Cristanel Razafimandimby

Valeria Loscrí
email: valeria.loscri@inria.fr

Anna Maria Vegni
email: annamaria.vegni@uniroma3.it

Alessandro Neri
email: alessandro.neri@uniroma3.it

A Bayesian and Smart Gateway Based Communication For Noisy IoT Scenario

Keywords: IoT, Belief Propagation, Markov Random Fields, Cloud, Smart Gateway

Nowadays, Internet of Things (IoT) coupled with cloud computing begins to take an important place in economic systems and in society daily life. It has got a large success in several application areas, ranging from smart city applications to smart grids. One major challenge that should be addressed is the huge amount of data generated by the sensing devices, which make the control of sending useless data very important.

To face this challenge, we present a Bayesian Inference Approach (BIA), which allows avoiding the transmission of high spatio-temporal correlated data. In this paper, BIA is based on a hierarchical architecture with simple nodes, smart gateways and data centers. Belief Propagation algorithm has been chosen for performing an approximate inference on our model in order to reconstruct the missing sensing data. BIA is evaluated based on the data collected from real sensors and according to different scenarios. The results show that our proposed approach reduces drastically the number of transmitted data and the energy consumption, while maintaining an acceptable level of data prediction accuracy.

I. INTRODUCTION

In recent years, Internet has become the main vector of information sharing. It took an important place not only in our economic systems, but also in our daily life. However, beyond the interconnection of computers and mobile terminals, its expansion capabilities are still significant since it is the enabler of the interactions among a large number of heterogeneous devices. The sensors are typical examples of such devices. This new extension of Internet is called Internet of Things (IoT), connecting, in addition of billions of human beings, also tens of billions of objects [START_REF]Internet of things council[END_REF]. Moreover, areas that were relatively unaffected by the Internet (such as automotive, eletric power distribution, agriculture, etc.) will be devastated by this network extension [START_REF] Mirza | Smart health monitoring systems: an overview of design and modeling[END_REF], [START_REF] Liu | Toward reliable data analysis for internet of things by bayesian dynamic modeling and computation[END_REF], [START_REF] Petrolo | Towards a smart city based on cloud of thoings[END_REF], [START_REF] Qinghai | Application of internet of things in smart grid power transmission[END_REF], [START_REF] Razafimandimby | A neural network and iot based scheme for performance assessment in internet of robotic things[END_REF].

Nevertheless, IoT raises yet many challenges and one of them is the management of massive amount of data generated by sensing devices. Storing this big data locally and even temporarily will not be possible any more. Therefore, harnessing cloud computing capacity is needed, but unfortunately this is not enough. However, it was observed that, with the increase of sensor density, data generated by IoT devices tend to be highly redundant. Thus, uploading raw data to the cloud can become extremely inefficient due to the waste of memory and network overloading.

To address this issue, either the IoT devices should avoid the generation of useless data or the gateway device should be able to stop uploading of redundant data from some devices, to reduce consumption of network and cloud resources.

From the above considerations, in this paper we present a Bayesian Inference Approach (BIA), which allows to remove a great amount of spatio-temporal correlation data in an IoT domain. BIA is based on Pearl's Belief Propagation (BP) algorithm that is an iterative technique mostly used for solving inference problems [START_REF] Yedidia | Understanding belief propagation and its generalizations[END_REF]. In the IoT context, the belief of a device is related to the physical quantity measured by the device sensors. BP infers the measurements of other neighboring nodes, especially in cases where the data are missing. In BPbased approaches, each node determines its belief by merging its local measurement with the beliefs of its neighboring nodes, and its beliefs obtained in the past run. BP provides therefore a spatio-temporal cooperation among several devices. A good correlation between data is important in such inference problems since it dictates the accuracy of data inference, and hence reduces the estimation error of the global information.

The main contributions of this paper can be summarized as follows:

• Adoption of a Bayesian Inference Approach that allows avoiding the transmission of useless data in heterogeneous IoT networks. The BP algorithm has been chosen to infer the missing data;

• Use of smart gateway based communications in order to decrease the estimation error in the cloud;

• Performance assessment based on data collected from real sensors.

This paper is organized as follows. Section II provides some related works on data propagation mechanisms in IoT context. Section III describes our reference cloudbased architecture for the IoT scenario. In Section IV, we present the proposed Bayesian Inference Approach based on BP algorithm for data sharing in a noisy IoT scenario. Section V provides the experimental results for the assessment of the proposed BIA technique in different real scenarios. Finally, conclusions are drawn at the end of the paper.

II. RELATED WORK

In this section, we present several works closely related to ours. In order to clarify the difference of our work with those existing in the literature, we classify the related works according to the fields where they were treated, i.e., (i) in Wireless Sensor Networks (WSNs), and (ii) IoT domain.

A. Wireless Sensor Networks context

Energy saving is considered as the most important part in WSNs, since sensors have to operate on extremely limited energy budget. A good survey of energy saving in WSNs context was proposed in [START_REF] Anastasi | Energy conservation in wireless sensor networks: A survey[END_REF]. Data reduction is one of best approaches to achieve energy-efficiency in data acquisition. Its main goal is the reduction of the amount data to be transmitted over the network such that the energy spent for communications decreases. Many data prediction approaches have been proposed in several works [START_REF] Komurlu | Active inference and dynamic gaussian bayesian networks for battery optimization in wireless sensor networks[END_REF], [START_REF] Kumar Soni | Reducing the data transmission in wsns using time series prediction model[END_REF], [START_REF] Tan | Data reduction in wireless sensor networks: A hierarchical lms prediction approach[END_REF], [START_REF] Zhao | A systematic probabilistic approach to energy-efficient and robust data collections in wireless sensor networks[END_REF]. In [START_REF] Wu | Data prediction, compression, and recovery in clustered wireless sensor networks for environmental monitoring applications[END_REF], the authors have combined data prediction and lossy compression scheme to jointly achieve accuracy and efficiency of the data processing in clustered WSNs.

Even if many approaches have been developed for data prediction in the WSNs context, all the proposed approaches deal only with homogeneous data. However, the heterogeneity of IoT devices requires that the employed prediction model has be applicable to a variety of applications with heterogeneous data. Moreover, the prediction models used in the WSNs context are often too computationally expensive to run or do not provide room for further data reduction. All these points make many existing methods in WSNs unsuitable for the IoT context.

B. IoT context

One of the most distinguishing aspects of the IoT is the fact that the data are acquired from a variety of sources. As far as we know, there exists only two works that take in account this heterogeneous aspect of IoT. The first work was proposed in [START_REF] Hassani Bijarbooneh | Cloud-assisted data fusion and sensor selection for internet of things[END_REF], and the other was proposed in [START_REF] Vegni | A bayesian packet sharing approach for noisy iot scenarios[END_REF].

In [START_REF] Hassani Bijarbooneh | Cloud-assisted data fusion and sensor selection for internet of things[END_REF], the authors presented a cloud-based Adaptive Sensing Belief Propagation (ASBP) protocol with energyefficient data fusion for IoT applications. Our work differs from [START_REF] Hassani Bijarbooneh | Cloud-assisted data fusion and sensor selection for internet of things[END_REF] in the following aspects :

• We assume that the correlations between different kind of data (e.g. temperature, humidity, light and voltage) are a priori known. Consequently, we do not need to compute the correlation matrix each time;

• The knowledge of the correlation is used only to decide what data have to be sent or inferred in the cloud. Therefore, we do not operate the sensor selection optimization problem in this work;

• We propose a smart gateway concept in order to decrease the inference error in the cloud. Hence, we provide a dual prediction scheme: one in the gateway, and the other in the cloud. Both predictions are based on the BP algorithm.

Then, the authors of [START_REF] Vegni | A bayesian packet sharing approach for noisy iot scenarios[END_REF] in turn presented a theoretical bayesian based approach for data sharing in the IoT context. In this paper, we go a step further than [START_REF] Vegni | A bayesian packet sharing approach for noisy iot scenarios[END_REF] by proposing an extensive experimentation scenario and smart gateway based communications.

III. NETWORK MODEL

As depicted in Figure 1, in this paper we propose a BP approach in a cloud-based architecture consisting of simple nodes, smart gateways and data centers. Each entity in our architecture plays a different role w.r.t the functionalities, the computational and communication capabilities. Our IoT network model may include multiple subnets associated with different applications. Each subnet is composed of IoT devices connected to each others for data sharing, and a smart gateway that relays the data flows to the cloud. The cloud in turn is responsible of inference, storage and all the cloud-based services.

In a given IoT application, the sensor nodes periodically collect environmental data, such as temperature, humidity and illuminance, and forward them to the gateways using a multi-hop routing protocol. Then, the gateways collect the data and decide what has to be sent to the cloud. This decision depends on the fact that the gateway knows or not the priori probability of inference error of the used approach. Figure 4 shows an example of data considered in our IoT applications. These data are a subset of the data collected from 54 sensors deployed in the Intel Berkeley Research lab [START_REF] Madden | Intel lab data[END_REF]. This figure depicts precisely the correlation between the temperature, humidity, light and voltage data. As we can noticed, there is a good correlation between temperature and humidity data. Indeed, it is really easy to draw the regression line between temperature and humidity data here. Therefore, it will be more efficient to infer temperature value from humidity value or conversely (i.e., infer humidity value from temperature value).

IV. BAYESIAN INFERENCE APPROACH

In this section, we describe our BIA technique. As mentioned before, our main goal is to avoid sending useless data, while keeping an acceptable level of data content accuracy. BIA is based on Pearl's BP algorithm that will be described below.

A. Model

As a starting point before any inference procedure, the design of a graphical model should be provided. Graphical models are schematic representations of probability distributions [START_REF] Christopher | Pattern recognition and machine learning[END_REF]. They consist of nodes connected by either directed or undirected edges. Each node represents a random variable, and the edges represent probabilistic relationships between variables. Models which are comprised of directed edges are known as Bayesian networks, whilst models that are composed of undirected edges are known as Markov random fields (MRF) [START_REF] Wang | Markov random field modeling, inference & learning in computer vision & image understanding: A survey[END_REF]. As in [START_REF] Vegni | A bayesian packet sharing approach for noisy iot scenarios[END_REF], we present an inference approach under the hypothesis of MRF, modeled by means of Factor Graphs. It follows that our goal is to estimate the state X of the sensed environment starting from the sets of data collected by each sensor node. If X is modeled as a MRF, by taking advantage of the Hammersley-Clifford Theorem, the joint probability distribution of X with a set of cliques 1 C is given by

p X (x) = 1 Z exp{-E(x)}, ( 1
)
where Z is the normalization factor, and

E(x) = c∈C ψ c (x c ), (2)
is the energy function, ψ c is the potential associated with clique c ∈ C, and x is the set of nodes belonging to the clique indexed by c.

