Roberto Saia
email: roberto.saia@unica.it

Salvatore Carta
email: salvatore@unica.it

An Entropy Based Algorithm for Credit Scoring

Keywords: Business intelligence, Credit scoring, Data mining, Classification

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

Introduction

The processes taken into account in this paper typically start with a loan application (from now on named as instance) and end with a repayment (or not repayment) of the loan. Although the retail lending represents one of the most profitable source of income for the financial operators, the increase of loans is directly related to the increase of the number of defaulted cases, i.e., fully or partially not repaid loans. In short, the credit scoring is used to classify, on the basis of the available information, the loan applicants into two classes, reliable or unreliable (or better, referring to their instances, accepted or rejected). Considering its capability to reduce the losses of money, it is clear that it represents an important tool, as stated in [START_REF] Henley | Construction of a k-nearest-neighbour credit-scoring system[END_REF]. More formally, the credit scoring techniques can be defined as a group of statistical methods used to infer the probability that an instance leads toward a default [START_REF] Mester | Whats the point of credit scoring?[END_REF][START_REF] Henley | Statistical aspects of credit scoring[END_REF].

Whereas that their processes involve all the factors that contribute to determine the credit risk [START_REF] Fensterstock | Credit scoring and the next step[END_REF] (i.e., probability of loss from a debtor's default), they allow the financial operators to evaluate this aspect. Other advantages related to these techniques are the reduction of the credit analysis cost, a quick response time in the credit decisions, and the possibility to accurately monitor the credit activities [START_REF] Brill | The importance of credit scoring models in improving cash flow and collections[END_REF]. The design of effective approaches for credit scoring is not a simple task, due to a series of problems, the most important of which is the imbalanced distribution of data [START_REF] Batista | A study of the behavior of several methods for balancing machine learning training data[END_REF] used to train the models (small number of default cases, compared to the non-default ones), which reduces the effectiveness of the machine learning strategies [START_REF] Japkowicz | The class imbalance problem: A systematic study[END_REF].

The idea behind this paper is to evaluate an instance in terms of its features' entropy, and to define a metric able to determinate its level of reliability, on the basis of this criterion. In more detail, we measure the difference, in terms of maximum Shannon entropy (from now on referred simply as entropy), between the same instance features, before and after we added to the set of non-default past instances an instance to evaluate. In the information theory, the entropy gives a measure of the uncertainty of a random variable. The larger it is, the less a-priori information one has on the value of it, then the entropy increases as the data becomes equally probable and decreases when their chances are unbalanced. It should be observed that, when all data have the same probability, we achieve the maximum uncertainty in the process of prediction of future data.

On the basis of the previous considerations, we evaluate a new instance in terms of uncertainty of its feature values: comparing the entropy of the set of non-default past instances, before and after we added to it the instance to evaluate. A larger entropy will indicate that the new instance contains similar data (increasing the level of equiprobability), otherwise, it contains different data, thus it represents a potential default case (in terms of non-similarity with the values of the non-default cases).

In our approach we choose to operate without take into account the default cases. Such strategy presents a twofold advantage: first, we can operate proactively, i.e., without the need to use default cases to train our model; second, we overcome the cold-start problem related with the scarcity (or total absence) of default cases, considering that in a real-world context they are much less than the non-default ones.

Given that in most of the cases reported in the literature [START_REF] Lessmann | Benchmarking state-of-the-art classification algorithms for credit scoring: An update of research[END_REF][START_REF] Brown | An experimental comparison of classification algorithms for imbalanced credit scoring data sets[END_REF][START_REF] Bhattacharyya | Data mining for credit card fraud: A comparative study[END_REF] the Random Forests approach outperforms the other ones in this context, we will compare the proposed approach only to this one.

The main contributions of our work to the state of the art are listed below:

(i) calculation of the local maximum entropy by features (Λ), which gives us information about the entropy achieved by each feature in the set of non-default cases (it allows us to measure the differences between instances in terms of single features); (ii) calculation of the global maximum entropy (γ), which represents a meta-feature based on the integral of the area under curve of the Λ values (it allows us to measure the difference between instances in terms of all features); (iii) formalization of the Difference in Maximum Entropy (DME) approach, used to classify the unevaluated instances as accepted or rejected, by exploiting the Λ and γ information; (iv) evaluation of the DME approach on two real-world datasets, by comparing its performance with those of a state-of-the-art approach such as Random Forest (in our case, without using the past default cases to train the model).

The remainder of the paper is organized as follows: Section 2 discusses the background and related work; Section 3 provides a formal notation and defines the problem faced in this paper; Section 4 describes the implementation of the proposed approach; Section 5 provides details on the experimental environment, the adopted datasets and metrics, as well as on the used strategy and the experimental results; some concluding remarks and future work are given in the last Section 6.

Background and Related Work

A large number of credit scoring classification techniques have been proposed in literature [START_REF] Doumpos | Credit scoring[END_REF], as well as many studies aimed to compare their performance on the basis of several datasets, such as in [START_REF] Lessmann | Benchmarking state-of-the-art classification algorithms for credit scoring: An update of research[END_REF], where a large scale benchmark of 41 classification methods has been performed across eight credit scoring datasets.

The problem of how to choose the best classification approach and how to tune optimally its parameters was instead faced in [START_REF] Ali | On learning algorithm selection for classification[END_REF]; in the same work are reported some useful observations about the canonical metrics of performance used in this field [START_REF] Hand | Measuring classifier performance: a coherent alternative to the area under the ROC curve[END_REF].

Credit Scoring Models

Most of the statistical and data mining techniques at the state of the art can be used in order to build credit scoring models [START_REF] Chen | The contribution of data mining to information science[END_REF][START_REF] Alborzi | Using data mining and neural networks techniques to propose a new hybrid customer behaviour analysis and credit scoring model in banking services based on a developed RFM analysis method[END_REF], e.g., linear discriminant models [START_REF] Reichert | An examination of the conceptual issues involved in developing credit-scoring models[END_REF], logistic regression models [START_REF] Henley | Statistical aspects of credit scoring[END_REF], neural network models [START_REF] Desai | A comparison of neural networks and linear scoring models in the credit union environment[END_REF][START_REF] Blanco-Oliver | Credit scoring models for the microfinance industry using neural networks: Evidence from peru[END_REF], genetic programming models [START_REF] Ong | Building credit scoring models using genetic programming[END_REF][START_REF] Chi | A hybrid approach to integrate genetic algorithm into dual scoring model in enhancing the performance of credit scoring model[END_REF], k-nearest neighbor models [START_REF] Henley | A k-nearest-neighbour classifier for assessing consumer credit risk[END_REF], and decision tree models [START_REF] Davis | Machine-learning algorithms for credit-card applications[END_REF][START_REF] Wang | Two credit scoring models based on dual strategy ensemble trees[END_REF].

These techniques can also be combined in order to create hybrid approaches of credit scoring, as that proposed in [START_REF] Lee | A two-stage hybrid credit scoring model using artificial neural networks and multivariate adaptive regression splines[END_REF][START_REF] Wang | A comparative assessment of ensemble learning for credit scoring[END_REF], based on a two-stage hybrid modeling procedure with artificial neural networks and multivariate adaptive regression splines, or that presented in [START_REF] Hsieh | Hybrid mining approach in the design of credit scoring models[END_REF], based on neural networks and clustering methods.

Imbalanced Class Distribution

A complicating factor in the credit scoring process is the imbalanced class distribution of data [START_REF] He | Learning from imbalanced data[END_REF][START_REF] Japkowicz | The class imbalance problem: A systematic study[END_REF], caused by the fact that the default cases are much smaller than the nondefault ones. Such distribution of data reduces the performance of the classification techniques, as reported in the study made in [START_REF] Brown | An experimental comparison of classification algorithms for imbalanced credit scoring data sets[END_REF].

The misclassification costs during the processes of scorecard construction and those of the classification were studied in [START_REF] Vinciotti | Scorecard construction with unbalanced class sizes[END_REF], where it is also proposed to preprocess the dataset of training through an over-sampling or a under-sampling of the classes. Its effect on the performance has been deeply studied in [START_REF] Marqués | On the suitability of resampling techniques for the class imbalance problem in credit scoring[END_REF][START_REF] Crone | Instance sampling in credit scoring: An empirical study of sample size and balancing[END_REF].

