Life Symptoms

8/10/2019 Life Symptoms

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SYSTEMSRESE R H

Fred Wael chl i

Peter Wni wart er and Czesl aw Cempel

Robert a Snow and Arvi d J B oom

Paul Ledi ngt on

Zbi gni ew Wl l i am Wol kowski

3

9

35

47

61

67

The f f i c i l J our nal of t heI nt er nat i onal Feder at i on f or

Syst ems ResearchCont ent s

ook Rev ew

El even Theses of General Syst em Theory GET

L i f e Sympt om The Behavi our of OpenSyst em w th Li mted Energy D s si pat i onCapaci t y and Evol ut i on

Ethi cal Deci si on Maki ng St yl es i n t heWorkpl ace Underl yi ng D mnsi ons and Thei rI mpl i cat i ons

Rel evance, Formal i ty and Process Toward Theory of Sof t Syst em Pr act i ce

CorrespondenceThe Concept of Coherence Consi dered as aSyst em I somrphi sm


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L i f eSymptoms t he Behavi our of OpenSyst ems wi t h Li m t ed Ener gy Di ssi pa-t i on Capaci t y and Evol ut i on*

Pet er W ni war t er* and Czesl aw Cempel

Abst r act For i ncome di str i but i ons, c i t y s i z edi st ri but i ons and word f r equenci es weobserve skewed or l ong- t ai l ed di st ri but i ons of t he PARETO ZI PF t ype I n gener al f or proper t i es of uni t s bel ongi ng t o t he same ast rophysi cal , bi ol ogi cal , ecol ogi cal ,urban, s o c i a l p o l i t i c a l economc or mechani cal machi ner y syst em we observesi m l ar regul ari t i es referred t o as Par et o l aw Zi pf s l aw or r ank- si ze l awW gi ve a short hi st ori cal over vi ew over t he di scovery of these empi r i cal r egul ar -i t i e s Then we revi ew a vari et y of t heoret i cal t ent at i v es none of whi ch can expl ai n t hat si m l ar regul ari t i es are observed i n such an i ncredi bl e w de r ange of

sci ent i f i c research areas Fi nal l y, depar t i ng from a very speci f i c model descri bi ng t ri bovi bro- acoust i c pro-cesses i n machi nes we propose a general i zed t heoret i cal f ramework i n t er ms ofenergy t r ansf or mat i on w t h l i m t ed i nt er nal energy di ssi pat i on capaci t y, whi ch i s

appl i cabl e t o al lf i e l d s The proposed model uni f i es a l ar ge vari et y of concept s and appl i es a coherentt er m nol ogy t o f i e l d s whi ch have at f i r s tsi ght not hi ng i n common For t he observedl i f e sympt oms, t heoret i cal predi ct i ons can be compar ed w t h past and f ut ureempi ri cal obser vat i ons Wat i s most i mpor t ant i s t he model s i nf erence power from t he obser vat i ons of aset of uni t s at a gi ven moment of l i f e t i me( a snapshot of t he system, one canpr edi ct t he aver age behavi our of a si ngl e uni t over i t s ent i re l i f e t i me

Keywor ds Sel f - organi zat i on, evol ut i on, energy t r ansf or mat i on, ener gy di ssi pat i on,i nt ernal structure, i nf or mat i on, aut ocat al ysi s, Par et o- Zi pf or r ank- si ze di st ri but i ons,machi ne vi brat i on di agnost i cs, bi r t h and deat h processes, sympt om l i f e curve,r esi dual l i f e t i me Address *Bor dal i er I n s t i t u t e 41270 BoursayFrance Poznan Uni ver si t y ofTechnol ogy, 60- 965 Poznan, Pol and

1 I nt r oduct i on

Wat do vi br at i ons of el ect r o- mot or s and machi nes i n gener al have i n common w t hat oms of s t a r s w th chem cal compounds of t he ocean, w t h ani mal s of bi ol ogi cal

r

Thi swork has been p a r t l yf i nanced by gent of t he TEMPUS o f f i c eof t he European Economc Communi t y, russ l s

P bl i h


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spec i e s ,wi t h i nhabi t ant sof c i t i e s ,wi t h mar ket val ues of f i r ms ,wi t h wor ds of al anguage . ? r educ t i oni s ts c i e n t i s twoul d consi der t he above quest i on as r i d i c u l o u s ,i noti nsane

nd a syst ems s ci ent i s t ?

ny sc i ent i f i c ac t i vi t y- i ncl udi ngsyst emssci ence - i s dr i ven by

i a s t r i v ef oreconomy of t hought f roms p e c i f i cobservat i ons t o gener al model sor t heor i es ) any model or t heor y compressi ng t he descr i pt i on and si mpl i f y-i ng t he comprehensi on of present or past observat i ons can be consi der ed ass c i e n t i f i c

i i a s t r i v ef or predi ctabi l i t y f romgener al model s or t heor i est o s p e c i f i cobser va-t i o n s ) any model or t heory mus t be abl e t o be conf r ont ed t o s p e c i f i cpast orf u t u r eobservat i ons

The obj ect i ves of syst ems sci ence are s t i l lt he same as s t a t e dal most 40 years agoby t he Soci et y f or Gener al Sys t ems Research t o i nv es t i gat et he i somor phy of concepts, l aws and model s f r o mvar i ousf i e l d s ,and t o hel p i n usef ul t r a n s f e r sf romone f i e l dt o anot her

t o encourage devel opment of t heor et i cal model s i n f i e l d swhi ch l ack them3 t o m ni m ze dupl i cat i on of t heor et i c ale f f o r t si n d i f f e r e n tf i e l d s ,and4 t o pr omot e t he uni t y of sci ence t hr ough i mpr ovi ngcommuni cat i ons among

s p e c i a l i s t s

I f we want t r a n s d i s c i p l i n a r yquest i ons t o be t aken s e r i o u s l yby t he t r a d i t i o n a lcompar t ment s of s c i ence,we must be abl e t o produce sys t ems t heor i es ,whi charemore than si mpl i f i eddi agrams of f eedback l oo ps ,verbal st r eams of syst ems j ar gonor t e r r i b l ycompl i cat ed s e t s of d i f f e r e n t i a lequat i ons wi t hout any reference t oexperi ment al data To put i t i n a mor e f ashi onabl e way, sc ien t i f i c systemmodel s or t heor i esmust bef al s i f i abl e i n t he sense of Popper Thi s c r uc i alaspect of sci ence i s unf or t unat el yq u i t eoften negl e c t ed ,not onl y i n syst ems l i t e r a t u r e

