Damien Voyer

François Musy

Laurent Nicolas

Ronan Perrussel

Probabilistic methods applied to 2D electromagnetic numerical dosimetry

Keywords: Numerical dosimetry, electromagnetism, stochastic method, polynomial chaos, sparse grid

come

Introduction

Electromagnetic dosimetry attempts to evaluate the interaction between electromagnetic waves and biological tissues; the coupling between the electromagnetic field radiated by a cellphone and the human body is an illustrative example. Numerical simulations are the only tool to estimate accurately the specific absorption rate -SAR -in the human body [START_REF] Leveque | Dosimetric analysis of a 900-mhz rat head exposure system. Microwave Theory and Techniques[END_REF], Scorretti et al., 2004]. Up to now most of the works has been focused on determinist problems in which the values of the input parameters are supposed to be certain. However, these parameters are inherently known with some vagueness; uncertainties appear indeed in the description of the human bodye.g. the nature of tissues or the morphology -but also in the description of the sourcee.g. the position of the cellphone or the frequency - [Stavroulakis, 2003, Hurt et al., 2000]. Thus, determinist calculations are not suited to properly describe the complexity of the problem. This issue is particularly crucial in the normative context.

In order to obtain statistic information such as the mean or the variance of the SAR, the Monte Carlo method could be applied [START_REF] Newman | Monte Carlo Methods in Statistical Physics[END_REF].

However, the convergence rate of the method is slow: 1/ √ K where K denotes the number of realizations. When the modeling of the 3D interaction between the human body and a cellphone is considered with many details in the morphology, one calculation already requires large computational resources. This consequently makes prohibitive the use of the Monte Carlo method. To deal with this issue, another method -the spectral stochastic finite element method -has been introduced in mechanics in the early nineties [START_REF] Ghanem | Stochastic finite elements: a spectral approach[END_REF].

It is based on a spectral decomposition of the random space using the polynomial chaos. There are two approaches: the so called intrusive method where the determinist solution is widely recast [START_REF] Ghanem | Numerical solution of spectral stochastic finite element systems[END_REF] and the so called non intrusive method that uses determinist computations with a restrictive number of realizations a priori chosen [START_REF] Ghiocel | Stochastic finite-element analysis of seismic soil-structure interaction[END_REF]. In this paper, we will focus our attention on the non intrusive method because of the limitation of the numerical resources. Indeed, the intrusive method leads to an algebraic system that is larger than the system built in the determinist case. This is a serious drawback in complex problems where these matrix systems are already large in the determinist case. Completing the previous strategy, a collocation method using Lagrange polynomial has recently came out [START_REF] Chauvière | Computational modeling of uncertainty in time-domain electromagnetics[END_REF]. This technique is an alternative method to reduce the number of realizations; the difference with spectral methods lies on the fact that the description of the random variable is based on a nodal approach. The numerical cost can be further decreased using a regression approach, sparse grids computed from Smolyak algorithm or a suited coordinate system.

In electromagnetism, only few works have been led; let's however quoting two significant examples: the intrusive spectral stochastic finite element method has been applied to an electrostatic problem where the permittivity of materials is described by a random law [START_REF] Gaignaire | 3D spectral stochastic finite element method in electromagnetism[END_REF]; the collocation method has been implemented in a scattering problem where uncertainty is introduced in the source term, in the geometrical shape and in the material [START_REF] Chauvière | Computational modeling of uncertainty in time-domain electromagnetics[END_REF]. The objective of this paper is to show the feasibility of the probabilistic methods in electromagnetic dosimetry. For this purpose, non intrusive methods are used and several developments, such as the sparse grid or the suited coordinate system, are investigated to reduce the numerical costs. In order to evaluate their accuracy, the electromagnetic problem has been reduced

to a 2D problem so that the results can be compared with those obtained by the Monte Carlo method.

2 Some probability concepts 2.1 Expansion of random variables

Related Hilbert space

The manipulated random variables are supposed to be described in the vector space of random variables with finite variance that is denoted L 2 (Ω, P ), where Ω is the sample space and P a probability measure on Ω.

A continuous random variable X of this space is characterized by a probability density function f X . The mathematical expectation E [X] is then given by:

E [X] = +∞ -∞ xf X (x) dx. (1)
It can be shown that the space L 2 (Ω, P ) is a Hilbert space with the inner product and the norm defined as follow:

X, Y = E [XY ] and X = E [X 2 ]. (2)
Any random variable of L 2 (Ω, P ) can be expanded on the polynomial chaos -this is the spectral description -or be interpolated using Lagrange polynomials -this is the nodal description -.

Spectral description

Let us suppose that X is a random variable depending on a single random parameter. It can be expressed from a canonical random variable such as a normal or a uniform random variable [Schoutens, 2000]. Let us take for example a standard normal variable ξ. Then X can be decomposed as follow:

X = +∞ j=0 X j H j (ξ) , (3)
where {H j } +∞ j=1 denotes the sequence of Hermite polynomials. In particular one has H 0 = 1, H 1 = ξ and H 2 = ξ 2 -1. The Hermite polynomials form an orthogonal basis with respect to the inner product defined in (2):

E [H i H j ] = i! δ ij , ∀i, j ∈ N, (4)
where δ ij is equal to one if i = j and else is equal to zero.

Let us now suppose that X is a random variable depending on D random parameters. Then X can be expressed introducing as many standard normal variables ξ 1 , ξ 2 , ..., ξ D as there are random parameters:

X = +∞ j=0 X j ψ j (ξ 1 , ξ 2 , . . . , ξ D ) , (5)
where {ψ j } +∞ j=1 denotes the polynomial chaos. Those polynomials are built from a product of unidimensional Hermite polynomials:

ψ j (ξ 1 , ξ 2 , . . . , ξ D ) = D i=1 H αi (ξ i ) , (6)
where

D i=1
α i = d j with d j the total degree of the polynomial ψ j .

In the numerical implementation, the total degree of the polynomial chaos is limited to a value d. The dimension of the polynomial space is then D+d d and it grows fast with D or d.

Nodal description

In the univariate case, X can be interpolated from P collocation points {ξ p } P -1 p=0

using Lagrange polynomials:

X interp = P -1 j=0 X j L j (ξ) , (7)
where Lagrange's polynomials L j are defined by:

L j (ξ) = P -1 p=0 p =j ξ -ξ p ξ j -ξ p , (8)
in order to satisfy:

L j ξ i = δ ij , ∀i, j ∈ 0; P -1 . (9)
In the multivariate case, X can be interpolated from a product of unidimensional Lagrange polynomials.

Statistic information from determinist codes

Let us consider X the output random variable of the problem. For a better understanding, only the case of a single input random variable will be treated; the random space can then be described by a single normal variable ξ. The problem is to approximate the random variable X using the same code as for determinist computations. The methods presented here evaluate the approximate solution from few realizations of the input random variable ξ a priori determined.

Projection method

In the numerical implementation, the expansion given in ( 3) is truncated to an order P -1 so that the approximate solution is expressed as:

X appr = P -1 j=0 X j H j (ξ) . ( 10
)
The projection method is based on the orthogonality property of the Hermite polynomials [START_REF] Puig | Non-gaussian simulation using hermite polynomial expansion: convergences and algorithms[END_REF]. From (3), one finds:

X j = E [X H j ] E H 2 j , ∀j ∈ [0, P -1] . (11)
In ( 11), the difficulty is to evaluate the numerator:

E [X H j ] = +∞ -∞ X (ξ) H j (ξ) e -ξ 2 2 √ 2π dξ. (12)
The integral in ( 12) can be approximated by using the gaussian quadrature formula:

E [X H j ] ≈ P -1 p=0 w p X (ξ p ) H j (ξ p ) with w p = (P -1)! H ′ P (ξ p ) H P -1 (ξ p ) , (13)
where {ξ p } P -1 p=0 are the roots of the Hermite polynomials of order P . From the truncated expansion ( 10), the whole probabilistic information of X can be approximated. For example, the mean µ and the variance σ 2 are given by:

µ = E [X] = X 0 , σ 2 = E (X -µ) 2 ≈ E (X appr -µ) 2 = P -1 j=1 X 2 j j! . (14)

Least square minimization

The method is based on a least square minimization of the discrepancy between the input variable X and its truncated approximation X appr given in (10) [START_REF] Webster | Application of the Probabilistic Collocation Method for an Uncertainty Analysis of a Simple Ocean Model[END_REF]. The technique consists in minimizing the error between X and X appr at K points ξ k K k=1 expressed by:

err = K k=1 X ξ k -X appr ξ k 2 . ( 15
)
Minimizing err leads to the following linear system:

K k=1       H 0 H 0 • • • H 0 H P -1 . . . . . . . . . H 0 H P -1 • • • H P -1 H P -1       ξ=ξ k       X 0 . . . X P -1       = K k=1       XH 0 . . . XH P -1       ξ=ξ k . ( 16
)
Usually the points ξ k K k=1 are chosen to be the roots of an Hermite polynomial of degree equal or higher than P .

Collocation method

The collocation method is based on a nodal description [START_REF] Chauvière | Computational modeling of uncertainty in time-domain electromagnetics[END_REF]. From (7), it is required that the residual X (ξ) -X interp (ξ) is zero at the collocation points {ξ p } P -1 p=0 . The property reported in (9) immediately gives the value of X j :

X j = X ξ j . ( 17
)
It seems natural to choose the collocation points {ξ p } P -1 p=0 as the roots of the Hermite polynomial of order P since ξ is a normal variable.

As for the spectral description, the whole probabilist quantities can be extracted from the nodal approach. For example, the mean µ is given by:

µ ≈ E [X interp ] = P -1 j=0 X j +∞ -∞ L j (ξ) e -ξ 2 2 √ 2π dξ. (18)
The integral can be evaluated using the gaussian quadrature formula. One finds:

µ ≈ P -1 j=0 w j X j (19)
where w j are the weights associated to the roots of the Hermite polynomial of degree P given in (13).

