Inter-subjective relationship of higher-order among spatial-temporal wavy environmental factors a methodological trial based on a standpoint of "Relationism-First" Текст научной статьи по специальности «Математика»

Electronic Journal «Technical Acoustics» http://www.ejta.org 2006, 6

Mitsuo Ohta1, Yoshifumi Fujita2

1 Hiroshima University, 1-7-10 Matoba-Chou, Minami-Ku, Hiroshima,732-0823 Japan, email: ryxyj592@ybb.ne.jp

2Onomichi University,1600 Hisayamada-Chou, Onomichi, 722-8506 Japan, e-mail: fujita@onomichi-u.ac.jp

Inter-subjective relationship of higher-order among spatial-temporal wavy environmental factors -a methodological trial based on a standpoint of "Relationism-First"

Received 13.11.2005, published 02.04.2006

In this paper, first, partly is noted the suggestions by well-known philosophical emphasis of Herakleitos, Hegel etc. (i.e., several of famous other philosophers) based on their original standpoint that the truth exists not in fragmentarily individual things but only in their relational fact or process (i.e., event) itself through some concrete self-exercise of existing contradiction. That is, it is stated that a central core and/or primary existence is not in only mutual intermediation of time series type among past, present and future, but also mutual intermediation and/or relationship among different environmental factors in especially dynamic styles (more explicitly, some temporal) harmony and/or objectively latent (severe or hierarchical) contradiction. It seems true even if apparently it has no connection according to only our individual professional sense. After all, such a viewpoint of “Relationism(us)-First” seems to be exceedingly important to all things including our human being evolving after the beginning of only material nature with Big Bang. Two kinds of actual example of the above (hierarchical type) mutual correlation in the time series and mutual correlation distributed in the space among different environmental factors are considered. More concretely, the proposed method is applied especially to the acoustic environment in the actual indoor living surroundings. Then, the mutual intermediation among sound and light waves (served for utility) and leaked EM waves (served for risk) around personal computer under playing a game is investigated through some principle experiment. As the result, some effectiveness of the proposed methodology is experimentally confirmed by taking the mutual intermediation among only physical environmental factors as an example.

1. INTRODUCTION

Recently, due to the spread of the modern technology, (especially with wide use of IT instruments) the closed interior space in the room and car, as if smog, have been filled with miscellaneous waves such as electro-magnetic (including light) [1-6], sound waves [7-10] and so on. This problem seems to be related even to our environment (or information) ethics [11, 12], too. This is gradually facing to the problem in every relationship of the world

composed of our life and cultural environment, which have some inter-independence property with our will (see Appendix I).

In this study, we positively take the standing point that the primary property -“Relationism-First” on everything should be found in principle first (see Appendix II) and after then, based on it, every type of inter-independence properties should be individually studied as the secondary property. That is, every linear and non-linear type multi-correlation analyses should be considered at the first stage of a study (i.e., for a search of truth). Only after then, by decomposing the compound effect into each factor according to our study purpose, the measurement and evaluation only for our specific interesting factor should be considered (i.e., a search of effectiveness) individually.

More concretely, for the compound and accumulation effects, at once, as a new principle trial we have proposed some evaluation method of wavy environment in the actual indoor living style, especially by limiting our study to the correlation problem between past and present states (in time region) or only two different kinds of factors (in space region) on environmental wave motion. Furthermore, by paying our attention to only natural scientific environmental factors except the cultural environmental factors from which we cannot remove some active-subjectivity even in each element, and based on the mutual intermediation among only natural scientific environmental factors as the first step of study, we have done theoretically (see Appendix III) and experimentally on trial some principle measurements and evaluations on acoustics and/or electromagnetic (abbr. EM) environment in the electrified modern living environment of closed room type.

2. MUTUAL CORRELATION IN TIME REGION (EX. SOUND FIELD)

2.1. General theory: time series regression model of orthonormal expansion type representation

Consider a stochastic process x(t). Let its instantaneous values at a discrete time k be xk. All sort of linear and nonlinear correlation information between xk and p-variable past value xk-1 (A(xk-1,xk-2,...,xk.p)) are contained in the conditional probability density function (abbr.

pdf) P(xk | xk-1) of xk for given xk-1. Especially, when xk is to be predicted from xk-1, the

expectation of xk for given xk-1 and its prediction error s k can be directly expressed by its definition as

(i.e., the usual regression function).

If all sort of relation between xk and xk-1 can completely well be presented by Eq. (1), sk becomes an accidental error and can be represented by a white noise model with mean 0. For

this purpose, the conditional pdf P(xk|xk-1) of Eq. (1) must be constructed as precisely as

possible, reflecting the effective substantial information such as non-Gaussian and nonlinear properties originally contained in the stochastic process.

First, the joint pdf P(xk,xk-1) for the time series xk and xk-1 is expanded as follows. The standard distribution representations P0(xk) and P0(xk-1) are considered that they can approximate the essential configurations of the whole fluctuations of xk and xk-1, respectively. Using those distributions, the joint pdf is expanded in the orthonormal form only as its mathematical frame as follows:

(1), (2)

n/ \ tW \ tW ^ A (1) / \ (2)/ \

(3)

œ œ

where nA(, n2,---, np )■ ZâZ Z - Z .

n=0 n =0 «2 =0 np =0

Now, two function wm(1)(xk) and Wn(2)(xk-1) are orthonormal polynomials satisfying the following orthonormality conditions:

j W{m1 (Xk ) Y[n (Xk ) P0 (Xk ) dXk = Smn , (4)

]J ••• jwl2)(xk-1 )wn2)(x k-1 )P0 (x k-1 )dxk-1 =n^m,^ (m â(mi’ mp ))• (5)

i=1

All sort of linear and nonlinear correlation information concerned with the regression between xk and xk-1 are reflected hierarchically on each expansion coefficients Amn.

Forming the marginal pdf of Eq. (3), the pdf P(xk-1) for xk-1 is given easily as

œ

P (xk-1 ) = j P (xk 1 xk-1 /dxk = P0 (xk-1 ) Z ^0nW!,2) (xk-1 ) • (6)

n=0

Using the well-known Bayes’ theorem [13] (see Appendix III), the conditional pdf P(xk|xk-1), which is essential in extracting various types of linear and nonlinear correlation information, is given as follows in the expanded form using Eq. (3) and (6):

P ( xk |xk-1 ) = P (xk, xk-1 )/P ( xk-1 )

œ œ

= p,(x)Z ZA.ym'(xiM2)(xk-i)/Z-in^» (x-i)■ (7)

m=0 n=0 / n=0

Then, the desired regression relation € is given by Eq.(1) and its coefficient cm is constant

in the expansion expression using the j-th orthogonal polynomial Wn(1)(xk) of xk (satisfying the orthonormal condition (4)), as follows:

1 œ j œ œ

4 =Z Z Amn CmW() (xk-1 ) / Z A0nW!,2) (x k-1 ) , xk = Z CjWiJ) (xk ) • (8),(9)

m=0 n=0 / n=0 j=0

By Eqs. (2) and (8), the new autoregression model for the stochastic process xk can be easily given as follows:

xk =

Z Z AmnCrn^n2’ (Xk-1 )/Z (k-1 )

+sk ■ Q0)

Here, sk is the white noise diagnosis input to the forementioned autoregression model (white noise with mean 0). Viewed from the standpoint of applying the constructed model, it is easy to show that it is the same as the prediction error defined by Eq. (2). The reasoning is similar to the analysis of the ordinary well-known AR model.

2.2. Development of autoregression model using one-variate Hermite expansion type distribution

Gaussian distribution, which is one of the most typically standard type probability distributions, is used as the reference distribution P0(xk) and P0(xk-1) (employed as only the 1st expansion term). Then,

P0 (xk ) = N(xk; ), P0 (xk-1) = n N(xk-i; ), (11), (12)

i=1

where N (x; ju,&2 ) exp {-(x-^)2/2ct2 |^V2nr (13)

with xk-i), A((xk-i -l)) stationarity (i=0,1,2,...,p).

