The Tenth lnternational Conference on lnformation
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‑1‑

CONTENTS
Keyoore speatters
Graph Embedding from Theory to Applications′
団 in King

5

Research Trend on Developing Smart Remote patient Monitoring Systems

forthe COVID‑19 Era and Beyond
Sabatt Moわ ar7′ ηed7

Lea17 Yυ9

丁ime Series Forecasting wlth Artificial Neural Nemorks

MaffPemaricar and Na〔 urar ScFences
An Eslmalon of a Scale Parameter Based on the Fourler‐

Mellin Transformハkira MorimorollUncertainty Principles Related to Fractional Fourier Transforrn

Mawaだ IBaわ ″and RyJIcわ ′ハs力 わ0

15

A Rennark on VVeighted Eslnnates for Mulllinear Founer MulJpliers with

M破 ed Normra
ね and Yoshrroわ Macわ oasわ ′MaF F可 ′19

B:g Data and Machine Learning:A19o「 ithms for Analysis― with Case Studies
yousυ o ZOυ ,と eaわ とυο,andハ r7ne Zο υ

23

A New 2 5D Schema ofthe Regularand semi― regular Polyhedra and T‖ ingsiRο ber C Meυ raρ r

Classes‖ and lV

29

Managemerr arPd socFar ScFences
A Solution fbr Ride‐ sharing Route Choice PrOblern based on Cenetic

Cわ aOZe Song andと e′ L′

A19orithm

35

1ndustrial Neh″ ork and Cluster)Restructuring Production Chain Based onSpecialization and Division of Labour afterthe 2020 Pandenlic
と′Ke

41

■gガ curfure arld Engineerrag
Reduction of Pressing Force and Friction Force in Mi「 o Ultrasonic KnurlingTechnology Creating High Precision Texture
Sわ Oerυ ス0たl Yasυ ρo″ Sa々 a47omOわ Isa raρ aka

‑3‑

57

The Prediction of PM2′ 5 Concentration using an lmproved

Backpropagation

Sた ″Han and le′ たノ

influence of Arbors on indoor Natural Ventilation in Lower

61

Floors of

Bu:ldings by Nume‖ cal SimulationとねO Mir7gcヵ eng,Sυ ng Иわηρel月 o CttenweF

67

Acceleration and Displacement RespOnse Characteristics of System with

Fnclon SutteCted to Random Vibralon(EfFect of Damping Ralo andNatural Penod)′κυrrfa73

月οηg s力 e17

77

Sわ Oe″ ハοれ KarSυAn Approach for Deformed:mage Deteclon with Template Matching

Restitulon CoefFicient at Collision beMeen a Bottom of Sma‖ Structure
and a Plate by Rocking Vibration

Kaお υ177′ κυ″ra,sゎ fge″ ハο層

81

Reduction Method of Residual Stress for VVelding in stainless Steel by
Uitrasonic Vibration
ハkira rVaた azaFQ κυ″ra Kaぉ υmi Sわ oe″ ス。れ S力 rgeο′Kosわ ′ ″υ,Tsuyosわ ′Malsuyama

85

Behavior of Exhibits Fixed with Nylon Gut by Seismic Mot :On
Yυ Tamυ ra,Kalsυ m′ κ′υ″ra,sゎ Oe″ ハο々

89

1SODS:AniSODATA― Based lnlial Centroid A19o百 thm
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わOr7y P力 an,gar7d C力 治―
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SLN‐ D2CNN Modelfor Lymph Node Metastasis Diagnosil S

RtrOang Ce,G″ o/1/eCわ en,κ azυ tt Sa″ la,ytrtt rerala

‑4‑

99

ISBN 4‑901329‑11‑8

Procccdings ofthc Tenth lntcmational◎202 1 1ntemational lnfom■ ation lnstittlte

Confcrcnce on lnfom■ ation(InfOrllllation'2021)

Graph]Embedding from Theory to Applications
Proi lrwin KingP″ s′ 滋 ″′グ ルrar″ αrノα′Ⅳθ〃″α′Ⅳθ″ οtt S9̀ル タ

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Abstract
Graph cmbedding rcfers to the problem of prttecting the elements in a graph,including
nodes,edges,substructures,or the whole graph,to a lo、v―diinensional space while preserving

the graphis structural inforlllation,Graph embedding is an essential technique for analyzing
various types of large― scale networks such as social nchvorks, trafttc ne●〃orks, semantic

networks,etc.To cope with the growing scale and d市 ersify7ing structure of modcm networks,
researchers have proposed novelrnethods for graph cmbedding for feature engineering.In thistalk,we present the recent advances and fllture directions in the theoretical development graphcmbedding and introduce some conllnon applications for social neヽ

vork analysis,such as nodeclassiflcation,link prediction,cornmunity detection,and social recolllinendation,

Bio
Prol Kingis research intcrests include inachine icarlling,social computing,、

veb inteHigence,

data Fllining,and multiFnCdia info■ nation processing.In thcsc research arcas,he has over 210

technical publications injoumals and conttrences.In addition,he has contributed over 30 bookchapters and cdited volumes.Ⅳ loreovcr.ProA King has over 30 research and applied『ants.Onc

notable patented system hc has developcd is the Veri(3uidc Systenl, previously known as thc
CUPIDE system,which detects similar sentcnces and pcrforms rcadabiliサ

analySiS Oftext― based

documents in both English and in Chinese to promotc acadcnlic integrity and honesty.Pro■ Kingis the Book Serics Editor for"Social Media and Social Computing"、vith Taylor and Francis.He

is also an Associate Editor oftlle ACM Transactions on Knowicdgc Discovcw iolll Data alld a‑5‑貴)rmer Associate Editor ofthc IEEE Tra1lsactions on Ncural Networks and IEEE Computational

inteHigcnce Ⅳlagazine.Hc is a member ofthe Editorial Board ofthe Open lnforrllation Systelns

Joumal, Journal of Nonlinear Analysis and Applicd Ⅳlathematics, and Neural lnfoIHlatioll
Processing‐ Lettcrs and Revielvs Journal.Hc has also served as Special lssuc Gucst Editor for

Neurocomputing, Intenlational Journal of lntelligent Computing and Cybcrnetics, Journal of
intcHigent lnfoI Hlation Systeins,and intemational Joumal ofComputational intcHigent Research.
Hc is a IEEE Fe1low and a scniorlnember ofACM.Currentlyt he is serving thc Neural Ne●

vork

Technical Comlllittec and thc Data Mining Technical Comlnittee under thc IEEE Computational
intclligence Sociely.He also selγ es lntemational Neural Neヽ vork Socicly as thc President.

Morcovet hc is the General Co― Chair of the WebCon2020, ICONIP2020 alld in various
capacities ill a number oftop conferences such as WWⅥ:NIPS,ICML,IJCAl,AAAI,etc.Proi

King is Professor at thc Department of Computcr Scicnce and Engilleering, and a follller
Associate Dcan(Education),Faculサ

Of Engincering rat Thc Chincse Univcrsity of Hong Kong.

Hc had 、vorked at the ATざ こT Labs Rescarch, San Francisco and、vas also teaching Social

Computing and l〕 ata Mining as aヽ /isiting Professor at UC Berkeley in carly 2010s.Hc reccivcd

his B.Sc.degrec in Engineering and Applied Science■ olll Califbmia lnstitutc of′ Tcchnology,
Pasadena and his M.Sc.and Ph.D.degree in Colnputer Science froln the Universiサ

Califbmia,Los Angeles.

‑6‑of SOuthcm

Procccdings ofthe Tcnth lntemational

ISBN 4‑901329‑11‑8

Confcrcnce on lnfomnation(InfOrlllation'2021)◎ 2021 1ntcmational lnfom■ ation lnstittltc

Research Trend on]Developing Smart Remote Patient Monitoring SystemLS ibr
the COVID‐ 19 Era and Beyond

Pro■ Sabah MOhammcd

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Abstract
As infollllation technology continucs to dramatica‖ y evolvc,Inany rcscarchers and strategy dccision
making believe thc lntemet of Things(IoT)COuld play a pivotal role in reshaping industry all togethcr.It
is the donlino cffect、 vind of changO that we nced to understand and plan br.This particularly ilnportantin thc COVID‐ 19 era and beyond、 vherc wc need to crcate a robust connected healthcare ccosystem. In

hcalthcare,loT mtt just redeine how apps,de宙 ces and people interact alld collnect with one anothcr todclivcr hcalthcare solutions. Thc bcneflts arc more than obvious. It could help rcducc costs, improvc
outcomes and disease managcment,and enhance patient cxperienccs.This invited talk will shcd light on
the current and ftlttlre trends taking place in the patient rnonitoring fleld and the kcy market drivcrs thatdesign cngineers nced to considcr.

Biography
Dr. Sabah Mohal■ Fned rCscarch interest is in intelligent systems that have to operate in largc,
vn domains. His
continuous research is inspired by his PhD work back in 1981 from Brunel Univcrsity(UK)on theemployment of the Brain Activity Structllres for decision making(plaming and leaming)that cnablenondeterlninistic, cooperative, highly connected, survivable, adaptive or partiaHy kno、

processcs(C.g.agcnts, mobilc otteCtS)and collaborat市 e processes to act intelligently in theirenvironmcnts to tilncly achicve thc required goals.Having traincd in medicinc、vith a computer sciencc

PhD in Artincial lntelligcncc(Al),Dr.Mohammcd is hH Professor at the departmcnt of Computer
Science at Lakehead Univcrsity(OntariO Canada)sinCe 2002 and core proRssor at the BloTcchnolo野
program at Lakchcad.Dr.Mohammed efforts in establishing healthcare reltted programs at Lakehead arenotable like the specialization Hcalth informatics, BloTechnology and the Bioinfollllatics programs at

Lakehead. With a research background in industry and acadenlia,hc has a strong intemational research‑7‑reputation for his work on clinical decision suppOrt systems supporting remote areas, ubiquitous andextreme en宙 ronments.Prior to his wo■ at Lakehead University,Dr.Mohammed was the chair ofthrcc

computer scicnce departments at HCT,Philadelphia and Applied Science Universities.Dr.Mohammed is

the Editor in Chief of the of the IGI Global lntemational Joumal of Extreme Automation andConnect市 ity in Hcalthcare(IJEACH),Associate Editor ofthe IEEE Access and the founding EiC ofthe
lnt.J.of Emerging Technologics of Web lntelligence(JETWl).HC iS Currently the supervisor of theSmart Hcalth FabLab at Lakehead University.Dr.MOhammed chair the special intercst group on Smart
and Connected Hcalth with the IEEE ComSoc eHealth TC.Dr.Mohammed is currently working on thedevelopment of loT and mobility technologies that have ilmpact on remote patient monitoring in Rural
Areas.Dr.Mohamlned is also a Profcssional Engineer of Ontario,InfollllatiOn Processing Professionalwith CIPS and Senior Member of IEEE with research suppo■ ed by maiOr 3randng organizations like

NSERC,MITACS,ONCAT and CFI.More infollllation on Dr.Mohammed can be found on his
institution websitc http://8ash.lakeheadu.ca/― mohammed.

‑8‑

ISBN 4‑901329‑11‑8

Procccdings ofthc Tcnth lntcmational◎ 2021 1ntemational lnfol■ llation lnstittltc

Confcrcnce on lnforlnation(InfOrlnation'2021)

Tilne Series Forecasting with Artiflcial Neural Networks
Prot Lcan Yu
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Abstractln this talk,artincial neural networks(ANNs)are uSCd as an importallt prediction tool for time series

brecasting. The four main forms using ANNs to predict tinle series are introduced. In particular9 somc
illlportant issues about data preparation in ANN forecasting are involved in this talk. FinaHyO some related
rescarch progress on AblNs in tilne series forecasting donc by presenters are briefly given.

Short Bio
Pro■ Lcan Yu rcceived his Ph.D. degrec in NIIanagement Sciences and Engineering fronl Academy of

Mathematics and Systems Sciencc,Chinese Academy of Sciences(CAS)in 2005.Hc is currently a profcssor

and PhD supervisor of School of Economics and Management,Beting Universiサ of Chemical Technolo〔 ジ.

He is a、 vinner of National Science Fund for Distinguishcd Young Scholars,National Progranl lor Support of
Top‐Notch Young Professionals and̀̀Hundred Talents Pro8ranl''ofChinese Academy of Sciences.Hc is acted

as a guest editoL managing editot associate editor and editorial members of many intemational joumals
including Computersゼ 貶Operations Rescarch and Joumal of Computer Science.So fat he has published flvc

monographs(ヽ vo mOnOgraphs have been published by Springer― Verlag)and OVer 100 SC1/SSCI articles insome top jourllals including IEEE Transactions on Evolutionary Computation and IEEE Transactions on
Kno、 vledgc and Dam Engineering.At thc same tilne,he rcceived many awards and ho■ ors,such as̀̀EIsevier

Most Cited Chinese Rcsearchers''from EIscvier9̀̀China Youth Science and Technology Award''from theOrganization Department of the Central Comnlittee ofthe CPC,

The 100 National Best PhD Theses Award"

from Acadcmic Degrees Committee of Sttte Council and Ministy of Education of China, ̀First Class Prizc

for Bcuing Sciencc and Tcchnology Award"from the Bcting Municipal Govemment,First Class Prize for
Natural Sciencc Award of Minist7 of Educttion(MOE),Bcuing Mao Yisheng Youth Science alld Tcchnology´nvard,and̀̀]し u Jia― xi Young Talcnt Award"of Chinese Academy of Sciences.His research intcrests includc

business intenigence,big data inining,cconomic forecasting and intenigent flnancial inanagement.

‑9‑ISBN 4‑901329‑11‑8

Procccdings ofthc Tenth lntcmational◎ 2021 1ntcinational lnfomation lnstittlte

Confcrcnce on lnfom■ ation(Inhmlation'2021)

An estilllllatiOn of a scale parameter based on the
Fourier… Mellin transform
Akira 1/1orimoto
Faculty Of Educatiο n,Os̀法 aK´ οfl‐ u Universfoぁ OSa■a5828582,Japan

morimoto@cc osaka k)oiku.ac jp

Abstract
The ⅣIellin transform is well knownぉ a scale invariant transform The FOurier― ⅣIellintransform is not only scale invariant but also time shift invariant Batsed oll the Fourier‐

1/1ellintransform,an algortthm,which checks whether two speech signalsノ (ι )and,(ι )have a relation―γ)and estimates α and β,iS proposed Several experiments have shown theg(ι )=β ∫(α ιuse負 1lness of the algorithm.

Keywords : the Mellin transform,the Fourier― Nrellin transform,scale invariant, tin■in、

le shiftariant,spe∝ h signal

lntroduction

The Mellin transform 11,2,31 is well known as a scale invど iant translorm For speech signalノ (ι )and its scale transform j亀 (t)=∫ (α ι),We can estimate■Om∫

α>O by the Mellin transform(See§2).

shift transformん ,γ (ι )=∫ (α t― γ),We Cannot estimate the scale α(ι )and itS SCale―.

The absolute value of the Fourier transfornl is tiFne shift invariantη′e apply the ⅣIellinlfαfrom∫ (ι )and
transform to the absolute value of the Fourier transform,then we can estimate
Mellintransforlllん ,.(ι )ThiS method is called the R)urier― Mellin transbrm(See§ 3)The Fourier―are widely applied in various ields,for example,malllmalian hetting円
Levd inlage description Юl,etC・
可―「,rhythlll desc五 ptionレ l,In§ 4,we propose Algorithm 9 which checks whether two speech signals∫ (ι )alld g(ι )have)=β ∫(α ι‑7) If the relation exists,、 ve can estilnate αand βby the algorithnl

a relation g(ιSeveral experilnents have shown the usefulness of the algorithm.

2

The h/1ellin transformヽVc Denne the Mcllin translcbrm according to lll

Deflnition l.For ω>0,the Mellin transform of a ftlnction∫

is

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ω

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Example 3.Denne√ )け
(ι

川={岬π
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we set,(ι )=∫ (ι ‑2)and,α (ι )=θ (α ι)With α =0.7.In the upper le■line corresponds to g(ι )and the red broken line corresponds to g0 7(ι)・of Figure l,the blue real

USing the equation(1),we

make a graph of α against ω illustrated in the upper right of Figure l The Praph iS like a constantfunction,because the range of fluctuation is about O.5%of O,7. lrhen we estilllate the scale α at
O.7 Wesetん (ι )=メo7(ι 2).In the lower le■ of Figure l,the blue real line and the red broken
hne correspond to θ(ι )andん (ι ),respectively. ヽヽb lnake a gaph of α against ω illustrated in thelower right of Figure l ヽVe cannot estilllate a fI・ om the graph. The tin■ e shiR interferes with anestirnation of(■

.

α=07

α 07

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06985
0698
06975
′ 10

0697
085

08
075

07
0.65
0.6

055

Figure l:Upper left:,(ι )=.′ (ι ‑2)(blue real line)and θ。7(ι )(red broken hne)Upper right:αagainst ω.Estiinate αat 0 7 Lower left:g(ι )(blue real line)aIIdん (ι )=/117(ι 2)(red brokenhne).LOwer right:(■ against ω

3

The Fburier‐ Mellin transform

DeanitiOn 4.The Fourier transform Of a function∫

is

″
Ю=m=だ
Property 5.Tん θFοttγ

tter ι
ttπ 」ο
鶴げん )=∫ (α ι)jS(ια ιづmCSん ψヽｌ Ｊ ノｒヽ 一 α／′ ヽヽ
︲︿∫し7'Cr ιγαπ硼 ら 四鴨 げ

１ 一αん (ξ )=
Property 6.7he Fοι∫(t)C 'ξ atノ (ι 一 γ )づ S

″I∫ (― γ)](()=C ̀γ ξ ノ(ξ
「

T″

ι
θ
竃ポθ
た,IF1/(一 γ)!(ξ )=IF∫ (ξ )ト

‑12‑

)

Deinition 7.The Fourier― Mellin transform of a fllnction∫iS

別関,0=J+∞ ■0レ 屯いwhere ρ≧ l is a COnstantγαηψ 観 げ ∫α,βνθ7:れ ι
α>0,ι んθFο arづ θ―

Property 8.Fο r αscα

7・

,γ (ι

)=β ∫(α ι‑7)お̀θイIプ し,β ,γ ](P,ω )=α (ω
Fノ ｀

+1‑pl

p′

β rル ィI∫ ](β ,ω )Algorithn■ 9.Forノ (ι )and g(ι ),We decide whether θ )=∫α
(ι

,β ,γ

(2)

(t),and estirrlate

αand βin the

fo1lowing steps:

1.Take the natural logarithm of the equation(2),we haVe
R(P,ω )=10g(FゝυЪ,β ,γ ](ν ,ω ))‑10g← 戸ルイI√ ](P,ω ))=(ω +1‑P)10g α+plog β
2. Fix p=4. For several ω,we estimate log αand log βby the least square rnethod.
3 Usillg the estixnation of β,p10t a graph of
つ
α =(

)…

(3)

against ω

4.If the gaph of α is like a constant function,鸞 decide θ(ι )=ん,β ,γ (ι),alld estinlate α by

the step 2.

Exalnple 10. ヽヽre apply Algorithm 9 to speech signals.

ミヽ play the same speech signal withdi■ crent salnplirig rates which arc 12000 Hz and 16000 Hz, alld rccord thcI11. Thc upper left of

Figure 2 is graphs of two speech signals 「rhe upper right of Figure 2 is graphs of the absolutenlues of the Fourier transforms.ヽ Ve make a raph of R(P,ω ),p=4 against ω (See the middle
石
e plotα =1.3338 and β =15016.ヽ ヽlefl of Figure 2)Using the least square method,we estimate
a graph of α against ω. the middle right of Figure 2 is like a constant function,because the range
α =1.3338 Then we decide the second speech is Just a tirne― shiftedof the nrst speech with the scale α
In the case of difFcrent spceches,thc lower left of Figurc 2 is thc raphs of two difcrent spccch
ζ
4e plot a graph of α against ω ヽヽe decide two speeches have no relation,because theヽsignals. ヽOf fluctuation is abOut 21/c of.

lo、

ver right of Figure 2 is not like a constant function.

Acknowledgements
This work was partially supported by JSPS KAKENHI Grant Numbers 20K03653

References
111 R Godemellt,Allalysis IH,

Allalytic and Dittrelltial Functiorls,Mallifolds alld Rね

maIIn

Surfaces'',Springer,2015
The scale representation".11l IEEE Transを でtions on Signal Processillg,41,3275‑
3292, 1993,doi: 10.1109/78.258073.

121 L Cohen,

131 A De Senaa,nd D.Rocchesso,

A Fast Mellin and Scale

Process 2007,089170(2007),doi:10.1155/2007/89170‑13‑

ηransbrm",EURASIP J Adv Signal

Ist Signal i bluc、

2nd Signal:red

Ab∞ 1■ tc values of Foun∝ transfoms

鰤

卿

鰤

ｚ
ＯＨ

RO,ω ),′ =4

1345
134
1335

133
1̲325

132
Di

c

nt spccclles

Figllre 2:Upper le乱 :the flrst speech(bllle),the Second speech(red)Upper righti the absolllte
nlues of the Fourier transforms.Middle left:R(P,ω ),ρ =4.Middle right:the graph of α against
石ω The range offluctuation is about 2シ 6 of α =1.3338. ヽヽe decide the second speech is some scale
trallsforln of the flrst speech. LOwer lefti difFc・ rent speeches. Lowc・ r righti the graph of α against

ω. The gaph is not like a constant function

The R)urier― Mellin transform and mammalian hearinず ,J Acoust Soc Am.1978
Jan;63(1):17483.doi:10.1121/1.381708.

i41 R A Altes,

151 U NIarChand and G Peeters,

Scale and shift invariant time/iequency representation

using auditory statistics: Application to rhythm description'', 2016 1EEE 26th lnterna‐

tional Workshop on Machine Learning for Signal Processing (Ⅳ lLSP), 1‑6, 2016, doi:

101109/MLSP.2016.7738904
Юl S Derrode and F Ghorbel,

Robust and Ettcient Fowbr― Mellin■ ansbrm Apprclximadonsfor Gray― Level lmage Recollstruction and Complete lnvariant]Description'',COmputer lゾand lmage Understanding,83,57‑78,2001,doi: 10.1006/cviu 2001.0922.

‑14‑

ision

ISBN 4‑901329‑11‑8

Procccdings ofthe Tenth lntemational◎ 2021 1ntcmational lnfomation lnstittltc

Confcrencc on lnfomation(InfOrlllation'2021)

Uncertainty Principles Related to■ actional
Fourler ttbansform
レIawardi Bahria and Ryuichi AshinOb
a Departmerlt of ⅣIathematics,Hasanuddin University,Ⅳ Iabsar 90245,Indonesia
e― Inail:b

Ina、 vardibahri◎ gmail.com

ⅣIathematics and lnforlrlatics,Osaka lKyoiku University,Osaka 582‑8582,Japane― mail:器 hino◎ cc.osalo― kyoiku.Ж .jp

Abstract
A direct relation between the Fourier tral■ sform and the iactional Fourier transfornl isstudied Some prOperties of the fl・ actional Fourier transforrll are investigated udng this relaaretion. Several versions of uncertainty principles involving the fractional Fourier transforll■presented.
Kcν υοtts:li・ actional Fourier transforIIl,Donoho― Stark uncertaillty principle,fI・ actional、 vavelet

transbrm
AMS Subiect Classincation:1lR52,42A38,15A66,83A05,35L05

l nractional Fourier■ ransform(FRFT)∈L2(R)are deined by

The inner product of Z2(R)and Fourier transform of∫
げ ,の L21Rl=.氏 ∫←面

a丹 0=券

化ス

1(R)iS denned bv.〆

The fractional Fourier transforln of∫ ∈五

2)ッ
ξ
ζ
,

jι

(CSC

∫0ご

{∫ }(ξ )

に 出
・

=ス

ge
用化0仏 山

θ
, θ≠η
θ=券
7「

￨,
l,

θ=2η πθ=(2η +1)π ,2CZ.

Here,δ is the Dirac delta function andθNote thatFθ {ノ }に

θ

=

=鶏

(2)

θ∫ °2)ザ 虎
ξα
ι
氏
一
虎
ξ
≠
♂
=θ θ 昇∫
。
氏
2+ξ

)=θ

Cθ

ltl♂

2墨

c(2墨

♂(2ザ 轟 T{♂
=θ θ

‑15‑

2ザ

Cθ

dι

∫。}に CSCの・(3)

Donote

ん )=♂

2,デ
ι

(ι

∫ ),

(4)

(ι

tllen we haveノ 冊 0=夏 財 m,讚ノぽ2ず 以。=珊 制 H⇒讚

NOw we provide the different proof of Parseval formula fOr the FRFT using the direct relation

between the FT and FRFT.

Lemma l.1(FRFT Parse聡

1)。

乃 r αι
ι∫,g c ι2(R),ι んC力 ′ιθυ仇 ク γ℃ιαιづθη んθι
お」＾６(∫ ,g)ん

2(R)=(Fθ {∫ },Fθ {g})ん 2(R),

αηご
ウイ

￨￨∫

￨IL2(R)=￨IFθ {∫ }￨IL2(R)・

2 Uncertainty Principles for FRFT
Our interest is to derive t、 vo uncertainty principles involving the FRFT.They are generalized fOrnlsof the lincertaillty principles related to the conventional Fourier transform

Theorell1 2.1(FRFT uncertainty priIIciple).五 θιノ ιθjη L2(R)J Fθ {∫ }∈ ι2(R),ι んθη ι
んθ

2.。
洗
酔ピ側 歓≧
明が ス
Ψ αЮド
ス
→

θθ
7rljη ク
づ
ηθ
ttν ん
θ
ι
ご
sr
メ
9zα ι
;ι

Extension of the above theorern is showed by the fOllo、

Theorem 2.2,

ving result.

・ι
びηαθγ
んc sα 77ι C Cθ ηαjι づθηs αsづ πTllθ θ■37η 2.l υθんαυθ

呼 幌Юン)6
スピ脚レスぽぽ枡げξ≧
カ

7・

0

1≦ S≦ 2.
石ヽヽe state the following result,、 vhich describes the sharp Hausdor■ i、ung inequality related tO

the FRFT.

Theorem 2.3(FRFT HausdOI卜 YounJ.乃 r αην l≦ r≦ 2 sttcん ιんαι÷十 :=1.動 θηttr Cυ θηη∫jη ιr(R),づ ιん
θ
θ
ι
α
s
ルη を
Cι

恥

Q四
Pγ θ9二

月 ば

→

到 山 僣

″ 早
く

ス

脚

陶

)ψ

・

m

Applying the sharp HausdOrf― YOung inequality related to the conventional FOurier trans―

forlll results in

いノЪ
ψ
―
丹
0→
(聞 → ・
(4囲
〔
‑16‑

Ｓ

ｙ

務

＼ｌｌノ

ん

２

Ъ

刊

ｒ

ｄ
︲
ｅ
︲
．

＜ 一

ｓ

ｌ

〇

協

Ｆ

堰

ｓげ
ｅ
ｄ
ｉ

ｓ
ｈ
ｔ
︒ げ
ｂ

い

︒
ｔ
ｎ

呻仲

ｄ
ｅ

ｎ
１

ｅ
ｄ

IIIcludingん

(1

(1勾

石
ヽ
e further have
ヽ
ヽ１′ノ

α

ん

<r1/2r s‑1/2,)1/6／ Ｆ ｔ ＼

θ}(ξ CSC θ)IS dξ CSCθ√漁

祀Ｌ

Using(5)(ノ￨ljF{∫(10

wlite the above identity as
ｄ

ヽ︱′ノ

∫

漁

Ｃ

御
一２

ｒ

／ １ １ ヽ<r1/2rs‑1/26

(1→

Thus
α

ヽ１︐ノ

∫

／

(15)

ご

∫

ヽ︑

√

′／

九

／１１ヽ

一

嗜到血ギ
→
″
≒
丹
げ
離
→
転

′九

／ １ １ ＼

一

＜一

１ ′

ξ

ヽ

ｒゝ

∫

一

ノ
′漁

θ

Ｓ

ｎ

／ ′ １ ＼

Or,equivalently,

1/2r sγ(10□、vhich flnishes the proof of the theorem

Theorem 2.4(FRFT Donoho‐ Strak'uncertainty Principle)。 Sttpθ Sθ ιんαιE αηごTα 鶴θαStt篭 わic
sげ R.Suppθ sθ ;ん αι∫ ∈ Ll(R)∩ LS(R)υ ん 1≦ S≦ 2s包 硫 ιんαι:十 ÷=1.動 θη二″ αηνszbsθ ιjι∫

jS CE― Cθ ηCCη ι%ι θd ιθ Èηl(R)― ηογηιαηJ Fθ {∫ }づ S6T― cθ ηεθηιttι θご ιθ Tづ η ttr(R)‑2θ γtt υ θ

んαυθ

￨￨′

θ
プ{∫ }￨ILr(R)≦ lθ llE11/rlT11/γll∫ ￨IL3(R)(1つ(1‑6E)(1‑CT).S=2,θ 9鶴 αιづθη

f7L pα 7・ jじ Caι αちルγ(17)becθ ttCS

θ

(18)

(1‑6E)(1‑(T)≦ lθ lν/IEIITI。

r(R)ω づιん1≦ r≦ 2 sacんCι ∫∈五Theorem 2.5.ι cι E αηαT bθ mθ αszttbι θ5%bsctsげ R αηごι
ι
ι
ι
α
sf
づ
ηι
んcヵ ι
ι
ουづ
観 ,サんθ
tt ι
θEれ Lr(R)現θ
mを ιんαι:+:=1・ J∫ tS CE― bα ttι づι電 tη θ
9鶴 α
νんθ

陽 洲Щに

畔 畔 幽
〔

血

9嵩 rψ T貿

科

olcTIM則

0

θηα を
θη
オ
tθ η
αιθ
r ι
んθαごごづθ m 2.5. びηごθθηs αsづ ηrん θ
んθsα me cθ ηα づ
4sszmθ ι
TheoreII1 2.6. ン"θηθηθんαsttι θごιθEグ ηLT(R)― ηθ鶴 ,ιんθ
S6E― cθ ηcθ ηιんθルηcι jο η∫ じ
ι
んαιι
jι

守

研

Jι

叶 β知剣 器 rψ Ъ̲

‑17‑

O②

Acknowledgments.
Thc fil・ st author is partially supported by glant ioI1l h/1inistry of Rcscarch,Tcch11010gy alld Highcr

Education,Indonesia under PDl」 PT scheme. The second author is partially supported by JSPS

KAKENHI Grant Nulnber 20K03653

References
11l L.B.Almeida,The fi・ actional lburier transforrn and tilne― frequency represelltations,IEEE
Trarls.Signal Processっ 42(11),3084‑3091,1994.

pl X Guanlei,W.Xiaotong,and X.Xiaogang,The logarithnlic,Heisenberピs and S1lort― tilne

uncertaillty principles ttsocitted with fractional Fourier transform,Signal PrOcessillg,89(3),339‑343,2009.

pl V.Namiぉ ,The■ a面 onal order Fourier transbrm and its apメ たatiOn to quarltum mecharlics,
IMA J.Appl.Math.,25(3),241‑265,1980.
いlJ.Slll,N.Zhang and X.Liu,A nolrel■ actional wttelet transform aIId its applications,Sci.