Reduction of the number of calculations

When a lot of random variables are required for the problem, the methods described in the previous section become less efficient since more determinist calculations have to be performed. In order to reduce the numerical cost, several techniques can be applied.

Sparse grids

Sparse grids can be used to choose a restrictive number of nodes either with the projection method or with the collocation method. Let us consider first the case of the projection method. In the multivariate case, (12) involves the polynomial chaos defined in (5) and becomes:

E [X ψ j ] = R D (Xψ j ) (ξ 1 , • • • , ξ D ) e -(ξ 2 1 +...+ξ 2 D )/2 (2π) D/2 dξ 1 . . . dξ D . (20)
In order to evaluate (20), univariate quadrature rules can be extended to multiple dimensions by an appropriate tensor product rule:

E [X ψ j ] ≈ ξ1∈Pp 1 . . . ξ D ∈Pp D (Xψ j ) (ξ 1 , . . . , ξ D ) D m=1 w pm (ξ m ) = (V p1 ⊗ . . . ⊗ V p D ) (Xψ j ) (21)
where the set of nodes {P p1 , . . . , P p D } and weights {w p1 , . . . , w p D } are those implied by the underlying unidimensional quadrature rules {V p1 , . . . , V p D }. Consequently, the product rule evaluates the function Xψ j at the full grid of points P p1 ⊗ . . . ⊗ P p D . In D dimensions, the product rule therefore requires P D evaluations of the function Xψ j if the underlying univariate rules are all based on P nodes. While for example a gaussian quadrature rule exactly evaluates a univariate polynomial of order 7 with 4 function evaluations, the corresponding product rule with 10 dimensions requires 4 10 = 1 048 576 evaluations which is generally prohibitive.

Smolyak proposed an algorithm to evaluate integrals over several dimensions with a substantially smaller number of function evaluations than the product rule [START_REF] Xiu | High-order collocation methods for differential equations with random inputs[END_REF]. This is achieved by combining sequences of univariate rules with different accuracy levels. The set of nodes used by the sparse grids rule can be written as:

P D,k = k-1 q=k-D p ∈ N D q P p1 ⊗ . . . ⊗ P p D ( 22
)
where p = {p 1 , . . . , p D } and:

N D q = p ∈ N D : D i=1 p i = D + q (23)
when q ≥ 0 and N D q = ∅ when q < 0; for instance 22), the sparse grids rule combines tensor products of lower degree P i ⊗ P j such that 3 ≤ i + j ≤ 4. The nodes of these products as well as the resulting sparse grid are shown in the lower part of the figure. The integral over multiple dimensions given in (20) can then be approximated by:

N 2 2 = {[2, 2] , [1, 3] , [3, 1]}.
E [X ψ j ] ≈ k-1 q=k-D (-1) k-1-q D -1 k -1 -q p∈N D q (V p1 ⊗ . . . ⊗ V p D )(Xψ j ). (24)
Sparse grids can also be exploited with the collocation method: the selected nodes given in ( 22) are used to build a Lagrange polynomial basis.

Regression method

This technique is derived from the least square minimization. In ( 16), it appears that the linear system is built in a cumulative way: at each new iteration k, terms depending on ξ k are added to the matrix and to the second member which had been obtained in the previous iteration k -1. Consequently, it is possible to solve this matrix equation without performing the whole of the K

Univariate nodes

Product rule P 1 P 2 P 3 P 3 ⊗ P 3 computations. This is the aim of the regression method: the solution is calculated for each iteration k and the algorithm is stopped when the convergence is achieved [START_REF] Berveiller | Stochastic finite element: a non intrusive approach by regression[END_REF]. The points ξ k K k=1 are organized according to the greatest density probability.

P 1 ⊗ P 2 P 1 ⊗ P 3 P 2 ⊗ P 1 P 2 ⊗ P 2 P 3 ⊗ P 1                                                          Sparse grid

Choice of the coordinate system in the random space

The efficiency of probabilistic approaches depends actually on a judicious choice of the coordinate system in the random space. The expansion of random variables using the Hermite polynomials was at the very beginning a spectral representation of the fields built from normal variables [Wiener, 1938]. However, the convergence turns out to be slow when the random variables are not normal. Let us consider for example a random variable X characterized by a uniform law on the interval [X a , X b ]. The representation using a standard normal variable ξ G can be calculated analytically [START_REF] Field | On the accuracy of the polynomial chaos approximation[END_REF]:

X = X a + X b 2 H 0 (ξ G ) + +∞ j=0 (-1) j η j √ π 2 j (2j + 1)! X b -X a 2 H 2j+1 (ξ G ) , (25)
where

η j = |-1 × 1 × 3 × . . . × (2j -1)|.
However, using a uniform variable ξ U defined in the interval [-1, 1], the expansion on the Legendre polynomials is immediately given by:

X = X a + X b 2 Lg 0 (ξ U ) + X b -X a 2 Lg 1 (ξ U ) ( 26
)
where {Lg j } +∞ j=0 is the sequence of Legendre polynomials. In particular, one has Lg 0 = 1 and Lg 1 = ξ U . The Legendre polynomials form an orthogonal basis with respect to the inner product defined in (2).

Thus a suited choice of the coordinate system improves the convergence in the representation of the random variables and consequently leads to a better accuracy of the probabilistic methods. This approach has recently been developed through the generalized polynomial chaos: the polynomial basis is built according to the nature of the distribution of random variables [START_REF] Xiu | The Wiener-Askey polynomial chaos for stochastic differential equations[END_REF].

3 Application in electromagnetic dosimetry

Description of the problem

Electromagnetic dosimetry deals with the problem of the interaction between the human body and the electromagnetic field in the low frequency range or the high frequency range. The methodology described here may be applied in low frequency problem but this is not considered in the present paper. In high frequency, the problem concerns the coupling between the human body and the electromagnetic waves radiated from a cellphone or an antenna. This issue may become very complex if a realistic scene is modeled. In this paper, the problem is reduced to a 2D geometry so that the Monte Carlo method can be applied for comparison. The geometry of the problem is described in Figure 2; it could be the leg of a human adult that is modeled by an infinite cylinder with different layers to take into account the presence of different biological tissues; three layers characterized by different permittivities and conductivities are introduced to describe bone, muscle and fat. The structure is illuminated by an incident plane wave or by an infinitely long filament source in free space.

Thus the electromagnetic problem is invariant following the direction of the cylinder axis and a symmetry appears. To solve numerically this problem, the finite element method has been implemented with second order absorbing boundary conditions allowing the scattering waves to radiate out of the domain [START_REF] Bayliss | Radiation boundary conditions for wave-like equations[END_REF]]. The frequency is set about to 1.2 GHz and 3 000 to 4 000 elements are used for the discretization.

The effects of the electromagnetic waves in the body are quantified by calculating the SAR ; it measures the quantity of electromagnetic power absorbed by 1 kg of tissue:

SAR = 1 2 σE 2 ρ (W/kg) ( 27
)
where σ is the conductivity of the tissue, ρ is the mass density of the tissue and E the amplitude of the electric field. In this paper, we are interested in the maximal SAR locally absorbed in the body.

In order to properly describe the reality, the variability that appears in the properties of the tissues -permittivity and conductivity -but also in the morphology -thickness of the tissues -or in the characteristics of the source -frequency and position of the punctual source -has to be introduced. The problem consists then in evaluating how those uncertainties affect the maximal SAR in the leg.

Statistic calculations using the Monte Carlo method

To calculate the statistic response of the maximal SAR, the Monte Carlo method can be applied. Using a given number of samples, one calculates the maximal value of SAR for each realization. The estimated mean µ SAR and variance σ 2 SAR can then be computed as follows:

µ SAR = 1 K K k=1 SAR k and σ 2 SAR = 1 K K k=1 (SAR k -µ SAR ) 2 , ( 28
)
where K is the total number of samples and {SAR k } K k=1 are the values of the maximal SAR for the K realizations.

In the first example treated in this paper, an incident transverse electric wave whose electric field has an amplitude E = 1 Vm -1 illuminates the leg. Some randomness is introduced in the properties of the tissues. More precisely, the permittivity and the conductivity of the three kinds of tissues are considered to be random variables with lognormal distributions. The mean values of these parameters are obtained from [Council, ] -see also [C. Gabriel and E.Corthout, 1996] -. The variance values have been chosen arbitrarily in order to compare the robustness of the different methods. The parameters are reported in Table 1.

Figure 3 shows an illustration of the electric field and SAR computed using the mean values given in Table 1.

The repartition of the maximal SAR computed from 10 000 samples is given in Figure 4. The mean and the variance estimated from those data are equal to µ SAR = 5.19 10 -5 Wkg -1 and σ 2 SAR = 1.31 10 Table 1.

Probabilistic calculations using a spectral description

The space of random variables is built from the polynomial chaos made of six normal variables to describe the six uncertain tissue parameters. The total degree of the polynomials is first limited to d = 2; this leads to consider 28 polynomials. The total degree d is too low to accurately describe the lognormal laws but it already implies 3 6 = 729 determinist calculations if spectral methods are applied as they are initially proposed. The results concerning the mean are close to those obtained with the Monte Carlo method -the relative difference is Figure 4: repartition of the maximal SAR calculated from 10 000 samples.

less than 1% -but there is a difference concerning the variance: roughly 17% for the projection method and 12% for the least square method -see Table 2 -. In order to refine the result, the total degree d is increased to 4; 210 polynomials are then handled. However, there would be a priori 5 6 = 15 625 determinist calculations to make, which goes beyond the number of calculations realized using the Monte Carlo method.