œ

œ

œ

The orthonormal polynomials satisfying Eqs. (4) and (5) are the well-known Hermite Polynomials:

The pdf of xk and xk-1 are represented by statistical Hermite expansions, which can handle any non-Gaussian distribution [12]. Eq. (9) is written as

1 1

xk = Z Ci~T=Hj ( - L)/CT) ( =M C1 = (16)

j=0 yjj '

By substituting Eqs. (11) to (16) into Eq. (10), the objective time series regression model is developed as follows:

Next, consider the relation of the foregoing expression to the well-known AR model. Consider in particular, the case of p=1 and assume that xk follows the Gaussian stochastic process. Then, Eq. (18) is written as

Letting ^=0 in the foregoing expression, the result is the same as the well-known one-variate AR model for p=1.

In the ordinary multidimensional AR model, the linear correlation information among variables xk-i (i=1,2,...,p) are reflected on the parameters ai. To establish a non-Gaussian nonlinear time series regression model generalizing the forementioned model including the model in the first expansion term, the first term of P0(xk-I) of the expansion should be analyzed at the start for the multidimensional correlation information of Gaussian distribution, reflecting the linear correlation information among multivariables. The derivation analysis is shown in subsection 2.3.

In this case, the product of independent Gaussian distribution is used as P0(xk-1) as shown in Eq. (12) and the linear correlation information among the variables is not reflected at all in

the first term of the expansion. Consequently, when xk-1 is of multidimension (p^ 2), the model cannot be generalized by an expansion with finite number of expansion terms including the well-known AR model in the first expansion term. In this sense, the match to the AR model is shown only for the one-variable case (p=1), where the correlation information among variables need not be considered at all.

with

Amn =(^_Hm ((Xk ]n [H (k-i

[f • " j [ Hm ((xk - M)/]n [ H ((Xk-i - ]

i=1

(18)

(19)

Considering A0o=1, Eq. (17) is modified as follows:

(20)

2.3. Development of autoregression model using multivariate Hermite expansion type distribution [10]

The purpose of the development is that as much statistical information as possible should be reflected on the reference pdf P0(xk-i), which is placed at the first term of the expansion in the series expansion distribution representation to aim a rapid convergency of expansion too. The following (correlative) multidimensional Gaussian distribution is used instead of Eq. (12):

Po (x k-i) = N (x k-i; uR 12,,i/2exp 1 -1 (x k-i - u ) R- (x k-i - u) i

with

vA(u, n, —, u)

R A

((-1 - V)(xk-i - v)

r0 r1 r2 • •• rp-1

r1 r0 r1 • •• rp-2

^ ••• r1 ro • •• rp-3

rp-1 rp-2 rp-3 • •• ro

>

(21)

J

ri&((k-V)(xk-i-^)) ( =^2).

Then, the pdf of xk-i is given by the well-known distribution representation by the multidimensional Hermite expansion

p(xk_,) = N(x,-,;u,R)^,, H^-■ (R(x.-. -U))- (22)

An ‘n I• • • n I

n=0 l1 • tl2 • p •

where R is the upper triangular matrix satisfying the following relation (this decomposition is possible since R is a positive-definite matrix):

R = RRr . (23)

Thus, Hnn^_n (-i (xk-i - u)) and b^ ^ are the multidimensional Hermite polynomial and quasi-moment function [i4], respectively, which are defined by

H^.n,, (R-'(x„- u))H(-i)n'*'*-*n'

•expJ-2(x,-, -v)TR-1(x-T exp{--2(x,-, -Vf R ‘(x,-, -v)¡,

k-1 k-2 k-p

(24)

where

Kn2-np AÍÍ •" Í Gnini-np ( (k-1 - V)) (xk-1 ) dxk-1

G,v,r..n, (R-1 ((--1 - v))) (R'Z)

g;, .... ( z )A(-r n2 *■

A

Z^R 1(xk-1 -u)

1 T ^n, + n, +-----+ n„

-ZT RZ d 12 p

(25)

Z dz 2n2 • ••dzpp

exp {-ZTRZ/2} .

J

Then, the time-series regression model for the scalar stochastic variable xk in Eq. (10) is developed as follows:

(27)

p

Z 4n H„,,..n, (R-1 (x k- - u))n ^

xk=v+a--------------------:---------------7--------+s (26)

Z A0nHn^.n, (R-1 (xk-i - u))niA/ni

n=0 /=1

with

A~ = (" H" ( k^M n1ln,J-" n,! G'"n’' n' ( 1 ( ‘ " U)

= ff^/"H"(,,r, G'«- n, (( (k -u))p(xk,xk-iH--i.

Especially when xk is the Gaussian process, the expansion coefficients in Eq. (26) are given as follows:

I 1 (if ( = n2 = ••• = n = 0)

4' = (0 (otherwise) (28)

and

I rja (if ( = 1 and n = 0 (i ^ j) for any i)

Ain = {0 ' (herl) • (29)

By definition, the lower-order multidimensional Hermite polynomials are given as follows:

H00-0 (-1 (k-1 - u)) = 1, (30)

H1 (-1 (xk-1 - u)) A [Hi0-0 (-1 (xk-1 - u) H01-0 (i^-1 (xk-1 - u)), ■■", H00-1 (-1 (xk-1 - u))]

= R-1 (k-i- u). (31)

Substituting Eqs. (28) to (31) into Eq. (26), we directly have

p

xk - V = [ri,r2^--,r,]R-1 (xk-i -u) + s, = -Zai (xk-i - v) + ■s,. (32)

i=1

Letting v=0, the foregoing expression coincides with the AR model. In other words, when the stochastic process is Gaussian, Eqs. (26) and (27) agree with the well-known AR model. In other words, the autoregression model proposed in this paper includes the well-known multi-variates AR model as a special case. Theoretically, this suggests partly the validity of the proposed model.

2.4. Another autoregression model based on marginal distribution

2.4.1. General theory

As the reference distribution P0(xk) and P0(xk-i) in subsection 2.1, the marginal distribution for xk and xk-i are employed intentionally in the following. In other words, based on the product of P0(xk) and P0(xk-i), the joint pdf P(xk,xk-i) can be represented in expanded form as follows:

P (k , xk-l ) = P (k )P (k-l )Z Z Bmn^mn>(Xk )^,i2)(xk-l ) (33)

m=0 n=0

with

Bmn ={d{m1(xk )^n,2)(xk-i ) > where ém(1)(xk) and ^n(2)(xk.1) are orthonogonal polynomials satisfying the following relations:

J (xk )9[n] (xk )p (xk )dxk = Smn, (34)

JJ-J^t k-1 )l2)(Xk-l )P (Xk-1 )dXk-l =n Smini • (35)

i=1

Then, the conditional pdf P(xk |xk-1 ) is given by

œ œ

p (xk ixk-i )=p (xk )z z (xk )<5>1(2) (x k-i )• (36)

m=0 n=0

Using the foregoing expression and by the same derivation as in subsection 2.2, the regressive relation for xk and xk-1 is given as follows:

1 œ

xk = Z ZBmndW(!,(x,.-i)• (37)

m=0 n=0

where dm is the expansion coefficient in the expansion representation:

*m

1

xk = Z j (xk), (38)

j=0

which corresponds to Eq. (9). Thus, the following another autoregression model can be derived from Eqs. (2) and (37):

1 w

Xk = Z Z Bmndm^n,2)(xk-1 ) + ^k , (39)

m=0 n=0

where sk is the white noise with mean 0.

2.4.2. Development of autoregression model (development by statistical Hermite expansion distribution representation)

The pdf for Xk and xk-1 are represented as follows, in the general representation form which can handle any type of non-Gaussian distribution:

w __

P(xk) = N(xk;^o2)ZamlHm ( -m)/°), ai1^Hm ((xk -, (40)

m=0

and

p w p

P (xk-i)=n N (xk-i; ^ °2 )Z °i2) n H ((xk -- (41)

i=1 n=0 i=1

with

^(flHni ((xkx - . (42)

As to the linearly independent series of polynomials to compose the orthonormal polynomials satisfying Eqs. (34) and (35), the following Hermite polynomials are employed, since Gaussian distribution is placed in the first term of expansion representations (40) and (42) (1A(, A,-, lr)):

m

$ (xk ) = Z ^ Hj ( - »)/^)/^T! , (43)

j=0

#n2) (xk-1 ) = Z ^n Hk - V)/°)/) • (44)

1=0 i=1

The coefficients ^mj(1) and Àn1(2) are calculated beforehand by a well-known Schmidt’s orthogonalization.