Empi r i cal observat i ons of Par et o- Zi pf di st r i but i ons

2. 1 Par et o, t he di str i but i on of i ncomes i n economc sys t emsThe f i r s text ensi ve di scussi onof t he pr obl emhow i ncome i s d i s t r i b u t e damong t hec i t i z e n sof a s t a t ewas made by Vi l f redoParet o[ 9] i n 1897 On t he bas i sof dat acol l ected f r o mnumer ous sour ces Par et o ar r i ved at t he f ol l owi ngl aw

I n al l pl aces and at al l t i mes t he d i s t r i b u t i o nof i ncome i n a s t a b l eeconomy,when t he o r i g i nof meas ur ement i s at a s u f f i c i e n t l yhi gh i ncome l e v e l ,wi l lbegi ven appr oxi mat el y by t he empi r i cal f or mul a 1 ) n = a S**Ywher e n i s t he number of peopl e havi ng t he i ncome S or gr eat er ,a and y areconstants

1


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Fi gur e 1 I ncome di s t r i but i oni s an exampl e of a skewed or l ong- t ai l ed di s t r i but i on

2

1 000 000

[Number o persons]mw t a x a b l e m

I ncome di s t r i but i onexampl e of

l ong t ai l ed behavi our

S t a x bl ei ncomeIi ncome[monetaru uni t s]

o 1 2 3 4 5

Not e t hat i t i s d i f f i c u l t to represent t he data graphi cal l y w thi n ordi nary ari thmeti c scal es The data are

t axabl e i ncomes of 937 i n France but any other count ry and year yi el ds di s t r i but i onsof t he above type

I t i sext r emel y i n t e r e s t i n gt o n o t e t h a t empi r i cal obser vat i onsof Par et od i s t r i b u t i o n sare i not mar kedl y i nf l uenced by t he soci o- economc s t r u c t u r eof t he communi ty

under st udyi i not mar kedl y i nf l uencedby t he d e f i n i t i o nof i ncome

The Pareto l aw hol ds f ora f ewhundr ed burghers of a c i t y s t a t eof t heRenai ssance

up t o t he more t han l oo ml l i on t axpayer s i n t he USA E s s e n t i a l l yt he same l awcont i nues t o be f ol l owedby t he d i s t r i b u t i o nof i ncome despi t e t he changes i n t hed e f i n i t i o nof t h i s t e r m

Not e t h i s empi r i cal evi dence i s a cont r adi ct i ont o any i deol ogys t r i v i n gf or equald i s t r i b u t i o nof i ncomes As we s ha l lsee bel ow t h i s goal i sj u s tas u n r e a l i s t i candunnat ur al as t he goal t o make al l c i t i e s of a country of t he s ame number ofi nhabi t a nt st o make al l busi ness f i r m of equal s i z eor t o us e i n a t e x t al l wor dsw t h equal f r equency

Pareto was i nt r i guedby t he gener a l i t yof hi s di scover y These r e s u l t sare very r emar kabl e I t i sabsol ut el y i mpossi bl e t o admt t h a t t hey ar e due onl y t o chance Ther e i smos t c e r t a i n l ya cause whi ch pr oduces W endency of i ncomes t o arranget hemel ves accor di ng t o a c e r t a i ncurve.


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Fi gur e2 The dat a of Fi gur e 1 i n a l og- l ogpr esent at i on y s t he exponent of t hePar et o- Zi pfl aw Note t he al most per fec t cor r el at i on coef f i ci ent

. 2 Auer bach t he di s t r i but i on of c i t ysi zes i n count r i esLooki ngf or a new measur e f orpopul at i onconcent r at i on Auer bach[ 1] anal yzed t hed i s t r i b u t i o nof c i t i e swi thi na count r y He r anked t he c i t i e s i n decr easi ng or der ofi nhabi t ant s and di scover ed a r e l at i ons hi pbet ween r ank and s i z eof t he type 2 SG a b e t

wi t h S j t he s i z eof t he c i t yr anked j a and beta are constants .

100000

ncom d stri buti onl og l og pr esentati on

10000

y 39

10000

coefficient999

[numer of persons]

w t h i ncom 5

1000

I oni c

s . t axabl e i ncomeunlts

100

10 Door 100 000 1 000 000


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Fi gur e 3 shows t he same dat a as i n Fi g 2 af t er nor mal i zat i on The graph shows t hecumul at i ve pr obabi l i t y as a f unct i on of t he di mensi onl ess symptom S So S i s t he i ncome and So t he l owest i ncome of t he obser ved set For transdi sci pl i nar y compar i sons we pr ef er t he nor mal i zedpr esent at i on

s an exampl e l etus consi der t he c i t y s i z ed i s t r i b u t i o nof France s ee a l s oFi gur e4 :

Tabl e 1 Exampl e o a r ank si ze di st r i but i on

t

13

I ncome di s t r i but i ondi mensi onl ess

1 l og l og presentat i on

001 y= 39

.099

P r obabi l i t y observea val ue > S So

0,001

00001

S/So dimensionless

000001

i 0 i 0 0

Ci t y s i z ed i s t r i b u t i o n Rank Si z e

SPar i s 1 8 549 898Lyon 2 1 170 660Mar sei l l e 3 1 070 912Bor deaux 4 935 882Toul ouse 5 612 456


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Fi gur e 3 shows t he same dat a as i nFi g 2 after nor mal i zat i on The graph shows t hecumul at i ve pr obabi l i t y as a f unct i on of t he di mensi onl ess symptom S/ SoS s t he i ncome and So t he l owest i ncome of t he obser ved sec For transdi sci pl i nar y compar i sons we pr ef er t he nor mal i zedpr esent at i on

01

0 0001

0 00001

P r o b a b i l i t yt o obser ve

a val ue > S So

I ncome di s t r i but i ondi mensi onl ess

l ug l o g presentati on

I nmme I ol di me~si oni ess]

l oo

s an exampl e l e t us consi der t he c i t y s i z e di s t r i but i onof France s e e a l s oFi gur e4

Tabl e 1

Exampl e o a r ank si ze di st r i but i on

Life Symptom the Behavi our of pen system w th Li mted Ener gy D ssi pati on Capaci ty and Evol ut i on

13

C i t y s i z ed i s t r i b u t i o n Rank Si zeS

P a r i s 8 549 898Lyon 2 170 660Mar sei l l e 3 070 912Bor deaux 4 935 882Toul ouse 5 612 456


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Fi gur e5 Dat a of F i gur e 4 t r ansf or med t o t he nor mal i zed domai n of pr obabi l i ty S i sthe c i t y - s i z eand he s ma l l e s tor t hr eshol d si ze f or c i t i e s(here 1 000)