China lnf.Sci,55(6),1270‑1279,2012.
I司

A.PIttad,S Manlla,A,Mahato,and V.K.Sillgh,Generalized continuous wavelet trarlsforIFla.ssociated、 vith the fl・ actional Fourier transfornl,」. Comput、 Appli. ]/1ath., 259, 660 671,

2014.
Ю]H・ M OZaktぉ ,Z.Zalevsky,and M.A.Kutり,The Fl・ actional burier Tl・ allsform with Appli―

cation in Optics and Signal Processing,John Wiley&Sons,Chichester,EIlglarld,2001.
[7]J.Slli,X・ Liu,and N.Zharlg,OFl uIICertaitty principle for signal coIIcentratioIIs with ttactional

恥 urた I transbrm,Stnd PrOCesdng,92(12),28302836,2012.

Ztted,On the relationship between the Fourier and iactional Fourier traIIsbrms,IEEE卜]Z・
Signal Processing Letters,3(12),310‑311,1996.
I・

Zayed,A conЮ lution and product theorem for the■ actional tturier transforΠ l,IEEE
Signal Processing Letters,5(4),101‑103,1998.

pl Z・

I・

[101S.K.Singh,The fl・ actional S― traIIsforI1l on space of type S,Journal of Matllematics,vol.
2013,Article ID 105848,2013,9 pages,https://dOi・ Org/10・ 1155/2013/105848.

[1l H.Dal,Z Hib∞ ,W.Wang,A new iactional wⅣ elet transform,Communicationsin Nonlinear
Science and Numerical Simulatio11,44, 19‑36,2017.
[1刻

[1倒

olution theorem related toBallri and R.Ashino,Logarithmic urlcertainty principle,co即 √va■
coritinuous fractional 、・clet transforrn and its properties on a generalized Sobolev space,International Jourrlal of゛懇 elets,MultireЮ lution and lnformation ProcessiIIg,15(5),2017.
M・

R.Roopkum田 ,Quaterllio血 c olle― dimensional■ tttiond Fourier TI・ mshrm,Optik,127(4),2016, 11657‑11661.

[141D.I.Donoho and P.B.Stark,Uncertainty principles al■

Math.49(3),1989,90931.

‑18‑

d sigllal recovery,SIAM J.Appl.

ISBN 4‑901329‑11‑8

Proccedings ofthc Tcnth lntcmationalく)202 1 1ntemational lnfo■ nation lnstitlltc

Conferencc on lnfom■ ation(InfOrlnation'2021)

A REⅣIARK ON WEIGHTED ESTIⅣlATES FORFOURIER PIIULTIPLIERS WITH
ⅣIIXED NORIIIヽIULTILINEAR

MAI FU」 ITA AND YOSHIROH MACHIGASHIRA

Weighted estimates for multilinear Fourier multipliers satistting Sobolev regular―
ity、 vith ll■ ixed norllll are discussed. Our result can be understood as a generalization

ofi41 by using the Lr̲based Sobolev space,1<γ ≦ 2 with m破 ed norm.

1.INTRODUCT10N
In this talk,、 ve consider the boundedness of Fourier lllultiplier operators. Roughly

speaking, the purpose of this study is to investigate ̀̀smoothness and integrable
index'' of lnultipliers lⅣ hich are lllettured by the Sobolev spaces deined in several
vays. In this section,、 ve give a prototype of lnain result,that is to say,η =̲lli=1、

in Theorem 2.1.

五∞(Rξ ),the

Let Ⅳ =1.This means we consider the linear setting.For m∈linear Fourier lnultiplier operator rm iS deflned byЪ 00=F￢

哺

=F枷

知

朝

o=募

μ

mom凝

氏

fOr∫ CS(R),Where z,ξ cR(See seCtiOn 3 br the deinitions of fllnction spaces).

As an example of this operators,namely,systeIIIs,we recall the Hilbert transforn■,that is,the Analytic Signals.The lnultiplier 7π of the Hilbert transforln on lR
Next,we recall the cut― of function,scalling andis g市 en by鶴 (ξ )=― tSgn(ξlocalization.Let Ψ ∈S(R)be Such that)・supp Ψ⊂{ξ ∈R11/2≦ lξ l≦ 2},′(ξ /2ん )=1,
Σ理A・

ξ∈R＼ {0}・

∈Z

ヽヽ石
e set

鶴′(ξ )=7)(2′ ξ)Ψ (ξ ), ブCZ・
sure the boundedness of rm, that is, stability of this system
Our ailn is to橿 〕
under the condition鶴 ′∈〃」,where∬ f iS the L2̲baSed Sobolev spaceln the llext section,v√ e give the notation and main result in the general setting.

2.THE RESUET
hnear Fourier nlultipher operator第 2お deined by
For 772 C L∞ (RⅣ n),the Ⅳ―Ъ

1■ 十ξN)鶴(A,… っ ∫N)0)=謬
疑ノ憮 η)N e2.rに)1に 1)…

■に Ⅳ )α ξヽ
fOr∫ 1,.… ,■v ∈S(Rつ ), Where r c Rり , ξ= (ξ l).… ,ξ 」√)∈ (Rη )Ⅳ andご ξ =
η
Let
RIF
c
S(RⅣ
dξ
α
・
l.…
Ⅳ
ξ
)be suCh thatsupp

:1/2≦ 剛≦Ψ⊂ ∈RⅣ π2},Σ Ψ
ヽ
に/2句 =1,ξ ∈RⅣ れ
{0},
{ξ

た∈Z

‑19‑

and set

鶴′(ξ l,― .,ξ Ⅳ)=m(2θ ξl,…
ヽVc

denote by‖

写 η llLPlletl)×,2′ξⅣ)Ψ (ξ l,… .,ξ Ⅳ), ノ∈Z.

×LPN(ω N)→ L'(tυ )thesmallest constantθ

satisサ ingⅣЪ (A,… っん )￨￨五 pい )≦ θΠ II∴ ￨IL%←の,A,̲っ ん ∈S(Rり‖,=1(See Section 3 for the deinition of function spaces).

ln the un、 祀ighted case,Tomita lltt proved a Hё rmander type multiplier theorem

for multilinear operators,namely,if s>Ⅳ η/2 thenP侭 2)κ
・ )× 一×ι‖7L引 lι れ 侭'N侭 つ →ι〕り

￨1鶴 ′￨￨〃 JttNり

for l<pl,̲.,PⅣ ,p<∞ Satisサ ing 1/Pl+… ・+1/PⅣ =1/P,Where∬」(RⅣ れ)iS the
L2̲baSed Sobolev space of usual type. Grafakos― Si 161 extended this result to thectte p≦ l by uSing the Lr̲based Sobolev space, 1 <T≦ 2. For further results inthis direction,see[5,9,101.Let l<pl,.… ,pⅣ <CЮ and 1/Pl+・ …+1/PN=1/2
1n the weighted case,Rttita― TOmita 14]proved that if η
/2<s,≦ 2,2>η /S.andりt∈ スPisi/η fOr t=1,̲.,Ⅳ ,then‖LIILれ し 1)× …×L'Nぃ N>ι Pい )κ

(1)

where

pN and lfj((Rπυ=υ :ル 1.… υダ)Ⅳ )iS〕り￨1鶴 」‖巧 (侭・ )N)'

the Sobolev space of product type.This

result can also be obtained from another approach of 171. See 18,ll for the endp9int
cases.
The fo1lo、 ving is our inain resultヽ Ⅳhich can be understood as a generalization ofF]・ Taking亀 =2,づ =1,… .,Ⅳ in(2),we haК (1)・ Si[1勾 Obtained some neighted
estilnates for multilinear Fourier multipliers、 vith the Lr̲btted Sobolev regularity,

1<r<2.
Theoreln 2.1.ι θι l<pl,… .,pⅣ <∞ ,1/Pl+… ・+1/PN=1/P,F=(Tl,・ ..,rⅣ )∈(1,21Ⅳ ,TN≦ rⅣ ̲1≦ …・ ≦ r2≦ γl,J=(Sl,.… ,SA7)C RN αηご η/rづ <S,≦ η ■)rt=1,̲.,Ⅳ .Asszmθ
pを

=ん

η
>η /S, αα υづ∈Apハ /η

ルr t=1,̲.,Ⅳ

θη

O)

‖Ъ

‖Lれ ぃ 1)× ̲× L2Nい N》 LP級 )(〕

:メ

‖%￨1暉

侭

η
声 ),

υ
ん
θ υ=υ『/Pl… ・υηご夏んe sobο ιθυspaccげ pttα aCι ι
ttθ υん「((Rり Ⅳ
)tS ι
%pN α
jι

鶴zπ θ
d ttθ rzι3.PRELIMINARIESLet η c N be the dilnension of the Euchdean space.「 rhe Lebesgue measure in
Let Ⅳ be a natural
number, Ar ≧ 2. ′へn operator r acting On Ar̲tuples of functiOns deined on Rπ iscalled the Ar― linear operator. For t、vo non― negative quantities̲4 andコ B,the notation
A(3 means thatス ≦ θB fOr some unspecined constant θ >O independent of
ス and B,and the notation五 ミ B meansthat A s 3 and B、 ス.Let S(Rれ )Rη is denoted by α″ (See,fOr example,111,Chapter l,刻

‑20‑

)・

and S′ (Rη )be the schwartz spaces of all rapidly decreasing smooth functions andtempered distriblltions, respectively WVe deine the Fourier transforrn F∫ and theinverse Fourier transform F 1∫ of∫ C SCRη )by

FAO=m=(.「ほ錮 dF‐ A→ =沸山

胴♂ 守 0(スη

(See,fOr example,13,Chapter ll)・ Let O<P<∞ and tυ ≧ 0.The weighted
Lebesgue space ιP(り )COnSiStS of all measurable fllnctions∫ on Rれ Such that

M40=α .回 %0→

勒<は

Let l<p<∞ .ヽ b say that a weight lり belongs to the ⅣIuckenhoupt class̲4ρ if
〜

SP(嵩

υ
″
。
兎
兎υ
)(嵩
")ご

)1‑メ d″)21<∞,

where the supremum is taken over all balls B in Rれ,IBl iS the Lebesglle measure of=1・ It iS well known
isboundedoll
LP(υ )if and Only if
imal
operttor
M「that the Hardy― Littlew6od mⅨ

βand P′ is the colliugate expOnent of P,that is,1/P+1/P′υ ∈ スP(13,Theorem 7.31).

ψ
M卿 =に .卜 ‐Ⅳ突ポ
→ <はFors c R,the Sobolev space〃 j(Rつ )COnSiStS of all∫ ∈ S′ (Rη )SuCh that

The norm of the Sobolev spЖ e of product type∬」((Rり N),J=(Sl,… ,,SN)∈ RⅣ
for F∈ S′ ((Rれ )Ⅳ )iS also deined by[.「 ￨(1+lξ

l12)鈍

″ .…

(1+lξ Ⅳ12ド

N/2Fに

ヽ︱ ′ ノξ
ご‖FII可 (侭・ )″ )=(ノ,)12

where ξ=(ξ l,… ,ξ Ⅳ)∈ (Rη )N・こヽヽe recall the deinition Of Lp― spaces with m破 ed norm(121).Letグ =(Pl,… ・,PN)C(0,∞ )N The Lebesguespaces with m破 ed norm L'((Rη )Ⅳ )COnsists of all metturable
fllnctions F on(Rπ )N SuCh that・ )N)=￨￨￨IF(″ 1,・ … ,χ N)￨ILPlはllFIIL賓 侭2,dω l)・ …

￨IL,N ttη ,d″

N)<∞

'

where(″ 1,・ … ,″ Ⅳ)∈ (Rπ )Ⅳ andご κt is the Lebesgue measure with respect to thevariable χj,を = 1,.… ,Ar. The norm of the Sobolev space of product type withm破 ed norm″

F((Rπ )N),」 =(Sl,…

FCS′ ((Rπ )Ⅳ )iS alSO deined by固嗽 Rっ 崎 =牌‐,SⅣ )∈ RN andデ

ω
卜

鈍…

⑤

珈

=(γ l,… .,TN)C(1,∞

虐 olた

Lemma 3.1(p,Youngゝ.

ιグ=(pl,… ・,pⅣ )∈inequality br m破 ed norm司 ).ι θ

11,∞ ]N,ι んθη
‖∫

,

.侭 っめ

where ξ=(ξ l, ・,ξ N)C(Rπ )N and(3)=(1+lξ j12)1/2,t=1,… .,Ⅳ
The fo1lo、 ving lemmas、 vill be used in the proof of「 rheorem 2.1.

)Ⅳ ,br*gllι ,((R2)N)≦‖∫ ￨ILプ ((R・ )N)￨lgllL(1, ,1)((Rπ )・ N)・‑21‑

Lemma3.2(12,Hausdor作 ヽ三oung's inequality for mixed norm司ηαPN≦ PⅣ ̲1≦ …・≦pl,ι んθη[1,21Ⅳ α‖F[∫ lll五 .((Rη )N)≦
υ んθtt σ =(Pl,一,P特￨￨∫ ￨IL■)。

Lθ ι
グ=(pl,… ・,pⅣ )∈(R.)N))α ηα p:tS ιんC Cθ ″ 鶴クαιθ θη οηCη ι げ

PJ,t=1,̲.,Ⅳ.

4.KEY LEMMA
The follo、 ving leFlllma is a key lemma in the proof of Theoren1 2.1.

Len■ lna 4.1. Lcι γ > 0, デ = (γ l,・ …,rⅣ ),γ Ⅳ ≦ TN̲1 ≦ ―・ ≦ r2 ≦ Tl, J=ηごη/Sα <9t<Tゎ づ=1,… .,Ⅳ .7ん θηθcsι tttα ιc,SN),η ルt<St≦ ηα,ι ん(Sl,・ …

lЪ (/")げんθι
ごsヵ r αιι

(Rn)Ⅳ

"CRれ

… っん)0)l κⅣ・r)Π ν Fl)。 )1/%ll鶴 ￨1暉 (釈

(1洗

̀=1

ι
ん Supp鶴 ⊂ {ξ =(tCl,…
,プ ∈ Z αηご 鶴 ∈ IF((Rπ )Ⅳ )υ づ

,ξ

N)∈

:lξ l≦ r}・

REFERENCES
ll:M Asano,On boundedness of multilinear Fourier multiplier operators on weighted Hardy
spaces(」 apanese),Reports of harmonic analysis semin銀2016,Vol.32,75‑76.

121A.Benedek and R̲Panzone,The spaces LP,with mixed uorm,Duke Math J 28(1961),
301‑324̀

13]J.Duoandikoetxea,FtDu■ ler Analyds,Graduate Studies in Mathematics 29,Amer.Math Soc,
P■ ovidence,RI,2001

FI M Rlita and N.Tom比 も Wethted nOrm hequ」 批bs for mdtihear Founer muLゎ lbr%■ ans.Amer.Math.Soc.364(2012),63354353.
レIL.Grahbs,A.Mi̲vachiand N Tomita,On lnllldhnear Luner muLiメ おrs Of hmtted smooth―ness,Canad.J.Math.65(2013),299‑330.

161 L GrahkOs and Z Si,The Hё rmander multiplier theorem for multilillear operators,J Reine

Angew.Math.668(2012),133‑147

171 G.Hu and C― C Lin,ヽVeighted norm inequalities for multilinear singular integral operators

and apphcations,ノ ヽnal̲Appl(Singap)12(2014),269‑291
eighted version of Carleson measure alld multilinear Fourier18]W.Li,Q.Xue and K Yabuta,ヽ ヽ石

multiplier,Forum Math 27(2015),787‑805.

Iq A Miyachi and N.Tomita,Minimal smoothness conditlons liDr bilinear Fourier multiphers,

Rev.Mat.Iberoam.29(2013),495530
1lq A.Mサ ach and N.Tomta Boundedness cHte五 on br b五 near Fourお r md伍 メ綸■Operator跳
Tolloku Math.J.66(2014),5576
111l W Rudin,Real and Complex Analysis,Third edition McGraw― Hlll Book Co,New York,1987
1121 Z Si,SOme weighted estimates for multilinear Fo1lrier multiplier operators,Abstr.Appl.Anal.
2013,2ヽ rt.ID 987205, 10pp.

1131N.Tomita,A Hё rmander type multiplier theorem for nlultilillear operator,」.Funct Anal.

259(2010),2028‑2044.

ⅣIAI Fu」 ITA,Eγれαづ
Jα ごarθ ss: fuj ita― m89Cex.osaka― kyoiku.ac.3p

YosHIROH NIACHIGASHIRA,DIvls10N OF
Ⅳlパ TH,ScIENCES,AND INFORMATION TECHNOLOGYIN EDUCATION,OSAKA KYOIKU UNIVERSITY,KASHIWARA,OSAKA 582‑8582,JARAN
Eznα α
ごご肥ss:machiCcc.osaka― kyoiku.ac.jP
J α

‑22‑

￨

ISBN 4‑901329‑11‑8

Proceedings ofthc Tcnth lntcmationalく)2021 1ntcmational lnfollllation lnstituteConfercncc on lnforlnation(InfOm■ ation'2021)

Big Data and Machine Learning:Algorithms for Analysis‐

with Case Studies

Yousuo Zou*,Lcah Luo**,and Anne Zou****Cοι″θι P中 ″,t/4ル ιパノ
ら ル麟rgiル a Cυ 96923,3SA
ク グ G αrr,3θ 3Umersノ ク D″ ν″′ ι/Sc・ プ"′**DepαrrPP2ι ″■キ■Deparr″̀″

EnJ″ ιθ″辱 α′グCο ψ 夕た″ま た″θι,シraC僚解 し物ルθrs′ りぅシ ′αθttθ ,Ⅳ y′ 32イ 4υ 34

Eノ ι
ε″たηノ

̀9′

″
′
′υ″ルθ浴ノ′q′ CO″ ′ たr scた ″ιι,乃 nderι ノ
祝 23θ ′均 ″″ /b″ ′P″ εθ,ヽ黙 カッノ

̀,刀V3η 35,jもA

Abstractln this paper the authors try to introduce 3 catcgories ofalgorithms recently used in big dattl and machine leaning

analysis:a.Statistical and probabiliv methods,b.Neutrai neヽvorks algo五 thms methods,and c.the Optimized fLInCtion
analysis based on analメ iC mathem・atics and numcncal methods(e.g.the Stcnger Methods or the SINC Methods),、
vhich the author are using to train students at University of(〕 uarn.The paper also gives examples of case studies toshov/how to cmploy SRヽ C Methods to do analysis and to solve linearrcgression,and particularly noniincar regression
problems.
ⅣrcthOds,Case studies
Key Words Algorithms,Big Data Analysis,Optimized allalysis methods,SINC

l.Introduction
ln the study of data analysis and machine leaming,in order to reducc the eror of analysis and makc
accurate prcdicJon forね ture pcrformance,wc nced to select right analysis algorithms for the pa■ ems of
selected data.The rccently used algorithIIIs br dattl analysis and machine leaming we teach our students
can be classiflcd into three categories.The its categow is to search thc highcst probability to make decision

brain neⅣ e systems to[1]:the 2nd category of methods is using electronic circuits to simulate humanゝreach the bcst physical sttltus tO make decision.This is the traditional computcr scicncc methods whichhave been very complicatedly developed with hundrcds oflayers ofneurai networks[21.The 3rd categoryof methods combines matllematical and comptlter sciences,called optimized analytic function methods or

newly devcloped SINC Methods,which have been initiated and developed by one ofthe authors'former
PhD Adviscr of 1990s,Professor Frank Stenger and his rescarch team (eSpeciaHy his postdocs,PhDs andMaster students).Thercfore,we cali thcse methods the Stenger Methods[3].The abOVe threc analysis
categories are different approaches,butthe result is the same:the smartest decision― making.
In the abovc rnentioned 3 categories ofalgorithms,thc lSt and 2nd categories have been wcllintroducedin publications,espcciJly in various tcxtbooks taughtin colleges and univerdties woJdwide[4,5],we will
not repcat therll to discuss here. In the follo、 ving we will concentrate on thc 3rd catcgo7 ofalgorithms,theStcnger Mcthods or SINC Mcthods.We will start from a group of PDEs(partial dittrcntial equations
generated by the cquation ofthe Lcast Squared Error Expression.Then we discuss the FnethOds to solve thegoup ofPDEs in case studies according to difFerent pattems ofthe experirllental data to ind the optilnizedfunction,yρ り,WhiCh can best describc the selected experimental data.We win ten hOw the sINC Methods、
vork and how to use them to solve real world problemsin data analysis and lnachine leamingo We will also
give a casc study using a sct of the real― world tourism industrial data and the optirnizcd analytic inction
rnethodS tO sho、 v the accuracy ofanalysis ofthe inethods.

2.Optimized Function AlgorithIIIs Based on the Least Squared Error‑23‑

ⅣIethods

NoⅥ しassume we have a goup of expcHmental data from
regularides)of natllre that are hiding in thcse experimental
computadonal errors ofalgorithms).
χノ

χ2,

χ3

χ

ツ′

ノ

ツ3,

ン

which we want to discovcr the laws(ordaa(eXCluding instrllmcnt erfos and

"

r〃
,

̲2・

:

Lct's use the principle ofLcast Square rnethod to flnd the unknown
forlnat(or fOIIllula),yβ り,W力…′χ1,χ 2′ ・″̀″ ̀X=作

la、

v exprcssed in lnathematical,

crり =Σ Ll[yjα )一 yi]2="Eι ..

のAccording to Expressioǹυ ,We can have[making use ofdata sct(̀,]:)義 =012(y[α )一 乃
器=Σ 降

継=Σ L12(yi(x)一 yI)f指 =0の

轟=Σ 12(ỳ̲̲yI)∫ 麟: =0lヒ

1n theお 1lowing we will discuss how to solve the Equations(〃
to do data analysis and machine lcarning.

abOVe to flnd the optimized function,】

り
,

̀β

3.Case Studies
3.1.Case l:Linear Data Patterns
lf the selected dataset r̀ノ above is a lincar pattem,Equations̀り Can be casily solved in the regularlinear regression methods either by traditional statistical regessiOn method or by the optinlized analytic

function method,which nceds to solve a group of linear algebraic equations using linear algebraic

knowledge.Thc detailcd computational procedllres can be seen in regular rnathcmatics or computer science
textbooks.

3.2.Case 2: Nonlinear Data Patterns
lfthe selected datasets 6り abOVe are nonlinear pattems,the method to solve Equations rツwill bc
complicated.For a weak nonlinear case,we can use some mathematical transfollllations to turn it into agroup of linear algebraic equations to flnd their nonlinear analytic regression solutionS,or9 use a、 vcak

nonlinear approximation method to obtain an approximatc analytic regression soludon 16].HowCVet ifthesclected datasets r̀ノ abOvc appear as a strong nonlinear casc,we wouldn'thaVe the usual set of anJy」 csolutions.But we can usc computers to get numeric approximate solutiorls based on di∬ brent computationalalgorithms,such as Newton― Gaussian itcration method or by SINC methods.The detailed steps andprocedurcs for nonlinear regression using optimized analytic and numeric functions can be scen in
textbooks and rcscarch papers published by Professor Frank Stenger[7].

The widely uscd new computttional methods,the Stenger Methods(Or sINC Methods)are mainly
developed by Professor Frank Stcnger and his graduate students at Univcrsity of Utah and at various
universities in thc US and other countries. SINC methods are based on linear algebra complex analytical‑24‑

ftlnctions, Fourier transfo11llation, Ne、 vlon iteration and etc. SIN(〕

methods are highly cfRcient, moreaccurate high― perfolHlance computational algorithms compared to currently existing computational

methods.SINC methods can re‐ write the whole sets of e対 sting computational algorithms and make arcvolution in l■ ture computational engineering and computational science.No otherrnethod ofcomputationaccomplishes such breadth of applicability. Due to their cfncicnctt thcsc mcthods make possible theaccuratc solution of frequently occurring computational problems、 vhich were hitherto extremely dimcult,or impossible to ca口 り out.ParaHel computation,c.g,,the solution of lnultidilnensional problcms falls out

very simply and ettciendyお r algo」 thms based on ttVC methods.In the fo110wing we give an cxample asa real― 、
vorld case study using a sct of tourisln industHal data, which is very illlportant to the cconomy

development for the island of(3uanl,to sho、 v the accuracy of thc optiinizcd anabた ic function mcthods
applying into data analysis and inachinc learning.

3.3.Case 3:Data Analysis of Japanese Tourists Visited(Guam in 2004‑2017
The number ofJapanese amvals to Guanl annuaHy■ oln 2004 to 2017 are listed in Table l.
Tabie l.Japancse Tourist Arrivals to Guam Annua‖ y during 2004‑2017

Number of

Number of

Arrivals (yi)Predicted (Yl)

Year

χI

2004

10

2005

1

894035936219

2006

12

1

2007

3

179
929618893275937874950826934132

2m31
2009
201,

‐
4‐

882782887792834801

479881907765908574911278827096

5
161

2011

7

201'

13

2013

9

2014

10

2015

11

2016
2017

2
13

1‐

826880790282152757674343741870677964The data pattem can be visualized in Figurc i belo、 v.It shows thc selectcd data is a highly nonlincar、ve can usc thc classical Ne、vlon― (3aussian itcration lncthod to solve the group of
nonlincar algebraic cquaions gcnerated from Equations̀ッ .The nature ofthe Ne、 vlon― Gaussian iteration
pattcrn.TraditionaHyしmethod is to use inflnite linear ftlnctions with extremely short tilnc‐ interva1 lo sirnulate the nonlincar ctlrve

step by step.Butthis classical rnethod causes huge computer's CPU computational ettrts and consumes a
lot ofcomputer's memoFy Therefore,l is not ahigh‐ perforlnance computing mcthod.In this study we havedevcloped a new type of high‐ pert)lHlance algorithnl, use a set of flnite sirnplest nonlinear analytic
functions to replace the classical linear hnctions to approximate the selected nonlinear data curve.The

detailed algoHthms and computational proccdures can bc scen in[6,7,8].

‑25‑

I

COmpa‖ sOn of Actual and Predicted‖ umber ofllap● anese Tourlsts Visited Cuam:n2004‐ 2017‐‐

1 1200000 .
1000000

1

0 1‐ ‐

1

2002‐‐ ‐ J ・

― ‐

2004

2006

2008

‐

2010

.

̲̲

￨

2016

2018

1

― ―

2012

2014

Fig.1.Comparison oforiginal data(Japancse arrivals annual to Guam,blue curve)and the
optimized analメ iC inc● on predicted data(red curve)

4.Accuracy and ErrorAnalysis ofthe Nonlinear Regression Using the Optil■ ized Function
AlgoFithmS
Thc computational results ofthe error analysis are listed in the fo1lo、 ving Table 2 using the standard
total deviation and Pcarson correlation coefΠcient lnethods.

Table 2.Statistical analysis oferrors and Pcarson correlation cocfncicnt

Error tvpe

Pcarson correlation

coefncient

393182929.8
855353.2143

・Standard totュ l deviationｙ

Total variancc

４
一・

data and lncan value

１

Tot』 difFerence oforiginal

Q(X)=Σ 14(yi̲y(χ l))2一
ソMcan valuc oforiginaldata

Error value

Error forIElula
４・Σ

Total least squarc error

Σし フ
,―

3872.47)δ
4=寺 Σ140二 ̲刀
ぞ26012994643
77543.50161

δ14
Σ:4(.̲■ )Cyi一 万Σ14し :̲夕 )20。

997687109

Thc accuracy and error analysis are used to compare the accuracy and crros generated by difFerent
analysis methods(or algOrithms),therefore we can decidc which method should be selected for high‐perfoIHlance computing in data analysis and machine leaming research.Fronl the Table 2,wc can see thecoreladon coettcient ofthc selectcd nonlincar regresJon method is vev high,0.9977,almost 100%.Thc
errors betwcen function predicted and original data are among the least of other traditional statisticalregression lnethods.

‑26‑

5。

Conclusionln the above,、 ve have introduced the three categories of algorithms of analysis being used in big data
analysis and machine learlling research:neural nctwork methods,statistical and probability mcthods,and
optirnized analytic function nlethods,among、 vhich,the autho「3 elllphasized on the category ofthc Stcnger
Mcthods or SINC Methods starting■ om a group of PDEs or partial differcntials Equations r39 from the
Lcast Squared Error 14ethod to siinulate and predict sclected datasets.For the di3brent data pattems,thepaper made case studies on both linear and nonlinear cases to solve Equations(3)using thC Optimized
analytic function methods.The paper also includes a special case study with real― worid data of Japanese
tourists visited GLlaln in 2004‑2017 to sho、 v thc accuracy and ettctiveness of the optinlized analytic
如nction lnethods in big dattl analysis and machine leaming research.

References[1l Janles,G.,Witten,D.,Hastie,■ ,and Tibshirani R An lntroduction to Statistical Lcarning:with
Applications in R(Sp」 nger Texts in Statistics)lst ed.2013,Corr.7th printing Edition,@SpHnger(2017),ISBN‑13:978‐ 1461471370,ISBN‑10:1461471370.
[2]Aggattal,C.C.,Neural Networks and Deep Lcarning,A Textbook,@Springer intemational

Publishing AG,part of Springer Nature(2018).ISBN 978… 3‑319… 94462‐ 3,ISBN 978‐ 3‐ 319‑
94463‐ 0.

[3]Stenger,R,Numerical Methods Based on SINC and Analytic Functions,@Springer,New York(1993).

14]Wang,L.,and Wang,X.D.,Introduction to AlgOrithms of Machine Learning,pp.388(inChnese),@TSinghua U‖ versれ y Press,Beuing(2019).(In chinesc:王 冨 =王 晩末:机 器学コ尋恰,

388更 , @清 準大学出版社,北 京, 2019).ISBN 978‑7‑302‐ 52456‑6.

