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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Machine Learning on Simulated and Real Farm Data Based on an Ontology-Controlled Data Infrastructure</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Alexander Muenzberg</string-name>
          <email>alexander.muenzberg@dfki.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Christian Troost</string-name>
          <email>christian.troost@uni-hohenheim.de</email>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Daniel Martini</string-name>
          <email>d.martini@ktbl.de</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Francisco Mendoza</string-name>
          <email>f.mendoza@uni-hohenheim.de</email>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Rajiv Srivastava</string-name>
          <email>rajiv.srivastava@uni-hohenheim.de</email>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Thomas Berger</string-name>
          <email>thomas.berger@uni-hohenheim.de</email>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Liv Seuring</string-name>
          <email>l.seuring@ktbl.de</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Nils Reinosch</string-name>
          <email>n.reinosch@ktbl.de</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Thilo Streck</string-name>
          <email>thilo.streck@uni-hohenheim.de</email>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ansgar Bernardi</string-name>
          <email>ansgar.bernardi@dfki.de</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>German Research Centre for Artificial Intelligence (DFKI)</institution>
          ,
          <addr-line>Trippstadter Str. 122, 67663 Kaiserslautern</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>In A. Martin, K. Hinkelmann</institution>
          ,
          <addr-line>H.-G. Fill, A. Gerber, D. Lenat, R. Stolle, F. van Harmelen (Eds.)</addr-line>
          ,
          <institution>Proceedings of the AAAI 2022 Spring Symposium on Machine Learning and Knowledge Engineering for Hybrid Intelligence (AAAI-MAKE 2022), Stanford University</institution>
          ,
          <addr-line>Palo Alto, California</addr-line>
          ,
          <country country="US">USA</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>University of Hohenheim</institution>
          ,
          <addr-line>Schloss Hohenheim 1, 70599 Stuttgart</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>The SimLearn project uses semantic information processing and machine learning to combine processmodel simulation data with real-world farm data in order to to support decision making in agriculture. This paper describes a system architecture for high-performance extraction, storage, processing and machine learning of data extracted from simulation models (Big Data) or collected from farmers. Ontologies are used to link data to expert knowledge. Neural networks are pre-trained on simulation output to be later employed in prediction of decision-relevant outcomes (e.g. crop growth, soil mineralization) after transfer learning from observed farm data.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Farmer decision support</kwd>
        <kwd>artificial neural networks</kwd>
        <kwd>ontology-controlled systems</kwd>
        <kwd>machine learning architecture</kwd>
        <kwd>big data</kwd>
        <kwd>agent-based bioeconomic modelling</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>Machine learning can be used as a digital tool for handling big datasets and such learning
methods are becoming increasingly important in agriculture to minimize the losses and enhance
the profit of farmers by providing precise recommendations for crop management [ 1]. The
potential for the application of machine learning models is, however, often limited by data for
specific farm conditions, which is often fragmented and typically not comprehensive enough
to support generalization towards practically relevant innovative crop management variation
or expected climatic changes. At the same time, theory-based agricultural models incorporate
generic structural domain knowledge that can support generalization beyond observed
conditions, but parameterizing them to provide reliable and detailed predictions for the conditions
of a specific farm remains challenging. As described by Berger et al. (2020) [ 2], the Project
SimLearn, funded by the German Federal Ministry of Education and Research, explores new
approaches to support the decision-making of farmers by combining machine learning and
theory-based simulation modeling, in which neural networks are first trained on large sets
of simulation outputs generated by process-based simulation models to implicitly learn the
theoretical domain knowledge incorporated in these models. Subsequent transfer learning
with more fragmented, locally-specific farm data is hypothesized to finally yield more reliable
predictors that can anticipate the efects of innovative farm management strategies e.g. for
timing and intensity of fertilization or tillage [2]. In efect, the use of simulation-generated data
for initial training overcomes the lack of suficiently manifold real world farm data, while model
adaptation by transfer learning eases the fine-tuning towards the particularities of an individual
farm.</p>
      <p>This article describes the SimLearn system architecture and how it technically combines
ontologies with knowledge from agricultural data, Big Data technologies, simulation model
data, and machine learning processes. Our approach bears some similarities with the
architecture of Klose (2020), who outlined how to combine ontologies of scientific data and Big
Data technologies [3]: In their approach, agricultural raw data were semantically processed
for the three representations geo-information, time series and semantic facts (an agricultural
knowledge graph) which, due in part to its size, resided in the NoSQL Database Cassandra, in a
