Dalibor Štys
email: stys@jcu.cz

Petr Jizba
email: p.jizba@fjfi.cvut.cz

Štěpán Papáček
email: papacek@jcu.cz

Tomáš Náhlík
email: nahlik@jcu.cz

Petr Císař

On measurement of internal variables of complex self-organized systems and their relation to multifractal spectra

Keywords: Rényi entropy, principal component analysis, generalized dimensions, multifractal spectra

We propose a method for characterizing structured, experimentally observable, complex self-organized systems. The method in question is based on the observation that number of self-organized systems can be mathematically perceived as consisting of several interconnected multifractal components. We illustrate our key results with ensuing applications. The relation of the results obtained to known examples of strange attractors is also discussed.

Introduction

Self-organized (SO) systems typically refer to physical and biological systems in which patterns or structures present at the macroscopic level arise solely from a coherent interaction among lower level components of the system. The best known examples are undoubtedly living organisms which range in their complexity from simple cells through herds, flocks, insect colonies to humans and their herding behaviour or cities. There are many models used to generate analogies of specific features of such observable structures. The comparison of these models to observed dynamical systems is the question which awaits yet the answer. It is purpose of this paper to point out that some signatures that are met in analysis of SO systems may be inferred by the statistical approach based on a multivariate analysis. This approach has at the moment a widely utilized version epitomized by the principal component analysis (PCA) alongside with many new developments including, e.g., analyses developed for data exhibiting distribution skewness [1]. It should be, however born in mind that many realistic intensity distributions found experimentally in images of SO systems such as Belousov-Zhabotinsky reaction (see Fig. 1) or living cells (see Fig. 2) are rather complex and cannot be mapped on a simple (skewed) normal distribution. Thus, the question of multivariate analysis on data-sets coming from SO systems remains open, regardless of its wide utility, for instance, in various fields of biology and medicine [START_REF] Martens | The Informative Converse paradox: Windows into the unknown[END_REF].

In this paper we describe a surprisingly successful application of the PCA for charting the state space of the Belousov-Zhabotinsky reaction. The key message which we wish to convey here it the modus operandi which illustrates the basic logical steps that should be utilized on the way to the state-space description of self-organized systems. In passing, we will also see what potential obstacles can be expected along the route.

2 Measurement in self organized systems

The problem of orthogonal coordinates

The principal component analysis has been first introduced by Pearson as early as in 1901 [START_REF] Pearson | On lines and planes of closest fit to systems of points in space[END_REF]. Its application consists of three steps: (1) normalization of each data-set, (2) calculation of the covariance matrix and (3) calculation of principal components, i.e. orthogonal coordinates which determine directions of main variance in the data. When principal components are calculated, it may be calculated covariance of each of the original data-sets with each principal components. These covariances are called loadings.

Experimentalist's experience is often such, that loadings are naturally coinciding with components of one known process or feature. For example, chemical compounds characterizing one biochemical process have highest loading on the same principle axis. In Ref. [START_REF] Stys | The cell monolayer trajectory from the system state point of view[END_REF][START_REF] Stys | Analysis of biological time-lapse microscopic experiment from the point of view of the information theory[END_REF] we have discussed the necessity to characterize microscopic images of living cells in chemical, as well as, in physical space. The chemical space needs to be characterized with chemical potentials which are in logarithmic relation to activities. In equilibrium thermodynamics, both these variables are related to standard thermodynamical variables of temperature, pressure and volume through systems state function.

It is somehow naturally assumed, that pressure, volume, temperature and number of molecules are orthogonal state coordinates of the system. At least, that is the impression from textbooks on physical chemistry. In fact, the only mathematically correct statement is that state function of the ideal gas is a manifold in the orthogonal state space with coordinates pressure, volume, temperature and number of particles. For our discussion it is, however, more valid to discuss the Gibbs free energy. For ideal gas, the state function is a planeeventually hyperplane, in the space with coordinates G, T and ℘ i (i.e., Gibbs energy, temperature and partial pressures of chemical components in the system). With some manipulations we for the condensed phase case come to widespread formula

G = G 0 + RT n i=1 ln c i , (1)
where c i are concentrations of system components. G 0 denotes standard Gibbs energy of given system and R the universal gas constant. All equilibrium thermodynamics is devised in this state space. In chemical thermodynamics, in order to obtain more realistic description, activity a i (or fugacity) replaces the partial pressure of ideal gas component. The correction factor, so-called activity coefficient γ i , is in function accounting for transformation of coordinates in order to obtain formally the same equation as that for ideal gas.

G = G 0 + RT n i=1 ln a i = G 0 + RT n i=1 ln c i + RT n i=1 ln γ i , (2)
Activity coefficient is non-linear function of concentration of all species present in the sample. From physico-chemical point of view, it accounts for all molecular interactions in given system. Generally, manifolds of state functions are accessible only experimentally even for such simple systems as two component mixtures of miscible liquids and their vapours. Principle components approach [START_REF] Pearson | On lines and planes of closest fit to systems of points in space[END_REF] looks at the problem from different point of view. The resulting variables, principal components, may be assumed merely as practical descriptors of the system. When the problem is treated from more elementary point of view, the principal components are best approximation to internal orthogonal coordinates in state space appropriate to stochastic (macroscopic) variables of which each has normal distribution. Instead of constructing the state function as manifold in a given coordinate system, we find coordinate system in which the state function is a plane in multidimensional space. When equilibrium physico-chemical system is examined, we may consider principal components best approximations to log-activities as functions of all systems variables.

Orthogonal coordinates of in the phase space and generalized fractal dimensions

A nice and extensively studied example of self-organizing object is the Lorenz attractor (cf., e.f. Ref. [START_REF] Lorenz | Deterministic nonperiodic flow[END_REF]). The beautiful butterfly wings structure is plotted in orthogonal phase-space coordinates which originally had physical meaning of total flux of matter, temperature difference between incoming and outgoing stream and deviation of temperature gradient from linearity. Certainly, these are not parameters which are easily measurable in model Bénard cell, where is to the measurement accessible the diameter (in general shape) of the cell and temperature of the lower and upper plate.

Results of measurements of real objects are to a large degree stochastic. The real system is subjected to external fluctuations and repeated use of for example -mechanical measurement device naturally brings up normal distribution of measured value probability. Digitization of analogue signal has similar effect, however, often leading to distortion of the signal. These are just few of many sources of stochasticity in real measurements.

The quest for proper measurement of self-organizing systems is to describe them by measurable variables which reflect their internal structures. As well as principal components best reflect the axes according to which a given dataset may be best separated. Self-organizing systems, however, are not homogeneous, they have their observable, self-maintained, dynamic structures. Thus the first problem to be addressed, before the multivariate analysis is performed, is to find a method how to characterize the internal structure.

We essentially measure what may be measured by accessible equipment. Or, in more precise expression, the measured system has to be examined only in relation to its phenomenological variables which are the measured sub-set of all possible variables representing system attributes, as was precisely formulated for example by Žampa [START_REF] Zampa | 4th WSEAS conference[END_REF] (see also [START_REF] Stys | The cell monolayer trajectory from the system state point of view[END_REF]). The internal, in real system at least within statistical error orthogonal, coordinates, are not accessible to the experimentalist. We proposed earlier [START_REF] Stys | The cell monolayer trajectory from the system state point of view[END_REF] to extract the information content of the given data-set using Rényi entropy gain approach. Rényi entropy has a close connection to generalized dimension of the multifractal objects [START_REF] Grassberger | Characterization of Strange Attractors[END_REF][START_REF] Grassberger | Measuring the strangeness of strange attractors[END_REF]. We, at given image resolution yardstick, use Rényi entropies at different parameter, calculated simply from occurrences of different signals, as first attempt to determine measure in the state space.