[51 Ben,K,Mao,X.,Zhang,y,Zhcn3 D.,Cal,D.,Artincial lntelligence:Theory and Pracuce,pp 331
可末,毛 新軍,張 彦鋒,邦(in Chinesc),@China Machinc Press,Beling(2016).(In Chncse:責笛,察 敦波,人 工智能実践教程,331, @机 械工立出版社, 北京,2016),ISBN 978‑7‐ Hl―
53869‐ 1.

[6]ZOu,Y,chen,Z.,and Xu,J.,Binding Visualization Method and Numeric Mcthod Togetherto
Analyz℃ Large Data― with A Case Study Journal ofaivances in Mathemttics and Computer
Sciencc,15(4),(2016),1‑10,17]Stenget F.,Handbook of SINC Numerical Mcthods,@CRC Press,20H,republished in(2017),pp482,ISBN9781138116177.

[8]Jarn3 S・ ―S・ ,SWanson,C.,Lec,R,and Zou,Y,64 Bands Hybrid Noise Reduction and Fecdback

Canccllation Algorithm for Hcaring Aid,Interpational Joumal ofControl and Automation,7(1),(2014), 427‑436.

‑27‑

Corresponding Author Yousuo Zou,PhD,
Division ofMatheinatical and Computer Scienccs
College ofNatural and Applied sciences

University ofGuam
303 University DHve
Ⅳlangilao,GU 96923,USA

Email:ヵ zou@tritOn.uog.edu‑28‑

ISBN 4‑901329‑11‑8

Procccdings ofthc Tenth lntemational◎ 2021 1ntcrllational lnfomation lnstitutc

Confcrcncc on lnforlnttion(InfOm■ ation'2021)

A New 2.5D Schema ofthe Regular and Senli‐ regular
Polyhedra and Tilingsi Classes II and IV
Robelt C.Meurant′′″げ rra″ ″。 ′Dた crα E″ ガ/ぉ ,麻 ′′ι′υねИォ κ′PTttssa4シ ο″′助
タの ′
″グ
̀/sプ
̀s∫
̀わθ
″‐
Satrzg/′ 4Sカ ル01‑'麟
οE″ ・ 4/″
∂Sみ ′
ε
α′
′
ο孔″brrお ο
ε力&2″
ε 4Res̀α ″̀c Drrὶaring PC Iた
7θ・ E″ α′″′ ′ α″rcな れαfiι ο″θ̀ο″αイ∂θ‐
Dο 77g 6∂ j BL電 1,げteο Fgb2‐ 乱̀οcrο ″ ルD● R̀′ zb″ εげ κο

E″ g′ ″pl∫ 島

1. Abstract/1ntroduction
lnspired by Critchlow [11, I previOusly advanced a ne、 v order in spacc to account for the
rcgularities and relationships of the regular and sellli―

rcgular polyhedra,in threc classes I― III

of{2,3,3},{2,3,4},and{2,3,5}symmCW9 and IS CXtension to the rcgular and scm卜

regular●lings of thc plane,ofヽ vo classes IV&V of{2,3,6}and{2,4,4}wmmet7[2].Each classconsistcd of 7 polytopes, togethcr with a further enantiomorphic 8th snub polytope, whichfunctioned as a transition polytope.Wlthin each class,3D polyhedra(2D polygonal arrays)
wcre prescntcd in invcrted

T' follll, conSiSting of a horizontal base truncation sequcnce

bc●vccn positivc(十 vc)p01ar and ncgative(二 VC)p01ar polytope:PL十 ̲TP十 ̲QR一 TP
and a veltical transcendent sequencc:1°

PL ;GR(with
SnbQR
in
SR‑3°
QR― (1.5° SnbQR)‑2°

cither enantiomorph follll).In this work,I ttstlmc that the reader is familiar with thtt earlier

research,which PDF is dow憾 oadablc from my homepage[2].The recOgni●

on of the rcgularpolyhcdra of ttvc&二 vc tctrahedra,octahedron&cubc,and icosahcdron&dodecahedron as
extrcmc polar folllls,rnediated by the pcrfect forlns ofthc Class I一 III quasi‐ regular polyhcdraof the rcspectivètctratetrahedron'(2‐ colorcd octahedrOn),̀OCtahexahedron'(cubOCtahedron),and icosidodccahcdron(and cOrcsponding Class IV&V quasi‐

regular 2D polygonal tritthcx

and square― square arrays),waS a relcvant cri伍 calinsight infollling another ofmy papers[3].

In this prescnt papet l advancc a cubic 2.5‐ dimensional schcma to bettcr describe tlle

morphological structurc of each class, by flrstly positing a null polytope VP; thentransforlning the structural order of each class fronl the inve■

cd T follll ofい 〃O Sequenccs,

into a cubic scheina of twvo expansion sequencc clusters,whereby in either,a sced polytopc
vay,

cxpands in cithcr of h〃 o ways into two kinds of intc11llediay polytope,thcn in thc other、
to a fully dcvcloped polytopc. I dcscribe this in relation to the most illlportant Ciass II of{2,3,4}symmCtり ,aS it COrresponds to thc polyhedra that constitute aH 16(10 diStinco oftheClass HI honcycombs.To con■ 1111血 e validity ofthe ordct l also describe Class IV of{2,3,6)
symmetiγ of the regular and scnli‐ regular tilings of thc planc,which like Class IIだ 貶 III, isasymmetric:polar opposites are not the salne though recolored polメ opeS,but differcnt
polytopes.Thc diversc correspondenccs of thc ordeF aCrOSs classcs are ngorolls.In a 10nger
dcvclopment of this paper9 1 anticipatc describing an flvc classes of the revised new order inspace,characterizing the polylopes and thcir expansion sequcnces and clusters thercoi
Ke,甲vords:aH‐ space‐ flHing,polyhedra,honcycomb,tiling,structllral rnorphology,scmi‐

Supplementary lnfortnation:Colored ngurcs and doヽv■ loads http://、regul〔 鴫 order、ハνwirlnCurant con1/its/si‐ 21 1ltmlvη瞥 rmeurant.com/1s/papers/oolvgon‐
A Ncw Orderin Space[2]:available at PDF 06 at http:″ 、

01B b Sの ′ψαε

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Nomenclature+ve,posit市 e: vc,negrative;C,class;CB,Cubc;CO,Cuboctahcdron;DD,Dodccagon(12‐ gon)∫ E,
Edgc;E° ,Ncutral Edge;F:Facc;GR,Great Rhombicぅ GRCO,Great Rllombic Cuboctahedron;HX,

Hcxagon;NS,Ncutral Squarc;ntrl,Neutral;OG,Octagon;OH,octahcdron;P/PL,Pole/Polar;PL+μ+/ve Polar;QR,Quasi‐ regular;RS,Rotatcd(tRuncated)Squarc;ミ 、Rotatcd(tRuncated)Trianglc;,

RX,Rctated Hcxagon;Snb,snubi SnbCO,Snub Cuboctahedron;SnbQR,Snub Quasi‐ regular;sQ,
Squarc;SR,Small Rhombic:SRCO,Small Rhombic Cuboctahedron;■ TetrahCdron;■ L Trunctted;
TC,Truncated Cube;TH,Tr卜 Hex(aray);TO,Truncated O∝ 油 edron:TR TrunCated Polar:TrP+μ,

Tmncated+/二 vc Polar;TR,Triangici V+μ ,+/二vc Vertex;V° ,Nclltral Vcrtcx;VPC,Verticial Polytopc.

2. Honeycomb/riling lnvestigations
lnspired by Grtinbaum and Shcphard[4],I later invcstigatcd thc structtral morphology ofthe
all‐ space‐

flHing polyhcdral honeycOmbs of Class I― III of{2,3,312,3,3},{2,3,312,3,4),and{2,3,412,3,4)symmetり ,and thC corresponding polygonal dlings ofthe plane of Classcs IV&
V of{2,3,6}&(2,4,4}symmetw[5‑7].I gained signincant insigllt into the honeycomb orderwhen l positcd for cach class C the null quasi‐ rcgular polytopc, as thc vertcx of zero
dimension,with zcro extension,but with+vc and ttvc polar verticcs V+and V,and neutral(ntrl)VertiCes v° ,all coincident in thc verticial polytope VPc=V++VO+V ,while a1lowing

spatial cxtcnsion in the expansion sequences.This insight was flrst in relation to thc various

3D honcycombs,cspecially the polyhcdral honeycomb Class III of{2,3,412,3,4}symmetry,and later extcndcd to the 2D honり oomb Class IV&V of{2,3,6}&(2,4,4}symmetry[5‑71.

③
③

計
一
﹂

9

③
Fig l.Archetypal expallsion sequence diamond clustcrs at iowcr(lell)and uppcr(right)Texts ofupper left and lowcr right dialnonds rcfcr to thc faces oftheir lowcr and upper polytopes,respectivcly.
0° faccis

v l° facc is PF(lcn);10 face is TrP■ 2° is● vice truncated=double frcqucncy facc(right).

Seed polytopc cxpands in 2 ways,as onc polc morphs wh‖ e othcr separates by+1,andッ たmorphcd polc separatcs by+l whilc separated pole morphs,andッ た′ッ̀ッθ
パα;tllcn

̀rsa,lo common rhombic QR.

Further progress was madc through the organiZing principle of the common follllal structllreof an cxpansion sequence clustet of contracted seed honcycomb that in thc flrst stagc,
expands in eithcr of two ways toヽ vo intellHediary honcycombs; and in thc sccond Stage,

‑30‑

￨̲

cxpands■ 1■ her in thc other of theヽ vo ways,respectivelン ちto the nllly expandcd honeycomb[5‑7].A common patcm to an 16 Class III{2,3,412,3,4)honcyCOmbs(of 10 diStinct follus)[6:輌 g.2]then bCCamc e宙 dent.The schcma was also secn in the Cltts IV&V honeycomb
2D tiling arrays,a1lowing its rccognition in the Class IV̀乾

V polytope arrays,and abstraction

to the Class I― III polytopes.This rcvised ordcr and 2.5E)schema of thc polyhcdra cnablcd

deep insight into tlle structral morphology ofthe rcgular&semi― regular polytopes(Fig.1)

3.The r〔wised order ofthe Class II polytopes and their 2.5D schema
Thc initial step ofintroducing the null polytope,in this Class II,thc null CO VPII,is to locatc

資on thc central transcendent vertical axis,below the QR CO,in effect a O°

clcmcnt.But thisdocs not providc adequate rclation to thc other polyhedra.The appropriate follllal Structurethen bccomcsヽ vo overlapping diamonds separatcd verticaHy(omitting SnbCC)),reCOgnizing
ヽvo groups of4 ofthe no、 v8elemcnts,in which cach element of one group has a uniquc pairin the other group,logically pairing the lowcr forln with its upper trtlncatcd follll(Figs.2,3).

TR‐ V

Fig.2.Ovcriapping diamonds ofthe schema:Class H(lC食)&On neutral axis(center),Class IV(nght).

This suggested investigating the corresponding transfbrmations on cach ofthe χ,」げ,and z axes

ofthe flgurc,whcre the●vo overiapping diamonds could now bc recognized as the lowcr andupper fraces ofa cube in proieCtiOn,in which thosc

χ,y,Z aXes could be exalnincd(Fig.3).

Z

/X

Y、

↓

Fig 3 Ciass H{2,3,4}(lcft),gCnera1 2 5D schema(ccnter),Class IV{2,3,6}(right),On negat市

c axis.

This schema shows a high dcgrec of regulariり l As prcviously mcntioned,thc vertical axis
transfollllations corrcspond to trllncations,hcnce thc nuH polytope VPII can be dcduced to bc

a truncation ofthc QR CO:V+,VO,&V coincidc in thc vclticial VPH:VP=V+十 VO十 V .

‑31‑

χ―

In the lower dialllond sequencc cluster9 thc seed follll of the nuH VPII expands on theaxis to thc PL CB,and夕 Laxis to thc PL+OH:° Hヽ
′ CB;then on the ¨χaxis thc OH,and onⅣ、theル axis the CB,ё xpand to the common neutral SRCO:OH′ SRCOヽ cB.
In thc upper diamond sequence clllstct thc seed follll ofthe neutral QR CO expands on theTC;thcn on thc ‐χ‐axis to the l■ "TC,andy― axis to the TP+TO:T° ヽcO′
χaxisthe TC,and on
GRCOヽーthcッ aXiS the TO,expand to the col■ mon neutral GRCO:T。 ′Tc,correspondingly.

Polyhcdra axes are cominon to aH polyhcdra in a class,but vary class― to‐ class.Class II―ve,ntJ,&+ve axcs are deAned as thc nollllal Ⅸ eS of thc(100),(110),&(111)plancs,
respcctively.(〕 H vertices and CB faces are二 vc,thc edges of both in"vo orientations arc ntrl,

while OH l田 t faces and CB vcrticcs are+ve:The QR CO is composed ofttve RSs and+ve
RTs.Transfo111lations ofthe constitucnt polytopes(faceS/edges/vcnices)Ofthe 8 polyhedra or
polygonal arrays in a class can thcn be characterized by axis ofthe 2.5D schema.For Class II:
On thc z― axis(↑ ),二 VC Cicmcnts increasc l° lo。

↑

RS5,SQ5↑ OG5,町 ↑RSI,SQI↑ OGI);ntrl

dcmenも separate,so adidning vc■ ices become udt dktancc aparti(■↑で,2× (E8↑ E2),

NS8↑ NSf),thc 2× (E8↑ El),bchg h 2 sets of dfFcrc■ oHentalons and+vc dcments
increasc l° :(vざ ↑ミ t,TR古 ↑HXさ ,V「 ↑ミt,TRI↑ HXl).
On the χ―axis(′ ),二 Ve elements increttc l° :(V。 ′ SQ3,RS5′ OG5,V. ′ SQl,RS/1′ OGI);
N elements increase l° :2× (VO′ EO,EO′ NS);and+Ve elcmcnts separate,so a可 Oining
vcrtices bccOme unit distance apart:Nも ′ V「 ,TR古 ′ TRl,RTよ ′ 遭 t,HXさ ′ HXl).

On thcソ ーax施 (ヽ ),″ αグ∫′ο Jg/r r2砂 ,we dements scparatc,so attd五 ng
学 s″ 竜″′′'暉
vcnices becomc unit distancc apan:(vlヽ v。 ,SQヽ SQ5,RSIヽ RS5,OGIヽ OG5ゝ ntJ
cに medshcκ ase l° :(E8ヽ で ,NS8ヽ E8,Efヽ で ,NSfヽ E,光 and+ve dcments hcreasel° :TR古 ヽ vま ,HXさ ヽ Rlよ ,TRIヽ
v「 ,HXlヽ 迅た )(rcfCr Figs.1‑3).
The Class IV ivc axcs are deflned as the nollllal axcs ofthe mid―faces of thc trianglcs of

thc PL TR array.the ntrl axcs in● vo scts of oricntations as the nollllal axcs of the rnid‐ edgcs
ofthe PL TR and PL IIX arrays,respectively9 and thc+vc axcs as the nollllal axes ofthc rnid‐

faccs ofthe hexagons ofthc PL IIX array.rcspectivcly.Hcncc thc PL+￢ 日R aray V and PL

HX aray HX are一ve,the cdges of both polar arrays in、 vo scts are ntrl,while the PLtt TR
array TR and PL HX array V arc+vc.The QR TR■HX(TH)array is composed of一 ve RXs
and ttve RTs.Transfomations of thc consutucnt polytopes(facCS/edges/vertices)of thC 8
Class IV polygonal arrays can then bc characterizcd by axis ofthe 2.51)schcma:
On the z― axis(↑ ),二 Ve elcmcnts increase by l° :oO ↑ RX5,HX5↑ DD5,V■ ↑RXl,HXI↑

DDIゝn,l demcnts separate,so thtt a碕 omhg vc■ ices became unit dstance apa■ :(可 ↑で,2× (E8↑ El),NS8↑ NSf),the 2× (E8↑ Ef)bcing in 2 sets of difFerent orientalons;whilc+ve

dements hcК ttc by l° :(寸 ↑RTよ ,TRよ ↑RXさ ,寸 ↑RTl,TRI↑ RXl).
On thc x― axis(′ 〕,二ve elements increase by l・ :(VO ′ HX5,RX5′ DD5,Vl′ HXl,RXI′

DDlゝ ntn dements increase by l・ :(可 ′ E8,E8′ NS3,で ′ Ef,Ef′ NSf);and+vc
clements scparatc,so that adioining Vcrtices bccome unit distancc apart:(Vよ′V「 ,TR古 ′TRl,RTよ ′ RTよ ,RXよ ′ RXl).
On thc v― axis fヽ ),だ 翻 /Jg sicPs R2, Vc clemcnts scparatc,so adioining Vcrticcs bccomc

unit distance aparti(Vlヽ V。 ,HXlヽ HX5,RXIヽ RX5,DDiヽ DD5),ntrl elements increase byl°:(E8ヽ V。0,NS8ヽ E8,Efへ vP,NSPヽ El);and+ve elements increase l° :(TR古 ヽvま ,RXさ

ヽ Rlま ,TRIヽ v古 ,RXlヽ 迅t).ざB.AH 2D polytope arrays(Figs.2&3)repeat tO inЯ‑32‑nity).

Thc snub follll is clcarly a trarLSitiOnal follll,aS C宙 denced in the jiterbug sequenccs I

recognized in my early rescarch[2]for eaCh polytopc Class lttV contraction SRQR→

SnbQR→ QR;in Class H,SRCO→ SnbCO→ CO;and in Ciass lv SRTH→ SnblI→ TH.Thc
Snub polytope in cither or bOth of its enantiomorphs thlls sits at the ccnter of thc schematic

2.5E)cubc its class,FnCdiating the lower and highcr diamonds.Class II SnbC(D or Class IV

Snb■ l is,益 bcfore,bc■ veen the l° QR COo■ m andthe 2° SRCO orSRTH,respect市 ely.
̲TPキ ̲QR― T「 一PL
Thc original linear horizontal truncation polytopc sequence ofPL十is dcvolved in the 2.5E》

schema to a rcvised̀M'‐ shapcd sequence;while thc originai neutrallincar vertical transcendcnt scquencc now extends to includc the nu‖

vcrticial polytopc VR

4.Commentaryln this papct there are scvcral key threads. The notion of scqucnce cluster of elcments isabstracted from Class IⅡof the polyhedral peHodic arrays(hOneycombs),rccOgnized inClasscs IV&V of tlle 2D polygonal pcHodic arrtts(tilings);sccn tO thcrcforc characteHzcthc 2D Classes IV&V ofthe regular&scmiregular polytopes(2D polygonal arrays),whiChhave thc salnc geometric follll: then here generalized to aH ivc cI〔 sses of the rcgular &semiregular polytopes,as in the exclnplary Class II of{2,3,4)symmet7.Thc scquence
cluster(or SCqucnce paiぅcan be seen as a diarnond arrangernent of帥 o× two― step sequcnces,from the inferior nilly contracted central compollnd,in thc flrst step expanding lc■

2%right tointellllediary polar ttve&=ve compounds,respectively;then in the second step cxpanding
furthcr to right at le■ , rcspcctively. to converge in the cominon superior i11ly cxpanded

compound.At each step,in either sequence,+ve faces e■their hicrarch"or separatc by un■

her expand to the next highcr rank in

distancc(edge len〔 磐1),frOm adioining tojaccnt.

Mcanwhile,一 ve faces show the converse:they e■ her separatc by unit distance,or cxpand tohigher lcvel, rcspectively. Thc facial clements that separate in thc flrst step, expand in thesecond,andッ ノ̀̀νθパα.This beautifbl pattern offollllal cvolution seems to be indamental tothe polytopes(as individual compounds),as wen as the honeycombs&tilings(the pcriodic
rcgular&semi‐ regular repetitiolls of compounds to f11l al1 3D&2D space,rcspcctively).The

2.5D schema shows lower& upper dialnonds; in the lowet thc+ve&二ve verticial faces

develop from thc sccd VPc to cxpand icft&right to+vc̀%二 ve polar‐ faccd PL+′ compOundsi

thcse+vc&二 vc faces scparate right&lci to recombine in thc SR̲which thcn jitterbugs,
contracting through the central snub to the QR in thc upper diamond from which thc
trllncated +ve &―vc ねces separatc left & right to thcir truncated polar compounds; then
expand rightだ 乾lci to their double‐ frcquency faccs to recombine,cullninating in the GR.

In carlier rcscarch, l organizcd thc regular & semi‐

regular 2D & 31) polytopes bysymmetry into■ ve parallel classes,characteHzed by an inverted

T'pattem of horizontal
truncation sequcncc & vertical transccndence sequencc of 7 compounds(8 including thetransitional snub foI111,in cithcr enantiomorph).That pro宙ded a useil schema to apprcciatetlle relationships between thesc polytopes.In this papct l integrate the nu‖

polytope of zero

dimension for each class that l later recognized in thc 3D honeycombs and tllen 21)tHings,topresent a cubic(here shown cuboid)2.5D schema that bettcr accounts for the intrinsic order
within cach polytope class,While thc relations bc●vcen class are unaltercd,the class―to― classcorrespondcnccs remain rigorous: within each class, the corresponding polytope stands in‑33‑

follllally cqu市 alcnt rclationship to its neighbors.In cach ciass there arc now 8 compollnds(9counting thc transitional snub compound,in either enantiomorph).The Virtual nuH polytopes
can be imagined as the QR compollnd ofthcir ciass,but of zero cxtent,so all+ve,ntrl,&二veverticcs of the QR coexist in thc same verticial point.There are thus 5 such null polytopes,
one for each class;whilc by analo3y9 thc real QR reprcsents thc truncated fo111l ofthe null VR

In this papcr l concentratc on Class H of the polyhedra of{2,3,4)symmetrys as they arc

the most important and characterize thc maior Class IⅡ

honeycombs Of{2,3,412,3,4)

symmetry;and also refer to Citts IV of thc polygons of{2,3,6}symmCtw tO Validate thc

2.5D cubic schema cxtcnded to the 2D casc.Ciasses II&IV(&III)are nOn̲symmetHc,in
thattheir polar forms are notthe same(c.■thC Class l or V reoriented Tμ or recolorcd SQ+μ ).

5.(Conclusion
This nove1 2.5[)schema ofthe regular and serni‐ regular 3E)p01yhedra

陀2E)polygonal arrays
proves vital towards charactcrizing their structural mo,phologyp and is applicablc acrossciasses;thc bchavior in one class is perfectly reflected in the other classcs,as in the excmplar

jittcrbug sequences.In addition,tlle schema recognizcs for each class a null polytope VPc,
whose vi■ lual properties are deducible from thc schema.Thc schcma cxploits thc samc motif
ofdiamOnd expansion sequence cluster dcrived fronl the Class III aH‐

space‐ flHing polyhedralhoneycombs and Class IV&V polygonal tiling pattems ofthe plane,so appears archetypal.
In fulure research,I anticipate developing this paper to includc an flvc classes I―

V ofthercgular and sellli‐ regular 3D polyhedra and 2D polygOnal tilings to prcscnt a complctcly

revised new order in space;then in iater work,reapply the schema and componcnt dialnonds
to the flve classes I―V Ofthe all― spacc‐ flHing honeycombs and tilings,in ordcr to gain further

insight into their structural morphology.with potential applications to latticc structure,bonc

scaIFolding, polymcr compositcs,kinetic space structures, and in gencral,to apprcciatc andappropriately utilize the inhcrcnt subtle and profound harlllonic structurc of cmpirical spacc.

6. Referencesl.

2.

K Critchlo、 v,Ordcr in Spacc Thames alld lludson,London,1969.

R C Meurant,A Ncw Orderin Spacc― Aspccts of a Thrcc¨ fold Ordcrin3 0fthC Fundamcntal
Symmetrics ofErnpirical Space,as cvidcnced in thc Platonic and Archilnedean Polyhcdra一Together vvith a Two‐ fold Extcnsion ofthc Orderto includc thc Rcgular and Semi‐

・
ofthc PIanar Surface.ル″′
″α′
′
0″ α
ノノο″″
″α′グ シ aι
Esscx,1991,11‑32.Download PDF 06 at http://、rcgular T:lings

・
″ε′
″′
as,Vol.6 No.1,Universiv ofSurrcy,
̀Srr・ゃ、、v.rlllcurant.com/its/papcrs/poiv2on‐〜

1.htnll

3.R.C.Mcurant,Thc〜 ″th ofPCrfection ofthe Platonic Solids People alld Physical En宙 ronment
Rcsearch PAPER Conference on Mytll Architecture History Writing,Universiサ
New Zcaland,July 1991.PDF 07 at http:〃 、v、 v、 v rmcurant comAts/Dapers/D01V20n‐

OfAuckland,
l html4. B.Griinbaum and G.C.Shephard,Tilings and Patterns.W.H Frceman,New York,1987.
5.R.C.Mcurant,Towards a Mcta‐ Order ofthe An‐ Spacc̲Filling Polyhedral Honcycombs through6.

the Mating Of Primary Polyhedra.′ η″″′οηJο 7″ α′
力″,Vol.19,No.6(B),Junc 201̀,2Hl‑2124
R C.Mcurant,ExpansiOn Scqucnccs and their Clusters ofthc All Spacc‐ f11ling Pcriodic

Polyhcdral Honq/combs.べ∝ 脇α ο″■,7 αちV01.20,No.10(A),Oct.2017,7345‑7362
7.R.C.Mcurant,Towards a Ncw Ordcr ofthc Polyhcdral Honeycombs:Pa■ HI:Thc Dcvelopedr′

Mctaordcr,Form alld Counterforrn.[ゅr″ α′′
ο″力 ′″αちV01.22,Nol,Jan 2019,2345.

‑34‑

ISBN 4‑901329‑11‑8

Procccdings ofthe Tcnth lntcmationalく)202 1 1ntcmational lnfonnation lnstitutc

Confcrcnce on lnforlllation(Infom■ ation'2021)

A Solution fbr Rde‐ sharing Route Choice Problem

based on Genetic Algorithm
Chaoze Songttand Lci Li***G″ ″ α″ S̀乃 οダ″
Q′ S″ ὶια″グEngi″ θ ルg″ θsaノ υ物ルθrts′ 秘 KOν ″ι43ο り ο′θイー
δ58イ ゝ
彎 α″
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**Fα θ ′ヶ 9′ SC力 ″ει α″グ Ergi″ θιP・″■勇 HOSetιレ ′ツιrs′ ヵ崎 KOgα ″ι47ο ″ ο ノ∂イー∂58イ ノ9,α ′

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Abstract
The growth ofthe amount ofvehicles has leads to many problems.To solvc thesc problcms,、
vc did a
research about ridesharing・ Ridesharing is a pattem of transportation in which people with sinlilar
itineraHcs and time schedules utilize spare scats in the vehicle and share the travel cost[2].In thiS paper,

we calnc up with a new mathematical modei to solve the ride‐ sharing route choice problem andexpcrimentcd it in a virtual trafflc sccne.According to thc result,our modcl perforlns bctter than thc

prevlous one.

Keywords:ride― sharing,(]enetic A180rithm,■ oute choice,optinlization problcm

l.Introduction
ith the devclopment of econonlic globalizatiot people's living standard has beenヽ′
improved a lot which contributed to a large growth ofthe amount ofprivate cars.Becausc ofprivate cars, people's lives have bccn much more convenient. However,on the other hand,problems such as trafflc congestion,the occupation of city space,air poHution,and the over―consumption of energy have not been solved yet.Furthellllore,On account of thc increasc inthc population,the amount ofvehicles has grown as well.While there are too rnany unoccupiedscats in the moving vehicles、 vhich is a large waste ofresources.

So far, most researches in the fleld of ridesharing are about the indamental thcow ofridesharing such as the current status and tcndency of五dc‐ shaHng,thc organizing pattcm ofridc‐ sharing and so on.Thc rescarchers have donc rnany qualitativc analysis upon rnany aspccts

of五 de― sharing which have enriched the ndc‐ sharing theory.There are also some rescarchers
who havc done some quantitative analysis.However,researches on thc ridesharing route choicc
are alFl10St about lnathcmatical lnodeis based on one―to‐

many organizing pattcms.Moreovcr,

the ねctors and constraint conditions are comparatively siFnpleX. For the calculation of themathematical models,they mainly utilized heurisuc algOrithms and greedy algo五 thm[1].In
Zhou's paper[1],he came up with a mathematical model and applied itin a宙 rtual ride― sha」 ng
sccnc as an cxperiment.Nevcrtheless,the scale ofthe trannc scene is relatively smaH.

‑35‑

In this paper,we proposed a new mathematical modcl and tested itin the same map withZhou,but、 ve enlarged the scale including the amount of vehiclcs and pttsengers.FinaHy,、vehave got an optimal route which has a better perfolHlance.

2.ⅣIathematical Model
The probicm consists ofa set D=1/J,2… ,″ of4 Vehiclcs,a sct R=rf,2… ,り ofrpassengers,and a set/=″ ,2,… ,12/Ofν StatiOns.Each vehicle′ belongs to set D.Each
passenger r belongs to setレ l Each station ml‐ belongs to setレ l Each strect is regarded as aline linked with two vertices(statiOns).

2.1 0ptimized OtteCt市 e Function

れ
れ
ΣΣ皓χ
=n

(1)

,・

銑,.̀the cOstthtt vehde,pass through the street Hnked with statbn

and sぬdon 4.χ ttη

is a decision variable.Ifthe passengerj riding vehicle,passcd the strect linked with station″

おand station″ ,χ ttη WiH be f,dhe即 e Xttn Wi‖ be.Otlr opdmization ottec」 Ve、 ゎθminimize thc total cost.

2.2(Constraint Conditions

Σ 肛

ι
れ.χ ttn≦ 乃
Fふ

≧1

・=1
Σ瑠

】 し

)]XIn― EXlふ ={卜itttθ

4.1‑bl≧̀.,

あ1≦ 14≦ α
l

WheК

ι

,η

塩

=[′
QΣ

鳳免1° pr琳 >Qis thc theoretical time cost、 vhen a vehicle passes through the strcet linked with station′and station″ .乃 is the max travel total dmc of passcngerブ

η.ConStraint(2)ensures that thetheoredcal total travel● me is shotter than the max traveltotal dme ofthe passengerノ ・θ
おiS thC

amount ofunoccupied seats in vehicle F、 vhen vehicle′ is at thc station rn.Therefore,constraint‑36‑

(3)cnsures that therc is at least onc unoccupied seat in the vehicle so that it can contain new

passengers.Constraint(4)ensures that all the passengers in this system will be picked up,
namely,there will be no one who can not get a car.OJ・

is the o」 gin of passengerブ・θ
d iS thedcstination ofpasscngerノ .COnstraint(5)deflnes the origin and destination ofpassengerブ
the timing when vehicle i arrives at station m.わ.α tt iSたis the timing when vehicle′ departs fromstation m.Constraint(6)ensures the practical time cost longcr than the theoretical one.
Constraint(7)is the time window constraint.

