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<?xml version="1.0" standalone="yes"?> <Paper uid="C94-2155"> <Title>A CLASSIFICATION METHOI) FOR JAPANESE SIGNS USING MANUAL MOTION DESCRIPTIONS</Title> <Section position="1" start_page="0" end_page="0" type="metho"> <SectionTitle> A CLASSIFICATION METHOI) FOR JAPANESE SIGNS USING MANUAL MOTION DESCRIPTIONS </SectionTitle> <Paragraph position="0"> Ishii-machi, Utsnnomiya, 321, JAPAN atlachi@gnrn .infm'.n t sm~mniyn- u.a('...i I) SUMMARY In this paper, wc prol~OSe a <:lassili<'ation method for sigus in ./ape<nest ,b'ig. I)(tngutqlC (JSI,). The metho<l is l>as<'d on I:\],c similaril,y I>el,wceun n+eH+nal .loli+Jtz dc.+i:rilJlion.+(M M \[)s) M' signs. M M l/s a~c the verbal dcs<:ripti<nm of signs, The measure (ff similarily I>ctw('en MM I)s is derivc<l from ihcir h,n#cst common subsc'quc+~c< (I,C,'-;) of MM I)s. liy (:Oral)u/inK fcal.urc vc(;\[ors of u propcrti(~s fr<)m a. linile sc.i of MM1)s and i)hUting them in the n-dimcnslonal I';u<:lidcau space, the similarity between signs can he r,'g;u'dcd as a.n internal angle I~el,',vcen Ihc vectors. '\['he result, of mH' experimenl is I,}l~I, I}le signili<:anl sign families can be obt;fin(~d,</Paragraph> </Section> <Section position="2" start_page="0" end_page="961" type="metho"> <SectionTitle> I. INTRODUCTION </SectionTitle> <Paragraph position="0"> Stokoe (1960) is I.he lirsl, linguist I.o deal with the Sl;I;llC\[,llre Of signs in l.he S;lllle way as I,ha(, of oral words. lie uol:ed t.haI. I.here were three kinds of i~aramet.<!rs in de~cril>ing l, he sigu iu A mcri<a.,/ig, /..n.</u(tgc (ASI.) a.~ follows: ( I ) t, hc Ioca, l,i<m of qle signs rclal,iw~ I,o <,he body, (21) IJ~e haIM-shal)e <>f hau<ls involw~d in arl:iclda.l.i,g the sign a.nd, (3) the m<>v<!lucul, of hands. Oi.her linguists (li'rie<hna.n 1977, Battis<>u 1,q7;';) ha.vc claimed <,hal, a follr|,\]l paralneLer is ol>lip;al.ory, thai, is, the spal.ial orieul.al.i<m of the hamls rela.l:ive lo l.he body. In ./(tpane's~: .Ni/In l.anguaff((JSI,), a, few liuguisl,,~ ('l'a.nolcami 1979, Kanda 1982) took I:he similar apln'oaches, Thus, we m'ed I.<> ,specify th<, Ioc<dio,, h(utd-.~hap<~ movemcnl and ori6n, l(i.lio~ of lilt \[muds t<> describe t.he sign. Furthermore, il. is int.eresting 1.1> u<)l,c t.hal, a change in <rely one of l,I~<~ signilicam elem<mts iu handshape, local.ion, orient.ati<m and movement often results iu changing i.h<~ meauiug; (ex., antonym, synonym). The uotat.i<>n sysl.ems pr<q~osed I>y liuguisl.s <:au pr<wi<h&quot; a very detailed aud broader reprcsmllatiou I,o describe signs. It is, hmvew~r, not easy l,o l:rallsforlii l.he siga iul.o the nol.al.i<m. For Mils r<'as(),: it, is 1.oo <<)st Io col= led; a large am<told, of sign data.</Paragraph> <Paragraph position="1"> C,msich'r, f<>r examph', a miuimal pair iu lhc movemcul: as shown iu l&quot;iK.\].</Paragraph> <Paragraph position="2"> It is clea.r thai the nliIfimal pair { 'I:i\]~Y O~.nl.),q: O\[ I&quot;i~ 1: The Minimal Pair of Signs (q:iJfi (a.m.), 'l:t~ (p.m.)) t~ (p,m.)