3 W l l i s - Yu l e , t he di st r i but i on of speci es, gener a and f am l i es i n bi ol ogi calsyst emsBased on f i e l dobservat i on i n Ceyl on i n 1912 W l l i s [ 1 5 ] f i r s t not i c ed tha t t hed i s t r i b u t i o nof speci es wi t hi n t he gener a of an ecosystem f ol l ows a r e g u l a r i t ywhi ch i s of t he Par et o- Zi pf type

t h i s type of cur ve hol ds not onl y f or al lt he gener a of t he wor l d, but a l s of oral l t he i ndi vi dual f a m l i e sboth of p l a n t sand ani mal s, f orendem c and non- endem cgener a, f or l oc alf l o r a sand f aunas i t obtai ns too f or al l t he deposi t s of Te r t i a r yf o s s i l sexam ned Furtheranal ys i sof dat a have shown[ 20, 21] , t h a tsi ml ar r e g u l a r i t i e shol d a l s of or t hed i s t r i b u t i o nof par as i t eson hos t s t he d i s t r i b u t i o nof i ndi vi dual swi thi nspeci es andt he d i s t r i b u t i o nof gener a wi thi nf a m l i e sof any obser ved ecosystemat any t i me

. 4 Z i p f t he di st r i but i on of words i n l anguagesI n hi s magnum opus Zi pf [ 23] r e p o r t sr e g u l a r i t i e sof t he above type f or a wi devar i ety of f i e l d s but hi s mai n i n t e r e s ti s human l anguage f or whi chhe anal yzedwor d- f r equencyd i s t r i b u t i o n s

J ames J oyce s Ul ysses i s t he r i c hes t known t ex t wi th al most 30 wor ds andwor d occur r enci es r angi ng f r o m t o 2 653 The empi r i cal d a t acan be appr oxi mat edal most t oo p e r f e c t l yby a Par et o- Zi pf d i s t r i b u t i o n Zi pf f ound r e g u l a r i t i e sof s i m l a rtype f oral l types of Engl i sht e x t f or al l types ofl anguages and f or al l t i mes, even f or Chi nese t e x t and a l s of or spoken l anguageof chi l dr en of d i f f e r e n tages The exponent 7 i s i n al l cases c l o s et o 1 The onl y except i ons reported by Zi pf ar e t e x t swr i t t en by schi zophr eni cs ands c i e n t i f i cEngl i sh

nor mal i zed

Pareto di str i buti onof c i t i e s

1 94

_ cor r el coef 985

~s =eo __

1 _

Ci t y si z e S/ SoI di mensi t mesel

t o 1 1


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Fi gur e 6 Speci essi ze di st r i but i on of Macr ol epi dopt era, data from20 , t ransf ormed t ocumul at i ve probabi l i t y domai n 15 609 i ndi vi dual s were captured bel ongi ngt o 240 speci es

bi ol ogi c als pec i es - s i z ed i s t r i b u t i o n

gamma = 36

Conel . we11 0 975

s number o n di vi dual swthi n a speci es

10Q

Fi gur e 7 Wr d counts f or texts i n any l anguage yi el d Paret o Zi pf di st r i but i ons I nnormal i zedf orm t he graph shows the probabi l i t y of a wor d t o occur mor e thanS t i mes i n t he text

0,01

0 1

0, 0001

J ames J oyce s Ul ysseswor d count s

wor d occurence S number

r 099

Correl . coeff = . 0999

1 1 1 19W0

I n thi s part i cul ar case S = S/ So, s i nce t he l owest occur r ence of a word So - 1 For exampl e t he wordQuarks occurs onl y once i nt he enti re t ex t Dataf rom Zi pf 23 ,t r ansf or med t o cumul at i ve probabi l i ty domai n


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Zi pf a l s or e p o r t s t ha t t he d i s t r i b u t i o nof s c i e n t i s t swi t hi na research di sci pl i nei s ofParet o- Zi pf t ype The observed symptom of a s c i e n t i s ti s measur ed as t he numberof c i t a t i o n si n t he physi cal or chemcal a b s t r a c t s

W i t i n gt h i spaper , t he f i r s taut hor has di scover edt h a t t he s i z e - d i s t r i b u t i o nof pro-gr ams on t he hard di sk of a comput er ar e of Par et o- Zi pf t ype Pr ogr am si ze i s

measur ed i n ki l obyt es

For PC u s e r sone has t o combi neEXE

and OM

i l e s i norder t o observe an al most per f ec tr e g u l a r i t y

. 5 Si mon, t he s i z ed i s t r i b u t i o nof busi ness f ar msHer ber t Si mon, who won t he nobel p r i z ef or economcs i n 1978, has i nt ensi vel yst udi ed f i r m s i z e s Whet her sal es asse ts number of empl oyees , val ue added, p r o f i t s or c a p i t a l i z a t i oar e used as a s i z emeas ur e, t he observed d i s t r i b u t i o nal ways ar e of t hePar et o- Zi pftype Thi s i st r u ef or t he dat a f or i ndi vi dual i ndus t r i es economc s e c t o r s and f oral l i ndust r i es taken t oget her t hol ds f ors i z es of pl ant sas wel l as of f i r ms[ 13] Take any annual number of t he For t une 500 magazi ne and you c an v e r i f yt h i sas s er t i on whi ch a l s ohol ds f or any na t i on aleconomy and a l s o f or mul t i nat i onalcompani es on a wor l d l ev el

We have anal yzed t he For t une data over a per i od of 30 years[ 17] and f ound, t h a tt he par amet er y of t he s i z e - d i s t r i b u t i o n sr emai ns al most const ant Thi s s e l f - s i m l a r -i t y of t he d i s t r i b u t i o ncurves hol ds i n per i ods of ov er al leconomc gr owt h as wel l

as i n per i ods of economc r ecessi on and despi t e t he f a c t tha tf i r ms appear

anddi sappear From he 50 l a rg e s ti ndus t r i alf i r ms i n 1954 onl y 20 can be f ound amongt he 50 l ar ges t3 decades l a t e r t he o the r30 have decl i ned i n s i z e been absor bed i nmer ger s and ac qui s i t i onsor si mpl y have gone out of busi ness On t he ot her hand,12 of t he 50 l ar ges tf i r ms wer e not even ranked among t he 500 l ar ges ti n 1954 ordi d not even ex i s tat t h a t t i me

To obser ve a const ant s i z e - d i s t r i b u t i o ndes pi t et h i si nt ens i ve s huf f l i ngar oundwi t hi nt he systemi s q u i t er emar kabl e

As Her ber t Si mon s t a t e di n t he concl usi onof hi s paper We need t o know mor eabout t he r e l a t i o n sbet ween t he d i s t r i b u t i o n sand t he gener at i ng processes