Then, Eq. (38) is given by

Xk = Z Z dr4 Hi (k - ^)/^)// ’ (0 = ^4 - ^o/A00^11 > d1 = ^411 ) •

(45)

j =0 i=0

The time series regression model (39) for xk can be explicitly developed as follows:

1 W n P

xk = Z Z Z Bmndm4il2)n H ((xk-i -V)/v)//t +Sk

(46)

m=0 n=0 l=0 i=1

i=1

with

(47)

2.5. Application to sound environmental field [8-10]

To examine in principle the practical usefulness of the time series regression model proposed in this paper, the method is applied to the sound environment data, which is an example of the non-Gaussian stochastic process. The content of the experiment is as follows. The following data are used.

1) Sound data recorded in a sound experiment laborlatory (called data 1),

2) Sound data recorded from home-use washer (called data 2).

Using the autoregression model of Eqs. (17) and (18) as well as Eqs. (26) and (27), the sequential prediction of the time-series data is attempted. The real situation of our experiment and related evaluation of prediction error are given in more detail in Appendix IV.

Figure 1 shows an example of sequential prediction of the time series. The results are compared to those of the well-known AR model; M is the number of terms in the expansion. It can be seen from the result of experiment that a better prediction result is obtained by the proposed model than the traditional AR model. It should be noted that the prediction error in the proposed method is completely equal to that of the traditional AR model when M=2, which obviously indicates that the prediction error decreases gradually by considering a larger number of expansion coefficients.

90.0

• Experimentally observed values Theoretically predicted values:

Figure 1.

AR Model

Proposed regressive model: 1st approximation 3 rd approximation

A comparison between the theoretically predicted values and the experimentally observed values for the actual time series

so.o

70.0

0

10

20

30

t

2.6. Probability distribution prediction once after correlation analysis based on idea of “Relationism-First”

It can be obviously seen from Figure 2 that data 2 are strongly non-Gaussian, and a considerable error is produced if only the Gaussian distribution of the first expansion term is used. That is, it seems to be necessary to apply the proposed method, which considers the higher-order statistical information and the nonlinear correlation information. Accordingly, some effectiveness of the background idea: “Relationism-First” (to Individualism-2nd) has been partly proved through this principle experiment in time region analysis.

Figure 2.

Cumulative distribution function of data 2

3. MUTUAL CORRELATION IN SPACE REGION (EX. LIGHT, SOUND AND EM FIELDS)

From the methodological viewpoint, it is desirable that our analytical method can be easily extended to the problems with arbitrary number of environmental indexes and environmental factors not only in the fields of the same kind but also in the fields of the different kind including the humanities. To cope with actual problems, this must be necessary in principle. However, in this paper, as a trial at an early stage of our study, the proposed method is limited to the analysis of the correlation between only two environmental physic factors.

3.1. General theory: spatial regression model of orthonormally expanded regression type

Let us consider the electrified modern living environment of closed room type especially under the exposure of electromagnetic (abbr. EM), sound and light waves leaked from VDT under playing the game on a personal computer [11, 12] (notice that light wave is discriminated from EM wave only technically in the international law of EMC, differing from a pure scientific field).

For the evaluation of such an environment under exposure of EM, sound and light fields, it is necessary to know the mutual correlation information between environmental factors as minutely as hierarchically as possible based on the idea of “Relationism-First”. Since originally these environmental factors fluctuate in a non-Gaussian distribution form, it is difficult to find this correlation minutely only by employing the usual standard type correlation analysis based on the idea of “Artificial Operation Facility First” in contrast to the above “Relationism-First”, in terms of only linear type regression function. So, in this paper, let us introduce a general correlation analysis hierarchically including all sort of correlation) based on the idea of “Relationism-First”, by limiting in trial the problem between two special random variables. In general, the correlation between two random variables x and y can be

determined completely in terms of the conditional pdf, P(y|x), of y conditioned by x or P (x\y), of x conditioned by y:

P (y|x) = P (x, y)P (x), P (x|y) = P (x, y)/P (y), (48)

where P(xy) and P(x) or P(y) denote the joint pdf of x and y, and the pdf of x or y, respectively. In order to get the hierarchical expansion type general expression for this conditional pdf, let us expand it into orthonormal series expansion form in the same way as in subsection 2.1:

Py) = P0 (x)P0 (y)Z Z Ap (xp2) (y) Amn = (pp (x)pp) (y), (49), (50)

m=0 n=0

where <> denotes the expectation operation with respect to x and y, and pm(1)(x) and pn(2)(y) denote two orthonormal functions P0(x) and P0(y), respectively, satisfying the orthonormal relationship:

(x yp[n (x)P0 (x) = 5mn , i_o^!m2) (y )PP (y )P0 (y )& = 5mn . (51), (52)

Here, Smn denotes Kronecker’s delta. When x and y fluctuate dominantly in a Gaussian distribution form, pm(1)(x) and pn(2)(y) are given as follows:

p (x) = Hm ((x - M)/ox)/)!, Pp) (y) = Hn ((y -vy )/&y)/yfn\, (53), (54)

where Hm() denotes the m-th order Hermite polynomial, and jux, /uy are means of x and y, respectively. Also, ax and ay are standard deviations of x and y, respectively. From Eq. (49),

the marginal pdf P(x) of x is expressed as follows:

P (x) = Z Am0P!i!)(x). (55)

m=0

Upon substituting Eqs. (49) and (55) into Eq. (48), we can obtain

o o / o

P (y ( x)= P0 (y )Z Z AmnPm(x p2)(y)/Z Am0P(n!(x). (56)

m=0 n=0 / m-0

This determines all sort of correlation of y to x. To determine the mutual correlation between x and y, moreover, the conditional pdf P (x|y) is needed. In the similar way, the

conditional pdf P (x|y) of x conditioned by y can be obtained such as

X X

P(x|y) = P0(x)Z ZAmP’Mpf’W/ZAP-'W. (57)

m-0 n=0 / n=0

3.2. Various type regression function

Now, let us derive concretely various type of regression function. The average tendency in some sense between x and y can be grasped by these. In order to derive the regression functionyk(k=1,2,...) with respect to x in advance, let us expandyk such as

/ = £cj!>(y) . (58)

i=0

To obtain the regression function, we can calculate the conditional expectation^yk|x^ . Upon employing Eqs. (51), (52) and (58), we obtain the objective expression:

x k / x

(y^) = Z Z CknAnPm Z Am0Pm:) . (59)

m=0 n=0 / m=0

X

In the similar way, upon expanding x such as

l

xl =Т j (x )

j=0

we can obtain the inverse regression function:

X l ! X

{xl |y) = S ТDmA^ (У) Т ^ (y).

(б0)

(б1)

Especially, when two Gaussian distribution forms are chosen as P0(x) and P0(y) as stated in subsection 2.2, Eqs. (59) and (61) reduce to the following concrete forms, respectively:

(б2)

X /X

(y I x) = My + \ СУ Т [ Am1Hm ((x - Mx )lCx )l)! ] Т [ Am0Hm ((x - Mx )/Cx )

L m=0 / m=0 і

and

I x _—і / X |— _—і I

<x|y> = Mx + L С Т [AinHn ((у - My ))y )/)] Т [AonHn ((y - My )СУ )/)J к (б3)

3.3. Objective probability prediction once after correlation analysis based on idea of “Relationism-First”

Once after employing mutual correlation information in the above, the whole probability distribution of only one variable can be obtain in an individual form. First, let us estimate the probability distribution of y from the fluctuation of x. Upon integrating Eq. (56) with respect to x, it can be expressed as follows:

P. (y )=Po (у )Т EM2)(y )

i=0

with

/ X ! X \

E, = ( Т AmrV{m (x) /Т Am0^mi) (x) ) ,

(б4)

(б5)

\m=0 / m=0 / x

where Ps(y) denotes the estimated pdf of y and < >x denotes an expectation operation with respect to x. In the similar way, the estimated pdf Ps(x) can be obtained as follows:

P.(x) = Po(x)Т F/y1(x)

j=0

with

IX j X \

F = ТAjn^n)(у)/ТAonV{n](y) ,

(бб)

(б?)

where < >y denotes an expectation operation with respect to y. When two Gaussian distribution forms are especially chosen as P0(x) and P0(y), Eqs. (64) and (66) reduce to the following forms, respectively:

Ps (y) = [y((Vy )]exp{-(y-My)7^} j1 + ZEjHj ((-My)/°y)/)| (68)

with

X / X

Т AmrHm (У-My )!Су )/Ä Т Am 0H m (у - My / Cy J/Ä

(б9)

and

(70)

with

F = AjnHn (x-UX )/°x )// A0nHn (x-UX )/°x )//

(71)

3.4. Application to electromagnetic, sound and light waves leaked from VDT

We have applied the proposed method to the environment under the exposure of electromagnetic, sound and light waves leaked from VDT under playing the game on a personal computer (sometimes by expecting faintly that this method may be some future help of the explanation of VDT syndrome). We have experimented in a usual laboratory. We have measured either when only one personal computer has been operated or when two personal computers have been operated. In each case, the rms-value of electric field, the sound pressure level and illuminance of light have been sampled at every 10 second, and 500 sets of data have been obtained. We have employed HI-3603 VDT/VLF Radiation Survey Meter (Holaday Industries, Inc.) for the measurement of the electric field strength [11, 12].

