Bruno Chianca Ferreira

Guillaume Dufour
email: guillaume.dufour@onera.fr

Guthemberg Silvestre
email: silvestre@enac.fr

A Lightweight Fluid Model for Mobile Ad hoc Distributed Systems

Keywords: distributed systems, edge, swarm, modelling, mobile, ad hoc, cps

Emerging edge applications introduced new computing timevariant topologies with mobile nodes connected via ad hoc networks. Such topologies are fundamentally different from cloud infrastructures due to the lack of hierarchy and clear network function separation. Sometimes, nodes that are sources are also destinations and routers, hence, creating dynamic flow patterns traversing the network. The latter, thus, can change the average performance of a distributed system, such as throughput and latency. This work introduces an analytical model based on fluid quantities to study data flows of distributed systems in mobile ad hoc networks. Using an approach based on a network of queues with evenly distributed bandwidth over concurrent flows, this lightweight model enables fast, coarse-grained analysis of different distributed systems configurations. They enable the analysis of different topologies, mobility and data flow models with a small footprint. The model was implemented, validated and evaluated with stress workloads to confirm its accuracy.

Introduction

A Distributed Computing System is a set of individual networked nodes that collaborate to execute a task or execute individual tasks serving a common purpose. Such computing nodes can be static, as in traditional cloud infrastructures [START_REF] Yousefpour | All one needs to know about fog computing and related edge computing paradigms: A complete survey[END_REF] or HPC centres, or they can otherwise be mobile [START_REF] Wang | Edge server placement in mobile edge computing[END_REF], which is a configuration more common in Cyber-Physical Systems (CPS), Internet of the Things (IoT) and Mobile Edge Computing (MEC). Mobile nodes add new challenges to the study and design of distributed computing due to its dynamic nature and unreliable network links. Such dynamic behaviour results in continuously-changing routes within the network, rendering the network traffic unpredictable under certain circumstances. This study introduces a new lightweight, analytical model to investigate the data flow in such mobile architectures, and how certain topologies may hinder the overall system performance. To scale, our approach models message passing as fluid quantities and the topology as a network of connected queues.

Mobile Computing Challenges and Opportunities

Mobile Computing architectures can be exploited by different types of paradigms and applications. Although the concept is not new [START_REF] Forman | The Challenges of Mobile Computing[END_REF], the challenges have evolved over time with the adoption of new communication technologies and advancements of the computing capacity [START_REF] Satyanarayanan | The computing landscape of the 21st century[END_REF][START_REF] Satyanarayanan | The Role of Edge Offload for Hardware-Accelerated Mobile Devices[END_REF]. Furthermore, as applications become more data-centric (e.g., edge applications that require processing large amounts of sensor data), the amount of data required to be transferred increases. So, the focus of the challenges shifts to how to make data available to applications whilst maintaining the ability to comply with the performance goals [START_REF] Yousefpour | All one needs to know about fog computing and related edge computing paradigms: A complete survey[END_REF][START_REF] Trivedi | Sharing and caring of data at the edge[END_REF]. For latency-sensitive applications, the most common paradigm adopted are the Edge and Fog computing, where data is preprocessed at the edge servers before being sent to the cloud. In addition to enabling lower latencies by preprocessing data, edge servers can also be leveraged to increase data safety. For instance, a CPS swarm connected via ad hoc networks can be sent on a mission to survey and collect data that must be stored on a distributed store during the mission before offloading to an edge cloudlet [START_REF] Gaynor | Towards distributed wilderness search using a reliable distributed storage device built from a swarm of miniature uavs[END_REF]. In other applications, collected data must be distributed among all nodes for sensor data fusion [START_REF] Cicala | Scalable distributed state estimation in UTM context[END_REF]. Such swarms can assume different topologies depending on how the mission was planned and evolves, creating challenges and opportunities to tame the network flow, and thus reduce congestion and delay. Concerning the communication infrastructure, the main characteristics of mobile swarms is how the mobility and network density affect their connectivity [START_REF] Zhang | Mobile Conductance in Sparse Networks and Mobility-Connectivity Tradeoff[END_REF][START_REF] Khan | On the connectivity of vehicular Ad Hoc Network Under Various Mobility Scenarios[END_REF]. Since the functions of such nodes during their runtime are usually complementary, data flows can be leaving, arriving and traversing the node simultaneously. Due to the limited communication range, as shown in Figure 1 and comprehensively surveyed in [START_REF] Vashisht | MAC protocols for unmanned aerial vehicle ecosystems: Review and challenges[END_REF], communication and routing usually happen in a multi-hop manner. Hence, some nodes, which have a strategic location in the topology, might experience excessive traversing traffic flow. It is therefore valuable the ability to study the behaviour of the network flows for different topologies and applications. This can be used to prevent unwanted congestions by employing different deployment strategies or employ control laws on the mobility to balance the traffic flow across the topology.

Traffic Flow in Mobile Distributed Applications

As mentioned in [START_REF] Brambilla | Swarm robotics: A review from the swarm engineering perspective[END_REF] and [START_REF] Bagnato | Designing swarms of cyber-physical systems: The h2020 cpswarm project: Invited paper[END_REF], one of the first steps of modelling a swarm of CPS is to define the deployment topology or self-organizing models. It is, therefore, crucial to have the ability to search several different topologies and path planning alternatives for better traffic flow, which requires a lightweight model for the network employed as a faster than real-time simulator. Mobile nodes have the intrinsic advantage of being able to move during runtime and thus rearrange the topology. By being able to quickly re-evaluate the traffic flow during a mission, the nodes can be potentially rearranged in real-time to improve the performance as done in [START_REF] Minelli | Self-optimization of resilient topologies for fallible multi-robots[END_REF] for connectivity maintenance. Topology control is a popular topic in WSNs [START_REF] Li | A survey on topology control in wireless sensor networks: Taxonomy, comparative study, and open issues[END_REF][START_REF] Coutinho | Underwater wireless sensor networks: A new challenge for topology control-based systems[END_REF], and is used as a way to increase network coverage or reduce energy consumption. While discrete network models provide a granularity level, that is usually not required for traffic flow optimization. Hence, models based on fluid mechanics have been proposed as a scalable alternative [START_REF] Sonenberg | Networks of interacting stochastic fluid models with infinite and finite buffers[END_REF][START_REF] Berg | Performance Modeling of a Bottleneck Node in an IEEE 802 . 11 Ad-Hoc Network[END_REF][START_REF] Roijers | Fluid-flow modeling of a relay node in an IEEE 802.11 wireless ad-hoc network[END_REF][START_REF] Marsan | Using partial differential equations to model TCP mice and elephants in large IP networks[END_REF]. By assuming a macroscopic point of view of the network flow, such fluid models do not keep granular information about each message. Therefore, they can simulate larger topologies and message flows faster, enabling fast mission planning and opening the possibility of its reevaluation during runtime.

Contributions

The main contribution of this work is the proposed lightweight, analytical model for distributed computing in mobile ad hoc networks. Such a model can be used to study swarm robotics deployments aimed at simulating network flows and finding events that can hinder the performance of mobile distributed systems. Due to its modularity, the model can potentially be extended to study routing or MAC protocols.

Outline

In the following Section 2, the paper defines the proposed analytical fluid model, and in the subsequent Section 3 it defines, based in existing state-of-theart approaches, a detailed system model that allows applications to be modelled and tested. The proposed model's accuracy is later validated in Section 4 in two ways:

-Modelling a data flow model and implementing on a network simulator (OM-Net++), a mobile ad hoc computing emulator (MACE) and in the proposed analytical model.

-Modelling the steady state performance of a bottleneck node and comparing the results with the fluid model proposed in [START_REF] Berg | Performance Modeling of a Bottleneck Node in an IEEE 802 . 11 Ad-Hoc Network[END_REF].

The model is then used to verify the ability to extract useful metrics for studying distributed systems such as throughput and latency, by comparing stress loads on different topologies. Later, it is used to investigate the behaviour, during the whole simulation runtime, of factors that might hinder the performance of a specific topology, by exposing transient queue levels and average latency in bottleneck nodes. Finally, the scalability of the model is assessed. The results are presented in Section 5 and Table 1 lists most of the notations used in the paper to aid understanding.

Analytical Fluid Model

In this section a fluid model which allows modelling with accuracy the message passing in the network is introduced. The model can be implemented together with the models from Section 3 to build a simulator. In this model, each node in the network is abstracted as a queue, and messages are abstracted as fluid quantities flowing through them.