Si ncet he gr aphs of t he empi r i cal dat aar emonot onousl ys i m l a r we w i l lnot bur dent he r eader wi t h exampl es

Over t i me t he Par et o- Zi pf l i n e seems t o ac t as an at t r act or f or devi at i ng

poi nt s [ 17]

For exampl e i n t he comput er i ndus t r ywe hada s i m l a r s i t u a t i o nas i nt he case of t he l ar ges tFrench c i t i e si n Fi gur e I M was t oo bi g and t he nextt en f ol l owi ngcompani es wer e too smal l The evol ut i on of t hel a s t 10 year s hasbr ought t he devi at i ons al most back i n l i n eagai n due t o i a r e l a t i v edecl i ne of t he gr owt h r a t e of I Mi i an above aver age gr owt h r a t e of E si i i several mer ger s and ac qui s i t i onsamong t he t op comput er compani es


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Fi gur e 9 The same dat a as i n Fi gur e 8 as a nor mal i zed Par et o- Zi pf di st r i but i onr eveal i ng a d i s t i n c tquant i t at i v e r egul ar i ty

. 8 Cempel , t he di st r i but i on of vi br at i onampl i t udes i n mechani cal machi ne sys t emsResear ch i n t he f i e l dof vi br at i on di agnos t i c s [ 4]has r eveal ed t h atl o n g - t a i l e dPar et o- l i ked i s t r i b u t i o n sar ea good appr oxi mat i on f or the data yi el dedby empi r i calmeasur ement s of vi br at i on sympt oms f or a s et of r unni ng machi nes t he r e g u l a r i t i e sar e obser ved i ndependent l y of t he machi ne type e l ect r omotor s,di e s elengi nes .

. 9 Do we l i v e i n a Par et o- Zi pf wor l d?

The observat i on of s i m l a rphenomena f or i ncomes, c i t i e s s pe ci e s wor ds, e a r t h -quakes, chemcal el ement s, machi ne v i br a t i ons how can t h i spossi bl y make sense?

3 Model s expl ai ni ng Par et o- Zi pf di st r i but i ons

3 Mat hemat i cal f orm of t he di str i buti ons: l i m t sof empi r i cal curve- f i t t i ngA var i et y of mat hemat i cal d i s t r i b u t i o n shas been pr oposed t o f i t empi r i cal l ongt a i l e d d i s t r i b u t i o n sof t he di scussed t ype Quandt [ 111 compar ed mor e than 8d i f f e r e n tmat hemat i cal f unct i ons and comes t o t he concl usi on, tha t al l t he pr oposedl aws ar e ver y si ml ar I f one l aw y i e l d sa good adj ust ment of t he data then t h i s i sa l s o the case f or sever al other l aws

Sear chi ng f or best empi r i cal f i t s does not l eadt o a be t t e r compr ehensi on of t heobser ved phenomena Unl ess t h e r ei s strong t heor et i c alevi dence, t he most si mpl e l aw l i k e t he Par eto- Zi pf d i s t r i b u t i o ni s t o be preferred t o mor e compl i cat ed

L i f e Symptom t he Behavi our of Open System w t h Li m t e d Energy Di ssi pat i onCapaci t y and Evol uti on

9

chemcal el ement sI n t he uni verse

s- _

1

146

Con coef f 977

/ So r e l a t i v eabundance of el ement He

H 1


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Fi gur e 9 The same data as i n Fi gur e as a nor mal i zed Par et o- Zi pf di s t r i but i onr eveal i ng a di s t i nc t quant i t at i ve regul ar i ty

chemcal el ement si n t he uni verse

S/ So r e l a t i v eabundance of el ement

f

1 8 Cempel , t he di s t r i but i onof vi br at i on ampl i t udes i n mec hani cal machi ne systemResear ch i n t he f i e l dof vi br at i on di a gnos t i c s[ 4]has r eveal ed, t h a t l o n g - t a i l e dPar et o- l i ked i s t r i b u t i o n sar e a good appr oxi mat i on f or t he data yi el dedby empi r i calmeasur ement s of vi br at i on s ympt oms f or a s et of r unni ng machi nes :t he r e g u l a r i t i e sare obser ved i ndependent l y of t he machi ne type e l ect r omot or s,di e s elengi nes

. 9 o we l i v ei n a Par et o- Zi pf worl d?The obser vat i on of s i ml ar phenomena f or i ncomes, c i t i e s s pe ci e s wor ds, e a r t h -

quakes, chemcal el ement s, machi ne vi br at i ons: how can t h i s possi bl y make sense?

Model s expl ai ni ng Par et o- Zi pf di str i but i ons

3 Mat hemat i cal f orm of t he di s t r i but i ons: l i m t sof empi r i cal curve- f i t t i ng v a r i e t yof mat hemat i cal d i s t r i b u t i o n shas been pr oposed t o t empi r i cal l ongt a i l e dd i s t r i b u t i o n sof t he di scussed type Quandt [ 1l l ] compar ed more t han d i f f e r e n tmat hemat i cal f unct i ons and comes t o t he concl usi on, t h a t al l t he pr oposedl aws ar e very s i ml ar I f one l aw y i e l d sa good adj ust ment of t he d a t a then t h i s i sal so t he case f or sever al other l aws

Sear chi ng f or best empi r i cal t s does not l e a dt o a b e t t e rcompr ehens i on of t heobser ved phenomena Unl ess t h e r ei s strong t he or e t i c alevi dence, the mos t si mpl e l aw l i k e t he Par eto- Zi pf d i s t r i b u t i o ni s t o be preferred t o mor e compl i cat ed

L i f e ymptom the ehavi our of open ystem w th Li mted Energy D s si pat i mCapaci t y and Evol ut i on

19


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3 . 4 Mandel br ot - W ni war t er : f i r s t at tempt , a h o l i s t i cext remum pri nci pl eMandel br ot , t he i nvent or of Fractal s[ 7] , has st udi ed i n detai l t he theory of codi ngand gi ven an expl anat i on f or t he regul ari t i es of word count s i n t er ms of an extre-mum r inciple w t h i n a t e x t the quant i t y to be opti m zed mni mzed i s t he aver age cost perword