3.The Proposed Algorithm
ln this paper,we llsc Genetic Algo減

thm to solve thc above― mentioned mathematical model.

Genetic Algorithms encode a potential solution to a speciflc problenl on a siFllple chromosomc‐

likc data structurc and apply rccombination operators to these structurcs to prcscrvc critical
infol:Hation.Gcnctic algOrithms are o■ cn vicwed as function optilnizers,although thc rangc ofproblems to、vhich genetic algorithms have been applicd are quite broad.An iFnplementationof geneJc algorithms begis whh a population of(typically random)chromOSOmes.One thenevaluates these structllres and aHocated reproductive opportunities in such a way that thesechrornosomes which represent a better solution to the target problenl are given more chancesto ̀reproduce' than those chromOsomes which are poorer solutions. The '300dness' of asolution is typically deflned with respect to the current population[3].

4.Experilnentation and】 Results
We tted the map ofZhou's paper[1],and enlarged the scale ofthe cxperimcnt.
passengcr

dcmandamount
4
8

四ｄ
ｎ
ａ
Ｄ ｍ
・ｃ
Ｏ ｄ

0‐ D pair

passctlgcr

amount

6‐ 4

6

9

10

4‐ 5

7

3‐

6

Figure l map

Table 1 0‐ D Pairだ 財passengcr alnount‑37‑

As shown in the ngure,there are 9 stations.In the virtual scene,there arc 3 vehiclcs,cachvehicle can contain 4 passengers. There are 9 origin‐destination pair travel demands. The

amount ofpassenge∬ ofeach demand is shown in Tablel.
The parameters' scttings of the genetic algoHthm are: population size=80,nurnber ofgenerations = 100, crossover probability = 0.4, mutation probability = 0.1, and selectprobability=0.8.
Thc igurc2 shows the proccss that Genetic Algorithnl found the optimal solution whosc
valuc is 138.Tlle optimal route plan is shown in Tablc2.
Car

Routc

1

2‐ 6‐

8

6‐ 3‐

4

3

3‐ 6¨ 9‐

6

Cost

175
170

26

4‐ 3‐ 6‐ 5

6

1‐ 2‐

6

7

7‐ 4‐

3

1(〕 5

場●０■種

5‐ 2‐ 1

5

100

20

1モ

‖
)

155
160
146

11

140
135

9

・20

3‐ 6‐

9

Table 2 Result dtta

‑38‑

References[1]ZhOu,Hc― ping,ct al."The route choice and rate optimization modd of taxi―
力 α αιグ 働 α″gS力 α 磁 ルθが タ ゲ 胸 Jθ ′ει"グpooling."ル 磁 θ′
θy a♭ ′″ J■ Jθ κθり 8.4(20日 、

20‑24.

[2]Shen,Bi10ng,Yan Huang,and Ying Zhao."Dynamic rideshaHng."Sigspα riα ′身,θ θ滋′7.3(2016)i3‐ 10.

[3]Houck,Ch」 stopher R。 ,JcffJoincs,and Michael G.Kay."A LVenedc algorithm for func」 on
optimizationi a Mttlab implementation."Ncs2‑′

θ″ 95,09(1995):1‐ 10.

14]Alonso― Mora,Ja宙 cr,ct al."On‐ demand high― capacity ride‐ sha● ng via dynamict面 p‐ vehicle

aSSiemment,"Prθ ε dings̀/励 ιAり ″θηαJ И
̀θ

̀de″

ノ

た″ S l14.3(2017):462‑467.

̀/Sθ

̀θ

[5]Agatz,Nicls,ct al."Optimization for dynamic Hdc‐ shttng:A rc宙 ew."E″ 99θ α″力 ′ηα′Rθ sθ αrc力 223,2(2012):295‑303.
(々 ,θ rar,θ ttα ′αβ[6]Da宙 s,Lawrence."Handbook ofgenetic algorithns."(1991).
17]Chan,Neison D.,and Susan A.Shaheen."Ridesharing in North AmeHca:Past,present,and
future."7レ α″Qρ θr′ ″ιソ′θws 32.1(2012):93‐ 112.

18]Furuhata,Masabumi,ct al."Ridesha」 ng:The sttte― oithe― art and futllre directions."
ル αηψ α ″′わ″Rω ι″ θみParr Bf ttr73θ あ 10gicα ′57(2013):28‑46.

‑39‑

ISBN 4‑901329‑11‑8

Procccdings ofthe Tenth lntemational◎ 2021 1ntem江 lonal lnfom■ ation lnstitutc

Confcrencc on lnforlllation(Infollllation'2021)

Industrial Network and(Cluster,Restructuring Production(Chain Basedon Specialization and]Divisio■ of Labour after the 2020 Pandelllic
LI Ke
Cο ″鱈 θグ Eι θ″ο″たS,Ⅳ ル0″ し物ルαT″ ス 2b″ Q Jψ α″

―α
″
θ
E″ α
〃∫′
′
、
た@″ ルοブρAbstract
Atterthe 2020 pandemic,the wllolc world willlook remarkably different with thc consideration ofglobal

supply chain. This paper devclops a gencral equilibriuln modcl with endogcnous industrial cluster andendogenous industrial network ofdivision oflabour to fol11lalise and explore the interrelationship and rules ofindustrial cluster,ne● vork ofdivision oflabour,the econonlies of spccialization and agglomeration under thc

mst,

nevv era ofpost‐ pandemic global econOmy.The modcl suggests that institutional efflciency and mutual‐and competition among oounties and industnes will facilitate important circular effects,、

vhiCh propcning andshaping the arrangcment and allocation of industrial clusters,the position located at thc supply chain,and
consequently the status of economic grow"慟 .In particular,the improvements in institutional efHciency andmuttlal‐ trust over economic and technology systems will expand thc demand lbrtransactions and net、 vork size,
which in turn win deterllninc the dcvelopment of cluster and network scope,as wcn as the position at the

network.
Keywords: Industrial ne"vork, Industrial cluster, Specialization, Division of labour, Inia‐

marginal

analysis,Supply chainl.Introduction
Even a■er the 2020 pandemic subsides Bradually,tlle world will be remarkably different with thesystem of global supply chain.The supply shock that begun in China in Februay of 2020 and thedemand shock foHowed as thc global economy shut down exposed the、 veaknesses and vuinerabilitios

China
in the pЮ duction strategies and supply chains of fli11ls.Thosc events,oombilled with the US‐
trade war,have triggered a rise in economic nationalism.As a result,Π lanufacturers worldwide wi‖ beunder grcatcr political and competitive pressures to increase thcir domestic production, growemploymentin thcJ「 home countries,reduce or even elinlinate their dependence on sources perceived
as risky,and rethink tllcir usage of invcntow from the global supply chains.All the concem haverccalled our attention on the rclevant issuc ofindustrial clustcr and industrial ne● vork[16].
There are enolll10uS Studies have been conducted lately on the issues of industnal cluster andindusmal neぃ″Ork,which reflect substantial concem over economic growth and devclopmentthroughglobal division oflabour and specialization.Among them,Michael Porter[25,26,27,28,29,30,31,
32,33]has diSCussed thè̀industrial cluttcr'。 n the foundations ofmttket economies which contains
interrela d and dynamic mi滋 ures of cooperat市 c arrangements alld competttive relationships.This

rescarch stream can be traced back and Jgni■ cantly in■ uenced by Alfred Mttshalrs notions of"industrial disttictゞ 'and"industrial atmospheres"[17,18],and alSO Piore and Sabelゝ tellll of"ne対 ble

specialiation"[24].Porter deincs a cluster as a geo3Taphic concentration(̀̀ge03Faphical pro対

mity")of compcting and cooperating companies, suppliers, service providers,and associated instittltions,which is resulted lЮ nl the relationships alnongね ctor conditions,demand conditions,related andsupponing industties,corporate statew,and structure and rivalry[27].MoreOVer,industrial cluste∬
have been recently also studied as groupings ofinterrelated f1lHis thatinnovate and gencrate econolnic
gro、 、
強 ,such as'oollective efrlciency"[34],the function alld effect of kno、 vledge extemallies alld
spill― overs[3,5,7,8],and

the dynamic nature of interactive leaming necessav for innovation[2].
Furthcllllore,Chandler argues that historicany, ccononlies of scale and scopc have been achievcd
mainly by large private and public enterprises[6].Similarly,Lmnick[15]and Florida and Kenny[9]Jso point out that iarge and high― end corporations a.re at the Heart of the innovation process andgrowth since they have,unlike small i111ls,the abiliサ to cOmbine technology,investment,clearly‑41‑deincd organizational strllctures,and thc adoption oflabollr practices of■ exible special協■lon,lust¨time"production,and outsourcing;and multi‐ skillcd and multi‐ taskcd employces.Regarding the
dctcrminants of clustet Nclson alld Willter[20]alld Nelson and Samp誠 [19]point Out tllat location
choicc by flilils iS driven by transpo」 慶ltion cost minimization and optimal combination ofkey location‐in―speciflc inputs for an optillnl levcl of production in order to maxiinize proflt,and how institutional

冨 angement affects econoΠ lic perfollllancc.The institutions arc as standard''social technologics",andeconomic growth results fronl thc co― evolution of physical and social technologies. According to
Storper[36],f1111lS in Clusters or industrial districts are aimed at securing competitive advantage.In
gencral,「1111ls in Clustcrs can take advantagc ofpositive extemalities and also force theln to competc
morc icrccly with the nl:1ls、 Vithin other clusters、 vhich Ⅵ/ill provide the inccntive for the clustered

輌111ls to innovate[25].HenCC,Clustercan be regarded asincrcasing various arallgemcnts ofnetwOrk)d、th,specincaHy at thelevel ofthe regional cconomy where promotion ofentrcpreneuriai netwOよ s and clusters can occur[4,f11 11ls,it can be considered as a broader scalc as a foundation for econolnic gro、

14,34,38].
Regarding industrial neヽ vorks,the litcraturc on ne● vorks has historical roots in both the theory of
the f1111l and the literature on

growth poles''.In particular,the latter recognises the leading fllHls'rOIC

and potential fbr positive spill― overs fbr a number ofnon‐commercial painers,through ageographically concentrated production andprocess of polarisation"or̀̀propulsivc development"[23].In

Perroux's original follllulation,a gro■ vth pole refelTed to the linkages be■ Ⅳccn fll11ls and industries.
̀̀Propulsive f1111ls''are those f1111lS that are large relativc to other rlillis and generate induced 3To、ゃththrough illter¨ industv linkages as tlle industry expands its outpllt[23].ThiS theOry has signiicallt

ilnpactin the promotion of linkagc smdies"that,ratller than bcing related to the idea of
geo.oraphicalproximity''[291,it iS mOre valid to develop and discuss the importancc oflinkages within trans‑local
fll ills,subsectors,commodiサ chains,as well as global supply chains[21].An thesc argumcnts sttcss
the importance of nc● vorks and linkages within lvider sp
es as a、 ″ay to beneflt frorn abilities andadvantages that cannot be reaped in iocal econolnies alone.Besides,there are different rneanings overnct、 vorks depending on other theoretical approach adopted,such as theories of transactions costs,

resource dcpendency,strategic management,and social nettork theow.There ttc basicaHy threescts of concepts,based on stratew,neヽ vork management,and social dimensions[39],HarrisOn etal.[13]havc SCen technological learning as one of thc dynalnic agglomeration outcomes to bc
derived fronl combining geographical closeness and follllal transactions based or infollllal
relationships.In a context where thc agglomeration of fi111ls and institutions is rclevant to enhance
local competitiveness and make relational activitics easier,the explicit interactive dilnensiOn ofnet、 vorking providcs an indication of the relational thickness ofthe system as weH as its openness

with respect to linkages across different localities[1,H,12].As for Eisingerich,Andreas,Bell,andTracey[9],there is a social network to develop regional cluster perfollllance.High perforlning
clusters are underpinned by nchⅣ ork strcngh and ne● vork openncss,but that the effects ofthese on
the perfollllance ofa cluster as a whole are moderated by environmental uncertainty.The networks
are inゞ rtlinents that may hclp irms to voluntarily expand their own compctences by mcans ofcomplementav partners beyond liinitations of their own organisation and of the localities whcre
they are settied.In this context,the process of leaming"offers a dynarnic pcrspcctive on the natureof both networking and clustering[9].HenCe,foHowing the competence vie、 v,networking can bebeneflcial because it may stirnulate communication and convcy nev/stilllluli towards illils,thus

enhancing leaming opportunities that may lead to technological upgrading and iinproved
competitiveness.
Although the notions of industrial cluster and industFial ne● vork have been widely applied,thcy
stin largely remain fuzzy as a concept especiany when we considertheir o、 々n interrelated relationships
and their relationships with the factors and variables from the whole economy,such as the institutionalarrallgcments, trading efflciency, the level of specialization and agglomeration, as well as theirdynalnic evolutiona理 /.The currellt literatures have addressed mallly important aspects ofcluster andnetwork,yet there is ttill short ofЮ bust frameworks to combine and explore them togetller under onc

competitive market.Frorll these perspectivcs,furthcr studics on overiapping ineaning of industrial‑42‑

clusters and netヽ 〃orks necd be conducted.In this paper,it、 vill regard industrial clustcrs and ne● vorks

as●Ⅳo folllls of production organisation,and they may be complementa理/、 vith each other.This

paper introduccs a thcoretically driven l「 alnework to provide structure and process rclated measuresthat can be used to explain how cluster and neい Ⅳork actually operatc and interrelate within all
economy.The otteCiVC Of this paperヽ to bHng together the hter¨ ind市 iduJ strategic dedsion
making and the neむ Ⅳork of division of labour in order to explore the conditions underlying thedevelopment ofdifferent types and level ofindustrial ne●vorks,institutional efflciency and lnutual―

trust, as well as geographicaHy and non‐ geographicany clustered. In particular, this paper wiH
exallline the relationship alllong institutional arrangement,flxed leaming and entry cost,lFanSaCtion
conditions,and the cluster governance structure and process at the corporate level,the cluster levcl

and/or the cconomy level.

2.A Model and FramoⅣ ork with lndustrial Cluster alnd lndust】 饉al Ne憫Ⅳork ofI)ivisionofLabour
2.l The basic lnodel
Following Yang[40],let'S COnsider an cconomy with a continuum ofconsumcr―

produccrs ofmass

銃 ̲This assumption implies that population sizc is vcry large. It avoids an integer problem of thenumbers of different specialists,which inay lead to non‐ cxistencc ofcquilibrium u7ith the division oflabour[37].Each consumer― producer has identical,non― satiated,continuous,alld rational prcference
reprcsented by tllc fo1lowing utiliサ funCtiOn:ε(la) tt=f(χ ソ),
C′

where χι=(χ 十 たχ・χd)and yC≡ (y+た y・ yd)are tlle al■ ounts of the two flnal goods that are
consumcd,χ andノ are tte alnounts ofthe mo g00ds that aК scFprovded,ノ alld/are the alllounts
y orz.Frac」 on it
ofthe tto goods that are purchased from the marktt alldた ,C(0,1)alld i=χ ′of a good sold disappears in ttansit duc to an iceberg transaction cost,or tt is a trading efflciency
cocfncient,、 vhich represents the conditions goveming ttansactions.Rcgarding the efFect ofgeographic
concentration or Po■ er's̀̀geographical proximiり ''[27],we furtherassume tllatた i=(1‑ι I)・ 鶏,andhcre tt is the cocfncient ofrelative geographic disttncc,andメ 6 relates to the genera1lrading conditions
alld thc institutional en宙 ronmcnt that affect trading ettcicncy.ス .)iS COntinuously increasing andquasi― concave.For simplicity without losing the gcneraliり,it iS assumed tllat f(・ )=(χ

C)・

(yC).

Each consumer― producer's production functions are:

(lb)χ

′

=χ +χ

S=

傷

{ι χ

一

F,(z+たz・ Zα )α

・

(ι χ

一

F),(z+たz・ Zd)β

。

(ι χ

一

F)},

y orz.
andれ =(1‑1)・ 埒 ,and i=χ ′ノ =ッ tゾ =ι y b
ノ =z十 グ =ι z一 b

and b c(0,1),

and わ∈(0,1),

whereノ andノ are the amounts oftllc"vo inal goods produced,zp is the alnount ofthe intcllllediate
good produced,zd is tlle amount ofintemediatc good z purchased from the market,ガ ,ノ and zS arethc amounts ofthe goods sold. F isthe ixed leaming and en色 ら/COStin producing good x;and b isthc
flЖ刻 learning altd cntt cost in producing good y and z.F is the parameter rcpresenting tlle elastici″

α is thcof output of good x、 vith rcspect to input level of intelHlediate good z.Morcover,parameter
vhich
will
efflciency cocfHcient and gcncral offcct ofroundabout production with intellllediate goods,、
hdicate one feature ofeconomた s ofspeciJization and α ≧ 1[40].BeSides,β k emp10yedto hdし た
the de8rce and iCVel of industtrial cluster,which means the efaciency coefEcient ofindustrial cluster)and lcan be deincd as β=α tt θ―θ.Here,θ representt the level ofcoordination cost,mangcmentθ∈(0,1);and θiS the institutional
cost and exogenous transaction costs of industrial clustct andefflciency and mutual― trtlst coefRcient to describe extemal econonlic and technology systems for
specialization and industrial agglomeration,and ι ∈(0, 1). With the concern of the econolnies of‑43‑

agglomeration and the econOmies of specidization and di宙 sion of labout whth are the mttor
features of hdusttiJ cluster,under certain conditions we can expectβ ≧1,Which mealls there win
be increasing retums in producing the flnal good x with cluster pattem. Ho、 veveち there win also

involve aH sorts of internal coordination cost, management cost and endogenous and exogenoustransaction costs for manufacturing product x with cluster pattem.Ifwithout cluster,the f1111ls Win als。

encounter exogenous and endogenous transaction costs,such as transpo躙
姥Ition cost,Ineasurement costofquantity and quality ofpЮ ducts,infollllation searching and matching cost,anticipated moral hazard,

knowledge block and many marketing related expenses, ctc.. IIencc,there is a trade‐ off here forengaged f1111ls to decide whether to organise an industrial cluster orjust thЮ ugh the nolHial market
劇es,which wiH be analysed laterin this paper.
The cndowlncnt constraint for each individual cndowed with one unit ofworking time is given as
follows:(lC) ̀χ +ι y+Iz=1,
vhere 4 isthe amount oflabour aHocated to the production ofgood i.This systeFn Ofproduction implics、
that each individual's labour productivity increases as she narro、 vs down her range of production
aclvities.As shown by Yang[40],the aggregate production schedule for three indi宙 duals

discontinuouslyjumps from a low pЮ Яle to ahigh pro■ le as each personjumps from producingthree
goods to a produ∝ ion patem in which at least one person pЮ duces only one good(specialization).
The di■ brence be● Ⅳeen the摯 Ⅳo a38Tega無 〕production proflles is considered as positive ne● vork ettcts
ofdivision oflabour on aggregate productivity.lrhis ne● vork ettctimplies that each person's decision
ofher level ofspecialization,or gains froFn SpeCialization,depends on thc numbcr ofparticipants in alarge nettork of di宙 sion of labour,while this number is detelllHnedけ an individuals'decζ ions inchoosing their levels of specialiation(SO‐ Called the Young theorem)[43].SinCC ecOnomies of
spechHation is individual specinc(峰 arning by doing mutt be achた ved through indi宙 dual specinc
practice and cannot be transferred between individuals),labOur endowmcnt constraint is speci「led foreach individual,so that increasing retums are localized.
The budget constraint fbr an individual is,(ld)′ χ(χ S― χα)+ρ ν(yS一 ya)+pz(ZS― Za)=0.
Due to the continuunl number ofindividuals and the assumption oflocalized increasing returns intllis iarge economy,a Walrasian regilne prevails in this lnodel. The speciflcation of tlle l■odel
generates trade― offs be急 〃cen economies of division of labour and transaction costs. Thc decision

problenl for an individualinvolves deciding on what and how much to produce for self―

consumptiOn,

to sdland to buy from the market.In other words,thc indi宙duJ chooses 9 variablcs,such as χ,ガ ,∠y,プ ,ス z,が ,4,and therc wHI be 29 amount ofpossibL comer and inte● or solutbns.

In order to narrow dowll the list of the calldidates,Yang and Ng[41]used dle Kuhn‐

Tuckcrconditions to establish the foHowing lellllna.
JJ″
ιtt ffEαch力罐
″ソ
se=お r鶴Ostο ″ι8oo4 dЙ 蓉″θ′btt αJsell″ θsαttι gθθ4″ θr bりS̀ヴ
お CttpЮり山 講ιs嘘 ″ ″ ″滋
′ a
4・

̀sa
̀′
We deine a cοげ yα r10″ as a combinationof zero and posidve vrariabLs whた h are compatiblc

with Lcmma l.There are 14 conflgurations IIom which the individuals can choosc.A combination of
aH individual's conflgurations constitutes a″ ar陸 ′s″ ′″″θ,or Sれ θtt for short.There will betotally 7 market structures compatible with Lemma l.

"θ

2.2 Conflgurations and EcollonliC Structures
Let's frstly examine all possible stl■ lcttlres that might occur in equilibHum.

‑44‑

ε
′
π rS″ rrz/θ И
二И″″りS″ ν

"グ

S″ 山

eB

(1)Structure A(Autarly without lnte11llediatc Good z)COnsists of aH indi宙 duals choosing
conflguration A (self‐ Sufflciency),whCre an individual produces an thc●
consumption and without any intellllediatc good z.

vo flnal goods for sclf‐(2) StruCture B (Autarky with lntelHlediate Good z) COnsists of an individuals choosing
conflguration B(Self̲sufflciency),where an individual produces an the mo flna1 800dS fbr self―
consumption and with intellllediatc good z lor producing good x.
rZα
IS加%θ ′
″es w'ル Parr″ ′Dル なゎ″″ bθ γrfん ,乃 3̀解 グPご(1)Structure PA iS a partial division of labour smcture which contains conigurations(Xy/z)and(Zy/X).

ν)and(y/X).
(2)StruCture PB is a partial division oflabour structure which contains conflgurations(ん ″lgurations(刃ν)and(y/x).
(3)StruCture Pc is a partial division oflabour structure which contains con「・Zα bθ arrr S歯 ″
′
″
″″
ε
θ
II G9″ ?た たDル な′″ガ S″ κttte工s

̀CC″(1)Structure CCA iS the complete d市 ision of labour with industrial cluster which contains
conflgurations(Vγ Z),(〃 Fy)and(y/X).

(2)StruCture CCB is the completc d市 ision of labour without industrial cluster which contains
conflgurations(為ケZ),(7yxy)alld(y/X).Note that the deflnitions and contents oftheir conflgurttions
arc as same as Structure CCA,yet it docs not apply the industrial cluster pattcrin the inanufacture ofoff between different flxed
good x.The rough explanation for this difference is based on the trade―learling and entry costs, the institutional efEcicncy and mutual‐ t■lst coefflcients of different

econolnic and technology systcms, the transaction costs and the level of coordination andmanagement costs ofindustrial cluster.The solid and explicit analysis、

vill be addressed belo、 v.

According to Sun,Yang and Zhou[37,40],and Yao and Li[42],a general equilibrium is deflned
as a set ofrelative prices ofgoods and aH individuals'labour anocations and trade plans,such that,(1)Each individual maximizes her utility,i.e.,the consumption bundle generated by her labour
allocation and trade plan maximizes her utiliサ function for given pHces;(2)All markets cicar.More

speciflc,Yang[40]has addressed thc following theorem:h″ gθ θ α″J αcθ ″rliF ″鷹 グ α α″″ lde■ rica′ cθ J"嘘 7‑
ηりoore″ ff ttθ r α″ ι θ″ッ
̀お"洸̀θ
θ″θ″農S″∫dぉPLッ 控
ソ
α
″
cθ
″
χ
rsゃ
漁
rario
″
ご
ι
″
グ
C′
′■
ヾ 職 t Cι S,α ″J′ 晨%力 κ油わ″メ ′
′
̀riθ
gc′
ri露
gι
Far
:Jめ
醜 醜 tsι′ね′Ⅳatr僣″″滋
ル劉,″,α ″ごrin″ 滅ルα′Ψげ ψ ′Cね Jう
α″ノ″Jis滋

̀:o″

″

ι′

ilibガ ″れ"″̀θ̀ὰParetooptt
Since theoptirnumdecision is always a comer solution and the interior solution is never optimal

according tO Lemma l,we cannot use sttdard lmarginal analysis to solve for a general equilibrium.
We adopt a threc‐ step approach to solve the gencral equilibrium.The flrst step is to narrow down theset of candidates for the optimum decision and to identi″ conigllrttions that have to be considered.

Wc can identitt structurcs from oompatibL combinations of conigun江 lons,whth we have donc
above.In the second step,cach individual's tltility maximiation decision is solved for a givcn structllre.

The utility equaHzation condition be● Ⅳeen individuals choosing different conflgurations and themarket clearing conditions are used to solve for the relative price of traded goods and numbcrs(meaSure)of indi宙 duals choosing different conflgurations.The relat市 e price and numbers,and
associatcd resourcc a1location are reた lTed to as comer equilibrium for this stl■ lcture. Gcneralllm relative prices in the structure,noequilibHuIIl occurS in a ttucture where,given comer equilib●m
theirchosenconflgurationsin this stl■ lcture. In the third、
individuals have an incentive to deviate工
ep五
ces
into
the utility function for each
step,we can substitutc the comer equilibjum relat市

constituent conflguration in the given stnlcture to compare the utility betwecn this conflguration andany altemative conflgurations.「 Fhis comparison is caHed a total cost‐ beneflt analysis.The total cost‐beneflt analysis yields the conditions under which the utility in cach constituent conflguration ofthis
StrLICture is not smaHer than any altemative con「 lguration. With the existence theorem of generalequilibrium pЮ ved by Sun,Yang and Zhou[37],we can cOmplctely partition the pararnetcr space into‑45‑

subspaces,within cach of、 vhich the comer equilibriuFn in a Structure is a general equilibrium.As
paralneter valucs shift bctween thc subttaces,the general equilibrium will discontinuously jump

be ccn sttuctures.The discOntinuOusjumpsofstructurcandall endogenousvariables are called infra‐
marginal comparative statics of general equilibrium,and the three steps constitute an lnfra‐ marginal
analysis.

FoHowing this procedure,we can solve for comer equilibHa in an structures.The solutions ofcomer equilibria in 7 structures,thc relative prices and relative number of different specialists arc

summanК d in Table l.
3.General Equilibrium and lts infra

marginal Comparat市 e Statics

Through infra‐ marginal analysis.it will partition the parametcr space into subspaces、 vithin eachofwhich a particular structure occurs in equilibrium.Witllthe Theorem l,we can then compare comer
equilibrium per capita real incomes across ali structures,and the comparison partitions the seven‐dimension(κ ′ιわ′F,θ ′θ)parameter space into several subspaces,within each ofwhich onc comcr,α ′equilibriunl is thc general equilibrium.As parameter values shi■

be●vccll diЯ brent subspaces,thegcneral equilibrium discOntinuously jumps between comcr equilib五1■

a.This is referred to as infra―

arginal comparative statics ofgeneral equilibrium.