Cold Start

The cold start problem [START_REF] Zhu | Active learning with sampling by uncertainty and density for word sense disambiguation and text classification[END_REF][START_REF] Donmez | Dual strategy active learning[END_REF] arises when there are not enough information to train a reliable model about a domain [START_REF] Lika | Facing the cold start problem in recommender systems[END_REF][START_REF] Son | Dealing with the new user cold-start problem in recommender systems: A comparative review[END_REF][START_REF] Fernández-Tobías | Accuracy and diversity in cross-domain recommendations for cold-start users with positive-only feedback[END_REF].

In the credit scoring context, this happens when there are not many instances related to the credit-worthy and non-credit-worthy customers [START_REF] Attenberg | Inactive learning?: difficulties employing active learning in practice[END_REF][START_REF] Thanuja | Applications of data mining in customer relationship management[END_REF]. Considering that, during the model definition, the proposed approach does not exploit the data about the defaulting loans, it is able to reduce/overcome the aforementioned issue.

Random Forests

Random Forests represent an ensemble learning method for classification and regression that is based on the construction of a number of randomized decision trees during the training phase and it infers conclusions by averaging the results.

Since its formalization [START_REF] Breiman | Random forests[END_REF], it represents one of the most common techniques for data analysis, thanks to its better performance w.r.t. the other state-of-the-art techniques. This technique allows us to face a wide range of prediction problems, without performing any complex configuration, since it only requires the tuning of two parameters: the number of trees and the number of attributes used to grow each tree.

Shannon Entropy

The Shannon entropy, formalized by Claude E. Shannon in [START_REF] Shannon | A mathematical theory of communication[END_REF], is one of the most important metrics used in information theory. It reports the uncertainty associated with a random variable, allowing us to evaluate the average minimum number of bits needed to encode a string of symbols, based on their frequency.

More formally, given a set of values v ∈ V , the entropy H(V ) is defined as shown in the Equation 1, where P(v) is the probability that the element v is present in the set V .

H(V ) = -∑ v∈V P(v)log 2 [P(v)] (1)
For instance, if we have a symbol set

V = {v 1 , v 2 , v 3 , v 4 , v 5 } where the symbol oc- currences in terms of frequency are v 1 = 0.5, v 2 = 0.2, v 3 = 0.1, v 4 = 0.1, v 5 = 0.1,
the entropy H(V ) (i.e., the average minimum number of bits needed to represent a symbol) is given by the Equation 2. Rounding up the result, we need 2 bits/per symbol. So, to represent a sequence of five characters optimally, we need 10 bits.

H(V ) = -∑ v∈V P(v)log 2 [P(v)] = 1.9 (2)
In the context of the classification methods, the use of entropy-based metrics is typically restricted to the feature selection [START_REF] Dash | Feature selection for classification[END_REF][START_REF] Kwak | Input feature selection for classification problems[END_REF][START_REF] Jiang | A relative decision entropy-based feature selection approach[END_REF], the process where a subset of relevant features (variables, predictors) is selected and used for the definition of the classification model.

In this work, we instead use this metric to detect anomalous values in the features of a new instance, where anomalous stands for values different from those in the history of the non-default cases.

Notation and Problem Definition

This section introduces some notational conventions used in this paper and defines the faced problem.

Notation

Given a set of classified instances T = {t 1 ,t 2 , . . . ,t N }, and a set of features F = { f 1 , f 2 , . . . , f M } that compose each t, we denote as T + ⊆ T the subset of non-default instances, and as T -⊆ T the subset of default ones.

We also denote as T = {t 1 , t2 , . . . , tU } a set of unclassified instances and as E = {e 1 , e 2 , . . . , e U } these instances after the classification process, thus

| T | = |E|.
Each instance can belong only to one class c ∈ C, where C = {accepted, re jected}.

Problem Definition

On the basis of the Λ and γ information (explained in Section 4.1), calculated before and after we added to the set T + the unclassified instances in the set T (one by one), we classify each instance t ∈ T as accepted or rejected.

Given a function eval(t, λ, γ) created to evaluate the correctness of the t classification made by exploiting the λ and γ information, which returns a boolean value σ (0=misclassification, 1=correct classification), we formalize our objective as the maximization of the results sum, as shown in Equation 3.

max 0≤σ≤| T | σ = | T | ∑ u=1 eval(t u , λ, γ) (3)

Our Approach

The implementation of our approach is carried out through the following three steps:

1. Local Maximum Entropy by Features : calculation of the local maximum entropy by features Λ, aimed to obtain information about the maximum level of entropy assumed by each feature in the set T + ; 2. Global Maximum Entropy : calculation of the global maximum entropy γ, a metafeature defined on the basis of the integral of the area under curve of the maximum entropy by features Lambda; 3. Difference in Maximum Entropy : formalization of the Difference in Maximum Entropy (DME) algorithm, able to classify a new instance as accepted or rejected, on the basis of the Λ and γ information.

In the following, we provide a detailed description of each of these steps.

Local Maximum Entropy by Features

Denoting as H( f ) the entropy measured in the values assumed by a feature f ∈ F in the set T + , we define the set Λ as shown in Equation 4. It contains the maximum entropy achieved by each f ∈ F, so we have that |Λ| = |F|. We use this information during the evaluation process explained in Section 4.3.

Λ = {λ 1 = max(H( f 1 )), λ 2 = max(H( f 2 )), . . . , λ M = max(H( f M ))} (4)

Global Maximum Entropy

We denote as global maximum entropy γ the integral of the area under curve of the maximum entropy by features Λ (previously defined in Section 4.1), as shown in Fig. 1.

f 1 f 2 . . . f M λ 1 λ 2 . . . λ M γ Features (F) Entropy (Λ)
Fig. 1: Global Maximum Entropy γ

More formally, the value of γ is calculated by using the trapezium rule, as shown in Equation 5.

It is a meta-feature that gives us information about the maximum entropy achieved by all features in T + , before and after we added to it a unevaluated instance. We use this information during the evaluation process (Section 4.3), jointly with that given by Λ.

γ = λ M λ 1 f (x) dx ≈ ∆x 2 |Λ| ∑ k=1 ( f (x k+1 ) + f (x k )) with ∆x = (λ M -λ 1 ) |Λ| (5)

Difference in Maximum Entropy

The Difference in Maximum Entropy (DME) Algorithm 1 is aimed to evaluate and classify a set of unevaluated instances.

It takes as input a set T + of non-default instances occurred in the past and a set T of unevaluated instances, returning as output a set E containing all instances in T , classified as accepted or rejected on the basis of the Λ and γ information.

In step 2 we calculate the Λ a value by using the non-default instances in T + , as described in Section 4.1, while in step 3 we obtain the global maximum entropy γ (Section 4.2). The steps from 4 to 26, process all the instances t ∈ T .

After the calculation of the Λ b and γ b values (steps 5 and 6), performed by adding the current instance t to the non-default instances set T + , in the steps from 7 to 13, we compare each λ a ∈ Λ a with the corresponding feature λ b ∈ Λ b (steps from 8 to 12), counting how many times the value of λ b is greater than that of λ a , increasing the value of b (step 9) when this happens, or that of a otherwise (step 11); in the steps from 14 to 18 we perform the same operation, but by taking into account the global maximum entropy γ.

At the end of the previous sub-processes, in the steps from 19 to 23 we classify the current instance as accepted or rejected, on the basis of the a and b values, then we set them to zero (steps 24 and 25). The resulting set E is returned at the end of the entire process (step 27). This section describes the experimental environment, the used datasets and metrics, the adopted strategy, and the results of the performed experiments.

Experimental Setup

The proposed approach was developed in Java, while the implementation of the stateof-the-art approach used to evaluate its performance was made in R1 , using the random-Forest and ROCR packages.

The experiments have been performed using two real-world datasets characterized by a strong unbalanced distribution of data. For reasons of reproducibility of the RF experiments, the R function set.seed() has been used in order to fix the seed of the random number generator. The RF parameters have been tuned by searching those that maximize the performance.

It should be further added that we verified the existence of a statistical difference between the results, by using the independent-samples two-tailed Student's t-tests (p < 0.05).