Assumng that t he cos t of a word dependson t he cost s of i t s const i t ut i ng

l e t t e r s Mandel brot showed t ha t t he resul t i ng opt i mal di st ri buti on i s of t he Pareto-Zi pf type Based on a general pri nci pal of evol ut i on or sel f - organi zat i on whi ch s t a t e s that t hecompl exi t y of a sel f - organi zed system can onl y grow or remai n const ant f i r s tl awof genesi s) [ 19] , we put f or war d t he hypot hesi s, that Par et o- Zi pf type di st ri but i onsare common to al l processes of sel f - or gani zat i on ( second l aw of genesi s) [ 20] Gener al i zi ng Mandel br ot s argument s from words to energy quant a, we specul at ed,that t he observed Par et o- Zi pf regul ari t i es are the r e s u l t of a gener al ext remum

pri nci pl e, whi ch maxi mzes what we have cal l ed t he energy redundancy ( bi ndi ngenergy or s ynergy) w t hi n a sel f - organi zed systemThi s approach seems very gener al and a t t r a c t i v e however - besi des f or s ys t ems ofnucl eons - i t i s d i f f i c u l tor i mpossi bl e to veri f y

3 5 Roehner - W ni war t er : second at t empt , Pareto Pareto = ParetoThe Gauss i an di st ri but i on i s known to be a l i m t di st ri buti on of random var i abl es I t i s wel l known that t he r andom sum f two Gauss i an di st ri but i ons G and G2

yi el dsa new di st ri buti on G3 whi ch i s al so Gauss i an

G GGI t i s t oo general l y ass umed, t ha t t h i s property i suni que f or t he di st ri but i ons cal l ed nor mal , bel l - shaped or Gauss i an We have shown that Pareto di stri buti ons are possi bl e l i m t di st ri but i ons of sums ofrandom var i abl es[ 16] The random sum f t wo Paret i an di st ri but i ons P, and P2 yi el ds a new di st ri but i onP whi ch i s al so Paret i an P, P2 = P3

Based on t h i s s t a t i s t i c a lstabi l i ty of Pareto di st ri but i ons, we have expl ai ned t hes t a b i l i t yof empi r i cal di st ri but i ons as t he resul t of a st ochast i c process

St taSt

The di st ri buti on at t i me t +l depends on t he di st ri buti on at t i me t mul t i pl i ed by af actor a characteri zi ng t he t o t a l growth of t he system pl us a devi at i on A added atrandomI f t he i n i t i a l di st ri but i on i s Paret i an and i f t he di st ri buti on of f l uctuat i ons A i sParet i an, then the resul t i ng di st ri but i on must al so be Paret i anThi s s t a t i s t i c a ls t a b i l i t yi s cert ai nl y an i nterest i ng and i mpor t ant f eature, expl ai ni ngt he ext r eme per s ever ance of Pareto- di st ri but i ons over t i me, but i t does not expl ai ni n a sat i sf actory way thei r ori gi ns Stat i ng that every observed regul ari t y i s t he st ochast i c resul t of pri or regul ari t i es,can be mat hemat i cal l y correct, but i s not a very sati sf yi ng expl anat i on

E l i

2 1


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W t h respect t o our f i r s tat t empt however , i t has become c l e a r ,t h a t t he f ol l owi ngf e a t u r e sar e c h a r a c t e r i s t i cf or Par eto- Zi pfr egul a r i t i e s i nal l obser ved f i e l d s

Fi gur e 10 Thr ee l e ve l d e s c r i p t i o nof ahi e r a r c hi c alsystem el ement s /quanta s ma l ldots ,e. g i n ha bit a n t s , uni t s do t t edc i r c l e s ,e. g ci t i es ,system f at c i r c l e ,e. g country)

4 The TV model L i f e and death of machi nes

i 3 l e ve lhi er a r c h i c aldescr i pti on s eeFi gur e 10+- el ements or quanta uni t s systemwi t h obser vabl e boundar y

i i b i r t hand death of uni t sas p a r t of ani r r e v e r s i b l eevol ut i onar y process

i i i h o l i s t i cor gl obal system behavi our ener gy opti m zati on)

3 . 6 Cempel - Wni war t er t h i r dat t emptopen ener gy t r ansf or mat i on sys t emswi th l i m t e d di ssi pati oncapaci ty

I n the f ol l owi ng we present a modelwhi ch has been o r i g i n a l l ydevel oped toexpl ai n t he obser ved s ympt oms of r un-ni ng machi nes of equal type We s h a l lthen gener al i zethe ass umpt i onsof t he machi ne model t o any systemofener gy t r ansf or mat i on uni t s

The wear of a machi ne, and thus i t s condi t i on, i s r e l a t e dt o t he ener gy di ssi pated i nt he t r i bo- Vbr o- acoust i calprocesses t aki ng pl ace wi thi n the machi ne Tr i bomeansr ubbi ng, Vi br omeans v i b r a t i n gand Acoust i cal means noi se j us tthi nk of the br eak-down of your l a s t c a r

Thi s appr oach was t he bas i s f ort he el abor at i on of t he TVA machi ne model i na na l yt i c alf o r m The model al l ows t o determne t he condi ti on of a machi ne f r o m pass i ve di agnost i c exper i ment s i . e measur ement s whi ch ar e non- dest r ucti veandwhi chdo not i nt e r r uptt he r unni ng of the machi ne) and i t may be used f orcondi t i onf or ec as t i ng[ 3]

4 1 A s i n g l euni t r unni ng t o death a machi ne as an open ener gy t r ansf or mat i onsystem

W descr i be a mechani cal machi ne as an open system i n t er ms of ener gy f l ows The ener gy f l ows cover al l types of ener gy such as k i n e t i cener gy and chem calener gy Ti me i s meas ur ed as i nt e r na l t i me f the system l i f e Ener gy f l ow per i nt e r na lt i me uni t i s expressed i n t er ms of power dE d

Peter Wni warter abd Czesl aw Cempel


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For exampl e mcro- f i ss i onsaccumul at e, f orm ng bi gger and bi gger macr o- f i ss i ons When one of t he macro- f i ssi ons covers at l e a s th a l ft he di amet er of a r o t a t i n ga x i s ,t he systembreaks down s ee Fi gure 14 bel ow)

Fi gur e 14 I nf ra- St ruct ures or I n- For mat i on m c r o f i s si ons as an exampl ef or t he

acc umul at i on of i nt ernal structure

i ndependent i sl ands of m c r o f i s si ons l ef t grow i n t o a cont i nuous macr o- f ass i on l eadi ng t o t he breakdown oft he s t ruc ture r i g h t

The d i f f e r e n t i a li ncr ement of i n t e r n a l l yaccumul at ed di ssi pat ed energy i s f or mal l y

2 dF, . [ 0, V O) ] =

s ot [ O, V O) ] dO+- sE, . , [ O. V O) ] dV60 6V

Repl aci ng on t he r i g h thand s i d eF, accor di ng t o expressi on 1 we gete

3 dEj O, V O) ] = D[O V O) ] dO+SVf P[O V O) ]d0}dV

I t i s known f r o mt r i bol ogy,t h a t t he i n t e n s i t yof t he i n t e r n a lwear process i t spower

D) i s gover ned mai nl y by t he power V of t he ext er na l l y di s s i pa t e dout put v i b r a -t i o n ,heat et c.