/ mcaus the antonym senmnticaily a.ud repre s<mts I.Iw symmetry visually. Typical sign <licti<niary c<msist.s of ilhlstral.ions <,' l)hot,ogralflls aim t.h<&quot; wM)ai descril)l.i<m.',, we called the descripti<ms m.an,ual mot~o.n dc.scriplions (MM I)s) represented as l;exI, written in nat= ural language.</Paragraph> <Paragraph position="3"> It can be considered thai; a. MMI) represents iul'of llHll,iOII exl,r~qc|,cd frOlll ~1, s0ri0,,s of the l\[lallllal /noLiotts of I.hc sign. 11. is not <lilIicult to find the symmetry o\[' signs by the c(mt.rast t>ef.ween tw<> MMI)s. lV<u ' c'xa.ltl-I>le, the toni.fast <)t' wor<ls '~i (right) aml ~F= (left,) can I>c ol)I.ained \['r<mL c(mll)ariug MMI)s of-'t:~ (a.m.) wil.h /l: ~2 (l>.m.) a.~ foll<wvs.</Paragraph> <Paragraph position="4"> .~if-(I)X.~.'~+~ ,l'+f~+ ~'/::Cc&quot;~C/ia~,l,'~::+,'C'C, f ~::fl19 g:@ We d<!,~<:rihe a. classificali<m reel;hod for sigu,s using mat.h<~nlatical tcchlfiqm.s ha,sod on I.he similarity b<&quot; l,ween M M I)s.</Paragraph> </Section> <Section position="3" start_page="961" end_page="962" type="metho"> <SectionTitle> 2. DATA STRUCTLTRES FOR MMDS </SectionTitle> <Paragraph position="0"> This section descril)cs l,hc rema, rlC/ablc characteristics of MMI) and a tra.nsfc, rmat.ion met.hod ddvd from l, hetn. The method i~icans l.hat MMI)s can he tra.usfornted into I,he n-dhnel~sio\]tal /'eal:ure vectors.</Paragraph> <Section position="1" start_page="961" end_page="961" type="sub_section"> <SectionTitle> 2.1 Tim Re.markat)le Characteristics of MMDs </SectionTitle> <Paragraph position="0"> MMI)s nwan a kin,.I of the verl)a.l d(,scril)lions of the sigti, which are written in Japanese hmgiuagc' and has remarkal)le characterist.ics as follows: * MM Its have tnot'e c(inslraint:s ,m synt,aclic pal,l,erHs alld wi)rds Lhall getteral ,\]al)alt(!s( + Solll,OliCl~s, Ill or, her words, t;here are some I,:hM ()f synLacl,ic pal,terns in MMDs, ~, \[n Japimese, syn(inytus at0 often marl,aM wit.h t,h(' COtlltl'lOtl ~'a,tzjl-cllara(:l,l~i!s. F()r exa, lllDle , each set, of</Paragraph> <Paragraph position="2"> groups ;it'('. COllS\[,\]'llC(,(~d by \[;ll(?lll such aS</Paragraph> <Paragraph position="4"> Thus, the combitmtion (if ka,:ji-charact;ers means semantic concatcqla.t.iotl. Sat o (1992) has als(t 1)oiut.d out them in his papt'r.</Paragraph> </Section> <Section position="2" start_page="961" end_page="962" type="sub_section"> <SectionTitle> 2.2 Transfi}rn).atioll into F,tmt'ure Vectors </SectionTitle> <Paragraph position="0"> To represcttt the (list.ril)ution of words ma.thetnatically, it is convenient, to considered as poh++t.s in the .-dimensional Euclidean Sl>;ice. The coordinates of poitfl.s can t)e given as the ~'>,./imc'usioual fl~ature vectors. Then, an infernal a.ngle llel.'.,vc:en the veer.ors can I>e considered as tim similarity t)ctwecll tJle worlls. In this case, l)rol)ez'ties of the feature vectors need t.o tuany poinl.s of view. (i.e., word frequency, part. of specch, CO-O(XqlI'I'OIIC(t I'Olal, iC)q, ~ltl(\[ SO (/It). \]ti l)al,t,(',rlt recogni-I:ious, the sam( + al)l)rC, a ches I tave nm(\[(~ use of recognizing l)ictures and let, tl~+rs Therefore, we ,%+;o seh'cl t;his al>prr)ach which is sigt~.s art' F, lott:(~d in the ,-(limensiotutl li',ucli(leau SlmCC.. I&quot;eal.url' vrctors <:ah hc ()l)tained hy cotlstru(:ting a Ill\]ire stal.e a.ut.omal.on a.ccel)ting MM l)s as fc, llc, ws.