DataSets

The two real-world datasets used in the experiments (i.e., Default of Credit Card Clients dataset and German Credit datasets, both available at the UCI Repository of Machine Learning Databases 2 ) represent two benchmarks in this research field. In the following we provide a short description of their characteristics:

Default of Credit Card Clients (DC). contains 30,000 instances: 23,364 of them are credit-worthy applicants (77.88%) and 6,636 are not credit-worthy (22.12%). Each instance contains 23 attributes and a binary class variable (accepted or rejected).

German Credit (GC). It contains 1,000 instances: 700 of them are credit-worthy applicants (70.00%) and 300 are not credit-worthy (30.00%). Each instance contains 21 attributes and a binary class variable (accepted or rejected).

Metrics

This section presents the metrics used in the experiments.

Accuracy. The Accuracy metric reports the number of instances correctly classified, compared to the total number of them. More formally, given a set of instances X to be classified, it is calculated as shown in Equation 6, where |X| stands for the total number of instances, and |X (+) | for the number of those correctly classified.

Accuracy(X) = |X (+) | |X| (6)
F-measure. The F-measure is the weighted average of the precision and recall metrics.

It is a largely used metric in the statistical analysis of binary classification and gives us a value in a range [0, 1], where 0 represents the worst value and 1 the best one. More formally, given two sets X and Y , where X denotes the set of performed classifications of instances, and Y the set that contains the actual classifications of them, this metric is defined as shown in Equation 7.

F-measure(X,Y ) = 2 • (precision(X,Y ) • recall(X,Y )) (precision(X,Y ) + recall(X,Y )) with precision(X,Y ) = |Y ∩ X| |X| , recall(X,Y ) = |Y ∩ X| |Y | (7)
2 ftp://ftp.ics.uci.edu/pub/machine-learning-databases/statlog/ AUC. The Area Under the Receiver Operating Characteristic curve (AUC) is a performance measure used to evaluate the effectiveness of a classification model [START_REF] Powers | Evaluation: from precision, recall and f-measure to roc, informedness, markedness and correlation[END_REF][START_REF] Faraggi | Estimation of the area under the roc curve[END_REF]. Its result is in a range [0, 1], where 1 indicates the best performance. More formally, according with the notation of Section 3, given the subset of non-default instances T + and the subset of default ones T -, the formalization of the AUC metric is reported in the Equation 8, where Θ indicates all possible comparisons between the instances of the two subsets T + and T -. It should be noted that the result is obtained by averaging over these comparisons.

Θ(t + ,t -) =          1, i f t + > t - 0.5, i f t + = t - 0, i f t + < t - AUC = 1 |T + | • |T -| |T + | ∑ 1 |T -| ∑ 1 Θ(t + ,t -) (8)

Strategy

The experiments have been performed by using the k-fold cross-validation criterion, with k=10. Each dataset is randomly shuffled and then divided in k subsets; each k subset is used as test set, while the other k-1 subsets are used as training set, considering as result the average of all results. This approach allows us to reduce the impact of data dependency and improves the reliability of the results.

Experimental Results

As shown in Fig. 2 and Fig. 3, the performance of our DME approach is very similar to the RF one, both in terms of Accuracy and in terms of F-measure, where we achieve better performance than RF with the DC dataset. By examining the obtained results, the first observation that rises is related to the fact that our approach gets the same performance of RF, despite it operates in a proactive manner (i.e., without using default cases during the training process). Another observation arises about the F-measure results, which show how the effectiveness of our approach increases with the number of non-default instances used in the training process (DC dataset). This does not happen with RF, although it uses both default and non-default instances, during the model training.

We can observe interesting results also in terms of AUC: this metric evaluates the predictive capability of a classification model, and the results in Fig. 4 show that our performance is similar to those of RF, although we did not train our model with both classes of instances.

It should be noted that, as introduced in Section 1, the capability of the DME approach to operate proactively allows us to reduce/overcome the cold-start problem. The credit scoring techniques cover a crucial role in many financial contexts (i.e., personal loans, insurance policies, etc.), since they are used by financial operators in order to evaluate the potential risks of lending, allowing them to reduce the losses due to default. This paper proposes a novel approach of credit scoring that exploits an entropybased criterion to classify a new instance as accepted or rejected.

Considering that it does not need to be trained with the past default instances, it is able to operate in a proactive manner, also reducing/overcoming the cold-start and the data imbalance problems that reduce the effectiveness of the canonical machine learning approaches.

The experimental results presented in Section 5.5 show two important aspects related to our approach: on the one hand, it performs similarly to one of the best performing approaches in the state of the art (i.e., RF), by operating proactively; on the other hand, it is able to outperform RF, when in the training process a large number of non-default instances are involved, differently from RF, where the performance does not improve further.

A possible follow up of this paper could be a new series of experiments aimed at improving the non-proactive state-of-the-art approaches, by adding the information related to the default cases, as well as the evaluation of the proposed approach in heterogeneous scenarios, which involve different types of financial data, such as those generated by an electronic commerce environment.

Algorithm 1

 1 Di f f erence in Maximum Entropy (DME) Input: T + =Set of non-default instances, T =Set of instances to evaluate Output: E=Set of classified instances 1: procedure INSTANCESEVALUATION(T + , T ) 2: if b > a then

Fig. 2 :

 2 Fig. 2: Accuracy Per f ormance

Fig. 3 :

 3 Fig. 3: F-measure Per f ormance

Fig. 4 :

 4 Fig. 4: AUC Per f ormance

https://www.r-project.org/

Acknowledgments. This work is partially funded by Regione Sardegna under project NOMAD (Next generation Open Mobile Apps Development), through PIA -Pacchetti Integrati di Agevolazione "Industria Artigianato e Servizi" (annualità 2013).


Andreas Mladenow
email: andreas.mladenow@univie.ac.at

Niina Maarit Novak
email: niina.novak@ifs.tuwien.ac.at

Christine Strauss
email: christine.strauss@univie.ac.at

Internet of Things Integration in Supply Chains -An Austrian Business Case of a Collaborative Closed-Loop Implementation

Keywords: IoT, Closed-Loop, Open-Loop, Cross Organizational Collaboration, Supply Chain, RFID

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Recently, Cisco, the US based technology and software company, estimates that about 14 trillion dollars can be earned with the Internet of Things (IoT) until 2022 [1]. Mobility [START_REF] Mladenow | Mobility for 'Immovables'-Clouds Supporting the Business with Real Estates[END_REF][START_REF] Hyben | Consumer acceptance on mobile shopping of textile goods in Austria: modelling an empirical study[END_REF], globalization and a society with a very diverse consumption and leisure behaviour cause increasingly complex of supply chains with a vast variety of customized goods, partially manufactured at multiple locations [START_REF] Mladenow | Collaboration and Locality in Crowdsourcing[END_REF] and marketed worldwide [START_REF] Cheng | Advanced manufacturing systems: supplydemand matching of manufacturing resource based on complex networks and Internet of Things[END_REF]. This imposes particularly high demands on logistics providers [START_REF] Mladenow | Crowdsourcing in logistics: concepts and applications using the social crowd[END_REF] -which act as connecting elements in our increasingly integrated world [START_REF] Mladenow | Crowd Logistics': The Contribution of Social Crowds in Logistics Activities[END_REF]. Systems ought to be dynamic and flexible [START_REF] Makarova | Barrierefreiheit im Internet und Suchmaschinenranking -eine empirische Untersuchung[END_REF], but at the same time robust and cost-effective. The IoT provides a completely novel control architecture, which meets the described demand for highly flexible intralogistics systems and has thus the potential to shape the future of logistics in general [START_REF] Speranza | Trends in transportation and logistics[END_REF].