Message Queues

In order to model the flow through the topology, each transferred message is abstracted as M(a(t), p(t), e). Each abstracted message has an accumulated travel delay, henceforth called age α(t) with α ∈ R + , which will be detailed in Section 2.2; a position p(t) with p ∈ N, 0 p < n, that represents in which node the message is currently located; and the end node e with e ∈ N, 0 e < n . When a message is flowing from one node to another, they are placed at an output queue as a corresponding amount of data. In each node, the queue evolves during execution and data leaves the queue at a rate according to the available bandwidth connecting the two nodes. When data is located at more than one non-empty output queue, they share the available bandwidth. Each queue Q is a set with |Q| = n, and each element represents a destination node

Q j = {Q 0 j , Q 1 j , Q 2 j , ..., Q n-1 j
}, while the total queue level at a node j given by Equation 1:

Q j (t) = n-1 i=0 Q i j (t) with p(t) = j and e = j (1)
Therefore, when a message is transmitted, it is added to a queue that drains at its maximum rate B jk (t), with B jk ∈ R + , which is the available bandwidth between j and k. Assuming that every destination is equiprobable, the individual queue drainage at j for messages with e = k is therefore given by:

D k j (t) =      - Q k j (t) Q j (t) B jk (t), if Q k j (t) > 0 0, otherwise (2)
Since the system is discretized with time increments δt, B jk = B jk δt. Each queue is increased if there is flow arriving from other nodes with a rate higher than the possible outgoing flow. The arrival at j's queue with destination k, i.e. j is a routing node from a node i towards k, is defined by Equation 3.

a k j (t) =    n-1 i=0 i =j Q j i (t) Q i (t) B ij (t), if Q j i (t) > 0; R i,k (t) = j 0, otherwise (3)
If the receiving node is not the final destination, its queue will receive a positive arrival flow with the same ratio as the previous hops send. Therefore, each individual queue level derivative is:

Q k j (t) = - Q k j (t) Q j (t) B jk (t)1 Q k j (t)>0 1 j =k + + n-1 i=0 i =j Q k i (t) Q i (t) B jk (t)1 Q j i (t)>0 1 R i,k (t)=j (4)
By observing Equation 4 for the case when j = k, i.e. data arriving at destination node, the rate change of the queue can be only Q k j (t) ≥ 0. At the end of the simulation, the value of Q k j (t h ) when j = k will be the total data received at node j. These equations permit observing, during the simulation execution, the queues' dynamics.

Modelling Average Dynamic Communication Latency

As mentioned in Section 2.1, each message M has an associated parameter α(t), which represents the evolution of the message's age. The age, an abstraction for end-to-end delay of a message, is incremented every time the latter is being transferred or waiting in queue before arriving at the final destination. Since messages are not simulated individually in the proposed model, the average age will be modelled by using momentum conservation. Thus, it can be inferred at any moment, what is the actual expected end-to-end delay taking into consideration not only the current queue levels in each node, but also the accumulated latency from previous hops. For each individual queue Q k i , there is an associated age α k i , where α ∈ R + , 0 < α < t h , and the evolution of the age in each queue is modelled by:

[(α k j (t -δt) + δt)(Q k j (t -δt) -d k j (t -δt))+ + n-1 i=0 i =j H k i (t)=j (α k i (t -δt) + δt)d k i (t -δt)] -α k j (t)Q k j (t) = 0 (5)
Since, besides the current age, all the elements of the equation are known, α k j (t) can be isolated and calculated at each time step.

Mobile Ad Hoc System Model

This section introduces a model for mobile distributed systems by modelling its auxiliary subcomponents composed of: the network, routing, latency, mobility and message flow models. The models discussed in this section are needed to enable the implementation of the fluid model proposed in Section 2 as a mobile distributed system simulator.

The Network Model

Unlike infrastructure-based wireless topologies, ad hoc networks do not rely on a central entity to control connectivity, and nodes are connected when in radio reach from each other. These network topologies, which are composed by wireless mobile nodes, are modelled as an undirected graph T = (V, E). The set of vertices N is composed by n nodes, where N i , with i ∈ N and 0 ≤ i < n, and the set of edges E is composed by the edges e = (N j , N k ), where the distance d jk ≤ d r , being d r the communication range. The latter is defined by the wireless radio technology modelled, which allow a maximum bandwidth B ∈ R + defined in Mbps.

For simplicity, there is no membership control and every node in the vicinity of one of the nodes participating in the connected graph T , is henceforth considered a participating node. In order to establish connectivity between the nodes, the Euclidean distance between them is calculated, and when d jk ≤ d r , the nodes can communicate with one-hop distance. When d jk > d r , the nodes can potentially still communicate with every other node in the same connected component via multi-hop routing.

The Multi-Hop Routing Model

There are many routing protocols applicable to mobile ad hoc systems [START_REF] Oubbati | Routing in flying Ad Hoc networks: Survey, constraints, and future challenge perspectives[END_REF], and for this study, a proactive, greedy, location-based routing protocol was modelled inspired by [START_REF] Füßler | Mobicom poster: Location-based routing for vehicular ad-hoc networks[END_REF], since all the required metrics are simulated. Given the number of nodes n participating in the topology, with n ∈ Z, the routing table R is a matrix with dimensions n × n. The line index i of R represents a node in the topology, while each column j represents a destination node from i, ∀(i, j) < n. Therefore, the value of R i,j represents the next hop data currently in i with destination j. In this model, to update the routing table, the system periodically evaluates the current position of the nodes and runs the Djikstra algorithm [START_REF] Dijkstra | A note on two problems in connexion with graphs[END_REF] to calculate the shortest path for each origin/destination pair. The table is therefore updated with the next hop towards every destination that yields the shortest path.

Bandwidth

The bandwidth provided by the MAC/PHY technologies of a wireless stack is considered to be fully available for a node. However, considering a technology where all connections share the same channel such as some versions of IEEE802.11, this system bandwidth is shared among the sources injecting data into the node and all the other nodes receiving data from the former. Considering the set of nodes serving data flows to node j, S j , and the set of nodes O R being served as next hop R j,n for node j with n destinations, the bandwidth available for the link between nodes j and k as seen at node j is:

Bjk (t) = B |S j (t)| + |O R (t)| (6)
However, the receiving node k will eventually be served by other nodes and serve other nodes as well. So, the actual bandwidth available Bjk might be lower than what is expected by only observing j; i.e., every link will be limited by the lowest available bandwidth between two nodes. Considering any destinations n being served by k:

Bjk (t) = Bjk (t), if Bkn (t) > Bjk (t) Bkn (t), otherwise (7)

Latency Model

There are two main drivers for delays on a distributed system: the communication and the computation delays, and this work focuses on the former. It is expected that a multi-hop communication scheme has an impact on the overall network latency due to an accumulation of factors that add delays at each hop:

-Medium Propagation -Delay added due to the propagation of information in the medium. In this work, radio waves in the air are considered and their velocity approximated as C = 299.792.458 m/s, so the latency t mp ∈ R + is therefore t mp (t) jk = d jk /C. -Serialization -Delay added for actually transferring serialized data. Considering the current available bandwidth between the nodes Bjk (t) ∈ R + measured in Mbps and the amount of data to be transferred D ∈ R + measured in MiB, the latency t s ∈ R + is therefore t s (t) jk = D ( Bjk (t)/8) .

The total end-to-end expected latency from origin(o) to destination(d ) t od (t) ∈ R + is therefore:

t od (t) = kn=d j0=o jn=R n-1 j,k (t) kn=R n j,k (t) t mp (t) jnkn + t s (t) jnkn (8)
Additional delays added by hardware computation and due to medium access layers are not considered since they are dependent on specific hardware and chosen MAC protocol. The end-to-end latency can be estimated based on the path followed and each hop's delays estimations [START_REF] Liang | Hop-distance estimation in wireless sensor networks with applications to resources allocation[END_REF][START_REF] Oliver | Probabilistic estimation of end-to-end path latency in wireless sensor networks[END_REF].

Mobility Models

Since this study proposes the observation of distributed systems deployed in dynamic networks with time-varying topologies, the introduction of mobility models is required. With them, the nodes' positions periodically change and the state of other models are updated accordingly by recalculating distances between nodes. The following mobility models are implemented for the evaluation in Section 5. A comprehensive list of mobility models that are useful to ad hoc computing, in particular when dealing with FANETs, can be found in [START_REF] Oubbati | Routing in flying Ad Hoc networks: Survey, constraints, and future challenge perspectives[END_REF].