At this place we discuss self-organizing multifractal object whose stability is based on their character of chaotic attractor. This allows us to build direct analogy with the Lorenz attractor. Each individual multifractal contribution to resulting spatially distributed signal, i.e. image, has its own spectrum of generalized dimensions. There should be as many components as there are dimensions of the phase space.

Each component of the real multifractal object should have its own generalized spectrum. In our practical approach this means that each of the Rényi entropy values at each alpha has its occurrence in the image. We determine the information contribution of each data point to the object by calculation of difference in Rényi entropy of the data-set between the data-set including and excluding the examined object. This is the point information gain (PIG) P IG α,x,y introduced recently in Ref. [START_REF] Stys | The cell monolayer trajectory from the system state point of view[END_REF]. For given data-set, i.e. image, the three-dimensional spectrum in coordinates Rényi entropy, the dimensionless α coefficient and occurrence of a given values in the set is a unique characteristic of the image. We are well aware of the fact that the relation of PIG to individual component of the generalized spectrum of individual component of the observed SO is only vague, but we do not have better technical way how to proceed. PIG for given point x,y at given alpha is calculated according to formula

PIG α,x,y = 1 1 -α ln n i=1 p α i,x,y - 1 1 -α ln n i=1 p α i . (3)
where p α i,x,y and p α i ) are probabilities of occurrence of given intensity in the image without and with the examined point. In the first approach, calculation of PIG from whole image, distribution of intensities within the object of study is not considered. Then occurrence and entropy represent the same feature. Inclusion of spatial information may be done by defining the reference frame, in our case the cross whose shanks intersect in examined point. We shall show below that the later method allows in the examined case better estimation of orthogonal principle components.

In the next step we calculate integral information as potential state variable. We calculate sum of all PIG values, the point information gain entropy PIE, and point information gain entropy density PIE/points, the sum of all PIG levels at given alpha. Unfortunately it is likely that in non-symmetrical systems PIG, PIE and PIE/ points is dependent on choice of coordinates. This is given by the measurement device, for illustration we may consider that we examine the structure of Lorenz attractor while having only one arbitrary plane from which it is observed.

PIE/ points α = n i=1 PIG α,i . (4)
In this article we, on measurable systems, experimentally examine following hypothesis:

1. The orthogonal coordinates obtained by principle component analysis are practically usefull approximation to the internal orthogonal coordinates of the asymptotically stable system which gives rise to observed self-assembling object. 2. The covariances (loadings) between each calculated PIE/points or PIE values and the given principal component are reasonable and practically usefull approximation to intensities of spectral lines of individual multifractal component, i.e. chaotic attractor -in observed set which gives rise to observed self-assembling object.

Results

Observables in general projections of a strange attractor

An obvious way to determine validity of our approach is to prepare simulated data and expose them to the aforementioned analysis. Recent calculation of fractal dimension of the Lorenz attractor was done by Viswanath [START_REF] Viswanath | The fractal property of the Lorenz attractor[END_REF]. He reported that calculated values are very sensitively dependent on a numerical precision of the implemented calculation. Addition of noise would add additional, and surprising, dimension to such demanding calculation. This we wish to demonstrate on an illustrative example.

In Fig. 3 we show snapshots of the evolution of a toy model of Lorenz attractor [11]. There we show results of simulation in the absence of noise. We further show results of the same simulation with on-negative Gaussian noise applied in all three orthogonal directions. This toy model, in which the numerical integration is performed by the Euler method with a relatively large integration step, shows impressive robustness of the Lorenz attractor system of equations. The influence of Gaussian noise is in a sense puzzling: instead of generating random behaviour of the system it leads to de-coherence. When noise is applied in y axis it leads to preference of one wing of the butterfly and when applied in the z axis the system collapses into one point of focus. We do not provide any proof of generality of this observation, however, this result seems to be in agreement with observations of Jalnine et al. [15] who predicted collapse of chaotic behaviour in the van der Pol oscillator at increasing noise. Similar results using different approach to noise generation were also reported by Zahri [START_REF] Zahri | Numerical Solutions of a Stochastic Lorenz Attractor[END_REF]. The model is freely available [11] and the reader is encouraged to explore it. In any case, it illustrates that any simple assumption about emergence of normal distribution may fail in the case of systems based on strange attractors. Obviously, however, the attempt to obtain image of internal orthogonal structure in chaotic attractor including noise would be extremely sensitive to computational performance and we refrained to include it into our analysis. We limit ourselves to experimentally observed SO systems, where the Nature calculates the trajectory for us with best achievable precision. Since we do not have any information on probability density function of the processes contributing to observed phenomena in experimental self-organizing systems, it is necessary to provide some logically feasible distribution. On the basis of the central limit theorem, it is natural to expect that the normal distribution will be the best choice. Under this assumption we use principal component analysis. As a first approximation to the state-space variables we use the Rényi entropy values for individual alpha parameters.

Measurable variables in projections of general strange attractor

In Fig. 5 we show the basic steps of our analysis. We first calculate information structure of a given image. For each point we calculate the PIG, the Rényi entropy difference at given α calculated from experimentally determined probability density function including and not including the examined point [11,[START_REF] Stys | The cell monolayer trajectory from the system state point of view[END_REF]. At the moment we have implemented two methods of sampling of the image for the probability density function calculation. First is the obvious approach in which the number of points of given intensity is summed and normalised. In the second approach, the image is sampled for each of the points using a cross, whose shanks intersect in the examined point. The probability density function is calculated for the intensity distribution along the shanks. More detailed description of the approach was given in [START_REF] Stys | Analysis of biological time-lapse microscopic experiment from the point of view of the information theory[END_REF][START_REF] Urban | Preprocessing of microscopy images via Shannon's entropy[END_REF]. We examined typical images in the course of self-organization of emergent structures of the Belousov-Zhabotinsky reaction.

The question remains whether PIE/points values may be used as coordinates in the phase space. This was examined experimentally. We utilized plain approach to computation of principal components as implemented in Unscrambler software [6]. One of successful attempts is depicted in Fig. 5, where we show decomposition of the system trajectory of the Belousov-Zhabotinsky into series of states which are asymptotically stable under current conditions. The reason why we can not provide one single recipe for the analysis originates comes from the process of observation itself. The geometrical setup affects the course of selforganization. From that follows that proper method of sampling of the image has to be adopted accordingly. In other SO systems, such as living cells or flocks, the effect of geometry may be less pronounces because the geometry is determined by objects themselves. There the example is, however, less instructive because the number of important principal components is typically six or more. In this respect we may only say that such a method was successfully tested on several typical data-sets but its generality has not been proven. In the last step we have examined the contribution of the original Rényi's fractal dimensions to the final ones. In Fig. 5 we depict the contribution of individual components to the whole image for 1st, 2nd and 3rd principal component. The first obvious thing is observation that there is not any qualitative difference between information carried in 1st and 2nd principal component. This may be seen from parallel course of dependency of individual PIE/points covariances when plotted against α. Some differences may be seen in 3rd principal component, where namely the contribution of the blue color deviates significantly. Following the line of arguments given in part in previous section we suggest that the principal components found for each asymptotically stable state is the best approximation to orthogonal coordinates of the chaotic attractor whose reflection are the observed measurable variables. By system state we understand, for example cluster found on the Belousov-Zhabotinsky reaction trajectory. Measurable variables in the case of self organizing systems must include also structure of the system. In the same way as in standard physico-chemical description where a function combining in principle all concentrations in the system makes up the true coordinate -activity, the determined PIE/points values combine into one principal component orthogonal inner coordinate describing macroscopic behavior of the self-organizing system.