4 D[ O, V O) ] = D[ V O) ] + D[ O, V O) ] w t h e

We t heref ore can assume i n t he f i r s t approa , t h a t t he t ransf ormat i on l aw ofi n t e r n a l l yaccumul at ed d i s s i p a t e dpower and ext ernal l y d i s s i p a t e dpower V s

24 P W ahd C esl aw empel


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cons tant dur i ng t hel i f et i me of t hesystem hence i s not a f unct i onof 0 and canbe r epl acedbyThi s s i mpl i f i esexpr essi on 3 end we get

5 dEj O, V o) ] = D[O V O) j dO+0dVD[V 0) ]dV

as expr essi on f or t hed i f f e r e n t i a lbehavi our of i n t e r n a l l yaccumul at ed d i s s i p a t e denergy

4 3

Wear ampl i f i es wear , pos i t i vef eedback l eadi ng t o aut ocat al yt i c or non-l i near behavi ourPost ul at e 2 The ext er na l l y di s s i pa t edpower V s pr opor t i onal t o t he amount ofdi ssi pat ed energy Ein accumul at ed i n t e r n a l l y:

6 dV 0) a dE, a , O

w t h a = constant at f i r s tapproach

Thi s means , t ha t t he el ement ar y i nc r e as eof i n t e r n a l l yaccumul at ed di ssi pat edenergy dE a O i s r e l a t e dt o t he energy o r power ) i ncrease of external d i s s i p a t i o ndV O , by t he conver si onc o e f f i c i e n taRepl aci ngt he d i f f e r e n t i a ldE, , O) i n 6 accor di ngt o 5 we obt ai n

7 dv 0) = a{D[O V 0) j d0+0 d D[ V O) ] dV)

and t he d i f f e r e n t i a lequat i on f o r external d i s s i p a t i o npower 8) dV O) _

aD[ O, V 0) ]d0

I - - a 0dVD[ V O) ]

4+4 Breakdown t i me

The denom nat or of 8 vani shes f orae d [ V 0 ]=

Accor di ngt o our assumpt i ons a and ar e const ant over i n t e r n a lt i me and we candef i ne t he breakdown t i me b

9) b =

= dE,

aO

d [ V 0 ]dD

dVAs t i s seen , t he br eak down t i me determned by t he i n t e r n a ls t r u c t u r eof t hesystemand t he way of energy d i s s i p a t i o ni n s i d et he system

4 5 D f f er ent i al equat i on gover ni ngdi s si pat i on r -I nt r oduci ng 9 i n t o 8 we get

L i f e Symptom t he Behavi our of Open System w th Li m t ed Energy D s si pat i onc apac i t y and Evo l ut i on

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10 dV( O)aD[ O, V( O) ]

dO 1- 010Sol vi ngequat i on 10 wi t hrespect t o i n t e r n a l l yaccumul at ed di ssi pat ed power D weobt ai n

11 D 0Do

1- O/ Owi t h 0 5 O < O and D t he i n t e r n a l l ydi ssi pat ed power D t t i me 0 - 0

Wth respect t o external d i s s i p a t i o npower V we obt ai nV

( 12

V( 0)

1- b

wi t h 0


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Fi gur e 15 L i f e t i me behavi our of sympt oms of wear Every type of symptomappr oaches i n f i n i t eval ue asympt ot i cal l y at t he vi ci ni t y of t he breakdownt i me O Ob 1 The l e s s t he val ue of t he exponent T, t he more sensi t i ve i st he symptom

12, 00 -

10, 00 -

E 6, 00 -

6, 00 -

v

4, 00-

2 W -

7

Sympt om i f ecurve

y=2

O Du

0, 1

0, 2

9

0, 4

0, 5

0, 6

0, 7

0, 6

0, 9

dl mem onl ess L i f e t i me

I n the case of machi nes, t hese component s i nf l uenci ngt he l i of a machi ne, maybe smal l di f f er ences i n q u a l i t y a Monday c ar ) , di f f er ences of f oundat i ons s u p p o r t ) ,di f f er enc esi n l oad i n t e n s i t yand di f f er ences i nt he q u a l i t yof mai nt enancef or t he i ndi vi dual uni t s ,t o name onl y t he most i mpor t ant

For one u n i t , these component s and many ot her f a c t o r s ,m ght be known andconsi der ed as de t er mi ni s t i c For a gr oupof uni t s ,we have t o acknowl edge t hem as

r andom due t o our l ack of know edge Taki nga s t a t i s t i c a lappr oach i nst ead of t he det er mi ni s t i cone, we consi der a gr oupof N d i f f e r e n tuni ts of t he same type bei ng each at d i f f e r e n tl i f e - t i mest age Measur i ngt he empi r i cal symptom val ue S, f or each u n i t ,we can make an orderedempi r i cal s t a t i s t i c sof the t ype

15) P( Sc S) = r p( S) dSc = nS > S)

I N

Were P( S S) i s t he cumul at i ve p r o b a b i l i t yt o obser ve empi r i cal symptom val uesS, whi ch ar e g r e a t e ror equal t o a pr escr i bed val ue S, and n i s t he number ofmachi nes w t h t h a t property The cumul at i ve p r o b a b i l i t yP can be expr essed_as t he probabi l i ty densi ty p(SJi nt egr at edf r o mS upwar d t o i n f i n i t y For a gi ven s et of d i s c r e t eobser vat i ons, we approxi mat e t h i s i nt egr alby t he r a t i o

L i f e Sympt mns t he Behavi our of Open system w th Li mted Energy Di ssi pat i onCapaci t y and Evol uti on

7


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of u n i t sn wi t h an observed symptom al ue super i or or equal t o S, di vi dedby t het o t a lnumber of uni t sobserved NNot e: i n engi neer i ng t he p r o b a b i l i t y 15 s c a l l e dr e l i a b i l i t y; t i s si mpl y anempi r i cal est i mat e f or t he c o r r e c tf unct i oni ng of a machi ne f orwhi ch t he observedsymptom S exceeds a val ue SThe general s t a t i s t i c a lr e l at i ons hi p[ 8] 16 p S dS

=p O

dOgi ves us t he p o s s i b i l i t yt o c a l c u l a t et he probabi l i t y densi t y i n t he t i me domai n Oand i n t he symptom domai n SFor t he symptom domai n we get