Attraction Model The attraction model was created to emulate the situation where a node is given a command to keep the position on a specific coordinate but it is unable to execute the command exactly due to external disturbances, such as lateral wind, consequently the node fails to keep its expected position P(t) ∈ R 3 . To model disturbances, the attraction coordinates A(t) ∈ R 3 , being a set [x, y, z], has each Cartesian coordinate frequently modified by a random, bounded variation (t) ∈ R 3 at a pre-defined frequency. At each time step, the position is changed by a δ p (t) = δt/V p (t)(A p (t) -P p (t)) based on a pre-defined velocity V ∈ R + , with δ p (t) ∈ R 3 being a set [x, y, z]. It is, hence, calculated by Equation 9and, as a proportional controller, the closer the node gets to the attraction point, the slower it moves.

P(t + 1) = [x(t) + δ px (t), y(t) + δ py (t), z(t) + δ pz (t)] (9)
Random Walk Model When the goal is to have a mobility model that allows the nodes to move freely in a pre-defined area, the Random Walk model is more suitable. It mimics applications where nodes do not have pre-defined mobility paths, or when they have but the scheduling of nodes in such paths is stochastic.

In such a model, a limiting arena L a ∈ R 3 is pre-configured, and an initial position P(0) = [x 0 , y 0 , z 0 ] is defined in runtime. A random velocity V 0 ∈ R is also defined in runtime and it characterizes the initial direction given to each node. At each simulation time-step, the position is updated by a δ p (t) (distance equivalent to the velocity and the time-step) and calculated as shown in Equation 9. When there is a collision of a node with a wall, the velocity has its signal inverted in the axis of the wall hit. As a consequence, the nodes keep bouncing inside the arena, but for simplicity, collisions between nodes are ignored.

Data-Flow Model

This data-flow model describes how the generated messages are distributed among the participating nodes during runtime. It mainly simulates the behaviour of messages being created by applications in one node and transferred to other nodes participating in the algorithm of the distributed application.

-Round Robin -each node becomes the source of traffic per round, and the source node is changed with every pre-defined service period defined by λ. -Stochastic -the source node is selected randomly at each round according to a Poisson distribution. The flows are served following a pre-defined λ. -Fixed -in this model, the source node (selected based on experiment objectives) is fixed during all the execution, and the destination is defined by a set of nodes. When left empty, all nodes will serve as destination. The data flows are served following a pre-defined λ.

Model Validation

To validate the behaviour of the proposed fluid model, a scenario where two source nodes inject data flows towards two different destination nodes via a bottleneck, as shown in Figure 2a, was simulated with the model, a simulator (OMNet++) and an emulator (MACE). First, periodic flows of 1kB with arrival rate λ = 1 from S 0 to D 0 and S 1 to D 1 . After 5 seconds, a second periodic flow of same size but arrival rates λ = 0.1 from S 0 to D 0 and λ = 0.5 from S 1 to D 1 is introduced. Figure 2b shows the evolution of the total delivered data for each tool and destination node, showing that even having fluid quantities that mix in the bottleneck node, it is possible to achieve results with the same precision as a discrete simulator without the need of representing each network packet. In [START_REF] Roijers | Fluid-flow modeling of a relay node in an IEEE 802.11 wireless ad-hoc network[END_REF], the author proposed a fluid model for representing the behaviour of a bottleneck node in an ad hoc wireless network. Their model, which aims in estimating steadystate values, was implemented and validated with a discrete network simulator. The same scenario and models described in the paper were implemented and compared to our model, achieving similar results as shown in Figure 3 for an exponential distribution of the mean flow size.

In this scenario, mean flow size f = 0.12M bit and system capacity C = 5M bps 4 are fixed, while the mean flow arrival increases to achieve a system load ρ = (λf )/C close to 0.5, which is the maximum stable load due to the fact that each arriving flow must be served twice before reaching the destination.

Implementation and Evaluation

In this section, the described models' implementations are used to evaluate and illustrate its ability to study data flow in mobile ad hoc distributed systems. Some stress-test traffic is injected with the dataflow models described in Section 3.6 so that the topologies reveal potential hotspots, and the impact they have on hindering the overall system's performance. In order to evaluate the effect of the data flow, the injected traffic is gradually incremented through the network which is configured as in Table 2 and runs in a regular Intel i7-8550U home computer with 16GB of DDR4 RAM. The evaluation then continues in subsections that expose different features, starting from congestion throughout latency and scalability. The evaluation was run with the three different 5 topologies illustrated in Figure 4. 5 With a fixed number of 18 nodes.

Data Throughput

Even though a mobile ad hoc topology can implement any type of distributed application, as long as the application requires that data transmission is associated with the execution of the required task or function, the introduction of network latency shall hinder the system performance. In applications that require data transfer, the data needs to be copied or moved before the computation associated with such data can start. Some protocols optimize the data usage to avoid unnecessary traffic flow, but reducing unwanted latencies will allow the system to transfer more data in the same amount of time. In Figure 5a, the goodput, which is the useful data delivered at final destination, is represented as it grows together with the injected load until saturation occurs. Also, the topologies saturate at different levels of traffic, and with different steady-state levels of goodput. Such saturation can also be observed in the latency increase as shown in Figure 5b. It is noticeable that regarding latencies, the topologies behave differently. This is specially evident in the ring topology, where the nodes do not have alternative routes, which results in higher latencies due to queue formation.

Congestion

As mentioned in 1.1, when running distributed applications in ad hoc networks, unbalances are likely to occur in some nodes as a consequence of the multi-hop traffic flow. When running topologies such as illustrated in Figure 4, some end-to-end preferred routes will be established. As a consequence, due to the data flow's characteristics, some nodes will have more data traversing it than others. Such nodes are more prone to congestions, which might increase the endto-end latency and as consequence reduce the performance as shown in Section 5.1. Since the first goal is to observe the formation of hotspots in the topologies, the queues in each node are modelled boundless and no queue management algorithm is put in place. In Figure 6a each node was offloading 0.5 MB of data with the other nodes in the topology from Figure 4b in a round robin scheduling and interval of 100ms. It is possible to observe that four nodes were preferred routes of the data flow and allowed the formation of queues. The shadows in the plots represent the standard deviation of the collected data, because since the mobility imposed on the nodes has a random component to their behaviour, each simulation results will differ slightly.

Latency

Communication latency is mainly characterized as described in Section 3.4 and Section 2.2. When abstracting unbounded queues in each node, due to the formation of transient or permanent bottlenecks, the network packets will undergo an extra latency besides the one created by the bounded bandwidth available for communication. When waiting in a queue to be served by the communication system, packets are undergoing an unexpected latency that can be estimated by Little's Law [START_REF] Little | Little's Law[END_REF]. Figure 6a also illustrates the expected waiting time in each node when using Little's law. Even though this estimation gives an insight of additional expected latency, it is incomplete since it takes in consideration only the current state of the system. The model described in Section 2.2 however, since it represents an average latency based on the history of the propagated end-to-end latency, can estimate the latter without the need of measuring each message individually.

Figure 6b shows the average total latency expected for the messages measured in each of the nodes. It is possible to observe the higher magnitude compared with Figure 6a due to the fact that it does not represent the expected added latency by each node's queue, but the average age of each message that has traversed the node.

Model Scalability Evaluation

One of the main advantages of fluid models compared to discrete models is scalability. The results in Figure 7a, which corresponds to a topology with five nodes, with three of them injecting flows of 1kB with an increasing arrival rate, shows that with OMNet++ the simulation runtime surpasses the time horizon even with slow flow arrival. The runtime with the fluid model is barely influenced by the arrival rate, i.e. the number of network packets. Albeit not majorly impacted by the frequency of injected flows, the fluid model has runtime more impacted by the number of nodes in the topology. Figure 7b illustrates, for different arrival rates, a randomly deployed topology with increasing node count. Even though the runtime increases, it remains lower than the simulation time horizon.