By applying Eqs. (62) and (63) to the first 400 sets of data, we have obtained the regression curves of electric field strength to the sound pressure level, sound pressure level to electric field strength, electric field strength to illuminance of light and illuminance of light to electric field strength. These theoretical curves have been compared to experimental conditional expectations. The results when only one computer has been operated are shown in Figures 3, 4, 5 and 6.

These theoretical regression curves in each figure have been calculated by truncating the series expansion form in the denominator up to the 8-th order polynomial and taking the first expansion term, from the first expansion term to the 2-nd expansion term, from the first expansion term to the 3-rd expansion term and from the first expansion term to the 4-th expansion term in the series form in Eqs. (62) and (63) and they are called ad the 1-st approximation, the 2-nd approximation, the 3-rd approximation and the 4-th approximation.

......2nd approximation

-----3rd approximation

------4-th approximation

A comparison between theoretical regression function of electric field strength to sound pressure level

Figure 3.

2.6

2.5

72

74

76

78

SO

82

Sound pressure level] dBAJ

<

CQ

77

£X

~o

o

LT)

• experimental conditional expectations^/

i

1st approximation 2nd approximation

« 3rd approximation 4-th approximation

2.6 2.7 2.8 2.9

Electric field strength[V7m]

Figure 4.

A comparison between theoretical regression function of sound pressure level to electric field strength

----- 1st approximation

------2nd approximation

-----3rd approximation

-----4-th approximation

' experimental conditional expectations

2.6 2.7 2.8 2.9

Electric field strcngth[V/m]

Figure 5.

A comparison between theoretical regression function of illuminance to electric field strength

u

U 2.65

• experimental conditional expectations /

\\ • M

• ------ 1st approximation

/ ------2nd approximation

/ ------3rd approximation

' ------4-th approximation

1.5 2 2.5 3 3.5 4 4.5

Illuminance [Lx]

Figure 6.

A comparison between theoretical regression function of electric field strength to illuminance

Next, by applying Eqs. (64) and (66) to the first 400 sets of data, we have estimated the probability distribution of the electric field strength based on sound pressure level fluctuation and the one of sound pressure level based on electric field strength. Here, we have employed the lower and higher order mutual correlation information Amn. The results when only one computer has been operated are shown in Figure 7.

The theoretically estimated pdf has been calculated by replacing the series of right hand side in Eqs. (68) and (70) with no expansion term, from the first expansion term to the 3rd expansion term and from the first expansion tern to the 6-th expansion term (they are called as the 1st approximation, 4-th approximation and 7-th approximation). Then, Et and Fj have been calculated by truncating the series of the denominator up to the 8-th polynomial and the series of numerator up to the 6-th polynomial in Eqs. (69) and (71).

i

g 0.2 u

0

S 0.8 15

p 0. 6

CL

0-4

Figure 7.

A comparison between the theoretically estimated cumulative probability distribution curves of sound pressure level based on the electric field strength fluctuation

72 74 76 7a 80 82 84

Sound pressure levelfdBA]

In this experiment, although environmental factors have fluctuated in non-Gaussian distribution form and the linear correlation quantity has been rather small, as expected usually only in each individual (professional) sense, by using hierarchically many of the higher order mutual correlations following to the proposed method, the whole probability distribution form could be well estimated individually. That is, it has been shown that the proposed method is useful for the correlation analysis of the environment under EM, sound and light field exposure. Accordingly, some effectiveness of the background idea: “Relationism-First” to Individualism-2nd” has been partly proved through this principle experiment in space region analysis.

4. CONCLUSIONS

In this paper, partly suggested by the well-known philosophical emphasis of Herakleitos and Hegel and etc. (i.e., several of famous other philosophers) [15] based on their original standpoint that the truth exists not in fragmentarily individual things but only in their relational fact or process (i.e., event) itself with some concrete self-exercise of existing contradiction, we have stated that a central core and/or primary existence is not only mutual intermediation of time series type between past and present, but also mutual intermediation (i.e. relationship) in space region among different environmental factors(even if apparently it seems to have no connection according to only individual professional sense). That is, such a viewpoint of “Relationism-First” seems to be exceedingly important to all things including our human being evolving after the beginning of only material nature with Big Bang. Originally, all sorts of phenomena that are not intermediated by some identity are merely disjointed individual alien existences. Inversely, any identity that is not intermediated by a whole image of phenomena (sometime) with latent contradiction (mainly from the idea: “Relationism-First”) can produce no new anything whatever.

Concretely, from the above viewpoint, we have selected some types of modern hightechnology pollution as an example of study. That is, we have showed in trial some hierarchical type quantitative methodology among different type environmental fields such as light, sound and electromagnetic waves. In our analysis, first, their mutual intermediation including linear and/or nonlinear type higher order correlations has been investigated along to the aspect of “Relationism-First”. Next, based on this correlation analysis, we have studied selectively the fluctuation form of individual behavior of only each of waves(light, sound or electromagnetic waves) in the probability distribution form. After all, through such a study of “Relationism-First” (i.e., onotological relationship), we can expect that the viewpoint of first grasping every type of mutual intermediation among environmental factors in different fields (observed not only in a time series analysis but also in a space analysis) will become an essential key for solving not only the high-technology pollution but also many difficult problems including many of our cultural field too (if possible, in the form of (temporal) harmony between utility and risk or product and control) in the present day.

More concretely, in the present paper, as two kinds of actual example of the above hierarchical type correlation in the time series and (in contrast with this) the similar type correlation distributed in the space among different environmental factors, we have applied the proposed method especially to the acoustic environment and the mutual intermediation among sound and light waves (served for utility) and leaked EM waves (served for risk) around personal computer under playing a game through some principle experiment. As the result, we have partly confirmed in principle its effectiveness of the proposed methodology by taking only the mutual intermediation among only physical environmental factors as an example.

ACKNOWLEDGEMENTS

We would like to express our cordial thanks to Prof. A. Ikuta and Assist. Prof. H. Ogawa for their kind advices and earnest cooperation.

REFERENCES

1. USSR Ministry of Health Protection. Temporary health standards and regulations on protection of the general population from the effects of electromagnetic fields generated by radio-transmitting equipment (summary: Russian-Japanese translation). N°2963-84 (1984).

2. T. S. Tenforde, W. T. Kaune. Interaction of extremely low frequency electric and magnetic fields with humans. Health Physics, vol. 53, 585-606, 1987.

3. IEEE standard. Safety levels with respect to human exposure to radio frequency electromagnetic fields, 3 kHz to 300 GHz. IEEE, C. 95.1, 1991.

4. Fundamental of environmental electromagnetic engineering. Institute of Electronics and Communication Engineers (Japan). Corona Co. Ltd, 1991.

5. E. N. Skomal. Man-made Radio Noise. Van Nostrand Reinhold.

6. D. R. J. White. EMC handbook. Don White Consultants, 1971.

7. M. Ohta, E. Uchino. The Course of Science and Technology, and Acoustics: Past, Present and Future-Turning to Information Acoustics. Chinese journal of acoustics, vol. 11, N°3, 213-223, 1992.

8. M. Ohta. Several dynamical state estimation methods for environmental system of acoustic noise and vibration type. I. Methodological style and establishment of a general theory (in Japanese). Japanese society of automatic control: System and control (explanation), vol. 23, N°10, 27-33, 1979. II. State estimation theory of energy system and its application of living environment (in Japanese). Japanese society of automatic control: System and control (explanation), vol. 23, N°12, 26-33, 1979.

9. M. Ohta, K. Hatakeyama. Stochastic system theory of acoustic environment and its digital signal processing. Japanese society of automatic control (explanation, special issue), vol. 31, N°11, 823-831, 1987 (in Japanese).