</Paragraph> <Paragraph position="1"> It. is well known that: limt.e state aul.(m,ata rec(tg\]lize tinite st.a.te la.ngua.ges (see Aho,A.V., el; al. 197'1). If a class of i)alt.erns can I,e de.scribed in a liuite st.a,.e l,~l, llgtl;I,Ir0, ;I \[\[tPSil;e st,aLe &lll;otl'\]+l,|,Oil (:;Ill 1)C/! (X)\]ISLI'I\]CI,I'(I to recogltize MMI)s ilcscril)ed this class of l)atteruls.</Paragraph> <Paragraph position="2"> Exmnl)l,u.2.1 Let A=4'i~.0)g~~'\]L~ {-.I.-Y'+, I~,=,\]~!:\]~(\])~J~J'~: I-'PY'7~) and (~=iil,jr\]'=c\])/J',t:~ ~ \[lilt-J* 7+ be MM Its. The lit\]ire sl.at, e (,l'a.llSi|,iOll diagram ot' a a.ut,otua.t,otl acCC.ltting the set, of MMD is shown in Fig. 2,2.</Paragraph> <Paragraph position="3"> ~iT.a) I=+)+ Z., .... +&quot;----~O &quot; '.___t%(c) Fig '2: A \]i'inil.e Stale q'ransit.ion Diag, ia+m Then, a regular exprc'ssion derive(I from I.he al)/)ve diagra.m is shown l h0 fi)l\]owing.</Paragraph> <Paragraph position="4"> I!\]ach ka~C/\]~- or&quot; kana- character of the almve reg\]ilar cxpressiotPS cau be considered as i)roperlies (,\]1 I;h0 J'l?;itm'e vectrors for Ishe sigr,. The feat.ur(~ vect.ors for t.ho sign derived fro\],\] MMI)s arc. shovvu iu Tal)le I.</Paragraph> <Paragraph position="5"> +,, \],+ ,:,:, + ++ it, +++ + ,- ,,-,,, 0,+ + A I 1 0 l 1 1 0 0 I I (~ ) 1 I 1 ) l l I 1) (J \[ l I Thus, l.hc signs can be rcl)rcseut.cd as l~-(lhneusiotud l+eat, m'e vect,:m'+;, w}|\]ch call })e (leliued as b+/ re+tots \[0,1\].</Paragraph> <Paragraph position="6"> Furthermore. we can find a Mud ,:>f +ynt.actic pat.t.crn</Paragraph> <Paragraph position="8"/> </Section> </Section> <Section position="4" start_page="962" end_page="966" type="metho"> <SectionTitle> 3. SIMILARITY BETWEEN SIGNS </SectionTitle> <Paragraph position="0"> This se,::|i(m describes how a situilarity t)etwe(!u signs is cotttpul.ed. To conq)ut.e sintihu'ily, we inl.ro(luc0d l\]+e Io+Ig+,sl-commo'n-sub,+cqu+ n( ( ./)+++clio, (I,(1~).</Paragraph> <Section position="1" start_page="962" end_page="962" type="sub_section"> <SectionTitle> 3.1 Similarity he|;ween MMI)s </SectionTitle> <Paragraph position="0"> The resull, of the I)revious ,:tiscussi(,us (:au I:,(, suln+ ularized a,q foll,::.vs: I, Similarity lml.wcen two signs ca:n I)c c(msidored as similarity hetweeu t.vvo MMI)s.</Paragraph> <Paragraph position="1"> 2. Whc'u ,:h~.scril:,ing si~n,s matheumt.i,:ally, il, is ccmveuien(, t.o rcgar,.l t,ltc'lU as l)()ili\],s ++t' \['e,~d,llre ~,'(~(Tl,()lis iu (.lie n-dimeusi,:mal I'~uclideau .-+l>aCe. The simi larity measure hetweeu l.wo signs i~ c<>usMered a.'-; +t,1! #tll~\]O ()f I,WO Vectors.</Paragraph> <Paragraph position="2"> 3. If a \[initc state aul.oumla acc(!iH.hl ~ .MMI)..+ curt he</Paragraph> <Paragraph position="4"> l,e(. ,I -: (~+t,+t..~ ..... (t,~) aad 11 :: (bl,l:~ ..... b,) l)o pl-dill\]CllBiOllal \['(++lllll'e Ve( t,(H':-; ()1&quot; ,++;iglt~, Then, l, he Bitllilarity tt.