Related Work and Limitations

In [START_REF] Berg | Performance Modeling of a Bottleneck Node in an IEEE 802 . 11 Ad-Hoc Network[END_REF] and [START_REF] Roijers | Fluid-flow modeling of a relay node in an IEEE 802.11 wireless ad-hoc network[END_REF], the authors proposed a fluid flow model for representing a bottleneck being served by multiple sources and serving one node. In [START_REF] Roijers | Performance analysis of differentiated resource-sharing in a wireless ad-hoc network[END_REF], the authors expanded the work by modelling resource sharing techniques for performance enhancement. In addition to modelling bottlenecks, our work went further with the ability to represent flows with different routes and mobility, hence being suitable for dynamic networks. Furthermore, our model allows the study of queue and latency dynamics during the whole execution, not only steady-state. The work presented in [START_REF] Sonenberg | Networks of interacting stochastic fluid models with infinite and finite buffers[END_REF] also introduced a fluid model for ad hoc networks, but with a focus on energy consumption. In the domain of static networks, other works created fluid models based on differential equations, such as in [START_REF] Marsan | Using partial differential equations to model TCP mice and elephants in large IP networks[END_REF] and even the creation of a framework in [START_REF] Bonaventura | Fluid-flow and packet-level models of data networks unified under a modular/hierarchical framework: Speedups and simplicity, combined[END_REF]. This work is also inspired by the fluid model described in [START_REF] Cecco | Modélisation Fluide de Réseaux[END_REF]. The main limitation, when compared to discrete simulators, is when there is a need to investigate detailed network behaviour and implement different wireless stacks. Our model does not implement detailed contention algorithms, so its overhead must be taken into consideration by using an average usable bandwidth value. The current model is insensible to flow size, so different average flow sizes yield similar results.

Conclusion and Future Work

In this paper, a lightweight analytical model was introduced, implemented, validated and tested. Its applicability as a tool for faster than real-time simulations of different deployment topologies for swarms of mobile distributed systems was demonstrated. The model, even running on a personal computer, can simulate hundreds of nodes in less time than the simulation time horizon. With this model, future work will allow research of self-stabilizing topology control mechanisms, optimized node positioning and replica placement schemes for distributed systems. The work can be expanded also for the study of QoS, routing and medium access protocols.

Fig. 1 :

 1 Fig. 1: Topology model representation based in distance between nodes.

k jjj

 k Queue at p = j for messages with destination e = k D k Drainage of queue at p = j for messages with destination e = k a k Arrival of queue at p = j for messages with destination e = k f Average flow size ρ System load

Fig. 2 :

 2 Fig. 2: Model validation with a network emulator and a simulator

4Fig. 3 :

 3 Fig. 3: Model validation for average steady state queue level and transfer time for arbitrary particle during system load saturation.

Fig. 4 :

 4 Fig. 4: Topology samples used for experimentation.

Fig. 5 :

 5 Fig. 5: Network saturation while injecting 3MB, Round Robin w/ variable frequency.

Fig. 6 :

 6 Fig. 6: Stress load injection of 0.5MB, Round Robin (λ = 10).

Fig. 7 :

 7 Fig. 7: Scalability evaluation with time horizon of 100s.

Table 1 :

 1 Notations

	Symbol Description
	δt	Time-step
	n	Number of nodes in the topology
	d jk	Distance between nodes j and k
	dr	Radio communication range
	R	Routing table
	Sj	Set of nodes serving data flows for a particular node j
	O R j	Set of nodes being served as next hop for a particular node j
	tmp	Medium propagation latency
	ts	Serialization latency
	t od	End-to-end latency
	P	Position of a node
	A	Attraction position of a node
	δp	Position variation for a node
	V	Velocity of a node
	La	Limiting area for a mobility model
	λ	Flow creation frequency
	α	Age of a message
	p	Position of a message
	Q

Table 2 :

 2 Network Configuration

	Bandwidth:	54 Mbps
	Time Horizon:	100 s
	Processing Latency:	1 ms
	Route update interval: 1 s


A New Method to Measure Soil Density in the Field using SfM -新方法による現場土密度測定

Keywords: Structure from Motion, Post-disaster Investigation, Soil Density, 自然災害調査、現場土密度

Introduction and problem

In the field, soil density has been traditionally measured in geotechnical engineering and in soil sciences using the sand-cone method (ASTM D1556/D1556M and JIS 1214), that consists in dropping a known amount of sand with a known density into a roughly calibrated hole. The method requires important amount of sands and some relatively heavy equipment, not appropriate for remote and hardly accessible mountain areas, and it does not provide any control on the quality of the method. The same issue exists with the balloon method as well.

Objectives

To solve this issue, the present contribution proposes the use of photogrammetry based on SfM-MVS, so that the method can be used in irregular soils that are coarse grains, and with limited equipment transported in the field. Furthermore, the method the author proposes can be used along outcrops vertically and on horizontal surfaces, whereas a perfectly horizontal surface was necessary up to present. Protocol: For each sample-set, a square ruler was placed around the holes to be used as a scale in the photogrammetric method, then a set of 38 to 46 photographs was taken with overlap and with angle change < 30˚ between each photograph and without jumping location, but following wangling lines, like an aircraft would do to take aerial photographs 1),2),3). The photographs were then fed in the SfM-MVS (Structure from Motion -Multiple View Stereophotogrammetry) program of Agisoft® Metashape-Professional, to first add known control points where the scale is located, then to calculate sparse point cloud, then the dense point cloud, then mesh the point-cloud as an arbitrary shape (not a topographic element) to obtain a true 3D and not a 2.5D. The data is then textured, and the DEM and ortho-images extracted. In the field, the volumes of the dug pits would be compared to the mass of the material dug out to obtain the density of the material. In the present case, we are only interested with the holes' sizes, therefore we compared the hole volumes calculated from SfM-MVS with volume of equivalent water, filling the holes in the hard foams. To compare the results, the author used the standard method of RMSE (Root Mean Square Error) to estimate the range of error between water-measured data (supposed to be the closest to the real size of the hole), and the SfM-MVS acquired data (eq. 1):

𝑅𝑀𝑆𝐸 = √ 1 𝑛 ∑ (𝑍 𝑖 𝑚 -𝑍 𝑖 𝑟 ) 2 𝑛 𝑖=1
………………………………………. (eq.1)

Results and Discussion

Results show good agreement between the watermeasured hole volume and the SfM-MVS data, with the best linear fit correlation line of y=1.022*x+3.167, where x is the SfM-MVS calculation and y represents the water measurement.

The water-measures are thus slightly higher than the volumes calculated using SfM-MVS. The RMSE of the upper 50% of the data is ~5 and the lower 50% displays a RMSE of 2.6 (about half of the top 50%).

The author interpreted this result as being a function of the small crannies that are filled with water and that can't be calculated from SfM-MVS, which had a millimeter scale infra-millimeter (after software calculation). Therefore the discrepancy between the two dataset can be potentially linked to the size of the surface of the hole walls and the roughness of the grains.

Conclusion

The photogrammetric-based 'Gomez-method' to measure field density proves to be a reliable method with a control on the potential error (error control from the photogrammetric method), providing a more reliable method of field density measure and calculation. At present, the author is preparing further result presentation with full-scale field data, showing the usability and reducing the weight of the equipment carried in the field.

  The present research is based on a set of 12 samples produced in the laboratory in expended hard foam to reproduce holes dug in the field during destructive soil density test. The blocks were dug at different depth and sizes to represent different sets. The holes were dug by hand, plugging the foam out with a blunt instrument, without any particular control on the shape to reproduce roughness and unknown in field experiments (Fig. 1). Because the proposed method uses photogrammetry, it was essential to reproduce a real texture with real colors, so that the photographs could reproduce real holes in the field. The samples were therefore sprayed with regular sand over an impermeable coating. The impermeable coating was essential for the laboratory measure of the pit volume using equivalent water volume.

Fig. 1

 1 Fig. 1 Photograph of four of the test samples in the laboratory (Kobe University, Dept. of Maritime Sciences, Laboratory of Sediment Hazards and Disaster Risk)


Pascal Engel

ARE PRAGMATISTS ABOUT TRUTH TRUE DEMOCRATS?

Introduction [may be skipped by those having an overall view of these debates]

Many pragmatists, from Dewey to Rorty, hold that their views provide a defense of democracy or are consonant with it. They diverge, however, on the role that truth ought to play in this defense: Deweyan pragmatists consider that truth has nothing to do with democracy, whereas Jamesian and Peircean pragmatists insist that we cannot do without truth in a democratic state. In this respect their debate mirrors the opposition between Rawls' conception of political liberalism, according to which there is no room for truth in democracy, and Joshua Cohen and others, for whom it is indispensable. I want here to bring together these two debates, and to try to defend, against the pragmatists, both Deweyan and Peircean, the claim that we cannot get rid of truth if we want to defend democratic politics.