B. Belief Propagation

Once the model has been defined, queries can be performed on the model to find the marginal probability distribution for one node or a set of nodes in the network graph. We use BP algorithm for this purpose and also for the computation cost reason. BP is a well known algorithm for performing inference on graphical models [START_REF] Yedidia | Understanding belief propagation and its generalizations[END_REF]. In general, we assume that some observations are made and some other data about the underlying environment will be inferred. The choice of data to infer is based on the strong correlation between data.

Given the i-th device, let us denote with ε i the observation of the phenomenon we intend to share (e.g. temperature) and with x i the random variable associated to the phenomenon we want to infer, (e.g. humidity).

If we associate each IoT device of our subnet with a random variable X i , which represents the local information (such as temperature and humidity), the joint probability can be written as:

P X (x) = i ψ i (x i ) i,j ∈E ψ ij (x i , x j ), (3)
where ψ i (x i ) is the evidence function, E is the set of edges encoding the statistical dependencies between two nodes i and j, and ψ ij () represents the potential function. Note that the graphical model parameters (i.e. ψ i and ψ ij ) can be estimated from the observed data by using a learning algorithm like in [START_REF] Ghahramani | Graphical models: parameter learning[END_REF] and [START_REF] Arthur P Dempster | Maximum likelihood from incomplete data via the em algorithm[END_REF]. Figure 2 illustrates an example of the MRF model. The filled-in circles represent the observation nodes (i.e., N εi ) and the empty circles represent the hidden nodes (i.e., x i ). The potential functions are associated with the links between 1 Clique is defined as a fully connected subset of nodes in the graph. x i whilst the evidence functions are associated with the links between N εi and x i .

We recall that p(x i ) represents the marginal distribution of i-th node, and the BP allows the computation of p(x i ) at each node i by means of a message passing algorithm. The message from node i to j related to the local information x i is defined as:

m ji (x i ) ∝ ψ ji (x j , x i )ψ j (x j ) u∈Γ(j),u =i m uj (x j )dx j , (4)
where Γ(j) denotes the neighbors of node j and the incoming messages from previous iteration are represented by m uj .

Eq. ( 4) will be performed between all nodes in the model until the convergence will be reached. Thus, the prediction i.e., the belief at each i-th node, is computed through all the incoming messages from the neighboring nodes and the local belief, i.e.:

xi = belief (x i ) = kψ i (x i ) u∈Γ(i) m ui (x i ) ( 5
)
where k is a normalization constant.

It is worth to mentioning that the BP is able to compute the exact marginalization in the case of treestructured graphical models. Figure 3 illustrates the message passing process in BP.

V. EVALUATION & DISCUSSION OF THE RESULTS

A. Experimental Setup

In this section we provide the experimental results of our approach. Real data collected from 54 sensors deployed in the Intel Berkeley Research lab have been used. As mentioned before, these sensors collect temperature, humidity, light and voltage readings, as well as the network connectivity information which makes possible to reconstruct the network topology. Each data collection has been performed every 30 seconds. The original data consists of 38 days of readings. However, we will focus only on the first three hours of readings in this work. Figure 4 illustrates the scatterplot matrix of our data. In a nutshell, it shows the relationship between data during the first three hours of readings of the 54 sensors. We can notice that there is a good correlation between temperature and humidity data. Hence, we can easily infer the humidity data from temperature data and vice versa. In this paper, we decided to infer humidity from temperature. The temperature is in degrees Celsius, whilst the humidity is a value ranging from 0-100%. We assess our approach w.r.t. (i) the number of transmitted data, (ii) the average value of the estimation error, (iii) the average value of the distortion level, and (iv) the energy consumption.

The number of transmitted data represents the total number of data transmission performed by all the sensors during the first three hours. The inference error is an important metric for any inference procedure. The goal is to have an errorless inference approach, i.e. an approach that is able to estimate the true value of data during all the inference procedures. However, this is almost never the case but we want that this error is as low as possible. In addition to the inference error, computing the distortion level is also important. This allows us to determine the difference between the real and the estimated value. The distortion level can be expressed using the Mean Squared Error (MSE) metric, which is defined as:

M SE = 1 n n i=1 ( xi -x i ) 2 , (6)
where xi and x i are respectively the predicted and true value during the n-th reading.

In our energy consumption evaluations, we assume that the energy cost for sending each temperature and humidity value is 14 mW. This energy cost has been obtained on the Mica2Dot Berkeley mote as reported by [START_REF] Anastasi | Performance measurements of motes sensor networks[END_REF]. Furthermore, all of our assessments are based on three different scenarios. In scenario s1, the gateway sends to the cloud all the temperature and humidity data it receives. This means that the cloud does not perform any inference. In the second scenario s2, the gateway sends only the temperature data to the cloud, and the cloud in turn infers the corresponding humidity data by using the BP algorithm. Finally, in the scenario s3, we consider that the gateways are "smart" devices, meaning that before sending their data to the cloud, they first compute the probability p(e|T, h) of making an inference error e on the cloud given the temperature T , and the humidity h. If there is a strong chance that the error magnitude exceeds a predefined threshold, the gateway send both humidity and temperature data to the cloud, else the gateway send only the temperature data, and the humidity value will be inferred in the cloud using the BP algorithm. The computation of p(e|T, h) is done by means of the BP algorithm also. It should be noted that this computation requires the knowledge of the a priori probability of inference error, i.e., p(e).

B. Obtained results

As mentioned before, we evaluate the performance of our approach in terms of number of transmitted data, average value of the estimation error (i.e., ER), average value of the distortion level (i.e., M SE), and energy consumption (i.e., EC). Our approach was implemented in C++, and the assessments were performed with respect to the ground truth.

Table I illustrates the obtained results during the first three hours of readings. We can notice that our Bayesian inference approach drastically reduces the number of transmitted data and the energy consumption, while maintaining an acceptable level of prediction accuracy and information quality.

We can notice also that we decrease considerably the estimation error by using the scenario s3. Indeed, the gateways are smarter in this case. By computing the a posteriori probability of inference error, they will be able to estimate the right moment and the data type to send in the cloud. However, this increases the number of transmitted data (and hence the energy consumption), as compared to scenario s2. This is due to the fact that in s2 gateways send only the temperature data without worrying of the risk of inference error in the cloud.

Figure 5 shows the variation of the estimation error during the first three hours of reading. This corresponds to a MSE of 0.04 for scenario s2, and 0.02 for s3.

VI. CONCLUSIONS

In this paper, we have presented a inference-based approach that allows avoiding transmitting useless data in an heterogeneous IoT network. The strong correlation between data was taken into account for this study. Through extensive simulations and by using the real data collected from 54 sensors deployed in the Intel Berkeley Research lab, we have showed that our Bayesian inference approach reduces considerably the number of transmitted data and the energy consumption, while keeping an acceptable level of estimation error and information quality. We have also shown that the use of smart gateway decreases significantly the inference error. Note that even though we used a data source from WSN to validate our approach, it can be easily applied to different types of data sources provided by IoT devices. Future works will explore the possibility of doing the error prediction directly on the sensor nodes.

Figure 1 :

 1 Figure 1: A cloud-based IoT network model.

Figure 2 :

 2 Figure 2: An example of MRF model.

Figure 3 :

 3 Figure 3: Message passing process in BP algorithm.

Figure 4 :

 4 Figure 4: Correlation between data during the first three hours of readings.

Figure 5 :

 5 Figure 5: Variation of the estimation error.

Table I :

 I Results obtained during the first three hours of readings.

	Scenario #Transmitted data EC (W) M SE	ER
	s1	20346	284.844	-	-
	s2	10173	142.422	0.04	0.26
	s3	12496	174.944	0.02	0.037

ACKNOWLEDGMENT

This work was partially supported by a grant from CPER Nord-Pas-de-Calais/FEDER Campus Intelligence Ambiante.


Barbara Mittler

Damien Ehrhardt

Mediatisation in 19 th Century Music The 'hero' Franz

1999 to 2001 in the Altenburg, Liszt's residence in Weimar in the years 1848-1861, which is discussed here. Nicolas Dufetel and I would pay homage to our host in Weimar, Prof. Dr. Detlef Altenburg who unfortunately passed away seven months ago. He was inter alia the former president of the Gesellschaft für Musikforschung

Playing on his reputation as virtuoso gained during his Parisian years, he met an impressive number of colleagues and prominent figures throughout his travels which were highly organized with an effective time management.

Beyond the interpretation of his time, Liszt still remains a figure of interculturality as other heroes like Alexander von Humboldt. They are very important in a world more and more plagued by extremism and nationalism. Interestingly, Liszt was a cosmopolitan and the leader of national schools. He decided to become Hungarian largely because of the success of his benefit concerts in Vienna for the victims of the flood in Pest in 1838. If the situation had been different he could have identify with any other country. A great part of his family was German and French was the language he spoke the best. His identity is not clearly defined, but instead of being homeless ("sans papier"), he can be considered as beyond identity papers ("au-delà des papiers").

But against all odds, the hero Liszt during the Weimar years does not appear on the pictures published by Richard Pohl in 1855. These pictures, which are designed to publicize the salon held by him and his companion the Princess Carolyne zu Sayn-Wittgenstein at the Altenburg, were published in the oldest German illustrated newspaper, the Illustrirte Zeitung, intended for a wide audience that exceeds the only musical world. A special care has certainly been taken in the making of these illustrations: they embody more than the mirror of the salon they represent, but they are "ways of worldmaking" (Nelson Goodman).