In order to obtain analytical solution of the infra― marginal comparative statics for some spcciflc
ranges of parameter values,、 ve conduct a closc exalnination of per capita rcal incomes in different
structures,which is given in Table 2.
Following Yallg[40],it Can be shown that a general equilibrium in this model is Pareto optimal.This
irst 、
velfare theorem in this model with illter― individual nehⅣ Orking decisions and endogcnousneヽ vork size of division of labour implies that the market inction is to coOrdinatc inter¨ individualneヽ vorking decisions and to fl11ly utilize ne● vork cffects of division of labour on aggregate

produ∝ ivity,nettork oftransactions,and level o∬ spccialization and roundabout production.
In this model,the institutiond ettciency and mutud‐ trust rdated parameters(κ ′α′β),dl play
crucial roles in detellllining the per capita real income and the propcrties ofthe intemediate goods
and indust五 J duster undcrthe d市ヽ
bn of hbour structure,and th誠 お#>0,争 >O and券 >0・

Industrial cluster and roundabout production bOth are rela∝ d to the vertical division of labour
be● ″ecn high― end and low中 end producers in a long production chain,while the comparison between
their institutional efBciency and inutual― trust will be vital for the flnal decision in ne● vork structureof division of labour. Based on tlle above model,、ve can sce that an economy with a higher
institutional cfRciency and mutual― trust enables each individual to specialize in a narrow rangc of
production and to c可 oy cCOnOmies ofspccialization.Thc bcneflts gained frOm increasing rctuns tO
specialization alld the d市 iJon of labour wi1l outwei3h the transaction costs of markets.Industrial
cluster in a competitive market is all effect市 e wtt to promote di宙 sion of labour and product市 iサ
progress ifthe institutional efttciency and mutual‐

trust ofecononlic and technology systems arc morecompetitive.We can summarize the above analysis into Proposition l.
ど
■

j′

ι
θ″ fr

ズ加 θ′ ″ ι″砂"″rra滅 暉 ψ 巌 ″り げ ″ θ冶 面 撻 加″ ″θ た7aJげ 曲 穂io″ グ ねうθtt ИS
9お j″ η ″ π rrac 励 勝 油 燿 ルッ′Jグ ″ツおわ″ グ rabθ ″ 滋
6■ 0凛…
α″ rty″ aθ ″″ι
aセ dbお海″ qF ι
αうθ 琴 〃 Ra歯″力じ たッιJ q′ rra″暉 薇 農閣
滋 Cmi ″ グ rraθ
̀α
滋″
″
α′
ιgθ θ魔 ″JJθ ″ ″ rra″ 暉 ヵ ″α
̀ッ′g′ ″θr姥 ′″ ぷ iθ ″′ 刀 r/滋rα ′g//cCrグ「 ̀流̀scttsψ
″ ″″滋 うθ″ ′″ ″ C′ ′
θ″ お 力なλ%ル
ι″ ″ カ ルθ″ ′″ J″ ε ″′α″ r″ j′ Jレ 吻
a蟷 ″ 助′『̀Jθ
smIIcrノ 馘ガ ICar■″g rθJげ 滋″r "力ediα″ gθθご ち ″″ 加
′rJJ̀」 ル ″α′
θパ グ ル′加にF織曲政̀rι″グ ι″ ″ ″力 うθ ち 滋θ [のCIグ ″ッおわ″ q′ 滋わθ rメ リ f/Jrag ttCた ″ッ♂η4rrr′ ιノ タ″θ″
̀̀Jθ
Cte確
′
ル″
澱
動磁″
ε
r θッetthe撫 滋′ ge■o認J ttdグ ″ ″″滋 肋 ″ ′″ d ctiO″ ,JJJθ
ι
ぉ
囃
グ
̀ι
∫け饉 re″ 轟 加 d蔭 αE Ct ster″″ P″ ィ 〃グ ル″ ″ ′ ome ttθ わ 短 ″ グ れ
″″
″
『
̀Fこ
"″
Ogressら餞 edθ ″滋′
′ル滋″νjJ″ ″ ″cttFkt4g decおioas9 α″″″力″ ″θαttersθ
c徳′″ グ crivlilry′ψ「
θ″ ″C撫 α″J力 ″ ″θ′gι erare漁 lo b″ ∫加 αω η ctttC競
carransaαJθ ″ 帷

̀Jグ
te■

"鷺

‑46‑

Propos社lon l explicidy suggests a highly efflcient ttansaction institution will suttdentサout、 vcigh the transaction costs and provide cach individual an incentive to spccialize and to trade、vith each other by folllling a ne● ″ork ofdivision of labour.
Since therc are more sophisticated interrelated effects among industrial cluster, net、

division oflabour and production supply chain,thereけ〃ork of

we nCedヵ ■her expend our discussion onthese interrelationships in the rest ofthis section.
Scι ″α Jθ

″ι″α″ gθ θグzお ∫″αrJgr ttα ″′″″ gθ θ″鶏I.F積e″ icar豫′″gα ″″ι″′7̀θ Srsげ 加″『「″α′お わ <F

From above analysis,wc can eaSily derive that空<O and空 <O whcn they arc under the

structures ofaumrky and paiial division oflabOur,which indicates thc■ xed leanling and enり cOStS

havc negative cffect for thc development of nctwork of division of labour and the level of
specialization and roundabout production.Howcvet when we derive them underthe smctures of∞ mメ ∝ed宙 Jm J hbur・ somdtterestitt Кtt em∝ 」鴫 ,7>Q7<0田dΨ>0,7<0,Whth implた s that under the compLte division of hbour,the higher ixed bamingand ent理 /coSt Of flnal good、 vill has positive effect in increasing the productivity as wen as the percapita real income,while thc one for intelllleditte good still has ncgttive cffect on productiviけ .In
other、 vords,ifthe entw barrier for「 Inal good x in tellll of iXed learning and entry costs goes up,

which may cause by the tcchnology barrier,patellt,special know‐ how,R&D and innovation costand systems,etc.,itヽ ″ill gcnerate higher producer and proflt for the producers of flnal good x,
Besidcs,it has been addressed by many literature[22]thtt 10W― end and high‐ end sectors in onc
end sectors
production supply chain usuaHy have different flxed leaming and enttty costs,and high‐have higher one with regard to their R8じ D inputs and varied costs for products development andqualiサ oontrOl, Ctc.. If the dcgrec and effect of industtial cluster is stronger, i.e, the efRcicncy
coo8儡 cient of industtial cluster

B,WhichεβiS iargcr,even with b<F weゞ ill can have ucG4>υ εmeans the industrial cluster is still prevailing as the optimal decision fOr the flrm.Hence,in tlle teHHof produc」 on supply chain,the high‐ cnd■ lHl,althou811 thCy have larger ixed leaming and entッ
costs, still can maintain their position in a compctitive market if their efflcicncy coefflcient of
hdustriJ duster tt higher,whに hお dctemined by the trade‐ off betteen:1)the LVC1 0f coordination

cost,mallagemcnt cost and endogenous transaclon costs:2)the inStitutional elFlciency and mutllaト
trust coefflcientto describe extemal econonlic and technology systems for spccialization and industrial

agglomcration,and that can be indicated by」

1競 f4,>O and duCC′

く 0.Thercfore,to be thc high‐ cnd

or low‐ end of thc production chain is not the personal choice anymore,it is substantiaHy up to theinstitutional cttcicncy and mutual― trust ofeconomic and tcchnolo8y related systems,such as propcrサ
protection systems for intenectual propeJけand private prope」 崎ら the technology spi11‐ overs effectvcH as thc efflcicncy
mechanisIIl,and infollllation exchange and communication inechanisln,etc.,as、
for coordinating and lnanaging the industHal clustcr.
Sincc this rnodel docs not congne itselfto onc counttγ
only,it refers to one economy,and has

no limit on the territory of One country.According to Portcr[29],a cluster of indepcndent andinfoIHlaHy linked companies and institutions represents a robust organizational foll:i that ol偽rsadvantages in cfflciency,cffectiveness,and flexibility.Porter[27]addreSSes thc local concentration

processes that accelerate under the effect ofglobalisation.Thc competitive advantages ofcompanies
and industrial sectors participating in global competition are geographically concentratcd,pril■ arily
duc to agglomeration cffects.Hc also mentions that it is nol individual inarket players but rather

regional clusters tlnat participate in global competition.Howevcr,based on this model,under the

ncw cra of giobalization and rcgionalization,we can also expend this economy among different
countries with di■じrent production chains. From our analysis, the competition alnong different
countbs for higll― end alld low‐ end producers of one production chJnヽ mainly based on thecompetition of the institutional efEciency and mutual― trust among their econonlic and technology

systcms. The function of ale institutional seting and efEciency of the cconornic and technology‑47‑systems and the trading efEciency are cruciany vital to detelllline the level ofclustr,the ne憫 Ⅳork ofdivision oflabour,level ofspecialization and agglomeration,and consequent level ofproductivity andreal incomc,rathcr thall Porter's̀̀geographical pЮ ximity''or geo3Taphic concentration[27],whiCh

can be approved by the rcsdts from Tめに2,and also by tlle inequditicまd(秒>O when α≦β,

罰学 <o・vllem>ぃ μ
動ち

耐m even thetllese incqualtts tt Lble 2 i面

geo3Taphic distance is iarger,if the emciency coefflcient of industrial cluster

βoveⅣ Vhelms thenegative eΠ ttct ofgeographic distance and the effect ofroundabout production,industrial cluster is still

the optilnal decision and an effective way to promote division oflabour and productivity pЮ

gress.In

other words,rthe institutiond arrangcments and settings are not ettdent enough,even the geographic
Ю undabout production,
instcad of industrlal cluster.Hence,this model proves and implies that the industnal cluster can beorganized geographicany or/and non… geographically.

distance is sufflciently short,people will stili choice the regular trading andjθ 2 r/ヵα′膀θルレ 0■dル圏 θ 加″r edittc
なか ′′″ル jθ ″お″θ″′″β ル″,rra
「
̀′
"″
̀α
gθ θ
ゐ s弓″ Jliars cα ″″α″θ″ ″力
″
J
か
″
ル
″ル
C′
Jθ
グ
な
ν ry cヵ α滋′̀′Taking structurc CCA and CCB into consideration,、ve can flrst derivc the foHowingSc

relationships:摯<o md摯

<Q摯

<h耐 摯

<a

The frtt group of inequalitics implies ifthe hi3h― end■ 111l ha宙 ng a higher ixed leaming and entry
costs or entry barrier,the relat市 e number of hi311‐ end■ 111ls will decrease which means when theentV barrier ofhigh‐ end■ 111ls going up,it wili be more dittcultto become a high‐ end im,and its

rclative number、″ill go down.The second group of inequalities silnply indicate that if the flxed
leanling and entry costs of intellllediate goods going up,then the traction volumc of thelll will
decrease, and the incentives for purchasing intellllediate goods froln markct、viH shrink.
Consequently,the rclative number ofhigh‐ end flms which depending on them will also go down.
αriθ ユ助″″

動 ι rel醸ar― ″洲 ′″″̀″Rcgarding̀セ

働閣b″ グ Ψ ιεjα Jお ι
S″ J′ ル ″ιψ ιcr ra清"̀ηιθ′ι dttisわ″ グ ルうθ″r cθ Jὴ滋

st灘腱ね ″″ グ

structures CCA and CCB,we can frst derive the following rclationships:″り α ′"cた摯 >軸d宇 刈.

These t、 vo inequalities indicate thatto become the high‐end producer is depending on its institutional

efflciency and inutual‐ trust ofecononlic and technology systems.The higher institutional efflciency
and rnutual―trust win generate rnorc high‐ end flillls in a production chain.Therefore,the institutional

efflciency and mutual― trust is most crucial factor in detelHlining the competition among different
countrics fbr the high‐ end and low‐ end production.

ria 4
Scθ ″
α

J̀̀ノ クルお爾レ′H bりFrセ 漁′
θ
わ″グニα
う
θ
″r

Considering structurcs CCA and CCB,we can derive the foHowing inequalities:
摯

>hd摯

>鴫

which ineans、 vhen the flxed leaming and entry costs of high‐ end flHms are higher,then thc relative
numbcr of intellllediate goods and parts suppliers wiH increase. Since the entry barrier for the
production of intellllediate goods and parts are relatively lower,it、 vill be more casily to enter thisarea,and the ёompetition and high substitution and replacement effect among thenl are inore severe.
The inteilllediate goods and parts suppliers are forced to closely follow and surround the flnal good

producer tO suⅣ 市e.In other words,the high― end irlns can control the inJ goods market throughtheir high flxed leaming and entり/cOStS,such as the brand image,special know‐ how,patent,andmarkct nc● vork,Rど 財E)and innovation capability,and ctc.,and they wili be inore likely to be the hub‑48‑

ofthe ne、 vork ofdivision of labour and also can control the intelHlediate goods and Parts suppliers

through OEM(Original Equipment

Ⅳ〔anuibctuHng),subCOnttacting and other manners.On thecontrary,the low‐ cnd f1111lS haVe to encountcr thc serious substitution and rcplacement cffect andcompetition anlong theln,and also the chaHenges from the newcomers which consecutively entering
these markets.
The above analysis ofdifferent scenario can generate the fo1lowing proposition 2.
ど■2=bο ″ら ″力た力 加Jた αres rJJ̀ノ搬ガ
υ物ル 滋 ′ Srr″ α″rιsげ αzrarty α″′ ′α tal″ ッおわ″ツ"ositio
『
̀/″
jθ

ッ′ι
J″ g″ ″′ッ c∬ お λ″ ′″響 醸 わCC//FCr/ar滋
η ″ ′″ グ ″c静0活 グ ″ ツお ″ グ ル うθ″′
̀″
̀ル
おわ″げ
″ ′″
J″ rrlila″ ′り IIzル ″′Cθ Й
α′Z′ ッα″′″ ″′
ψιグ specidた″わ″″″ ″″″力仇〕「̀ルCr"加 CFetting
力 ι力 た ′ 溜 ″たα i″ g″ ″casr颯 α′gθ θご plilrr力 ″ ∬ 筋 ッ
″ ιθ

ルα

ら
滋 θ′″ 沈 β、′̀ψ″ ぐ,″ カル 説 ιθ ιヵ r ttternediategθ θお ′
″ 力6
̀ο
̀′
"妙 ″′ dКtbiタ タ′′ク f/″ な か ι 屁frmヵ αツJ″ gα 力な 力′ 舞 eノ iCarttJ″ gα ″ご′″rry″agatiッ θ ttCrθ
「̀力C∬ ち ″ ′rFJariソ θ″‖鵬 b″ a/れ ψ ‐観 Jノ″ ぽ 蘭 irJ dcc祀 縣 e"力 jβ 力 cα ″s″力(笏 働 ′facグ ルα ′埓
うιω ″′α力な か β グル 醜 jα″グ (閣 Fry casrs a/力 な か ι″′′ ′御 gθ J″ gψ ,″ ″″ bι ″θ″ 4″
な

′
「
″ ″ιι
′ 滋

ッ
̀″
ιr c̀P′ ″ ″ aJレ

̀ZJr″cgrs̀√ θ″θ
g tte″ ″″ごわ″‐ι″′′″グ″α卿″′ω″″rrliasル「 力亀″― ′αル
油
Srir″ria″
α
Jヴ
cた″
α
′″″″
α
C力
α
滋
お
″α
ttJy
b
′
ごθ
″
滋
β
ctttio″
′れ
ra″
″
αあ″
η
グ
り
′
̀θ
g,sysim′ り 劉りι″ι
rlia″ ″
″ご″ ″θ
ι
′Jη″ツ
″′滋 加
αη″θ″κ α″鰐′αttθ ″g力ρツ
ク 7カ ὶθ mparlilria

̀力
̀″
"″
′α″Jα ″
″aJ‐tFttStル α ″ α″ のヮα″Sわ ″ 滋 働 ι″ι″ J曖 グ ″ルおわ″ q′ たわθ″
顧 Cた ″ッ α ご ″ ′̀お"θ″ α″αJθ ″ ″ ″ ″ 加 α raレe脇ご
ι
加
力
igL―
″
″″ わ″ こ′C力
おお加 crecsc加 講
′
ノ Ψ

"e″
θ
rヵ ι
ル
′
′
膠
4り ̀ret磁なヵ― ″′″′″滋ε″みなカル d″rraJ ttθ メ α
Jgり θ
お″α彙
cr ttra暉 カルι
「
ねうθ 弓
い ｀■
0″
′″ ′″θ″ Jlitery″ うιttθ ヵ″う 油θ″曲 0活̀θルα J″ gα ″″ rry s̀s,
げ
グ
グ
jθ α
J α
rrange確 じα″″sarrlilrg α″ ″θ″ ソJrar
ツリ 働 溜Par躙 ば ″滋 ζη獅 響燒 た dお ‖cら 力 ιtts・ rilr ′′θ
λ ルdtttrtal cI ster c b̀θ rga″ たθ
o″ ̀αげ 加d Striαl cJパ ′″ ″0電e■ry α″″ι″ こル
「 ̀′jraJJy
=滅
j̀α
g′ ο
grttλ

θr/a″ J″θ=g̀Ogrηルiむ.

The above Proposition 2 indicates that as the institutional efflciency and lnutual―

trust develops,

the functiOn of intelillediate goods will improve,the neい Ⅳork ofdivision oflabour will expend andthe econonlies of specialization and agglomeration will increase.Our analysis is consisting withsome ofthe observations,such as Storper[36].BeSides,Porter[25]also mentions that the increased
innovation by flinis generates new niches and needs within and outside the cluster,leading to theemcrgOncc of new flrlns and thus the expansion of the cluster and the economy as a whole.The
expansion and gronth of the cluster can lead to a more cohesive set of activities by the fllHIs andbecome inanifest as integration.Expansion and groⅥ鷹h rnay also be a fbundation for rnoving upwardon the global supply chain.Increased interatiOn in the global Fnarket brings new prcssures to local

production systems in developing and developed countries. Mixed with market pressures are anumber of govemance‐ related issues that detelllline whether and how a local production systeFn(CluSter Or industrial district)remains in or moves up a global supply chain.Their arguments can be
explicitly demonstrated by this model,while there are further insights from the propositions which

are not clearly addressed before,such as,under the complete division of labour,the higher flxed
leaming and ently cost ofhi3h… end producer will has positive effect in increaJng the producd宙 りand expend the nch″ ork;ifthe high‐ end f1111l having a highcr flxed leaming and entc/costS,it will
be more difflcultto become a high― end flrln;it will not be the individual decision anymore to become
hi3h‐ end or low‐ end producer,rather it will substantially depend on the competition ovcr

institutional efflciency and mutual‐ trust of econornic and technology systems among different

trust leads to an
cnd production;
thc high― cnd illlls have been chance to control the market through their high ttxed leaming andcntry costs,and are morc likely to be the hub ofthe neい Ⅳork ofdivision oflabour.Comparing with
regions or countries; the ilnprovement in institutional efEciency and mutual―

cxpansion in the ne● vork ofdivision oflabour and bring lnore producers into high―geographic distance,the institutional arrangement and setting are more vital for thc emergency and‑49‑

evolution of industrial cluster,and industrial cluster can be organized geographica‖y or/and■ on―

geographicaHy.
Our forgoing propositiOns also indicate that,a variew of eCOnOmlc structures may cmcrge inconcurrencc with economic development.They also support Adam Smith's[35]argument that thedivision of labour icads to the invention and the utilization of roundabout productive machines.
Furthellllore,they illustrate Young's proposition[43]tlltt the division oflabour for an economy ischaracterized by three components:the level of individual's specialil″ Ltion,its diversity of process,the ne、 v utilization of a good,its roundabout production,and the emergencc ofthe vertical divisionoflabour.This model also oppos■ es the traditional argument that thegeographical proximiサ "[29]is rnore crucial to detelllline industrial cluster and cconomicき、、、
th Or econolnic development,and
we indicate the institutional setting of a particular economy are more valid for the cmergency andevolution of industrial cluster and ne●4。

vork ofdivision of labour.

Concluding Remarks
This paper develops a Walrasian general equilibriuln rnodel based on inter¨ individual nch7orking

Ⅳork ofdivision oflabour in a competitivc
market.In this rnodelthere is no monopoly power,substitution among di■
じrent specialists are a‖ owed,
therefore to be cluster hub does not need to be as a large corporation,which has been occurred anddecisions to invcstigate the role ofindusmal cluster and ne●

obseⅣ ed h recent decades[6,10].
The function ofthe institutional setting and efEciency ofthe econoIIlic and technology systems,andork ofdivision oflabour, level of specialization and agglomeration,and consequent level of productivity and real
income,rather than Portcr's̀̀geographical proximity"or gcographic concentration[27].InduStrial

the trading efttciency,are crucially vital to deterlnine the level ofcluster,the neb〃cluster in a competitive market is an effective way to promote division of labour and productivity
progress if the institutional efttcicncy and mutual― mst of ecOnonlic and tcchnology systems arc

more competitive,and it has no adversc cttcts on welfarc and does not gcncratc distortions in acompetitive market.Hencc,a competitive market will f■ llly explore total positivc ncい Ⅳork effects ofdivision of labour on ag3regate productivity.
Industrial cluster in a competitive market is efflcient and it ensures the ne●vork cttcts ofdivision of labour can be mlly exp10ited when the institutional ef「 lciency and mutual― 廿ust ofindustrial cluster ovenvhelms the general effect ofroundabout production,and industrial cluster canpromote aggegate productivity by eniarging the network e]bcts of the division of labour against
transaction costs. Hence, our attention should be placed on the ilnprovement of institutional
efaciency and lnutual‐ trust ofeconolnic and technology systems,promotion ofinnovation and R8ι E),
and maintain the institutional setting for ice entっ ′and learlling p■ ocess.Some pronlising ex"nsionof this model are to a1low morc lavcrs of roundabout production,lo count more varieサover tllC
conditions oftrading efEcicncy and geographic distance,and to expend to the dynarnic process for theⅣork and institlltional settings.
Especiany a■ erthe 2020 palldemic,the lvorid wili be expected rllarkedly different with the systeminterrelationship amOng industrial cluster,industrial neい

ofglobal supply chain.The institutional efFlcicncy and lnutual―

trust、 vill become FnOre Vital and crucial

to dete11lline the global produc」 on network,particularly for the high一end produc伍 on pattem.

5.Ack■ owledgemellts
The atlthor appreciates helpful comments from Paul Ⅳ11lgrom,Eric Maskin,Aris Spanos,George
prendergast,Nancy Fox,IIiroshi Ohta,and WapⅣ ick McKibbin. Earlier versions ofthis paper havebeen presented at the senlinars held at Nihon University,Taiwan lndustHal Technology Rescarchlnstitute(ITRI),St.JOSeph's University,Aoyama Gakuin University,and Monash Universi″ ,and I
anl gratefulto participants for valuable corllinents and discusslon.I am rcsponsiblc for any remaining
crror.

‑50‑

References[1]Amin,A.and Thrit,N.,1994,Living in the global,in Amin,A.and Thrift,N.(eds),Institutions
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‑52‑

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ISBN 4‑901329‑11‑8

Proccedings ofthe Tcnth lntemationalく)2021 1ntcmational lnfolnation lnstitlltc

Conferencc on lnfollllatiOn(Inforlllation'2021)

Reduction of Pressing Force and Frictiom Force in Miro lUltrasonic

Knurling Techmology Creating High Precision Texture
Shigcrtl Aoki☆ , Yasunori Sakai**,Tomohisa Tanaka***ar雫′′
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Abstract
Sliding sttcc in mechanical systcnn is rcquired to move smOotllly and stop at慶 ピget position.
Sliding surfacc call move and stop by ttplying adequate tiction forcc.FHction force is controlled bydeveloping technology creating smali texture on the surface with a few to a few hundrcd micromcter
intcrvals.On thc other hand,ultrasonic vibration is used in many manufacturing flelds.In this paper,thc efFcct of ultrasonic宙 bration is examined by the nmdamental exPcriment.In thc experimcnt making

a groove on the surface wlth an indenter using a 2 dilncnsional table,prcssing forcc and■iction forcc

arc mcasured.■ cse forces arc reduced using ultrasonic vibration
Keywords:Knurling,Ultrasonic vibration,Texturc,Pressing forcc,Friction forcc

l.IIltroduction
FHction on thc sliding surfacc of the machinc is controncd by crcating vcry small texture
witll a few to a fcw hundrcd micromctcr intcrvals.By applying this technology to sliding

surface of large industrial machincs such as airplancs gencrators and machine tools andgctting lo、 v■ iction surface,Inachine efttcicncy increascs drasticany.To rcalize low friction

surfacc,a proccssing technology crcating small wcar rcsistant tcxturc with high precision andhigh‐ efflcicncy is requircd.Howcvcr,a practical proccssing tcchnology creating sman texturc

is not complctcd in convcntional tcchnology. On thc othcr hand, ultrasonic vibration isapplicd to many pЮ ccssing technologics[1].It iS Weil known that rcsidllal strcss in weldcd
joint is reduccd and surね cc roughncss is improvcd in drilling of composlc matc面

al.Thcn,

thc purpose of this study is to dcvclop processing tcchnology creating very smaH tcxturc onlarge sliding surface by applying ultrasonic vibration to knuJing and rcsol宙 ng problems ofthe convcntional tcchnology.In this papcr,a indamental cxperiFnent rnaking groovc using an
indenter is conductcd and the pressing forcc and thc friction forcc arc measured.As a rcsuit,
both forces arc reduced using ultrasonic vibration.

‑57‑

2.Processillg]Experilllent Using Uitrasonic VibratiOn
Hom is designed and ltladc to transrnit vibration of thc Langcvin―

けpC transduccr to surfacc

of workpicce cfttcicntly. The frequency rcsponsc ttnction is mcasurcd using acccleration

sensor changing frcqucncy of input tO transducer. 31.5 kHz is the pcak frcquency of thefrequency rcsponsc function[2].
Using the horn,an cxpcrimcnt is madc crcating groovc on the surfacc ofthc、

vOrkpiece byan indcnter using uliasOnic vibration.Figurc l shOws the expcrilnental sctup.Tlle spccirnen
is flxcd by bolts On 2‐ axis fccd tablc. Tip shape of the indcntcr is cOne. Thc indenter ispresscd in vertical dircction and thc workpiecc is id in lateral dircction.The indenter is flxed
at the tip of hom and ultrasonic vibration is applied in vertical dircction during proccssing.A
thrcc dimcnsional dynamomcter is set ulldcr workpiece and thc pressing fOrcc and thc friction
force arc mcasured for va」 ous targct dcpth ofgroove, MateHal of wOrkpiccc is aluminium(A2017).
Figure 2(a)and(b)ShOW thc prcssing forcc
and thc friction forcc in which target dcpth issct as 30mm and 50mnl, rcspectively. Rcd
line is thc pressing forcc and bluc linc is thefriction force.Thc workpiecc is fcd in iatcral
direction aftcr tip of thc indenter rcachcs tlle

targct dcptll.The workpiccc is proccssedwithout

ultrasonicvibration.

UItrasonicvibration is applicd aftcr 30s. Froln both
Fig.l Experimental setup
flgurcs, thc prcssing brcc and the friction

Presslng』 bFCe

彎

一
二島
彙置

―…
…Fttctilon
― …
３
麟

鶴
鱒

麟

菫

餞

綺

隷

翫 書お鵞

鶴nelSe(a)30μ(b)501tmm

Fig.2 Prcssing forcc and friction forcc‑58‑

forcc arc rcduced whcn ullrasonic vibration is applied.Then,ultrasonic vibration is effectivc
to rcducc both forces.

3.Pressing Force alld Friction ForceThc target depth othcr than sho■ rn in Fig.2 is set and thc averagc valuc ofthc prcssing forcc
and thc fl・ iction force is obtaincd.Figure 3(a)and(b)ShOW thc rcsuLs.BIue linc shows force、
vithout uitrasonic vibration and red linc shows force、vith ultrasonic vibration.Thc prcssing

force and thc friction forcc are reduced using ultrasonic vibration during proccssing.

Next, ratio of thc prcssing force and thc lriction forcc on workpiccc with ultrasonic宙bration to thtt without ultrasonic vibration is cxamincd.Figure 4(a)and(b)ShOW ratio ofthc prcssing force and ratio of the friction force,respcctively.Ratio of both forccs incrcascswith thc increase of target depth.For thc largc targct dcpth)ratio thc prcssing forcc tcnds tobc constant.

Third, in ordcr to cxanlinc rcduccd force, differcncc bcヽ vecn thc prcssing force and thcvith ultrasonic vibration is shown infriction forcc、vithout ultrasonic vibration and thosc、

Fig.5(a)and(b).For pressing forcc,rcduccd forcc is approximatcly prOportional to tattct
dcpth.

4.Conclusions
Thc tcch■ ology using ultrasonic vibration on knurling is cxamincd for creating sman texturc
on a largc sliding surfacc to control friction force,For the fundalncntal cxperiinent gr00VC iS

madc using an indentcr and thc prcssing force and thc■ iction forcc are mcasuredお r various
targct dcpth.Obtained results arc summarizcd as folows.
(1)ThC prcssing forcc and thc friction force arc rcduced using ultrasonic宙

/

￨

￨

ノ

/

/

/

一

顆

写

驀

With v:bratiOn

l

40

60

0

80

剪

鰺

洵

20

諄

l
ノ

骰
0

Wに hOtlt Vlbra● on

一ノ

WithOut vibratio●

一Ｚ ︶ こ 謹一ョ●︼●■ ﹄︐

ｏ２妥 Ｅ３●Ｌ︵Ｚ︶―

bration.

20

40

60

Tllrgel depthillm)

Target depth(lun〕(a)Pressing forcc(b)F五 c● on force

Fig.3 Pressing forcc and friction forcc‑59‑

(2) Ratio of thc pressing forcc and tllc friction forcc using ultrasonic vibration to those

without ultrasonic vibration increttcs with thc incrcasc of targct dcpth.For a large targct
depth,ratio ofthe pressing force tcnds to bc constant,E)ifference bc■ ″cen the pressing force without ultrasonic and that using ullrasonicvibration is approxirnatcly proportional to targct dcpth.

4.Acknowledgements
Thc study on this paper t supported by Grants‐ in‐ Aid for Scientiac Rcscarch
No.18K03890.

Referellces[1]V.K.Astashcv,V.I.Babiも ky,Uitrasonic Proccsses and Machincs,Springer‐ VcJag,
Bcrlin Hcidcibcrg,2010.

[2]S.Aoki,Y.Saki,T.Tanaka,A Fundamental Experiment for Micro Ultrasonic Knurling
Tcchnology Crcating High Precision Texture on Sliding Surfacc,Infollllation,23‑3(2020),
205‐ 212.
1

３占
撥 目 ●２ ε ¨■ 一

重

/

′

08

/

言06
ε

/

/

04
還
‐
属
■ 02

/
ノ

0

0

20

40

Tttrget depth(

60

80

/

0

20

m)

40

60

80

Tatter depth(沖 m)(a)PrCSSing forcc(b)Friction fbrcc

Fig.4 Ratio ofprcssing force and friction force fOr the case with vibratio■
to thosc、 vith vibr,tinn
′

2

選
3

76
凛

S

14

=2

8

11

言
2

X

零

20

40

60

80

0

●

0

20

40
Target depth(llm)

Trget depth(lun,①)Friction force(a)Pressing forcc
Fig.5 Rcduction ofprcssing forcc and‑60‑

friction force

60

80

ISBN 4‑901329‑11‑8

Procccdings ofthe Tcnth lntemational◎ 2021 1ntcmational lnfollllation lnstimte

Confcrencc on lnfollllatiOn(Inforlnation'2021)

The Predictio■ ofPM2.5 Concentration lUsing an

lmproved IBackpropagatiom
Siqi Hall and Lci Li
θα″グE4gttθ θ″′
43〃Os̀′ じηルC″ α洸′″ Sθ 力οο′グ Sε ″″θ

̀パ

′
ο′∂イー
∂5∂ 4 Jψ α″夕 κοgα θみ7bゎ′Sθ ∴α ′,′ 〃θ′αθみ″α″Is″ ′
.力 α
″
″
・ア
・
″
@s″ .力 ο@力 σὰプAbstractAs

smog"has becoming a topical issuc ill both domestic and intcmational,people realized that eventhe blindly development ofindus珈 り has bЮ ught a tcmporary progress of standard ofli宙 ng,but there areheavy coasts to pay.(Dne ofthe inost painhlis the air poHution.Att poHution indexes,such as PN12.5,have

graduaHy entcred the public eye,and bccomc an important referencc for weather forecasts and peopleis
travel.This paper is based on standard BP ncural nctwork,through the improved AM‐ BR GA― BR PCA―
GA― BP to predict the concentration of PM2.5.■ e modelis progralnmed and simulated with MATLAB,
and the feasibility ofthe modelis proved by experiments.

Keywords:PM2.5,BP neural network,additional momelltum method(AM),genetic algorithm(GA),principal component analysis(PCA)

1.Introduction
PM2.5 is a particulate matter with a particle size of 2.5 μm(1/10000f2.5 mm)or less.It iseasy for hamful substances such as micr∞

rganisms to adhere.PM2.5 research is a higll― pro■ にissue because it has a great impact on the air environment and human health.The traditional
regression statistical rnodel and numerical prediction lnodel are the lnethods used for predicting
the air qualiけ in mOSt Cities domestic alld abroad,buttllese methods cannot meetthc management

and utilization of lnassivc data,and the accuracy is lo、vl For complcx nonlinear systems, BP

artindJ neural nettork can perfom beter ttnc,on appЮ ximation and obtain hi3her itthg
accuracy and prcdiction accuracy.
However9 in practical application,BP neurai ne

ork also has rnany defects.In the proccss oferror reduction, it is casy to fall into the local nlinimum value,and the convergence speed ofletting algorithm is slow≒ This article is based on the standard BP ncurai network,thrOugh the

improved ANII‐ BR GA‐ BR PCA‐ GA― BP to predict the concentration of PM2.5 and draw
meaningful conclusions.