In order to get a grip on these debates, however, we need to make two distinctions. The first is between a theory of truth and a conception of truth's importance for various purposes, epistemic, practical or political. It is one thing to hold that truth is such and such a property, or concept, and another to say whether it is good or bad for various objectives, among which democratic politics. The second is between different theories of truth, in particular between substantive theories of truth, such as the correspondence, the coherentist or the pragmatist theories, on the one hand, and so-called deflationist or minimalist theories of truth, which say that truth is a very "thin" notion which carries no metaphysical import. These distinctions are important because it is not always clear, in these discussions whether enemies or friends of truth talk about whether a certain metaphysical conception of truth matters or does not matter for democracy, or whether they defend only a shallow conception.

I proceed here as follows. I shall first spell out the distinction between various views of truth, and explain which ones are supposed to matter, and in what sense, for a defense of democracy, if one is a pragmatist. Then I shall try to show that pragmatism fails to provide an adequate defense of democracy whether or not it eschews truth. This will be premised both on the view that we need a robust conception of truth as correspondence and that such a conception is the one that we need for democracy.

The aim of this article is limited. It deals only with the kind of role and justification that pragmatists give to truth within democracy. It does not take into account arguments about democratic procedures, such as voting and the justification of the majority rule.

Truth : substantive or shallow ? [ those interested in political philosophy only can skip this paragraph]

To the notion of truth are attached a number of truisms or platitudes [START_REF] Wright | Truth and Objectivity[END_REF]): that it is true that p is equivalent to p, that p is true if and only if things are the way p says they are, that truth is objective, that a proposition can be justified without being true, and that truth is the norm or goal of inquiry. According to most classical philosophers, from Aristotle to Russell, and according to many contemporary philosophers, these truisms, although they give a "nominal" definition of truth (Kant), are not sufficient to define it, and should be associated to a substantial theory of truth as correspondence to facts or external reality, or as a form of coherence of our thought, as the identity of thought and reality, or as the ideal limit of our inquiries [START_REF] Dokic | La vérité peut-elle survivre à la démocratie ?, Agone 2013 « Alethic Functionalism and the Norm of Belief[END_REF]. According to other philosophers, such substantive theories of truth stumble on unsurmountable difficulties, and truth cannot be defined. It is not a deep metaphysical property, but a very shallow one, which can be reduced to the logical behaviour of the truth predicate, and as a device of assertion. According to such "deflationist" or minimalist theories, there is no more to truth than the fact that "'P' is true iff P", and to the fact that asserting that P and asserting that P is true are equivalent, and all the so-called substantive properties reduce to these ones (Horwich 1991). Ramsey's "redundancy" theory [START_REF] Dokic | La vérité peut-elle survivre à la démocratie ?, Agone 2013 « Alethic Functionalism and the Norm of Belief[END_REF]Engel 2002), Tarski's (1936) "semantic conception" of truth, Quine's and Davidson "disquotational" theory of truth, belong to the deflationist family.

What is the pragmatist's stance towards these different notions of truth? Here there are delicate matters of interpretation, but most commentators agree with the following crude map (for an extended map, see Tiercelin 2014). On the one hand, all pragmatists recognise the truisms of the nominal notion of truth (who doesn't ?). Where they differ is whether one should adopt a substantive or a deflationary view. Classical pragmatists like Peirce hold that truth is the ideal limit of our inquiries, which amounts to a form of ideal coherence theory (Peirce,). James often defends a view of this sort, but he associates truth with the practical success of our inquiries. It is not clear that he defends the "crude" form of pragmatism which is often associated to his name, which says that truth is nothing else than the practical effects that our conceptions have, but he most often comes close to it. Dewey defends something which is closer to a verificationist conception: truth is "warranted assertibility" [START_REF] Dewey | Propositions, Warranted Assertibility, and Truth[END_REF], Russell 1940). Most classical pragmatist conceptions of truth are epistemic or anti-realistic: they take truth to be the ideal limit of our beliefs and inquiries (Peirce), or a property of the practical success or our beliefs (James), not a property of their correspondence to reality.1 More recent versions of the view, such as Putnam's "internal realism" which he often calls a kind of pragmatism" (Putnam 1990) also take truth to be ideal rational acceptability, hence an epistemic property.

Richard Rorty is almost unique among the pragmatist in defending a form of deflationism about truth. He argues that the notion of truth has no explanatory use, and does not involve any essence, or any deep metaphysical property or object (the True). In particular he holds that the traditional realist view of truth as correspondence of our thoughts, judgments or sentences with reality is meaningless, and that, in consequence all the debates about realism and antirealism in philosophy are empty. According to Rorty, there is no more to truth than the fact that our statements are justified, where justification is agreement between the members of a community. The fact that truth is nothing but justification, for Rorty, does not imply that truth can be define as an epistemic property of our beliefs. Being justified is not an epistemic status, actual or ideal, but just a property of our assertions when they are, so to say, mutualised. According to Rorty, we first agree on some statements, and then approve them as true. As he says "'True' is just a little "rhetorical tap" that we give on the back of our assertions when we like them and find that they concord with what our peers accept. This is a version of the view, once defended by Strawson (1949) according to which true is a predicate which serves to express our approbation of our assertions. Along with this performative use of the notion of truth, Rorty lists its disquotational use, and its "cautionary" use. According to Rorty this use allows us to distinguish truth from justification: "Your theory is justified but it is not true" does not mean that truth outstrips justification or that there is a reality which could undermine your local justification, but only that there is a further justification, possibly held by another, more comprehensive group; it does not mean that there is a reality which could undermine. All these uses, according to Rorty, imply that there is no hidden essence of truth: truth is just the addition of these uses, which are contextual, community-bound and culture -bound. Truth can neither be the ideal rational acceptability nor a norm [START_REF] Rorty | Is Truth a Goal of Inquiry? Davidson vs. Wright[END_REF]). It's merely a matter of linguistic devices and of the utility of assertions within a community.

"Given that it pays to talk about mountains, as it certainly does, one of the obvious truths about mountains is that they were here before we talked about them. If you do not believe that, you probably do not know how to play the usual language-games which employ the word "mountain." But the utility of those language games has nothing to do with the question of whether Reality as It Is In Itself, apart from the way it is handy for human beings to describe it, has mountains in it" [START_REF] Rorty | Is Truth a Goal of Inquiry? Davidson vs. Wright[END_REF] It is often hard to distinguish Rorty and other similar views of truth from straight relativism or scepticism. But even if we do not ascribe to him such sweeping consequences, most of his arguments in favour of his version of the deflationist theory are weak. It is not the place here to rehearse these (Engel and Rorty 2005), but the main objections to Rorty's conceptual claims about truth are the following. First it is just not true to say that truth is merely a device of assertion, for to assert that P is true is not just to assert P; it is also to express one's belief that P is true, and that P is true in a sense which exceeds the fact that one believes it, namely that P is objectively true [START_REF] Price | Three norms of assertibility[END_REF], Engel 2013). Rorty's eliminativism about truth makes no room for this. Second there are conceptual ties between justification and truth, but these ties do not amount to an identity. To be justified in believing that P entails that one is justified in believing that P is true, but that does not entail that "justified" and "true" mean the same thing. Third "justified" and, according to Rorty, "true" do not mean "justified (true) for a community". If we happened to be brain washed, or victims of an evil demon, would we say that our beliefs are justified for one audience (that of brains in a vat) but not for another (that of those who manipulate the Matrix). No, it seems that we would say that our beliefs are justified, but false.

The pragmatists on truth and democracy [those who know the literature on pragmatism and democracy can skip this paragraph]

A deflationary theory of truth does not say that "truth" is an empty word or a mere fiction, as it is claimed by Nietzscheans and postmodernists. It says that truth has a use in our language and in our lives, but not a significant one. There is no direct implication between a deflationary theory of truth or of the concept of truth and a deflationary view of the importance of truth for the practical, the ethical or the political domains, for one can hold that the nature of truth is one thing, and its consequences or significance in these domains I another thing. Thusand paradigmatically - [START_REF] Rawls | Political Liberalism[END_REF] holds that whatever view we hold about truth, political liberalism "does without the concept of truth" 2 . The unimportance of truth for the political realm is, for Rawls, perfectly compatible with the claim that a substantive conception of truth is correct. Rorty's view has often been compared to Rawls, in that both hold not only that truth has no relevance for democracy, and that it is unwelcome and dangerous to invoke truth in the context of political deliberation and in the context of assessing the justification of democracy. The difference is that Rawls accepts that truth could have, metaphysically speaking, such and such a nature, although it is irrelevant. He nevertheless claims that a traditional correspondence conception of truth, according to which truth is adequacy to an external reality, should not be invoked in discussing theories of justice and our conceptions of the good, but only the reasonableness of our conceptions. Rawls certainly means by "reasonableness" something more substantial than what Rorty means by "justification"he has in mind a standard of justification which has a chance of being objective, which, in his view, means that it has a good chance to meet a kind of consensus. But on the one hand, Rawls accepts that consensus is not the same as truth, and, on the other hand, he holds that political pluralism does not command that there should be, on any matter of public policy, a consensus. There can be irreducible disagreements, which are part of a pluralistic democratic society, and their existence is precisely the reason why a substantive notion of truth ought to be replaced by a notion of reasonableness.