Liszt and 19 th Century Music Salon

But before studying both illustrations, let me say a few words about 19 th century music salon, especially during the July Monarchy in Paris. With the emergence of a new aristocracy in search of easy money, the salon is less than before linked with spirit and reasoning and becomes the favorite place of high-society entertainment.

If music constitutes an important ingredient of the salon culture, its superficiality is highly disapproved by most demanding critics like Robert Schumann. But salons were useful as a gateway for the virtuoso careers.

However, Franz Liszt regrets the subalternity of musicians. For him, the artist should reveal itself to the public and the materialistic society as a creator or a "priest of an unspeakable and mysterious religion". In the salons of the Parisian high society, he was struck by the discrepancy between the high mission he concedes to the artist and the social reality of the latter. In his own salon, Liszt could take the opposite course to the Parisian places of sociability. Do these illustrations symbolize Liszt's conception of the music salon? 1 st illustration: Library and music salon, 1 st floor, Altenburg

In the foreground appear two pianos fitted head to tail: an Erard grand piano and a Broadwood that belonged to Beethoven, of which Liszt was particularly proud. The piano on the right, on which a candelabra is placed, seems to be Beethoven's one. It looks like the instrument now kept in the Hungarian Museum in Budapest. At the back of the room, there are three bookcases. Between the two pianos and the back of the room is a table with displays at the two ends and a clock flanked by two candlesticks in the middle. On the floor is placed a mat polar bear skin, which brings a rustic touch in the entire room.

The image can be divided into two parts horizontally. The lower part includes the pianos, the table, the chairs, the armchair, the clock, the candlesticks, the candelabra, the carpet: that means, current items of furniture in 19 th century salons. Appear in the higher part of the picture the bookcases and the windows from which shines the light. In this way Liszt intended to honor the books of his salon as a symbol of knowledge, which have to bathe the room as well as the natural light.

The most enlightened place of the entire picture appears on the left grand piano that sparkles. The right one symbolizes obviously Beethoven; the left one, more recent, could be attributed to Liszt. The disposition of its reading desk, the chairs around him and the storage rack for music scores suggests that the left piano is the composer's working instrument with two chairs for lessons or four-hand piano. That is not the case by the piano on the right which seems to be more rarely used. The armchair at the right is far from it. The instrument is certainly kept in the manner of a museum piece.

This illustration can be read from the bottom up. Under my reading, this picture shows two periods of music history: the base is represented by Beethoven who parts from classicism to pave the way to the neo-Weimarian fusion of the arts. From this point of view, the bookcases symbolize not only the knowledge, but also the opening of music to the other arts.

In addition, an intimate atmosphere suitable for the cult of music emerges from this visual representation because of the presence of many personal items and the master's library. Therefore, the members of Liszt's circle wanted certainly to transmit through this picture the spiritual dimension of music. Not the master is present, but his spirit.

nd illustration : Music salon, nd floor, Altenburg

On the second floor, the main music room is situated just above the library-music salon. Even if it is the main music room, its area is smaller than the library and music salon.

At the center of the main music room sits a grand pedal piano, illuminated by daylight. Also known as "giant piano", halfway between piano and organ, it is the work of a Parisian factor named Alexandre et Fils. It belongs nowadays to the Kunsthistorisches Museum in Vienna. On Pohl's illustrations, the giant piano was placed on a pedestal, and the chair before him seems tiny. It is certainly to accentuate the contrast between its big size and the small size of another musical instrument, placed in the back of the room, against the wall: a spinet that had once belonged to Mozart. To better visualize the space occupied by these two instruments, a chair, identical to that in front of the giant piano, was placed in front of the spinet. Both chairs are used as a standard to measure the two pieces of furniture. In addition, the giant piano is illuminated directly by daylight, unlike Mozart's instrument. In his article, Richard Pohl explains this contrast. The spinet as symbol of the past is opposed to the giant piano, at the cutting edge of the production of musical instruments:

Während ich staunend bei dem Rieseninstrument verweilen wollte, trat Liszt an ein kleines, vom Alter dunkelbraun gefärbtes Klavier von einfachem Eichenholz, mit schwarzen Tasten und Metalltangenten, und sagte: "Das ist eine Reliquie, die ich Ihnen zeigen wollte: Mozarts Instrument!" -Nur ein Menschenalter liegt zwischen Mozarts Klavier und Liszts Riesen-Pianoforte -aber von jenem bis zu diesem, welcher unendliche Fortschritt! Beide bezeichnen, hier nebeneinander stehend, den Anfang und die höchste Spitze unserer heutigen Klaviertechnik. Sie sind die zwei Grenzscheiden der musikalischen Kultur des 18. und des 19. Jahrhunderts! This opposition corresponds to the neo-Weimarian idea of progress as a historical dimension. This progress led from the Altdeutsche Schule to the Neudeutsche Schule, by going through the era of absolute music. These various periods of history were determined by Franz Brendel, a disciple of Hegel: they correspond, as in the philosophy of history, to logical moments of the elucidation of the Spirit.

Finally, the image can be read from left to right, from the past to the future: the spinet is on the left, the giant piano on the right. We can draw a horizontal line through the keyboard the spinet and the lower keyboard of Liszt's piano. On both sides of this median line other force lines can be drawn. They accentuate the increase of the space occupied by the successive instruments.

The three music salons of the Altenburg

During the years 1848-1861 the music salons of the first and second floors are the place where the events and the master classes are held, and where the artists and the intellectuals meet together. The room of the second floor -despite its small size -is the most important, because of the presence of the giant piano and its location close to Liszt's apartments.

According to descriptions of Richard Pohl and Peter Raabe, each floor has its own music salon. An additional music room on the ground floor was certainly intended to chamber music, with a Viennese grand piano, music stands and many scores, especially in the domain of chamber music.

We can state the symbolism of each salon: the room in the ground floor is devoted to the intimacy of chamber music in the classical tradition; the first floor the fusion of the arts realized in Liszt's vision of program music; the second floor the postulate of progress as a historical dimension.

These pictures, which are designed to publicize the Liszt salon, underline its specificity as a cenacle defending the aims of the Neu-Weimar-Verein, a vision diametrically opposed to Parisian virtuosity salons. Can we explain the absence of the composer on these illustrations because of his great fame (Celebritate sua sat notus)? Or is it a form of deification? If Liszt compares the artist with a priest, I think that the most important for his circle is that he trades the image of a devilish virtuoso for that of a serious symphonist. Liszt likes to base discourses about new aesthetics on the genius loci of the cities where he lived. In Paris, the place where virtuosos made their reputation, Liszt became a well-known pianist. In Weimar, the situation is different: he considers himself as Goethe's successor. He would now be the symphonist who realizes the synthesis between the Wiener and the Weimarer Klassik. It seems clear that the image of the pianist virtuoso is no longer sufficient. For him and his circle it is time to reconstruct the hero and the publication of these two illustrations is part of this reconstruction.

To begin, I would deeply thank the Alexander von Humboldt Foundation


Shreyas Saxena

Jakob Verbeek

Convolutional Neural Fabrics

Despite the success of CNNs, selecting the optimal architecture for a given task remains an open problem. Instead of aiming to select a single optimal architecture, we propose a "fabric" that embeds an exponentially large number of architectures. The fabric consists of a 3D trellis that connects response maps at different layers, scales, and channels with a sparse homogeneous local connectivity pattern. The only hyper-parameters of a fabric are the number of channels and layers. While individual architectures can be recovered as paths, the fabric can in addition ensemble all embedded architectures together, sharing their weights where their paths overlap. Parameters can be learned using standard methods based on backpropagation, at a cost that scales linearly in the fabric size. We present benchmark results competitive with the state of the art for image classification on MNIST and CIFAR10, and for semantic segmentation on the Part Labels dataset. . . .

Introduction

Convolutional neural networks (CNNs) [START_REF] Lecun | Handwritten digit recognition with a back-propagation network[END_REF] have proven extremely successful for a wide range of computer vision problems and other applications. In particular, the results of Krizhevsky et al . [START_REF] Krizhevsky | Imagenet classification with deep convolutional neural networks[END_REF] have caused a major paradigm shift in computer vision from models relying in part on hand-crafted features, to end-to-end trainable systems from the pixels upwards. One of the main problems that holds back further progress using CNNs, as well as deconvolutional variants [START_REF] Noh | Learning deconvolution network for semantic segmentation[END_REF][START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] used for semantic segmentation, is the lack of efficient systematic ways to explore the discrete and exponentially large architecture space. To appreciate the number of possible architectures, consider a standard chain-structured CNN architecture for image classification. The architecture is determined by the following hyper-parameters: (i) number of layers, (ii) number of channels per layer, (iii) filter size per layer, (iv) stride per layer, (v) number of pooling vs. convolutional layers, (vi) type of pooling operator per layer, (vii) size of the pooling regions, (viii) ordering of pooling and convolutional layers, (ix) channel connectivity pattern between layers, and (x) type of activation, e.g. ReLU or MaxOut, per layer. The number of resulting architectures clearly does not allow for (near) exhaustive exploration.

We show that all network architectures that can be obtained for various choices of the above ten hyper-parameters are embedded in a "fabric" of convolution and pooling operators. Concretely, the fabric is a three-dimensional trellis of response maps of various resolutions, with only local connections across neighboring layers, scales, and channels. See Figure 1 for a schematic illustration of how fabrics embed different architectures. Each activation in a fabric is computed as a linear function followed by a non-linearity from a multi-dimensional neighborhood (spatial/temporal input dimensions, a scale dimension and a channel dimension) in the previous layer. Setting the only two hyper-parameters, number of layers and channels, is not ciritical as long as they are large enough. We also consider two variants, one in which the channels are fully connected instead of sparsely, and another in which the number of channels doubles if we move to a coarser scale. The latter allows for one to two orders of magnitude more channels, while increasing memory requirements by only 50%.