To reduce this number using the projection method, sparse grids have been experimented. The nodes for the sequence of univariate quadrature rules P 1 , P 2 and P 3 are set to be the roots of Hermite polynomials of degree 1, 3 and 5. This choice is such that zero is a root shared by the three sequences; consequently, the construction of the Smolyak grid leads to a lower number of nodes. In this case, the sparse grid P 6,3 is composed of 97 nodes instead of 15 625 nodes for the product rule. But the variance calculated using this grid is far from the expected value; this is due to the fact that Smolyak algorithm guaranties a small error when the degree of the integrand Xψ in ( 20) is not too large [START_REF] Xiu | High-order collocation methods for differential equations with random inputs[END_REF]. In the present case, the degree of X is a priori infinite; however, the weight of higher degree components decreases more and less fast following the non linear dependence on the input random variables.

To take into account higher degree components in integral computations, the sparse grid has to be extended. For example, a fourth sequence P 4 composed with the roots of the Hermite polynomial of degree 7 can be added. To save numerical cost using the least square approach, the regression method can be applied by increasing progressively the numbers of nodes. The analysis reported on Figure 5 shows that the value of the variance converges when K is close to 800 and the result is not so far from the one evaluated using the Monte Carlo method -the relative difference is approximately 2%; see Table 2 -.

(a) estimated mean µ SAR against the number of nodes K.

(b) estimated variance σ 2 SAR agings the number of nodes K.

Figure 5: study of convergence using the regression method.

Probabilistic calculations using a nodal description

A Lagrangian basis is first built from the product rule using the roots of the Hermite polynomial of degree 3; that is to say the basis is composed of 3 6 = 729 4. roots of the Legendre polynomial of degree 2; that is to say the basis is composed using 2 5 = 32 nodes. Even if there are less nodes, the results are closer to the ones obtained by the Monte Carlo method: the relative difference is less than 1% on the mean and approximately 2% on the variance -see Probabilistic methods enable to compute not only the mean and the variance but also higher order moments or the probability density function. Figure 7 shows a comparison of the probability density function of maximal SAR estimated from Monte Carlo and collocation methods. The curve obtained with the collocation methods is smoother than the curve given by the Monte Carlo method. The reason is that, when using the Monte Carlo method, the probability density function is determined only from 10 000 samples which is not enough to properly describe the probability density function. On the contrary, when using collocation method, the probability density function is plotted from the nodal expansion (7) ; a larger number of points can be calculated without spending a lot of time.

Conclusion

In this paper, the feasibility in using probabilistic methods to evaluate the stochastic response in a 2D electromagnetic dosimetry problem is demonstrated.

The different approaches experimented -projection, least square minimization and collocation method -give accurate results with only a few hundreds of calculations while the Monte Carlo method involves 10 000 samples. However, the collocation method using sparse grid seems to be the most efficient method; but one has to be wise: the accuracy depends on the specificities of the problem treated, mainly the number of random input parameters and the non linear dependence on the random input variables. To ensure the validity of the computed results, the only solution is to make a convergence study by increasing the number of nodes with the collocation method or the number of polynomials with the spectral method. The reduction of the numerical cost is essential in the perspective of studying 3D realistic situations. This issue will be the next step of this work. The difficulties to overcome concern not only numerical aspects -saving time consumption is obviously more crucial in a 3D problem than in the 2D case -but also the modelling of the variability in the human body -the choice of realistic laws for random variables or the description of the uncertainty in the morphology remain open problems -.

  Figure 1 shows the construction of the sparse grid by the Smolyak rule in a simple example with D = 2 and k = 3. The nodes for a sequence of univariate quadrature rules P 1 , P 2 and P 3 are shown in the top of the figure. The product rule P 3 ⊗ P 3 evaluates the function at all two-dimensional combinations of nodes prescribed by P 3 which are shown in the upper right part of the figure. As expressed in (

Figure 1 :

 1 Figure 1: an example of sparse grid.

  Figure 2: the 2D geometry problem.

Figure 3 :

 3 Figure3: electric field and SAR computed for the first example with the mean values of the parameters given in Table1.

Figure 6 :

 6 Figure6: electric field and SAR computed for the second example with the mean values of the parameters given in Table4.

Figure 7 :

 7 Figure 7: probability density function computed from collocation methoddashed curve -and Monte Carlo method -continuous curve -.

Table 1 :

 1 -10 W 2 kg -2 . parameters of the different lognormal laws.

	Quantity	Mean	Variance
	Relative permittivity of bone	12.2	0.6
	Conductivity of bone (Sm -1 )	0.185	0.030
	Relative permittivity of muscle 54.4	1.0
	Conductivity of muscle (Sm -1 )	1.055	0.100
	Relative permittivity of fat	5.41	0.04
	Conductivity of fat (Sm -1 )	0.0580 0.0008

  The sparse grid P 6,4 then counts 533 nodes. The computed results are more accurate; the variance is closer to the one calculated with the Monte Carlo method -the relative difference is roughly 8%; see Table 2 -.

Table 5

 5

	-.

Table 5 :

 5 summary of the results for the second example.

tion; Smolyak algorithm can be implemented using other sequences than those described in Subsection 3.3. For example, the nodes for the sequence of univariate quadrature rules P 1 , P 2 and P 3 can be chosen to be the roots of Hermite polynomials of degree 1, 3 and 9. Then the sparse grid P 6,3 is composed of 121 nodes. The variance calculated using this grid is closer to the value obtained with the Monte Carlo method -the relative difference is approximately 1%; see Table 3: summary of the results for the first example using nodal methods.

Other kind of distributions

In the second example, the source is an infinitely long filament of constant current I = 1 A ; this implies that the electromagnetic problem is described in the transverse magnetic mode. The position and the frequency of the source as well as the dimensions of the three tissues are supposed to be random variables with uniform distributions. The different parameters are reported in Table 4. Table 4: parameters of the different uniform laws.

Figure 6 shows an illustration of the electric field and SAR computed using mean values given in Table 4.

The statistic response of the maximal SAR has been calculated using Monte Carlo method from 10 000 samples. The estimated mean and the variance are µ SAR = 88.52 Wkg -1 and σ 2 SAR = 255.65 W 2 kg -2 . As for probabilistic methods, polynomial basis have been built in two different ways using either normal variables or uniform variables. Let us first consider the coordinate system composed by standard normal variables. The collocation method is applied. A Lagrangian basis is built from the product rule using the roots of the Hermite polynomial of degree 3; that is to say the basis is composed using 3 5 = 243 nodes.

The results are not accurate: the difference with the Monte Carlo method is roughly 1% on the mean and 7% on the variance -see Table 5 -. Let us now consider the coordinate system composed with uniform variables defined in the interval [-1, 1]. A Lagrangian basis is built from the product rule using the


Tiago Cardoso

Luis M Camarinha-Matos

Pro-Active Asset Entities in Collaborative Networks

Keywords: Collaborative Networks, Assets, Virtual Organization Breeding Environment, Professional Virtual Community, Interoperability

In a Collaborative Network (CN) scenario it would be desirable that CN members could be able to start collaboration within their Virtual Organization Breeding Environments or Professional Virtual Communities in a short time-frame, whenever a new Business Opportunity appears. As a contribution towards such dynamic scenario, this paper proposes the concepts of Assets Entity, Pro-Active Assets Entity and Integrated Market of Pro-Active Assets Entities. The first concept can be used to model attributes and all functional and intelligent content elements a CN member can provide (its Assets). The second is responsible for the representation and promotion of an Assets Entity. The later offers an adaptation of the market place concept where each Pro-Active Assets Entity registers itself, brokers post their needs and try to find the best providers, through a bidding and negotiation process.

Introduction

The area of Collaborative Networks (CNs) has consolidated its conceptual baseline, namely in terms of Reference Modeling, as well as Methods and Tools, identifying distinct perspectives of this scientific discipline, as presented in [START_REF] Camarinha-Matos | Collaborative Networks: Reference Modeling[END_REF][START_REF]Methods and Tools for Collaborative Networked Organizations[END_REF]. Nevertheless, important critical issues remain regarding the fast creation of such organizations.

Whenever a new Business Opportunity (BO) appears, the CN members, either companies, other organizations and / or professionals; should be able to start collaboration, within their Virtual Organization Breeding Environment (VBE) or Professional Virtual Community (PVC), in a short time-frame. In the typical, case one of the CN members -the initiator, or a broker, identifies the needed competencies and takes care of selecting all the needed CN members in order to create a Virtual Organization (VO) that will satisfy the requirements of the BO.

From the CN members' perspective, when they join this organizational structure, they are already willing to collaborate, adding their value to Virtual Organizations. Two main forms can be identified for this value: 1 -through the provision of services; 2 -through the provision of Intelligent Content. Depending on the economic area of the CN, different examples can be found for these two kinds of Assets: an example of Service Asset can be an assembling process or a consultancy service; an example of Intelligent Content Asset can be a business Process Model, a CAD document or even a Multimedia cultural documentary on a given city, for the case of a tourism CN.

Nevertheless, as the CN evolves, the number of members gets bigger and the chances of an Asset from a specific CN member to be chosen are reduced. Moreover, current approaches, lack mainly in two perspectives: 1. Passive Entities -Web Services, or content available through WebPages, are passive entities in the sense they stay still waiting for a client initiative instead of behaving in an auto-initiative manner in order to look up for new Business Opportunities and pursue negotiations in order to achieve commitments. 2. No Aggregation -The Assets a CN member can provide are treated in an independent form -no aggregation is made. If, for example, a Business Opportunity BO1 can be satisfied by 5 distinct assets (A1 ...A5), taking into account that there may be CN members able to provide more than one of the needed assets, the selection of CN members to form a VO that will satisfy BO1 can range from 1 up to 5 distinct CN members. The reduction of the number of CN members would reduce the needed agreements and potentially improve the work flow but, with current approaches, this reduction remains a coincidence.