Since we have started the analysis from the theoretical assumption of multifractality and calculated first technical approximation to Rényi's entropy, we may suggest that covariances between the PIE/points and principal components Fig. 4. Scheme of the analysis of experimentally observed self-organized systems. First, information on structure is extracted in the form of point information gain -PIG. Sum of all PIG levels provides point information gain entropy density -PIE/points. The vector of point information entropy densities is used as experimental dataset for the principal component analysis. Data clustering is performed on the data-sets which provides best experimentally achievable separation of the data-set into self-similar clusters -individual asymptotically stable states. For each of the clusters is performed separate analysis which provides, besides other information, spectrum of covariances between each principle component and original PIE/points value for given α parameter. These give, in our opinion, rough impression of how a generalized multifractal spectrum of the underlying attractor in projection to internal orthogonal component may look like. are first technical approximation to multifractal spectrum of asymptotically stable dynamic systems determining systems dynamics. However, both above assumptions need further investigation. We provide all materials regarding the Belousov-Zhabotinsky reaction discussed in this article as well as all necessary software applications. Interested reader is encouraged to examine these primary data.

Materials and methods

BZ reaction

We used the kit provided by Dr. Jack Cohen http://drjackcohen.com/BZ01.html. The reaction mixture was composed out of following solutions: A. 25gm sodium bromate dissolved in 335ml water to dissolve to which 10ml of concentrated sulphuric acid (95-98%) was added, B. 10g sodium bromide dissolved in 100ml of water, 10g malonic acid dissolved in 100 ml of water, and D. 1, 10 phenanthroline ferrous complex (Fisons, Loughborough). The reactio was started in following order: 6ml of solution A was added to the glass beaker, then 0.5ml of B, and quickly mixed in 1ml of C. The brown mixture was left to lose bromine (by an open window) until it is pale straw colour or colourless (2-3 minutes if agitated or if in a flat dish). 1ml of the redox indicator D was added, mixed thoroughly and poured into a 9cm glass or plastic petr dish, on a white (illuminated) background. The reaction was followed by colour camera Canon PowerShot G9.

HeLa cell microscopy

HeLa cells (Human Negroid cervix epitheloid carcinoma)were obtained from ECACC -European collection of cell cultures.The cells were grown at low optical density overnight in a 37 • C temperature in a synthetic dropout media with 30% raffinose as the sole carbon source. The nutrient solution for HeLa cells consists of: 86% EMEM, 10% newborn-calf serum, 1% antibiotics and antimycotics, 1% L-glutamine, 1% non essential amino acids, 1% NaHCO3 (all components from the PAA company).

In total, 5000 original phase-contrast images of growing cells were taken at 1-min intervals. The image collection was performed at 37 • C by using the Olympus IX 51 with an automated state, integrated incubator, and photographic Camedia C7070 camera. The objective with 20 magnification was used in an image capture.

Fig. 1 .

 1 Fig. 1. Examples of structures observed in the course of Belousov-Zhabotinsky reaction. From the upper right to bottom left we depict images of 38th, 140th, 277th and 425th minute of the reaction trend.

Fig. 2 .

 2 Fig. 2. Two typical structures of living HeLa cell observed by the microscope. The figure comes from Refs. [12, 13].

Fig. 3 .

 3 Fig. 3. Examples of behaviour of a toy model of Lorenz attractor. Model was prepared in Netlogo3D [17] program environment. Gaussian random noise was added in three dimensions separately. The noise was added as positive random number with normal distribution. Panel A shows original, noise-free, model. Addition of noise in x axis (panel B) shows expected randomisation of the trajectory. Addition of noise in the y axis, however, leads to formation of narrow stripe of trajectories (panel C) and addition of noise in the z-axis (panel D) leads to collapse of the chaotic attractor structure.

Fig. 5 .

 5 Fig. 5. Various approximations to generalized multifractal dimensions which arise in the course of the analysis. At panel A are given initial PIE/points values for the image 148 of the course of Belousov-Zhabotinsky reaction. Panels B, C and D provide covariances of first, second and third principal component and all utilized PIE/points values for the first cluster (images 56 -135) which include the image under discussion. We propose that first, second and third principal components represent three independent contributions to the image.

4. 3

 3 Software packages For calculation of PIG, PIE and PIE/points values were used software packages developed by the School of Complex Systems. Stable versions of these softwares are available at http://www.expertomica.eu/software.php and are constantly updated. Latest versions are available upon request. For calculation of the Lorenz attractor model was used modification of the model provided to the user community by Salzano in 2005 largely modified by Dalibor Stys [11]. The model is also available at http://www.expertomica.eu/software.php The principal component analysis was performed using Unscrambler software provided by CAMO company [6].

Acknowledgements

This work was partly supported and co-financed by the South Bohemian Research Center of Aquaculture and Biodiversity of Hydrocenoses (CZ.1.05/2.1.00/01.0024)


Distributed Storage Management

Using Dynamic Pricing in a Self-organized Energy Community Ebisa Negeri, Nico Baken Delft University of Technology, Delft, The Netherlands {E.O.Negeri, N.H.G.Baken}@tudelft.nl

Abstract. We consider a future self-organized energy community that is composed of "prosumer" households that can autonomously generate, store, import and export power, and also sel shly strive to minimize their cost by adjusting their load pro les using the exibly of their distributed storage. In such scenario, the aggregate load pro le of the selforganized community is likely to be volatile due to the exibility of the uncoordinated sel sh households and the intermittence of the distributed generations. Previously, either centralized solutions or cooperation based decentralized solutions were proposed to manage the aggregate load, or the load of an individual sel sh household was considered. We study the interplay between sel sh households and community behavior by proposing a novel dynamic pricing model that provides an optimal price vector to the households to atten the overall community load pro le. Our dynamic pricing model intelligently adapts to the intermittence of the DGs and the closed-loop feedback that might result from price-responsiveness of the sel sh households using its learning mechanism. Our dynamic pricing scheme has distinct import and export tari components. Based on our dynamic pricing model, we propose a polynomial-time distributed DS scheduling algorithm that runs at each household to solve a cost minimization problem that complies with the sel sh nature of the households.

Our simulation results reveal that our distributed algorithm achieves up to 72.5% reduction in standard deviation of the overall net demand of the community compared to a distributed scheduling with two-level pricing scheme, and also gives comparable performance with a reference centralized scheduling algorithm.

Introduction

With the growing concerns for sustainable energy, an increasing number of diverse types of small-scale distributed generations (DGs), such as solar panels, are penetrating into neighborhoods. As a consequence, households are evolving from passive consumers towards active prosumers (producer-consumer) that can autonomously generate, store, export or import power. According to the EU parliament, all buildings built after 2019 will have to produce their own energy on site1 . As households take power into their own hands, they tend to self-organize and form an "energy community" [START_REF] Melo | Energy Balance in a Renewable Energy Community[END_REF], for example at neighborhood level, to locally exchange power with each other and to in uence the market with "the power of the collective." In such an autonomous community, the aggregate community load pro le is likely to be highly volatile mainly because of two reasons. Firstly, the production of the DGs is highly intermittent. Secondly, the households could use the exibility o ered by their distributed storages (DSs), through charging and discharging, to sel shly adjust their load pro le to minimize their cost, which could add up to a volatile aggregate pro le such as large peaks that result if many households charge their DS at the same time. Indeed, DSs are becoming more attractive at the household level, especially along with intermittent DG, because they can increase demand-side exibility and decrease the consumers' costs for electricity supply [START_REF] Mulder | Electricity Storage for Grid-connected Household Dwellings with PV Panels[END_REF]. The volatility has various disadvantages. Firstly, a large number of high cost and carbon intensive "peak-plants" are required to provide power alongside the intermittent sources to compensate the variability. Moreover, the power peaks resulting from the variability may lead to infrastructure damages and expensive capacity upgrading. Thus, leveling the volatile overall community pro le is crucial.