All chain-structured network architectures embedded in the fabric can be recovered by appropriately setting certain connections to zero, so that only a single processing path is active between input and output. General, non-path, weight settings correspond to ensembling many architectures together, Scales Layers Input Output Figure 1: Fabrics embedding two seven-layer CNNs (red, green) and a ten-layer deconvolutional network (blue). Feature map size of the CNN layers are given by height. Fabric nodes receiving input and producing output are encircled. All edges are oriented to the right, down in the first layer, and towards the output in the last layer. The channel dimension of the 3D fabric is omitted for clarity. which share parameters where the paths overlap. The acyclic trellis structure allows for learning using standard error back-propagation methods. Learning can thus efficiently configure the fabric to implement each one of exponentially many embedded architectures, as well as ensembles of them. Experimental results competitive with the state of the art validate the effectiveness of our approach.

The contributions of our work are: (1) Fabrics allow by and large to sidestep the CNN model architecture selection problem. Avoiding explicitly training and evaluating individual architectures using, e.g., local-search strategies [START_REF] Chen | Net2net: Accelerating learning via knowledge transfer[END_REF]. (2) While scaling linearly in terms of computation and memory requirements, our approach leverages exponentially many chain-structured architectures in parallel by massively sharing weights among them. (3) Since our fabric is multi-scale by construction, it can naturally generate output at multiple resolutions, e.g. for image classification and semantic segmentation or multi-scale object detection, within a single non-branching network structure.

Related work

Several chain-structured CNN architectures, including Alex-net [START_REF] Krizhevsky | Imagenet classification with deep convolutional neural networks[END_REF] and the VGG-16 and VGG-19 networks [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF], are widely used for image classification and related tasks. Although very effective, it is not clear that these architectures are the best ones given their computational and memory requirements. Their widespread adoption is in large part due to the lack of more effective methods to find good architectures than trying them one-by-one, possibly initializing parameters from related ones [START_REF] Chen | Net2net: Accelerating learning via knowledge transfer[END_REF].

CNN architectures for semantic segmentation, as well as other structured prediction tasks such as human pose estimation [START_REF] Pfister | Flowing ConvNets for human pose estimation in videos[END_REF], are often derived from ones developed for image classification, see e.g. [START_REF] Long | Fully convolutional networks for semantic segmentation[END_REF][START_REF] Noh | Learning deconvolution network for semantic segmentation[END_REF][START_REF] Tsogkas | Deep learning for semantic part segmentation with high-level guidance[END_REF][START_REF] Zheng | Learning high-level prior with convolutional neural networks for semantic segmentation[END_REF]. Up-sampling operators are used to increase the resolution of the output, compensating for pooling operators used in earlier layers of the network [START_REF] Noh | Learning deconvolution network for semantic segmentation[END_REF]. Ronneberger et al . [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] present a network with additional links that couple layers with the same resolution near the input and output. Other architectures, see e.g. [START_REF] Farabet | Learning hierarchical features for scene labeling[END_REF][START_REF] Honari | Recombinator networks: Learning coarse-to-fine feature aggregation[END_REF], process the input in parallel across several resolutions, and then fuse all streams by re-sampling to the output resolution. Such architectures induce networks with multiple parallel paths from input to output. We will show that nearly all such networks are embedded in our fabrics, either as paths or other simple sub-graphs.

While multi-dimensional networks have been proposed in the past, e.g. to process non-sequential data with recurrent nets [START_REF] Graves | Multi-dimensional recurrent neural networks[END_REF][START_REF] Kalchbrenner | Grid long short-term memory[END_REF], to the best of our knowledge they have not been explored as a "basis" to span large classes of convolutional neural networks. Misra et al . [START_REF] Misra | Cross-stich networks for multi-task learning[END_REF] propose related cross-stitch networks that exchange information across corresponding layers of two copies of the same architecture that produces two different outputs. Their approach is based on Alex-net [START_REF] Krizhevsky | Imagenet classification with deep convolutional neural networks[END_REF], and does not address the network architecture selection problem. In related work Zhou et al . [START_REF] Zhou | Interlinked convolutional neural networks for face parsing[END_REF] interlink CNNs that take input from re-scaled versions of the input image. The structure of their network is related to our fabric, but lacks a sparse connectivity pattern across channels. They consider their networks for semantic segmentation, and set the filter sizes per node manually, and use strided max-pooling for down-sampling and nearest neighbor interpolation for up-sampling. The contribution of our work is to show that a similar network structure suffice to span a vast class of network architectures for both dense prediction and classification tasks. Springenberg et al . [START_REF] Springenberg | Striving for simplicity: The all convolutional net[END_REF] experimentally observed that the use of max-pooling in CNN architectures is not always beneficial as opposed to using strided convolutions. In our work we go one step further and show that ReLU units and strided convolutions suffice to implement max-pooling operators in our fabrics. Their work, similar to ours, also strives to simplify architecture design. Our results, however, reach much further than only removing pooling operators from the architectural elements. Lee et al . [START_REF] Lee | Generalizing pooling functions in convolutional neural networks: Mixed, gated, and tree[END_REF] generalize the max and average pooling operators by computing both max and average pooling, and then fusing the result in a possibly data-driven manner. Our fabrics also generalize max and average pooling, but instead of adding elementary operators, we show that settings weights in a network with fewer elementary operators is enough for this generalization.

Kulkarni et al . [START_REF] Kulkarni | Learning the structure of deep architectures using 1 regularization[END_REF] use 1 regularization to automatically select the number of units in "fullyconnected" layers of CNN architectures for classification. Although their approach does not directly extend to determine more general architectural design choices, it might be possible to use such regularization techniques to select the number of channels and/or layers of our fabrics.

Dropout [START_REF] Srivastava | Dropout: A simple way to prevent neural networks from overfitting[END_REF] and swapout [START_REF] Singh | Swapout: learning an ensemble of deep architectures[END_REF] are stochastic training methods related to our work. They can be understood as approximately averaging over an exponential number of variations of a given architecture. Our approach, on the other hand, allows to leverage an exponentially large class of architectures (ordering of pooling and convolutional layers, type of pooling operator, etc.) by means of continuous optimization. Note that these approaches are orthogonal and can be applied to fabrics.

The fabric of convolutional neural networks

In this section we give a precise definition of convolutional neural fabrics, and show in Section 3.2 that most architectural network design choices become irrelevant for sufficiently large fabrics. Finally, we analyze the number of response maps, parameters, and activations of fabrics in Section 3.3.

Weaving the convolutional neural fabric

Each node in the fabric represents one response map with the same dimension D as the input signal (D = 1 for audio, D = 2 for images, D = 3 for video). The fabric over the nodes is spanned by three axes. A layer axis along which all edges advance, which rules out any cycles, and which is analogous to the depth axis of a CNN. A scale axis along which response maps of different resolutions are organized from fine to coarse, neighboring resolutions are separated by a factor two. A channel axis along which different response maps of the same scale and layer are organized. We use S = 1 + log 2 N scales when we process inputs of size N D , e.g. for 32×32 images we use six scales, so as to obtain a scale pyramid from the full input resolution to the coarsest 1×1 response maps.

We now define a sparse and homogeneous edge structure. Each node is connected to a 3×3 scalechannel neighborhood in the previous layer, i.e. activations at channel c, scale s, and layer l are computed as a(s, c, l) = i,j∈{-1,0,1} conv a(c + i, s + j, l -1), w ij scl . Input from a finer scale is obtained via strided convolution, and input from a coarser scale by convolution after upsampling by padding zeros around the activations at the coarser level. All convolutions use kernel size 3. Activations are thus a linear function over multi-dimensional neighborhoods, i.e. a four dimensional 3×3×3×3 neighborhood when processing 2D images. The propagation is, however, only convolutional across the input dimensions, and not across the scale and layer axes. The "fully connected" layers of a CNN correspond to nodes along the coarsest 1×1 scale of the fabric. Rectified linear units (ReLUs) are used at all nodes. Figure 1 illustrates the connectivity pattern in 2D, omitting the channel dimension for clarity. The supplementary material contains an illustration of the 3D fabric structure.

All channels in the first layer at the input resolution are connected to all channels of the input signal. The first layer contains additional edges to distribute the signal across coarser scales, see the vertical edges in Figure 1. More precisely, within the first layer, channel c at scale s receives input from channels c + {-1, 0, 1} from scale s -1. Similarly, edges within the last layer collect the signal towards the output. Note that these additional edges do not create any cycles, and that the edge-structure within the first and last layer is reminiscent of the 2D trellis in Figure 1.

Stitching convolutional neural networks on the fabric

We now demonstrate how various architectural choices can be "implemented" in fabrics, demonstrating they subsume an exponentially large class of network architectures. Learning will configure a fabric to behave as one architecture or another, but more generally as an ensemble of many of them. For all but the last of the following paragraphs, it is sufficient to consider a 2D trellis, as in Figure 1, where each node contains the response maps of C channels with dense connectivity among channels.

Re-sampling operators. A variety of re-sampling operators is available in fabrics, here we discuss ones with small receptive fields, larger ones are obtained by repetition. Stride-two convolutions are used in fabrics on fine-to-coarse edges, larger strides are obtained by repetition. Average pooling is obtained in fabrics by striding a uniform filter. Coarse-to-fine edges in fabrics up-sample by padding zeros around the coarse activations and then applying convolution. For factor-2 bilinear interpolation we use a filter that has 1 in the center, 1/4 on corners, and 1/2 elsewhere. Nearest neighbor interpolation is obtained using a filter that is 1 in the four top-left entries and zero elsewhere.

For max-pooling over a 2 × 2 region, let a and b represent the values of two vertically neighboring pixels. Use one layer and three channels to compute (a + b)/2, (a -b)/2, and (b -a)/2. After ReLU, a second layer can compute the sum of the three terms, which equals max(a, b). Each pixel now contains the maximum of its value and that of its vertical neighbor. Repeating the same in the horizontal direction, and sub-sampling by a factor two, gives the output of 2×2 max-pooling. The same process can also be used to show that a network of MaxOut units [START_REF] Goodfellow | Maxout networks[END_REF] can be implemented in a network of ReLU units. Although ReLU and MaxOut are thus equivalent in terms of the functions they can implement, for training efficiency it may be more advantageous to use MaxOut networks.

Filter sizes. To implement a 5 × 5 filter we first compute nine intermediate channels to obtain a vectorized version of the 3×3 neighborhood at each pixel, using filters that contain a single 1, and are zero elsewhere. A second 3×3 convolution can then aggregate values across the original 5×5 patch, and output the desired convolution. Any 5×5 filter can be implemented exactly in this way, not only approximated by factorization, c.f . [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF]. Repetition allows to obtain filters of any desired size.