Given this context, the following question arises: "Is it possible to create a new conceptual framework able to model the value of CN members within the organization, composed of new constructs that behave in a social and auto-initiative manner, representing and promoting all the elements that CN member can provide, in order to improve the tackled Business Opportunities, as well as the business success chances?" This paper introduces four concepts aligned with this research question:

1. Assets -This concept is the abstraction of distinct kinds of elements a CN member can provide. With this "uniformization", as a base modeling mechanism, the two kinds of assets identified can be treated in the same way whenever a model is created for the formation of a Virtual Organization. For example, the assembling service and some needed CAD document are two assets that can be treated as building blocks in the corresponding VO model -one is a Service and the other is an Intelligent Content. 2. Asset Entities (AE) -The aggregation of all the Assets a CN member provides, improving the possibilities to reduce the number of CN members needed for the formation of a VO, as well as the corresponding negotiation effort. 3. Pro-Active Asset Entities (PAE) -Here, auto-initiative is added to the AE concept through the introduction of behavior elements. This concept is inspired in the Multi-Agent Systems (MAS) applied to the AE concept within a CN context. The main objective is to represent an AE and lookup for Business Opportunities where one or more of the represented Assets can be included. 4. Integrated Market (IM) -Finally, in the context of a CN, the concept of an Integrated Market where all the PAEs register themselves and where brokers model and post client's needs -the Business Opportunities (BO). This structure will be the place where PAEs look up for BOs where they can match the Assets they represent. Whenever a match happens, the PAE is responsible for pursuing the needed activities to achieve an agreement, in a bidding-like negotiation process. The scope of an IM can be the one of a VBE (or PVC).

Contribution to Technological Innovation

Information and Communication Technology evolution is moving towards autonomy of existing systems and devices, giving them the capacity to observe the surrounding environment, cooperate with neighbors and behave independent of human interaction. Intelligent Manufacturing, where machines provide their functionality and behave in an auto-initiative basis towards collaborative work, is an example of this reality.

The Internet of Things, where sensorial ability, along with processing and storage, in an auto-initiative social behavior of The Things, is another example.

The contribution of this paper to technological innovation is made through the introduction of four concepts aligned with these trends. These concepts support a development framework aiming the creation of collaborative platforms through an active representation and promotion of CN member's Assets. This representation provides built-in functionality to carry out tasks like business opportunity search, bidding and negotiation, all in an auto-initiative semi-automated basis.

Related Work

The proposal of Pro-Active Assets Entity to model Enterprises and Free-lancers assets within Collaborative Networks is mainly inspired in Service Oriented Computing (SOC) and Multi-agent Systems (MAS). Baseline Concepts and Definitions -Web Services in particular and Service Oriented Computing in general introduced a new abstraction paradigm in software development facilitating inter-enterprises' collaboration. This approach evolved through three main phases that can be identified by their main keywords: Publishwhen enterprises became able to "wrap" some functionality and wait for worldwide potential clients to call them; Register / Find -when UDDI registries appeared and web-services became "findable" and finally Compose -when the creation of "Value Added Services" became possible, as a result of the integration of simpler services through mechanisms like workflow or technologies like BPEL4WS. This paradigm presented "a design principle intended for the construction of reliable distributed systems that deliver functionality as a service, with an additional emphasis on loose coupling between interacting services" [START_REF] Srinivasan | An overview of service-oriented architecture, web services and grid computing[END_REF].

Other initiatives, like OSGi, coming from software components research area, provide standard interoperability functionality to compose and change composition of services dynamically. The framework proposed by OSGi Alliance, has already other proposals built on top of it, like Apache FELIX, providing the interoperability means to integrate distinct applications / bundles.

Nevertheless, the Web-Service approach is limited in the sense that services are entities that stay still waiting for a clients' call. Nothing is done by the Web Services themselves to "attract" clients or make "promotions", for example. Furthermore, some authors defend that Web-Services will evolve to big groups, or "Service Parks", "owned" by big players who define the groups' rules [START_REF] Petrie | Service Agents and Virtual Enterprises: A Survey[END_REF]. It is not clear yet if this will become the reality, but if it does Small and Medium Enterprises may see their possibility of adoption of this paradigm restricted / subjugated to major players' rules -a potential near-future limitation of this paradigm. However, the organization of SMEs as a long term cooperation alliance (such as a VBE or PVC) opens the possibility of creating "service parks" or "service markets" within the alliance.

Recently, in [START_REF] Franco | Modeling extended manufacturing processes with service oriented entities[END_REF][START_REF] Franco | MANBREE: Supporting Structural and Functional CNO Modeling With Service-Based Entities[END_REF] the concept of Service Entities (SE) is proposed "as constructs that may help structural and functional CNO modeling". Here, a group of Web-Services can belong to one SE and be enriched with attributes towards better interoperability.

On the other hand, the usage of Multi-agent Systems, as a second inspiration area, represents "a promising approach to both model and implement the complex supporting infrastructures required for virtual enterprises and related emerging organizations" [START_REF] Camarinha-Matos | Multi-Agent Systems in Virtual Enterprises[END_REF]. This work points out the main limitation of this approach as the lack on robustness of current solutions in Wide Area Networks, like the Internet.

Nevertheless, the agents approach presents promising characteristics for this domain. In [START_REF] Wooldridge | Agent-based computing[END_REF], Wooldridge defines the top 4 Software Agents' properties that constitute important inspiration points for the PAE architecture: autonomy (agents operate without the direct intervention of human or others and have control over their actions and internal state), social ability (agents are able to cooperate with humans or other agents in order to achieve their tasks), reactivity (agents perceive their environment and respond in a timely fashion to changes that occur in it) and proactiveness (agents do not simply act in response to their environment, they are able to exhibit goal-directed behavior by taking the initiative).

In the case some PAE interaction is needed, typically the case when a single Asset cannot apply to a business opportunity by itself, the production of Value-Added-Assets (VAA) can take place, following workflow interaction patterns between distinct PAEs. Here, inspiration ideas have been retrieved from Multi-agent Systems (MAS), through the existing interaction between distinct Software Agents. [START_REF] Rabelo | Advanced Collaborative Business ICT Infrastructures[END_REF].

This proposal also extends ideas from the evolution of the Semantic Web, namely the Intelligent Content (I-Content) concept, defined as "information content with explicit semantic description through which machines and people can share meaning and value" [11]. Although the I-Content concept adds semantic to content, it still remains static content. Pro-Active Assets Entity extends the I-Content concept adding pro-activeness and auto-initiative behaviors.

Concerning the little interaction between MAS and SOC research communities; although this is a reality, some initiatives start to connect them. One example is a new trend on the Semantic Web with the introduction of Pro-Activity information in the description of Web Services. Nevertheless, the few initiatives addressing this approach mainly exist in the MAS research area.

In the case of the "Proactivity Layer of the Smart Resource Platform" proposed in [START_REF] Khriyenko | Proactivity Layer of the Smart Resource in Semantic Web[END_REF] or the "Proactive Self-Maintained Resources", described in [START_REF] Terziyan | SmartResource -Proactive Self-Maintained Resources in Semantic Web: Lessons Learned[END_REF], Semantic Web Languages are used, illustrating this benefit applied to MAS. In both cases, the "agentification" of resources, or smart-devices, is made through this approach. In the first case, the objective was their integration. In the second case, the aim was the definition of an ontology-driven rules' approach for modeling context-sensitive agent behavior.

Web Services and Agent Technologies on Collaborative Networks -In [START_REF] Petrie | Service Agents and Virtual Enterprises: A Survey[END_REF], an early proposal was made, defending that "as Web Services become more sophisticated, they effectively will become software agents themselves". The authors defend that WSDL and UDDI are insufficient to support service discovery and composition, mainly because of the lack on semantics. The authors argue that importing ideas from Multi-Agent Systems would provide the means to create such sophisticated "Service Agents", needed in the formation of dynamic Virtual Enterprises. This work also points out research directions, like the combination of DAML-S and UDDI approaches.

Another example of work integrating the two is presented in [START_REF] Ramirez | Multi-Agent Systems Integration in Enterprise Environments Using Web Services[END_REF]. There, the authors propose an "embedded Web service architecture (EWSA), inspired in the Software Components' research area, which allows agent-based applications to be integrated into enterprise application environments using Web Services". The main objective of this solution is the reduction of time-to-market of the agent-based applications. Nevertheless, EWSA together with the proposal made in [START_REF] Franco | Modeling extended manufacturing processes with service oriented entities[END_REF] mainly target the formation and evolution life cycle phases of an organization like a CN. Furthermore, these two proposals focus on functional perspectives of enterprises and lack on other kinds of Assets. For example, an enterprise that sells a business process model or an individual that provides touristic multimedia content on European cities, are not covered by any of these approaches.

Research Contribution and Innovation

Given the assumption of Asset as: anything an enterprise, organization or a freelancer member of a CN can provide and that can be represented / triggered by a software component; and the assumption of Value Added Asset as: an asset that results from the composition of simpler Assets, or other VAA; the concept of Service Entity, presented in [START_REF] Franco | MANBREE: Supporting Structural and Functional CNO Modeling With Service-Based Entities[END_REF], can be extended as Assets Entity -a concept that includes the Assets an entity can provide, as well as a set of Attributes from that entity (an enterprise, another organization or a free-lancer member of a CN).

Definition 1 (Assets Entity (AE)) -is a tuple AE=(AT, AS), where:

• AT = {attr i | i ∈ N} -the set of Attributes of the corresponding entity.

• AS = {a i | i ∈ N} -the set of Assets the corresponding entity can provide.