17 P S = p Oa

wher e p O i s t he densi t y of obser vat i on i n t he t i me domai n The der i vat i ve

can be cal cul at ed f r o mt he symptom i vecurve 14 as Y i

d SoS18 T

We as sume t he densoty of empi r i cal obser vat i ons t o be of t he f o r m

19 p O =

S30 ; wi t h n Z

Put t i ng now 19 and 18 i n t o 17 and t he r e s ul t i n t ot he i nt egr alof 15 one canf i nd f or t he cumul at i ve symptom d i s t r i b u t i o n

20 P Se 2 S =YSol

Sa dS~ =d

Y SaSz S

One can see f r o mabove, tha t i ndependent l y of t he way of obser vat i on - t heexponent n i n 19 t he cumul at i ve symptom probabi l i t y di s t r i but i on i s of

Pareto type For t he si mpl est condi t i on, wher e t he f r equency of obser vat i ons of a uni t i s notr el at ed t o t he sympt oml i f e behavi our n = 0 , one can obt ai n t he f ol l owi ngbehavi our f or t he cumul at i ve symptom di s t r i but i on

Y

21 P S, = ~ =~Sal

; wi t h Y>

; wi t h yandn2

dOdS

Thi s means : i f t he sympt oml i f e curve of a uni t i s of t he type 14 due t o a

l i m t e d po t e nt i a lof energy d i s s i p a t i o n then t he cumul at i ve di s t r i but i onof

symptom f or a group of uni t s wi l l be of Pareto type

4+8 I nf er ence: pr edi ct i ve powerAccor di ngt o our theory t he exponent Y i n 2, 1 s t he same as t he exponent Y i n 14 and r e l at est he behavi our of a s et of u n i t sof a systemat a gi ven t i me wi t h t heaver age behavi our of a s i n g l euni t over t i me

28

Peter w ni warter and Czesl aw Cempel


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I n pr ac t i c e,havi ng det er m ned t he exponent y f r om an empi r i cal cumul at i vesymptom di s t r i but i on 21 ,we can predi ct t he average behavi our of a gi ven uni tus i ng the symptom i f ecurve 14I f one can observe several sympt oms of evol ut i on of t he same system havi ngdet er m ned t h e i ry val ues, one can choose t he mos t s e n s i t i v esymptom based on t hep r i n c i p l eof m ni mal y val ue[ 4]

For exampl e, i n t he f i e l dof econom cs we observe f ort he f i r ms of a gi ven countryr e gul ar i t i esof t ype 21 f or annual s al es ,p r o f i t s ,number of empl oyees , c a p i t a l i z -a t i o n et c Accordi ng t o our t heory, these ar e di f f er entsympt oms of t he sameunder l yi ngenergy t r ansf or mat i on process For pr edi cti onwe shoul d s el ec tt he mos ts e n s i t i v esympt om . e t he one w t h t he l owest y val ue Mor eover , havi ng det er m ned t he m ni mal y s ympt oms f or syst ems of d i f f e r e n tn a t u r e ,l i k et he exampl es shown i n t h i spaper , we can t r yt o drawsome concl usi onsas bel ow

At hand of t he above exampl es, we have shown t he gener al p o s s i b i l i t i e sof ourt heor et i c alappr oach, but we l eave i t t o t he s pec i al i s t sof a gi ven f i e l dof s c i e nc e ,t o do amore i n dept h anal ys i s

5 Concl usi on

Al l processes of sel f - organi zat i onor evol ut i onpr oduce sympt oms of t he Par et o- Zi pft ype on any obser vabl e l evelof or gani zat i on second l awof genesi s)

I twas shown here , t ha t t he present at i on of Par et o- Zi pf d a t a i n t er ms of nor mal i zedcumul at i veprobabi l i t y al l ows t o i order d a t a i n a common and compar abl e way For exampl e see t he chem cal

el ement d i s t r i b u t i o n sof Fi gure 8, whi chcan be descr i bed by a si mpl e l awa f t e r or der i ng Fi gur e 9

i i t o make i nf er ences and draw concl usi ons f r o m t he d i f f e r e n tval ues of t heexponent y+ Previ ousl y t hec o e f f i c i e n t sy and P i n Paret o or Zi pf d i s t r i b u t i o n swer e onl y mat hemat i cal f i t t i n gpar amet er s I n our model y has meani ng i nt er ms of energy t r ansf or mat i on and l i f e- t i me

i i i f or an i ndi vi dual u n i t , i n t he pr esent ed model of open syst ems w t h l i m t e dd i s s i p a t i o nc apa ci t y,t he c o e f f i c i e n ty det er m nes t he behavi our over i t s l i f e -t i me s ee t he symptom i f e curve of Fi gur e 15

f h f S h d E C i l i

9

Type of evol vi ngsystem y Pareto comment

Uni ver se chem el . 146 Fi g 9 very ol dBi ol ogi cal s pec i es . 36 F i g 6 ol dUr ban c i t i es . 94 F i g 5 youngLanguage wor ds) 0. 99 F i g 7 youngEconom c i ncomes) 2. 39 F i g 3 very young


22/26

i v i f appl i ed t o a set of uni t s s ys t em , t he model r eveal s Paret o- l i kebehavi our ,not possi bl e t o expl ai n by pr evi ous s t a t i s t i c a lconsi der at i ons see[ 12] f orexampl e) Recent st udi es of t h i s probl em have shown t hat t hi s model gi vesgeneral r e s u l t si n t he f orm of Fr echet di st r i but i ons[ 5] The Pareto di s t r i but i oni s t he asympt ot i cappr oxi mat i onof Frechet onl y

v)

t he coef f i ci enty permts t o make i nf er ences f rom t he obser vat i onof a set of

uni t s concer ni ngt hei r futurebehavi our and t he aver age l i f eext pect anci es of t heuni t s const i t ut i ngt he system

Ref er ences

1 F Auer bach, Das Geset z der Bev6l ker ungskonzent r at i on Pet ermans M t t ei l ungen,r i 1 1913 , 59

2 P Bak and K Chen, 1 ,es syst mes c r i t i q u e saut o-organi ss. Pour l a Sci ence, hors

s er i e,Sept 1991) see al soP . Bak, C Tang and K W esenf el d, Sel f - organi zedc r i t i c a l l y ,Phys . Rev. A 8 1988) 3643 C Cempel , The wear process and t he machi ner y v i b r a t i o n- a Tr i boVi br oAcust i cal

model , Bul l. Pol i s hAcademy of Sci ences, Techn Sc 35 , N 7- 8 1987 , 347- 3634 C Cempel , Condi t i onevol ut i onof machi nesand i t sassessment f r o mpassi vedi agnos-

t i cexper i ment Mechani cal Sys t ems and Si gnal Pr ocessi ng5 1991)5 C Cempel , Damage I n i t i a t i o nand Evol ut i oni n oper at i ng Mechani cal Syst ems