There are a few works in the literature on scheduling a system of multiple storage units ([3]- [START_REF] Vytelingum | Agent-based Micro-Storage Management for the Smart Grid[END_REF]). In these works, however, either the storage units are centrally scheduled without obeying the autonomy of the households, or households cooperatively play a game in a decentralized way with similar learning behavior to achieve a desired communal pro le. Recently, dynamic pricing based demandresponse strategy is gaining attention as a coordination mechanism. When the households are very exible (for instance, by using their DSs), their responsiveness to the dynamic price might lead to a closed-loop feedback that could cause volatility, as demonstrated in [START_REF] Roozbehani | On the Stability of Wholesale Electricity Markets Under Real-Time Pricing[END_REF]. Thus, in addition to re ecting the aggregate load pro le, a dynamic pricing model needs intelligence to capture the exibility of the households to respond to price signals.

In this paper, we consider a self-organized neighborhood energy community that is composed of sel sh prosumer households, where power can be exchanged horizontally between the households within the community, and bidirectionally between the autonomous energy community and the rest of the grid. The energy community is controlled using a multi-agent based electronic market proposed in [START_REF] Kok | PowerMatcher: Multi-Agent Control in Electicity Infrastructure[END_REF], where the households can trade with each other using local tari s. A household-agent coordinates the resources at the household to optimize the household consumption, while a community-agent watches over the overall load pro le of the energy community and coordinates the household-agents accordingly. The community is assumed to have smart grid capabilities [START_REF] Ipakchi | Grid of The Future[END_REF], such as intelligent devices at each household that can exchange information across a communications platform.

The main contributions of this paper are:

-We study coordination in a future energy community that is formed by a group of self-organized sel sh prosumer households that can generate, store, import and export power, whereby the aggregate load pro le is likely to be highly volatile due to the exibility and sel sh behavior of the prosumer households as well as the intermittence of DGs. -We propose a dynamic pricing model that embodies a learning mechanism to iteratively adapt to the responsiveness of the households in the self-organized energy community and the intermittence of the DGs. Our pricing model has distinct import and export tari s that handle the power import and export of the prosumers. -We propose a polynomial-time distributed DS scheduling algorithm that runs at each household to solve a cost minimization problem of the sel sh household, and at the same time attening the overall community load pro le using our dynamic pricing model. -Our simulation results reveal that our distributed scheduling algorithm gains comparative performance with a reference centralized scheduling algorithm, and also achieves up to 72.5% reduction in standard deviation of the overall net demand of the community compared to a two-level pricing scheme.

The rest of the paper is structured as follows. Section 2 presents the mathematical model of the DS scheduling problem. In Section 3, the dynamic pricing model is presented, followed by our distributed algorithm in Section 4. The simulation results are presented in Section 5. Finally, our concluding remarks are presented in Section 6.

System Model

We present a formulation of the problem of nding an optimal schedule for DSs to atten the demand pro le of a self-organized neighborhood energy community.

The distributed storage systems are scheduled o ine over a scheduling time period (24 h) that is divided into time steps, i.e. = {1 2 } that have equal duration of time units.

Distributed Storage (DS)

Each DS is battery storage and is described by the parameters that are summarized below [START_REF] Ahlert | Sensitivity Analysis of the Economic Bene ts from Electricity Storage at the End Consumer Level[END_REF].

: the maximum energy storage capacity (in kWh).

: the maximum power capacity of the recti er (in kW).

: the maximum power capacity of the inverter (in kW).

: the time required for a full charge cycle (in h).

: the cycle e ciency (%). : the recti er e ciency (%).

: the inverter e ciency (%). : maximum depth of discharge allowed (%).

We neglect the self-dissipation of the battery, because it has a negligible e ect for the length of our scheduling period. In addition to the above parameters, the variables and are used to denote the amount of power that is charged into and discharged from, respectively, the DS in time step . Assuming a symmetric cycle e ciency, , we denote the storage charging e ciency and discharging e ciency by and , respectively, where = = p . The state of charge (SOC) of the DS at time step is denoted by (in kWh)

Generally, the SOC of a DS at the end of a time step can be obtained from the SOC at the end of the previous time step as shown in Eq. 1. The term added to accounts for the net rise in the storage level in time step which is the di erence between the stored energy due to charging of the storage and the discharged energy from the DS. The number of time units per time step ( ) is used in Eq. 1 to convert power (kW) into energy (kWh). The maximum SOC of each DS is bounded by its maximum storage capacity (Eq. 2). The SOC cannot fall below the maximal discharging depth (Eq. 3). The rate of charging a DS is limited by the maximum charging rate ( ) and the maximum power capacity of the recti er (Eq. 4), whereas the discharging rate of the DS is limited by the maximum power capacity of the inverter (Eq. 5).

= + μ ¶ (1) , (2) (1
) × ,

Demand and Production

The accumulated power demand of all the appliances of a given household in time step is denoted by , whereas we designate the total power production of all the distributed sources owned by the household in time step by . In this work, we assume that forecasts of and are available for the entire scheduling period. We de ne the scheduled demand of a household in time step , denoted by , as the di erence between the demand and the self supply of the household in the time step (Eq. 6). The amount of power the household imports from or exports to the grid cannot exceed the power capacity of the cable connecting the household to the grid, denoted by , as shown in Eq. 7.

The scheduled demand of the overall neighborhood in time step is given by the sum of the scheduled demands of all the households in the neighborhood as shown in Eq. 8. We represent the net demand of the community ignoring the DSs by , for each time step (Eq. 9).

= ( + ) ( + ), (6) , (7)
= X , households (8)
= X ( ), households (9)

The Cost

Since a household can import power from the grid as well as feed the surplus power into the grid, we will have two di erent tari s. We denote the import tari and the export tari in time step by and , respectively. The electricity cost of a household in time step is denoted by , and is given in Eq. 10. Clearly, is a positive cost when power is imported ( 0), and is a negative cost (income) when power is exported (

0). = ½ × , if 0 × , if 0 , (10)

Optimization Problems

Given a self-organized neighborhood energy community of prosumer households, each with forecasted values of demands and self productions and owning a DS with known capacities and e ciency parameters, the problem of optimally scheduling the DSs over a scheduling period to achieve a attened overall community load pro le is addressed di erently by the centralized and distributed scheduling strategies.

The centralized scheduling strategy gives the community-agent the authority to centrally schedule all the DSs of the households in the community. The community-agent rst computes the average value of the net demand of the community (Eq. 11), and then schedules the DSs trying to minimize the deviation of the overall scheduled demand of the community from the average value. The corresponding quadratic optimization problem is formulated in Eq. 12, where X 1

, and Y 1 represent the charging and discharging schedules, respectively, of the DSs. Although this approach does not comply with the autonomy and sel sh nature of the households, we use it as a reference.

= 1 X =1 (11) minimize X 1 1 X ( ) 2 (12)
subject to: Equations 1-9

In the distributed scheduling technique each household-agent autonomously schedules its DS to sel shly minimize the cost of that household. The communityagent coordinates the household-agents by providing a novel dynamic pricing based incentive to achieve a attened overall pro le of the self-organized energy community. While the linear programming formulation of the household cost optimization problem is given in Eq. 13, the dynamic pricing model and the details of the distributed algorithm are deferred to Sections 3 and 4, respectively. minimize

X ( 13
)
subject to: Equations 1-7

3 The Dynamic Pricing Model

Our dynamic pricing model is based on a scenario where the autonomous households trade electricity with each other on a local electronic energy market [START_REF] Kok | PowerMatcher: Multi-Agent Control in Electicity Infrastructure[END_REF] in the community whereby the autonomy of the energy community allows the community-agent to propose local price-vectors to achieve desirable communal goals. In our dynamic pricing model, the community-agent proposes a price vector, then each household-agent sel shly schedules the storage unit of that household by solving Eq. 13 and replies with the corresponding scheduled demand of the household. Based on the response of all the households, the communityagent adjusts the price vector using an intelligent learning mechanism. This is repeated iteratively to obtain an optimal price vector that yields a attened overall community pro le.