~asure l+elv.'e,~m sigus, dcm,t,ed, hv ,&quot;;(A, 1C/), cau lw delinc'd as f.lh+ws: I)l!',t&quot;. l:The Shnihu'ity belweeu t&quot;eal.u re \:+.<:t,cm,</Paragraph> <Paragraph position="6"> N~,,,~<,,+, IIAIF ,:~,,, t,,+ ,:,,,,u.,t,,>d +,+ ,,h,, ~,.,~, .+' m l i t ~ V<~(:tP+ + I' :~ l (+'r~ , I I ) ~:+~ I ~ I > <&quot; COmlml.ed as the +tun o\[ + ,++: A bi - I iu feature ve<:t.C/>rs A aml H,.</Paragraph> <Paragraph position="7"> II,ecall t.he feature w'ctm's of TaMe 1 itt th0 last sec+ ~.~o,+. IIAII + ,.+,,, \[+,+ deliued a~ a hmgl.h ~+1' MMI) relat.ed t. w~<:l,t,&quot; A. In the same way, (A, II) ,::au t'.! ,:Mil,e,A a~ a leugi:h ~+1' a Io:,.:i,.,,I torn're.on sul~seque?~ce of MM l)s .'ehtted I,c> vcc't.rs A and IL We shall discus.s il. h+t detail.</Paragraph> </Section> <Section position="2" start_page="962" end_page="963" type="sub_section"> <SectionTitle> 3.2 13cmgest (~Olllll|Oll S'ul~se.qu..~m.<',~ </SectionTitle> <Paragraph position="0"> A s,tl',scqtwuce ol + a given sl.ring is al~,y si.riug ot>l,ained by delet.ittg zero m' more sylubcds from tim giveu st.ring. A Io,gcsl +o+nmov subsequcn+~ (I+(JS) c+l' t.wc, st.rings is a suhseqm+t~ce o\[' bot,h l.ha(, is a.,+; long as a.uy ol,hc?r ('O/lllllOll SIIIISCCIlII+IICC.</Paragraph> <Paragraph position="1"> An h('+S vnea.ns tha.t the muuher of ttlatchithg char+ ;,el.ors ccnl.~idez'iug l.he ch;m~cter uMer c<m~l.raint. Ig,' examlde, fl' X = abcl;,doh and Y :: l;d+aba, then all l+(IS c.f X aud Y in fiche, and has leugth 4 as shown m Vig. 3.</Paragraph> <Paragraph position="2"> 't'lw othc.r l,(~S of X aml Y arc 6dab aud k+'ab, aud also haw' leltglh ,1.</Paragraph> <Paragraph position="4"> l&quot;or a given ~equcuce .\&quot; ~ xtx~...xt+ we deline IJie ith prelix of X , fur i := 0+ 1,...,/, as .\++ -- .l:j;c..+,...+:~. l;'or exanlple, if X =- abr:d+, t.hen X:+ - abe au,.l ,YC/) is the empty sequence 't'he,~, au I+CS ,A&quot; A and \[.i, <lou.tcu I)y L(:,~'(A, H), ca.n be cOlUlmled eIl\]ciett(,ly as the following recursiw, f,:n'ttmla u~iu~ I)yl\],+mti(&quot; I>r'ogi'alt~tuil~g (\['or \['url.hox dclail,~ uf h(IS, see Thomas II, et. al. 1991).</Paragraph> <Paragraph position="6"/> <Paragraph position="8"> Ot}viously, the above sinfiM\]'ily rneasurc satisties thern.</Paragraph> </Section> <Section position="3" start_page="963" end_page="964" type="sub_section"> <SectionTitle> 3.3 An Exl,{u'inmnt </SectionTitle> <Paragraph position="0"> We now show res,lll.s (}f all eXl)erin,eut, and verify t.hc situilarit.y measm'P t}el.weett signs. W(' used daLa it, The Illaslrat+d h'i.qn l)iclwnary (Maruyama 198d) for the following reasons. We ma(D use lhe sinq)le (lescripi.ion data. (1,527 entries), whM, were r{m(lered machine rea{labh> dal.a. By mergin.g t.he same MMI)s, itt advauc{', 1,51/1 entries were ol)taiu('.d ~. For exatuF, le, ::}&quot;~</Paragraph> <Paragraph position="2"> { l,msitler, for exa.mph,, parts oft,he apF, roxiumte shHilar pairs as shc, wu in T;d)le 4. A l)ah' {//J;t (daughMr), .&l, :&quot; (.'