Ordering convolution and re-sampling. As shown in Figure 1, chain-structured networks correspond to paths in our fabrics. If weights on edges outside a path are set to zero, a chain-structured network with a particular sequencing of convolutions and re-sampling operators is obtained. A trellis that spans S + 1 scales and L + 1 layers contains more than L S chain-structured CNNs, since this corresponds to the number of ways to spread S sub-sampling operators across the L steps to go from the first to the last layer. More CNNs are embedded, e.g. by exploiting edges within the first and last layer, or by including intermediate up-sampling operators. Networks beyond chain-structured ones, see e.g. [START_REF] Farabet | Learning hierarchical features for scene labeling[END_REF][START_REF] Long | Fully convolutional networks for semantic segmentation[END_REF][START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF], are also embedded in the trellis, by activating a larger subset of edges than a single path, e.g. a tree structure for the multi-scale net of [START_REF] Farabet | Learning hierarchical features for scene labeling[END_REF].

Channel connectivity pattern. Although most networks in the literature use dense connectivity across channels between successive layers, this is not a necessity. Krizhevsky et al . [START_REF] Krizhevsky | Imagenet classification with deep convolutional neural networks[END_REF], for example, use a network that is partially split across two independent processing streams.

In Figure 2 we demonstrate that a fabric which is sparsely connected along the channel axis, suffices to emulate densely connected convolutional layers. This is achieved by copying channels, convolving them, and then locally aggregating them. Both the copy and sum process are based on local channel interactions and convolutions with filters that are either entirely zero, or identity filters which are all zero except for a single 1 in the center. While more efficient constructions exist to represent the densely connected layer in our trellis, the one presented here is simple to understand and suffices to demonstrate feasibility. Note that in practice learning automatically configures the trellis.

Both the copy and sum process generally require more than one layer to execute. In the copying process, intermediate ReLUs do not affect the result since the copied values themselves are non-negative outputs of ReLUs. In the convolve-and-sum process care has to be taken since one convolution might give negative outputs, even if the sum of convolutions is positive. To handle this correctly, it suffices to shift the activations by subtracting from the bias of every convolution i the minimum possible corresponding output a min i (which always exists for a bounded input domain). Using the adjusted bias, the output of the convolution is now guaranteed to be non-negative, and to propagate properly in the copy and sum process. In the last step of summing the convolved channels, we can add back

C • L • S C • L • 3 D+1 • 3 • S C • L • 3 D+1 • C • S C • L • N 2 • 4 3 doubling C • L • 2 S C • L • 3 D+1 • 3 • 2 S C • L • 3 D+1 • C • 4 S • 7 18 C • L • N 2 • 2

Analysis of the number of parameters and activations

For our analysis we ignore border effects, and consider every node to be an internal one. In the top row of Table 1 we state the total number of response maps throughout the fabric, and the number of parameters when channels are sparsely or densely connected. We also state the number of activations, which determines the memory usage of back-propagation during learning.

While embedding an exponential number of architectures in the number of layers L and channels C, the number of activations and thus the memory cost during learning grows only linearly in C and L.

Since each scale reduces the number of elements by a factor 2 D , the total number of elements across scales is bounded by 2 D /(2 D -1) times the number of elements N D at the input resolution.

The number of parameters is linear in the number of layers L, and number of scales S. For sparsely connected channels, the number of parameters grows also linearly with the number of channels C , while it grows quadratically with C in case of dense connectivity.

As an example, the largest models we trained for 32×32 input have L = 16 layers and C = 256 channels, resulting in 2M parameters (170M for dense), and 6M activations. For 256×256 input we used upto L = 16 layers and C = 64 channels, resulting in 0.7 M parameters (16M for dense), and 89M activations. For reference, the VGG-19 model has 144M parameters and 14M activations.

Channel-doubling fabrics. Doubling the number of channels when moving to coarser scales is used in many well-known architectures, see e.g. [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF][START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF]. In the second row of Table 1 we analyze fabrics with channel-doubling instead of a constant number of channels per scale. This results in C2 S channels throughout the scale pyramid in each layer, instead of CS when using a constant number of channels per scale, where we use C to denote the number of "base channels" at the finest resolution. For 32×32 input images the total number of channels is roughly 11× larger, while for 256×256 images we get roughly 57× more channels. The last column of Table 1 shows that the number of activations, however, grows only by 50% due to the coarsening of the maps.

With dense channel connections and 2D data, the amount of computation per node is constant, as at a coarser resolution there are 4× less activations, but interactions among 2×2 more channels. Therefore, in such fabrics the amount of computation grows linearly in the number of scales as compared to a single embedded CNN. For sparse channel connections, we adapt the local connectivity pattern between nodes to accommodate for the varying number channels per scale, see Figure 3 for an illustration. Each node still connects to nine other nodes at the previous layer: two inputs from scale s -1, three from scale s, and four from scale s + 1. The computational cost thus also grows only Channels Scales Figure 3: Diagram of sparse channel connectivity from one layer to another in a channel-doubling fabric. Channels are laid out horizontally and scales vertically. Each internal node, i.e. response map, is connected to nine nodes at the previous layer: four channels at a coarser resolution, two at a finer resolution, and to itself and neighboring channels at the same resolution.

by 50% as compared to using a constant number of channels per scale. In this case, the number of parameters grows by the same factor 2 S /S as the number of channels. In case of dense connections, however, the number of parameters explodes with a factor 7 18 4 S /S. That is, roughly a factor 265 for 32×32 input, and 11,327 for 256×256 input. Therefore, channel-doubling fabrics appear most useful with sparse channel connectivity. Experiments with channel-doubling fabrics are left for future work.

Experimental evaluation results

In this section we first present the datasets used in our experiments, followed by evaluation results.

Datasets and experimental protocol

Part Labels dataset. This dataset [START_REF] Kae | Augmenting CRFs with Boltzmann machine shape priors for image labeling[END_REF] consists of 2,927 face images from the LFW dataset [START_REF] Huang | Labeled faces in the wild: a database for studying face recognition in unconstrained environments[END_REF], with pixel-level annotations into the classes hair, skin, and background. We use the standard evaluation protocol which specifies training, validation and test sets of 1,500, 500 and 927 images, respectively. We report accuracy at pixel-level and superpixel-level. For superpixel we average the class probabilities over the contained pixels. We used horizontal flipping for data augmentation.

MNIST. This dataset [START_REF] Lecun | Gradient-based learning applied to document recognition[END_REF] consists of 28×28 pixel images of the handwritten digits 0, . . . , 9. We use the standard split of the dataset into 50k training samples, 10k validation samples and 10k test samples. Pixel values are normalized to [0, 1] by dividing them by 255. We augment the train data by randomly positioning the original image on a 32×32 pixel canvas.

CIFAR10. The CIFAR-10 dataset (http://www.cs.toronto.edu/~kriz/cifar.html) consists of 50k 32×32 training images and 10k testing images in 10 classes. We hold out 5k training images as validation set, and use the remaining 45k as the training set. To augment the data, we follow common practice, see e.g. [START_REF] Goodfellow | Maxout networks[END_REF][START_REF] Lin | Network in network[END_REF], and pad the images with zeros to a 40×40 image and then take a random 32×32 crop, in addition we add horizontally flipped versions of these images.

Training. We train our fabrics using SGD with momentum of 0.9. After each node in the trellis we apply batch normalization [START_REF] Ioffe | Batch normalization: Accelerating deep network training by reducing internal covariate shift[END_REF], and regularize the model with weight decay of 10 -4 , but did not apply dropout [START_REF] Srivastava | Dropout: A simple way to prevent neural networks from overfitting[END_REF]. We use the validation set to determine the optimal number of training epochs, and then train a final model from the train and validation data and report performance on the test set. We release our Caffe-based implementation at http://thoth.inrialpes.fr/~verbeek/fabrics.

Experimental results

For all three datasets we trained sparse and dense fabrics with various numbers of channels and layers. In all cases we used a constant number of channels per scale. The results across all these settings can be found in Appendix A.3, here we report only the best results from these. On all three datasets, larger trellises perform comparable or better than smaller ones. So in practice the choice of these only two hyper-parameters of our model is not critical, as long as a large enough trellis is used.

Part Labels. On this data set we obtained a super-pixel accuracy of 95.6% using both sparse and dense trellises. In Figure 4 we show two examples of predicted segmentation maps. Table 2 compares our results with the state of the art, both in terms of accuracy and the number of parameters. Our results are slightly worse than [START_REF] Tsogkas | Deep learning for semantic part segmentation with high-level guidance[END_REF][START_REF] Zheng | Learning high-level prior with convolutional neural networks for semantic segmentation[END_REF], but the latter are based on the VGG-16 network. That network has roughly 4, 000× more parameters than our sparse trellis, and has been trained from over 1M ImageNet images. We trained our model from scratch using only 2,000 images. Moreover, [START_REF] Kae | Augmenting CRFs with Boltzmann machine shape priors for image labeling[END_REF][START_REF] Liu | Multi-objective convolutional learning for face labeling[END_REF][START_REF] Tsogkas | Deep learning for semantic part segmentation with high-level guidance[END_REF] also include CRF and/or RBM models to encode spatial shape priors. In contrast, our results with convolutional neural fabrics (CNF) are obtained by predicting all pixels independently. MNIST. We obtain error rates of 0.48% and 0.33% with sparse and dense fabrics respectively. In Table 3 we compare our results to a selection of recent state-of-the-art work. We excluded several more accurate results reported in the literature, since they are based on significantly more elaborate data augmentation methods. Our result with a densely connected fabric is comparable to those of [START_REF] Wan | Regularization of neural networks using DropConnect[END_REF], which use similar data augmentation. Our sparse model, which has 20× less parameters than the dense variant, yields an error of 0.48% which is slightly higher.

CIFAR10.