In the proposed pricing model, the cost of a unit power varies from one time step to another. The optimal tari for each time step is determined iteratively. At the ( + 1) iteration cycle, the tari for the time step is obtained by adjusting the corresponding tari in the previous iteration cycle using an incremental factor ( × ):

+1 = (1 + ( × )) (14)
The incremental factor is composed of two terms: the learning factor ( ) and the deviation factor ( ). The learning factor is a constant (0 1) that determines to which extent the deviation factor overrides the old price vector. Empirical optimal values of are provided in Section 5. The deviation factor captures the variation of from its average value. Let be the overall scheduled demand of the neighborhood in the time step for the iteration cycle. Let be the average of the overall scheduled demand (Eq. 15), then the deviation factor, is given in Eq. 16, where determines whether the incremental value should be positive or negative. If , then we add a positive incremental value to the tari to reduce consumption in this time step:

= 1 If , then we subtract an incremental value from the tari to increase consumption in this time step:

= 1. = 1 X =1 (15) = × ( ) 2 P =1 ( ) 2 (16)
re ects the e ect of the o set of the scheduled demand from the mean value on the price vector. The pricing model increases the tari on the time steps where the overall scheduled demand of the neighborhood ( ) is above the average, and reduces the tari when is below the average, thereby providing incentives to the sel sh households to atten the overall scheduled neighborhood demand. Since the price vector is improved iteratively depending on the reaction of the households, the intelligent learning employed by our dynamic pricing model e ectively handles the price-responsiveness of the households, thereby minimizing the closed-loop feedback e ect. In e ect, the aggregate load pro le of the self-organized energy community could be managed.

Following the suggestion in [START_REF] Houwing | Demand Response with Micro-CHP systems[END_REF], the power feed-in tari s are obtained by subtracting the transport part of the import tari s (Eq. 17), where is the transport part of the import tari . The pricing model can be modi ed to achieve objectives other than attening the overall pro le by simply substituting the in Eq. 16 by the desired target value for each time step.

= , ( 17
)
4 The Distributed Algorithm

Our design of the distributed algorithm re ects the autonomy and sel shness of the households, while simultaneously striving to atten the aggregate load pro le of the self-organized energy community using our novel dynamic pricing model. The block diagram describing the execution of our distributed scheduling algorithms is shown in Fig. 1. The algorithm embodies a xed number of iterative cycles that search for an optimal price vector that yields the best level of atness for the overall scheduled net demand of the energy community ( ). We describe the atness of in terms of its standard deviation:

= v u u t 1 X =1 ( ) 2
U pd a te th e ta r iffs f or e ac h tim e s tep

S o lve h ou s e h o ld op tim iz a tion D S o f th e h o us e h o ld

R D

A t e ac h h o u s e ho ld A t t h e c o m m un ity -a ge n t

, P Fig. 1. A block diagram for the distributed algorithm.

The algorithm is initiated at the community-agent. At each iteration step, the community-agent sends the recent tari vectors ( ) to each household-agent. Upon receiving the tari vectors, each household-agent solves its sel sh cost optimization problem (Eq. 13) with the up-to-date tari s, and sends its resulting scheduled demand to the community-agent. When the community-agent receives the scheduled demands of all the households in the current iteration cycle, it computes the tari vectors for the next iteration cycle using Eq. 14, and the iteration continues. Once the desired xed number of iterations is performed, the community-agent picks the best tari vectors that yielded the smallest value of , and the corresponding schedules of the DSs are adopted.

Simulation

In our simulation, storage systems installed at all the households have the same parameter speci cations. Lead-acid battery storage is used as a reference, since it is regarded as the most economical choice [START_REF] Ahlert | Sensitivity Analysis of the Economic Bene ts from Electricity Storage at the End Consumer Level[END_REF]. The parameter speci cations for lead-acid suggested in [START_REF] Ahlert | Sensitivity Analysis of the Economic Bene ts from Electricity Storage at the End Consumer Level[END_REF] are listed in Table 1. The data for the demand and electricity production of a household are acquired from Alliander 2 . The distributed sources of a household are a PV panel and a micro-CHP. The data were obtained by eld measurements that were taken every 15 minutes for a duration of 24 hours using smart meters installed at the households. The micro-CHP generation is constant (1 kW) over each period of operation, and the data speci es the start time and end time of each period of its operation. To make alternative pro les for each household, we randomized the values according to a normal distribution. For demand and PV panel production, the randomized pro les were generated with mean value equal to the measured data and standard deviation equal to 15% of the mean, for each time step. For the micro-CHP production, di erent variants of the start time and end time of the production periods are generated using the normal distribution function with mean values equal to the corresponding measured values and standard deviation of one time 2 Alliander is the largest electricity distribution network operator company in the Netherlands owning 40% of the distribution networks. The transport part of the electricity import tari is = 0 04 . The data is obtained from ECN 3 . Thus, for each time step the feed-in tari is obtained as = 0 04 . The proposed algorithm is simulated with di erent demand and generation data sets representing each of the four seasons of the year. In addition to the centralized scheduling and the dynamic pricing based distributed scheduling, we have a simulation scenario in which households autonomously schedule their DSs to minimize their cost responding to xed two level tari s (day and night tari s).

The relative performance of the scheduling algorithms was similar under the data sets representing the four seasons, thus we present only the results obtained using the data sets representing the Spring season due to limited space. Fig. 3 shows the overall scheduled demand of the community obtained using the centralized and the distributed scheduling techniques. The large negative net demands of the neighborhood in the time steps 32-45 and 67-80 result from the accumulated production of the micro-CHPs and the PV panels that exceed the total demand. Apparently, both the centralized and distributed scheduling techniques have achieved signi cant improvement (75.6% and 75.0% reductions in , respectively) in the overall scheduled demand pro le compared to the net demand of the community. It is interesting to see that the distributed technique, that maintains the autonomy and sel shness of the households, has achieved a comparable performance with the centralized technique that makes a simplifying assumption that all the DSs are centrally managed. The achievement of the distributed technique stems from the intelligence of its dynamic pricing model based incentive.

The comparison of the performance of our dynamic pricing based distributed scheduling technique to that of the two level pricing scheme shown in Fig. 4 reveals that our distributed algorithm achieves a pro le with signi cant improvement in atness compared to the two level pricing. Apparently, the scheduled demand using two price levels did not show signi cant improvement on the shape of the overall net demand, implying that the pricing scheme does not incentivise the households enough. Our simulation results based on the data representing the four seasons of a year reveal that our dynamic pricing based algorithm can achieve up to 72.5% improvement compared to the two-level pricing scheme in terms of the standard deviation of the overall scheduled demand.

A comparison of the performance of the distributed algorithm under di erent values of the learning factor ( ) is shown in Fig. 5. The gure shows that the standard deviation of the overall scheduled demand decreases slowly for smaller values of , whereas, it drops rapidly for larger values of . On the other hand, the standard deviation curve is more stable for smaller values of . Furthermore, no signi cant improvement in is observed after a xed number of iterations. Hence, the algorithm is expected to perform well with few iterations using the larger values of (0 2 0 5). The reference parameter values in Table 1 are perturbed to assess their impact on the performance of our distributed algorithm. The results in Fig. 6 reveal that varying the e ciency parameters, the maximum charging and discharging rates of the DS results in low variations (mostly between -10% and +10%) in the performance of the algorithm, where increasing the values of the parameters increases exibility of the households to respond to the dynamic price, thereby slightly increasing performance. Varying the community size also resulted in small performance deviation which results form the randomization of the proles of the households. On the other hand, with very low storage capacity, the households have limited exibility to store and release power in response to the dynamic price, thereby leading to larger values of .

