2 ) δ(⃗ r 1 -⃗ r 2 -⃗ r) (B9)
where δ() denotes the Dirac delta function. Inserting the following Fourier transform representation of the Dirac delta,

δ(⃗ x) = 1 (2π) 3 d ⃗ k e i ⃗ k•⃗ x , (B10)
we obtain

P (⃗ r) = d ⃗ k ψ 0 ( ⃗ k) 2 e i ⃗ k•⃗ r (B11)
where ψ 0 is the Fourier transform of ψ 0 (⃗ r). The Fourier transform of a Gaussian function is also a Gaussian, hence the harmonic confinement gives

P h (r) = 4πr 2 3 4πR 2 * 3/2 e -3r 2 /4R 2 * (B12)
where we have included the jacobian 4πr 2 . For the infinite well confinement we solved the problem numerically. We generated independent vector pairs ⃗ r 1 and ⃗ r 2 within a sphere of radius R distributed according to (B7) and extracted the probability distribution of the distance r ≡ |⃗ distance between two points within a sphere of radius R).

For generic confining potentials the distribution is not a Gaussian one.

We consider now the case of confinement of an ideal polymer in a flower-like shape conformation as in Fig. 5(c). For simplicity we will assume that each petal has the same length l and we number them 1, 2, . . . n according to increasing genomic position. Let us again for simplicity consider two points on the flower with positions ⃗ r 1 , ⃗ r 2 and are located in the middle of petals i and j. The genomic distance between these points is therefore s = l|i -j|. Given p p (⃗ r * ; l), defined as the probability distribution that the mid-point of the petal is at a distance ⃗ r * from the center of the flower, the probability distribution that the spatial distance between the two points is equal to ⃗ r is then given by P (⃗ r) = d⃗ r 1 d⃗ r 2 p p (⃗ r 1 ; l)p p (⃗ r 2 ; l)δ(⃗ r 1 -⃗ r 2 -⃗ r). (B13) For an ideal polymer p p (⃗ r * ; l) is a Gaussian distribution and so is P (⃗ r) obtained from the previous formula. Most importantly, this result is independent of the genomic distance s, hence it predicts a scaling R ∼ s ν with ν = 0. This holds for distances s > l, i.e. beyond the length of a petal. different data. For a microphase separation we expect a constant value of f α for a distance range corresponding to the characteristic length of the domains. The data in Fig. C.1 show that f α ≈ 0.6 for the shortest tags distance |i -j| = 1 (except for K562 which, as discussed previously, displays some anomalous behavior compared to the other cell lines). The data also show that f α remains approximately constant for some range of genomic distances. This range appears to be somewhat cell-line dependent. As discussed in the main text, the distance distribution analysis is more reliable for tag distances which are not too distant (|i -j| ≲ 5 ), as the differences between R α and R β are larger.

  Fig. A.1.

3 FIG. 4 .

 34 FIG.4. Log-log plots of scaling behavior of the total mean squared radius RT = ⟨r 2 ⟩ from the raw data (black squares). The solid lines are power-law fits (6) over the region |i-j| ≤ 5, corresponding to genomic distances ≤ 150 kb. The dashed lines are power-law fits of the region ≥ 450 kb. The fits give two distinct exponents and illustrate the short vs. long scale behavior of RT. See [43] for more results for other cell lines.

FIG. 5 .

 5 FIG. 5. Possible phases of chromatin: (a) crumpled globule, (b) confined, due to an external potential, and (c) flower. (a) is a candidate for the α phase and (b,c) for the β phase. In (a) different segments of the chromatin fiber are colored differently to illustrate the geometry of the globule. The rapid condensation leads to collapse at the local scale involving vicinal regions. In (b) and (c) strong confinement implies R β ∼ s 0 for s sufficiently long.

FIG. 6 .

 6 FIG.6. Distance distributions of consecutive tags (|i-j| = 1) for individual cells (blue bars) from the HCT116 strain. Similar distributions are obtained for the Auxin treated HCT116 ensemble, as well as other cell-types. Solid black lines correspond to fits of ⟨Pi,i+1⟩ i with (4) for the untreated HCT116 cell line. The observed agreement between the single-cell distance distributions and ⟨Pi,i+1⟩ i corroborates the existence of at least two distinct topologies of chromatin organization at the single-cell level.

FIG. A. 2 .

 2 FIG.A.2. Plots of the exponents να, ν β and ν as function of the tag position i around which they are calculated (see text for details). In the cell lines HCT116 and IMR90 να > ν β , while να ≈ ν β for the K562 cell line.

r 1 -FIG. B. 1 .

 11 FIG. B.1. Solid line: Numerical solution of the probability distribution P (r) of spatial distance r between two points separated by a long genomic distance s for confinement in the case of infinite well-potential (B1) with R = 1. Dashed line: Gaussian fit of P (r).

  FIG. C.1. Plot of the average fα, the fraction of the α phase as a function of the genomic distance (solid colored line). The light-colored area indicates the standard deviation.

TABLE II .

 II The first three columns give the mean values of the critical exponents να and ν β and of fα averaged over all data in the range |i -j| ≤ 5 (corresponding to a genomic distance s ≤ 150 kb) for the different data sets. The analysis of the HCT116 and IMR90 cell lines gives consistent values of these exponents with να > ν β . For the leukemia cell line K562 να ≈ ν β . The two last columns give the mean values of the scaling exponent of the total mean radius RT (Eq.

						(5),
	refer to Fig. 4 for details) at short range (s ≤ 150 kb) and
	at long range (s ≥ 450 kb) with uncertainties indicated in
	parentheses, referring to the last digit.
	Data set	να	ν β	fα	ν short	ν long
	HCT116	0.35(7) 0.12(5) 0.64(5) 0.21(4) 0.33(20)
	HCT116 (+Auxin) 0.40(3) 0.10(2) 0.60(5) 0.23(2) 0.29(03)
	IMR90	0.29(8) 0.11(4) 0.61(8) 0.14(5) 0.32(13)
	K562	0.37(8) 0.33(7) 0.53(8) 0.23(5) 0.22(11)

ACKNOWLEDGEMENT

Discussions with M. Barbi, M. Bardou, T. Foldes, M. Liefsoens and M. Nollmann are gratefully acknowledged. LR acknowledges doctoral thesis support from the Lab-MUSE EpiGenMed within the I-Site MUSE (ANR-16-IDEX-0006). MS acknowledges financial support from Fonds Wetenschappelijk Onderzoek (FWO 11O2323N). EC wishes to thank the Laboratoire Charles Coulomb of the University of Montpellier, where part of this work was done, for its kind hospitality. This project was supported by the LabEx NUMEV (ANR-10-LABX-0020) within the I-Site MUSE (ANR-16-IDEX-0006).

From fits of the experimental distance distributions P ij (r) with the two phase model (4) one obtains estimates of f α and f β = 1 -f α , the fraction of the two phases for pairs of labels i and j.