2.Artiflcial Neural Network

2.l Back Propagation Neural Network‑61‑

Supposc̀̀M''reprcsents the number ofthe input signals in the input layet̀̀I''represents thenumber ofthc nodes in the hidden layer and̀̀P"represents the numbcr ofthe nodes in the output
laycr.Thc input ofthe input laycr is rcprescnted by tゝ ,thc weight beむ ″cen the input iayer andthc hidden layer is reprcsented by″ ルr,and the weight bemcen the hiddon hyer and the output
layer is represented by,%P.yP represents the output ofthe output laye■process,the input/output ofcach 10yer is calculated by thc foHo、

綺=Σ 影笙fX‰ Jχ ″ (1)昨 =Σ lX ttP路
(3)
;竺

yf=【

In the sample learning

vittg equation.

IJr)

(2)

yP=yP=Ψ (IJP) (4)Thcn,thc learning error oftlle Pth neuron in the outputlayer becomes Eq.(5).

EPO()=DP01)― yP00

(5)

The error energy of each ncuron is :EIPcヽ ).Add the error encrgics ofthe neurons in the
output i句 /er to obtain Eq.(6).
E(]ヽ )=12Σ Fκ P2P″ スχP=1(6)

2.2 Additiollal Momentum Back PropagatiOn Neural Network
Thc so― called additional momentum method is to add part of the last weight attuStment
quan面 サ and regard it as the weight attuゞ ment qualltity of this leaming,which is also thedittrence be

ゾ
cen AM― BP algorithm and BP algorithm.The foll:lula for wcight attustmCnt is asfollowsI△W(N+1)=″ ε[W(N)■ V(N‐ 1)]‐ η∂E(Ⅳ )∂ 拗(Ⅳ )(7)In the above folHlula,ル ff represents the added inomentunl coefRcient,and N isthe number

oftraining.From equation(7),when″ c=0,the weight attustment ofthis ieaming is dctellllined
according to the gradient desccnt rnethod.When the training weight ofthc nc●

vork is c10se to the

local ■
linilnuln of thc error surねce, the local gradicnt value becomes very smaH. Adding

momentum terrn can avoid thc possibility offalling into a local minimum.

3.Genetic Algorithm
3.llmplementation of Genetic Algorithm(1)Encoding.Before solving tlle problem,thc genetic algorithm flrst reprcscnts thc data in thc
solution space as thc gcnotype string st■ lcture data in the genetic space.E)ifferent points inthcsc string structure data are composed of different combinations ofstring structure data.

(2)Initialize thc populajon,detcrmine the population size,the maximum iteration ordinal
number and other parameters,and use the random mcthod lo generate a feature string、 Ⅳith acertain lellgth as the initial population(3)Fitness value cvaluation.For dittrentissues,the itness fllnction is selected in difお‑62‑

rent ways.

According to speciflc issues,the fltness function is used to calculate the itness values of aH
individuals in the group.

(4)SeleCtiOn operation.Using roulette method t)r sclection operation, keeping thc bc前
individual to thc next gcncration,folllling a ncw

oup.

『
to produce new individuals.
(5)CrosSOVCr operation、 Exchanging individual chromosomes(6)MutatiOn Operation.Using mutation operator to change the chromosome in thc indi宙

dual toproducc a new individual.
(7)Judging thc termination condition.And outputting thc indi宙

dual with the ma対 mum flinessvalue obtained in the evolution process as the optirnal solution.

3.2 Genetic Algorithm‐ Back Propagation Neural Ne憫Ⅳork
Gcnctic algorithm optilnization 13P neural network is divided into three palts:deterlllination
ofBP neuFal nCtwork structurc,genetic algorithnl optilnization and BP neural ne●vork prediction.

Thenumberofinputandoutputparametersoftheflttinginctiondetellllinesthestructurcofthe
BP ncurai ncい Ⅳork,and then deterlnines the length of the individual genetic algorithm.Genetic
algorithm is used to optilnize thc、Ⅳcights and thresholds of 13P neural network.Each individualin the popJttbn,onⅢ ns JlthC Waghts and threshoに s ofa nemork.The nd市 duJ cdcJttes
the itness valuc of the indi宙 dual throu311 ntness ftlnction,and the genetic algorithm inds thc
individual corresponding to the optilnal fltness valuc through selection,crossovcr・and lnutation.

BP neurai neむ ″ork prediction using genetic algorithm to get the optilnal individualto the ne"vorkinitial weight and threshold valuc assigninent,the ne● Ⅳork prcdicts function output a■ er training.

3.3 Principal Component Analysis‐ Genetic Algorithm‐ Back Propagation Neural Ne● vork
PCA is a spccial inultivariate statistical lnethod that transfolllls multiple index problcms into

fewer indexcs one,which is,the process of using dimensionality rcduction to transform multiple
variables in a high― diinensional space into a few inain variablcs.Howevet these sman amounts
ofdata can stiH retain the info111latiOn in thc original data、 vell and can reflectthe lnain contcnt of

the original variables. cach principal component is not transformed randolllly but is a linear
combination ofthe original variables.

‑63‑

Figurel:Schematic diagraln ofthe geometric meaning ofPCA

Suppose in加 o― dimensional plane Xく χl,χ 2)'CXtract sample ofcapacity n,the scatter plot
ofthe observed values ofthis samplc is showll in Figure l.According to Figure l,The sample
points are approxilnately scattered in an ellipsc,with silnilar dispersion along the χl axis andχ2 aXiS,and χ. and χ2ShOW a clear linear correlation. Frorn the knowledge of rnathematicalstatistics,the degrec ofdispersion can be l■ easured by the variance ofthc variable,and themagnitude ofthe variancc reflccts thc amount ofinfol:1lation conttlined in the variablc.From theknowledgc ofrnathematical statistics,thc degrcc ofdispersion can be incasured by thc vaHance
ofthe variable,and the magnitude ofthc variance renects the amount ofinfollllation containedin the variable.Rotate the coordinates in Figure l counterclock、

vise by an angle of α,so thatthe χlaxis rotates to the long axis direction ofthe enipSe yl,and thc

χ2aXiS rotates to the short axis

direction ofthe cHipse y2,WhiCh becomes a ne、

v coordinate system.According to the rottltion of

coordinates,follllula(8)is obtained.

:ち二
I:::::主 I:::11(8)

yl and y2 are newly obtained variables.It can be clearly scen thatthesc n sarnple observations arc
alinost irrelevant in the new coordinate system.And the new obtained vanable is a line釘

oombination of χlandχ 2,Figure 2 shows thatthe dispersion of n salnple obseⅣ ations along the axis
ylis thc largest,that is,the variance of yl is much largerthan that of y2,WhiCh mcans that most of
the infolillation in the original data is contained by the ylaxis,while the variance ofthe y2 aXiSiS

relatively much smaHcr.At this point,the loss of variable y2 0nly causes a relatively smaH loss ofinfollllation.Here, y. andッ2 are the linear combinations ofthe original variabies

χl and χ2・

4.Prediction of PM2.5
4.lThe experilllental data
Experilnental dattl are the daily lnean concentration ofPM2.5 and other weather conditionsin BeJing,China from January l,20H to Septcmbcr 30,2018.PM 10,S02,CO,N02,03,‑64‑

maKimul■ and minimum temperatures arectthe PNI12.5 concentration on the day.

Table l:Represcnts part ofthe experirncntal dataⅣlaxilnum

MinlmumTellnperature

Temperature

9

2011/1/2

Date

PM10

S02

CO

N02

03

PM2.5

‑4

81

111

28

1.5

62

52

45

9

‑2

145

168

69

3.4

93

14

2011/1/3

4

‑5

74

98

29

1.3

52

56

47

2011/1/4

6

‑3

149

147

40

2.8

75

14

114

‑4

119

117

38

2.3

67

44

91

2011/1/1

2011/1/5■■

AQI

4.2 Experilllental results and analysis

お試集猥調繰差

012

0.1

0̲03

建

0.06

004
002
0

0

5

10

15
20・ 働

一 BP,一 ―AttBP,

20

25

け

CIA… BP,― PCA‐ GA‐ BP"v‖

Figure 2:Error curvcs of4 prediction inethods

Table 2:Comparison ofresults of4 prediction lnethods

Test indicatOrs

MSE

Tilne/sBP

0.0977171BP
GA‐ BP

0.0962126

0.0160106

PCA‐ GA‐ BP

0,006181

ANI―

It can bc scen■om Figure 2 and Table 2 that compared to the BP model,the ANII BP model
has relatively smaH fluctuations and has relatively small prcdiction crors.Thc ntting dcgree of‑65‑

BP algorithm is poot and the AM― BP algorithm has greatly improved its prediction accuracy andrunning time.The experiment proves the optimization abiliサ

of genetic algorithm in complex

nonlincar systcm.The algorithnn that combines thc gcnetic algorithrn and the BP neurai nc●

vork

improves the opづ mizttion ability ofthe BP neurai network,prevents the BP neural neい vork■ om
falling into a local lniniFllum during the training process,and accelerates the convergcnce spccd.

PCA can cffcctively reducc the input dilnension ofthe 13P ncural ne● ″ork,remove unnccessary
input variables,and flnally accelerate the convergence speed ofthe BP neural ncヽ

vork.

Referencesil]異 凌云,BP神 経 同絡学 コ算法的改選及其庇用 [J],倍 息技木,2003,27(7):42‑44.
[2]張 恰文,放 希琴,吋 培俊 ,郭 傲末,費 久尤 ,踪 家雨 ,基 予 Pcarson相 美指林的BPネ 申姪
圏絡PM 2.5預 測模 型 [J],青 島大学学扱 (自 然科学版 ),2017年 02期.

[3]張 徳羊 ,MATLAB神 経 同絡編程 ,[M].北 京 :化 学 工J2出 版社 ,(2011).
[4]周 品,MATLAB神 径 国絡投 it与 鹿用 ,[M].北 京 :清 準大学出版社 ,(2013).
[5]輔 力群 ,人 工 神径 同絡理沿 、没汁及庇用 ,[M].北 京 :化 学 工立 出版社 ,(2004).
[6]洲 文差,対 提高 BP神 経 団絡乏化能力的分析和恵錯,声 末科技 ,(7):72‑73.
[7]http:〃―.Weather.com.cn/[8]httpS:〃 WWwocnblogs.coln/wangduo/P/6773601.html?utm source〓 itdadao&utm
erral

‑66‑

mcdium=refISBN 4‑901329‑11‑8

Procccdings ofthe Tcnth lntcmationalく)2021 1ntemational lnfo■ nation lnstitlltc

Confcrcncc on lnfomlation(InfOm■ ation'2021)

Inlluence of Arbors on lndoor Natural Ventilation in]Lower Floorsof Buildings by Numerical Silnulation
Liao ⅣIingcheng*,Sung Wenpei**,1lo Chienwciネ **十g,1va″ b″α
′C功 ′
″‐
ηυ″
′
ッ
ars′ ヶグ ル″ο′0,,Dヒραr"̀″ fι α″
′
ι
θ
r″ ″
′
′7θ Tα れη法θ θИκ″ゴ,ィ ′̀力
ルルα″β OC,,3″ α〃f′ ″̀οο く)ε r′̀ρ励 加Jθ

■*〃´″ο″α′C/2ノ ″―拘 佛 ブ
ッ ブ
勧 ′″ ι′′冶 C″ ιИκカメたcrν ″ ′ノ7θ 乃 た力″Pag,
ヶグ ル 磁′οJο ,ち と ρα″
̀パ
̀,ィ
̀げ
ル ルα″倶 OCノ ,3″ α「″′力 AI・ (b″ο〃 Itt α ″οリ
"Oι
̀ψ
F′

摯十■
Nα rめ raF C力 J′ ―
賄 じ″ν
̀rsプ

ι力″οす
o響,Departttθ ″′グ ια″αS̀■′ι/″ヶ グ 露″ηαJた ο
物′
ψα″rR aCノ ,五L″ θ″
66鋭 ″「x96̲‐ α′̀力′
たo′ ″′′,イ ′ノ7θ 7brr・ 力 ″&Abstractln spatial landscapc planning,arbors bcautify the en宙 ronment,increase thc grecn coveragc ratc,

and enhance environmental comfort, but their inlluences on surrounding wind felds and indoor
ventilation in ncighboHng buildings are not widely discussed.Hencc,with computationai nuid dynamics(CFD)numeriCal simulation as the research method and the student dorrnitory of the Nttional Chin‐ Yi
University ofTechnology in Taichung City,Taiwan as the sample,this study explores thc influenccs ofarbor planning in the open space outside a building on thc natural ventilation ofthc indoor space oflo、 ver

8oors.This study compares the influences of various variabics on indoor air exchangc rates,including
form ofplot plan,planting distance,porosity ofarbors,and height ofarbors.The goal is to increase thegreen coverage ratc and introduce natural vcntilation so as to provide indoor ventilation and maintain

good indoor therlnal comfort.This can help comply、

vith the characteristics of a subtropical FnOnSOon

climatc in a place whcre thc site is iocatcd,thus providing reference lor ftture plot plans and the dcsign

ofthc arbors around buildings.
kir cxchangc ratc,
Keッηvords: Urban hcat isiand, Indoor natural ventilation, Arbors pattem, ´Comput江 lonal■ uid dynamics(CFD)

1.Introduction
According to rclated reseaFCh Ofurban micro― climates,as one ofthe most effcc've waysto
ilnprove the outdoor climate and environment planting arbors to incrctte the green coverage
ratc helps to reduce the influence of urban heat islands[l‑41. In spatial landscape planning,arbors beautitt thC en宙 ronment,increase thc grccn covcrage rate,and enhance en宙 ronmental

comfort[5], but their innuenccs on surrounding wind ttelds and indoor ventilation inneighboring buildings(in partiCular,the lo、 ver刊 oors of buildings)are nOt、 videly discussed.
Thcrefore,in orderto introduce natural ven」 lation,the arbor planning ofneighboring buildings

must be taken into consideration.With computational nuid dynamics(CFD)nume」

‑67‑

Cal

simuladon as the research method and the student dollllitory ofthe National Chin‐

Yi Universityof Technology in Taichung City,Taiwan as the sample,this study explores the in■ uences ofarbor planning in the open space outside a building on the nattlral ventilation of the indoor
spacc oflower Ooors.Results offcr a reference for iture arbor desi3n around buildings.

2.14ethod
2.l Research area
The research arca is located in Taichung City,central Taiwan,which mainly has asubtropical inonsoon climate.The sample building is a newly―

built student dolulitory with 2■oors underground and 7 floors above the ground,and it is a reinforced concrete structure.BI
and B2 are parking lots,the ground flooris a hall with a height of 5m,and the 2nd to 7th noors

are dolHi rooms、vith a height of 3.6m.The building is southettt‐ north、 vest‐ o● ented,and thc
north and west sides are reJdential areas with a hclght ofabout 3‑5 storics.The south side is aparking lot with an asphalt pavcmcnt,while thc cast sidc is grccn space ofthe camplls.

2.2 Assessment basis
The air cxchange rate is the number oftimes thatthe amount ofair equivalentto the intemal
volume is exchanged per unittime,as shown in Eq.1.The higher the rate is,tlle higller is indoor
air change frequency and the casier the air can circulate.The air exchange rate varies with thetypes and purposcs ofbuildings.The standard hourly air exchange rates of places are shown in

Table l[6].
０二 Ｖ

η

(1)

wherc,n is the air exchange rate(dmeS/hr),Q is tllC air cxchangc(m3/hr),and v isthe inte」

orvolume(m3).

2.3 Numerical simulation
2.3.l Si口 mulation softwareThis study adopts WindPerfect E》 X 2018, which is developed by E― Sirn, a Japanesecompany. As 3‑dimentional thellllal fluid analysis software based on the theow of■uidmechanics, it can analyze the influenccs on Ⅵ/ind flelds between buildings and surrounding‑68‑environments.Itis computer― aided sottare widely used for the analysis ofwind environment
on an llrban street scJe[7‑8].

2.3.2(Climate conditions
The outdoortemperature is set atthc average temperature of28.0°

C in summerin TaichungCity,and the annual wind speed ofl.61n/sec is taken as the benchark fordiscussion according
to thc annual statistical data■ om the Taichung meteorological station of the Central Wcather

Bureau[9].
Table l.Standard houny air exchange rates ofplaces 16]
Ow HaCe篤

藩 棚

■

Homc

Offl∝

Kitchcn

15

Bcdroom

6
6

Living room

PhCe胤

冷 棚

Waiting r00m

Mcdicalinstitution

Trcatmcnt room

Toilct10

Opcrating room

12

Classroom

SchoolWork,lacc

10

6

ward

Mccting room

Ballquct hall

Rcs● urant

喀 OW

iC誠

15

Sttdium

Workroom

10

Factow

Kitchcn

Transbrlncr
rcЮm

Pahting room

Eating area

3.Results and discussion
Based on the siFnulation rcsults,the flow rate and ventil〔 ■ion are calculated to obtain the air

exchange rate.Figures l‑4 below compare the influcnces of various variables on indoor air
exchange ratcs.Figure S shows the simulation results offlow lields in various folHls ofplot
plans.

ln telllls of the form of plot plan,the indoor air exchange rate of doublc‐ row staggeredarbors is thc highest,while that of double―

row arbors is the lowest.Companng the nurnber ofarbors,double― row arbors are the mostcommon,ha宙 ng a high green coverage rate and greatly
innuencing the indoor air■ ow introduction.The influcnce of planting distance is the greatest
on the flrst floor.As the air exchange rate is propo■ ional to the planting distance,planting
distance has no signiflcant influence on the air exchange rates on the second and third floors.

Thein■ uence ofarbor porosity is the grettest on thc■ st■ oor.The air cxchange rate is loughly
proportional to this porosity,and such porosity hぉ no signiflcantinlluence on the air cxchange‑69‑rates on the second and third loors.The height ofarbors has no signincantinnuencc on the air
exchange rate on the nrst fl。 。r,but greatly influenccs air exchange rates on the second andthird■ oors.
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ご 豊

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熟繭離爛曖 書轟・ 3F

Fig. 1. Influenccs of fbl11ls of p10t plans on

―●

3F

︱

ｌ

機

弩 Ｊ

薔

、

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、

lli..̲

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い

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Fig.

lndoor alr exchange rates

‑1・

l,燃

撼
坤

Fig. 3. In3uences of porosity of arbors on

︱

藤

︐︐鷲 ︱

烙

藝 ●
・

⁚

ｌ

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郵

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Ｌｒ層ま●﹄裏O'

れ特 ●f捕 崚Ⅲ… ,… 2F=‐

2F

indoor air cxchange rates

薔︵豊憲魯重︶襲‑lF

0F…

2. Iniucnces of planting distanccs onFig.

轟 ‐●― ―・ ● ― ― ■

03
Tml坤

3撼

lF … …

…

indoor air cxchangc rates← 薇 ―←

'●

S'鶴

●r絲
―
・,,‐ 1・― ●■ 3,

4. Infuences of heights of arbors
indoor alr exchange rates
鍛
い４
・賤
刹

Doublc‐ row arbors

Doublc‐ ro■v staggcrcd arboぉ

繰

Sil131c‐ ro、v arbors

Fig.5.Silllulation results ofOow ields in various follllS Ofarbor plots

4.Conclusions
As onc ofthe rnost effective、 vays to improve thc outdoor climate and environment,planting

arbors to increase the green coverage rate helps to reduce the influcncc of urban heat islands.
Fronl the perspective ofurban greening,this rescarch focuses on less discussed areas― namcly,

the influenccs of arbors on ambient wind ields and indoor air ventilation in nelghboring‑70‑

bu‖ dings.Taking a student dorrnitory in Taichung,central Taiwan as the samplc building andComputationai nuid dynamics(CFD)nurnerical simulation as the research method,this study
cOmpares the influences of various variables on indoor air exchange rates,including follll ofplot plan,planting distance,porosity ofarbors,and height ofarbors.The 80alis to increase thegreen coverage rate and introduce natural ventilation so as to provide indoor ventilation andmaintain good indoor thel11lal com量)lt. This can hclp comply、 vith the characteristics of a
subtropical rnonsoon climatc in a placc wherc thc site is locatcd,thus providing rcfcrcncc for
future plot plans and thc design ofthe arbors around buildings.

5。

Acknowledgement
The authors would like to acknowiedge the support of Taiwan Ministry of Science andTechnology through grant No.MOST 106‑2221‐

E‑167‑006 and MOST 109‐ 2221‑E‐ 167‐ 020

References[1]COCC010 S,Pcarimutter D,KacmpfJ,Scartezini J‐ L.Therlnal Combrt Maps to estimatebα ′ Fθ ′the impact of urban greening on the otltdoor human coml)rt. L/7・

̀sムッ 護 ιケらα″Gr̀θ κ,4g.2018;35:91‐ 105.

[2]Fahmy M,Sharples S,Yahiya M.LAI based trees selection for mid latitude urban
developments:A microclimatic study in Cairo,Egypt.3zガ

グ′″gα″グ E

ν″θ″

′
.

̀′

2010;45(2):345‑57.

[3]Lobaccaro G,Acero JA.Comparativc analysis ofgに en actions to improvc outdoor thcll:ial
θ.2015:14:251‐ 67.
comfort inside typical urban street canyons.υ 7bα tt CI′ ルηα′[4]Yang Y,Zhou D,Wang Y,Ma D,Chen W,Xu D,et al.Economical and outdoor thellllal
comfort analysis ofgreening in lnultistory residential arcas in Xi'an.Ss′θ(3′ ′ノ α77グα′ηαわ′̀sSoθ Jθ ″.2019;51:101730.

[5]Jamei E,Raagopalan P,Seyedmallmoudian M,Jamei Y.Revicw on thc impact of urban
gcometry and pedcstrian icvel greening on outdoor therlnal comfort. Rθιソαb′ ι α″グ

gン Rι ソ′θ゛ミ.2016;54:1002‑17.
5後 s′ αttα b′ ιttθ ζ′
θ″ル麟′2α 卜 Bα sた スソJθ 4.New Taipei City:Architecttlre
16]ABRI.G″ θθ″Bz滋 力ηg Eソ αルα′and Building Rcsearch lnstitutc(ABRI),MiniStry ofthe lnterior,ROC(TaiWan);2019.
[7]Hsich C¨ M,Huang H― C.Mitigtting urban hett isiands:A mcthod to idenj取 pOtendal windcorridor for cooling and ventik■ lon,Compllters,E″ ッルθη θ′′ α刀グ しケbα ″ 跡 農

"η

‑71‑

S.

2016;57:130‑43.

[8]Hsich C― M,Jan F‐ C,Zhang L.A simpli■ ed assessment of how trce a1location,windenvironment,and shading affect human comfort。 しケらα2016;18:126‑37.

191 CWB.MOnthly mean wind vdodty(10 mintltes), 2020, Available from:https://、 v、 vw.cWb.gOv.t、 vⅣ 8月 E/C/Statistics/monthlymean.html.

‑72‑

g

Fθ κ∫占ルわα″ Grθ ιガ″
ッ 護 こISBN 4‑901329‑11‑8

Procccdings ofthe Tenth intemational◎ 202 1 1ntcmational infomnation lnstittltc

Confcrencc on lnforlnation(Inhrlllation'2021)

Acceleration and Displacement Response Characteristics of Systemwith Frictio■ Suttected tO Random Vibration(Effect of Damping Ratio and Natural Period)
Shigeru Aoki・ , Katsumi Kurita**t rJレ 。ル ″9,ο ″rα ″c∂ ′̀β

ル滋%S″ 滋′ル′
″ι′′グ ルイθ αガ
″θ′o炒,D9,α ″̀力̀gqノ
α″fα θ
たノθ
θ′′rο ″ο4 E― ″
,ュ ψα
cな ″

̀″

**π θ οんイβ′″9′ ο方′αη Cθ ′
tsグ ルグ S″ノα′ル θ力′θ′οy,物
″

a―

̀み
ε
′
α
θ
ノ
ブ
ρ

αrt鸞

̀α

ノ
″3ノ イι
′EnJ′ ιθ″

′ぼ んイθθみα″たα′E″ gi″ θ ルg

̀″ ―
―
″
οε
ノ
ム
α
ブ
′
■0な ″′
ノ
イ
θ
θ
θ′
′ゐ″ο
,■ ψα
4 3″ α
@″ θ

̀′

̀″

Abstract
Various types of deviccs have been developcd to reduce scismic response of the mechanicalsystems. Base isolation systenl is one of them.Thc authors have developed a base isolation systemwith 6甫 ction for relatively small mechanical system.In ordinatt case,rcsponsc of rnechanical systemdccreases with the increase of friction coefncient. Howcver, in the expcrilnent to exanlinc thc
effectivencss of base isolation systenl,it is found that acceleration response takes nlinimum valuc atsome frictiOn cOefrlcient. In this papcr, experilnental results are examined using the equivalentlinearization method.It is demonstrated that acceleration rcsponsc takes minimum value at somc
■iction coefflcient in some conditions. The effect of the damping ratio and the natural period is
exanlincd.

Keywords:Random vibration,Nonlincar vibration,Vibration isolation systenl,Friction coefEcient,

Equ市 alent linearization method,Scismic excttation,Damping ratio,Nttural period

1.Introduction
ln order to reduce seisllllc rcsponse of thc mcchanical system, various wpes Of devices
havc been developed.In such devices,friction characteristic is used in sornc devices and baseisolation systems with fricuon are prac」

cally used[1].

The authors have developed a base isolation system for prevention from overtuming of

rclatively small structures and shown the effectiveness of systenl by experiFnent andvith the increase ofnumerical analysis. In ordinav case, responsc of system dccreases 、
friction coefflcicnt. Ho、 vevcr, during expcrimcnt to cxanline thc effectiveness of the baseisolation systenl, it is observcd that acccleration response takes nlinilnum valuc at somefrictlon coefnclent in some conditlons.
In this paper,this factis examinedね rthe mcchanical systcm subiCCted to random vibration
using thc cquivalent linearization rnethod.As input,stationary white noise is used.The entct
ofthe damping ratio and the natural period is cxanlined.

‑73‑

2.Analytical inodel and equation of motioll
Thc mechanical system including base isolation system with friction is modeled as asingle― dcgrec― of‐ frcedom‐ system as shown in Fig.1. In this flgure,mechanical systerll, ε″ is damping coefricient,

771 iS mass of the

たレ is spring cOnstant F iS friction

chattcteristic, χ″ is absolutc displacement of the mechanical systcnl,

ッr is absolute

displacement of the ground. Friction force is assumed to be applied betwecn the mechanicalsysterll and the ground.

The equation of motion with rcspect to relat市

e displaccment of the mechanical systcm tothe ground z″ =χmッ̀iS given as″ωm277t+ω m2zn+√ =― yt
れ+2ζ η
ιwhcre ζ7η =cm/(2ymmた(1)α
猛=Vた れ/mtt arC thC damping ratio and thc naural'D and system,respcctively./is刀
circular iequency of the mechanical″.As■ iclon characte」 stic,

Coulomb friction shown in Fig。 2 is introduced./iS glvcn as the following equttion.

f=μ ノm/1を ml(2)

where μ is iiction coel■ cient and g is acceleration of gra宙 ty.Equation(1)iS Cquivalently
lincarized as+(2偽 ω観 +ε θq)″ m tt ωれ22m= 夕

●Ｊ

為

t

where c″ is equivalent damping coefncient.

3.Equivalent damping coefflcientEquivalent damping coefncient c′ 夕for stationary excitation is obtained using relative
vclocity response as t)1lows.

ε′
9 is detellHined as square of di■ じrcncc bct、 veen Eq.(1)and

名「

Fig.l Analytical model ofmcchanical system‑74‑

Fig.2 Coulolnb■ ictionEq。 (3)is minimized as

Sgn(2m)一 εθ92m)2]=0(4)∂i=fI(μθFrom Eq.(4),cι 9 iS given as
c。

9=趣

笙

t等 景声 デ堕」

(5)

It is assumed that probability distributionfunction of夕 m iS the norlnal distribution、 vith zeromean asf(夕 m)=v̀2π σをm exp(― 森)(6)where σ= is the standard de宙 ation of relative velocity response.Using Eq.(6),6ピ

9 is givcn

from Eq.(5)as
Ca9==17裁(7)

4.Analysis for stationary white noise excitation
For stationary whitc noise excitation with intensity品 ,q″ m is obtained as

q24=

50

(8)

赫

Substituting Eq.(7)into Eq.(8),quadratic equation of

σ2m is obtained as

―
π
θ
の
恥=0
γ%2+√ μ
π

(9)

2ζ nω

The standard deviation ofrelative displacement response is obtained as
σz

=

(10)

S。

The sttdard deviation ofabsolute accelcration response is obtaincd asq)252̲2+ωθ
のれ=イ (2ζmも、 十ε
5。

4q布 2

(H)

Results of analysis
ln Fig.3(→ and(b),the standard dc宙 ation ofacceleration and displacement response ofthe

system,respcc」 vely,are shown.In these ngtlres,ζ
・0・

01 and L(2π /α b)=2.Os.It is found thatthe standard deviation ofacceleration ofthe mechanical systeFn takes lninilnum valuc at somefriction coeflicient. Friction coefncient which takes nlinirnurn valuc decreases with thedecrease of excitation.On the other hant Standard de宙 ation of displacement decreases with

‑75‑

２
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08

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06

１

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00

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、
ヾヽ

―

10

ヽ=0 5 ntlls'…………… tSc=10m̀11'

０

２

ヽ︑

1

ヽ

５

５

‐

1

０

０

‐・― SF2 0 111=i3
1

３

５

ヽ

５

￨

︵ Ｙ８ 目８理計 もｏ●Ｅヽり理 Ｅ●■層一﹂∽

０

ｒ 日Ｙむ 雲ｇ費８●︐

中Ｏ ●ｏ ●やィ一０つ﹃●つ● ∽

￨

３

５

￨

――― ・
9。 40 5 mls3

̲.̲ t90=20 ml's3

や、
00

02

04

06

0.8

10

FHction ttcient

FHction coel童 ci(瀬 t(b)Displacement(a)Acceleration

Fig.3 Standard de宙 誠ion(̀筋 =0.01,■ ,=2.Os)
０
２

￨

￨

:

,

‐ ,。

昨 2 0 nti133 ̲

￨

￨

５

０

∽

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￨

‐‐‐‐‐・90 10■ 1118' 一一、̲1̲ SF2 0 ntls'

０
︲

ヽ｀

0 nt'「 s3

＼

一
ノ

0‐ ‐‐
̀S01

――― SFO̲5 ml.3'
５１

S。 =0 5 nt18' ̲̲

一や 鷲 日 ︶Я ︶﹁● ２ こ ●︐
ビ ０● 一﹁︶ ｏ﹁●■５︶
﹂
０一
∽

̲

０

●ｏｏ
︵ φ︻● ︶ ●ｏ﹁ 薇ｏ︻

Ｘ 一一
ビ一
●一●
´ｏ一 一
﹂ｏ ﹁

￨

ジ

11■̲一

ヽ

０

00

02

04

06

08

10

00

02

04

06

08

Frlction c∝ 雌 ciellt

FHction αxぱ 五Oient(a)多 =0.01,L=1.Os

05,L=1.Os(b)ク 司・10

Fig.4 Sttndard dcviation ofaccelcration(̀場 =0.01,為 =2.Os)

the increase of the friction cocfRcient. In Fig.4(a)and(b)ShOヽ V the standard deviation of

accderation for多 鋤 .01,為 =1.Osand 6司 .05,L=1.Os,respec」 vely The■ ic」 on coettdent
which takes minilnum valuc increascs as the natural pcriod is shorten The standard deviation
decreases、vith the increase ofthe damping ratio.