Within a context of an increasing number of AEs, new mechanisms to "promote" each AE become useful and needed. The concept of Pro-Active Assets Entity is introduced as a software component responsible for the representation and promotion of an AE, looking for Business Opportunities and behaving in a social manner for the provision of all the Assets of the corresponding Entity. The PAE is defined as follows:

Definition 2 (Pro-Active Assets Entity (PAE)) -is a tuple PAE=(AE, PS, BF), where:

• AE -The Assets Entity represented and promoted by PAE;

• PS = { p 1 , p 2 , p 3 }, a set of 3 Properties defined as follows:

o p 1 (Pro-activity) -enabling the PAE to look for Business Opportunities (BOs); o p 2 (Negotiation-ability) -enabling the PAE to make bids for discovered BOs in a semi-automated manner, as well as carry out negotiation processes in order to improve previously made bids;

o p 3 (Social-ability) -enabling an interaction with other PAEs to support the creation of VOs through IMPs, whenever Asset composition means are needed to apply to a given BO.

• BF={f g,i | g ∈ {1 -General, 2 -I-Content, 3 -Service}, i ∈ N} -The Built-In
Functionality from the PAE, divided into three groups whether the functionality is specific to one of the two kinds of assets (I-Content or Service) or it is common to any kind of asset, as exemplified in Table 1. From a provider's perspective, a PAE will work like a promotion helper for its assets, finding Business Opportunities, performing negotiation, and eventually promotions, towards the inclusion of the represented asset in VOs.

Finally, the concept of Integrated Market of PAEs is the place where PAEs register themselves, typically one IMP per VBE / PVC. As an IMP might have a large number of PAEs registered, finding potential compatible Assets within that space is an easier process and improves all the pre-collaboration negotiation effort, as well as guarantees ICT compatibility. These factors improve the possibility of a collaboration to start in a short time-frame window. Furthermore, the IMP performs monitoring and certification functionality on the registered PAEs in order to provide accurate information to support brokers' choices.

Definition 3 (Integrated Market of Pro-Active Assets Entities (IMP))

-is a tuple IMP = (PE, BO, PM, CR, BF), where: PE={pae i | i ∈ N} -the set of registered Pro-Active Assets Entities, BO={bo i | i ∈ N} -the set of announced business opportunities, PM={pm i,j | (∀ pm i,j ∃ pae i ∈ PE ∃ bo j ∈ BO)} -a set with Performance Measurement (PM) information, CR={cae i | (∀ cae i ∃ pae i ∈ PE)} -a set with Certification information on Assets Entities and, BF={ f 1 , f 2 , f 3 ,f 4 } -4 Built-In Functionality, where: f 1 (PAE Registration) -enabling distinct PAEs to register themselves, as well as the set of assets from the entity they represent; f 2 (BO Posting) -enabling brokers to post their needs / BOs; f 3 (Performance Measurement) -providing automated PAE performance measuring mechanisms, as well as enabling brokers to grade their performance, in order to increase the information on every registered PAE. As a result, more accurate data becomes available for future CN members selection processes. f 4 (Certification) -based on PM info, an IMP can certify some PAE's quality (introducing the notion of conspicuity associated to a Pro-Active Assets Entity).

From the broker's perspective an IMP is a "place" where he can specify some need and wait for distinct bids or proposals. There, instead of asking for the catalogue of some service or content providers, the broker only has to post the need, or Business Opportunity. Furthermore, the IMP concept extends the base ideas from UDDI registry systems, as well as blackboard architectures. The former provides the means needed to give registration functionality for PAEs and the later provides the means needed for Brokers to post their needs -the Business Opportunities.

Process / Motivating Scenario -One of the main contributions of the usage of the proposed concepts come from the changes in the interaction between CN members and brokers that only start the process specifying a need -the Business Opportunity. After that, the initiative goes to the other side for a specified amount of time where distinct PAEs submit their BIDs. Figure 1 shows a simplified BPMN diagram representing the interaction process between a broker and PAEs through the IMP. This simplified version of this process is divided into the 5 Tasks T 1 through T 5 . T 1 (Broker Need Specification) -The VBE / PVC broker divides the BO in simple Asset needs posting them in the IMP. For example "Enterprise A needs a watch production service" or "Person X wants to go on a tour in the country Y and is looking for multimedia cultural content concerning city K, as well as accommodation and travelling services". In both cases a composed asset can be considered and the broker that gathers this BO forms the VO that will provide a "Value Added Asset". T 2 (BO Analysis) -PAEs gathers BO info, analyze it and decide whether or not to bid. For the first example, PAEs from enterprises with a watch assembling service, for example, analyze the posts while in the second example, PAEs of tourism agents or free-lancers with touristic I-Content from the desired city, perform the same actions. T 3 (Bidding) -Each Pro-Active Assets Entity that finds the posting suitable make a bid and sends it to the broker. T 4 (Best Bid Choice / START) -The broker compares the received bids and chooses the best one. After the choice is made, the selected PAE is notified and the task execution or I-Content transfer can start.

• This choice can go through longer negotiation process between brokers and PAEs, like logistic details definition, for the first example. T 5 (Asset Provision End) -Finally, the process is concluded with the service end or the content provision finishing.

Discussion of Results and Critical View

Software development history can be divided into two major groups of distinct Development Paradigms (DP): Local-DPs and Distributed-DPs. The evolution from the Local-DPs to the Distributed-DPs' group raised some interoperability challenges concerning the parts to be integrated in the distributed system, namelly:

• the heterogeneity of the environment each part runs on,

• the autonomy of each part and • the existence of distinct owners of the parts of a system intended to be integrated. Nevertheless, it is possible to compare some of the major DPs of each group, find similarities on their main constructs and foresee trends.

In the Local-DPs programming, one of the first major DPs was the Functional Programming. There the main building blocks or constructs were the functions or methods. Web-Services, in the Distributed-DPs' group, play a similar role, for the distributed environment. In both cases, the building block is a function or method.

The next major DP, in the Local-DPs, was Object Oriented Programming (OOP) that came in the 60s with Simula. Here, the main building blocks were the Classes of Objects with many methods within a single construct, together with Attributes to store information concerning the modeling elements -the objects. Simula also added some useful features like the Encapsulation, Inheritance and the Polymorphism. Again, a parallel can be established with the Distributed-DPs' group. In 2008 the Service Entities (SE), proposed in [START_REF] Franco | Modeling extended manufacturing processes with service oriented entities[END_REF][START_REF] Franco | MANBREE: Supporting Structural and Functional CNO Modeling With Service-Based Entities[END_REF], play a similar role, putting together many webservices with attributes within a single construct -the Service Entities. This time, the keywords in the software development were Functions / Methods and Attributes.

More or less at the same time as the OOP, the Multi-Threaded Programming (MTP) appeared with the corresponding mechanisms for communication and synchronization among distinct processes, needed for parallel execution. These two DPs (OOP and MTP) opened the way for the Multi-Agent Systems (MAS). Here, the main building blocks were Software Agents and the new construct was their behavior, other than their autonomy, social ability, reactivity and pro-activeness, as referred in section 3.1. In the Distributed-DPs' group, little before the SEs, technologies like OWL-S (former DAML-S) introduced the semantic constructs needed to "facilitate the automation of Web service tasks including automated Web service discovery, execution, interoperation, composition and execution monitoring".

Conclusions and Future Work

In this paper a new approach for modeling CN member's Assets was presented -Assets Entities, Pro-Active Assets Entities and Integrated Markets of Pro-Active Assets Entities. The proposal is based on the concept of Asset as something an enterprise, another organization or an individual can provide. This concept extends the functional abilities covered by current approaches, like web-services, to any other kind of Intelligent Content, like a Process Model, for example. On top of this Asset concept, the concept of Assets Entity provides a single construct able to put together all the Attributes and Assets of an Entity (member of a CN). The concept of Pro-Active Assets Entity acts like an envelope that carries the Assets Entity, providing the means to represent it, finding suitable Business Opportunities for it. This is done through the introduction of the Integrated Markets. There, the PAEs register themselves and brokers become able to post some needs -the Business Opportunities. The Pro-Active Assets Entities, always looking for suitable Business Opportunities, check for a matching and if the result is positive start a Bidding Process. Finally, the client chooses the BID that best fits the needs.

In section 5, a simple analysis of the evolution of the trends on Development Paradigms shows that this proposal is aligned with the identified directions. In fact, Auto-Initiative and Autonomy are two important keywords for systems development.

The ongoing work aimed at the development of a prototype with the base proactiveness and auto-initiative mechanisms. The next phase of the work will target the evaluation of this proposal framework in Collaborative Networks and extend the mode to cover those cases in which no PAE submits a bid to a given Business Opportunity. In this last case, the broker needs to take some other initiatives, namely to convince some PAEs to change their current priorities or alternatively changing BO requirements.

Fig. 1 .

 1 Fig. 1. Broker / PAE Interaction Bidding Process trough IMP.

  [15] Establishing a relation between the Local-DPs evolution and the actual reality in the Distributed-DPs, the SE and OWL-S open now a new way for the proposal of solutions that add auto-initiative and behavior constructs to the Functions / Methods and Data Fields / Attributes ones.

Figure 2

 2 synthesizes this comparison exercise on the evolution of Local and Distributed Development Paradigms. The concepts presented in this paper provide a proposal aligned with these trends. The Pro-Active Assets Entity concept represents all the Assets form an enterprise or professional behaving in an auto-initiative manner, looking for business opportunities in Integrated Markets.

Fig. 2 .

 2 Fig. 2. From Functional Programming to Pro-Active Assets.

Table 1 .