The load pro le of a self-organized energy community composed of sel sh prosumers that can autonomously generate, store, import, and export power, is likely to be highly volatile due to the intermittence of the distributed generations and the autonomy and sel sh nature of the prosumers. We have introduced a novel dynamic pricing model that can help to atten the load pro le in such scenario by intelligently adapting to the price-responsiveness of the sel sh prosumers using its learning mechanism. We have proposed a distributed scheduling algorithm of distributed power storages that uses the dynamic pricing model to atten the community load pro le while each household sel shly tries to minimize its cost by solving a simple polynomial-time optimization problem formulated via linear programming. Simulation results reveal that our distributed algorithm has comparable performance with a reference centralized scheduling algorithm, and it can achieve up to 72.5% improvement in standard deviation of the load pro le of the community compared to a reference two-level pricing model.

Our distributed algorithm and dynamic pricing model can also be extended to schedule exible electrical units such as electric vehicles, heat-pumps, etc., and could be easily modi ed for objectives other than attening the overall demand.

Fig. 2 .

 2 Fig. 2. Demand and production pro les of a household.

3Fig. 3 .Fig. 4 .

 34 Fig. 3. Comparison of the centralized and distributed algorithms using the overall scheduled demand for N = 20.

Fig. 5 .-

 5 Fig.5. The e ect of the learning factor.

P e rf o r m a n c e d e v ia t io n s ( % v a lu e ) d u e to p a ra m e te r v a lu e v a r ia tio n s 1 5 Fig. 6 .

 156 Fig.6. Algorithm performance in response to perturbing parameters.

Table 1 .

 1 Parameter Values of the Storage System [1].

	kWh h (%) (%) kW kW (%) (%)
	5 5 80 85 1 0.5 95 98

European Parliament, "All New Buildings to be Zero Energy from

2019," Committee on Industry, Research and Energy, Brussels 2009.


D Benedikovic
email: daniel.benedikovic@u-psud.fr

C Alonso-Ramos

L Vivien

P Cheben

J H Schmid

S Wang

D.-X Xu

B Lamontagne

J Lapointe

S Janz

R Halir

A Ortega-Moñux

J.-G Wangüemert-Pérez

I Molina-Fernández

J M Fédéli

M Dado

High-Efficiency Fiber-Chip Surface Grating Couplers

Keywords: Grating couplers, refractive index engineering, subwavelength grating, silicon-on-insulator, silicon photonics

We report our latest advances in development of high-efficiency fiber-chip surface grating couplers with refractive index engineered subwavelength structures. We present different experimental demonstrations of high-performance gratingcoupled optical interfaces, developed on the standard 220-nm silicon-on-insulator technology in the near-infrared wavelengths.

I. INTRODUCTION

The coupling of light to or from microphotonic circuits is still one of the major practical challenges of silicon technology. The surface grating couplers afford effective approach to interface silicon chips, with relaxed alignment tolerances, wafer scale testing capability, and compatibility with integration and packaging technologies [1][2][3][4][5].

II. SINGLE-ETCH GRATING COUPLERS

We reported a set of subwavelength index engineered apodized grating couplers that desired only one fabrication step, while demonstrating the state-of-the-art fiber-chip coupling performance. In particular, we experimentally shown that by optimizing the thin film interference from the bottom oxide cladding, the peak efficiency of up to -2.2 dB and -2.5 dB are achieved near 1.55 µm and 1.3 µm wavelengths, as shown in Fig. 1 (red curves) [1][2][3]. The couplers are implemented on a standard silicon-on-insulator (SOI) wafer with 220-nm-thick layer. We also demonstrated the first subdecibel fiber-chip coupling efficiency of -0.7 dB (blue curve in Fig. 1) in this platform by utilizing the backside wafer processing, followed by metal mirror deposition [2]. The optical micrograph and scanning electron microscope (SEM) images of fabricated couplers are shown in Fig. 1.

III. DUAL-ETCH GRATING COUPLERS

We also developed a flexible dual-etch fiber-chip grating coupler with an extraordinary intrinsic directionality of 95%, independently on the buried oxide thickness [4]. The grating geometry comprises interleaved deep and shallow etched trenches and a short subwavelength index-matching section to reduce reflections [5]. The grating coupler was realized on regular SOI with 220-nm layer over 3-μm buried oxide. The measured coupling efficiency is -1.3 dB, as shown in Fig. 2, altogether with the SEM image.

Fig. 1

 1 Fig. 1 Measured coupling efficiencies as a function of wavelength of singleetch apodized grating couplers, with and without metal reflector underneath. Optical micrograph and SEM images of fabricated structures.

Fig. 2

 2 Fig. 2 Measured coupling efficiency as a function of wavelength of dual-etch coupler with interleaved deep and shallow etched trenches. SEM image of fabricated device.


Diana Elena Comes
email: comes@uni-kassel.de

Christoph Evers
email: evers@uni-kassel.de

Kurt Geihs
email: geihs@uni-kassel.de

Axel Hoffmann
email: axel.hoffmann@uni-kassel.de

Romy Kniewel
email: r.kniewel@uni-kassel.de

Jan Marco Leimeister
email: leimeister@uni-kassel.de

Stefan Niemczyk
email: niemczyk@uni-kassel.de

Alexander Rossnagel
email: a.rossnagel@uni-kassel.de

Ludger Schmidt
email: l.schmidt@uni-kassel.de

Thomas Schulz
email: t.schulz@uni-kassel.de

Alexander Roßnagel

Matthias Söllner
email: soellner@uni-kassel.de

Andreas Witsch
email: witsch@uni-kassel.de

Designing Socio-technical Applications for Ubiquitous Computing

Keywords: Ubiquitous Computing, Social Acceptance, Law, Usability, Trust

scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Since Weiser introduced the idea of ubiquitous computing (UC) considerable research has been done in this field and UC applications have then been developed [START_REF] Hoffmann | Towards an Approach for Developing socio-technical Ubiquitous Computing Applications[END_REF]. UC applications use sensors to gather information of heterogeneous environments, derive context to be able to adapt to changes, and dynamically integrate services to increase user experience. Additionally, devices are constantly getting smaller and are integrated into ordinary objects, becoming a commodity. Affordable mobile data connections connect people to data networks anytime and anywhere. Surrounded by deeply integrated information technology, users are overwhelmed by the increasing complexity of such systems. Furthermore, they are incapable of anticipating all consequences of technology use, such as emerging data protection2 concerns. While technological challenges for the implementation of UC systems have already been widely discussed, many challenges regarding the social acceptance of UC applications are still unsolved. The development approaches by Janzen et al. [START_REF] Janzen | Designing Ubiquitous Information Systems based on Conceptual Models[END_REF], and Resatsch et al. [START_REF] Resatsch | Do Point of Sale RFID-Based Information Services Make a Difference? Analyzing Consumer Perceptions for Designing Smart Product Information Services in Retail Business[END_REF], e.g., do not account for social issues like law, usability, and trust at all. The approach described in DIN EN ISO 9241-210 does not provide specific techniques that should be applied in single development phases. The ETHICS approach [START_REF] Mumford | Effective systems design and requirements analysis: the ETHICS approach[END_REF] includes several important aspects, but lacks the incorporation of legal issues. Thus, designers need further guidance, e.g., in terms of methods and techniques. To solve this problem, we propose a multidisciplinary development approach, including methods from law to ensure legal-compatible technology design 3 , from usability engineering to develop a user interface that fits the specific requirements of UC applications, as well as from trust engineering to increase user acceptance of the developed applications. The methods and theories have been combined for the development of the mobile UC application Meet-U.