"Once we accept the fact that reasonable pluralism is a permanent condition of public culture under free institutions, the idea of the reasonable is more suitable as part of the basis of public justification for a constitutional regime than the idea of moral truth. Holding a political conception as true, and for that reason alone the one suitable basis for public reason, is exclusive, even sectarian, and so likely to foster political division " (Rawls 1996: 129) Rawls is clear that democracy does not need, but also ought to avoid as a matter of principle, invocation of a substantive notion of truth. He does not tell us whether his view is compatible with a deflationary view, but he also makes clear that his view is not based on general doubts about truth as such , but only on a concern for truth's role in political debates. He holds that no substantive judgement can be applied in the public space of reason, even though one may admit that such substantive judgements are there to be had. 3Rorty's rejection of the relevance of truth in democracy is not based on the same kind of grounds as Rawls'. For Rorty truth does not matter in the first place because there is no substantive concept of truth to be had. A fortiori 4 the notion of truth cannot play any role in democracy or in any other political regime. It cannot play any role neither for the justification of democracy and it cannot play any role in the democratic politics in general. The reason is that democracy, for Rorty, cannot be justified, because no political view can be justified. Democracy is not a set of principles, ethical or political, which are in need of some kind of meta-ethical or philosophical justification. It is a way of life, our way of life in the contemporary world. Political philosophy ought not to be based on ideals of justice, but on "social hope". Democracy "can get along without philosophical presuppositions" (Rorty 1989). In his ideal culture of 'postmodernist bourgeois liberalism' [START_REF] Rorty | Is Truth a Goal of Inquiry? Davidson vs. Wright[END_REF], agreement to democracy is not an agreement on a set of principles but the product of purely contingent facts about history, geography, and socialization. There is no sense in which tyranny is better than democracy; we stand up for it without having any reason to think it is better than other political configurations. That is Rortyan ironism (Rorty 1988). Rorty is no Hobbes. He does not say that auctoritas non veritas fecit legem, since not only he denies that truth has any authority, but he also denies that there are any normative truths at all, even about the foundations of authority.

There is, however, a line of argument which is, on the face of it, less radical than this eliminativist stance, and which sometimes surfaces in Rorty's writings. It is a minimalist stance : although we can do without substantive truth, we cannot do without assertions, assertions have all the minimal properties that substantive truths have (disquotation, etc.) , and so we can keep the functions of truth without postulating any substantive concept of truth. To say that P is true is just say that P can be asserted with enough warrant. It is a verificationist stance: since any appeal to truth would amount to a form of Platonism, the best we can do is to side for justification. This stance is present, for instance, in Rorty's review of Bernard Williams ' Truth and Truthfulness (2002) Pragmatists try to coalesce the quest for truth and the quest for justification by trotting out what Williams labels 'the indistinguishability argument'. They claim that the activity of reaching agreement with others about what to believe looks exactly like the activity of trying to acquire true beliefs, and that there is no point in postulating two distinct aims for a single enterprise. Williams says that the basic objection to this argument is that 'a justified belief is one that is arrived at by a method, or supported by considerations, that favour it, not simply by making it more appealing or whatever, but in the specific sense of giving reason to think that it is true.' Brainwashing often brings agreement, as do exchanges between scientists in meetings of the Royal Society, but only the latter counts as acquiring truth. So, Williams says, 'the pragmatist owes us an answer' to the question of how we tell methods for acquiring truth from other methods of producing consensus.

As he rightly suggests, the only answer the pragmatist can give to this question is that the procedures we use for justifying beliefs to one another are among the things that we try to justify to one another. We used to think that Scripture was a good way of settling astronomical questions, and pontifical pronouncements a good way of resolving moral dilemmas, but we argued ourselves out of both convictions. But suppose we now ask: were the arguments we offered for changing our approach to these matters good arguments, or were they just a form of brainwashing? At this point, pragmatists think, our spade is turned. For we have, as Williams himself says in the passage I quoted above, no way to compare our representations as a whole with the way things are in themselves. 5Rorty's line here is close to Dewey's verificationism. Rorty often claims to be Deweyan. And indeed Dewey claims that democracy is a "way of life" (1969-91, LW 13:155) rather than a kind of state or a collection of political institutions (LW 2:325). On Dewey's view, democracy is a mode of social organization that "must affect all modes of human association, the family, the school, industry, religion" (LW 2:325), and a set of values held in common. Democracy is deep because it has an ethical meaning which is characterized by the fact that its ultimate aim is growth, and perfection. It is a form of perfectionism (Talisse 2010). If so, it receives a certain kind of justification, which is not based on any epistemic property, such as truth or justification, but on a moral claim: the institutions which are best are those which serve the aim of human flourishing.

Dewey does not defend a deflationist conception of truth, but a form of verificationism. Truth is the property of those of our assertions which are best warranted at a given time. No assertions, however, are immune to revision and infallible. On the contrary we ought to presuppose that we could be wrong, on the model of the experimental method in science. Dewey, as [START_REF] Anderson | The Epistemology of Democracy, Epistemè Cohen , J[END_REF] notes, imported this fallibilistic and experimentalist model ( which he borrowed from Peirce) into his thinking about democracy, which according to him is based on the diversity of opinions, their capacity to be renewed if proved not verified.

As many critics have noted (Misak 2008,Talisse 2010) there are tensions within Dewey's views. On the one hand democracy is not based on intellectual principles, even less on truths. On the other hand it has at least to be based on one substantial conception, which is the ideal of human flourishing. In this sense, there must at least be on truth, about the good for humans. This precludes pluralism, and implies that one must reject the views of those who believe that growth and human perfectibility is not the only moral end. Another tension is between the claim that democracy is a way of life and the claim that democracy favours a form of experimental method. The former implies an opposition to the idea that democracy ought to rely on any epistemic property such as truth and justification, whereas the latter relies on the idea that epistemic properties, such as the fact that certain procedures have tested, do matter for democracy. In this sense , Anderson suggests that Dewey had a kind of epistemic model of democracy: "Dewey's experimentalist model of democracy helps us see the epistemic import of several democratic institutions that sustain its dynamism, its capacity for change: periodic elections, a free press skeptical of state power, petitions to government, public opinion polling, protests, public comment on proposed regulations of administrative agencies. In Dewey's model, these are mechanisms of feedback and accountability that function to institutionalize fallibilism and an experimental attitude with respect to state policies. They push governments to revise their policies in light of evidence-public complaints, as expressed in both votes and discussionthat they are not working, or expected not to work. On Dewey's model, votes and talk reinforce one another, the votes helping to insure that government officials take citizens' verbal feedback seriously, the talk helping to define and articulate the message conveyed by votes." (Anderson 2006, 14) On the one hand Dewey associates democracy to the existence of legal and political arrangements such as representation and elections. On the other hand, he associates it with something broader, a certain kind of attitude and spirit: "The future of democracy is allied with the spread of the scientific attitude" toward practical affairs (Dewey LW ,14 : 167). Anderson takes Dewey's stress on deliberation and the capacity to dissent from one's fellow citizens to show his adherence to an "epistemic model" of democracy. But this is dubious, for Dewey does not stop saying that his model of scientific progress and of knowledge is not the progress of the acquisition of certain beliefs and not a form of intellectual progress in general, but a progress in the acquisition of certain practices. It is not a progress towards the truth of certain views, or towards certain political arrangements guaranteed through decisions which would make them justified, but a progress towards a certain kind of life. This ambiguity is still present today among the advocates of the so called "deep democracy" which is very much inspired by Dewey's thought: they both insist that democracy is a matter of being able to disagree and on the fact that it is a matter of participating to a common way of life 6 . But is there room, in such a model, to arrangements which are usually taken to be typical of democracy, such as minority dissent, where a group of citizens has the right to disagree from the choices of a majority? If these citizens dissent, how can they do so without saying that they dissent on the truth of certain claims? If they dissent only on the basis of their sharing a certain kind of life or that they make common "assertions", how can they disagree on the fact that the majority's assertions are wrong? 6 To see how divergent from Anderson' epistemic reading of Dewey can be among « deep democracy » theorists, see e.g. such declarations by Sandra Laugier and Albert Ogien , who when asked how the kind of political practices that they recommend imply, answer: "Elles induisent l'idée que chacun a la même compétence politique -d'autant plus s'il est spécifiquement concerné par une question qui travaille sa vie quotidienne, ordinaire. En ce sens, nous nous réclamons du pragmatisme de Dewey, qui exige que "l'enquête" démocratique, ce que nous appellerions aujourd'hui l'expertise citoyenne, ne relève pas d'une compétence scientifique réservée, d'un privilège épistémologique ».This is the crux of the matter : if every citizen becomes an « expert », how can one distinguish good from bad experts ? http://www.regards.fr/web/article/sandra-laugier-renouer-avec-la