Through IoT -applications and an increasing degree of self-organized supply chains it becomes possible that autonomously interacting objects and processes increasingly connect with the digital world of the Internet [START_REF] Atzori | The internet of things: A survey[END_REF]. It is not a closed nor an independent system, but it includes a variety of different technologies, including radio networks, sensors and networks, microprocessors, tracking and tracing (T&T) functions, Agent based Systems, Smart Labels, quick response (QR) codes or radio-frequency identification (RFID) [START_REF] Whitmore | The Internet of Things-A survey of topics and trends[END_REF]. As far as logistics are concerned, these technologies mark a paradigm shift [START_REF] Guo | Opportunistic IoT: Exploring the harmonious interaction between human and the internet of things[END_REF]. Against this background, since many years intensive research and development is being invested to implement suitable IoT-applications for the logistics sector. As of today, the IoT as a technology is used partially and already offers significant benefits for users. T&T systems offer the recipients of parcels the service to follow the progress and current status of a shipment while it is transported. This service is made possible via unique barcodes or 2D-codes which are scanned at specific transfer stations to uniquely identify a shipment, and to forward the current status automatically to a central data-system. This information about the current status can then be checked by the recipient of a parcel via a web-interface.

In the case of business collaborations [START_REF] Mladenow | Collaborative Shopping with the Crowd[END_REF], non-transparent and complex processes along the supply chain make it sometimes difficult to evaluate the economics gains of individual business partners [START_REF] Werner | Supply Chain Management: Grundlagen, Strategien, Instrumente und Controlling[END_REF][START_REF] Beamon | Measuring supply chain performance[END_REF]. Often the interests between partners differ greatly [START_REF] Bensel | Cost-benefit sharing in cross-company RFID applications: a case study approach[END_REF].

What are the potentials of IoT-based applications? Which holistic assessment methods are used along the supply chain to evaluate its economic efficiency? The corresponding evaluation deals with the performance-based distribution of costs and benefits along the supply chain, and with the necessary determination of target values for efficiency and resource allocation. Hence, the paper is structured as follows: the next section elaborates on the type of integration for a cross-organizational integration of IoT, highlights the effects on companies and deals with the economic feasibility. Section 3 analyzes an ongoing integration case, based on Siggelkow [START_REF] Siggelkow | Persuasion with case studies[END_REF]. Afterwards, section 4 discusses relevant aspects. Section 5 summarizes the major findings of our ongoing research and gives a short outlook on future areas of research and likely developments.

Background

The demand to introduce cross-organization IoT-applications occurs foremost towards the end of the supply chain, at the retailer [START_REF] Attaran | Critical success factors and challenges of implementing RFID in supply chain management[END_REF]. From an economical point of view, a decision in favor of IoT-applications leads at the same time to disadvantages resulting from a loss in subsidization for other important and strategic business projects related to achieving superordinate goals such as improving customer service satisfaction, innovation leadership [START_REF] Novak | Avatar-based Innovation Processes-Are Virtual Worlds a breeding ground for Innovations?[END_REF] or in general company reputation [START_REF] Irrenhauser | Evaluation of the economic feasibility of RFID in the supply chain[END_REF].

Type of integration

The collaborative closed-loop IoT-Appliction allows for a cross-organizational implementation of systems and software along a supply chain, enabling access to all relevant data in order to ensure smooth operations and control of processes. These inherent features make it obvious that the use of collaborative closed-loops is particularly suitable for delivery networks, which are characterized by an intensive flow of materials. It allows for a particularly reliable, automated and real-time-based control of the material flow. Moreover, the IoT-application RFID is used at this level e.g. in the area of container management. These two applications are examples of the typical applications fields along a value-added network, namely trading networks with an exceptionally wide range of products or production networks with a particularly high number of individual components.

The open-loop system represents the most intensive interrelation across company boundaries. In addition to the integration of several companies as well the end user is included. For the end-user the integration into the collaborative closed-loop network is particularly beneficial as this allows to verify the origin and authenticity of a product. This is especially important in economic sectors (e.g. the pharmaceutical industry) with a fundamental and growing interest regarding product control and traceability. The open circuit is not only beneficial to the consumer, but has positive effects on the entire supply network. This is because the technology significantly reduces the workload for example in case of complaints or product recalls.

External and internal effects on companies

Related to the cross-organizational implementation and use, external and internal effects on the company have to be differentiated. While in the case of internal effects the potential benefits have a direct influence on the companies' processes, no direct relationship can be observed in the case of external effects. Through the automation effect a rationalization of manual work occurs in connection with data collection. The associated information effect guarantees that the company receives reliable information about the current position and state of items throughout the network at all time. As a consequence of the information effect another effect occurs, which is the transformation effect. This effect allows re-arranging processes in a more effective manner and leads to further reduced inventory costs. Improved transparency enables reductions in costs and inventory (especially safety stock as stock-levels and item locations can be monitored, as well as expected delivery times along the entire value-added chain without reducing the delivery service level).

Potential benefits can be triggered by both internal and external effects. In the case of external effects there are two main benefits, which positively influence project profitability, namely increased efficiency and savings [START_REF] Widhalm | E-Appointment Plattformen zur Effizienzsteigerung und Umsatzgenerierung-eine Branchenanalyse[END_REF] (in terms of fines resulting from various contract infringements). A substantial reason for this is the technically supervised commissioning of goods, which further enables an error free delivery. This has immediate positive effects on the number of incorrect deliveries, and thus on the number of fines for wrong or delayed deliveries. Another indirect cost reduction are regress payments which can be prevented through the complete documentation of manufacturing processes and the possibility to verify which materials and components have been used. This is particularly important for industries using voluntary or obligatory safety and authenticity certificates, e.g. in pharmaceutical industries, as well as other industries were safety regulations are of particular importance. At the same time product counterfeiting can be detected easier and faster, which in turn increases product-image safety. Moreover, administrative expenses in connection with product recalls can be either completely eliminated or at least reduced.

Another external effect is the increase of efficiency and revenues caused by direct and indirect effects. Especially the shortening of processing times leads to increasing process efficiency. The avoidance and/or decrease of incorrect deliveries, further affects the reputation of the enterprise in a positive way, and thus contributes to an increase of customer orders.

The internal effects can be divided into three categories: (i) effects on upstreamprocesses, (ii) effects on downstream-processes, and (iii) effects on processes in other enterprises of the network. All three internal effects have in common that their potentials are exhausted when seizing the process components. At this point a superordinate potential is realized, as the collection and simultaneous generation of events is from now on done fully automatically rather than by hand.

The first type of internal effects is characterized by a positive influence on upstream-processes in a certain area, for example when taking a component from stock during the assembly process of a product, a production order is automatically triggered and forwarded to ensure that a new component is placed into stock in time. In the case of upstream-processes this results in less planning efforts as well as in a higher degree of machine utilization. The second internal effect, affects all downstream-processes. Thus, for example, with the acceptance of a new order, all downstream-processes are "informed" about the start of the manufacturing process of the new product, simply through the generation of a new event in the IoT-application. Following this, automatic actions are taken at the downstream-process locations, which increases process efficiency and leads to cost and time savings. This makes it possible that at the time of accepting a new order, necessary preparation procedures, e.g. related to the manufacturing process, could immediately start which avoids latencies and idle times. The third type of internal effects refers to various potential benefits realizable in the sphere of other partner enterprises in the supply chain.

All three types of internal effects have thereby a cost-minimizing influence on data management, the flow of material as well as on the degree of capacity utilization of the required production facilities. Savings related to data management result from automated data generation and data supply. The same is true for the flow of materials, where automated processes lead to a rationalization of manual, expensive and inefficient activities, and thus to a more efficient use of existing resources. This leads to better process planning and ultimately to a reduction of production resources. Moreover, due to an increased efficient use of the equipment further costs for example for storage or transportation vehicles can be reduced. In contrast to external effects, the identification of benefits related to internal effects greatly depends on the chosen IoT implementation, which is the reason why these effects cannot be identified easily on a general level.

Economic feasibility for the integration of cross organizational IoTapplications

Regarding the economic feasibility, a clear distinction for reallocation is made between both, performance-based as well as non-performance-based strategies for cross organizational IoT integration. The performance-based strategy contains a value-dependent profit allocation: in this case, the generated profit of a project is shared among the participants based on the contribution (value-added share) of each contributor to the product. This strategy implies that companies, which do not perform direct value-adding activities, such as logistics service providers, are neglected during the profit allocation process. This problem can only be solved via individually negotiated profit-share allocations. At the same time, the expenses incurred by a company cannot be directly concluded from the company's share of value-added to a product. Therefore companies may suffer losses, if the costs are higher than the share of value-added.