6.Conclusions
Analytical inethodお r calculation of the standard deviation of response of the mechanicalsystem vrith friction is proposed.The standard deviation of acceleration takes rninirnum value
at somc ttction coefrlcient.Thc cfFcct of thc damping ration and tllc natural period on thischaracteristic is shown.

References[1]Cal宙 aP.M., Cal宙 ,G.M., Historical development of■ iction― based seismic isolation
systems,Soil D)η amics and Earthquake Enginecring,106,(2018),14‐

‑76‑

30.

ISBN 4‑901329‑11‑8

Proccedings ofthe Tcnth lntcmationalく)2021 1ntcmational lnfo■ nation lnstitlltc

Confcrencc on lnfom■ ation(InfOm■ ation'2021)

An Approach for]Deformed lmage Detection with Template

Matching
Hong ShcnλαCα た″ υ′ルθぉ″ン
θOλ 3 ″″ 71ε 力″ο′長2θ γ′
ク qrSし た′ α′̀′″dり 1′ 吻 αgr 98′ ‐855′ ,ソ″
滋 ,Sὶy7b力
κγ″力η′6‐ イ5‑′ ,И θらα―′α″Abstract
Template FnatChing is a techniquc in digitalimage processing for detccting a spccifled partin an imagc、
vhich matches a template image.It can be used to assist in recognizing road signs so as to navigate arobotic car.Howevcr.it cannot work wen when the refcrence image is deforlned.In this papcr,、

vc present

a way to dctect a specifled template imagc from a deforrlled reference image by utilizing templatematching.

Expcrimen餞 1l results are reported and the hture、

vork is discussed.

Keywords:image processing,template FnatChing,deforlncd image

l.Introduction
dバ ving of robotic cars are developed rapidly.It

ln recent ycars,various tcchniques for seif―is important for a robotic car to correctly recognize road signs from reference inlages viewcd
from thc ca■ Template matching is a techniquc in digital image processingおspecined part iOm a reference irnage

r detecting avhich matches a template imagc. It can be tlsed to、recognize road signs to navigate a robotic car.The images of various road signs are kept as

template images.Thc metllod oftemplate matching works we1l only when a template image
complctcly mttchcs some part of a rcferencc image.Howcveちa road sign is always viewed

with some rotation anglc frorn thc camera cquipped on the car、

vhen a robotic car runs on aroad,hcncc thc reference image obtained■ onl the calllera is always det)l Hlcd. It causes thc
road sign camot be detected correctly ttoln the defollllcd image.
In our research,we tcy to defolHi the road sign as a template image to match the defolHicd
original image.Experiments are perfolllled to lnatch the rcfbrence image、 vhich is vicwed M/ith
somc rotation angic, not right in front of the robotic cart and thc cxperiFnCntal results arc
reported.

2.TemplateⅣlatchingTcmplate matching[ll[2][3141 is a technique in digital image processing for detccting a

spcciflcd part of a refcrence image which ma

hes a tcmplate image. It can flnd a desired

templatc in the large reference image by slidillg the template、‑77‑

vindow in a pixel― by‐ pixcl basis,

computing the degrec ofsilnilarity bet、

〃een the reference image and the template image.

Figure l shows the main pal■ ofthe tcmplate matching program.The variable nl stands fo「the reference imagc,and variables x and y aFe the Coordinates ofthe pixel in the image.The
variable n2 stands for the template image,and variabies s and t are the coordinates ofthc pixelin the template image、
mindif = width[n2]来 height[n2];for(y=0;yく height[nl]― height[n2]:y++)[if (y % 10 == 0)printf(″ line%dVn″ ,y);for(x=0;xく width[nl]― width[n2];x++)[sum=0;
fo「 (t=0;tく height[n2]it++)for(s=0;sく width[n2];s+十 )sum += abs( lmage[nl][x+s][y+t] ―image[n2][s][t] );if ( sum くmindif )for(t=0;tく he18ht[n2]it++)for(s=0;sく width[n2];s++)iIIage[n3][x+s][y+t] ニ

255 ‑ image[nl][x+s][y+t]:
Figure l. Part ofthe template rnatching program

Here,we have an execution example shown in flgure 2.

Figure 2‐

l shows the refercncc

ilnagc,and ngure 2‑2 shows the templatc image. The image shown in flgure 2‑l is scarched
and the degrec ofsimilarity bet、 veen flgures 2‑l and 2‑2 is computed.The matching results are
given in flgure 2‐ 3,in which the detected telnplate is expressed black and、 vhite reversed

画像処理・認識は知能情報処理の 一種 と考 える こ とができる.

Figure 2‑1.Reference image

処
Figure 2‐ 2.Template image

画像皿理・認識は知能情報
回理の一種 と考えることができる.

Figure 2‐ 3.Ⅳ Iatching results

‑78‑

￨

3。

DeforIIled lnlage Detection

Templ江 e matching works well when the retrence imagc is viewedjustin tlle nght front of
the robotic ca■

Howevet the reお rё nce image is usuaHy viewed with a rotation angle in allnostaH cases,and it wili be vic、 ved as a deR)rlned imagc.ヽ Vhen a rotation angle exists bet、 veen thc

tcmplatc and the rcttrence imagc,the conventiOnal template matching algorithm desc五above cannot dctect the template irnage correctly. Thc conventional

bed

vay of solving this、problem is to rotate the retrence image to detect the templtte imagc when a rotation cxists

bctween the template and the reference imagc, It is complltationally expensivc, and is notpractical fbr real‐ tirne processing.

In our rescarch,wedefollllthetemplateimageinvariousdefo111lableanglesinordertoFnatCh
the reference image,and kept them in the library. Since the template imagc would be a sma‖part ofthc reference imagc,thc computation tiFne Can be expected to be reduced
Figurc 3 shows thc experilnental rcsults.Figure 3‑l shows thc refercncc imagc,in、

vhich thcvhich is used as theroad sign is vie、 vs as an eniptical shape. The imagc of the road sign 、template image is shown in Figure 3‑2,which is rotated till matching thc rcference image.
Figure 3‐ 3 sho、vs the detectcd road si3n from the reference image.

Figure 3‑l Reference imagc

Figurc 3‑2 Road sign used asthe template image‑79‑

Figllre 3‐ 3 Detected template image

4。

Conclusions
in this papet wc have prcscntcd a 、
vay to detect the template ilnage nて )m a def。 lHled

retrence irnage by defollll the teFnplate irnage to acceleratc the conoputing processing。 「Fheexperimental result is reported.

The research is in progr∝ s.There are many interesting topics to be pursued around thisresearch. We need more expe五 mental results.This will be addressed in our niture work.

References[1]Template Matching Techniqucs in Computer Vision,R.Brunelll,Theory and Practice,

Wiley,2009.
[2]Grayscalc Template― Matching lnvariant to Rotation,Scale,Translation,BHghtness andContrast,H.Y.Kim and S.A.Ara旬 o,IEEE Pacinc̲Rim Symposium onlmagc and Video
Technology,Lecturc Notes in Computer Sciencc,vol.4872,pp.100‑113,2007[3]FAsT― Match:Fast Afline Templa

Matching,Kollllan S.,Reichman D.,Tsur G.and

Avidan S.,CVPR2013.
[4]The Template Updatc Problem.,Matthews,1.,Ishika■va,T.,Baker,S.,IEEE Transaclon

Pattem Analysis and Machinc lntclligcnce 26(6),810‑815(2004)

‑80‑

￨

ISBN 4‑901329‑11‑8

Proceedings ofthc Tcnth lntcmational◎ 2021 1ntcmational lnforIIlation lnstitLlte

Confercncc on lnforllllation(InhfllllatiOn'2021)

Restitution Coefrlcient at Collision between a lBottom of Small
Structure and a Plate by]Rocking Vibration
Katsumi Kuritaキ ,Shigcru Aoki**′ノ″″Cο ル gθ ρ
Fル α″Srri9ノ 7し θ力″0′ θy,Depα rrF2ι ′r9′ ん々θ力αれたαノEngi″ じθ′ル隻多
9′ θ
―
ー
―
″ο
θ
ル肋な夕
″,@″ ′た″″α
019り ″gの ツ′′ιイθffigasカ ゴ
4E夕 αノ
ら物りQ々 ′

*7ο ノ θん″′′レ**7bレ οMβ ″ ο
ル7ra″ ゴι″[ル 廷″ ″rr″ ι″′q′ 滋 ε
α
ルθ
ノ
ο
レ
S′ ″
ノ
′7セ θ
′
ブ
″′Cο ′
ルg?9′ ル′■ζ,ち Dl′ α9ρ「 ̀ι
̲7r9̲ィ θHigasカ メ
ー
.α θ
ルα
ο
″@g.″ αЮ―′gの ッ′
α0ら Sけ れα′
,Japa4 E― ″α
も
,ら りο
″
̀ノ

Abstract
lt is IInportant for overtuming prevention by seismic ground motion of sman structures instaned
inside buildings to understand characteristics of restitution coefFlcient at coHision. ln this study,
characteristics of restitution coefflcient at coHision、vere investigatcd based on vibration expcriments.

In case of the restitution coefncient tixed value,it、 vas difRcult to flt the rocking vibration、
bet、 veen

vaveforlns

observed and numerical analysis. However, in case of the restitlltion coeficient that is

introduced nonlincar efFects,they、 vere good agrce between them.

Keywords:Rocking vibration,Restitution coefncient,Sman structure,Free vibrationl.Introduction
it is iinportant topics for seisrnic disaster prevention to prevcnt overtuming of sma‖structurcs insidc buildings by seislnic ground motion. Therefore,it needs to understand theovcrtunling proccss of sman structurcs on seismic ground motion.According to Miyata

θ′α′(2018),they indicated that a small structure on the table shook by sine or seismic groundmotion havc generated rocking vibration,have overtllmed in non‐steady state[1]・

It indicttes

the irnportance to understand characteristics of rocking vibration. Since the bottom of sma‖structure conides、 vith the table repeatedly in rocking vibration,the restitution coefflcient at
collision is one ofimportant fhctor.
In this study,characteristics ofthe restitution coefncient at coHision in rocking vibration isinvestigated by vibration experilnent and numerical analysis.

2.Ⅳ lotion equation of free rocking vibration
A modei fbr the experilnent of frec rocking vibration is shown in Fig.1.Providing an initial
angle for it,the free rocking vibration is generated.The equation ofrnotion is as■ )‖ o、 vings,

fO∂

十 gR2・ n(ψ 一日)Sgn(θ )=0‑81‑

where frJiS inertial moment,θ is rotation angle,g is gravity acceleration.And the sng means a
ぬ nction of signal.A relation of angular velocity variation at coHision bet、

vecn the bottom of

specirnen and the table is

θ(′

+)=θ

θ(′

)
(2)

An exalnplc of results is shown in Fig.2. In casc of rcstitution coelTIcient̀=1.00,that isperfectly elastic conision,the amplitude and period on rocking vibration indicate the flxed

values,and pe● od 7=0.42s.In case of ι=0.95 and O:85,the wavel)lHis of rOCking vibration
indicate damped vibradon moづ on.The damping ratio c in these cases are ζ=0.04 and O.H,
respectively.And the periods indicate progressively shorter flom■

0.36 sto O.14 sin case of

θ=0.95,and 7生 0.28 sto O.12 sin case ofθ =0.85.

３
０４３■Ｉ当 一 ｔ
３一
︐

1234
T綺ぼ

Fig.l Model for experiment

o)

T"ば

3)

Fig.2 Results offrcc rocking vibration、 vavefollIIand numerical analysis.

by numerical analysis.

3.Experiment of free rocking vibration
An overvic、 v of free rocking vibration experilnent using the specilnen is shown in Fig. 3,

and rcsults arc in Fig. 4. In casc of the ttble madc by alunlinunl, the period and damping
decreased from 7‐ 0.49s to O.10s,and fromζ=0・ 07 to O.03,respectively.On the other hand,in case by cork sett they are from卜0.73sto O.10s,and from

ζ=0.06t00.03,respectively.

Comparison results bet、 veen the observed waveforln and the fltting by fonvard modelingare shown in Fig. 4. The wave shapes of flrst part between them are good agreemcnt.
However, it is difRcult to explain、 vavefo111lS betWeen them with phase diЯ brences at laterpart,assurning the restitution coefncient is flxed value.

‑82‑

事芝
倉 １ ８ 西首 工

―‑Ob3
―
―
Cal
‑―

at0 071

Fig.3 0utlinc ofmeぉ unng system.

γ薇 ●
)

Thぼ ●
)

Fig.4(3ompaHson ofwavefollllS betWeen observed andnumerical analysis.

4。

Numerical analysis with non― linear effects
Next, we used a model of quadrilateral hystercsis loop characteristic by Mase、va andWatanabe(1975)[2]shown in Fig.5 and do the numerical analysis.Assuming the lnodel ofquadrilatcral hysteresis loop character shoヽ vn in Fig.5,the restittltion cocfrlcicnt is expressedin the following equation,

θ=ソ 2/ソ l=1.00,ソ ≦ラ

(3‑a)

θ
=ち /h=イ K2/κ 3+0 κ 2/̀X4/κ 3Xれ ア'け'(3‐ b)

where/(χ ,■ )mdcttes the reacuon brce,κ ′,ん ,島 are a Jope of rcactbn brce
characte」 stic against displacement. And ソフ, ソ2 are velocity before and afler the conision,respectivcly. ' is a velocity of boundary bct、

veen the perfectly elastic coHision and theelastic coHision,cxpressed in the following equatlon,

ラ=島

(4)

where δO indicates a deforlnation of elastic limit,δ O=0.27 min is uscd in this study. From arclation betwccn the restitution coefRcient and the collision vclocity sho、

vn in Fig. 6, therestitution coefAcient is depending on conision velocity.
Based on results by experiment of free rocking宙bration,optimized parameters κ′,κ 2,andκ夕by fonvard modeling were estimated,and investigated.Comparison results between the
CXperiFnent and numerical analysis in case ofthe alunlinunl and the cork shoヽ vn in Fig,7,it is

ilnprovcd to introduce the modc,good agrecmcnt behⅣ ecn them.

‑83‑

1.1

:・ 1

:0.05
6o

0240010
Appl● 動 v輸

Fig.5 Quadrilatcral hysteresis

loop

R36 Rl搬

畑お 4ル

w:碗

κ3=3.00)

1‐ ]

輸
孵跳

10
５

⁝
︵

５

３

￨

:

￨

０

０

百
環

も

４

¨
掴
一
陣・・・
一
・︻
・

characteristic

"″

■0踊

40卜

￢h凛 蛉

褐ぼ→

Fig.7(3omparison ofwavefolllls between observed andnumcrical analysis

using nonlinear inodel.

5。

Conclusions
in this study, characteristics of restitution coefAcient at coHision of the table on rocking

vibration、 〃as investigated by excitation experilnent and its numcrical analysis.
It is possible to cxplain the、 vavcfollllS betWeen experiment and nulnerical analysis with themodel proposcd by Maesawa and Watanabe. It ineans the restitution coefFlcicnt at coHisionindicates non‐ linearity.

References[1]Miyata,M.,Kurita9 K.and Aoki,S.,Study on rocking vibration characteristics by■

ec andforced vibration for structures,Dynamics&Dcsign Contrence 2018(2018),219(inJapancsc).

[2]MaezaWa,s.and Watanabe,T,,Analysis on steady state rcsporlse of system w■hhysteresis loop characteristics(2nd repo■ ,for systcm with res」 tujon force hⅣ ing
quadrilateral hysteresis loop characteristics), Transactions of the Japan Society of

Mechanical Engineers,Vol.41,No.352(1975),pp.3458‑3469(in Japancsc).

‑84‑

ISBN 4‑901329‑11‑8

Proccedings ofthe Tcnth lntemational◎ 202 1 1ntemational lnfom■ ation lnstittltc

Confcrencc on lnbrlllation(InfOrlllation'2021)

Reduction Method of Residual Stress fbr Weldingin Stainless Steel by Ultrasonic Vibration
Akira Naka7atot,Ktlrita Katsumi**,Shigeru Aoki**,Shigcomi Koshimizu***,Tsuyoshi Matsuyama***geグ ルグ″S′ riα ′ルι力″ο′ο′′″″′Cο :′θ
′
,「 ο
ゎo■イ
9′ ο

*И いα″εθ
グCο ″ぉ′rrJた**π ο οんソた̀̀rr9ρ

十■十Иグ″ ″cθ。′ィθ̲θ θ′ノ,ノ lρ α″
ソ

ー
―
ノθ‐
イθ″igαsカ ノοI S力 i′イθHigα力″οo騨,7‐ ′θ―οノブ″″Cο :Icg● 9′ f77グ Srr″ ′ルσ
あ けo■イタOθ ″,Japθグ ル グ溶 ″″ノル
こ ル sr″ ″′

gω α―
た

,

̀秘
s・ /7プー′αしο′S力 ′rツ クー,‐
θθ″ ,Jαpa″
肋 ,乃 り ο ノイθ‐θ′勁 ″agの ッα‐イθ Higasカ メ′ο′οy,ノ ー/θ ―̀力

Abstract
Welding is ajoining method used for many structures.However,reddual strcss is gcnerated near
the bead. We have proposed a method of reducing residual stress using ultrasonic vibration during
welding in roned steel for general structtres.〈 )n the other hand, it is uscd thc stainless stccl for
important structures.ln this rescarch,thc ettctiveness of the method of reducing rcsidual stress using
ultrasonic vibration during welding was exalnined by built―

up welding using the stainless steel.

Keywords:Built up welding,Stainless Steel,Ultrasonic Vibration,Residual Stress,Accelcrationl,Introduction
Welding is a joining method used for rnany sttuctures,and to melt the material applying
heat locally. Since the tensile residual strcss is generated in the procOss of C001ing andhardening, and make less the fatiguc liFnit Of base material. Therefore, a method of、velding tensile residual stresses without a special device is developing using ultrasonicvibration load.According to pre宙 ous studies[11[2],they indicatcd thtt it was an effecjvc
rnethod to reduce thcヽ 〃elding residual stress using ultrasonic vibration load in case of built― up

welding with inetal block of roHed steel fbr gcneral structure SS400 and of butt、 velding、 viththin metal shects.

Since the mclting point of stainiess steel used for iinportant structurcs such as anuclcar reactor is highcr temperature than that of rolled steel for gcneral structure, it
expects that the welding residual strcss of stainless stecl is higher than that of roHcd
stcc1 lor general structure.The residual stress is one of the reasons that is caused stresscorrosion cracking.Thereforc, it is important to develop a method of、
residual stress in stainless steel.

‑85‑

velding rcducing

In this study,the effectiveness of welding residual stress reduction method using uitrasonicvibration load is investigated for austenitic stainless steel SUS304.

2.Experil■ ental 1/1ethods

2.1.Welding
Figure l shows a drawing of specilncn in this cxperilnent. The mate五

al is a block ofstainless steel SUS304. Bcfore welding,the surface of specilnen is polished and annealed.
And,the oxide layer on the surfacc of spcciFnen iS removed with hydrochloHc acid and CPL
solutionA thyristor― controlled C02/MAG automaic welding machinc was used to do a 150‑mm―

long weld on the center of specilnen.A FniXture gas of argon and carbon dioxidc、
a shielding gas to prcvent welding defecも〃as used assuch as blow holes.The welding conditions arc

shown in Table l.
Comparing the rcduction ofwelding residual stress,the specirncns、Ⅳith vibration 10rd at thefrequency of 36 kHz, of 58 kHz and without load、 vere prepared, 、vhere the acceleration
amplitudc is 2000 1n/s2,waS rneasured by acceleration pickup at the point shown Fig。

1.Sincechrolnium carbides were deposited near the bead a■ er welding, the surface was again
removed、 vith hydrochloric acid and CPL solution.

2.2.Fabrication of Weld Test Specilnens
Welding residual stresses in the bead direction at 15 points evew± 1 0 1nin■ onl the center ofthe bead were measurcd as shown in Figurc 3. X― ray residual stress measurement device wasused for the measurement of welding residual stress.To lirnit an area ofiFadiation by X―ray,it wtt covercd by black vinyl tape with a■ ame with 20 mm× 20 mm.
Tablc.2.Strcss lnetttlrcment conditions

Tabic 1. Ww elolng
ldi
cona11lon
ndi

Parsillg nlcthod

ISO‐ inclination lmcthod

Wire diamcter rmml

Mcぉ urcmcnt inodc

fixcd inethod

Welding current rAl

D市 crgcncc slit[dcgl1

Wclding voltagc rvl

Ligllt rcceiving slit rdc21

1

Cotlnting timc rsl

10

Wclding specd「 Al2.0

Shicld gas

Ar+C02

StCD

0.15°

Mcasurcmcnt rangc

143.00° 〜152.90°14905°

‑86‑

Bulb

Cr

X‐ rav

CrK‐ 3

Fig.2 Location of、 vclding residual stressFig.1.Welding situation
Fig.1.Welding
situationoftest
oftestplate
plate

mcasurement point
3.Experiョ mental results

2.2.Fabrication of Weld Test Specilnens
Figure 3 shows the results of residual stress measurement by built up、
the ultrasonic vibration at thc frcqucncy of 36 kHz,58 kHろvelding loadcd、 vith

and without loaded.The tensilercsidual stress is generated overall in bead direction,and increase to、vard to the end of
welding.Comparing results of welding residual stress between with and without ultrasonicvibration load, itvas reduced with ultrasonic vibration load. Ho、、bet、 veen the ultrasonic vibration load at the■vever, the reduction rateequcncy of36 kHz and of58 kHz,it、 vas alinost

same, was maxiinuln most 100 MPa, lt suggests that the di■

brence in hquency had little

cttct on thc amount ofrcsidual stress reduction.
０ ０ ０ ０ ０ ０
︒ ０ ０
０ ０ ０
０ ０ ０ ∞ ０ ０
６ ５ ４ ３ ２ １■ ２・ ３ｏ●０場ｏば﹇﹄︼２冒∽ｏお∽一
‐
80

‐
60

‐
40

‐
20

0

20

40

60

Mcasurcment position[mm]Fig.3.Rcsidual stress on the bcad direction

‑87‑

80

4.Conclusions
Built up welding was perfolllled on the block of austenitic stainless stecI SUS304 1oaded
by ultrasonic vibration, and the efFectiveness of、

velding residual stress reduction method

using ultrasonic vibration、 vas investigated. As a rcsult, thc method of welding loaded theultrasonic vibration at the tequency of 36 kHz and of 58 kHz can reduce welding residual
stresses for austenitic stainless steel SUS304. The effects of difference of ultrasonic
n℃ quency On welding residual reduction is smaH.

They indicate that the method of reducing welding residual stress by using ultrasonicvibration is efFective for austenitic stainlcss steel SUS304.

References
11]Shigeru Aoki,Tadashi Nishimtlra Tetsumaro Hiroi,SeJi Hirai and Kunihiko Mineki,
Rcduction in Residual Stress ofWeldedjoint Using Local Plasticity Caused by UitrasonicVibration(Welding of wheels),力 ″ α′グ Jη α″Sθ Cノ θケメ9r rcch″ θ′。ッ グ PJaSた ノタ,48‑
554,p.53‐ 56,2007.

[2]Shigeru Aoki,Tadashi Nishimura TetSumaro Hiroi,and Setti Hirai,Reduction of
Residual Stress for Welding Joint Using Ultrasonic Vibration Load,rrα ″sα

jθ

̀′

洗フα
″sθ cた ヶ″ 々ε
ηたα′Enttθ α C,77,657,p.1613‐ 1618,2001.
力α
r九

S・

‑88‑

∬ グ ルι

ISBN 4‑901329‑11‑8

Procccdings ofthe Tcnth lntcmationalく)2021 1ntcmational lnfonnation lnstitutc

Confcrencc on lnfom■ ation(InfOmlation'2021)

Behavior of Exhibits Fixed with Nylom Gut by Seislllic Motion
Yu Tamura彙 ,Katsumi Kurita**,Shigeru Aoki***И いα″
̀̀グ

ル
力″ο′
ο
イθHigas/1ル οJ Sた レaga″ α‐′rsι ,あ わoル イθrr9ρ ο
′″″Cο :′
Cο ク
グ ル歳 Sr″ ″′ルε
ク ,7‑′ θ‐
θ′
′
あ̀gι
ιθ
,υ ゅ
り,′ イ

,

"

ホホIbた οMar″ ο′′″′ル機 ″ο′οy,D̀′ arttι ″′ぼ Mac/1α ′ a′ E4gr″ ′″辱ッグ ルあ sプ ″9ρ J̀α ″0'′
̀g￠―″‰〔コ″α,あ り ο,yapa′′りθイθHigasカ ル04Sカ プ
Jc・

Abstract
lt is important for scisnlic disaster prevention of exhibits in the muscunl to understand bchavior

them by scismic motion. In this study,Bchavior of exhibits in the muscum flxed by nylon guts have
perforlned by vibration test.And conditions to prevent overturning ofexhibits flxed by nylon guts werc

investigatcd.The exhibit flxed by nylon guts have generated rocking vibration and sliding motion byseismic motion. It expects that the sliding motion at the bottom of exhibit caused overtuming. It iseffective for ovcrturning prcvention to increase l蔵 ction coefrlcicn

be● vecn the bottom ofexhibits andthc display table.

Keywords:Exhibits in the inuscum,Ny10n gut,Vibration test,Friction coemcicnt

l.Introduction
ln order to prevent earthquake disaster,the cxhibits in the muscunl are taken measures toprevent overturing.For example,there is a way oflowering the center of gravity on the
exhibits,of flxed by bolts and of put thc cxhibits on the felt seats[1]. In particular,anylon gut,which is used for accessories and flshing line, is the most effective way for

exhibits flxing on site[2].SinCe it is low costs,many museums usc it to flx exhibits.

However,the cxhibits「 Ixed with nylon guts were overturned by seisnlic motion on the201l off the paciflc coast of Tohoku earthquake[3].TherCfOre, it is important tounderstand bchavior of the cxhibits flxed with guts during an earthquake.In this study,
the bchavior of exhibits flxed with gut by seisFniC mOtion arc investigated by vibration
test.

2.Behavior of an exhibit lnodel by vibration test
Figure l shows the rnodel ofcxhibit rnade by acrylic llsed in vibration tcst.The sizc and inassare 70 X 70× 455 mln and l.83 kg,respectivcly.The ovcrtuming acceleration ofthe lnodel isabout 150(3al.

‑89‑2.The model was placed in the

An overview of the vibration test device is shown in Fig。

center ofa stand,and flxed with nylon guts.The 1995 Southerrl Hyogo Prcお cture Earthquake
江 JMA Kobe(Kobe wave),the 2004 N五 gata¨ ken Chuetsu earthqllake tt K¨0iigam wave)and the 2016 Kumamoto carthquakc at KiK―

NET NIG019

net KMMH16(Kllmamoto wavc)

were used as input waves forthe test.

…

識

,

畿

、

FigJ Exhibit model

The input wavefollll(N五 gata wave),and the response wavefollll at the top of modcl■

xed

by nylon guts with tension of 14.7 N arc shown in Fig.3.The response wavcfollll indicatcs
iarge amplitude■ o■ n10 sec againstthe input,and an asymmetric shapc at around 15 sec.These
are duc to generate rocking vibration ofthe modelland sHding motion ofit at the bottom ofmodel a■ er experiment sho、 vn in Fig.4.Thcrefore,it is expected that a rcason of ovcrtumcd

″
¨
声
﹃
呻

on the exhibits flxed with nylon gtlts is sliding rnotion ofthe inodel at bottonl by seislnic rnotion.

Acccleration
PiCk upOm―

Nylon gut

Specim//Exhibitlon

Ny10n
gut

Spcclmenstand

Exhibitlon
Vibration

stand

table

(a)Side view ofexperimental de宙 cc
Fig.2(b)TOp vielv ofexperimental device

Expcrilnental devicc

‑90‑

側
知
卿
醐
０
硼

︻﹁ ０ 一〇 ０く

硼
卿
硼
硼
硼
脚
脚
０
欄

︻
■ ０ ︼００く

硼
硼
硼

0

10

20

呻

30

40

1

]

Fig. 4 Bchavior of exhibits using

Fig.3 1nput and response acceleration
wavefoI11lS uSing Nligata wave

Niigata wavc

3.Effects of friction coeffncient at the bottonl of exhibits on behavior
in this section,cRcts of ttction coefflcient at the bottom of exhibits on behavior of theexhibits is investigated by vibration test.The conditions of vibration test and static friction
cocfncient are shown in Table 2.And the tension ofnylon guts、〃as set at 2.45 N and 4.9N.

The maxirnum input acceleration and status ofexhibits bchavior under a condition oftension

force of nylon guts with 4.9 N using Nligata and Kobe waves are shown in Table 2.Where asymbol O means stable condijon,△ is sliding motion,□ is rocking宙 bration,△ □ is sliding+vibration and× is overturn.In case ofNiigata wavc,the bchavior ofrnodel with a condition
oflow iiction case(A― W)indiCates sliding motion.Increasing a value of■ iction coel■ cient,the model did not generate sliding motion.The maximum input amplitude without sliding
motion in N五 gata wave is 336 Galin case ofA― W,884 Galin case ofA― C,and in case ofC― C.