The tensions have led recent defenders of pragmatism in normative politics to a criticism of Dewey and of his radical disciple Rorty, and to adopt a more fullfledged deliberative conception which they also call "epistemic". Thus Talisse has proposed a "Peircean"7 conception of democracy based on the following argument 1. To believe that p is to hold that p is true. 2. To hold that p is true is to hold that p "is a belief that cannot be improved upon, a belief that would forever meet the challenges of reason, argument, and evidence" 3.. To hold that a belief would meet such challenges is to commit to the project of justifying one's belief, what Peirce called "inquiry." 4. The project of squaring one's beliefs with reasons and evidence is an ongoing social endeavor that requires participation in a "community of inquiry" ( Talisse 2010: 111-112) Talisse pretends to derive from these claims "an epistemic argument for democracy": one should endorse a democratic political order because only in a democracy can one live up to one's epistemic commitments. If being someone capable of having beliefs entails being someone capable of giving reasons and justification, and if in turns this entails that one is committed to the social enterprise of examining, testing and challenging one's reasons , then one can satisfy one's commitments qua believer only within a political context inwhich it is possible to be an inquirer.

"Inquiry requires that characteristically democratic norms obtain; in order to inquire, there must be norms of equality, free speech, a freedom of information, open debate, protected dissent, access to decision-making institutions, and so on. Moreover, since the project of justification involves testing one's beliefs against the broadest possible pool of reasons, experiences, and considerations, inquiry requires more radicallydemocratic norms, such as participation, inclusion, and recognition" ( ibid 112)

In insisting that democracy entails certain kinds of epistemic commitments, the Peircean fully acknowledges that it has to rely on the notion of truth. For if one insists on the expression of one's beliefs in assertions, one is bound to insist on our assertions being (potentially) true, and rejected if proved false. One must be able to distinguish between thinking that one is right and being right, and if one is to dissent from others, and to criticize their beliefs and their actions, one must accept a certain notion of truth. Now this notion of truth, the Peircean argues, is not the correspondence or realist notion, but the ideal limit of inquiry or ideal rational acceptability conception. If one accepted a full-blown realist notion of truth, according to which truth can go beyond what our best inquiry can do, one would go beyond what human capacities can do, and no dispute could ever be resolved. Correspondence realist truth is not only the product of a spurious metaphysics, it is also a non-starter for democratic public reason (Misak 2008: 98).

Peircean pragmatists (such as Misak and Talisse) and Deweyan pragmatists (like Dewy and Rorty) both agree that realist truth has no place in democratic deliberation. But they part company when it comes to accepting a substantive theory of truth. Peircean accept an ideal limit theory of an epistemic sort, whereas Deweyans reject outright the notion of truth.

As I remarked above, Rorty's eliminative stance on truth does not allow him to make room for a deliberative model of democracy, and for the need to adjudicate claims that arise within diverse communities. Disagreement is not disagreement on the truth of certain claims, but only a matter of not sharing enough background beliefs with other communities. "Right" means only what your community agrees upon, and the agreement is not based on shared judgements, but on shared practices or "ways of life". In spite of Dewey's insistence on equating democracy with a scientific attitude and to the capacity of disagree, it is not clear that he can make room for truth within public reason. Peirceans, in contrast, claim to make sense of truth. They full acknowledge truth's importance for public reason. But do they make room for the concept of truth? They make room for the idea that political claims can be justified if they stand up to reason and to evidence, and to a surrogate of realist truththe idea that a claim is true only if it would , in an ideal state of inquiry, resist our best efforts to refute it. They also make room for the view that one can reason and argue the public space, and that such reasoning and argument can be good or bad in the sense of valid or invalid, correct or not. But can they make sense for the idea (which I listed above among the truisms about truth) that truth is supposed to be objective and independent from justification? Can they make sense of the fact that assertion is not only the expression of belief, but also the expression a belief which is supposed to be true, and objectively so? In fact what they propose is more a form of ersatz truth, which is a kind of ideal reasonableness (in this respect they are not very far from Rawls, who also wants to substitute reasonableness to realist truth). But do they have the means to distinguish between good and bad deliberation? When do we know that deliberation has been sufficiently comprehensive and reasonable, and how do we distinguish it from deliberation which is not reasonable and comprehensive enough? It is hard to see how this can be done without a full-blown and objectivistindeed realistconcept of truth.

Alternatively, as I suggested above in the case of Rorty, Peircean pragmatists can retreat to a minimalist conception of truth, according to which all there is to truth is to respect in one's discourse the truth platitudes. And indeed the commitments (1)-( 4) above listed by Talisse come close to these platitudes. But then their views will come close to those of Joshua Cohen's on the role of truth in public reason, to which I now turn.

Can we do without realist truth in democratic politics? [those familiar

with Cohen's views may skip this paragraph]

If truth is to play not only a role, but a dominant role within public reason and in a democratic state, it has to be the case that it satisfies three conditions at least, those of being:

(i) a substantive notion, capable of carrying the implication that truth claims are genuinely objective and susceptible of being mistaken (ii) an important notion, which has a genuine role with democratic politics (iii) that it can be the basis of a justification of democracy I have argued that pragmatists accounts, from Dewey to Rorty and to more recent writers, do not provide any of these three conditions, even less two of them or the three of them. An ideal rational acceptability account of truth , and falls short of satisfying the condition of giving us a substantive notion of truth, and most pragmatist accounts go no further than the minimalist concept. Dewey and the Peircean do stand up for (ii), although Rorty does not. The philosopher who is the closest to the view that there can be a justification of democracy is Dewey, but he bases his democratic principles on a notion of the good which is closer to a form of Aristotelian eudaimonistic ethics of the good than to an theory of truth.

Against such views a number of philosophers have reacted, in defense of both the importance of the concept of truth within public reason, and for the foundation of democracy. Their views are not literally pragmatist but they share with the pragmatists the idea that if truth is to play a role within democratic politics, it should rest on a definitely non metaphysical and non realist notion notion.

There is a permanent ambiguity, both in the philosophical debates about truth and in the political debates about its importance, between two kinds of truths or : on the one hand deep and doctrinal truths, such as truths about religious, ethical or metaphysical matters, which generally are associated with firm convictions, and factual or humdrum truths, which do not carry heavyweight beliefs. One of the main reasons for which Rawls and Rorty shun truth away from the public sphere is that doctrinal truths, if affirmed as such in this sphere, look sectarian: "Holding a political conception as true, and for that reason alone the one suitable basis of public reason, is exclusive, even sectarian, and so likely to foster political division." (Rawls 1996: 129) This may be correct. But why should it follow that humdrum truths could not be the object of consideration? They form in fact the largest body of truths that we use in everyday life and they can become all important: factual truths about whether the terrorists are still in town, whether there are weapons of mass destruction, or whether the prime minister had a bank account in Panama. Why should we distrust the concept of truth to the extent that we would deprive ourselves to invoke it in such ordinary cases? 8 They are no normally susceptible to prompt public debate when they are proven; but when they are not, they lie at the center of public debate and can be tied up to many deep convictions (think for instance of the "humdrum" belief that "Dreyfus was guilty"). Nobody, however is going to dispute or lead a public debate about whether the president's has lost eight pounds after a diet. The problem is that some factual truth can be become important, such as how much money the president's counsellor spends on his shoes. The no-truth theorists here can argue that any such homely truth can become important, and involve heavy weight beliefs which may enter in the public debate.