Requirements for the Design of UC Applications

UC applications support the user during his everyday life due to the use of sensor information to perform reasoning and adaptation [START_REF] Hoffmann | Towards an Approach for Developing socio-technical Ubiquitous Computing Applications[END_REF]. The resulting requirements for the development process are described in the following. Apart from the opportunities which UC offers, it also entails considerable legal risks. Particularly, the data protection risks emerging from, e.g., ubiquitous elicitation, transmission and usage of personal data or from ubiquitous monitoring have to be considered [START_REF] Roßnagel | Datenschutz in einem informatisierten Alltag[END_REF]. Therefore, important approaches to solutions in the scope of designing UC applications are, e.g., data protection by technology or freedom of action supporting architectures.

A challenge in UC is the creation of an unobtrusive user-friendly interface. Such an interface should not require specific skills or training. Additionally, an adaptive interface which can still be controlled by the user is required. If the system should autonomously adapt to an unexpected state, resulting in an unexpected behavior, the user might be negatively affected. Therefore, usability is a crucial issue in the development process, and expertise needs to be incorporated.

The on-going development of UC technologies will make applications more and more complex, thus enhancing the importance of trust is an important mechanism for perceived complexity reduction to the user. Furthermore, research on technology acceptance already emphasized that trust is a key determinant of technology adoption and usage [START_REF] Leimeister | Design, Implementation, and Evaluation of Trust-Supporting Components in Virtual Communities for Patients[END_REF]. Concerning unknown technologies and applications, the initial trust of the user is crucial. Creating this initial trust during the development of UC applications is an additional challenge in UC development.

Development Proposal for UC Applications

This section provides an overview of the phases and activities of our initial development proposal [START_REF] Hoffmann | Towards an Approach for Developing socio-technical Ubiquitous Computing Applications[END_REF] and the methods being applied. The core of the development proposal is an iterative development approach that consists of analysis, conceptual and software design, as well as implementation and evaluation. First activities in the development process include defining appropriate goals and writing application scenarios in the demand analysis in order to establish a multidisciplinary understanding of the purpose of the UC application. Furthermore, the scenario includes a business model for the envisioned UC application.

The extended scenarios are used afterwards to elicit requirements. Our approach considers conventional requirements that are generally used in system development. It incorporates furthermore methods for acquiring expert requirements. In order to acquire functional requirements from law, the first three tiers of the KORA method [START_REF] Hammer | KORA-Eine Methode zur Konkretisierung rechtlicher Anforderungen zu technischen Gestaltungsvorschlägen für Informations-und Kommunikationssysteme[END_REF] have been used. This procedure is analogously accomplished for usability [START_REF] Behrenbruch | Normative Anforderungsanalyse für ein RFID-basiertes Assistenzsystem für Arbeitsgruppen[END_REF] and trust [START_REF] Söllner | Vertrauensunterstützung für sozio-technische ubiquitäre Systeme[END_REF]. After the requirement analysis, the requirements need to be joined. Therefore, the procedure of the EasyWinWin-method is adapted to our special needs. The result is a shared requirements document with negotiated requirements.

The requirements document is the basis for developing a consistent concept design. In this stage the artifacts: use cases, application workflow, screen design and backend architecture are elaborated upon. There are persons in charge for every step which consult the experts in case if the person in charge is not able to treat single requirements. Experts continuously review the resulting artifacts. If necessary, new solutions get elaborated in multidisciplinary collaboration. The implementation of the application is planned and conducted during the stages of software design and implementation. During the iterative implementation, prototypes are built and then regularly tested against the negotiated requirements. The results are used to modify the application design. The application is evaluated using a combination of methods established within the involved disciplines.

4

Case Study: Meet-U

The development proposal of the previous section has been applied and refined during the development of the smart mobile application Meet-U [START_REF] Comes | Adaptive Applications are Smart Applications[END_REF]. Its goal is supporting people to organize meetings with friends that take place at public or private events, such as movies at cinemas or birthday parties. We designed Meet-U to be a ubiquitous application that supports its users in every situation by adapting to context changes and avoiding distracting users from their activities. Our first version of Meet-U has been developed to demonstrate different self-adaptive behaviors of mobile ubiquitous applications and considers only requirements and restrictions from computer science.

Results of a usability evaluation with users and a legal evaluation show that the first version neither satisfies the user needs, nor is it legal-conform. Besides, adaptivity is a helpful feature in ubiquitous environments, but it is not trustworthy. To turn Meet-U into a legal-compatible, user-friendly, and trustworthy application we utilized our multidisciplinary development approach.

Demand Analysis

A brief description of Meet-U's main goal to support meeting friends builds the basis for further development activities. Moreover, the three central user goals have been considered: planning an event, navigating to an event, and taking part at an event.

From this starting point, three different scenarios enriched with personas have been elaborated upon. The scenarios show a typical set of user interactions with the planned system. They are described from the perspective of a user and the level of abstraction does not contain any technical details. They serve as a basis for identifying tasks the user might accomplish and as foundation for the requirements analysis and interface design. We comprehensively described each user type by a persona, clarifying the users' needs. Knowledge about potential users simplifies acquiring requirements regarding usability and user trust. Personas turned out to be additionally helpful for the juridical assessment, e.g., to identify whether the system has to be used in a private or professional context. The demand analysis is completed by a business model. This ensures marketability at the first stage of development. We thus identified all possible conflicts between an economic business model and the affected laws. An unlawful business model blocks a legal-compatible application design. We propose expert reviews to ensure at least legal-conformity. We used the artifacts scenarios, personas and business model for a first validation with potential users. With the feedback we could adjust the artifacts to real user needs and expectations.

Requirements Management

After the demand analysis, we elaborated upon the requirements for the further development process. Accordingly, we elicited conventional requirements as well as expert requirements in order to realize legal provisions and promote usability and trust. The emerging functional requirements were completed by the requirements we obtained in the validation during the demand analysis. We formulated the requirements in a technical, but generally understandable language. We had to pay attention to the fact that requirements are formulated without offering concrete technical solutions. However, in our multidisciplinary collaboration we were aware of the challenge that in addition to conventional requirements, expert requirements would also influence the development. These expert requirements avoid domain specific terminology to facilitate mutual understanding.

In law, the difficulty insists that legal norms rarely contain functional requirements. Even usability and trust do not primarily focus on the system's capabilities. To gain functional requirements from law, we used KORA; for usability and trust, we used KORA based methods. This approach assures traceability to their sources. Additionally, the linguistic change from the respective terminologies to a more general understandable language is provided. To acquire requirements from law, we identified legal provisions from fundamental rights. These provisions were concretized to legal criteria which contain relations to technical functions as well as to the legal and social aspects. In the last step, the criteria were translated to functional requirements.

Usability considers norms such as DIN ISO 9241-110 to define requirements. Different provisions were derived, which got concretized, as proposed by the KORA method. Usability criteria contain relations to technical functions as well as to the usability aspects. They describe abstract problem solutions in relation to the provisions, but do not exhibit any connection to a certain technical problem-solving approach. In the last step, the criteria were translated to functional requirements.