10. M. Ohta, A. Ikuta. Stochastic signal information processing - Bayes' type digital filter using higher order mutual correlation and its application to state estimation. Journal of Acoustic Society of Japan (specific explanation), vol. 50, N°2, 140-148, 1994 (in Japanese).

11. Y. Fujita, M. Ohta, H. Ogawa. A methodological quantitative trial based on hierarchical mutual intermediation between different fields - A trial to some synthetic evaluation for hightechnology pollution (II). Technical Report of IEICE, vol. 104, N°223, 33-38, 2004.

12. H. Ogawa, M. Ohta. Inter-subjective relationship among different factors in indoor electromagnetic environment- a methodological trial for evaluation of compound and/or cumulative effects. Technical report of IEICE, vol. 104, N°455, 7-12, 2004.

13. M. H. de Groot. Optimal Statistical Decisions. McGraw-Hill, New York, 1970.

14. P. I. Kuznetsov, R. L. Stratonovich, V. I. Tikhonov. Quasi-moment functions in the theory of random process. Theory of Probability and its Applications. vol. 1, 70-97, 1960.

15. B. Russel. A History of Western Philosophy. Simon and Shuster, New York, 1945.

Mitsuo Ohta, Yoshifumi Fujita

Inter-subjective relationship of higher-order among spatial-temporal wavy environmental factors - a methodological trial based on a standpoint of "Relationism-First"

APPENDIX I

HIGH-TECH POLLUTION-ENVIRONMENTAL PROBLEMS OF WAVE MOTION TYPE

Even in the wave-motion type environmental problem, nowadays, we can see many actual phenomena (with few theory e.g., [1, 2]) composed of extensive environmental factors in different fields with mutual relationship among them. For instance, these examples are given as follows. The nervous system of mankind is so much affected by any field of sound, light and electromagnetic waves in the neighborhood of the specific frequency band from 15 Hz to 20 Hz (because calcium ions are occasionally lost out). This is particularly induced even by the signal modulated into high frequency band with the slow change of its amplitude. Furthermore, the generated order, generated time interval and each of their proper durations between sound and flash of lightning cannot be recognized as it is [3]. There are the biological priority effect between the sense of sight and the sense of hearing that the sense of hearing is reflected by the sense of sight with more strong ability of evoking attention, the promotion effect between different senses, the synergistic effect between sense and stress, participation in VDT syndrome such as general malaise, relevance to circadian rhythm due to the reflection to the pineal body by the exposure of light and electromagnetic fields, the change of brain waves in the case when we have received sound and light at the same time, chromesthesia, the cooperation effect of music and picture and so on. Since now these modern problems and high technology are relationally double-faced sides [4] of the same coin, we can give many concrete examples.

In fact, owing to the popularization of IT instruments such as cellular phone, cordless phone, personal computer and so on, both in the inside of the room and in the inside of the car, we are surrounded more and more by electronic instruments and live always under the exposure of artificial electromagnetic radiation as if smog. So, the environmental problems (such as VDT syndrome, electromagnetic wave erethism and so on) in which the reflection of compound effect and accumulation effect induced by mixture of sound, light, electromagnetic wave, heat and so on, must be taken into consideration are arising even if we choose the problems in the only limited field of the wavy physical science as an example [5-12]. However, as the present situation in every branch of knowledge, it seems that each problem is decomposed owing to our human professional interest first to some parts in fragments belonging to different fields and in the present condition that each part is separately studied. Furthermore, not only in the acoustic environment but also in the electromagnetic environment, it can be said that almost all are mainly the studies in the frequency domain and few are studies in the time domain. Even in basic studies to solve the problems, it seems that any of quantitative studies related to compound effect and accumulation effect between different environmental factors such as sound, electromagnetic wave and so on in electrified indoor environment cannot be almost found even as a motive and a trial. As stated in the above introduction, if we remember in principle the genesis of our existence, it can be said that there are in principle no any phenomena not related to other different environmental factors including the one in the humanities.

As stated in Appendix II, since originally we cannot live without the environment, in principle there is no spirit under no support of any material and there is no quality under no support of any quantity, our mind are naturally unified with our body. It can be said that

“Live” doesn’t exist without first recognizing the total balance and manifold mutual intermediations of all systems in inside and outside of ourselves which are the real fresh-and-blood creatures. That is, it seems indispensable that not only extending the separately fragmentary abilities acquired in the infancy and afterward filling up gaps between them but also training and educating that the total balance is the most important (not only for each person but also for the organization). Increasing in one-sided way the amount of the production of the high technology hardware and software such as the personal computer, the cellular phone, the game software and so on brings the change of the economic structure in the society by being drilled through the anti-natural properties such as abnormal accuracy and speed which the advance of artificial machines essentially posses. As a result, it brings necessarily the qualitative change of the social organization by being freed from the common ideas such as the politics, the ethics, the religion and so on. We cannot help but fear that, in another side, it makes the natural environment and the social environment rapidly change to the inhuman and immoral modes, and fall the (essential) human nature such as goodness, truth, beauty and philanthropy to the low level step by step together with the advancement and the speedup of the high-technology (which we cannot protect from the hacker). We think that this is the reason that the mutual intermediation between the natural science and the humanities which cannot be originally divided should be considered as a central theme to people of today who live at this time and in this ring.

Under a firm basis of the above-mentioned ideas, let us establish on trial concretely the corresponding methodology of our present study. That is, first, we have to try to extract all sort of mutual correlation information both in time and space regions among every kind of environmental factors from the viewpoint of “Relationism-First”. If possible, it seems better for us to first extract them especially in the hierarchical form of linear and non-linear correlations of higher order with the 1-st, 2-nd, 3-rd, ... orders. More explicitly, at the next stage of methodological concrete measure, in this paper, our study from two standpoints-time region and space regions has been given in principle in a marked contrast style.

REFERENCES

1. D. Middleton. Statistical-physical models of electromagnetic interference. IEEE Trans. Electromagnetic Compatibility, vol. EMC-19, 106-127, 1977.

2. D. Middleton. Canonical non-Gaussian noise models: Their applications for measurement and for prediction of receiver performance. IEEE Trans. Electromagnetic Compatibility, vol. EMC-21, 209-220, 1979.

3. Henri Pieron. LA SENSATION. Original Copyright by Presses Universitaires de France (Japanese translation), Hakusisha, Tokyo, 1987.

4. M. Ohta, E. Uchino. The Course of Science and Technology, and Acoustics: Past, Present and Future-Turning to Information Acoustics. Chinese journal of acoustics, vol. 11, N°3, 213-223, 1992.

5. Y. Fujita, M. Ohta, H. Ogawa. A methodological quantitative trial based on hierarchical mutual intermediation between different fields - A trial to some synthetic evaluation for hightechnology pollution (II). Technical Report of IEICE, vol. 104, N°223, 33-38.

6. H. Ogawa, M. Ohta. Inter-subjective relationship among different factors in indoor electromagnetic environment - a methodological trial for evaluation of compound and/or cumulative effects. Technical report of IEICE, vol.104, N°455, 7-12, 2004.

7. M. Ohta, H. Ogawa. A methodological trial of regression analysis with higher order correlation between electromagnetic and sound waves leaked by a VDT in an actual working environment. Journal of Electromagnetic Waves and Application, vol. 12, N°10, 1357-1367, 1998.

8. M. Ohta, A. Ikuta, H. Ogawa. A stochastic evaluation theory in multi-dimensional signal space for EM interference noise and its experimental relationship to acoustic environment. Trans. IEE of Japan (C), vol. 118, N°4, 465-475, 1998.

9. M. Ohta, Y. Mitani, N. Nakasako. A fundamental study on the statistical evaluation of receiver response for an electromagnetic wave environment in multi-dimensional signal space - theory and basic experiment. Journal of Electromagnetic Waves and Applications, vol.12, N°5, 677-699, 1998.

10. M. Ohta, Y. Mitani, H. Ogawa. Multi-dimensional generalization in space and time domain for Middleton's study in stochastic evaluation of correlative many EM noise processes. Electromagnetic Waves PIERS 24, ed. J. A. Kong, Chap. 5, 97-118, EMW Publishing, Cambridge, 1999.