In casc of Kobe wave,in casc of A‐ W itis 421 Gal.and in case of A― C and C‐ C it did not
generate sliding rnotion,It is possible to suppress sliding inotion by increasing the static iliction

coefEcient.

‑91‑

TablelFHction cocfAcients

Acrylic― Wood(A― W)

0.26

Acrylic― Cork(A‐ C)

0.45

Cork一 Cork(C― C)
Table2 Max input acceleration amplitude and status← enSiOn:4.9〔 N])
3JAXA●qu

卜W

0
駆… 中

C

A‐

ー

瑯

‖

962

口

0

0

0
4■

600

"臼

ロ

ロ

0

S●

ア

A向

968

l(H,1

1200
』

自

』

611

獅

983

●

ムロ

ムロ

翻

704

780

ロ

ロ

ロ

目一
鶴

O

347

1191

口一
瑯

0

250 : 331

1

il"

An

︲
口 一︲
６

蹴
t―…

l繊

ロ

●一

1 121

'23

口一
欝

62

ロ

０一
職

MAXA● ●● ll

口

簿
一
錮 ０一

0

ロ
似一

0
秘

０ 一

C

538

469

0

El― m

組

△

︲
０¨
２
︲

C‐

5。

C

A‐

撻

△

0
︲
０一
６

競

銅

O

知一
日

ルW

:

10■

m'13 l0232

090 : 100

郊

競

勝一
ｏ

MAX…
2‑

￨ " 1

4"

一
〇

騨ー A● CIml
E―

節

…
辮

336

0

: 60 1

SS2

￨￨

凛

229

0

C

C・

Lf41

10!20i301・

:

0

0

ロ

Conclusions
h ttt by seismic motion werc invesdgated byln this study,the bchavior of exhibits flxed wれvibration test.The results are as fo1lows,

1.

Exhibits fixed with nylon guts are generated rocking vibration and sliding motion byscisnlic motion.Overtuming of exhibits was caused by sliding motion at the bottom ofmodel.
2.

Increasing the coefncient of static iiction bet、 veen the bottom of the model and thedisplay stand,it is possible to prevent the cxhibits iorn sliding rnotion.

References
umi Toshinawa,Current scismic countell:leasures[1]TatSuO ohomachi,Masashi Takase,T温 〔
for displaying artwork and cvallttltion of the pettrmance of trial seisnlic‐ frce displays,P′ οθι
θ訪″」 グ ルιCル 〃巳nttη θθガ″g&9θ たヶ,No.507,(1995),191‑199.

[2]Japan Associadon ofMuseums(ed.).R̀ソ お

/Gタ ガ

G

̀′

̀メ

,r Pα

̀″

′
dθ Bθ θ崚 ″〃α″′ノ″gル 傷s̀露″ ルクた″′αお4g α″ノ 1欧 αttPθ ″′ルgC"Jra″ ′P/̀フθrriθ s α″グ ″b″ お グ И″ち Gyosei,(2016),p.230.

α′
′
θ
″て
ル R
[3]No」 yuki Tomit 贄″√ Eαr励 9 α
′ε
し物グ

な″″θ
θ
s/シ И″′″b″ 鷺θルを″ ′′′′
ッ rS̀お ″た おοル″θ41%bル Dθθs A4θ r ttnηル ヽ e為 ル ♂Z∫ Par′ 夕 Dα″θ

̀乃 ̀ッNihon Keizai Shilnbun,(2011‑6‐ 17),Evening Edition,p.16.

‑92‑

̀″

4

￨

ISBN 4‑901329‑11‑8

Proccedings ofthc Tenth lntemationalに)2021 1ntemational lnforlllation lnstitLltC

Confcrencc on lnfomlation(InfOm■ ation'2021)

ISOIDS:An ISOIDATAL‐ BaSed lnitial
Centroid Algorithm
Noah Gardnerl,Sahar Yarmohammadtoosky2,
Anthow Phan3,and Chih― Cheng Hung4
Kerlnesaw State Univosil光 ルfarietta,CA,USAl'3,4
1ran こ、fヾ∝sfty οF Science and Technο l。開Ъ■bhrall,Iran2
lngardn10@students.kennesaw ed、 1,2yarmOhamadishr@gmail.coln,

3aphan5◎ students kennesa、 /edu,4chungl̲Q3b,nesaW・ edu

Abstract
lterat市 e Sel卜 Organizing Data Analysis Technique(ISODATA)is a clus̲
tering algorithIIl b¨ ed oll tl〕 eK¨ }ンlearis algOrithrn tllat intends to ind tlle

correct number of clusters through merging and splitting lt is di6cult
to deterllline the correct number of clusters in many real― world apphca‐
tiolls, in patticular, reI1lote sensing image interpretation Compared toK― Means, the ISC)DA■ ヽ algorithm should be resilient to initial cluster

centers However,ISODATA is also sensitive to initial cluster centerswhich impacts the performance of the algorithm Ths work prOposes u針TA approach of splitting clusters to select quality initial
ing the ISC)Dノヽ
clllster centers,called lterat市 e Sel← Organizing Data Split(ISODS)The

prOposed approach is evaluated on several benchmark UCI data.setsお、vell as the Salina.s― A hyperspectral ilnage dataset. The results are evalu―
ヽVhen IS()DS is used
ated using standard clustering evaluation measures.

tOgether with ISODATA,the performance is improved and the generated
clusters more closely re.Femble the expected number of clusters
Keywords: Clustering,IS()DA■ ソ、 Initial Centroids,Remote Sensingllntroductionvhen the data collection takes place at a
Rernote ttnsing technology is used 、
remote distance ioni the subieCt nlatter, such as the study of dailyヽ veather
and long― term clinlate change, land cover mOnitorillg, ecosystern modeling of(getauon,and so on il,4 Mtlltispectrd imaging technolow is one of the
instruments for remote sensing used since the late 1960s 13]It haS been applied

to numerous electronic imaging apphcations,including food inspection,forensic
science,medical surgery and diagnosis,and military applications 14,5,61.Be―
cause of the difliculty of obtaining prior knoM′ ledge in remote sensing studies,
unsllpervised clcssiflcation and clllstcr analysis hsヽ
〔 oat importance comparod「
to supervised classiflcation i71.

Unsupervised learning is a machine learning technique used M/hen the datavith minirnum
human supervislon and without external guidance. In contrast to supervised
has no pre― existing labels and looks for patterns in the dataset、‑93‑

learning,where a training set ofinputs and observations are given to the lllethod,
unsupervised learning uses only the inputs al■ d should ind an interesting pat―tern in the dataNset. Cluster analysis is an example of unsupervised learning lnclustering analysis, unlabeled and unsorted data points are grouped and seg―
mellted according to silnilarities and differences to flnd structulle in the inputs,

Oup it into meanirlgful clusters,and understand the dataset better.
One of the nlost popular clustering algorithlns is called IS()DATA clustering,『based on the K― Ineans algorithnl M′ ith some variations The IS()DATA method's
preference in comparison with the K― means algOrithln is that the IS()Dノ ゝ
T2ヽ
algorithnl uses splitting and Hlerging forms for clusters The IS()Dノ TTA nlethod

a1lows starting from arbitrary cluster centers and obtains better partitioning
results than the K― Means algorithlll, but it is not entirely resllient to irlitialcluster centers. In this paper,a nOVel method using the IS()Dゴ
TTA approach of
splitting clusters to select quality initial cluster centers is proposed

The papeF is Organized as fo1lowsi Section 2 introduces K―

Nreans and ISO―

Dノ ヽ
TA clustering algorithlIIs. The new proposed algorithin is explaixled in Sec―石
tion 3. ヽヽe present the experilnental results in Section 4

Finally, Section 5contains concluding remarks.

2

Background

The K― Nleans algorithn■ is an unsupervised clustering algorithm and aiIIIs topartition̲ar obsertttions into κ clusters 181 Data points in the same cluster
are very silllilar to each other and hav℃
less variation compared to data points
assigned to other clusters The useF deines ttr,the number of expected clusters
Fo1lo、ving is a description of the K―

Means algorithrll:

For selecting the initial cluster centers, there are ttvo standard methods:

RandOm Centers,and K― Means++[91・In Randonl Centers,κ samples are

randonlly chosen from the dataset to serve as the initial cluster centers. In
Iく ̲Ⅳreansl‐ 1‑, l Sample is randolllly chosen frOrll the dataset to serve tt theinitial cluster center.「 rhen, κ ̲l samples are iterativ℃ ly selected, where theprobability of a sample being chosen as a cluster center is the distance of thesample from pre宙 ously chosen centers 191・ The K¨ Means algorithm is susceptible
to initial starting cluster cellters,

vhere dirererlt illitial values can result in a、

difFerent clas● 6cation llq.

ISC)DATA is another frequently used clustering algorithnl and is based on the
K― Means algorithm llll.Like K―

Means,cluster centers are iteratittly updated

and rettsigned to the samples in the datttet. However,IS()DATA determines
the nunlller of clusters dynanlically alld allσ ws for a diferellt nunlbe■of cluster

centers. In cOntrast,the K― Means algorithln requires a nxed user̲set parameterof the number of expected clusters

The advantage found within IS()DATA

vhich is achieved throughdiscarding clusters with a small nllmber of mernber samples,and merging anda1loⅥ /s lor discovery of a difFerent number of clusters,、

splitting clusters that lneet certain parameters.

There are some disadvantages to the ISODATA algorithm First,it is sen―lctors should bc nnctllncd for
optilnal perlormance based on the attributes of the dataset being tested. In
sitive to thc spccifled parameters. These paral■

addition,silnilar to K― Ⅳleans,it is sensitive to initial cluster centers,althoughless so than K― ⅣIeans due to the extra processes of discarding, splitting, and‑94‑

merging.「 Fhe initial centroids can arect both the qllality of clllsters prodllccd
and the number of iterations required to converge l101・

3]Proposed Method

The proposed cll■ ttering algorithn■ 's objective is to improve the result we obtainfronl the clustering algorithms by targeting the initial cluster centers. Inspiredby the ISODATA algorithm,Iterati(Sel← Organizing Data Split(ISODS)uses
the splitting prOcess frolll ISC)lDA]PA to create the required initial cluster centers

to use for a clustering algorithnl. The algorithnl is outhned belo、 v:o Step l: Choose one observation as a cluster center fron■ the datttet.
o Step 2: ̲Assign each element of the dataset to the cluster based on thenlinimum distance fl・ orn the cluster center.

o Step 3: Re― calculate new cluster centers for each cluster by computing
the mean of all patterns ttsigned to each cluster.

o Step 4: If the numbe■ of clusters is equal to

スr, then the process is「,then the clustersЙ
terminated. If the number of clusters is greater than、′ith the fewest mernb∝ s is discarded,and the algorithIII moves to Step

2o Step 5: Calculate the standard deviation of each cluster in each dilnen‐
sion. Therl,split each cluster along the dimenslon、vith the greatest stan―

dard deviation and lnove to Step 2.
This method began a.s a modined lsc)]DATノ ヽ process. However,the modin―
cation was unique in that there is a clear distinction fronl the proposed change

and the beginning of the original process. Although more complex than othermethods of generating initial cluster centers,this approach guarantees separa―tion bet、/een clusters. 2生 s a result,IS()DS can be used to generate clusters forⅣreansother clustering algorithms,such as l《 ―4Results

Due to the response of the IS()DATA algorithln to the discttding, merging,and sPlitting parameters,these paralrleters should be carefully selected. Since
the goal of this research is to explore the impact of initial cluster centers on

ISODATA,we use a relatively simple approach for generating ISODATA p計
rameters. 13ased on the available training data、 vith included labels,each classell asis sulnlnarized、 vith the mean and standard deviation of that class, as M′
the number of members in each class. Typically, since、 ve are、vorking、 vith

unsupervised learning algorithms,class information may llot be avallable.

For the nrst experimental results shown in Table l, we explore applying

ISODS to ISOD「A and K― ⅣFeans by llsing benchmark UCI I鮨 ,and lι πc,/じ石e also show results fl・ om applying Random Centers and K― N71eans++
1121.ヽ ヽe used 80%of the data for training and 20%of the data for testing
Centers. ヽヽ【to evaluate the models. Fo1loM′ ing standard practice,the models urere trained‑95‑

on the training data,then nt to the test data For the IS()DATA parameters,
we used the approach of surnmarizing the class data based on the informationin the trailling data The output labels(cluster assignments)were compared to
the ground truth labels contained in the test data using pair― counting llnettures
TrD evaluate the cluster results,external cluster vandation ineasures are used.
re lltilize pair― coullting meぉ ures、vhich rely on counting matching pairs be―、、

tween two sets of data to determine areement and disagreement 1131.The
measures applied are Rα πdれ dθ ″ (RI― ageement probability),ηαθπ (ARI),Mじ 猛 Jη 七 づ
ηdθ ″ (MI― disagreement probability),αのしSι Ca Rα ηα αSα θTec)))[14,1■ When companngand ttbθ 琵 七 れ dε ″ (HI― (P(α θrec)― P(α づpair― counting

gound truth labels to cluster assignments,RI can serve tt an estimation of theaccuracy ARI is silllilar to the RI,though it is corrected for chance and thus
does not count randornly generated labels 1161.

Table l: UCI benchmark dataset results averaged over 1000 iterations of ISO―DA■ヽ comprfLring three diferent initid cluster center algOrithms(Lづters sho、 vn due to averaglng ARI―

オ
・

)・

Clu針

adiuSted Rand index:RI― Rand indexiン II―R71irkin's indexi HI― Hubert's index

ISODATA
Clusters ARI

Iter.

Init.

RI

MI

HI

I歯
lSOυ S

KM++
Rand

13.46
1543
1190

2599
2.544
241

0.646
0628
0.607

0.826
0.816
0.802

0173
0184
0198

0.653
0631
0.604

Zjη θ
じ
う

ISODS
KM十 十
Rand

9.16

1.836

0。 313

0.618

0.382

0236

8,76
9.26

1.816
1.810

0.307
0.304

0612
0.608

0.388
0.391

0.224
0.217

K― ヽleans
rres

ISODS
KM十 十
Rand

2.29

3

0.623

4149
29402

3
3

0584
0569
14/づ

0.833
0.811
0.797

0.167

0.667

0.189
0.203

0.621
0.593

πθ

ISODS

3.145

3

0.882

0.947

0053

0895

KN三 十

5.388

3

0.839

0.926

0.074

0.851

Rand

+

24.775

3

0.834

0080

0840

0.920

Then,we applied IS()I)夕 促■生using difFerent initial cluster center approaches
to the Salinas― A hyperspectralimage dataset i171 Salinas̲A is a small subsceneof the Salinas imtnge. It has a size of 86 pixels by 83 pixels, each pixel con―taill.s224 bands,and each pixel is assigned to l of 6 classes, disregarding thebackground. IDue to the large numbe■ of dilnensions in this datttet,prinicipal
component analysis(PCA)is used tO extractた atures 118].In thiS experimental
ve use 3 prinicipal components as the input to the lllodel. ミヽ utilize
setup, 、
the same 80/20 test― train split as the pre宙 ous experiment and Z― Score NOrmal̲
TA parameter selection approach isize the data. Additionallン Ъthe same IS()Dノ ヽ

employed.ヽ Ve save the best performing model(baSed on test data performance)
for each initial cluster center approach and it each pixel to the Original datttet

‑96‑

￨

to obtaill the pictures shoM/11in Figure l.

Finally,the external cluster validation

Inettures are shown in Table??.

(a)Figure l: Heatlnap showing cluster assignments of each pixel using ISODATA
with difrerent initial cluster center methods (a)Salinas‐

Random Centers(ARI=0.798);(c)KM+十Centers(ARI=0758)

5

A GrOund Truth;(b)Centers(ARI=0.781);(d)ISODS

Conclusion

This study presents a method for generating initial cluster centers based on a石e tested
splitting approach,Iterat市 e Sel← Organizing Data Split(ISODS).ヽ ヽ

IS()DS on bechlnark datasets asvell as the Salin郡 ―A hyperspectral image、

dataset. Both tests on average shぃvs the performance of ISC)DS using externalκ measure.Ad―
cluster vahdation mealsures,especially on the α力ast̀α Rα ttd jπ αθditonally,ISC)DS may decrease the number ofiterations required for a clustering

algorithm such tt ISODATA or K― NIearls to converge.However,due to the com―
plexity of the ISODS approach collrlpared to other initial centroid algorithms,
specincally calculating the lneans of the clusters,the context should be consid‐
ered when applying this method ヽVhen used in corliunctiOn with ISODATA,ISC)]DS shows an average nurllber of clusters generated closer to the expected

outputAcknowledgements
supportα i by the College of Computing and Software Engi―
This research w
neering at Kennesaw State l」 niversitェ ミヽ also want to thank our Laboratory
for ⅣIachineヽ rislon and Security Research for providing us resources and men―

toringReferences
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duste五 gl■benchmark datasets スppι づ
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1131 Mohammad Rezaei and Ptti nanti set matching measures for externalcluster validity IEEE T7・ aη sacι じοns οれ κπOυ28(8):2173‑2186,2016

̀edθ

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ηd Dα ιαEπ θづηcerづ ng,1141 Lawrence Hubert and Phipps Arabie Comparing partitions.」 ο包鶴ὰ9ノαα
SSttCα ιづοη,2(1):193218,1985.
11司

Marina MeiL.Comparing clusterings by the trariation of information.
Lcarη を見9Tん θοη αηα」
(erη θ
ιl√αcん づηes Lθ ειz θNoι esJn Compし ι
92cθ
er Scづ θ
page 173‑187,2003.

1lq Wmhm M.Rand.Objecti(crite五 a br the ettluation of clustering meth‐ods ノb?ι rη α:げ ιんθスπθ
れCα πStα ι
づ
stづ
:ス θ
sο
α
ι
づ
θ
η,66(386):846‑850,
cづ

1971.

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tral iγ nage classincati。 11. Sztt Lα ηdづ γ
ザ‑98‑Syst,62,012002.

,

￨̲ISBN 4‑901329‑11‑8

Procecdings ofthe Tcnth lntemationalく)2021 1ntcmational lnfolnation lnstituteConfcrcncc on lnfom■ ation(InfOrlnation'2021)

SLN‐ D2CNN Modelfor Lymph Node Metastasis Diagnosis
Ruigang Ge',Guoyue Chen*す ,Kazuki Sartlta***,Yま i Terata****
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Abstract
Sentinel lymph nodc biopsy(SLNB)is a COmmOn tool to idcndtt breast cancer metasttis.Presently,
Sllヽ B dctcction of cal,ccr migration mainly rclics on nakcd eyc Obscwation bascd on pathologists'

cxpcrience.It is timc consuming and fatiguing to look at all thc tissuc samplcs undcr a inicroscope andto forln a diagnosis bascd on cell morphology,、 vhich may resultin missed diagnoscs.This paper ailns
to improve this situation using cOnvolu● onai ncural network(CNN)modciS.This rcse=ch adopts theislon of 2 currcnt mainstrcam C■ lN modcls(VGG16 and DensNet121)as thC baselinc of thc modcl,
vith a custont convolutiond
and the back― end is equippcd 、ねcilitatcd nct、 vork icaming and theaccelcrated training using migration leaming to develop a proposcd modcl おr the purposc of multi‐
modcl intcgration.An cxpcriFnCnt Of the model against its baselinc and each gcncric cvaluation indcx

of each modcl that makcs up the baseline was completed with the quali7 canCCr pathology dattet
providcd by thc Kaggle event.The experimcntal rcsults show that thc AUC accuracy valuc of the
proposal network modclis as high as O.986,which is more accuratc for discriminating with imagcs.

Keywords:Convolutionai neural nct、 vork,Whole stide imaging,Proposcd inodcl,Transfcr lcarning,
Bascline,Fcaturc cxtraction.

1.Introductioll
The prevalence of cancer in womcn has sparked strong social concern. According to the
Global Burden of Disease study[1],the incidence of breast cancer tops thc Hst,foHowed bylung cancer,ccrvical canccr,and endometrial canccr.It is、 vell kno、 vn that rnetastasis and therecurrence of brcast cancer are important factors causing death of patients. In clinicalmedicine,SLNB techniquc based on sentinel lymph node(SL19 tisSue section is considered
as tllc"gold standard‖ for brcast cancer metastasis diagnosis.Usillg Hematoxylin Eosin(H&E)staining in combination with the all‐ digital sectioning Whole slide imaging(WSI)[2]‑99‑technique to accomplish computer‐ aided pathology diagnosis. In particular,the usc of CNN
models, which is good at ilnage classi「lcation and recognition,has important scientiic andapplication value for the discrimination、
vhcthcr a tissuc is infectcd with breast cancer

metastasis in WSI pathology imagcs of SLNB.At prcsent,most studics arc gcncraHy basedon single ChlN or cu■ om sha1low ChlN models,with problems such as less reliability,
d市 ese feature extraction[3,5],low diSCriminative accuracy and poor generalization.
Therefore, this research proposes a modcl that combincs mainstrealn high‐quaHty 2 CNN

models(Vgg16 and Desnet121)as the bascline.Theヽ vo models are ftlscd and improved toform a combined model with multi‐ scale spatial featttre extraction and extending iature span■om natural illlages to medical images,i.e.,the SLN― D2ChlN model.Wc further improved
thc accuracy of breast canccr rnetastasis discHmination、vith this modcl.As for model training

tcchniquc,wc use Fnigration icaming as the fast training in the proposcd model baseline toobtain the highest accuracy.

2. Composition ofthe lnodel and experilnent preparation
Due to the varicサand mOrphology of breast cancers,different subclasses of breast cancers

cause problems such as approximation of texture features and ccH nuclcus spatial structurc

fcttures.Therefore,we adoptヽ vo mainstrcaln deep CNN models that have not only achieved
excellent results in the Large Scale Visual Recognition Challenge(lLSVRC)but alSO are
widely used and effective in research in various flelds today,draWing on existing competition
modcis for largc‐ scalc natural imagc lmagcNet training scts and rclatcd rcscarch in theirields.CNN models[4,5], 1.e., VGG 16 witll multiple 3x3 convolutional stacks andDcnsnet121 、vith dcnsc type connections,arc uscd as the bascline of our proposcd rnodcl,andthc higher‐ order prelinlinary fcatllrcs extracted from cach model of thc baseline are obtaincd

by a transfer icaming method.FinaHy,the features obtained by thc convolutional processing
learning are output through the Global Average Pooling(GAP)layer and the fL11ly connected(FC)layer with one ncural unit of Sigmoid to disc五 minate thc SLN― WSI ptthology imagcs

圏圏鰯
ttpr■
―・

Fttuに l Stntctwc ofぬ c pFOp● sed SL■ l,D2CNN

Figtlぶ ,2

‑100‑

・
露
薄
構哺澤種

:1貫

C● Ist、 ctlon bc● Vccn rc勁 鑢■2 co●v‐ layer

by the proposed model,and we name this proposed modcl as SLN― D2CNN(郎 shoWn in
Figure l).Where baselinc subsequently customizes the composition inside the convolutional

processing (shown in Figure 2), thiS COnlbined composition is based on the best method
derived ionl rensentv2 in lmagcNct classiflcation to obtain the bcst accuracy.

Thc experimental benchmark d江 郷et in this manuscript is derivcd from Kaggleゝdttaset[7],whiCh iS a collection of 400 H&E―

PCamstained high‐ resolution images sampled by a

40x obied市 e,decomposed into 327,680 color images of 96× 96 pixels in size with duplictte
items removcd,and afflliated with an improved version ofa subsct ofthe Camelyon16 dataset[8].In thC PCam dataset,cach image has a binaヮ

label,i.e.,images containing mettstatic

cancer ce‖ s are labeled as''1't no111lal tissuc irnages are labeled as0'',as shown in Figure3.

■ erefore,we convert the clinical dctection of SLN metastatic cancer cens into a positivc
l'1"and negativc"0"image binary classincation task.In order to reduce lnodel overntting andenhancc thc gcncralizability ofthe model,the method in Table l is used in this research.
Tablc l Data cnhanccmcnt and prc‐ proccssing
Method details

Metllods Nalne

for each batch size ofimages,we used Z― score
IInage nolHialization processing

nollllalization

donc andimage scaled tobeヽ veen O and l.

[inage flipping enhancement
processing algorithm

for each image,we■ ip it randomly from two
orthogonal
directions(horiZOntalandvei■cal),thttS there are four transfoms foreach ilnage.

Image randonl rotation processing

for each image we can rotate 90° ,0° or‐ 90°
after which、 〃e randomly rotate‐ 15° to 15°,.

In this study,85%of the PCam is randolnly selected as the training sct and thc rcmJning
150/O as cvaluation data for the perfollllancc ofthe model.In addition,the area undcr the R()C

curvc(AUC)and Validation set of loss are uscd tt evaltttion metrics in this experiment andcombincd with the evaluation data.To vcritt the rcliability of our model,wc conducted
controlled cxperiments ofthe proposal model SLN‐

D2CNN againstits baseline mode1 2CNN

and the single ChJN modelthat composed each model ofthe baseline.

■ ■、納

1綺 ↓議

F:=、 Fe'(Tht塚 肪

u■・ P・ I PatFt ttllo、 、,ti、 ゛喜鰤ぃPle dユ 鑢 ｀.ltll.'0‐ oギ ‐1・ ltttis in tt,●sIま ,、 、壼

=●1■ ゝ
凛ge ll゛ 菫轟、e,押PC tt clatas゛ t.鐵慮 轟 ●1● 、

I:̀atlo3 r=ヽ ul:、 of毯 、s ai難 it;stlipt)‑101‑

3.Experilnental results and conclusions
FroFn Figure 4, it can be sccn that the maximum detellllination acctlracy of each ChlN is

Vgg16:0.943,1)ensNet121: 0.963, baseline modc1 2CNN:0.970,and the proposal inodel
SLN― D2ChlN has thc highest valuc ofO.986.In ttldition,the validation rcsults from Figurc 5
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●ユLom cllrveぷ ●.nml申 蜘sshow that the SLN― D2CNN in the flrst 15Epoch in the validation set Loss also shows
signiicantly lower rcsults than each ChlN learned at the salne time as、 vell as the baseline
2CrlN. In this research, we proposc the breast cancer migration discrilnination proposedmodel SLN― D2ChlN by ision of2 valid pre― trained deep CNNs as a baselinc and subsequentleaming by cuStOm segmental convolution.With the PCam dataset we con■ 111l that SLN‐
D2CNN outperfoI:1ls the indi宙 dual ChlNs as well as the bぉ eline mode1 2CNN in telllls of

AUC accuracy.
Referellces[1]HCCr,ct al."Global burdcn and trcnds in premenopausal and postmcnopausal brcast
cancer:a population‐ based study."7乃 ιZα ″εθ′C)′θbα ′Heαノ
r/7&∂ (2020),e1027‐ e1037.

[2]Barker,ct al.Automatcd classiflcation ofbrain tumorけ
images using l∝ al rcpresentative tiles.擁 ″θα′ルη
αg̀/pe in whole‐ slidc digital pathololッ

α伊 お,30(2016),60‑71.

[3]MoJagh,MChdi llabibzadeh,et al.Brettt cancer histopathological image classincation.A
deep leaning approach.B,θ Jレ Jν :242818.(2018).

[4]Simonyan,Karen,and Andrew Zissellllan.Vcりscalc image recognition.α「mν メFtρ ″′″′αんdeep convolutional networks for large―

f1409.1556,(2014).

'ソ[5]Huang G,Liu Z,et al.Densely coFlneCted convolutional networks.Proceedings of′力θLEEEθθヾer̀ θ ″εθ″ρ θ′νお′
″″″
θεo解′
′
0″ 6″ ′′α″θ
′0刀 ,(2017),4700‑4708.
̀θ"′[6]He,K5ming,ct al.Identhy Mappings in Deep Residual Networks.E‖ rTιθκCθttP″ ′θ″/iSfθ ″だ
シri4gθ ろ Chα ,(2016),630‐ 645.
[7]The DataSet https:〃 gtthub.com/bttvceling/pcal■

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3o崚″ηεθWelcollle to INFORⅣ IAT10N'2021 0nline Conference

BACKGROUND AND AIⅣ IS
The most distinctive fcaturc in thc devclopment of modem scicnces and technologies is thatvarious scicnces,which were classified so far according to their rescarch ottectS andvith each other gradually. Thereforc, many new
mcthodologies, penetrate and combine 、disciplincs and technologies、 vere bom from boundary areas of thosc existing sciences.Today,from classical scicnces to modern technologies, almost all scienccs and tcchnologies are
dcpended on each other so closcly that thcy cannot exist and grov7 independently and have togrow in harmony、 vith each other.Thcre is an abstract,gcneral and cross― cutting concept thatconcems all scientific lncthodologics and sciences,it is"Inforlnationii.

The lntcrnational Confcrence on lnformation is an interdisciplinary intemational conference
scries.It providcs a foruln for all scientists and technicians throughout thc world to exchangc
scientific information such as original ideas,rescどch inethods and rcscarch rcsults related to all

scientific fields.

Thc first conferencc lnformation'2000 (Fukuoka, Japan), the second confcrence

lnforlnationi2002(Bctting,China),the third confercncc lnforΠ 正■lon12004(TokyO,Japan),thC
fourth conferencc lnformationi2006 (Cork, Ireland), thC fifth confercnce lnformation'2009(Kyoto,Japan),thc SiXth conference lnfollllation'2013(TokyO,Japan),thC Seventh conference
lnforlnation12015(Taipei),the cighth confcrencc lnforlllation'2017(TokyO,Japan)and thC ninth
confercncc lnformation'2018(TokyO,Japan)haS been held grandly separately.
The Tcnth ttnlinc confercnce,Informationi2021,、 vill bc hcld in Hosei University,Tokyo,
Japan on ⅣIarch 6‑7,2021.Inforlnationi2021 will include kcynote addresses,invitcd spcechcs,
special workshops,contributed prescntations(Lectures or Posters).ThC COnference procceding

will bc published by lntemational lnforlnation lnstitutc (ISBN 4‑901329)and aVailablc todelcgatcs at the time of registration.And the papers prcsentcd in the confcrencc will be selected
as rcgul〔 r papcrs for publication in INFORⅣ IATION:An lntemational lntcrdisciplinary Journal(ISSN 1343‑4500)or Otherjournals.

Keynofe Speakers
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A Rcl■ lark on Wcightcd Estimatcs for 1/1ultilincar Fouricr Multiplicrs with Mixcd Norm

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A Ncw 2 5D Schcma ofthc Rcgular and Sclni― rcgular Polyhcdra and Tilings:Classcs II and IVRο b̀″ ′C Mc7rrα 77r

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