 1 Example of Pro-Active Assets Entity built-in functionality.

	f 1,1 -Find Correlated PAEs
	f 1,2 -Look up in IMPs for BOs
	f 1,3 -BID on BOs
	f 1,4 -Promote Asset
	f 1,5 -Negotiate Asset for BO
	f 2,1 -Open / Show I-Content
	f 2,2 -Extract Info / Knowledge from I-Content
	f 3,1 -Call / Execute / Call-Back the service Asset
	f 3,2 -Create / Edit VAA.


Alysson Bolognesi Prado
email: aprado@ic.unicamp.br

Maria Cecilia
email: cecilia@ic.unicamp.br

Calani Baranauskas

An X-Ray of ICISO Portrayed Through the Lens of Actor-Network Theory

Keywords: Scientific communities, Actor-Network Theory, ICISO

Any scientific community relies on a shared set of concepts and methods that, when well established and known, can guide its members to better solving research problems. Actor-Network Theory states that human and non-human entities -such as scientific literature -work together when a scientific fact is constructed. We applied this viewpoint as social network analysis technique, to assess the bibliographical data from the last two ICISO proceedings. The resulting graphs highlighted persons and publications acting as points of convergence for each conference edition. These findings lead to a recurring structure cored on Ronald Stamper and his publications, and the book Semiotics in Information Systems Engineering.

Introduction

Kuhn [START_REF] Kuhn | The structure of scientific revolutions[END_REF] defines a scientific community as a group of persons who study a specific subject sharing a common paradigm, that is, a set of methods, values, language, principles and concepts. This shared viewpoint allows the proposition of problems and the acceptance of the respective solutions by the members of the community. Scientific literature plays a twofold role, either providing for the novice the stabilized facts widely accepted by the community, and communicating the newer theories, under development by the experts [START_REF] Brorson | Stabilizing and Changing Phenomenal Worlds: Ludwik Fleck and Thomas Kuhn on Scientific Literature[END_REF]. The actual paradigm is formalized, spread out and evolved through the literature.

As part of his work on Social Studies of Science and Technology, Latour [START_REF] Latour | Science in Action: How to Follow Scientists and Engineers through Society[END_REF] proposes, as a methodological principle, that the study of science should not be restricted to the analysis of its final products; instead, it should start from the discussions that evolve to the inception and refinement of such outcomes. By observing the science while it is produced, it is possible to witness the involved entities acting upon one another, making possible to understand how the resultant of the combined interests and possibilities shapes the path towards scientific discoveries.

The International Conference on Informatics and Semiotics in Organizations -ICISO -is the most traditional event to reunite periodically the community devoted to the research on Organizational Semiotics, reaching its 17 th edition in 2016. It is also part of a series of international conferences aiming to study the role and effects of information and communication in organizational contexts.

In this work, our goal is to provide an understanding of the current structure of the Organizational Semiotics community as expressed through the papers published in the last two editions of ICISO. We draw upon methods of Social Studies of Science and Technology to grasp the broader social context in which the more technical and methodical work of researchers is immersed. We expect to contribute to the selfknowledge about how the community is arranged, in an alternative way, complementary to common widely available scientometrics.

This paper is organized as follows: Section 2 presents the chosen theoretical framework to support scrutinizing the structure of associations that compose ICISO. In Section 3 we detail the data sources and methodological steps applied, followed by Section 4 presenting and discussing the results of such procedure. In Section 5 we discuss the findings, and concluding in Section 6.

Theoretical Background

The study of science-making from the viewpoint of the sociology is the root of the Actor-Network Theory (ANT) a theoretical and methodological framework that understands social phenomena as the result of entities, or actors, capable of influencing the behavior of the others; these actors are tied together by relationships of mutual benefit, constituting a network. Moreover, ANT claims that the role of actors in social phenomena is not restricted to humans, but can also be played by nonhumans.

One of the non-human participants of the collaborative construction of scientific facts is the scientific literature. Using another piece of literature in a paper may help building the adopted theoretical background, showing related results for the sake of positive or negative comparison, manifesting affiliation to a certain group or trend of opinion, or expressing the acceptance of a previous result taking it for granted and using it for further research. As an allegation of one publication is accepted by others in the form of citations, it progressively gains the status of scientific fact.

Only when it becomes tacit knowledge, the citation is no longer required. To give an example, Latour [START_REF] Latour | Science in Action: How to Follow Scientists and Engineers through Society[END_REF] asks "Who refers to Lavoisier's paper when writing the formula H2O for water?" The stabilized fact of water being composed of hydrogen and oxygen becomes incorporated into tacit knowledge, with no mark of being produced by anyone [START_REF] Linton | What is Water? The History of a Modern Abstraction[END_REF].

When a scientific publication P refers to another one R, authors of P are benefited by the previous results and statements provided by the other, since much of the content of R might be -at least partially -accepted by the target audience. On the other hand, the more R is cited, the more its authors are benefited by the acknowledgement of the relevance of their work and the spreading of R's content among P's readers. This relationship, shown in Fig. 1, provides mutual benefit for the human actors, being mediated by the non-human entities P and R. Even whether authors of P and R do not know each other, they become associated.

Tracing and analyzing these networks of relationships, one can understand how a scientific community is arranged, what are the sources of its adopted paradigm, how convergent are its interests, and if there is any pattern over time. Unlike other methods of bibliometric analysis, as the co-authorship [START_REF] Glanzel | Analysing Scientific Networks through Co-Authorship[END_REF] or co-citation [START_REF] Small | Co-citation in the scientific literature: A new measure of the relationship between two documents[END_REF] graphs, which focus only on the persons or the publications, the ANT approach does not privilege participants of any specific nature. It allows highlighting main scientists and important bibliography contributing to the subject of a conference, and the whole structure that emerges from their relationships.

Procedures of data gathering and summarization

Considering the editions of ICISO conference as samples of the Organizational Semiotics community, we chose to apply ANT's point of view to its bibliographic data freely available on the internet. Springer provides the proceedings of 2014 and 2015 occurrences of ICISO, along with the list of references for each published paper. This data were fed into a software originally intended to support systematic bibliographic reviews [START_REF] Prado | Expandindo revisões bibliográficas sistemáticas pela análise de redes sócio-técnicas científicas[END_REF], but that proved suited for our purpose, managing the publication list, the relations to references and authors, and generating the visualizations. Not all references could be used. For instance, web pages are not considered references since their authors -human actors -are not defined. Other papers have duplicate references that were accounted only once. Some similar author names were disambiguated using an automatic algorithm [START_REF] Levin | Evaluating the use of social networks in author name disambiguation in digital libraries[END_REF]. Whenever available, DOI is applied to retrieve additional information about the references and to solve duplications due to typos or divergences in credited titles.

Once the automatic procedure was finished, we carried out a manual inspection of the results and performed minor corrections by hand when necessary. This includes splitting nodes representing distinct persons with the same name abbreviation, and merging references with misspelled titles, using additional data sources and search engines when necessary. Not all nodes required manual inspection: possible splitting was checked only by the ones representing authors and with degree > 1 (177 of 3599, or about 5%); similarly, candidates for merging were screened using a Levenshtein distance < 3 prior to manual procedures. The final dataset is summarized in Table 1.

The visualization of the graph of bibliographic references is based on the proposal of Prado and Baranauskas [START_REF] Prado | Representing scientific associations through the lens of Actor-Network Theory[END_REF]. They applied the betweenness centrality measure [START_REF] Brandes | A Faster Algorithm for Betweenness Centrality[END_REF] to calculate the size of the vertices, representing the importance that each vertex has to keep the network together. They also used a spring forces layout algorithm [START_REF] Eades | A heuristic for graph drawing[END_REF], to obtain an automatic arrangement of vertices, what they argue is well aligned with ANT's view of a social group as a balance between the forces generated by authors through associations, bringing together the ones they are interested but keeping apart from the others. In comparison to the most commonly used graphs of co-authorship containing only human actors, this representation provides a better view of the

Analysis of Results

Using the titles of the papers published in each conference edition, we built the word clouds shown in Fig. 3. The 2014 edition is well aligned with that conference motto, as the words "service", "based" and "approach" are the most frequent, followed by "method" and "architecture". For 2015, however, the topics become more generic, and "information" becomes highlighted, followed by "semiotics", "systems", and as in the previous year, "based" and "approach", aligning the community production more to its roots of semiotics and information systems. From the graph data structures, some metrics were obtained, as shown in Table 2. Not all published papers share a path with the others, thus creating insulated groups of vertices, that is, distinct connected components [START_REF] Bondy | Graph theory with applications[END_REF]. Papers published in 2014 are aggregated in 11 components while the 2015 edition produced 10. However, there is always a major connected component gluing most of the vertices. In both years, this component comprises more than half of the whole graph, showing the convergence of the community persisting along the 2 years, despite of the different themes and scales of each conference edition. Fig. 4 shows the simplified versions of the actor-networks, composed only by the main actors and their associations for each conference edition, including published papers, references and authors with higher betweenness. Although papers published at each edition and well aligned to its theme are included, e.g., "Hierarchical Clustering Based Web Service Discovery" for 2014, and "A Semiotic Approach to Investigate Quality Issues of Open Big Data Ecosystems" for 2015 -our analysis will focus on the references they draw upon to make their claims, as the basis of the community. Considering the complete dataset, given the greater number of published papers in 2014, it is not feasible to print the whole graph in a single picture; therefore, we cropped it to show the central portion of the main connected component, producing Fig. 5. For the 2015 edition, having less than half of the features, it was possible to build Fig. 6 depicting the complete graph. Some of the actors cited in the text are pointed out.

In both years, the most relevant reference author is "Ronald K. Stamper" and the most relevant reference is "A Framework of information system concepts -The FRISCO Report". The nodes representing them are well positioned in the two generated layouts, at the center of the main connected component. Both constitute a path between two large blocks of published papers and their related references. Another reference worth noting is "Semiotics in Information Systems Engineering", being placed in the middle of dense clusters of papers in the two graphs, what led the analysis to its author, "Kecheng Liu", who provided more used references and authored some of the published papers in each conference edition.