In Table 4 we compare our results to the state of the art. Our error rate of 7.43% with a dense fabric is comparable to that reported with MaxOut networks [START_REF] Goodfellow | Maxout networks[END_REF]. On this dataset the error of the sparse model, 18.89%, is significantly worse than the dense model. This is either due to a lack of capacity in the sparse model, or due to difficulties in optimization. The best error of 5.84% [START_REF] Mishkin | All you need is a good init[END_REF] was obtained using residual connections, without residual connections they report an error of 6.06%.

Visualization. In Figure 5 we visualize the connection strengths of learned fabrics with dense channel connectivity. We observe qualitative differences between learned fabrics. The semantic segmentation model (left) immediately distributes the signal across the scale pyramid (first layer/column), and then progressively aggregates the multi-scale signal towards the output. In the CIFAR10 classification model the signal is progressively downsampled, exploiting multiple scales in each layer. The figure shows the result of heuristically pruning (by thresholding) the weakest connections to find a smaller sub-network with good performance. We pruned 67% of the connections while increasing the error only from 7.4% to 8.1% after fine-tuning the fabric with the remaining connections. Notice that all up-sampling connections are deactivated after pruning.

Conclusion

We presented convolutional neural fabrics: homogeneous and locally connected trellises over response maps. Fabrics subsume a large class of convolutional networks. They allow to sidestep the tedious process of specifying, training, and testing individual network architectures in order to find the best ones. While fabrics use more parameters, memory and computation than needed for each of the individual architectures embedded in them, this is far less costly than the resources required to test all embedded architectures one-by-one. Fabrics have only two main hyper-parameters: the number of layers and the number of channels. In practice their setting is not critical: we just need a large enough fabric with enough capacity. We propose variants with dense channel connectivity, and with channel-doubling over scales. The latter strikes a very attractive capacity/memory trade-off.

In our experiments we study performance of fabrics for image classification on MNIST and CIFAR10, and of semantic segmentation on Part Labels. We obtain excellent results that are close to the best reported results in the literature on all three datasets. These results suggest that fabrics are competitive with the best hand-crafted CNN architectures, be it using a larger number of parameters in some cases (but much fewer on Part Labels). We expect that results can be further improved by using better optimization schemes such as Adam [START_REF] Kingma | A method for stochastic optimization[END_REF], using dropout [START_REF] Srivastava | Dropout: A simple way to prevent neural networks from overfitting[END_REF] or dropconect [START_REF] Wan | Regularization of neural networks using DropConnect[END_REF] regularization, and using MaxOut units [START_REF] Goodfellow | Maxout networks[END_REF] or residual units [START_REF] He | Identity mappings in deep residual networks[END_REF] to facilitate training of deep fabrics with many channels.

In ongoing work we experiment with channel-doubling fabrics, and fabrics for joint image classification, object detection, and segmentation. We also explore channel connectivity patterns in between the sparse and dense options used here. Finally, we work on variants that are convolutional along the scale-axis so as to obtain a scale invariant processing that generalizes better across scales.

In Figure 8 we illustrate the 3D fabric structure when using sparse channel connectivity. In this case, each internal node corresponds to a single response map at a given resolution. Nodes receive input from 3 × 3 nodes from the scale-channel plane of the previous layer. Note that each edge represents a 3 × 3 spatial convolution. Therefore, the input that projects into any "neuron" in the fabric is a 4D tensor of size 3 × 3 × 3 × 3 across two spatial dimensions, a scale and a channel dimension.

Upsample + Conv

A.3 Additional experimental results

In Figure 9 we provide additional segmentation results on the Part Labels data set, both at superpixel and pixel level. In tables 5-12 we give detailed experimental results obtained using sparse and dense fabrics of different sizes, and give the corresponding number of parameters for each model.

The results reported here are measured on the test set, using models trained on the train set only. In the main paper results are reported on the test set using models trained from both the train and validation data. In both cases the number of training epochs has been selected to maximize performance on the validation data, when training from the train data only.

On all three datasets larger fabrics generally give better or comparable results as compared to smaller ones, despite relatively simple regularization by means of weight decay and early stopping. These results show that the number of channels and layers are not critical parameters of our fabrics, it simply suffices to take them large enough.

  i a min i to shift the activations back to recover the desired sum of convolved channels.

Figure 2 :

 2 Figure2: Representation of a dense-channel-connect layer in a fabric with sparse channel connections using copy and swap operations. The five input channels a, . . . , e are first copied; more copies are generated by repetition. Channels are then convolved and locally aggregated in the last two layers to compute the desired output. Channels in rows, layers in columns, scales are ignored for simplicity.

Figure 4 :

 4 Figure 4: Examples form the Part Labels test set: input image (left), ground-truth labels (middle), and superpixel-level labels from our sparse CNF model with 8 layers and 16 channels (right).

Figure 5 :

 5 Figure 5: Visualization of mean-squared filter weights in fabrics learned for Part Labels (left) and CIFAR10 (right, pruned network connections). Layers are laid out horizontally, and scales vertically.

Figure 7 :

 7 Figure 7: Visualization of the multi-scale signal propagation in fabrics. Layers are laid out horizontally, and scales vertically. Strided convolution and convolution after zero-padding up-sampling are used to adapt finer and coarser input signals to the node resolution.

Figure 8 :

 8 Figure 8: Visualization of the 3D fabric with sparse channel connectivity. Layers are laid out horizontally, and scales vertically, channels along the third dimension.

Figure 9 :

 9 Figure 9: Example segmentations on the Part Labels test set, from left to right: input image, groundtruth labels, superpixel-level predictions, and pixel-level prediction from our sparse CNF model with 8 layers and 16 channels. Successful segmentation in the top three rows, failure cases in the bottom three rows. All predictions are made independently across pixels, i.e. no CRF models have been used.

Table 1 :

 1 Analysis of fabrics with L layers, S scales, C channels. Number of activations given for D = 2 dim. inputs of size N ×N pixels. Channel doubling across scales used in the bottom row.

	# chan. / scale # resp. maps # parameters (sparse) # parameters (dense)	# activations
	constant

Table 2 :

 2 Comparison of our results with the state of the art on Part Labels. Year # Params. SP Acccur. P Accur.

	Tsogkas et al . [31]	2015	>414 M	96.97	-
	Zheng et al . [33]	2015	>138 M	96.59	-
	Liu et al . [19]	2015	>33 M	-	95.24
	Kae et al . [10]	2013	0.7 M	94.95	-
	Ours: CNF-sparse (L = 8, C = 16)		0.1 M	95.58	94.60
	Ours: CNF-dense (L = 8, C = 64)		8.0 M	95.63	94.82

Table 3 :

 3 Comparison of our results with the state of the art on MNIST. Data augmentation with translation and flipping is denoted by T and F respectively, N denotes no data augmentation.

		Year Augmentation # Params. Error (%)
	Chang et al . [1]	2015	N	447K	0.24
	Lee et al . [17]	2015	N		0.31
	Wan et al . (Dropconnect) [32]	2013	T	379K	0.32
	CKN [21]	2014	N	43 K	0.39
	Goodfellow et al . (MaxOut) [4]	2013	N	420 K	0.45
	Lin et al . (Network in Network) [18]	2013	N		0.47
	Ours: CNF-sparse (L = 16, C = 32)		T	249 K	0.48
	Ours: CNF-dense (L = 8, C = 64)		T	5.3 M	0.33

Table 4 :

 4 Comparison of our results with the state of the art on CIFAR10. Data augmentation with translation, flipping, scaling and rotation are denoted by T, F, S and R respectively.

	Year Augmentation # Params. Error (%)

Table 5 :

 5 Accuracy on Part Labels for CNF-sparse. Number of parameters given in parentheses.

	Layers / Channels 4	16	64
	2	91.95 (6K)	94.76 (23K)	95.14 (93K)
	4	93.94 (12K) 95.02 (47K)	95.34 (187K)
	8	94.87 (23K) 95.48 (93K)	95.46 (373K)
	16	95.15 (47K) 95.38 (187K) 95.26 (746K)

Table 6 :

 6 Accuracy on Part Labels for CNF-dense. Number of parameters given in parentheses.

	Layers / Channels 4	16	64
	2	93.57 (8K)	95.26 (124K) 95.33 (2M)
	4	93.67 (16K) 95.05 (249K) 95.20 (4M)
	8	95.09 (31K) 95.22 (498K) 95.39 (8M)
	16	94.92 (62K) 95.29 (995K) 95.34 (16M)

Table 7 :

 7 Error rate on MNIST for CNF-sparse. Number of parameters given in parentheses.

	Layers / Channels 4	8	16	32	64	128
	2	4.94 (4K)	2.32 (8K)	1.68 (16K)	1.40 (31K)	0.97 (62K)	1.00 (124K)
	4	2.96 (8K)	1.69 (16K)	1.14 (31K)	0.96 (62K)	0.98 (124K) 0.78 (249K)
	8	1.94 (16K) 1.12 (31K)	0.87 (62K)	0.69 (124K) 0.79 (249K) 0.57 (498K)
	16	1.13 (31K) 0.91 (62K)	0.71 (124K) 0.56 (249K) 0.68 (498K) 0.70 (1M)
	32	1.37 (62K) 0.88 (124K) 0.67 (249K) 0.61 (498K) 0.77 (1M)	0.73 (2M)

Table 8 :

 8 Error rate on MNIST for CNF-dense. Number of parameters given in parentheses.

	Layers / Channels 4	8	16	32	64	128
	2	3.47 (5K)	1.46 (21K)	0.73 (83K)	0.65 (331K) 0.59 (1M)	0.59 (5M)
	4	2.74 (10K) 0.88 (42K)	0.67 (166K) 0.54 (663K) 0.59 (3M)	0.51 (10M)
	8	1.65 (21K) 0.70 (83K)	0.60 (332K) 0.52 (1M)	0.39 (5M)	0.46 (21M)
	16	1.04 (41K) 0.60 (166K) 0.50 (663K) 0.55 (2M)	0.39 (10M) 0.47 (42M)
	32	1.29 (83K) 0.92 (332K) 0.64 (1M)	0.57 (5M)	0.61 (21M) 0.56 (85M)

Table 9 :

 9 Error rate on CIFAR10 for CNF-sparse. Number of parameters given in Table 11. .65 48.95 34.48 31.48 28.82 27.67 25.56 4 62.34 43.69 34.28 30.07 26.18 25.14 22.96 22.60 8 58.26 40.02 28.10 24.44 22.12 22.20 20.66 21.38 16 50.31 32.28 25.70 22.65 19.74 19.07 19.05 18.89

	Layers / Channels	2	4	8	16	32	64	128	256
	2	68.70 49

Table 10 :

 10 Error rate on CIFAR10 for CNF-dense. Number of parameters given in Table12.

	Layers / Channels	2	4	8	16	32	64	128	256
	2	68.70 50.96 33.66 23.92 18.83 15.72 13.79 13.11
	4	62.34 41.92 27.76 19.22 14.65 13.38 12.09 10.06
	8	58.26 35.12 22.53 15.57 13.05 10.88	9.42	9.31
	16	50.31 28.27 19.03 13.57 10.95	9.65	10.63 14.27

Acknowledgment. We would like to thank NVIDIA for the donation of GPUs used in this research. This work has been partially supported by the LabEx PERSYVAL-Lab (ANR-11-LABX-0025-01).