~o,O} u,ea:,s l,he a.Umy., +u,d i,l:,: oil,or pair { 4!i L. ~,~' (s,'./), ~; < (c'ry)} means the syu(utynl, Thlm, t, hese The sin,ilarity of mamufl mot.ions results in the si,ll ilarity of meauing, which is a kiml of sigu rormatiw> units. That is, a miuima.l pair //1:4 and ,~,f&quot; have a common seiHant.ic C(}lIlI)OIl(qlI; children of parents such as a mot,ion a hand is moved the forward related to the body , ;I,II(I ;Ill hl(lividlla\] S(qll~lll|,ic COlll|>o IR'nl the female or male sex such as usin A a little or thuulh finger.</Paragraph> <Paragraph position="3"> 'l'hcr(' are. howcvc,', a fi'w ,:XCCl)t.ions in t,hc ahow~ rule. For exanlple, each of a pair { f6'~fl~ (Yokoh(mm), i'P} C.'/.P (:-;?;'moth)} hav,~t differ<'nt meanhig, lint both o\[' them are de.rived fl'Ol'll t,hc Salll(~ iconic iilOI.iOll {)\[ \[,li(? ohjecg &quot;t'azors&quot;. From the lauguage pragmal+ics I:,oiul,s of view, the imt',ort;ml, thiug is that a meaning of sigus dlallgeS ill various COllLOX{ just. ;-is a Ii/(Nlllilig o\[' ~1 W{}P(\] &quot;sI',ring&quot; chang('s iu various COllI.cxl., The pohlt we wish to, cnfl>hasize is that, COIII\[}III ilig l,hc' sittiihu'ily h(!t,w(?en MM I)s resiilis th(! sigllilicaul, iiliniliial pair of sign, Fig '1: ,qiglls of ~1:4 da.ghl(r) ai.l ,/h, J&quot; (s(,t, C SS ,' &quot; '' ) ~&quot; O 4. A ,I,A.~ ~ 1\[ ICA 11( N ME \[ H 1)</Paragraph> </Section> <Section position="4" start_page="964" end_page="964" type="sub_section"> <SectionTitle> 4.1 Maf.heniat;i<:al N()t;ion </SectionTitle> <Paragraph position="0"> For a liuil(,set X, a hilmry rclatio, h'(X,X) Ihai, is rc./le:r*l,(, ,'+y?nm+l'r+c a?/d lran.sili+,( is calh'(I all cquivalri~c<' rdo/Zom For each rlctii(!nt a: lit X, we d(!filio a sol A .... which rolll,ahis all l,\]io (qOlilVlll,'. o\[ .\&quot; l,hiil arl' relal,(~(I l,o .c I)y 1,11o oquival(!ilC(' i'(@ll, i(lll, \],'oriiially, A.,.-: {:,;l(.,:,y)< \],'(X,)':)}.</Paragraph> <Paragraph position="1"> A,, is chmrly a suhsct ,:d' X. Th.:' elcilleili .r is il,sclr contained in A,. due 1,o l,lw rc~\[Ic, xivit,y of t'I,; I',~callse II, is i,r;insil,iv(! all,el S.yliilti(!l,ri(', oath rlilqtili(!r o\[ .,~:,. iS rolal,ed I,o all llie oLlicr iileiiii)Vl'S of ,4 .... This s(q A;,: is rol'erre(l I,(t ;is an t~qulvah~llCe (:lass ()\[ \]l'(.\', .\') wii, h rcsl)(Wl Io ,r. The Family ()1' all s.ch ('(i.ivah'.('(' cl.ss,~s deli.(~(I I)y I,}io r(~lal, ioll, which is ilSllally (l(.nol(M hy .\'ll(, \['l)rlllS ii l)a.rl,illOil OI1 X.</Paragraph> </Section> <Section position="5" start_page="964" end_page="965" type="sub_section"> <SectionTitle> 4.2 A Classilicat;i<m M(;t;h()d </SectionTitle> <Paragraph position="0"> Wr (lcscrihc how (:hisl,erhig a giv(;u finil,e set +)f' signs iisiiig the siiiiilaril,y ill(~a.gllr(, pr()l)()s('d hi ~(!cl, ion :/, Th(' shililat'ii,,y r(,htl,iou 5,'(A, 11) satisfies Ihv \['oi\[owiilg two</Paragraph> <Paragraph position="2"> .b'(A, l~), howev(w, (I,:)(~su'l sal,isfy th(! Lransitiw ~ c(m dii,i(m. The., we i.t,rod.c(~ I, hc following iu(!q.alii,y, Thus, ;t srt, of I h(&quot; si~. carl h(, classili.~d .sing thu l',ariil, i(m in,.hlc(.d hy tit(> eqtfivahmcc, rc.lali(n, ~/',, wii,h the apl)rol)riate thrc.,-;hohl c, ( 1 > ;~> 0 ).