Furthermore, the performance-based strategy implies an identical return on investment. This is a redistribution strategy, where each partner generates the same return on investment. This means that the profit allocation is based on the expenses incurred. Due to this expense-oriented calculation of return on investment, each company receives exactly the return of investment of the entire project. The advantage of this approach is thus to have a consistent return of investment throughout the entire network, which in turn increases the chances of a fast agreement between different company-partners and enables a fast implementation of the project.

On the other hand, the non-performance based strategy entails the compensation of losses. Those companies that suffer any losses due to a certain project, receive a compensation in the same amount. This implies that at least one partner benefits, as the positive net present value of the project is allocated to him due to the zero profit of the others. Therefore, it is ensured that none of the partners is worse off after the project than he was before.

In addition, the non-performance based strategy implies identical target allocation. The aim of this approach is to redistribute the relative impacts of the project (i.e. comparison of costs and benefits, which can only be positive, as the project wouldn't have been implemented otherwise), among the project partners, in such a way that each company generates the same profit in that specific project. In the case of a positive network effect, the total profit increases with the number of participants -e.g. as it is the case in many supply chains -this implies a win-win situation.

Besides, there is an identical profit allocation. The profits of all partners of the project are summed up, and subsequently evenly redistributed to all project partners, regardless of other factors. This approach might thus lead to losses for some of the project partners, provided that the received profits do not cover the expenses incurred. Therefore, this approach entails a non-negligible probability of ending up in a win-lose situation for some of the project-partners, which in turn may result in refusing to participate in the project.

In order to distribute costs and benefits in a fair manner along the supply chain a cost-benefit-sharing approach may be performed. By means of introducing a neutral instance, a basis for detecting and documenting company-specific and network-related costs and benefits, is being established. This contributes proposals for a fair distribution of investments and/or savings, without disclosing company-specific key figures to partner companies.

What are the costs and benefits of individual companies using standardized process modules and impact factors such as internal transport, material processing, storage and retrieval? Indicators which are worth reviewing include the overall profitability, cash flows and valuation records. Indicators which are relevant for forecasting include structural as well as quantity related indicators, efficiency indicators, quality metrics, and IoT impact indicators. Best practices of IoT-applications such as RFID include [START_REF] Irrenhauser | Evaluation of the economic feasibility of RFID in the supply chain[END_REF]:

• identification of relevant impact factors in terms of costs, and definition of standardized process modules for overall supply chain processes • allocation of relevant factors to costs and benefits.

• determination of target values for the assessment and evaluation of a cost model • integration of the identified benefit for companies in the cost model • individual evaluation of the economic efficiency of the use of IoT-applications for companies involved in the value-added process • balancing of interest-asymmetries by methods of cost-benefit-sharing and by including a neutral instance.

Analysis of an Austrian Retail Trader Business Case

Based on Siggelkow [START_REF] Siggelkow | Persuasion with case studies[END_REF], we analyse an ongoing case of a cross-organizational, "things orientated" [START_REF] Atzori | The internet of things: A survey[END_REF] IoT integration. The Austrian retail trading company has implemented a collaborative closed-loop RFID system with its tier-1 supplier. Moreover, it is presently being discussed, how additional IoT-applications could be integrated to both, the customer and tier-2 suppliers within the supply chain as depicted in Figure 1.

Fig. 1. Cross-company collaborative closed-loop implementation of an IoT-application

Furthermore, the concept of Vendor Managed Inventory (VMI) is applied in parallel to a cross-organizational use of IoT-applications by multiple, cooperating business partners. VMI serves as an incentive instrument for the supplier.

Moreover, for the tier-1 supplier it is obligatory to buy back all products that could not be sold from the retailer at full price. Therefore, the supplier has to take the entire risk in case of overproduction. Thus, the agreement has a similar effect like an incentive for retailers to increase their inventory to avoid stock-outs. Higher inventory levels imply less stock-outs -ultimately this is beneficial for the entire supply chain and thus also for customers.

In the case of VMI the manufacturer is responsible for the inventory management of the retailer. Therefore, the retailer pays only for those goods which have been actually sold. The supplier is thus forced to cover any costs in order to make improvements in his own warehouse -not in the warehouse of the retailer. In this context, it is often necessary to acquire the necessary and appropriate competencies, infrastructure and know-how at first.

In addition, the customer´s demand of goods depends on the price; and the retailer's (who in turn is a customer of his supplier) demand depends on the demand of his customers and the price. Hence, the risk reduction effect caused by a sub-optimal inventory level (higher or lower than the optimal inventory level) -lost profits and/or turnover or sunk costs -causes automatically a reduction of costs on the retailer's side, which in turn reduces the prices for goods. Consequently, the consumer's price elasticity increases the retailers´ demand of goods, which in turn is beneficial for the entire supply chain.

Such contractual agreements, however, do not only influence the rights of disposal in the retailer's warehouse, but also the quality of inventory management. The application of IoT in a VMI-implementation may not only generate cost advantages, but may also positively affect the relationship between the contracting parties, the efficiency of inventory management, the accurateness of the order policy, as well as the automatic recognition of expired products. Especially for suppliers who sell multiple products, an efficient inventory management system is of utmost importance; such system supports efficient use the shelf-space provided by the retailer, Furthermore, the supplier is able to improve his turnover in a specific shop or location. VMI particularly enables and suggests the display of additional products or an alternative product-mix at a certain retailer.

In the present case, the use of an IoT-application seems to be disadvantageous for the supplier due to various reasons, leading to the fact that the use of IoT is less profitable for the supplier than for the retailer without a pre-defined, appropriate compensation for the supplier. When receiving goods, the suppliers' effort can be reduced considerably.

Even once a production process has finished, there are hardly any benefits or savings for the supplier due to the fact that many suppliers produce only one single producttype or a limited number of different products. Furthermore, products are typically packed and stored in standardized dimensions, quantities and carriers. In addition, suppliers typically supply several different customers (i.e. wholesalers and retailers), of which, however, only few use the IoT-application. Thus, even though the supplier takes over a large part of the IoT-application's costs, he hardly ever has the possibility to benefit from the full potential of the technology in terms of profit. Unlike the suppliers, retailers benefit from IoT-applications from the very beginning. For example, activities associated with stock receipt can be significantly reduced during receipt (i.e. bulk dispatch): once the goods are received, the IoT-technology allows for further simplifications for example in connection with the storing process in form of automated storage space allocation and its registration in the database.

The use of IoT-systems further supports the order-picking and outsourcing process not only through the automatic registration of products, but also by providing a security control function [START_REF] Mladenow | Online Ad-fraud in Search Engine Advertising Campaigns[END_REF] during the loading of ordered goods, which automatically rechecks whether the right goods are being loaded into the right truck. This reduces the number of incorrect deliveries and commissioning, which ultimately allows for cost savings associated with the returns of goods and redeliveries. Even before the receipt of goods or after a successful delivery of goods the retailer may profit from the use of a IoT-application. Using real-time tracking and condition monitoring (e.g., temperature control for perishable goods), it is possible to detect delays or cooling unit failures at an early stage, which allows the person in charge to react in time and to find appropriate alternative solutions [START_REF] Richards | The Logistics and Supply Chain Toolkit: Over 100 Tools and Guides for Supply Chain, Transport, Warehousing and Inventory Management[END_REF].

Moreover, the Electronic Product Code (EPC)/RFID-Calculator, an open source Tool (based on visual basic for excel), is used to determine the economic feasibility for the cross-organizational IoT-application integration [START_REF]xls&usg=AFQjCNHf8D0N0HR4nQ7Hzcdphmxu2PG_vg[END_REF].

Discussion

IoT-implementations are increasingly applied in cross-organizational supply chains [START_REF] Li | The internet of things: a survey[END_REF]. Worldwide, millions of items are being moved every day, ranging from huge containers, over pallets to individual parcels. In order to ensure a smooth processing, it is of outmost importance that items arrive at the right place at the right time [START_REF] Christopher | Logistics & supply chain management[END_REF]. Manual processes (such as counting of containers before they are loaded on board of an aircraft), should be increasingly replaced by self-controlled systems and thus by smart IoT-applications which are integrated and therefore connected to each other [START_REF] Welbourne | Building the internet of things using RFID: the RFID ecosystem experience[END_REF]. Similar to internet data packets, when using IoT-applications shipments control and navigate through the logistics networks by routing themselves on their own [START_REF] Uckelmann | An architectural approach towards the future internet of things[END_REF]. The logistics service provider is subsequently informed that all shipments are being transported [START_REF] Bi | Internet of things for enterprise systems of modern manufacturing[END_REF]. From the perspective of a company this results in a considerable increase of efficiency [START_REF] Kärkkäinen | Increasing efficiency in the supply chain for short shelf life goods using RFID tagging[END_REF]. However, these economic gains in supply chains are not always equally distributed among the players in the supply chain [START_REF] Gelsomino | Supply chain finance: a literature review[END_REF].