Regarding well-positioned references and authors that appear in a single conference edition, we can cite for 2014 the "Review of web service discovery technology" by "Liu J. The FRISCO Report Fig. 6. Complete graph of associations for ICISO 2015. Some smaller components were repositioned for better fitting on the page During the manual inspection of data, some limitations of the used tool were detected. The person "Taylor A", pointed out as author of two references used in 2015, is in fact the abbreviated name of two distinct researchers: Alex Taylor, author of "On the naturalness of touchless" and Alva Taylor, author of "Superman or the Fantastic Four?". An additional node was created for each one, removing the original. This kind of interventions did not reshape significantly the graph as a whole, but

Ronald Stamper

The FRISCO Report

A Semiotic Approach to Investigate […]

Semiotics in Information Systems Engineering Kecheng Liu created one of the minor connected components. In another situation, author "Liu J." could not have his identity checked: he is credited as "Jiajun Liu" at IEEE for authoring "Determination of Activities of Daily Living of independent living older people using environmentally placed sensors", but the authorship of "Review of Web service discovery technology" could not be verified. In case of splitting, this node would have its relevance recalculated as a lower value.

Fig. 7. General pattern found in both conference editions

To a brief comparison to a purely quantitative bibliometric analysis, we ranked the number of cited publications and authors among the conference papers. The most used bibliography are "Semiotics in Information Systems Engineering" (12 citations) and "Information in Business and Administrative Systems" (4 citations). Comparing to ANT's results, both have also a relatively high betweeness, particularly for the 2015 edition, what makes them indubitably important for the community. However, the second one is cited only by papers of the same two groups of researchers, making it more localized into the community. Authors most often cited are Kecheng Liu (37 citations), followed by John Krogstie (23 citations), reputed scientists in the field of Information Systems. However, the citations for the latter come mostly from a single paper published at ICISO 2015; therefore, his publications cannot be seen as common ground for the community. There is a contrast between the good results obtained by "Ronald K. Stamper" and "The FRISCO report" using ANT and their lower citation count; we interpret this as if the ideas contained therein are becoming tacit knowledge within the members of the O.S. community. The major weakness of the used method is the dependence to the availability of data, as a relevant subset of the publications' bibliographical references is required to provide a representative outcome. The unavailability of full proceedings of a conference edition hinders a longer-term analysis.

Conclusion

Scientific communities evolve around a set of concepts and assumptions, drawn from distinct bibliographic references and authors. Some of these become tacit knowledge among the researchers and practitioners, and therefore are not always captured by the most traditional scientometric methods. In this paper, we applied an alternative approach to analyze the relationships between researches within a scientific community mediated by scientific literature, as proposed by ANT. Based on the ICISO 2014 and 2015 proceedings available online, we were able to construct graphs representing such associations, and apply algorithms to build visualizations of the core structures that keep this community standing up as an X-ray.

Our analysis highlights the very foundational work of Ronald Stamper towards defining a common ground for the Organizational Semiotics researchers through the "FRISCO Report" and other papers. Besides, the book "Semiotics in Information Systems Engineering" also appears as a central source of tools and methods enabling many other related scientific projects, while its author Kecheng Liu remains an active member of the community. These results corroborate ANT's choice of keeping human and non-human together and trace their relationships for the study of scientific communities.

Fig. 1 .

 1 Fig. 1. Relationship of mutual benefit established between authors of a paper P referencing another publication R. Solid arrows denote reference, dashed ones the provided benefit

Fig. 3 .

 3 Fig. 3. Word clouds generated from the titles of papers published in ICISO 2014 and 2015 -above and below, respectively

Fig. 4 .

 4 Fig. 4. Simplified graphs showing main actors for ICISO 2014 and 2015 -above and below, respectively

  et al."; and "Measuring and Comparing Effectiveness of Data Quality Techniques" by "John Mylopoulos et al.". Their titles suggest they are aligned to each conference theme, what adds proof to the relative relevance calculated to them, inside the subject of that particular edition.

Fig. 5 .

 5 Fig. 5. Detail of the main connected component of ICISO 2014 actor-network. The references and authors with higher betweenness centrality are labeled

Table 2 .

 2 General graph measures for each conference edition

	ICISO 2014	ICISO 2015

Acknowledgments. We thank the Brazilian Research Foundation CNPq (Grant # 308618/2014-9). The opinions expressed in this work do not necessarily reflect those of the funding agencies.

conference edition as a single social phenomena, since the number of connected components is significantly smaller. The final representation of the graph is exemplified in Fig. 2: papers published in the conference are represented as blue square vertices and their authors as blue circles; while the references and their authors are red squares and circles, respectively. If an author of a paper has also authored a reference, that first condition prevails. The size of each vertex is proportional to the logarithm of its betweenness centrality. We can use it to identify the relevant actors for each network and understand the main contributors to the shared theoretical background. When authors and publications are marked relevant in more than a single conference edition, we can suspect their importance are not due to the specific topic of that particular edition, but instead it is part of the community's adopted paradigm. Besides the full graphs, smaller versions were obtained by applying an intensive graph pruning algorithm [START_REF] Hennessey | A simplification algorithm for visualizing the structure of complex graphs[END_REF]. This succinct preview allows knowing the main actors that compose the backbone of the graph, before we drill down into the details of the whole network.

Fig. 2. Adopted representation for the actor-network graph

Buchdid and Baranauskas [START_REF] Buchdid | IHC em context, o que as palavras relevam sobre ela[END_REF] analyze conferences using word clouds [START_REF] Rivadeneira | Getting our head in the clouds: toward evaluation studies of tagclouds[END_REF] extracted from the titles of papers published in conference editions. Word clouds provided visual clues to the essence of the studied conferences at a glance. We believe that this high-level representation complements the lower level structural analysis of ANT and both together provide a better understanding of the work of the social group.

To support the study in relation to the particularities of each conference edition, we recovered their proposed topics of interest. ICISO 2014 called for papers about "Service Science and Knowledge Innovation", a young discipline that has attracted great attention by academy and industry because of the increasing need for a scientific approach to guide the study of services. ICISO 2015 tackled "Information and Knowledge Management in Complex Systems", such as large-scale projects, network of networks, and dynamic and evolving enterprises.


Janaina Antunes
email: tcheina@hotmail.com

The Roles and Challenges of Semiotics Unraveling Big Data in the Glocal Contemporaneity Ruled by Dromocracy

Keywords: Big Data, Digital semiotics, Cybercultural Dromocracy, Glocality

Big data is capable of hugely impacting the decision-making process, regarding that we are able to correctly interpret it. The challenge of analysing big data lies exactly on the balance between two things: its rapid-pace nature and our lack of a humanly possible capacity of following such speed. It is exactly Digital Semiotics that gives meaningful organization to big data, transforming it from data trash into a sea of useful information. Semiotics can tell us the nature of big data and it can also show us how to experience, manipulate and control it within the cultural conditions of global interactivity and of the velocity of production so typical of our era. Dromocracy, the life governed by a fast speed, is the name of the phenomenon which articulates the process of the so-called glocalization, which is a cultural development that staggers to the planetary territory and empowers to the infinite the hybridization of realms of existence, through such velocity. The role and the importance of Semiotics grow in Dromocracy, especially considering big data; and what sets Semiotics apart from any other science and makes it stand out is exactly that it could be the answer to understanding such world for all areas of knowledge, if, and only if, Semiotics is able to look inside itself for a deep, introspective adaptation to the ways of Dromocracy.

Introduction

Big data is capable of hugely impacting the decision-making, regarding that we are able to correctly interpret it. Nonetheless, the challenge of analysing big data lies exactly on the balance between its rapid-pace nature and our lack of a humanly possible capacity of following such speed. The greatest role of Semiotics in this scenario is to make big data "smaller". Through Semiotics we are able to divide it, restructure it and understand what is beneath and beyond it. Semiotics is the tool through which we can "translate", decode big data.

We will walk through this task analysing how the Unclassifiable, the Glocality and the Dromocracy are spread and how they work, being this way able to find a solution to their challenges through Semiotics strategies, and being able to define the new roles of Semiotics in our contemporaneity. We shall start with the most challenging part of the process: classifying things. A contemporary problem not only regarding big data.

Cyberculture and the Unclassifiable

The clear time lineage of culture, of the evolution of culture is gone in the advent of cyberculture (which is precisely characterized as a real-time interactive digital culture), because the latter makes it possible for a person to be influenced by cultures originally completely unlinked, completely out of a given time order, or geographical order. We may be jointly influenced by a Neolithic Asian art and by African Expressionism.

The fact nowadays is that the cyberspace brought us an enormous number of possibilities of influences from many different cultures, from different times and localizations. We are ravished with infinite influences, many times not being able to personally tell what they were or where they came from, consequently creating a great difficulty to name ourselves, because nowadays we are atemporal and nongeographical. [1, p5] The matter takes greater proportions regarding big data. Even if all its contents were very easily definable, we would still have much difficulty separating them into categories. With the introduction of contents that by themselves are already unclassifiable, our task as semioticians became herculean, especially since we do not know yet how to proceed in such scenario.

We are accustomed to work with a large taxonomization and with very concrete concepts, opening up just for their hybrids. But while hybrids have characteristics of different trends all mixed into one place, and while they may or may completely not be linked to the cyberculture, the unclassifiable is unique: origins and influences may be many, but they are impossible to be recognized or to be traced, making it impossible to be named and taxomizated.