Bul l. P o l i s hAcademy of Sci ences, Techn Sc 40, N 3 1992) , 1-146 C F. Ri c ht er ,El ementary Sei smol ogy, Fr eeman, San Fr anci sco 1958)

7 B Mandel br ot , The Fr act al Geomet ry of Nature Fr eeman, San Fr anci sco 1982)8 Popul i s ,Pr obabi l i t y, Random Var i abl es , St ochas t i cProcesses Mc ; Gr awH i l l ,NewYork 1965)

9 V, P a r e t o , Cour sd Econome Pol i t i que vol 2, book 3 chapt er Lausanne 1897)10 D Pumai n, La Dynamque des Vi l l e s ,Econom ca, Par i s 1982)11 R E Quandt , S t a t i s t i c a ldi scr i m nat i onamong al t e r nat i vehypot hesi s and some

econom c r e g u l a r i t i e s J ournal of Regi onal Sci ence 5 n * 2 1964 , 1-2312 H A Si mon,On a c l a s sof skew d i s t r i b u t i o n s Bi omet r i ka42 1955 ,425- 44013 H A Si mon and C P Boni ni , The s i z e di s t r i but i onof busi ness f i r ms Ameri can

Economc Revi ew 48 1958) , 607- 61714 J St ei ndl ,Random Process and t he Growh of Fi rm Char l es G r i f f i n ,Hi ghWycombe

1965)15 J . C. W l l i sand G U. Yul e,Some s t a t i s t i c sof evol ut i onand geogr aphi cal d i s t r i b u t i o ni n

pl ant s and ani mal s, and t h e i rsi gni f i canceNature 109 1922)16 B Roehner andP W ni war t er , Aggr egat i onof i ndependent Par e t i anrandom v ar i abl es

Advances i n Appl i ed Probabi l i t y 17 1985 , 465- 46917 B Roehner and P W ni war t er , Homeost at i ct endenci es of f i r m- s i z ed i s t r i b u t i o n sand

t he evol ut i onof econom csys t ems Proceedi ngsof t he s ix t h i nt er nat i onal Congress ofCyber net i csand System of t he WOGS 1984) , 999- 1005

18 C B. W l l i ams ,The s t a t i s t i c a lout l ooki n ecol ogy J . Ecol ogy42 1954 , 1-1319 P W ni war t er ,The Genesi s Model Par t Compl exi t y,a measur e f or t he evol ut i onof

sel f - or gani zedsyst ems Spec Sci ence and Technol ogy6 1983) 11- 202 P W ni war t er ,The Genesi sModel Par t I I Fr equencyd i s t r i b u t i o n sof el ement s i ng e l f -

organi zedsyst ems Spec Sci ence and Technol ogy6 1983 , 103- 112

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21 W ni war t er , I so- dynam cs of popul at i on- si ze di st ri but i ons i n hi er ar chi cal systemsProceedi ngs of t he Soci et yf or General Syst ems Research vol l 1985 , 87 95

22 P Wni wart er Si ze- di st r i but i ons and hi erarchi cal cont r ol i n bi ol ogi cal systemsBi ol ogi e Thor i que Edi t i ons du CNRS Par i s 1987

23 K Zi pf , Humn Behavi our and t he Pri nci pl e of l east Effort, ddi son Wesl eyCamri dge Mass 1948

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ppendi x Gener al i zed l i f esymptom

The present ed model expl ai ns t he Par et o- Zi pf r e g u l a r i t i e si n te rm of a gener al pr ocessof evol ut i on

1) Di ssi pat i on

on a mcr o- l evelwe observe t he di s s i pat i onof ener gy quant a

Dependi ng on t he type of energy t r ansf or mat i on, t he uni t accumul at es s t r u c t u r a lquant awi t hi na l i m t e d i nt e r nal pot e nt i a l These i n t e r n a l l yf ormed s t r u c t u r e sare i nf or mat i on i nt he i n i t i a lsense of t he wor d

2) Devel opment on an i nt er medi at e or u n i t - l e v e l ,we observe t he devel opment of uni t sfrom bi r t h t o deat h f ol l owi ng a sympt oml i f e curvei y b i r t hwe underst and t he begi nni ng of a d i s s i p a t i v eenergy t r ansf or mat i on process

wi t hi n a uni t

By deat h weunderst and t he end or br eak- down of t he di s s i pat i veenergy

t r ansf or mat i on process wi t hi n t he uni t i i B i r t hand deat h, and hence l i f e can be observed f or energy t r ansf or mat i on processes

of a nest ed hi er ar chyof energy t ypes el ect romagnet i c, gr a vi t a t i onal ,nuc l e ar ,i nor gani cchemcal , bi o- chemcal , economc, ment al and symbol i c energy

i i i Nat ural deat h o c c u r s ,when i n t e r n a l l yaccumul at ed d i s s i p a t i o nenergy, i t si nf or mat i oni n t he formof s t r u c t u r e ,reaches a l i m t val ue

3) Evol ut i on:

on a met asys t eml evel or macr o- l evel we observei a gl obal opt i mzat i on of energy f l ows l oad opt i mzat i on) f or a s e t of r unni ng or l i v i nguni t s

i i desi gn or code modi f i cat i on f or t he next gener at i on of uni t s adapt at i on) r e- desi gn, compl et e r ecodi ng or code- cr eat i on f oran e n t i r enew t echnol ogy e vol ut i on)

4) Recur si veness I n t h e f i e l dof Geomet r y f r a c t a l srepresent a s e l f - s i m l a r i t yof geomet r i cal shape i ndepen-dent of scal e

I n t he f i e l dof processes, l i k edevel opment and evol ut i on, we can speak of f r a c t a l - l i k eprocesses i. e a s e l f - s i m l a r i t yof s t r uc t ur i ngenergy t r ansf or mat i on processes i ndependentof scal e and type of energy

Tabl e gi ves an over vi ew of t he f i e l ds f orwhi ch Par et o- Zi pf di s t r i but i onsare observed

S t a r sand nucl ear energy t r ansf or mat i onNucl i des and at om are f r ozen i n- f or mat i on of s t a r l i f e - c y c l e s

Pl anet s and i nor gani c chemcal energy t r ansf or mat i onChemcal compounds and bi o- mol ecul es are f r ozen i n- f or mat i on of pl anet l i f e - c y c l e s

Ecosys t em and bi o- chemcal energy t r ansf or mat i onSpeci es and genera of pl a nt sand ani mal s are f r ozen i n- f or mat i on of ecosyst em l i f e -cycl es

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