Concerning economic feasibility, a distinction should be made between personnel expenses and expenses for resources. In addition, there is a distinction between onetime and current expenditures. The use of time and resources related to a specific process are identified and evaluated. The identified effects are quantified; expenditures and potential benefits must be documented accordingly. In particular, expenditures related to the use of technology and which might cause additional cost must be documented and shown. The result is a cost model focusing on capital value and payback time, which is used to determine the profitability in case of uncertainty. This allows to assess the overall effect of use across organizational borders. In addition, an expansion analysis can be carried out, which analyzes the essential factors for the use of IoT-applications such as RFID [START_REF] Irrenhauser | Evaluation of the economic feasibility of RFID in the supply chain[END_REF].

Atzori et al. [START_REF] Atzori | The internet of things: A survey[END_REF] distinguish between "semantic"-, "internet"-, and "things"-orientated IoT visions. In this regard, partners of cross-organizational collaborations already benefit from new promising developments in these areas [START_REF] Leminen | Towards iot ecosystems and business models[END_REF]. On that score, the shared information hub (SIH) and the total supply chain visibility (TSCV) support IoT-applications for supply chains.

SIH is a tool aimed at simplifying and improving data exchange, providing a solution for the typical problems of supply chain management [START_REF] Usländer | The future internet enablement of the environment information space[END_REF]. Due to a lack of data exchange, individual players in a supply chain usually perform their business planning on different assumptions, which result in a gradual and downstream domino effect ("informational Domino Principle"). Accordingly, the so-called bullwhip effect can be mitigated or even prevented [START_REF] Rogers | RFID in Retail Supply Chains: Current Developments and Future Potential[END_REF]. Using the SIH allows for cross-organizational and integrated planning in the context of supply chain management, based on a shared data pool. This approach is made possible through the use of IoT-applications, which provide real-time and automated information to all parties involved along the entire supply chain. In this way potential delivery delays, problems or even failures can be detected early on (e.g., the failure of a container's cooling unit in the food industry), long before it would have been possible with a conventional communication strategy. This allows that supply chain members can react early on and with the purpose of finding alternative and appropriate solutions in time.

The TSCV approach is an ICT solution allowing members of a complex value network to improve, intensify and automate their communication among each other. This makes it possible to restructure, improve and cut out previously inefficient process steps, which results in a more efficient use of available resources and higher performance. In addition, the improved coordination and communication between the business partners leads to a closer degree of collaboration and integration along the supply chain; this may positively affect the level of trust. Especially with regard to cooperation and joint projects, these network effects and ties play an important role for cross-organizational collaborations.

Conclusion and Outlook

In this paper we analyzed the integration of a "things"-orientated IoT-application [START_REF] Atzori | The internet of things: A survey[END_REF] for an Austrian cross-company collaboration. The retailer perceives the IoT-application on the supplier side as a competitive advantage compared to other suppliers. For the retailer the use of the IoT-technology implies both cost savings and a higher performance level. For these advantages retailers are willing to pay a higher price to suppliers or even decide to cooperate exclusively with suppliers that use IoT-applications.

At present, the integration of cross-organizational IoT-applications is still in its infancy, as a huge number of novel applications emerge on the market. Consequently, numerous concepts are implemented, which lead to a reorganization and new division of tasks and competencies of both manufacturers and their customers. In terms of crossorganizational collaboration, increased benefit can be achieved only if IoT-applications are being used across organizations, and only if the costs can be allocated to the individual partners of the supply chain. In this regard, a survey with multiple retailers shall be conducted to obtain quantified results, which can be used as a basis for future research. Hence, scenarios should be examined appropriately and accordingly to keep the risk of an IoTimplementation as low as possible.


Didier Schwab
email: didier.schwab@imag.fr

GazePlay : Creation of a community to help the development of a Free and Open-source plateform to make eye-tracker Video Games accessible to everyone

Objective

Develop a community composed of parents and professionnals in order to democratize free, open-source eye-tracker based video games. We would like to share our tools and experience in order to get feedback to improve them. The team leader, father of a girl with Rett syndrome, is associate professor specialised in human-computer interactions via language.

Methods

In order to develop and enhance existing augmentative and alternative communication (AAC), gaze is often considered as being one of the most natural methods to support individuals struck by the Rett syndrome to interact with their environment. It is generally believed that video games are a good way to improve basic requirements as gaze fixation and gaze pursuit as well as conventions like rewards and circular progress bars.

Results

Video games for eye-tracking and compatible eye-trackers are expensive. They both cost about several hundreds euros. To overcome this problem we have developed free software usable, on all major platforms (Windows, Mac, Linux), and compatible with existing eye-trackers able to control the mouse as well as low-cost eye trackers ( 100€). Being also a github project, GazePlay allows everyone to contribute be it with ideas or code.

Conclusion

This software is the first deliverable of a project aiming at the creation of a set of tools easily extendable and usable by individuals with disabilities, professionals and family alike. To achieve this goal, we adopt a cross-disciplinary approach including professionals from informatics, linguistics, psycholinguistics, cognitive science, speech language pathology.


Senior Member, IEEE Andrea Cozza

Power Loss in Reverberation Chambers by Antennas and Receivers

Keywords: Reverberation chamber, quality factor, antenna coupling, power dissipation, radiation efficiency

Antennas, and more generally any equipment under test (EUT) capable of coupling to impinging electromagnetic waves, are well-known sources of power loss in reverberation chambers (RCs). As such, it is fundamental to model their contribution to an RC quality factor. The standard model available in the literature is based on power dissipated in loads connected to an antenna. This paper argues about the inaccuracy of this description, where internal dissipation within an antenna (or EUT), associated to low radiation efficiencies, is neglected. An alternative model is validated by showing its selfconsistency in predicting change in loading effects as opposed to the standard model. It is expected to have practical importance for tests performed in the low-frequency range of RCs, where antenna-related dissipation is the dominant loss mechanism, and in particular for EUTs which can be expected to display poor radiation efficiencies.

I. INTRODUCTION

Coupling to reverberation chambers (RCs) necessarily passes through antennas, acting as gateways for microwave power, especially so for injecting energy into RCs that will build up into high-intensity fields. Their typically reciprocal nature means that they also receive power at the same time, with the same effectiveness as they radiate it into RCs, causing power leakage which is typically dissipated into external loads. But antennas do not simply behave as gateways: they may introduce their own power dissipation mechanism, measured by their radiation efficiency η a . These observations also apply to any receiver or EUT [START_REF] Hill | Electromagnetic Theory of Reverberation Chambers[END_REF].

Since they contribute to the overall quality factor of an RC, it is fundamental to know how to model their effect. The standard model available for predicting antenna-related losses was derived in [START_REF] Hill | Electromagnetic Theory of Reverberation Chambers[END_REF]. Its main drawback is that it regards as lost only the power dissipated onto antenna loads, a description here argued to hold only for lossless antennas. Antenna mismatch and radiation efficiency do appear in the standard model, but they only modulate the power impinging on the load, neglecting the fact that radiation efficiency is a measure of internal power dissipation. Furthermore, reflection from mismatched loads inevitably leads to a second lossy interaction with the antenna. This paper presents an improved model for antenna-related losses, taking into account these observations. The accuracy of the proposed model is demonstrated by its self-consistency in predicting change in power loss when different loads are connected to antennas. The two models disagree for weak A. Cozza is with PIEM, GeePs (UMR 8507), 11 rue Joliot-Curie, 91192 Gif-sur-Yvette, France. Contact e-mail: andrea.cozza@ieee.org. radiation efficiencies, with the proposed model predicting greater loading effects. This latter case can be expected for imperfectly shielded EUTs, which are not designed to act as efficient antennas. Applications also involve predicting RC loading in their lower frequency range, where cavity-related losses are no longer the dominant loss mechanism.