11. M. Ohta, H. Ogawa. A trial on hierarchical extraction of higher order correlation between electromagnetic and sound waves around a VDT environment - Practical use of background noise and probability prediction. Electromagnetic Waves PIER 34, ed. J. A. Kong, Chap. 12, 285-298, EMW Publishing, Cambridge, 2001.

12. H. Ogawa, M. Ohta, A. Ikuta. A trial on stochastic evaluation of near-by electromagnetic fields leaked from ITE group under parallel operating situation. Journal of Electromagnetic Waves and Applications, vol. 18, N°12, 1621-1635, 2004.

Mitsuo Ohta, Yoshifumi Fujita

Inter-subjective relationship of higher-order among spatial-temporal wavy environmental factors - a methodological trial based on a standpoint of "Relationism-First"

APPENDIX II

OUR METHODOLOGICAL BACKGROUND IDEA-THE CORE CHARACTERISTCS OF MUTUAL INTERMEDIATION: “RELATIONISM-FIRST”

Nowadays, it becomes a scientific common sense that after the Universe began in a gigantic explosion - Hot Big Bang (in some theory (e.g., Theory of Superstrings), though it is only theoretically said that by the division from 10 dimensions (ref. 11 dimensions in M theory) to 4 dimensions, this Big Band occurred, simultaneously sisters space and dark material were born.), it seems sure to us we human being was born from some material nature first and become to have partly even subjective consciousness through the evolution and development through the self-exercise of the material. We strengthened gradually our artificial force until overcoming partly natural environment by making it a tool. Then, sometime through our active partial opposite against nature, one side of view can be surely seen that we have creatively made not only a part natural environment but also the social and/or historical environments (On the other hand, there are also an another view a well-known Gaia hypothesis close to the so-called purpose cause that only the beginning doesn’t restrict the end but the end (might) restrict the beginning, the hypothesis that both the law of

causation from past to future and the germ of idea from future to past (for example, reactions

pursuit^predation^a save of a kind) originally exist at the same time even in the primitive material nature, and more positively a unique idea of the cosmology based on the principle of mankind (regardless whether it is right or wrong can be appeared.).

After all, all natural creation that evolves together with us and exists as an environment can become partly subjective existence too to create some part of environment (But, eventually, all creation seems too to be governed by an entropy increase of grand cosmic law). That is, it can be said that there doesn’t exist oneself without environment and there doesn’t exist our consciousness and spirit without matter. As stated in well known Herakleitos’s all things vicissitudes theory [1] (based on repulsive harmony) from the old times, all creations in the real world are not made by any God and any human beings, they eternally exist only as “processes” through the past to the future which is everlastingly burning and extinguished according to natural laws. From this viewpoint, the truth doesn’t exist in the individual fragmented fact, but exist only in the relational or systematized flow as proper characteristics of universe. Furthermore, if any kind of abstraction and analysis is inevitably necessary in the form of learning as Hegel pointed out [1], this mutual proper intermediation among these fragmented sides covers (lies) absolutely and widely (i.e., the truth exists only in the mutually relational facts). So, it will be necessary to analyze deeply and manifoldly more and more by focusing on this mutual intermediation itself (e.g., even though in a hierarchical form). If we continue to either neglect or disregard this mutual intermediation among them (which is still being evolved) as a subsidiary factor, it shows that we become to regard all living existence (i.e., all creation) as only a set of dead fragmented things. After all, it might show our conveniently selfish attitude of mind that we find not the truth but mainly the effectiveness (ultimately connected to our profit) as problem of major importance. From the viewpoint of the above stated principle, even though every type of existence is conveniently classified into different fields such as natural science, sociology, ethics and so on according to the purpose

of our studies, originally it can’t be helped to say there must be latently any kind of deep and manifold mutual intermediation [2] (objectively and/or subjectively) among them.

In this paper, some concrete methodology (with first a mathematical frame) focusing on the above mutual intermediation itself (which is still being evolved) and treating it quantitatively as much as possible, which is only a trial, is proposed (from viewpoint of “Relationism-First” as a background idea of study). Next, (without taking up one by one many of referenced so classically famous books [1] & papers because of too famous), only to the page limitation, let us list by focusing mainly (or selfishly) on several of related our recent papers[2-7] by which its motivation and instruction for giving the conceptual frame of the proposed method may be influenced and supported(Especially, if daringly emphasizing, even the well known 4 Zenon’s paradoxes quoted in an ancient Aristoteles’s “Physike”[1] seem to strongly indicate the necessity of standing on a viewpoint of “Relationism-First” (e.g., like as a mat. wave) at the same time and in the same ring, with having priority to standing on a viewpoint of Separatism (or Individualism)-First (e.g., like as mat. particle), even if there still now might remain dialectically any quantitative doubtful point (regardless whether it is right or wrong, e.g., like as in the differential and integral calculus).

Since we human being has been born as the result of evolution after the beginning of material nature style (with Hot Big Bang) as stated previously, even though our idea “freedom” based apparently on only our independent consciousness and subjectivity action, and all abstract and formal concepts are considered, they must posses latently an objective logic as the logos of substance supported by our sense and the interface contacted with the reality supported by any substance on their bottom of concept. It can be concluded that originally there is no any change of quality which is not supported by the rule of quantity. That is, if we first neglect artificially this mutual intermediation between quantity and quality and one between the natural science and the humanities, which are not separable in principle, we cannot find the advanced problem related to the higher order and/or our pure cultural type intermediation, only based on one-sided viewpoint of the craftsman skin type (sometimes, under some artificial confidence). Accordingly, we fear that the scale of the prospect for total image with organic cooperation of liberal arts and natural science is consequently reduced to some local style. In anyway, we cannot help but say they remain only the partial truth.

However, since originally we human being has only finite ability to discover, it is difficult to grasp a whole image of absolute intermediation directly and completely as it is. We cannot but recognize this intermediation to a certain limited extent and have to neglect necessarily the outside of this ability limit. As an ideal goal, we have to try to investigate this intermediation, at the same time in the same ring for the recognition of the totally consolidated image.

Even though one may have some different opinions on the above mentioned content, the above mutual intermediation itself among more than two environmental factors (which are apparently contrast in some case and cannot be divided originally in principle) should accomplish some role of the central core in close relation to ontology concerned (that is, more clear explanation on its mutual intermediation among artificially divided different fields has to be made and should be thrown one after another into relief for the future). Of course, this intermediation contains essentially such as one between quantity and quality, a set and its member, the object and the subject, speciality and generality, substance and spirit, (scientific and technological) force and (lifesaving and personal) love, natural science and liberal arts and so on. (There appear some hypotheses with totality similar to a hologram surpassing each fragment factors just like in a style of plasma holographic energy and bio plasma, and accordingly we ourselves should actively participate in some hidden immanence order). It seems that it is essentially and inevitably necessary to develop the study focusing not on each divided fragment but first on mutual intermediation itself among them (if possible,

quantitatively) step by step. Especially, it seems that such a development of intermediation study is essentially necessary at the present age with mental desert brought to us by hacking Homo faber with our artificial modernization of high technology in which only the operation precede all other sides under support of one-sided viewpoint.

Of course, our methodological trial proposed in this paper is only one trial, but we can extend formally the proposed method to the one among any number of different factors by gathering every type of indexes (including the questionnaire of human being reaction [8-13], as an example) in different special fields such as nature, technology, society, ethics and so on. However, especially in this paper, (although there are surely some specific properties clearly appearing only in the case with mutual intermediation among more than three factors) the one between only two factors is intentionally proposed to emphasize especially the hierarchization of mutual intermediation as a trial of early stage study. As a concrete example, we want to deal with an approach to the modern environmental problem related to the high-tech pollution, by restricting within only some wavy physical type field like EM (including light) and/or sound. One of its reasons is that it is expected in advance that the application only to the physical science side is basically easier than the one to liberal arts side (even in each element of which any subjective property cannot be neglected more or less) in its quantitative treatment and experimental confirmation. As a special case of high-tech pollution, the intermediation between past and present states of one factor or only each two spatial factors chosen from environmental multiple factors of wave motion type (which are apparently different phenomena each other at least even in physical sides) in environment around VDT is taken into consideration as a trial (this artificial restriction sometimes may neglect any (catalystic) type of the third, forth and more other environmental factors and so on). Then, first the effectiveness of the proposed methodological trial is confirmed in principle through some basic experiment by paying our special attention to mutual intermediation itself in time and/or space regions, especially as to its hierarchization not only in mutual relationship of only average and lower order type but also in every higher order type statistical (correlative) moments of the fluctuation (even if the concrete meaning of which has not still been clarified).