A Supplementary Material

A.1 Fabric visualizations

In Figure 6 we show fabrics learned on the three datasets used in the main paper. The connection strengths are visualized by setting edge widths proportional to the mean squared filter weights related to that connection (mean across the 3 × 3 weights and across all channels). The fabrics used for these visualization use dense channel connectivity.

Clearly, the learned connection patterns differ between the segmentation and the classification datasets, since output needs to be produced at different resolutions for these tasks. Interestingly, the pattern is also different between the two classification datasets. For the task of image classification, we have two models, CIFAR10 (bottom-left) and MNIST (top-right). In the case of MNIST, signal in the fabric is propagated in a band-diagonal pattern, exploiting multiple scales in each layer. With CIFAR10 we observe a similar pattern, but with a small difference. The signal is first processed at the finest scale for a few layers, and then propagated down. These results demonstrate that even for the same task, the fabric is able to configure itself in order to accommodate nuances of the dataset.

For the CIFAR-10 dataset we also show the pruned network, obtained by (arbitrarily) pruning all connections below the mean connection strength. After fine-tuning the pruned network, the classification error is 8.1% as compared to 7.4% for the full fabric, while removing 67% of the connections in the fabric.

A.2 Fabric structure

In Figure 7 we illustrate how the multiple inputs to a node in a fabric are combined. Input from a finer scale is processed by strided convolution, from the same scale by normal convolution, and from a coarser scale by first upsampling the signal by zero padding and then convolving the signal. The three input signals are then added, and then a ReLU activation function is applied to the result.


André Nicolle
email: andre.nicolle@ifpen.fr

Stefania Cagnina

Theodorus De Bruin

First-principle Based Modeling of Urea Decomposition 1 Kinetics in Aqueous Solutions 2

Keywords: Urea, decomposition, multiscale modeling, kinetics, ab initio, water cooperation 10

This study aims at validating a multi-scale modeling methodology based on an implicit 12 solvent model for urea thermal decomposition pathways in aqueous solutions. The influence 13 of the number of cooperative water molecules on kinetics was highlighted. The obtained 14 kinetic model is able to accurately reproduce urea decomposition in aqueous phase under a 15 variety of experimental conditions from different research groups. The model also highlights 16 the competition between HNCO desorption to gas phase and hydrolysis in aqueous phase, 17 which may influence SCR depollution process operation.

18 19 20 * effects on the potential energy surface (PES), but not on the corresponding kinetic rate 35 constants. These authors did not investigate the subsequent hydrolysis of isocyanic acid 36 leading to an additional ammonia production. In the present study, we demonstrated the 37 feasibility of a multiscale first-principle based kinetic modeling of urea decomposition in 38 aqueous solution. We performed a high-level electronic structure study on the main ammonia 39 production paths from urea decomposition including an implicit solvent model. Based on 40 these new results, we herein derived the corresponding phenomenological rate constants and 41 thermokinetic data to build a macrokinetic mechanism, which was subsequently validated

Urea decomposition kinetics is important for a vast variety of applications, including 22 agriculture [1], medical technologies [2] and energy [3]. In lean-burn automotive exhaust 23 aftertreatment systems, a urea-water solution is injected upstream of the deNOx catalyst to 24 generate ammonia for the selective catalytic reduction (SCR) process. Previous studies 25 showed that urea aqueous phase decomposition can compete effectively with water 26 evaporation rate [4] and urea polymerization [5]. While a number of recent studies [6] [7] 27 contributed to the elucidation of main urea decomposition pathways in aqueous solution, the 28 mechanism of ammonia and isocyanic acid release remains insufficiently understood, 29 although a molecular mechanism for the homolytic breaking of C-N bond seems more 30 plausible than an ionic one [8]. Among the homolytic decomposition channels identified 31 (ammonia elimination, hydrolysis and tautomerization), Alexandrova and Jorgensen [6]

Methodology

46

The electronic structure calculations were performed with the Gaussian 09 suite of programs 47 [9]. All geometry optimizations were performed at the M06-2X/6-311++G(d,p) level of 48 theory to correctly describe long-range hydrogen bonding [10]. Systematic conformational 49 searches were performed to identify the most stable structures. The T1 diagnostic for all 50 species involved in this work was less than 0.02, supporting the appropriateness of single-51 reference methods in describing the wave function. Frequency calculations confirmed the 52 desired character of the stationary points and IRC calculations effectively ensured the 53 connection between the reactants and products. In DFT calculations, we used the SMD 54 implicit solvent model [11], which is known to produce errors for solvation energies typically 55 lower than 1 kcal/mol for neutral molecules. Post Hartree-Fock energies were determined for 56 the most important reaction steps by performing CCSD(T)/aug-cc-pVTZ evaluations using 57 Molpro 2015 program [12] on the geometries previously optimized at the DFT level. The 58 ZPE-corrected Gibbs free energy was evaluated using the following formula:

59 60
In this equation  refers to the electronic energy and G corr to the thermal corrections to the 61 Gibbs Free energy, which envelopes the ZPE correction together with the translational, 62 rotational and vibrational enthalpic and entropic corrections, calculated using M06-2X at the 63 desired pressure and temperature. E solvation corresponds to the gas-to-water solvation energy, 64 calculated at the M06-2X level without any thermal correction.

65

The harmonic transition state theory was selected to compute the corresponding 66 phenomenological rate constants. Wigner correction factors [13] were computed to account 67 for tunneling effects. Free activation energies were computed over the 300-600 K temperature 68 range to get phenomenological rate constants in the Arrhenius-Kooij form (CSTR) reactor model implemented in Chemkin software package [14]. The same condensed-71 phase mean-field macrokinetic formalism was used as in our previous work [4]. The reverse 72 rate constants were computed from the corresponding forward ones and reaction Gibbs free 73 energies. The Weizmann-1 (W1) theory [15] was used to determine the enthalpies of the 74 energetic minima of the PES over the 300-600 K range and the obtained thermochemical data 75 were implemented in the mechanism using the NASA formalism [16]. As can be seen in 76 Table S1 (supplementary material), W1 theory coupled to SMD solvation model accurately 77 predicts the available experimental thermochemical data, demonstrating its suitability for the 78 present bottom-up kinetic modeling approach. Desorption rates were modeled from 79 recommended [17] sticking coefficients (0.1 for NH 3 , HNCO and CO 2 ) using Hertz-Knudsen 80 equation and equilibrium constants evaluated from thermochemical data. 81 82

Results and discussion

83

Our electronic structure calculations confirm, referring to the work of Jorgensen [6], that 84 water-assisted NH 3 elimination has a lower free energy of activation than hydrolysis (Figure 85 S1 in supplementary material). As shown in Table 1, the Gibbs free energy barriers at 300 K 86 and 1 atm for NH 3 CONH (Int 2) formation through water-assisted H-shuttling lie at 30.9 and 87 30.3 kcal/mol for respectively one and two H 2 O molecules involved, in good agreement with 88 the values obtained by Tsipis [START_REF] Tsipis | [END_REF], Alexandrova [6] and Yao [7] The subsequent hydrolysis of HNCO (Figure 2) proceeds through the formation of carbamic acid, which can in turn decompose through either intramolecular or assisted mechanism. In 105 the present study, we focused on the addition of water across the C=N bond of HNCO, as it is 106 energetically more favorable [24] than addition across the C=O bond due to the extended 107 concentration of the electron density on nitrogen [25]. Although a competitive bicarbonate 108 mechanism could also be considered in this study, it is not expected to change HNCO 109 hydrolysis kinetics since the transition state (TS) structures involved are very similar [26]. As 110 could be anticipated [27], the six-membered-ring TS involving two water molecules results in 111 a lower barrier (19.7 kcal/mol) compared to a four-membered-ring TS (38.9 kcal/mol).

112

According to Wei et al. [24], the former barrier lies less than 4 kcal/mol from the value

124

As can be seen on Figure 3, the energetic barriers for carbamic acid decarboxylation are also [41]. On the 177 right, the CO 2 liquid-phase mole fraction profiles during urea-water solution decomposition. [37] Figure 5 shows ammonia concentration profiles obtained using the ab initio kinetic model

  found

32 the

 32 first path to have the lowest activation energy, partly resulting from the resonance 33 stabilization in the first transition state. However, their study mainly focused on the solvent against experimental data, allowing rate-of-production studies of urea decomposition under realistic operating conditions.

44

 44

Figure 1 -

 1 Figure 1 -Relative ZPE-corrected electronic energies (in kcal/mol) obtained at the M06-2X and

113Figure 2 -Figure 3 -

 23 Figure 2 -Relative ZPE-corrected electronic energies (in kcal/mol) obtained at the M06-2X and

Figure 5 -

 5 Figure 5 -On the left, calculated (lines) and measured (symbols) species gas-phase NH 3 mole fraction, where

  scale modeling methodology based on electronic structure calculations using an 199 implicit solvent model, transition state theory and macrokinetic modeling was validated on the 200 important issue of homolytic urea thermal decomposition in aqueous solutions. The influence 201 of the number of cooperative water molecules on reaction kinetics was highlighted. The 202 obtained macrokinetic model is able to reproduce urea decomposition in the aqueous phase under a variety of experimental conditions from different groups. The evidence of occurrence 204 of urea decomposition in aqueous solution under typical SCR operating conditions should 205encourage engineers to include these hitherto neglected paths in their kinetic models[43].206Notably, the model reveals that HNCO hydrolysis in aqueous phase competes effectively with 207 its desorption, providing evidence of the contribution of condensed phase HNCO hydrolysis 208 during SCR process operation. While the present obtained thermokinetic data will allow more 209 accurate modeling of industrial and biological systems, further work is needed to extend the 210 model to urea polymerization in aqueous and dry media[44] [45] to get more accurate 211 predictions of urea decomposition at higher temperatures.