II. POWER TRANSMISSION THROUGH AN RC

The average-power transmission σ 2 (ν) of an RC measures the average power P o (ν) at the output port of a receiving antenna, as a function of frequency ν, when an available power P i (ν) is applied to the input port of a transmitting antenna, assumed to be identical to the receiving one, with no loss of generality. Brackets stand for the ensemble average.

The above definition corresponds to taking the variance of the S 21 (ν) scattering parameter as measured, e.g., by a vector network analyzer (VNA), hence

σ 2 (ν) = P o (ν) P i (ν) = |S 21 (ν)| 2 , (1)
having assumed diffusive conditions, hence

| S 21 (ν) | 2 ≪ |S 21 (ν)| 2 .
The actual power injected into the RC is not P i (ν), but rather P t (ν) = P i (ν)η a (ν)(1 -|Γ L (ν)| 2 ), with η a (ν) the radiation efficiency of the antennas and Γ L (ν) the impedance mismatch between the antennas impedances and their loads. Similarly, the output antenna receives on average a power P o (ν) = P r (ν) η a (ν)(1 -|Γ L (ν)| 2 ), with P r (ν) the average power available to the receiving antenna.

As shown in [START_REF] Hill | Electromagnetic Theory of Reverberation Chambers[END_REF], σ 2 (ν) can be expressed as a function of the quality factor Q(ν),

σ 2 (ν) = Q(ν) Q o a (ν) η 2 a 1 -|Γ a (ν)| 2 2 , (2)
where

Q o a (ν) = 16π 2 V λ (3)
accounts for power leaked by a perfectly matched and lossless antenna, expressed as a quality factor [START_REF] Hill | Electromagnetic Theory of Reverberation Chambers[END_REF]; V λ = V /λ 3 is the electric volume of the RC, with λ the wavelength. Eq. ( 2) assumes that Γ L (ν) ≡ Γ a (ν), i.e., the free-space reflection coefficient of the antennas, since the two RC-coupling antennas are usually connected to matched measuring devices, such as a VNA. Antenna losses also appear in Q(ν) as [1]

Q -1 (ν) = M Q -1 a (ν) + Q -1 c (ν), (4)
where Q c (ν) is the cavity-related quality factor, better known as intrinsic quality factor, while Q a (ν) accounts for antennarelated losses. M is the equivalent number of antennas, which equiv. load

P r < > h a 1-|G | L 2 ( ) P r < > (1-h ) a P r < > (1-h ) a h a |G | L 2 P r < > 2 h a |G | L 2 P r < > h a P r < > |G | L 2 1 2 3 G L
Fig. 1: Contributions to power dissipated by a loading antenna, with events related to received power in blue, and those leading to power radiated back to the RC in red. Three dissipation events marked from 1 to 3 are detailed in the text.

needs to be increased by one due to coherent backscattering for the input antenna, leading to a twofold increase in the power leaking through it [START_REF] Ladbury | Enhanced backscatter in a reverberation chamber: Inside every complex problem is a simple solution struggling to get out[END_REF], [START_REF] Junqua | On the power dissipated by an antenna in transmit mode or in receive mode in a reverberation chamber[END_REF]. Hence, the case of two coupling antennas requires M = 3.

The relation between Q a (ν) and Q o a (ν) was also derived in [START_REF] Hill | Electromagnetic Theory of Reverberation Chambers[END_REF], following the same reasoning used in expressing the injected power P t (ν) as a function of the input power

P i (ν), thus Q a (ν) = Q o a (ν) η a (ν)(1 -|Γ L (ν)| 2 ) , (5)
by considering the antennas only leaking power outside the RC; a generic Γ L (ν) is now considered. Thus, a weakly efficient antenna is regarded as ineffective at leaking, thus justifying a higher Q a (ν) that would make it weight less in (4).

III. POWER DISSIPATED BY AN ANTENNA/EUT

The standard definition of Q a (ν), as reported in ( 5) is here shown to be inaccurate, since it neglects two fundamental steps in the description of antenna-related power loss. Taking the example of the receiving antenna in the previous section, P o (ν) only represents the fraction of available received power P r (ν) dissipated into the antenna load. Even though radiation efficiency and impedance mismatch are taken into account, they are only considered from the point of view of the antenna load. In fact, for η a (ν) < 1, P r (ν) (1 -η a (ν)) represents the fraction of available received power dissipated internally by the antenna, due to ohmic losses. This source of lost power is currently not acknowledged in [START_REF] West | Best practices in measuring the quality factor of a reverberation chamber[END_REF], being distinct from the power dissipated into the antenna load.

For an antenna in receiving mode, the average available power P r (ν) undergoes a sequence of dissipative events illustrated in Fig. 1, marked as 1 → 3. Power is dissipated internally in 1, already described, as P r (ν) (1-η a (ν)), leaving P r (ν) η a (ν) to impinge on the antenna load, of which only

P r (ν) η a (1 -|Γ L (ν)| 2
) is dissipated into the load, marked as 2, the contribution acknowledged in [START_REF] West | Best practices in measuring the quality factor of a reverberation chamber[END_REF]. But for a general reflection coefficient Γ L (ν), part of this impinging power wave will be subsequently reflected back and be available for the antenna now in transmission mode. This amounts to P r (ν) η a (ν)|Γ L (ν)| 2 , and will therefore be submitted again to internal dissipation within the antenna, with a third contribution to dissipation equal to P r (ν) η a (ν)(1 -η a (ν))|Γ L (ν)| 2 , while P r (ν) η 2 a (ν)|Γ L (ν)| 2 will be effectively radiated back into the RC.

In the end, the total dissipation as due to the sum of the three contributions described insofar corresponds to P r (ν) (1η 2 a (ν)|Γ L (ν)| 2 ), i.e., the portion of available received power not radiated back. As a result, (5) should be updated to

Q a (ν) = Q o a (ν) 1 -η 2 a (ν)|Γ L (ν)| 2 . (6)
Since ( 6) was derived by including two additional contributions to dissipated power, ( 5) is necessarily a higher bound to [START_REF] Cozza | Likelihood of meeting isotropic conditions in reverberation chambers from power transmission[END_REF]. In other words, the standard model underestimates the contribution of antennas to dissipation phenomena in an RC. An example should help in understanding this situation. Consider a poorly efficient antenna: the available received power would be mostly dissipated within the antenna during two interactions, first in receiving mode and then when transmitting the power reflected by the load. This scenario is of practical importance, since η a (ν) ≃ 1 only for devices designed to radiate efficiently, i.e., antennas. But, as rightly pointed out in [START_REF] Hill | Electromagnetic Theory of Reverberation Chambers[END_REF], models such as [START_REF] West | Best practices in measuring the quality factor of a reverberation chamber[END_REF] and, as a consequence (6), also hold for any EUT capable of coupling to electromagnetic radiation. In this case, though, an EUT is usually not design to radiate, resulting in a likely low radiation resistance that may lead to a low radiation efficiency. The extreme case of η a (ν) = 0 corresponds to complete dissipation in [START_REF] Cozza | Likelihood of meeting isotropic conditions in reverberation chambers from power transmission[END_REF], while in [START_REF] West | Best practices in measuring the quality factor of a reverberation chamber[END_REF] it is rather predicted to be vanishing.

The proposed model also displays an interesting symmetry between the role of η a (ν) and of |Γ L (ν)|, as opposed to [START_REF] West | Best practices in measuring the quality factor of a reverberation chamber[END_REF]. An intuitive understanding of the reason for this symmetry can be gained by considering the case of an antenna with its output port connected to an attenuator terminated by a load with a mismatch Γ L (ν). If A(ν) is the power attenuation, this setup can be substituted by two alternative equivalent circuits. In the first case, the antenna sees a load that now has an equivalent power reflection coefficient |Γ L (ν)| 2 A 2 (ν). Alternatively, the attenuator can be paired with the antenna, resulting in an apparent radiation efficiency η a (ν)A(ν), while maintaining the load reflection coefficient Γ L (ν). The two equivalents must yield the same results dissipation-wise, with the same Q a (ν). Eq. ( 6) complies with this physical requirement, thanks to the symmetry of its denominator. As a result, the case of a perfectly matched antenna or of a low radiation efficiency have the same effect, resulting into a strong dissipation and thus

Q a (ν) ≃ Q o a (ν).