REFERENCES

1. B. Russel. A History of Western Philosophy. Simon and Shuster, New York, 1945.

2. M. Ohta, E. Uchino. The Course of Science and Technology, and Acoustics: Past, Present and Future-Turning to Information Acoustics. Chinese journal of acoustics, vol. 11, N°3, 213-223, 1992.

3. M. Ohta. Several dynamical state estimation methods for environmental system of acoustic noise and vibration type. I. Methodological style and establishment of a general theory (in Japanese). Japanese society of automatic control: System and control (explanation), vol. 23, N°10, 27-33, 1979. II. State estimation theory of energy system and its application of living environment (in Japanese). Japanese society of automatic control: System and control (explanation), vol. 23, N°12, 26-33, 1979.

4. M. Ohta, K. Hatakeyama. Stochastic system theory of acoustic environment and its digital signal processing. Japanese society of automatic control (explanation, special issue), vol. 31, N°11, 823-831, 1987 (in Japanese).

5. M. Ohta, A. Ikuta. Stochastic signal information processing - Bayes' type digital filter using higher order mutual correlation and its application to state estimation. Journal of Acoustic Society of Japan (specific explanation), vol. 50, N°2, 140-148, 1994 (in Japanese).

6. Y. Fujita, M. Ohta, H. Ogawa. A methodological quantitative trial based on hierarchical mutual intermediation between different fields - A trial to some synthetic evaluation for hightechnology pollution (II). Technical Report of IEICE, vol. 104, N°223, 33-38, 2004.

7. H. Ogawa, M. Ohta. Inter-subjective relationship among different factors in indoor electromagnetic environment- a methodological trial for evaluation of compound and/or cumulative effects. Technical report of IEICE, vol. 104, N°455, 7-12, 2004.

8. USSR Ministry of Health Protection. Temporary health standards and regulations on protection of the general population from the effects of electromagnetic fields generated by radio-transmitting equipment (summary: Russian-Japanese translation). N°2963-84 (1984).

9. T. S. Tenforde, W. T. Kaune. Interaction of extremely low frequency electric and magnetic fields with humans. Health Physics, vol. 53, 585-606, 1987.

10. IEEE standard. Safety levels with respect to human exposure to radio frequency electromagnetic fields, 3 kHz to 300 GHz. IEEE, C. 95.1, 1991.

11. Institute of Electronics and Communication Engineers (Japan), Fundamental of environmental electromagnetic engineering, Corona Co. Ltd, 1991.

12. E. N. Skomal. Man-made Radio Noise. Van Nostrand Reinhold.

13. D. R. J. White. EMC handbook. Don White Consultants, 1971.

Mitsuo Ohta, Yoshifumi Fujita

Inter-subjective relationship of higher-order among spatial-temporal wavy environmental factors - a methodological trial based on a standpoint of "Relationism-First"

APPENDIX III

OUR GUIDING PRINCIPLE FOR ANALYSIS

[1] From a viewpoint of “Relationism-First” that there is latently the objective logos of the material in the bottom of the subjective formal logic, before introducing hierarchical distinction of the master and servant or a priori rule in our analyses, we first take attention to data assemblage itself of two variables x and y sampled simultaneously (for an example, like a scatter diagram at the same time and in the same ring). As is well-known, it may be some partial truth there is also a viewpoint of pure axiology, in which the individual substance (i.e., supporting mother’s body) is once at least only formally disregarded as the first step of study and only the mutual objective relationship as its functional behavior is first considered including abstract style((sometimes, latent) with essential support of substance), and on the other hand there is some local viewpoint of operational side on the problem of the determination of sampled size and the reliability of sampled data in the actual stage.

[2] In case of analyzing the relationship between x and y, which of them is chosen as a criterion variable or a predictor variable and/or in case of searching causal relationship, which of them is chosen only in an operational side as an input or an output are not artificially decided at the first step of analyses. But, as such an inevitable target, any subjective sense matched to solve the problem is not introduced in advance in our study of “Relationism-First”.

[3] In order to describe deeply the relationship itself between two variables as more universally as possible, first we take attention to the simultaneous probabilistic assembly expression for a whole set of x and y. In regard to the deep structure of the relationship, we’d like to take the position that multiple hierarchical correlative configurations from the lower order to the higher order correlations can necessarily be found. As a result, a hierarchical series expansion form is introduced for the above analysis from the viewpoint of “Relationism-First”, without neglecting its (latent) substantial basis.

[4] In order not to loose the basic property (reflecting the mother’s body substance supporting the functional relationship) related to the existence itself of fluctuations on actual data x and y, we have the basic substantial features reflect mainly in the measure of lower order correlation. In the structural form on the expression for the functional relationship itself, it is expressed in the abstract style once at least by positively introducing the dimensionless quantities (parameters reflecting its substance basis). We’d like to have the degree of the reflection on the above basic substance weaken as the order of this correlation becomes deeper and higher, so as not to make some specific function of the super-structure thin owing to too emphasis of the substructure (see Appendix V about the concrete content).

[5] Once after observing the original parallel form (such as, of the scatter diagram as it is), as the next stage of study, in order to introduce a standpoint of some subjectivity (i.e., intersubjectivity) corresponding to the present problem in our study between x and y which may be stochastic variables, we decide the class order for these two stochastic variables such that,(as an example) we set y as a criterion (output) variable and x as a predictor (input) variable. Then, it is necessary to try to find any multiple regressive relationship information reflecting our artificially operational properties as slightly as possible for this mutual independence (even if any kind of artificial (abstractive?) analysis is inevitably necessary in terms of learning as Hegel [1] pointed out).

[6] In the data processing of the proposed extended regression analysis, we don’t force one to use artificially a priori limited mathematical frame of the regressive structure such as the usual linear regression in advance but we first employ any of well known universal mathematical logic as the structure of mutual functional relationship between the above dimensionless quantities (which has some analytical precedence(only as a mathematical frame, e.g., especially in the super-structure side) more than physical law with higher reflection to the actual substance). As much as possible, on the analytical viewpoint, we want to introduce any of axiomatic (sometimes, normative) judge reflecting universality as high as possible (for example, Bayes’ axiom satisfying the Coherence axiom by de Groot [2] directly connected to the conditional probability or the addition property of energy as a universal law (even if the physical basic law is actively applied at the first stage of study).

[7] Even though the concrete form of the relationship is regarded as operational fluctuation behavior of the actual substantial “material”, the degree of its functional freedom is first restricted by the magnitude of the objective existing range (for example, [0,ro], (-a>,rc>), [a,b]) on the actual data x and y (as seen in the substructure side). As the first step of analysis (for example, even in application of axiomatic Bayes’ principle), this information is positively reflected.

[8] Once after passing through the relationally mathematical (sometimes basic physical) formal logic, next, from the viewpoint of inter-subjectivity, as an example, as the present main object of study, we focus on selectively the form of subjective behavior of only x in the form of the probability distribution. However, first, we don’t directly and fragmentally derive any statistics like mean, variance and individual higher order moments according to our need (notice that these individual moment type characteristic quantities can be easily calculated mathematically afterwards once after the corresponding probability distribution form has been obtained).

[9] In the case when we process the data of x, y causally as a time series of input and output, tentatively, we can formally regard that the data are sequential occurrences of static relational behavior appearing in the cross time section at the same time for active real time phase even in the evolution process. That is, we can successively employ the same analytical static method as stated above (like the well known Kalman filter), but some risk such that the figures of lively change (i.e., evolution) are replaced to a set of sequential dead ones may be occurred. On the other hand, as in our present paper, the application of the Bayes’ principle in the dynamical state estimation theory (including the Kalman filter) can leads in some normative style even the first employment of a priori uncertain probability to some consistent objective probability along the recursive more stack of sampled data. It is an important logical necessity based on the assurance of the (normative) axiom (Conversely, it might be a good idea to search any method matched to finding reasonably the above a priori probability by use of experimental data). Thus, it seems so natural with help of its some normative property to employ this Bayes’ principle as one of the mathematically basic concepts for preparation in employing one thing and another many kinds of signal processing method such as fuzzy, neural network and so on, since the Bayes’ estimation is enough reasonable to be relied upon, just like as the physical fundamental law should be relied upon even though the evaluation based on the physical law is opposite for the present to our expected intuitive evaluation in the actual stage.