As semioticians we have to be able to analyse whether such taxonomies could be implemented, if they are applicable to, i.e., social media analytics; and run more widely into, i.e., free text or unscripted data analysis. This could be done through a combination of mechanical coding and automated coding systems. There is such a hunger, a supposed necessity to give those systems taxonomies, when actually, due to the velocity so characteristic of our contemporary digital world, the moment they are named, they no longer have the same purpose once had when they originated. There are so many semioticians in charge of these nominations; when, in reality, what we really need is semioticians knowing how to use tools, and developing such tools to decode big data, no matter what are their taxonomies.

On the other hand, there is such a big extent to which assumptions and biases get in the way of the Semiotics work, much more than the unnamed items, because they have to be identified and corrected before being decoded, whereas the first ones can be directly decoded disregarding the fact that they do not have a specified name. We have to wonder if taxonomies are more helpful or unhelpful: did the current pressure to name everything cause the rise of the aforementioned assumptions and biases as a result of mislabelling, or was the lack of definitions responsible for them?

That is where the true value of Digital Semiotics comes in: the contemporary processes that create big data are happening and will continue to happen independently of our ability to name them. Howsoever, Semiotics is the tool through which we can follow the process, predict the next steps, even considering how challenging it can be due to the velocity of our cyberculture.

Glocality and Velocity

The unclassifiability is emerging as the main cultural characteristic of the twenty-first century, born under the technological and cultural conditions of the contemporary world, a consequence of global interactivity and of the velocity of production. This is a phenomenon simultaneously local and international, situated in the cyberspace era, which utilizes cyberspace as a means for the internationalization of culture. It is deeply embedded in the typically cibercultural concept of glocality.

The process of glocalization staggers to the planetary territory and empowers to the infinite the phenomenon of this hybridization of realms of existence, transforming the world into a kaleidoscope of intersecting glocal strongholds for the circulation of information and data. [4]

Glocal is where we are when not localized in the local nor global. For instance, when we visit a virtual museum, we are not literally in the city of this museum, in its geographical localization; on the other hand, we are not at the place where our physical body is, because we are not experiencing those surroundings. We are experiencing the glocality of the museum that welcomes us through the virtual.

Glocality is the a worldwide phenomenon that affects all people through cyberspace and reaches even those without Internet access, which are influenced indirectly, because they suffer this influence on contact, however sporadic, with an individual who has a direct influence of cyberspace. The cyberculture undergoes a universal dissemination provided by all individuals who have contact with the cyberspace.

The glocal equates to a socio-technical homeostatic entanglement, obliterated and irreversible (…) at the regional, national or international level. [4, p 13]

In glocality we are always isolated, both in the so named Glocal Lato Sensu as in the Glocal Stricto Sensu. The first is the situation in which we are isolated by lack of access to internet, and the second is the one in which we are isolated from the territorial world around us protected by a Glocal Bunker, that is, our infinite gadgets that separate us from the physical environment in which our body is. Even though we are isolated geographically, we are also always united to everyone by cyberspace. An individual may be isolated from technology, but s/he can never escape the irreversible process of glocality.

The logic of relationships is not direct and dependent upon defined elements, but it is associated with a complex process of factors and trace elements, apparent and non-apparent, establishing transversal paths of relationship and causing countless reciprocal connection developments, conflicting and / or excludent that are beyond the reach of an accurate perception, yet thorough and experienced. [2, p 87] This union between global that circulates and the "where" the body is (or "where" it acts), which is the communication basis of this current civilizing process, occurs by several garments (which for now are smartphones, tablets, computers), but these garments are of no importance because the glocal lies not in them. The glocal quality of communication is given more in the functional sense than in the structural sense of experience. This is what sustains the inextricable link between the global network and what circulates instantly through the interactive or hybrid mass communication.

Communication is every day less and less confined to fixed locations, and the new telecommunication modes have produced transmutations in the structure of our daily conceptions. [3, p 25] The new status of glocality produces such transmutations, imposing a restriction: one that it is no longer possible to separate the content that is circulating internationally, nationally, or locally; or even in terms of the place that you occupy and the place where your body is. This new feature introduced by digital communication modifies the dynamics and the consistency of global communication that happens in the physical realm in which we operate. The process of glocalization also means cultural development to the extent that it permits miscegenation in the culture field, a content hybridization in the web without borders. The direct result of glocality on big data is this transmutation: glocality makes big data placeless, more than it ever was; because even though we could not specifically point out a location for any piece of data before, now we cannot trace its origins as well. Big data is not virtual anymore, it is glocal.

From this perspective without horizon in which the city access ceases to be a door or a triumphal arch to transform itself into an electronic hearing system (...), the break of the continuity does not occur either in space or in a limited urban sector, but mainly in duration (...) and successive or simultaneous occultations that organize and disorganize the urban environment to the point of causing irreversible decline of local. (...) Since then no one can be considered separately by physical obstacle or large "distances of time." [6, p8-10] The cyberspace and digital culture have eroded our ability to identify the cultural lineage of artefacts and even people. We are being ravished by so much data at such a rapid flow of information that at one moment or other people get fed up, because we are not yet adapted to this velocity, we did not have time to develop the skills to learn, to do so many things at once. Some people have developed more aptitudes to deal with the fast pace of the world, although no one has reached such a level of geniality to be able to run after this pace.

Dromocracy

This velocity aforementioned is the factor that moves and controls our lives and our society. This "era of velocity" is called Dromocracy. The expression was coined by Paul Virilio [START_REF] Virilio | Velocidade e política[END_REF] based on the greek prefix dromos, which means the social articulation towards racing, velocity, speed; and thusly making Dromocracy a world view and/or a life governed by velocity. Dromocracy is a phenomenon that articulates the glocal through velocity. It is a system, a process. It rose in the twentieth century, when it was still a social process happening more isolatedly. Nowadays, Dromocracy is still a social process, but it has also become a regime that rules our lives, it has become this era. It is the congruency among the media, the state, the market, the companies and most importantly, the individuals that live under this regime willingly and that feed such system with their collaboration: the regime of Dromocracy is not imposed or forced on anyone. Nobody (...) supervenes the "world" except by acting on it from the glocal context; no one can appear or speak to each other, as well as act in reality in a fast and effective mode except in and through the instant world of media signs, so the effect of glocalization; and even with severity, no one can predict about oneself or about any object or mark that has been or is being(…) Thus, everything becomes or tends to pass through the semiotic network in real time (...), socially structured as a kind of media-operating system (…) of contemporary culture in its interactive phase, established as Cybercultural Dromocracy. [4, pp. 25-26] What every single person on the planet is already doing is a new kind of decisionmaking. We are overwhelmed with information not only from cyberspace but also from every other kind of media, and despite the fact that we are not able to process all that, we are already considering it, no matter how unconsciously, when we make a decision. In this new reality, such tools as surveys (among others) to find out why people buy what they buy, are no longer reliable. It is not the answers that the people give that matter anymore; it is the signifiers within the answers -exactly because, as previously mentioned, we are not able to pinpoint our flow of influences and interests. Consequently, in that scenario, the only tool for such a task is Semiotics, only it can show us how that is actually working. The role and the importance of Semiotics grow in Dromocracy, especially considering big data.

5

The New Roles and Challenges of Semiotics: Strategies

The challenge, once again, lies on velocity. The moment something catches our eye is because it is already big enough to be seen (no matter how insignificant it may be considered), and at this moment, in our rapid pace contemporary world, it is generally already about to die. Nonetheless, we have to change our semiotic reading. It is not only about the changes in language, in media, etc. It is also about new archetypes -they changedwe are still practicing Semiotics based on archetypes that do not represent reality anymore.

However, things are changing in a pace that we cannot establish which are the new archetypes, so we come back to velocity: since archetypes and models change faster than we are able to identify and name them, we also have to be able to read these things not based on these old models, but we have to develop a new innovative method to do these readings without models. It is a new paradigm for Semiotics.

Big Data is endless and we will never be able to decode it entirely no matter how much time we spend on it, no matter how fast we do it, because it will always be changing, with new data appearing and disappearing at a faster pace than the human one. Acknowledging that fact is the first step to a new and urgently necessary Digital Semiotics based on ever-changing signifiers.

Semiotics' taxonomy will nevermore be as stable as chemistry's or biology's taxonomies are, if it ever was. Semiotics has to learn to deal with fluid structures, because the old fixedness of structures is already not enough to decode big data, and very soon it will be completely useless. There is still this fixedness, but we have to stop trying to make it last longer -the duration it is going to last does not matter anymore -what is crucial to be done is to adapt our methods or to create new ones that are as flexible and that flow as much as data and the contemporary culture do. It may seem counterintuitive, unnatural or even completely "unsemiotical", but the survival of Semiotics depends on learning how to analyse the data on our hands without standards and/or with fluid, ever-changing standards.

What sets Semiotics apart from any other area and makes it stand out is exactly that it could be the answer to understanding such world for all areas of knowledge, if, and only if, Semiotics is able to look inside itself for a deep, introspective adaptation to the ways of Dromocracy. There is no magic solution, and that is exactly why there is no research, no literature about this in the field of semiotics (even though very few academics, all cited here, have done so in other fields): we just have to learn how to deal with such challenges, not lose time developing theories that will not be accurate by the time they are developed, that is the simplest and most demanding solution.

For all that, the Semiotics field needs not only to develop new tools, but also adapt old ones. We can have a tool deeply based on structure, i.e. the square, but we can use it for completely unstructured objects of study, we simply have to make adjustments. We can indeed decode the unstructurable through structuring Semiotics tools without changing the unclassifiable nature of the object. We simply have to let go of the old habits that tell us that we need names and taxonomies to have something analysed. We have to look for a new framework of understanding, more flexible and supported by the dynamic comprehension of human phenomena beyond the visible and sortable; not at all less valid and representative, but quite the contrary: much more representative of our world even without the possibility of being represented by a specific name.