semantically pre-processed form. Knowledge was made available via a specifically developed
platform [3].</p>
      <p>While the focus of Klose (2020) was on semantically processing the real data of farmers and
sensor data and making them available [3], our approach is targeted at collecting agricultural
simulation results and measurement data, semantically process it, and enable predictions
using modern machine learning (ML) methods. Simulation output of theory-based models is
integrated into a high performance storage infrastructure. Simulation metadata is linked to
knowledge derived from data provided by the Association for Technology and Structures in
Agriculture (KTBL) and represented using a knowledge graph in an ontology. An automized
machine learning workflow is established for eficient learning of time series of high dimensional
multivariate agricultural system states.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Data Basis</title>
      <p>In SimLearn, machine learning models are trained on simulation output of the process and
expert-based modeling system MPMAS_XN. In a second step, they will be retrained on actual
farm data to achieve transfer learning. MPMAS_XN is a combination of the Mathematical
Programming-based Multi-Agent Systems model (MPMAS), which calculates optimal farm
production and investment plans and dynamically simulates their economic outcomes over time
and the soil-plant simulator Expert-N (XN), which simulates crop growth and soil processes over
time, including the actual yields obtained through the production plans selected by MPMAS
[4, 5].</p>
      <p>As external inputs, MPMAS_XN relies i.a. on a regularly updated KTBL expert dataset with
technical characteristics of over 5000 field operations and 2400 machine and equipment types,
daily time series of observed or simulated weather data, and multidimensional soil profile data.
MPMAS_XN generates diferent types of output including (A) farm-level multivariate data in
relational data structures (e.g. optimal production and investment plans for a given farm) and
(B) plot-level time series, i.e. multivariate daily-resolution time series of plant status (biomass,
phenology, maturity, nitrogen contents, etc.), soil status (moisture, carbon stocks, nitrogen, etc.)
adapted in-season management (field work dates, fertilization quantities) and final yields for
a given plant management plan, initial soil status and exogenous weather time series (among
others temperature, precipitation, humidity and wind speed).</p>
      <p>For the initial development of the data and ML architecture described in this article about
20,000 individual plot-level time series (data type B), each with about 400 variables and daily
time steps for more than 100 years were used.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Methods</title>
      <sec id="sec-3-1">
        <title>3.1. Ontology</title>
        <p>Semantic processing of the information provided by the data makes it easier for the machine to
interpret the data. The semantics are represented in the form of a knowledge graph using the
Resource Description Framework (RDF). The knowledge graph (hereafter also called ontology)
describes the format and structure of the agricultural data. The RDF knowledge graph is stored
as triple syntax (subject -&gt; predicate -&gt; object) in Turtle (Terse RDF Triple Language) files (in
.ttl file format). The knowledge of the graph can be queried using the query language Sparql
[6]. Relationships among the data can be queried through the ontology, such as fertilization
steps related to a specific crop and soil type. Among others, this information can be used to
explain parameters via a user interface. Additional technical information is annotated to classes
and properties in the ontology [3]. These are, among others, properties of the data that define,
for example, which data correlate with each other and thus serve as input and output for ML
models. In addition to the ML model information, information is annotated to control the Extract,
Transform, Load (ETL) processes. For example, if changes are made to parameters required
for machine learning processes, the properties and connections within the ontology must be
adjusted, but not the program code. This enables dynamic and automatic adaptation based on
the data stored in the ontologies. The ontology is thus the knowledge base on which a controller
in the system architecture (see section 4.1) makes decisions about which data parameters to use
for decision making. The ontology includes parts of the knowledge base of the GeoBox project,
which looks at agriculture from the perspective of a critical system infrastructure and pursues
the goal of resilient system architecture, high security, data sovereignty and usability [7] and
introduced the concept of a semantically annotated agricultural activity log for recording farm
data.</p>
      </sec>
      <sec id="sec-3-2">
        <title>3.2. Big Data Technology</title>
        <p>In the course of database development, various solutions for data storage were assessed.
Especially for the large amounts of time series data, diferent requirements for the temporal
performance when storing and reading the data had to be considered. Most of the simulation
data is delivered in comma separated or tab separated value format. For each simulated farm plot
there are separate data files and each line in these files represents a time series with parameters
(described in section 2) related to the plot. Furthermore, the data is mapped with additional
information that is contained in configuration files (e.g. .ini files). The files are read into virtual
data tables (so-called data frames). Both the sequential writing of the large time series tables
and the writing of complete data batches in conventional relational databases (SQL databases)
would take an enormous amount of time.</p>
        <p>There are special NOSQL (not only SQL) or NOSQL-like solutions for storing time series data.