REFERENCES

1. B. Russel. A History of Western Philosophy. Simon and Shuster, New York, 1945.

2. M. H. de Groot. Optimal Statistical Decisions. McGraw-Hill, New York, 1970.

Mitsuo Ohta, Yoshifumi Fujita

Inter-subjective relationship of higher-order among spatial-temporal wavy environmental factors - a methodological trial based on a standpoint of "Relationism-First"

APPENDIX IV

EXPERIMENTAL SITUATION RELATED TO TIME SERIES REGRESSION MODEL IN SOUND ENVIRONMENT AND EVALUATION OF PREDICTION ERROR

Figure A4-1 is the system diagram for the measurement in the sound experiment laboratory [1-3] (data 1). The input signal is a white noise of the center frequency 250 Hz with one-third octave band. Due to the reverberation characteristics of the room, there naturally exists the correlation among time series values of signal observed at different times, especially at the low frequency region. The acquired data are transformed into a discrete form by the A-D converter, at the sampling rate of 0.1 s (called case 1) or 0.09 s (called case 2).

The sampling interval should be essentially set in relation to the frequency bandwidth to be restored. In this experiment, two different sampling intervals are used due to the following reasons. The proposed method is applied to the discrete signal with any sampling interval. In the time region, the correlation between random process at time k and k - 1 is decreased (increased) when the sampling interval is increased (decreased). In other words, the order to be used in the time-series model depends on the sampling interval, even for the same signal.

Figure A4-1.

Block diagram of the acoustical experiment

The sound waveform for the washer (data 2) is recorded once on a tape recorder at the measurement site. The replayed data are transformed by the A-D converter in the sound experiment laboratory at the sampling interval of 0.08 s. For each case, 100 non-stationary data are recorded and are divided into training data and prediction data for the locally stationary interval. In other words, the autoregression parameters (expansion coefficients Amn in Eqs. (18) and (27)) are calculated from the training data, and the sequential prediction of the time series is attempted using the obtained expansion coefficients for the prediction data. Equation (17) is used for case 1 of data 1. Equation (26) is used for case 2 of data 1 and data 2.

Next, the parameters of the autoregression model are estimated using the training data. More precisely, Amn are estimated by the moment method following the definitions of Eqs. (18) and (27) ( called estimation 1). The parameters also estimated based on the infinite series expansion of Eqs. (17) and (26) for the autoregression model. Considering that there are only a finite number of data in the actual case and only a finite number of expansion coefficients can be utilized, the evaluation criterion that J = <£k2> should be the minimum is introduced and the autoregression parameters are estimated from external observations (called estimation 2).

In the case of Eq. (10), for example, the autoregression model

M-1 / M

Z Z A,n^r-’(xf-, )/Z z A)„^i21 (xt_, )

N =0 n +n2 +-+Np =N j N=0 n + n2 +-+Np =N

is used considering that the number of expansion coefficients is finite. Hereupon, A1n is determined so that

xk = C0 + С

+ єє

(A4-1)

Іґ

xk - cG - С

k G a

Z Z A1n^2|(xk-,)/Z Z Aon^n2|(xk-1 )

ra

N=0 n +Пл +—np =N

N=0 П1 +n~, +—np =N

2

(A4-2)

is minimized(least-squares method). In this case, ^on denotes the statistical data of only x^i and are estimated beforehand by the moment method.

Tables A4-1 to A4-4 show the evaluation of the error (mean-square error between the actual value xk and the predicted value €) given by

1

еЛ^—Z(xk - € I \ (n isthe number of data )

_ I n k=1 I

(A4-3)

for each datum, each case, and each estimation.

Table A4-1. Evaluation of error of predicted value to measured value (case 1 of data 1).

Estimation error Prediction error [dB]

AR Proposed time series regression model

Model M=2 M=3 M=4

1 1.0012 1.0012 0.9980 0.9918

2 1.0012 1.0012 0.9980 0.99бЗ

Table A4-2. Evaluation of error of predicted value to measured value (case 2 of data 1 ).

Estimation error Prediction error [dB]

AR Proposec time series regression model

Model M=2 M=3 M=4

1 1.0077 1.0077 1.0005 0.9904

2 1.0077 1.0077 1.0005 0.9974

Table A4-3. Evaluation of error of predicted value to measured value (estimation method 1 for data 2)

Prediction error [dB]

p AR Proposed time series regression model

Model M=2 M=3 M=4

1 — 1.3478 1.3283 1.3250

2 1.3335 1.3335 1.3051 1.3229

Table A4-4. Evaluation of error of predicted value to measured value (estimation method 2 for data 2)

Prediction error [dB]

p AR Proposed time series regression model

Model M=2 M=3 M=4

1 — 1.3448 1.3315 1.3257

2 1.3335 1.3335 1.3045 1.2524

It can be seen in particular from Tables A4-3 and A4-4 that the prediction performance of the proposed method is better forp=1(although it is smaller than the optimal orderp=2) if the higher-order expansion terms are considered than the AR model for p=2. Thus, it is verified also experimentally that the proposed method is a generalization, including the well-known (linear type) AR model as the special case.

Figure A4-2 shows the cumulative distribution functions (abbr. cdf) for the datai (derived from the prediction data), once after the above correlation analysis based on the idea of “Relationism-First”. To determine the extent of non-Gaussian property of the data, the figure also shows the result when the statistical Hermite expansion distribution expression is used, which is applicable to any type of non-Gaussian distribution with the Gaussian distribution in the first expansion term.

Figure A4-2.

Cumulative distribution function of data 1

It can be seen from Figure A4-2 that data 1 are considerably close to the Gaussian distribution. However, the result is closer to the actual value if the expansion coefficient reflecting the third-order moment also is considered.

REFERENCES

1. M. Ohta. Several dynamical state estimation methods for environmental system of acoustic noise and vibration type. I. Methodological style and establishment of a general theory (in Japanese). Japanese society of automatic control: System and control (explanation), vol. 23, N°10, 27-33, 1979. II. State estimation theory of energy system and its application of living environment (in Japanese). Japanese society of automatic control: System and control (explanation), vol. 23, N°12, 26-33, 1979.

2. M. Ohta, K. Hatakeyama. Stochastic system theory of acoustic environment and its digital signal processing. Japanese society of automatic control (explanation, special issue), vol. 31, N°11, 823-831, 1987 (in Japanese).

3. M. Ohta, A. Ikuta. Stochastic signal information processing - Bayes' type digital filter using higher order mutual correlation and its application to state estimation. Journal of Acoustic Society of Japan (specific explanation), vol. 50, N°2, 140-148, 1994 (in Japanese)

Mitsuo Ohta, Yoshifumi Fujita

Inter-subjective relationship of higher-order among spatial-temporal wavy environmental factors - a methodological trial based on a standpoint of "Relationism-First"

APPENDIX V

EXPRESSION OF THE HIERARCHICAL PROPERTY IN THE RELATIONSHIP CONFIGURATION OF INTER-SUBJECTIVITY

In the probability distribution form with both positive and negative fluctuation variables, the parameters of the distribution form are given by ^,y, uy and Amn. Then, the Gaussian distribution of the first term in the orthonormal expansion type probability expression is reflected by only /uy and uy. It is rational that the mean and uy (around mean) are reflected in the base of the expression since they are originally the fundamental information as the supporting basis (like the substructure) for the real substantial existence of the fluctuation.

In the subsequent parameters Amn (m ^ 0, n ^ 0) reflecting the mutual intermediation hierarchically, once after the statistical information as the base of the substantial fluctuation existence is first reflected, only the form of the existence mode (each fluctuation style of the correlation between different type fields) constructed upon its substantial base is reflected (in the form of functional style connected to the lower and upper structure of the correlation). Therefore, especially, it is rational that we dare employ such mutual correlation expression of every hierarchical type reasonably in the form of a non-dimensional quantity(internally reflecting its substance basis). Hereupon, Amn for m=0 or n=0 does not reflect the quantity on the mutual intermediation but reflect the higher order statistical moments on each individual variable (in the higher order style form of the fluctuation pattern on only each variable like the coefficient of well known skewness and kurtosis).

At the end, it seems to deserve special emphasis as a basic principle that every possible types of actual observation served for any analyses based on an idea: “Relationism-First” have to be realized on the substantial basis at the same time and in the same ring for all mutually correlated environmental factors without adding any human artificial operation to the best of our ability (if possible).