IV. VALIDATION PROCEDURE

The validity of (6) cannot be tested directly, since Q a (ν) cannot be estimated from experimental data without knowledge of the radiation efficiency of an antenna, while any estimate of Q(ν) assumes a negligible impact of antennas to an RC loading [START_REF] Holloway | Reverberation chamber techniques for determining the radiation and total efficiency of antennas[END_REF], [START_REF] West | Best practices in measuring the quality factor of a reverberation chamber[END_REF].

One way of solving this conundrum is to compare predictions issued from the two models. Suppose N further antennas were added to an RC, identical to the two used for measuring power transmission. Their power dissipation would be manifest as the average-power transmission through the RC would change, depending on the loads applied to the antennas port. An accurate model of antenna dissipation must then provide consistent predictions of their dissipation, independently of their loads. The accuracy of ( 5) and ( 6) requires that η a (ν) estimated from power transmission through an RC be independent from the loads connected to the N loading antennas.

Concretely, this amounts to take two sets of measurements of σ 2 (ν), as defined in (1): first with no loading antenna (σ 2 o (ν)), and compare the results with the case when N antennas were introduced into the RC (σ 2 N (ν)). From (2), σ 2 N (ν) is linked to the RC quality factor Q N (ν), having updated (4) with the contributions from the N loading antennas,

Q -1 N (ν) = M Q -1 a (ν) + Q -1 c (ν) + N Q -1 L (ν), (7)
with Q L (ν) the quality-factor contribution of the N loading antennas closed on loads with reflection coefficient Γ L (ν), whereas Q a (ν) assumes 50 Ω loads connected to the RCcoupling antennas. Then

N Q -1 L (ν) = Q -1 N (ν) -Q -1 o (ν). (8)
Recalling ( 2) and ( 6), it is possible to recast (8) as

N 1 -η 2 a (ν)|Γ L (ν)| 2 = η 2 a (ν) 1 -|Γ a (ν)| 2 2 ∆(ν), (9) where ∆(ν) = 1/σ 2 N (ν) -1/σ 2 o (ν)
measures additional loss from the N loading antennas.

Solving for η a (ν), yields

η 2 a (ν)/N = 1 -|Γ a (ν)| 2 2 ∆(ν) + N |Γ L (ν)| 2 -1 . (10)
Similarly, the standard model ( 5) founds

η 2 a (ν)/N = 1 -|Γ L (ν)| 2 (1 -|Γ a (ν)| 2 ) 2 ∆(ν) . (11)
V. EXPERIMENTAL RESULTS Models (10) and (11) bind the variation in power transmission ∆(ν), due to antenna loading, with their termination impedance, through the fact that antenna radiation efficiency must be invariant to loading conditions. Therefore it makes for a good test of self-consistency, by comparing results obtained with multiple terminations Γ L (ν).

Tests were carried out in an RC in CentraleSupelec, of dimensions 3.06×1.84×2.45 m 3 , equipped with a mechanical stirrer, here operated in 50 steps. This RC was shown to approximate isotropic diffusion starting from about 0.5 GHz [START_REF] Cozza | Likelihood of meeting isotropic conditions in reverberation chambers from power transmission[END_REF]. In order to apply (10) and (11), N + 2 identical antennas are required. A total of six monocone antennas were used, as those pictured in Fig. 2, with two of them used as transmitter and receiver, while the rest were placed (not connected to any cable) on styrofoam supports, acting at stand-alone loading antennas. These were oriented in such a way to have their axis orthogonal to their closest neighbours, in order to minimize any direct coupling.

The reference average-power transmission, σ 2 o (ν), was measured without the four loading antennas, while keeping the styrofoam supports in place, in order to take into account eventual loading effects. Subsequent measurements for the loaded average-power transmission σ 2 N (ν) were carried out with the four loading antennas on the styrofoam supports, closing each antenna on identical impedances, characterized by a reflection coefficient Γ c (ν) as defined with respect to a 50 Ω reference impedance. For the sake of applying ( 5) and ( 6), the actual mismatch Γ L (ν) observed from the antenna standpoint needs to be defined with respect to its own impedance, in general different from 50 Ω. According to [START_REF] Dobrowolski | Microwave network design using the scattering matrix[END_REF]Sec. 4.4.4]

Γ L (ν) = -Γ a (ν) + Γ c (ν) 1 -Γ c (ν)Γ a (ν) . ( 12
)
Power transmission σ 2 N (ν) was measured over the frequency range 0.6 -6 GHz, with 60000 evenly spaced samples, using a Rohde & Schwarz VNA, model ZVB8. Five different loading impedances were tested: open circuits (as SMA coaxial connectors), 50 Ω loads, and coaxial attenuators left in open circuit, with attenuations equal to 1, 3 and 6 dB. The rationale behind these choices was to span a large panel of impedance mismatches. In particular the open-circuited attenuators simulate intermediate conditions between the case of an open-circuited antenna and a 50 Ω impedance. Results in Fig. 3 show how the free-space mismatch Γ a (ν) (found for Γ c = 0, i.e., for a 50 Ω load) is translated into a different Γ L (ν) as soon as relatively high values of |Γ c | are considered. Of particular interest is the appearance of oscillations in the lower frequency range, indicating that the denominator in (12) becomes partially resonant.

The resulting sets of σ 2 N (ν) were smoothed over a 100 MHz sliding window, since cavity-dominated losses result into asymptotically vanishing differences with respect to the unloaded case, σ 2 o (ν). The ratios R

(ν) = σ 2 o (ν)/σ 2 N (ν) = Q o (ν)/Q N (ν)
, for the 5 loading configurations, are shown in Fig. 4, indicating how changing Γ L (ν) leads to a varying degree of antenna-related loading, not limited to the lower frequency range, as often assumed. The case of open-circuited loading antennas is interesting, as it was found to systematically result into R(ν) > 1, in contradiction with standard model ( 5), for which R(ν) = 1 whenever |Γ L (ν)| = 1, inde- Estimates of η a (ν) from ( 10) and (11) obtained from these data are shown in Fig. 5. It appears that standardmodel results are afflicted by a strong sensitivity to antenna loads, with oscillations in |Γ L (ν)| translated into η a (ν). The proposed model provides more consistent results, even though minor variations are observed between 1 and 2 GHz. Another measure of inconsistency with the standard model is that η 2 a (ν) in (11) had negative values, as well as η a (ν) > 1, as visible in Fig. 5 below 2 GHz for the strongly mismatched cases of an open-circuit and a 1 dB attenuator. These results confirm that the proposed model is more accurate than the standard one, as local differences are within a ±10% range and physical constraints on η a (ν) are respected. Finally, it can be noticed that the standard model inaccuracy translates into what appears to be an overall underestimation of η a (ν), which could become an issue when testing antenna efficiencies in an RC.

VI. CONCLUSION

The proposed model for antenna/EUT dissipation within an RC was proven to be self-consistent in its predictions, as opposed to the standard one. These results are expected to be of interest in application of RCs where power loss is not dominated by cavity surfaces, with antennas/EUTs contributing to it, a situation known to occur in the lower frequency range of use of RCs.

Fig. 2 :

 2 Fig. 2: Part of the experimental setup, with three of the loading antennas mounted on top of styrofoam supports.

Fig. 3 :

 3 Fig.3: Modulus of the reflection coefficients expected at the port of each loading antenna, as estimated from (12).

Fig. 4 :

 4 Fig. 4: Average power-transmission ratio R(ν) = σ 2o (ν)/σ 2 N (ν), measuring the increase in losses due to antenna-loading dissipation, for each antenna load.

Fig. 5 :

 5 Fig. 5: Radiation efficiency as estimated from: (a) the standard antenna loading model, according to (11) and (b) the proposed model, according to (10). Refer to Figs. 3 and 4 for shade coding.


Aurélien Gay

M Lopez

Pierre Cochonat

Nabil Sultan

Eric Cauiquil

Frederic Brigaud

Sinuous pockmark belt as indicator of a shallow buried turbiditic channel on the lower slope of the Congo basin, West African margin