Trust supporting requirements were derived based on the trust conceptualization of [START_REF] Söllner | Towards a Theory of Explanation and Prediction for the Formation of Trust in IT Artifacts[END_REF]. According to this, three dimensions for user trust in a system like Meet-U were identified: performance, process and purpose. The performance dimension reflects the capability of the system in helping the user achieve his goals, the process dimension indicates the user's perception regarding the degree to which the system's algorithms are appropriate, and the purpose dimension mirrors the user's perception of the intentions that the designers have of the system. These dimensions are themselves formed by several antecedents. The antecedents can be interpreted as under-specified functional requirements, and thus are translated into functional requirements.

About half of all Meet-U requirements were expert requirements, pointing to the impact of the involved experts. The other requirements were conventional requirements. Some of the requirements were congruent, because different stakeholders came up with requirements that meant the same. Other requirements were conflictive. Thus the resulting requirements had to be negotiated in a workshop by all stakeholders. A primary step of the workshop served to enforce a mutual understanding of all requirements. Therefore, we identified terms which could have different definitions in the involved disciplines. These terms were redefined to a consistent vocabulary, and summarized in a glossary. In the following steps congruent requirements were identified and formulated as one common requirement and in case of conflictive requirements we tried to work out a joint solution. If such a solution could not be found, the requirements with lower priority were cancelled. The unsorted requirements were, if possible, grouped to function blocks. The sorted requirements and the glossary were combined to a requirements document.

Concept Design

The basis for the concept design of Meet-U was provided by the requirements document. The concept design included the graphical user interface (GUI) and the backend software architecture, and was formed in iterative steps. The GUI design was mainly conducted by the usability expert who processed the following steps: gathering all data and functional elements, developing the information architecture and functional structure of the interface, and finally designing the screen design incorporating standard wire-frames. Functional and data elements represent information and functionality promoted to the user in the interface. Data elements are the atomic units acted upon when using a system, for example: an event, a contact, the user profile, and a notification. To illustrate relationships between data elements, we employed a concise site-map. This shows, for example, that the data element private event con-tains the data element participants list, which contains the contact profile. So the sitemap facilitates the mutual understanding for the expert reviews. Furthermore, functional elements are operations that can be carried out by data elements and their representations in the interface, e.g., selecting contacts from a list in order to create an invitation list, or creating or deleting an event.

We transferred the initial information model and functional structure based on the use cases illustrating the user interactions in the interface to solve a particular task. In our flow charts, the data elements and functional elements working as connectors between screen elements were shown. The flow charts were described in high level of detail, in order to allow expert reviews. As the use cases did not refer to a certain interface element, we had to make a translation step, supported by the perspective of usability. The interaction design considered the goals of the users and common mental models of solving the tasks. Further, if there was a cluster of related user needs, one screen was considered that incorporated all these together. A smartphone specific GUI-standard was considered as archetype users would expect it. We enhanced the information architecture and functional structure by legal and trust aspects of the requirements document. For example, as required from law, we placed the legal notice in a section that is always accessible in at most two clicks. Following this, we applied platform specific design guidelines for wire-frames and visual screen design. Additionally, the screen design of Meet-U was enhanced by trust related requirements. For example, the user could access an explanation why providing a specific information in his profile was needed, and what would be the result of not providing this information. For instance, the users were informed about the relevance of specifying their interests in order to receive adequate event recommendations and they were explained why a certain recommendation was given.

The final step was defining the back-end architecture design. In this step, we elaborated sequence diagrams, entity relationship models, and identified software components. The obvious components were the mobile device, the back-end server, and external services. The sequence diagrams were derived directly from the use cases and visualize the data flow between the software components. These artifacts were reviewed by the legal experts, in order to identify weak spots like sending the current GPS position and the destination to a navigation service. Instead of sending the current position and implicitly the IP-address to the external service, we built a more legal-compatible solution which uses the Meet-U server as a proxy to impede the identification of users. A mutual understanding was required to perform a review. Thus, we annotated the communication in the sequence diagram to display which information were transmitted. Furthermore, we developed a user-centered adaptation design. Each self-adaptation of the system could be canceled by the user in respect to the expert requirements. The use cases, flow charts, screen designs, and back-end architecture form the design concept.

Discussion

In the following, we describe our refinement while applying the approach, which was necessary regarding the predefined artifacts, the workflow and responsibilities for development activities, and the facilitation of mutual understanding.

For the application scenario as first artifact in the demand analysis phase, we had to define an appropriate level of abstraction. We chose an abstraction level that illustrates how the user interactes with the application and describes the environment of the application. They would serve as a foundation for the requirements analysis, but not restrict the technology design. The final artifact in the requirements management phase contained the set of negotiated requirements. We grouped these on the basis of function blocks rather than grouping by involved disciplines. This grouping reduced the probability of overlooking functional requirements in the following activities. The flow charts were drawn in greater detail so that experts from law and trust were able to review them and contribute to a socially acceptable design concept.

The common understanding of the application and its environment was achieved by scenarios elaborated upon in the demand analysis, and which then guided the development for all disciplines. We used natural language to formulate the scenarios and in the next step to define requirements. Natural language was appropriate to facilitate a common understanding rather than discipline specific terminology and representation formats. Necessary key terms that turned out to be ambiguous between disciplines were clarified, defined, and documented in the glossary. We proposed to annotate the requirements with two types of information. The disciplines by which it was declared and the source from which it was derived to reasonable dealing with the requirements and ensured that correct experts could be consulted for further work.

The consultation of legal experts during the design of the business model is crucial. This needs to be considered in the workflow. In our experience, there is a trade-off between legal and business concerns. To be able to design a legal-compatible application at least legal-conformity of the business model needs to be ensured. Further, the short iterations during conceptual design turned out to be very effective. The expert reviews helped to enforce a socially acceptable design of the application by deliberating on possible solutions.

Using our development approach, we were able to design a second version of Meet-U, explicitly incorporating insights from legal and usability provisions and trust theory. Based on the assessment of the involved experts, the resulting application design is more social-acceptable than the first version. Nevertheless, it remains unclear whether the intended users of Meet-U appreciate the derived design, as proposed by the experts. To evaluate this with intended users, we have to implement the design concept. This will be done in an iterative process where prototypes will be implemented and evaluated by experts as described in the development proposal.

We observed that due to the involved experts, the overall effort of the approach was very high. We needed a lot of input and workshops with them during the development. Even if this was essential for our development process, it is also a weakness of our approach, because high expert effort means generally high expense. Furthermore, our approach might lead to an expenditure of time. Since we assume that the same expert requirements will become important over and over again, a possible improvement might be software requirement patterns to ease the phase of requirements management. By identifying these requirements and transforming them to patterns, expert effort will be reduced and future development processes will be shortened.

Conclusion

In this paper, we present a novel development approach for UC applications. This approach explicitly addresses social acceptance by integrating methods from legal research, usability engineering and trust engineering. The main task was to manage the increased number of stakeholders and dependencies, respectively, conflicts between requirements of involved disciplines. Therefore, we adopted predefined artifacts, a defined workflow with responsibilities, and suggest how to develop mutual understanding required for collaborative development. The Meet-U case study shows that our approach conquers special UC requirements due to the strong collaboration between the disciplines. According to the involved experts, the result is an application design which respects law, is more usable, as well as being more trustworthy than the first version of Meet-U.

The authors cooperate in the VENUS project of the multidisciplinary Research Center for Information System Design (ITeG), http://www.uni-kassel.de/eecs/en/iteg/venus. They are listed alphabetically.

The European law pursues the data protection approach which is transposed into the European data protection directive 95/46/EC.

[START_REF] Resatsch | Do Point of Sale RFID-Based Information Services Make a Difference? Analyzing Consumer Perceptions for Designing Smart Product Information Services in Retail Business[END_REF] Legal-compatible technology design aims at the greatest possible compliance with higherorder legal goals. This differs from legal-conform technology design which refers to the prevention of lawlessness.