Table 1 -

 1 (respectively 29.5, 26.4 and 89 25.3 kcal/mol). The Free energy barrier associated to nucleophilic attack of water on carbonyl 90 is much higher than this value, favoring NH 3 elimination over urea hydrolysis. It is important 91 to note that relative DFT energies can differ from post-HF values by up to 10 kcal/mol (Figure2), which highlights the importance of a fine description of the electron correlation to Relative Gibbs Free energies at 300 K and 1 atm with respect to the reactants

	93
	94	get accurate energetic barriers.
	95
		Urea + H 2 O → NH 3 +HNCO+H 2 O	Urea + 2 H 2 O →	HNCO + H 2 O + NH 3	HNCO + 2 H 2 O →
						NH 3 +HNCO+2 H 2 O	→ NH 2 COOH + NH 3	NH 2 COOH + H 2 O
		complex	TS1	Int2	TS2	complex	TS1	complex	TS3	complex	TS3
		4.1	35.0	28.2	38.2	14.5	44.8	11.0	30.6	12.2	36.0
	96

  126highly dependent on the number of water molecules involved. As for HNCO, the attack of one

	127
	128	water molecule on C=N bond (barrier of 19.8 kcal/mol) is more favorable than an attack of
	129	water on C=O bond (barrier of 27.5 kcal/mol reported in [28]). The geometry of the six-
	130	membered cyclic TS (obtained by considering one water molecule) is globally similar to the
	131	gas-phase TS described by Tsipis et al. [29], although water's oxygen lies clearly out-of-plane
		(respective OCNO dihedral angles of 7.2° and 32.0°). Note also that this H-shuttling

132

mechanism is similar to that reported by Ramachandran

[30]

for ammonia-assisted 133 decomposition of carbamic acid in dry medium, who obtained a Free energy barrier of 18 134 kcal/mol, in contrast with Cheng et al.

[31]

who considered a four-membered ring TS 135 structure, thereby leading to a barrier similar to that of the unassisted decarboxylation. As the 136 number of water molecules increases, an additional local minimum appears in the energetic 137 potential. The energetic barrier obtained in the case of the assistance of two water molecules 138 (12.0 kcal/mol) is significantly lower than the reported value of 15.0 kcal/mol previously 139 obtained at a lower level of theory (with only one water molecule) by Ruelle et al. [32] and 140 the experimental value (15.6 kcal/mol) reported by Wang et al. [33] However, it is in good 141 agreement with the barrier of 10.3 kcal/mol recently claimed by Noble et al. [34] in the 142 presence of 6 H 2 O molecules.

on the herein obtained vibrational frequencies is typically of the order of a few percent and 171 since anharmonicity is not accounted for in this study, a significant uncertainty (>10%) 172 remains on the partition function.

  TableS2, supplementary material). This model reproduces well the onset of NH 3 release, but 181 it tends to overestimate the ammonia concentration at temperatures higher than 470 K. This

	182
	183	can be attributed to the concurrent formation of biuret (NH 2 C(O)NHC(O)NH 2 ) from urea and
	184	HNCO, which is not accounted for by the present kinetic model. In Lundström's experimental
	185	conditions [41], our reaction flux analyses at 400 K indicate that HNCO hydrolysis rate in
	186	aqueous phase contributes to 35% of HNCO consumption while HNCO desorption to gas
	187	phase represents 65% of its consumption. Therefore, according to this model, HNCO
	188	hydrolysis is expected to contribute significantly to NH 3 production in SCR process
		conditions.

180

(189 Note that urea selectivity to CO 2 formation is also well predicted by the present ab initio 190 kinetic model (Figure

5

). Further, the present model predicts that the carbamic acid maximum 191 mole fraction in aqueous solution should be of the order of 1 ppm under urea decomposition 192 conditions, calling for quantitative measurements of this intermediate. Due to the high Free 193 energy barrier involved, the contribution of urea hydrolysis should remain negligible under 194 the investigated conditions, although it can be anticipated [4] [42] that higher heating rates 195 would shift NH 3 conversion profile towards higher temperatures, thereby favoring direct urea 196 hydrolysis.

Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T.

Acknowledgments

213

SC would like to thank IFPEN for a post-doctoral grant. This research did not receive any 214 other specific grant from funding agencies in the public, commercial or not-for-profit sector.

144

Figure 4 -Calculated and measured [35] [20] [36] [37] [38] rate constants for ammonia elimination from urea S2 (supplementary material). As can be noticed from 155 the comparison with experimental data in Figure 4, within the uncertainties on molecular 156 parameters, the present multi-scale approach is able to generate accurate rate coefficients 157 (within a factor of 2) over an extended temperature range. Note that the rate constants of 158 backward reaction Int2 → Urea (3.08 × 10 09 s -1 at 500 K) and second step Int2 → NH 3 + 159 HNCO (1.54 × 10 09 s -1 at 500 K) remain much higher than forward reaction Urea → Int2 (2.04 160 × 10 -02 s -1 at 500 K) over a wide range of temperatures, therefore Int2 (NH 3 CONH) can be 161 assumed to be in quasi steady state (QSS). Under these conditions, our calculations indicate that the rate-limiting step switches between Int2 → NH 3 + HNCO at T<600 K and Urea → 163 Int2 at T>600K [39]. It is also worth noting that except for very high urea concentrations in 164 water solution (> 10 M), intrinsic reaction kinetics is not expected to be limited by cage 165 diffusion ( at temperatures of interest (T < 1000 K) [40].

Even though the rate constant is mostly sensitive to the TS1 relative electronic energy (Figure 168 S2 in supplementary material), the sensitivity to vibrational and rotational partition functions 169 of TS1 (respectively through frequencies and moments of inertia) is significant. As the error

Supporting information 216

Additional informations including the geometries of the most important stationary points 217 obtained in the present study are available as a supplementary material.

Supplementary Materials

Click here to download Supplementary Materials: Supp_Mat_submitted.docx


come

The magnitude and occurrence of hydro-meteorological extremes around the Mediterranean are likely to be significantly affected by climate change, which also implies a number of related risks for our societies. Although projections of future trends remain uncertain, our societies must be prepared for these possible changes. This chapter discusses various adaptation measures to natural hazards and risks.

Significantly, the measures being considered are "non-structural": i.e. not based on civil engineering works such as dams, reservoirs or embankments. This corresponds to changes in risk prevention policies in the countries around the Mediterranean. Costly structural measures, designed to control or reduce natural hazards, have shown limited efficacy in the face of extreme events and equally limited resilience to climate change. Structural measures are no longer considered as the only or even the primary possible response to risks, but are being coupled with adaptation measures based on land-use planning and regulations or designed to increase response and crisis management capacities.

The first section of this chapter demonstrates how exposure to natural hazards has dramatically increased in most of the countries around the Mediterranean over the last century, due to significant population growth and the concentration of the inhabitants in urban areas. Socio-economic and demographic changes in the Mediterranean basin have proved far more influential in shaping the consequences of natural hazards than climate change over the last 50 years, and this will remain valid for the near future. Land use planning and regulations accounting for natural hazards are a matter of priority in order to limit the risks.

The next articles in this chapter present an overview of recent progress and future perspectives for weather and flood observation and forecasting methods. Better quality monitoring and forecasting, along with improved organization of population information and rescue services, also provide efficient adaptation measures. They will not help us escape unavoidable catastrophic events but may significantly limit their consequences.

Version française L'intensité et la fréquence des événements hydro-météorologiques extrêmes sont susceptibles d'évoluer notablement en région méditerranéenne du fait du changement climatique. Les projections climatiques concernant ces extrêmes restent certes incertaines, mais nos sociétés doivent se préparer à ces évolutions probables. Ce chapitre évoque des mesures d'adaptation aux risques naturels hydro-climatiques. Il est intéressant de noter que les mesures d'adaptation considérées sont des mesures « non-structurelles » : i.e. elles ne sont pas fondées sur la construction d'ouvrages de génie civil tels que les barrages et les digues. Cela correspond à l'évolution des politiques de prévention des risques naturels dans les pays bordant la Méditerranée. Les ouvrages de protection couteux, dont le but est de contrôler ou de réduire le niveau de l'aléa naturel, ont une efficacité souvent limitée dans le cas d'événements exceptionnels et une faible résilience aux évolutions climatiques. La construction d'ouvrages de protections n'apparait plus comme la principale voire l'unique réponse possible pour limiter les risques. Les politiques de prévention mettent désormais en avant des mesures d'adaptation fondées sur la maitrise de l'occupation des sols et l'amélioration des capacités de gestion des crises et des catastrophes.

Le premier article de ce chapitre rappelle que le niveau d'exposition aux aléas naturels a considérablement augmenté en région méditerranéenne au cours du siècle dernier du fait de la très forte croissance démographique et de la concentration des populations dans les villes. Au cours des cinquante dernières années, les évolutions socio-économiques et démographiques en Méditerranée ont bien plus fortement pesé sur l'augmentation des dommages liés aux risques naturels que les changements climatiques. Cela restera vrai dans un proche avenir. La maîtrise de l'occupation des sols et de l'urbanisation est donc un élément essentiel des politiques de prévention des risques. Le reste du chapitre présente les progrès récents et les perspectives d'évolution des dispositifs d'observation et de prévision météorologiques et hydrologiques. L'amélioration des prévisions des sécheresses, des pluies et des crues, combinée à une meilleure organisation de l'information des populations et des services de secours, constitue un autre type de mesures d'adaptation et de prévention des risques. Ces mesures n'évitent pas la survenue de l'inévitable catastrophe, mais permettent d'en limiter notablement les conséquences.