TimescaleDB has advantages here because it is based on the relational database technology
PostgreSQL and maintains a clear relational structure with fewer redundancies. Furthermore, the
comfortable and well-known query language SQL is used by many developers [8]. Nevertheless,
the write performance has limits with very large data sets in the field of CPU and disk usage
[9]. The time series database VictoriaMetrics ofers very performant read and write capabilities
for measurements, but is subject to the limitation of storing only current or future data streams
[10]. Past simulated data cannot be loaded with this solution due to the limitations. Another
option for using NOSQL databases for storing time series data sets is the wide-column storage
Cassandra. This database ofers very good read and write performance for single-data rows
[11, 12]. Nevertheless, Cassandra has limitations in the case of storing large data batches [13].
Even reading such batches with diferent keys causes problems for the database. As a database
solution for data streams with unique IDs Cassandra is an excellent and performant solution
[11].</p>
        <p>The potential solutions discussed above have the capabilities to store data distributed across
multiple compute clusters to increase storage and compute resources available for processing.
Furthermore, there are also so-called data lakes that store data in a semi-structured manner. The
Hadoop Distributed File System (HDFS) is such a storage solution and also ofers distributed
storage across computing clusters, as well as a high read and write performance of timeseries
data batches [14].</p>
        <p>In order to achieve good performance both when storing time series as batches and when
sequentially streaming single records, as well as real-time analysis of the data, the Lambda
architecture described by Marz (2015) is used [15]. The Lambda architecture consists of a speed
layer (for high-performance data processing), a serving layer for structured data provision and
a batch layer for batch storage of large data [16]. For serving and batch layers, the Cassandra
and HDFS technologies explained above are used. The Spark Framework from the Apache
Foundation is used as the speed layer technology. The framework is used in the Python
programming language (named PySpark). PySpark allows high-performance processing of data
in the form of resilent distributed datasets (RDD) and data frames in the main memory of one
or more distributed computer clusters [17]. PySpark helps with the ETL process and with the
preparation of the data for the machine learning process.</p>
      </sec>
      <sec id="sec-3-3">
        <title>3.3. Machine Learning Models</title>
        <p>Using modern deep learning approaches, regressions are performed to predict time series related
to the data in section 2. Convolutional Neural Networks (CNN) perform well for predicting large
amounts of time series data. Through the convolutional layer, fixed time periods are sampled
and dimensioned, which can ultimately be subjected to prediction using regression [18, 2].</p>
        <p>
          The CNNs used here are built on simple deep neural networks (DNN), such as the multi-layer
perceptron (MLP). The MLP consists of many perceptrons deeply nested in several layers. A
perceptron is associated with several input values  and contains several weights wi which
are multiplied by the input values (00 + 11 + ... + ) . In the next step, an activation
function f is applied to the multiplied values to calculate the output y of the perceptron. Possible
activation functions include the rectifier linear unit function (ReLu) (
          <xref ref-type="bibr" rid="ref1">1</xref>
          ) or the sigmoid function
(
          <xref ref-type="bibr" rid="ref2">2</xref>
          ) shown below.
        </p>
        <p>() = (0, )</p>
        <p>
          1
() = 1 + − 
(
          <xref ref-type="bibr" rid="ref1">1</xref>
          )
(
          <xref ref-type="bibr" rid="ref2">2</xref>
          )
(
          <xref ref-type="bibr" rid="ref3">3</xref>
          )
The calculation of the output y is described in the following (
          <xref ref-type="bibr" rid="ref3">3</xref>
          ).
        </p>
        <p>=  ();  = ∑︁ 
=1</p>
        <p>Backpropagation is used to learn the weights during network training, in which their values
are corrected step by step using an error calculation (e.g. the mean squared error). Here, the
calculated errors are passed on from layer to layer. This is done by starting at the output and
passing the error backwards layer by layer [19, 20].</p>
        <p>In CNNs, three types of layers are applied. These are the convolutional layer, the pooling layer,
and the fully-connected layer. The convolutional layer pools regions of input parameters that are
connected to specific perceptrons (artificial neurons). Through the pooling layer, downsampling
is performed along the spatial dimensionality of the layer input [18]. Thus, the number of input
parameters is reduced. The fully-connected layer performs the same task as a layer in MLP and
performs classification, or regression based on the layer input. These three types of layers are
sequentially connected in the CNN [18].</p>
        <p>In our approach, a CNN is used because the convolutional mechanisms can reduce the large
dimensions or feature maps created by the large number of parameters over many years and the
CNN is more performant in its prediction of Big Data sets than conventional neural networks
for time series prediction [21, 22]. To predict the temporal development of soil and plant status
(e.g., plant growth status) over a period of time, a multi-step prediction is performed by the CNN.