</Paragraph> <Paragraph position="4"> (lotmcqucul,ly, for every monot(mi('ally decreasin~ li 0 ), the k-h'vcl hierarchy ('lusl;crs in the form of a dendrogranl can hc .hl,ained as shown iN Fig 5. llowevrr, \[,O ( Oll,~i,l'll(:\[ i,h(, (\]Cllth'ogl'alll is iioi, ol|r \])l'cs011L purpo,~e. The rca,~o, is l,hal, tim shuilarity measure 5'(A, B) has a l~ml, urc ()f the curve cos ~ 0. That is, as the. simila,ril, i0~ a.re close the nmxinmm ( S(A, B) = 1 ), gains of noise factor (i.e., inflection ) can be ignored. 'l'hcreforc, The low-level clusters ( < 0.5 ) are nol. necessary for our purpose. \Y=e want. t;o find the significant sign famili('s</Paragraph> </Section> <Section position="6" start_page="965" end_page="966" type="sub_section"> <SectionTitle> 4.3 An gXl)erilnent </SectionTitle> <Paragraph position="0"> To nmke discussions SilUl)lcr, wc used the sample (la.ta. of MMI)s (\]29 entries) including two key-words (chara.cl.ers) of K\] (mouth) 71 (ml, ries and ~-~ (lips) 58 entries; I)eca.us(L a. wor(I t(~. call be idmlt, itied wil.h a word 1PS71 in Ja.pa.ncse la.nguage. \Vc wanted 1.o obtain the re sull.s from oxtracl.ing sign families rathc'r than I.o obtain t.he hiera.r(:hy structure or th(! form o\[ a dendrograln.</Paragraph> <Paragraph position="1"> The purpose of classilications is l.o focus (m th(' mininml lmirs of signs.</Paragraph> <Paragraph position="2"> By merging the identical (lata I.hat. nmal,s 5'(~4, l~) = 1, 129 cntri(>s a.rc merged into 101 entries. The total amount of sign pairs satisfying N(A, B) >_ 0.6 are 25 p;drs, and a 3\[ x 31 similaril.y matrix is ot)i.ained. Th(m, the simila.rity ma|,rix is l.ransformcd into a (.ransil.ive lnatrix, and the cquiw:denco classes C}1.11 I)C ol)(,}liiio(l ~Is shown in Tabh> 6.</Paragraph> <Paragraph position="3"> We classified given signs (129 cnl,rics) into 11 chlst,(>rs a.nd ibund tha.I, tim la.rgesl, am(toni, of sign family is 3, 'v~ (REl))-fa.mily as Follows: 23 entries : at:: (red), g (st.r.~twl)c'rry), Jk{~ (h(redil.y), FI I1~{tl (Sundty), ,)~.PSe}g (tire), ~3.~ (('.xprc'ss), U > ~&quot; (~,.pp>), ~r~ta~ (im)od), ;,,.t s(, o,,.</Paragraph> <Paragraph position="4"> This sign family has an essential common MMI3 &quot; 'l?ha.t is, .;~'f/2 (hc.redily) dcrivod \[l',)lU &quot;bh)c,d&quot;, II Ilt'il l\] (Sltttday) deriw~d frc, ut the red UUlueric in the cahmdar, and Jg3?~ (exl)ress) derived \['rotu I.hc' red-,stamp cm the letter, and so on.</Paragraph> <Paragraph position="5"> Consider, flw example, a. family of sigus { +'l'?~:, &quot;7 &quot;-X, C_ /~ .1: 5,/;\[f:'~'? .(', i&quot;~'U~ } n,eans {sall+J, Worcestc'rsa'+l.cc, p+ per, red - paper, a.sl ri?+gc+lL }+ The l'aufily has :-m essetd;ial COIIIIIIOll SCIII;IIII,ic ('()lll\])oIt(qll,, which III(?;IIIS &quot;not sweet&quot;relweslmled a:-+ ct'<>ok.iug all ,:~1' \[iitgel'S. 'l'he ,:\[ifli+retwe of a. pair( 'i'?U &quot;~ (salt.y), i&quot;'~U&quot; (astringeul))is wh('ther t.u hc rut.at.cd ur ul> and down.</Paragraph> <Paragraph position="7"/> </Section> </Section> class="xml-element"></Paper>