Inclusion of such homely truth is one of the reasons why Joshua Cohen (2009) holds that we can accept a reasonably non-committal concept of truth for the purposes of public reason. This concept, he tells us, is not the metaphysical concept of truth, but a minimal concept which is available as part of a shared ground of argument. We should not exclude the concept, but we need not incorporate a philosophical theory of truth, any more than we incorporate a philosophical theory of reason when we include an account of reasonableness. We have an understanding that serves the purposes of public political argument, but does not go beyond those purposes (Cohen 2009: 29) According to Cohen, we can maintain talk of truth and use of the concept provided we limit it to the space of reasons within the public debate, without letting in the heavyweight convictions: "Recall that democracy's public reason is a terrain of argument, and it may suffice, when challenged, to present a case for liberty of conscience, for example, that lies on common ground, with shared premises. If the premises are assumed to be true, then nothing more is needed to make a case for the assertion that that proposition is true. An assertion about truth need not be understood as committing the speaker to presenting a full display, any more than the assertion that justice requires liberty of conscience needs to be understood that way. Even 8 Cohen 2009 quoted Hanna Arendt as a case of someone who does not even allow such truths : « Factual truth, like all other truth, peremptorily claims to be acknowledged and precludes debate, and debate constitutes the very essence of political life. The modes of thought and communication that deal with truth, if seen from a political perspective, are necessarily domineering; they do not take into account other people's opinions, and taking these into account is the hallmark of all strictly political thinking."

if assertions commit a speaker to presenting a justification, they need not express commitments to depth. (Cohen 2009: 36) With such "political" conception of truth, which combines a minimalist concept of truth with a defense of the importance of truth for the public debate, Cohen tells us that he is able to reintroduce the concept of truth which Rorty and Rawls had rejected from the public space, through restraining its use to only those commitments which do not carry strong doctrinal weight. The objective, he tells, is reaching enough consensus. To the no-truth theorist objection that even truth in a restricted domain can lead to a larger display of doctrinal convictions, he answers: "Even if claims about truth do invite a full display, there may be nothing objectionable about presenting a full display of a doctrine that leads one onto common ground. I might say that I have a case, founded on a broader doctrine that underwrites my view that a principle of equal basic liberties is true. At the same time, I am fully aware that others disagree with the doctrine, and have their own reasons for endorsing the liberty principle. What we share is an understanding of what justice requires, and a conviction about the truth of that requirement. I understand that others endorse that requirement and assert it to be true for reasons different from mine. A full display need not be divisive, then, but may involve my presenting my reasons for accepting the common ground we are all assumed to occupy. Of course, the full display will not provide a public justification, but it may nevertheless play a constructive role. (Cohen 2009: 37) The problem is that, although truth is on this view advertised as indispensable for public reason, it rests both on a minimalist account of truth (for public reason to function, it is enough that the concept of truth embodies the truisms of the deflationist conception). For political reason to function we only need, Cohen says, a concept of truth, not a theory of truth. This concept of truth is not antimetaphysical, but it is non metaphysical. It is neutral. Controversies about the nature of truth have no place in it, for they are politically idle (Cohen 2009: 15). On Cohen's view truth concerns matter in public reason, but only if they are insulated from other concerns that those of public reason, where the concerns of public reason are defined, as in Rawls' account, by the existence of a space of reflections and judgments where equal persons, drawn to conflicting issues can reasonable be expected to occupy. Rawls denies that truth has a place in this space. Cohen lets it in the space, and rejects what [START_REF] Raz | Facing Diversity: The Case of Epistemic Abstinence[END_REF] called "epistemic restraint" in Rawls view. But just as Rawls insulates the domain of the reasonable from the domain of truth, circumscribing the realm of truth to the domain of public reason seems to be practicing insularity just as much. In other words, why should the application of the concept of truth be restricted and why does it not apply across the board?

Cohen's defense of a "non-metaphysical" and neutral concept of truth, together with his claim that it has to be restricted only to concerns of the public space occupies a very narrow space between a deflationist view and a Rawlsian view. It raises three sorts of question. First how do we know that philosophical debates about the nature of truth do not impinge the domain of political reason? Can't the idea that there is a fact of the matter as to whether an embryo becomes a person count in public debate? Or can't the claim that truth comes from revelation be questioned? Second, what justifies the inclusion or the exclusion of a claim within or without public reason? This amount to disqualifying as politically illegitimate some reasons without denying that they are good reasons. This comes very close to Rawls doctrine of epistemic restraint. So it is not clear that Cohen has really reinstated truth in its place within democracy. Third, why should we avoid commitment to a heavier concept of truth than the minimalist one, in particular the realist concept? Assertion that P is assertion of the truth of P. Disagreement about P is disagreement about the truth of P. But if one does not presuppose that there is a fact of the matter as whether P, and that one can be right or wrong about P absolutely, how can public discussion go on? The fear, of course, of these Rawls inspired views, is that sectarianism looms, and that consensus could never be attained. It is perfectly open for a theorist of democracy that the best that we can do is to achieve consensus. But why should we say that consensus is, or amounts to truth ?

A second conception, which I shall touch only briefly which purports to reject Rawls's epistemic restraint views is Estlund's (2008). Estlund is no more a pragmatist than Cohen. But like the Peircean pragmatists, he relies on a notion of truth as ideal acceptability. Estlund, like Cohen, refuses to go without truth and epistemic concerns when it comes to the justification of democracy. But he does not want to go only with it. For reasons similar to Rawls, he holds that we cannot rely only on certain claims to be true in on order to justify democracy. Like Rawls he considers that we need to appeal to a concept of reasonableness. According to Estlund democracy exercises legitimate authority in virtue of possessing a modest epistemic power: its decisions are the product of procedures that tend to produce just laws at a better than chance rate, and better than any other type of government that is justifiable within the terms of public reason. Democratic principles are thus justified on the basis of a correct procedure, and Estlund view is a species of proceduralism. We need some requirement, distinct from truth, to validate our principles. Estlund calls it a qualified acceptability requirement. It is a requirement the role of which is to limit the role of truth in public decisions. In particular it rules out a government of experts, what he calls epistocracy : we cannot let all decisions be made by the knowers of the good, because even though there are truths there, and people who know more than others, there is bound to be disagreement between them.

So the main epistemic requirement, according to Estlund, for the justification of democracy is not truth, but acceptability. What is this requirement? We are said that it must be such that that it be justified in terms acceptable to all qualified points of view"(2008: 45) But this has the same effect as Cohen's version of restraint to political reason : the qualified acceptability requirement disqualifies as politically illegitimate some reasons-those that are not justifiable to all qualified persons-without denying that they are good reasons.9 5. Conclusion [may be skipped if one has read the rest] I have here tried to show that no pragmatist conception of democracy gives a proper place to truth in democracy, either because, like Rorty, it rejects it outright, or because it does not give a proper substitute or ersatz to it. The only concept of truth which is available, both for democracy and in other domains (science, ethics, epistemology) is a realist concept, which does not equate truth and justification, even ideal justification, and which does not take truth to have an epistemic nature. But even those theorists who intend to restore truth within democratic politics and claim to justify it "epistemically" adopt an epistemic concept of truth, and "fly from substance".

With the possible exception of Peirce , see Tiercelin

. Ramsey's conception of truth as success is critical of James[START_REF] Dokic | La vérité peut-elle survivre à la démocratie ?, Agone 2013 « Alethic Functionalism and the Norm of Belief[END_REF]

Political liberalism « "does not use (or deny) the concept of truth; nor does it question that concept, nor could it say that the concept of truth and its idea of the reasonable are the same. Rather, within itself, the political conception does without the concept of truth."( Rawls 1996, ibid. 127)

As Cohen 2009 : 8 notes . Cohen usefuly distinguishes the "no substantive judgment" view ( which I here ascribe to Rawls) and the " no concept view" which say that the concept of truth is just absent from public debates because there is no such concept, which I ascribe to Rorty.

The Philosophical Lexicon has this definition of A Rortiori : "for even more obscure fashionable continental reasons"

London Review of Books,24, 21, 31 oct 2002,.

It is very unlikely that such an account is actually Peirce's account. Peirce has little interest in politics , although he developed an ethics of belief an truth.

See Enoch 2009 on this objection.