Multi-step prediciton (recursive prediction) means that the 5th day is predicted on the basis of
start parameters and start conditions from day 1 to 4. Furthermore, the 6th day is predicted on
the basis of the days 2 to 5 (whereby the prediction of the 5th day is included in the network
input). Then from day 3 to 6 the 7th day is predicted, from day 4 to 7 the 8th day and so on.
The predictions are performed recursively for as many days until the maximum number of
prediction days specified by the user is reached. Figure 1 graphically illustrates the process of
multi-step prediction (adapted from [23]).</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Results</title>
      <sec id="sec-4-1">
        <title>4.1. System Architecture Approach</title>
        <p>The system architecture links a web view that enables human-machine interaction with
controllers that are linked to the ontologies as a knowledge base to dynamically access ETL or data
processes and ML processes. By adapting the ontologies, the ML processes can be dynamically
modified and extended.</p>
        <p>The architecture combines the described Lambda architecture, a Model-View-Controller
architecture (MVC) and microservices for ETL and ML processes. The encapsulation of data
model, web view, controller and the deployment as microservices allows an independent and
dynamic implementation of the processes. Parts of the architecture can be changed and only
have to comply with interface specifications without afecting other parts of the architecture.
Furthermore, independent implementation by respective experts (database developers, software
developers, ML developers and Web View developers) is possible. Figure 2 represents an
abstraction of the system architecture graphically.</p>
        <p>In summary, the architecture connects diferent modern approaches to encapsulation,
distributed development and best practices in the area of big data. These approaches are combined
with knowledge-based controlling of the processes. The human component influences the
knowledge base, represented as an ontology, and the triggering of the processes via API control.</p>
      </sec>
      <sec id="sec-4-2">
        <title>4.2. RDF Knowledge Graph (Ontology)</title>
        <p>In the ontology files used, relationships between individual properties of plots, soil conditions,
crop type, weather, climate, production and management processes, among others, are evident.
Figure 3 shows an exemplary excerpt of the ontology in a slightly modified and simplified VOWL
notation [24]. Classes are shown as ellipses, connecting  :   inbetween
as boxes. Boxes filled in grey denote datatypes of  :  . It shows the
relation of soil clay, silt and sand proportions to the class representing soil texture as well as
the linkage of the latter to the soil as a whole and to the plot. The soil itself can have further
properties. As an example,  is shown. Likewise for the plot: the figure
illustrates the plot size as one of several additional properties of that class. We use a common
naming convention in this ontology, where instances of a class can be linked by properties of
the same name as the class. The class then uses   naming and the property
.</p>
        <p>Figure 4 shows a section as an example of how special properties are used to control the
machine learning processes. For example, diferent properties of a class of time series data
exist with respect to performed production processes. In the figure, this is the property
, which is set from 0 to 1 when harvesting has been performed. The
property is a sub-property of     that tells the controller that
controls the ML processes that it is a parameter for the prediction of time series data by CNNs.
    is thus a technical property that is inherited from relevant
parameter properties. The SimLearn architecture contains such and similar properties for
controlling ML processes.</p>
      </sec>
      <sec id="sec-4-3">
        <title>4.3. Convolutional Neural Network (CNN)</title>
        <p>Using a CNN, we trained data sets of 320 randomly selected simulated plots (from a pool of
5000 simulated plots) in a multi-step procedure. The simulated plots contain time series data
sets over 100 years each (from 1980 to 2080). Subsequently, 256 plots were predicted. For the
prediction, the first 4 simulation days were entered as network input and then in sequential
steps, in which the predicted data sets were repeatedly included, a total of 6 years (from 2041
to 2043 and from 2061 to 2063) were predicted. Trained and predicted plots contain a total of
5 diferent soil characteristics (difering in soil texture, i.e. in clay, silt and sand content but
also in other variables) and 2 diferent crop rotations (maize and rotations between winter rape,
winter wheat, summer barley and winter barley). Furthermore, 32 diferent weather scenarios
and 13 diferent management plans were included.</p>
        <p>Figure 5 represents both the predicted curve and the actual simulated curve of the growth
parameters biomass above ground, generative biomass and leaf area index (LAI). Other parameters
shown are the nitrogen and water content parameters nitrogen uptake, nitrate (NO3) content at
0-30 and 30-60 cm soil depth, water uptake, volumetric water content at 0-30 and 30-60 cm soil
depth. The figure shows a section of 2 years and 10 months.</p>
        <p>
          Overall, the focus was on predicting values for growth-related outcomes such as above ground
biomass, generative biomass, the BBCH value (for the diferent development stages) and LAI;
nutrient-related outcomes such as nitrogen uptake, NO3 content at 0 to 30 and 30 to 60 cm and
nitrogen concentration in fruit, leaf, and stem; water-related outcomes such as water uptake and
volumetric water content at 0 to 30 and 30 to 60 cm. Figure 6 shows the root mean square errors
(RMSE) between actual and predicted timeseries values for biomass (above ground), BBCH
(development stage), and LAI (leaf area index) of 10 diferent plots. (
          <xref ref-type="bibr" rid="ref4">4</xref>
          ) shows the RMSE function
with the actual timeseries values  and the predicted timeseries values .
  = ⎷⎸⎯⎸∑︁ ( − )2
        </p>
        <p>
          =1
(
          <xref ref-type="bibr" rid="ref4">4</xref>
          )
        </p>
        <p>We calculated RMSE values for all the above outcomes. On the basis of the RMSE values of
each of the 256 prediction plots, statistics were calculated for minimum, median, maximum,
lower quartile and upper quartile. As an example, Table 1 shows the statistics of RMSE values
of biomass above ground, generative biomass, BBCH, LAI nitrogen and water uptake. The
diferent values of the variables were multiplied for the ML processes by a scaling factor which
is listed in table 1.</p>
        <p>Overall, it was determined that the plots containing single crop rotation maize data contained
lower RMSE values and therefore better predictions were obtained (e.g. the 5 plots 0_5_4_0,
0_8_26_0, 0_6_18_0, 0_10_18_0 and 0_9_36_0 in figure 6 contain the crop rotation maize and
have visibly the lowest RMSE values in the graphic). In addition, it was noticed that the majority
of plots with high RMSE values contained a silty loam soil (Lu, Ut4) as soil texture. 29 of the
256 test plots contained significant outlier RMSE values and were therefore predicted worse
than the remaining 227 plots.</p>
        <p>biom. ab. grd. gen. biom. BBCH</p>
      </sec>
      <sec id="sec-4-4">
        <title>4.4. Time performance of data processing</title>
        <p>The currently stored number of 7,300,000 MPMAS_XN data rows including over 400 columns
were stored in the databases (within the Lambda architecture). So far, satisfactory temporal
performance of the data flow has been achieved by using the aforementioned Big Data
technologies. Maximum processing speeds of 270 seconds for the ETL process and loading into the
databases and max. 25 seconds for reading out the large MPMAS_XN data sets were measured.
The CNN-ML process took 140 seconds per plot and the prediction of one year is performed
within 20 seconds. The tests ran on a cluster with Nvidia RTX A6000 GPU with 48 GB GPU
memory, 8 GPUs and 12 CPUs per GPU.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusion and Outlook</title>
      <p>In this paper, we present an ontology-controlled ML architecture for agricultural decision
support. The data flow is controlled by the user via an API. The processes presented in the
architecture model are able to reproduce the results of the simulation models to a satisfactory
degree. Satisfactory time performance of the data flow has been achieved by using a Lambda
architecture as common in Big Data environments. The user-controlled data flow ran
semiautomated (automated except for control interactions by the user) during tests. The ML net
obtained required information via parameters from the ontologies. Upscaling of the systems for
more computing performance is possible.</p>
      <p>Information on hyperparameter choices for the neural networks (training epochs, node
density, etc.) is currently obtained via special configuration files. To extend the dynamic
analysis capabilities, this information will be integrated into the SimLearn architecture ontology
in the future. Additional information such as computational bases and metadata of the simulation
data will be incorporated into the ontology. Future enhancements are, in addition to an extended
evaluation of the simulation data by ML networks, the expansion of the ML infrastructure.
Accompanying the optimization of infrastructure and ontologies, user interaction capabilities
will be gradually adapted. In addition, real farmer data and machine sensor data will be
incorporated into the data flow and ML networks. This is expected to lead to a significant
improvement in network predictions in the project. For the system we want to collect and
generate suficient data about agricultural processes to support the farmer in decision-making
in production management and yield optimization.</p>
    </sec>
    <sec id="sec-6">
      <title>Acknowledgments</title>
      <p>The research project SimLearn is funded by the German Federal Ministry of Education and
Research under grant FKZ 01|S19073A. Simulations are performed using the high-performance
computing resources bwHPC, funded by the Ministry of Science, Research and the Arts
BadenWürttemberg, the Universities of the State of Baden-Württemberg, Germany and Deutsche
Forschungsgemeinschaft (DFG) through grant INST 35/1134-1 FUGG.
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